diff --git a/ckpts/universal/global_step40/zero/4.mlp.dense_4h_to_h.weight/exp_avg_sq.pt b/ckpts/universal/global_step40/zero/4.mlp.dense_4h_to_h.weight/exp_avg_sq.pt new file mode 100644 index 0000000000000000000000000000000000000000..aeed0201bf8ca44a827ef08849231efd996e85ba --- /dev/null +++ b/ckpts/universal/global_step40/zero/4.mlp.dense_4h_to_h.weight/exp_avg_sq.pt @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5552a04c793f5a78ce624e36892a0934e0511feaa448d1a316323a99018e00d8 +size 33555627 diff --git a/ckpts/universal/global_step40/zero/8.attention.query_key_value.weight/exp_avg_sq.pt b/ckpts/universal/global_step40/zero/8.attention.query_key_value.weight/exp_avg_sq.pt new file mode 100644 index 0000000000000000000000000000000000000000..ac9d4e62625022fd6f29d8b6e4370f41d4f28e2d --- /dev/null +++ b/ckpts/universal/global_step40/zero/8.attention.query_key_value.weight/exp_avg_sq.pt @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1280675cdb1cb83a90d1fc2266ee8d0f0862d716d7be2a9b8d1873976dc3b8ba +size 50332843 diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/__init__.py b/venv/lib/python3.10/site-packages/numpy/_typing/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..29922d958efbdfa6ddee19f8b3904498f9222585 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/__init__.py @@ -0,0 +1,221 @@ +"""Private counterpart of ``numpy.typing``.""" + +from __future__ import annotations + +from .. import ufunc +from .._utils import set_module +from typing import TYPE_CHECKING, final + + +@final # Disallow the creation of arbitrary `NBitBase` subclasses +@set_module("numpy.typing") +class NBitBase: + """ + A type representing `numpy.number` precision during static type checking. + + Used exclusively for the purpose static type checking, `NBitBase` + represents the base of a hierarchical set of subclasses. + Each subsequent subclass is herein used for representing a lower level + of precision, *e.g.* ``64Bit > 32Bit > 16Bit``. + + .. versionadded:: 1.20 + + Examples + -------- + Below is a typical usage example: `NBitBase` is herein used for annotating + a function that takes a float and integer of arbitrary precision + as arguments and returns a new float of whichever precision is largest + (*e.g.* ``np.float16 + np.int64 -> np.float64``). + + .. code-block:: python + + >>> from __future__ import annotations + >>> from typing import TypeVar, TYPE_CHECKING + >>> import numpy as np + >>> import numpy.typing as npt + + >>> T1 = TypeVar("T1", bound=npt.NBitBase) + >>> T2 = TypeVar("T2", bound=npt.NBitBase) + + >>> def add(a: np.floating[T1], b: np.integer[T2]) -> np.floating[T1 | T2]: + ... return a + b + + >>> a = np.float16() + >>> b = np.int64() + >>> out = add(a, b) + + >>> if TYPE_CHECKING: + ... reveal_locals() + ... # note: Revealed local types are: + ... # note: a: numpy.floating[numpy.typing._16Bit*] + ... # note: b: numpy.signedinteger[numpy.typing._64Bit*] + ... # note: out: numpy.floating[numpy.typing._64Bit*] + + """ + + def __init_subclass__(cls) -> None: + allowed_names = { + "NBitBase", "_256Bit", "_128Bit", "_96Bit", "_80Bit", + "_64Bit", "_32Bit", "_16Bit", "_8Bit", + } + if cls.__name__ not in allowed_names: + raise TypeError('cannot inherit from final class "NBitBase"') + super().__init_subclass__() + + +# Silence errors about subclassing a `@final`-decorated class +class _256Bit(NBitBase): # type: ignore[misc] + pass + +class _128Bit(_256Bit): # type: ignore[misc] + pass + +class _96Bit(_128Bit): # type: ignore[misc] + pass + +class _80Bit(_96Bit): # type: ignore[misc] + pass + +class _64Bit(_80Bit): # type: ignore[misc] + pass + +class _32Bit(_64Bit): # type: ignore[misc] + pass + +class _16Bit(_32Bit): # type: ignore[misc] + pass + +class _8Bit(_16Bit): # type: ignore[misc] + pass + + +from ._nested_sequence import ( + _NestedSequence as _NestedSequence, +) +from ._nbit import ( + _NBitByte as _NBitByte, + _NBitShort as _NBitShort, + _NBitIntC as _NBitIntC, + _NBitIntP as _NBitIntP, + _NBitInt as _NBitInt, + _NBitLongLong as _NBitLongLong, + _NBitHalf as _NBitHalf, + _NBitSingle as _NBitSingle, + _NBitDouble as _NBitDouble, + _NBitLongDouble as _NBitLongDouble, +) +from ._char_codes import ( + _BoolCodes as _BoolCodes, + _UInt8Codes as _UInt8Codes, + _UInt16Codes as _UInt16Codes, + _UInt32Codes as _UInt32Codes, + _UInt64Codes as _UInt64Codes, + _Int8Codes as _Int8Codes, + _Int16Codes as _Int16Codes, + _Int32Codes as _Int32Codes, + _Int64Codes as _Int64Codes, + _Float16Codes as _Float16Codes, + _Float32Codes as _Float32Codes, + _Float64Codes as _Float64Codes, + _Complex64Codes as _Complex64Codes, + _Complex128Codes as _Complex128Codes, + _ByteCodes as _ByteCodes, + _ShortCodes as _ShortCodes, + _IntCCodes as _IntCCodes, + _IntPCodes as _IntPCodes, + _IntCodes as _IntCodes, + _LongLongCodes as _LongLongCodes, + _UByteCodes as _UByteCodes, + _UShortCodes as _UShortCodes, + _UIntCCodes as _UIntCCodes, + _UIntPCodes as _UIntPCodes, + _UIntCodes as _UIntCodes, + _ULongLongCodes as _ULongLongCodes, + _HalfCodes as _HalfCodes, + _SingleCodes as _SingleCodes, + _DoubleCodes as _DoubleCodes, + _LongDoubleCodes as _LongDoubleCodes, + _CSingleCodes as _CSingleCodes, + _CDoubleCodes as _CDoubleCodes, + _CLongDoubleCodes as _CLongDoubleCodes, + _DT64Codes as _DT64Codes, + _TD64Codes as _TD64Codes, + _StrCodes as _StrCodes, + _BytesCodes as _BytesCodes, + _VoidCodes as _VoidCodes, + _ObjectCodes as _ObjectCodes, +) +from ._scalars import ( + _CharLike_co as _CharLike_co, + _BoolLike_co as _BoolLike_co, + _UIntLike_co as _UIntLike_co, + _IntLike_co as _IntLike_co, + _FloatLike_co as _FloatLike_co, + _ComplexLike_co as _ComplexLike_co, + _TD64Like_co as _TD64Like_co, + _NumberLike_co as _NumberLike_co, + _ScalarLike_co as _ScalarLike_co, + _VoidLike_co as _VoidLike_co, +) +from ._shape import ( + _Shape as _Shape, + _ShapeLike as _ShapeLike, +) +from ._dtype_like import ( + DTypeLike as DTypeLike, + _DTypeLike as _DTypeLike, + _SupportsDType as _SupportsDType, + _VoidDTypeLike as _VoidDTypeLike, + _DTypeLikeBool as _DTypeLikeBool, + _DTypeLikeUInt as _DTypeLikeUInt, + _DTypeLikeInt as _DTypeLikeInt, + _DTypeLikeFloat as _DTypeLikeFloat, + _DTypeLikeComplex as _DTypeLikeComplex, + _DTypeLikeTD64 as _DTypeLikeTD64, + _DTypeLikeDT64 as _DTypeLikeDT64, + _DTypeLikeObject as _DTypeLikeObject, + _DTypeLikeVoid as _DTypeLikeVoid, + _DTypeLikeStr as _DTypeLikeStr, + _DTypeLikeBytes as _DTypeLikeBytes, + _DTypeLikeComplex_co as _DTypeLikeComplex_co, +) +from ._array_like import ( + NDArray as NDArray, + ArrayLike as ArrayLike, + _ArrayLike as _ArrayLike, + _FiniteNestedSequence as _FiniteNestedSequence, + _SupportsArray as _SupportsArray, + _SupportsArrayFunc as _SupportsArrayFunc, + _ArrayLikeInt as _ArrayLikeInt, + _ArrayLikeBool_co as _ArrayLikeBool_co, + _ArrayLikeUInt_co as _ArrayLikeUInt_co, + _ArrayLikeInt_co as _ArrayLikeInt_co, + _ArrayLikeFloat_co as _ArrayLikeFloat_co, + _ArrayLikeComplex_co as _ArrayLikeComplex_co, + _ArrayLikeNumber_co as _ArrayLikeNumber_co, + _ArrayLikeTD64_co as _ArrayLikeTD64_co, + _ArrayLikeDT64_co as _ArrayLikeDT64_co, + _ArrayLikeObject_co as _ArrayLikeObject_co, + _ArrayLikeVoid_co as _ArrayLikeVoid_co, + _ArrayLikeStr_co as _ArrayLikeStr_co, + _ArrayLikeBytes_co as _ArrayLikeBytes_co, + _ArrayLikeUnknown as _ArrayLikeUnknown, + _UnknownType as _UnknownType, +) + +if TYPE_CHECKING: + from ._ufunc import ( + _UFunc_Nin1_Nout1 as _UFunc_Nin1_Nout1, + _UFunc_Nin2_Nout1 as _UFunc_Nin2_Nout1, + _UFunc_Nin1_Nout2 as _UFunc_Nin1_Nout2, + _UFunc_Nin2_Nout2 as _UFunc_Nin2_Nout2, + _GUFunc_Nin2_Nout1 as _GUFunc_Nin2_Nout1, + ) +else: + # Declare the (type-check-only) ufunc subclasses as ufunc aliases during + # runtime; this helps autocompletion tools such as Jedi (numpy/numpy#19834) + _UFunc_Nin1_Nout1 = ufunc + _UFunc_Nin2_Nout1 = ufunc + _UFunc_Nin1_Nout2 = ufunc + _UFunc_Nin2_Nout2 = 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0000000000000000000000000000000000000000..f84d19271c23f19c86729545de59e8cae4a50f05 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_add_docstring.py @@ -0,0 +1,152 @@ +"""A module for creating docstrings for sphinx ``data`` domains.""" + +import re +import textwrap + +from ._array_like import NDArray + +_docstrings_list = [] + + +def add_newdoc(name: str, value: str, doc: str) -> None: + """Append ``_docstrings_list`` with a docstring for `name`. + + Parameters + ---------- + name : str + The name of the object. + value : str + A string-representation of the object. + doc : str + The docstring of the object. + + """ + _docstrings_list.append((name, value, doc)) + + +def _parse_docstrings() -> str: + """Convert all docstrings in ``_docstrings_list`` into a single + sphinx-legible text block. + + """ + type_list_ret = [] + for name, value, doc in _docstrings_list: + s = textwrap.dedent(doc).replace("\n", "\n ") + + # Replace sections by rubrics + lines = s.split("\n") + new_lines = [] + indent = "" + for line in lines: + m = re.match(r'^(\s+)[-=]+\s*$', line) + if m and new_lines: + prev = textwrap.dedent(new_lines.pop()) + if prev == "Examples": + indent = "" + new_lines.append(f'{m.group(1)}.. rubric:: {prev}') + else: + indent = 4 * " " + new_lines.append(f'{m.group(1)}.. admonition:: {prev}') + new_lines.append("") + else: + new_lines.append(f"{indent}{line}") + + s = "\n".join(new_lines) + s_block = f""".. data:: {name}\n :value: {value}\n {s}""" + type_list_ret.append(s_block) + return "\n".join(type_list_ret) + + +add_newdoc('ArrayLike', 'typing.Union[...]', + """ + A `~typing.Union` representing objects that can be coerced + into an `~numpy.ndarray`. + + Among others this includes the likes of: + + * Scalars. + * (Nested) sequences. + * Objects implementing the `~class.__array__` protocol. + + .. versionadded:: 1.20 + + See Also + -------- + :term:`array_like`: + Any scalar or sequence that can be interpreted as an ndarray. + + Examples + -------- + .. code-block:: python + + >>> import numpy as np + >>> import numpy.typing as npt + + >>> def as_array(a: npt.ArrayLike) -> np.ndarray: + ... return np.array(a) + + """) + +add_newdoc('DTypeLike', 'typing.Union[...]', + """ + A `~typing.Union` representing objects that can be coerced + into a `~numpy.dtype`. + + Among others this includes the likes of: + + * :class:`type` objects. + * Character codes or the names of :class:`type` objects. + * Objects with the ``.dtype`` attribute. + + .. versionadded:: 1.20 + + See Also + -------- + :ref:`Specifying and constructing data types ` + A comprehensive overview of all objects that can be coerced + into data types. + + Examples + -------- + .. code-block:: python + + >>> import numpy as np + >>> import numpy.typing as npt + + >>> def as_dtype(d: npt.DTypeLike) -> np.dtype: + ... return np.dtype(d) + + """) + +add_newdoc('NDArray', repr(NDArray), + """ + A :term:`generic ` version of + `np.ndarray[Any, np.dtype[+ScalarType]] `. + + Can be used during runtime for typing arrays with a given dtype + and unspecified shape. + + .. versionadded:: 1.21 + + Examples + -------- + .. code-block:: python + + >>> import numpy as np + >>> import numpy.typing as npt + + >>> print(npt.NDArray) + numpy.ndarray[typing.Any, numpy.dtype[+ScalarType]] + + >>> print(npt.NDArray[np.float64]) + numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]] + + >>> NDArrayInt = npt.NDArray[np.int_] + >>> a: NDArrayInt = np.arange(10) + + >>> def func(a: npt.ArrayLike) -> npt.NDArray[Any]: + ... return np.array(a) + + """) + +_docstrings = _parse_docstrings() diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_array_like.py b/venv/lib/python3.10/site-packages/numpy/_typing/_array_like.py new file mode 100644 index 0000000000000000000000000000000000000000..883e817d9a6c7927a8b1e722d2b0ca074fd37c19 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_array_like.py @@ -0,0 +1,167 @@ +from __future__ import annotations + +import sys +from collections.abc import Collection, Callable, Sequence +from typing import Any, Protocol, Union, TypeVar, runtime_checkable + +from numpy import ( + ndarray, + dtype, + generic, + bool_, + unsignedinteger, + integer, + floating, + complexfloating, + number, + timedelta64, + datetime64, + object_, + void, + str_, + bytes_, +) +from ._nested_sequence import _NestedSequence + +_T = TypeVar("_T") +_ScalarType = TypeVar("_ScalarType", bound=generic) +_ScalarType_co = TypeVar("_ScalarType_co", bound=generic, covariant=True) +_DType = TypeVar("_DType", bound=dtype[Any]) +_DType_co = TypeVar("_DType_co", covariant=True, bound=dtype[Any]) + +NDArray = ndarray[Any, dtype[_ScalarType_co]] + +# The `_SupportsArray` protocol only cares about the default dtype +# (i.e. `dtype=None` or no `dtype` parameter at all) of the to-be returned +# array. +# Concrete implementations of the protocol are responsible for adding +# any and all remaining overloads +@runtime_checkable +class _SupportsArray(Protocol[_DType_co]): + def __array__(self) -> ndarray[Any, _DType_co]: ... + + +@runtime_checkable +class _SupportsArrayFunc(Protocol): + """A protocol class representing `~class.__array_function__`.""" + def __array_function__( + self, + func: Callable[..., Any], + types: Collection[type[Any]], + args: tuple[Any, ...], + kwargs: dict[str, Any], + ) -> object: ... + + +# TODO: Wait until mypy supports recursive objects in combination with typevars +_FiniteNestedSequence = Union[ + _T, + Sequence[_T], + Sequence[Sequence[_T]], + Sequence[Sequence[Sequence[_T]]], + Sequence[Sequence[Sequence[Sequence[_T]]]], +] + +# A subset of `npt.ArrayLike` that can be parametrized w.r.t. `np.generic` +_ArrayLike = Union[ + _SupportsArray[dtype[_ScalarType]], + _NestedSequence[_SupportsArray[dtype[_ScalarType]]], +] + +# A union representing array-like objects; consists of two typevars: +# One representing types that can be parametrized w.r.t. `np.dtype` +# and another one for the rest +_DualArrayLike = Union[ + _SupportsArray[_DType], + _NestedSequence[_SupportsArray[_DType]], + _T, + _NestedSequence[_T], +] + +if sys.version_info >= (3, 12): + from collections.abc import Buffer + + ArrayLike = Buffer | _DualArrayLike[ + dtype[Any], + Union[bool, int, float, complex, str, bytes], + ] +else: + ArrayLike = _DualArrayLike[ + dtype[Any], + Union[bool, int, float, complex, str, bytes], + ] + +# `ArrayLike_co`: array-like objects that can be coerced into `X` +# given the casting rules `same_kind` +_ArrayLikeBool_co = _DualArrayLike[ + dtype[bool_], + bool, +] +_ArrayLikeUInt_co = _DualArrayLike[ + dtype[Union[bool_, unsignedinteger[Any]]], + bool, +] +_ArrayLikeInt_co = _DualArrayLike[ + dtype[Union[bool_, integer[Any]]], + Union[bool, int], +] +_ArrayLikeFloat_co = _DualArrayLike[ + dtype[Union[bool_, integer[Any], floating[Any]]], + Union[bool, int, float], +] +_ArrayLikeComplex_co = _DualArrayLike[ + dtype[Union[ + bool_, + integer[Any], + floating[Any], + complexfloating[Any, Any], + ]], + Union[bool, int, float, complex], +] +_ArrayLikeNumber_co = _DualArrayLike[ + dtype[Union[bool_, number[Any]]], + Union[bool, int, float, complex], +] +_ArrayLikeTD64_co = _DualArrayLike[ + dtype[Union[bool_, integer[Any], timedelta64]], + Union[bool, int], +] +_ArrayLikeDT64_co = Union[ + _SupportsArray[dtype[datetime64]], + _NestedSequence[_SupportsArray[dtype[datetime64]]], +] +_ArrayLikeObject_co = Union[ + _SupportsArray[dtype[object_]], + _NestedSequence[_SupportsArray[dtype[object_]]], +] + +_ArrayLikeVoid_co = Union[ + _SupportsArray[dtype[void]], + _NestedSequence[_SupportsArray[dtype[void]]], +] +_ArrayLikeStr_co = _DualArrayLike[ + dtype[str_], + str, +] +_ArrayLikeBytes_co = _DualArrayLike[ + dtype[bytes_], + bytes, +] + +_ArrayLikeInt = _DualArrayLike[ + dtype[integer[Any]], + int, +] + +# Extra ArrayLike type so that pyright can deal with NDArray[Any] +# Used as the first overload, should only match NDArray[Any], +# not any actual types. +# https://github.com/numpy/numpy/pull/22193 +class _UnknownType: + ... + + +_ArrayLikeUnknown = _DualArrayLike[ + dtype[_UnknownType], + _UnknownType, +] diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_callable.pyi b/venv/lib/python3.10/site-packages/numpy/_typing/_callable.pyi new file mode 100644 index 0000000000000000000000000000000000000000..ee818e90575b62622e5802c3f2dc56b875cec38b --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_callable.pyi @@ -0,0 +1,338 @@ +""" +A module with various ``typing.Protocol`` subclasses that implement +the ``__call__`` magic method. + +See the `Mypy documentation`_ on protocols for more details. + +.. _`Mypy documentation`: https://mypy.readthedocs.io/en/stable/protocols.html#callback-protocols + +""" + +from __future__ import annotations + +from typing import ( + TypeVar, + overload, + Any, + NoReturn, + Protocol, +) + +from numpy import ( + ndarray, + dtype, + generic, + bool_, + timedelta64, + number, + integer, + unsignedinteger, + signedinteger, + int8, + int_, + floating, + float64, + complexfloating, + complex128, +) +from ._nbit import _NBitInt, _NBitDouble +from ._scalars import ( + _BoolLike_co, + _IntLike_co, + _FloatLike_co, + _NumberLike_co, +) +from . import NBitBase +from ._array_like import NDArray +from ._nested_sequence import _NestedSequence + +_T1 = TypeVar("_T1") +_T2 = TypeVar("_T2") +_T1_contra = TypeVar("_T1_contra", contravariant=True) +_T2_contra = TypeVar("_T2_contra", contravariant=True) +_2Tuple = tuple[_T1, _T1] + +_NBit1 = TypeVar("_NBit1", bound=NBitBase) +_NBit2 = TypeVar("_NBit2", bound=NBitBase) + +_IntType = TypeVar("_IntType", bound=integer) +_FloatType = TypeVar("_FloatType", bound=floating) +_NumberType = TypeVar("_NumberType", bound=number) +_NumberType_co = TypeVar("_NumberType_co", covariant=True, bound=number) +_GenericType_co = TypeVar("_GenericType_co", covariant=True, bound=generic) + +class _BoolOp(Protocol[_GenericType_co]): + @overload + def __call__(self, other: _BoolLike_co, /) -> _GenericType_co: ... + @overload # platform dependent + def __call__(self, other: int, /) -> int_: ... + @overload + def __call__(self, other: float, /) -> float64: ... + @overload + def __call__(self, other: complex, /) -> complex128: ... + @overload + def __call__(self, other: _NumberType, /) -> _NumberType: ... + +class _BoolBitOp(Protocol[_GenericType_co]): + @overload + def __call__(self, other: _BoolLike_co, /) -> _GenericType_co: ... + @overload # platform dependent + def __call__(self, other: int, /) -> int_: ... + @overload + def __call__(self, other: _IntType, /) -> _IntType: ... + +class _BoolSub(Protocol): + # Note that `other: bool_` is absent here + @overload + def __call__(self, other: bool, /) -> NoReturn: ... + @overload # platform dependent + def __call__(self, other: int, /) -> int_: ... + @overload + def __call__(self, other: float, /) -> float64: ... + @overload + def __call__(self, other: complex, /) -> complex128: ... + @overload + def __call__(self, other: _NumberType, /) -> _NumberType: ... + +class _BoolTrueDiv(Protocol): + @overload + def __call__(self, other: float | _IntLike_co, /) -> float64: ... + @overload + def __call__(self, other: complex, /) -> complex128: ... + @overload + def __call__(self, other: _NumberType, /) -> _NumberType: ... + +class _BoolMod(Protocol): + @overload + def __call__(self, other: _BoolLike_co, /) -> int8: ... + @overload # platform dependent + def __call__(self, other: int, /) -> int_: ... + @overload + def __call__(self, other: float, /) -> float64: ... + @overload + def __call__(self, other: _IntType, /) -> _IntType: ... + @overload + def __call__(self, other: _FloatType, /) -> _FloatType: ... + +class _BoolDivMod(Protocol): + @overload + def __call__(self, other: _BoolLike_co, /) -> _2Tuple[int8]: ... + @overload # platform dependent + def __call__(self, other: int, /) -> _2Tuple[int_]: ... + @overload + def __call__(self, other: float, /) -> _2Tuple[floating[_NBit1 | _NBitDouble]]: ... + @overload + def __call__(self, other: _IntType, /) -> _2Tuple[_IntType]: ... + @overload + def __call__(self, other: _FloatType, /) -> _2Tuple[_FloatType]: ... + +class _TD64Div(Protocol[_NumberType_co]): + @overload + def __call__(self, other: timedelta64, /) -> _NumberType_co: ... + @overload + def __call__(self, other: _BoolLike_co, /) -> NoReturn: ... + @overload + def __call__(self, other: _FloatLike_co, /) -> timedelta64: ... + +class _IntTrueDiv(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> floating[_NBit1]: ... + @overload + def __call__(self, other: int, /) -> floating[_NBit1 | _NBitInt]: ... + @overload + def __call__(self, other: float, /) -> floating[_NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: complex, /, + ) -> complexfloating[_NBit1 | _NBitDouble, _NBit1 | _NBitDouble]: ... + @overload + def __call__(self, other: integer[_NBit2], /) -> floating[_NBit1 | _NBit2]: ... + +class _UnsignedIntOp(Protocol[_NBit1]): + # NOTE: `uint64 + signedinteger -> float64` + @overload + def __call__(self, other: bool, /) -> unsignedinteger[_NBit1]: ... + @overload + def __call__( + self, other: int | signedinteger[Any], / + ) -> Any: ... + @overload + def __call__(self, other: float, /) -> floating[_NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: complex, /, + ) -> complexfloating[_NBit1 | _NBitDouble, _NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: unsignedinteger[_NBit2], / + ) -> unsignedinteger[_NBit1 | _NBit2]: ... + +class _UnsignedIntBitOp(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> unsignedinteger[_NBit1]: ... + @overload + def __call__(self, other: int, /) -> signedinteger[Any]: ... + @overload + def __call__(self, other: signedinteger[Any], /) -> signedinteger[Any]: ... + @overload + def __call__( + self, other: unsignedinteger[_NBit2], / + ) -> unsignedinteger[_NBit1 | _NBit2]: ... + +class _UnsignedIntMod(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> unsignedinteger[_NBit1]: ... + @overload + def __call__( + self, other: int | signedinteger[Any], / + ) -> Any: ... + @overload + def __call__(self, other: float, /) -> floating[_NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: unsignedinteger[_NBit2], / + ) -> unsignedinteger[_NBit1 | _NBit2]: ... + +class _UnsignedIntDivMod(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> _2Tuple[signedinteger[_NBit1]]: ... + @overload + def __call__( + self, other: int | signedinteger[Any], / + ) -> _2Tuple[Any]: ... + @overload + def __call__(self, other: float, /) -> _2Tuple[floating[_NBit1 | _NBitDouble]]: ... + @overload + def __call__( + self, other: unsignedinteger[_NBit2], / + ) -> _2Tuple[unsignedinteger[_NBit1 | _NBit2]]: ... + +class _SignedIntOp(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> signedinteger[_NBit1]: ... + @overload + def __call__(self, other: int, /) -> signedinteger[_NBit1 | _NBitInt]: ... + @overload + def __call__(self, other: float, /) -> floating[_NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: complex, /, + ) -> complexfloating[_NBit1 | _NBitDouble, _NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: signedinteger[_NBit2], /, + ) -> signedinteger[_NBit1 | _NBit2]: ... + +class _SignedIntBitOp(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> signedinteger[_NBit1]: ... + @overload + def __call__(self, other: int, /) -> signedinteger[_NBit1 | _NBitInt]: ... + @overload + def __call__( + self, other: signedinteger[_NBit2], /, + ) -> signedinteger[_NBit1 | _NBit2]: ... + +class _SignedIntMod(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> signedinteger[_NBit1]: ... + @overload + def __call__(self, other: int, /) -> signedinteger[_NBit1 | _NBitInt]: ... + @overload + def __call__(self, other: float, /) -> floating[_NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: signedinteger[_NBit2], /, + ) -> signedinteger[_NBit1 | _NBit2]: ... + +class _SignedIntDivMod(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> _2Tuple[signedinteger[_NBit1]]: ... + @overload + def __call__(self, other: int, /) -> _2Tuple[signedinteger[_NBit1 | _NBitInt]]: ... + @overload + def __call__(self, other: float, /) -> _2Tuple[floating[_NBit1 | _NBitDouble]]: ... + @overload + def __call__( + self, other: signedinteger[_NBit2], /, + ) -> _2Tuple[signedinteger[_NBit1 | _NBit2]]: ... + +class _FloatOp(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> floating[_NBit1]: ... + @overload + def __call__(self, other: int, /) -> floating[_NBit1 | _NBitInt]: ... + @overload + def __call__(self, other: float, /) -> floating[_NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: complex, /, + ) -> complexfloating[_NBit1 | _NBitDouble, _NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: integer[_NBit2] | floating[_NBit2], / + ) -> floating[_NBit1 | _NBit2]: ... + +class _FloatMod(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> floating[_NBit1]: ... + @overload + def __call__(self, other: int, /) -> floating[_NBit1 | _NBitInt]: ... + @overload + def __call__(self, other: float, /) -> floating[_NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, other: integer[_NBit2] | floating[_NBit2], / + ) -> floating[_NBit1 | _NBit2]: ... + +class _FloatDivMod(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> _2Tuple[floating[_NBit1]]: ... + @overload + def __call__(self, other: int, /) -> _2Tuple[floating[_NBit1 | _NBitInt]]: ... + @overload + def __call__(self, other: float, /) -> _2Tuple[floating[_NBit1 | _NBitDouble]]: ... + @overload + def __call__( + self, other: integer[_NBit2] | floating[_NBit2], / + ) -> _2Tuple[floating[_NBit1 | _NBit2]]: ... + +class _ComplexOp(Protocol[_NBit1]): + @overload + def __call__(self, other: bool, /) -> complexfloating[_NBit1, _NBit1]: ... + @overload + def __call__(self, other: int, /) -> complexfloating[_NBit1 | _NBitInt, _NBit1 | _NBitInt]: ... + @overload + def __call__( + self, other: complex, /, + ) -> complexfloating[_NBit1 | _NBitDouble, _NBit1 | _NBitDouble]: ... + @overload + def __call__( + self, + other: ( + integer[_NBit2] + | floating[_NBit2] + | complexfloating[_NBit2, _NBit2] + ), /, + ) -> complexfloating[_NBit1 | _NBit2, _NBit1 | _NBit2]: ... + +class _NumberOp(Protocol): + def __call__(self, other: _NumberLike_co, /) -> Any: ... + +class _SupportsLT(Protocol): + def __lt__(self, other: Any, /) -> object: ... + +class _SupportsGT(Protocol): + def __gt__(self, other: Any, /) -> object: ... + +class _ComparisonOp(Protocol[_T1_contra, _T2_contra]): + @overload + def __call__(self, other: _T1_contra, /) -> bool_: ... + @overload + def __call__(self, other: _T2_contra, /) -> NDArray[bool_]: ... + @overload + def __call__( + self, + other: _SupportsLT | _SupportsGT | _NestedSequence[_SupportsLT | _SupportsGT], + /, + ) -> Any: ... diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_char_codes.py b/venv/lib/python3.10/site-packages/numpy/_typing/_char_codes.py new file mode 100644 index 0000000000000000000000000000000000000000..f840d17bbca0a56133bfc2d5f14bcbf4b7ebc747 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_char_codes.py @@ -0,0 +1,111 @@ +from typing import Literal + +_BoolCodes = Literal["?", "=?", "?", "bool", "bool_", "bool8"] + +_UInt8Codes = Literal["uint8", "u1", "=u1", "u1"] +_UInt16Codes = Literal["uint16", "u2", "=u2", "u2"] +_UInt32Codes = Literal["uint32", "u4", "=u4", "u4"] +_UInt64Codes = Literal["uint64", "u8", "=u8", "u8"] + +_Int8Codes = Literal["int8", "i1", "=i1", "i1"] +_Int16Codes = Literal["int16", "i2", "=i2", "i2"] +_Int32Codes = Literal["int32", "i4", "=i4", "i4"] +_Int64Codes = Literal["int64", "i8", "=i8", "i8"] + +_Float16Codes = Literal["float16", "f2", "=f2", "f2"] +_Float32Codes = Literal["float32", "f4", "=f4", "f4"] +_Float64Codes = Literal["float64", "f8", "=f8", "f8"] + +_Complex64Codes = Literal["complex64", "c8", "=c8", "c8"] +_Complex128Codes = Literal["complex128", "c16", "=c16", "c16"] + +_ByteCodes = Literal["byte", "b", "=b", "b"] +_ShortCodes = Literal["short", "h", "=h", "h"] +_IntCCodes = Literal["intc", "i", "=i", "i"] +_IntPCodes = Literal["intp", "int0", "p", "=p", "p"] +_IntCodes = Literal["long", "int", "int_", "l", "=l", "l"] +_LongLongCodes = Literal["longlong", "q", "=q", "q"] + +_UByteCodes = Literal["ubyte", "B", "=B", "B"] +_UShortCodes = Literal["ushort", "H", "=H", "H"] +_UIntCCodes = Literal["uintc", "I", "=I", "I"] +_UIntPCodes = Literal["uintp", "uint0", "P", "=P", "P"] +_UIntCodes = Literal["ulong", "uint", "L", "=L", "L"] +_ULongLongCodes = Literal["ulonglong", "Q", "=Q", "Q"] + +_HalfCodes = Literal["half", "e", "=e", "e"] +_SingleCodes = Literal["single", "f", "=f", "f"] +_DoubleCodes = Literal["double", "float", "float_", "d", "=d", "d"] +_LongDoubleCodes = Literal["longdouble", "longfloat", "g", "=g", "g"] + +_CSingleCodes = Literal["csingle", "singlecomplex", "F", "=F", "F"] +_CDoubleCodes = Literal["cdouble", "complex", "complex_", "cfloat", "D", "=D", "D"] +_CLongDoubleCodes = Literal["clongdouble", "clongfloat", "longcomplex", "G", "=G", "G"] + +_StrCodes = Literal["str", "str_", "str0", "unicode", "unicode_", "U", "=U", "U"] +_BytesCodes = Literal["bytes", "bytes_", "bytes0", "S", "=S", "S"] +_VoidCodes = Literal["void", "void0", "V", "=V", "V"] +_ObjectCodes = Literal["object", "object_", "O", "=O", "O"] + +_DT64Codes = Literal[ + "datetime64", "=datetime64", "datetime64", + "datetime64[Y]", "=datetime64[Y]", "datetime64[Y]", + "datetime64[M]", "=datetime64[M]", "datetime64[M]", + "datetime64[W]", "=datetime64[W]", "datetime64[W]", + "datetime64[D]", "=datetime64[D]", "datetime64[D]", + "datetime64[h]", "=datetime64[h]", "datetime64[h]", + "datetime64[m]", "=datetime64[m]", "datetime64[m]", + "datetime64[s]", "=datetime64[s]", "datetime64[s]", + "datetime64[ms]", "=datetime64[ms]", "datetime64[ms]", + "datetime64[us]", "=datetime64[us]", "datetime64[us]", + "datetime64[ns]", "=datetime64[ns]", "datetime64[ns]", + "datetime64[ps]", "=datetime64[ps]", "datetime64[ps]", + "datetime64[fs]", "=datetime64[fs]", "datetime64[fs]", + "datetime64[as]", "=datetime64[as]", "datetime64[as]", + "M", "=M", "M", + "M8", "=M8", "M8", + "M8[Y]", "=M8[Y]", "M8[Y]", + "M8[M]", "=M8[M]", "M8[M]", + "M8[W]", "=M8[W]", "M8[W]", + "M8[D]", "=M8[D]", "M8[D]", + "M8[h]", "=M8[h]", "M8[h]", + "M8[m]", "=M8[m]", "M8[m]", + "M8[s]", "=M8[s]", "M8[s]", + "M8[ms]", "=M8[ms]", "M8[ms]", + "M8[us]", "=M8[us]", "M8[us]", + "M8[ns]", "=M8[ns]", "M8[ns]", + "M8[ps]", "=M8[ps]", "M8[ps]", + "M8[fs]", "=M8[fs]", "M8[fs]", + "M8[as]", "=M8[as]", "M8[as]", +] +_TD64Codes = Literal[ + "timedelta64", "=timedelta64", "timedelta64", + "timedelta64[Y]", "=timedelta64[Y]", "timedelta64[Y]", + "timedelta64[M]", "=timedelta64[M]", "timedelta64[M]", + "timedelta64[W]", "=timedelta64[W]", "timedelta64[W]", + "timedelta64[D]", "=timedelta64[D]", "timedelta64[D]", + "timedelta64[h]", "=timedelta64[h]", "timedelta64[h]", + "timedelta64[m]", "=timedelta64[m]", "timedelta64[m]", + "timedelta64[s]", "=timedelta64[s]", "timedelta64[s]", + "timedelta64[ms]", "=timedelta64[ms]", "timedelta64[ms]", + "timedelta64[us]", "=timedelta64[us]", "timedelta64[us]", + "timedelta64[ns]", "=timedelta64[ns]", "timedelta64[ns]", + "timedelta64[ps]", "=timedelta64[ps]", "timedelta64[ps]", + "timedelta64[fs]", "=timedelta64[fs]", "timedelta64[fs]", + "timedelta64[as]", "=timedelta64[as]", "timedelta64[as]", + "m", "=m", "m", + "m8", "=m8", "m8", + "m8[Y]", "=m8[Y]", "m8[Y]", + "m8[M]", "=m8[M]", "m8[M]", + "m8[W]", "=m8[W]", "m8[W]", + "m8[D]", "=m8[D]", "m8[D]", + "m8[h]", "=m8[h]", "m8[h]", + "m8[m]", "=m8[m]", "m8[m]", + "m8[s]", "=m8[s]", "m8[s]", + "m8[ms]", "=m8[ms]", "m8[ms]", + "m8[us]", "=m8[us]", "m8[us]", + "m8[ns]", "=m8[ns]", "m8[ns]", + "m8[ps]", "=m8[ps]", "m8[ps]", + "m8[fs]", "=m8[fs]", "m8[fs]", + "m8[as]", "=m8[as]", "m8[as]", +] diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_extended_precision.py b/venv/lib/python3.10/site-packages/numpy/_typing/_extended_precision.py new file mode 100644 index 0000000000000000000000000000000000000000..7246b47d0ee1724f5697ec3e80965f6f5ec48330 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_extended_precision.py @@ -0,0 +1,27 @@ +"""A module with platform-specific extended precision +`numpy.number` subclasses. + +The subclasses are defined here (instead of ``__init__.pyi``) such +that they can be imported conditionally via the numpy's mypy plugin. +""" + +import numpy as np +from . import ( + _80Bit, + _96Bit, + _128Bit, + _256Bit, +) + +uint128 = np.unsignedinteger[_128Bit] +uint256 = np.unsignedinteger[_256Bit] +int128 = np.signedinteger[_128Bit] +int256 = np.signedinteger[_256Bit] +float80 = np.floating[_80Bit] +float96 = np.floating[_96Bit] +float128 = np.floating[_128Bit] +float256 = np.floating[_256Bit] +complex160 = np.complexfloating[_80Bit, _80Bit] +complex192 = np.complexfloating[_96Bit, _96Bit] +complex256 = np.complexfloating[_128Bit, _128Bit] +complex512 = np.complexfloating[_256Bit, _256Bit] diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_nbit.py b/venv/lib/python3.10/site-packages/numpy/_typing/_nbit.py new file mode 100644 index 0000000000000000000000000000000000000000..b8d35db4f5947fc1fc7f4672c3510f4a4264da6f --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_nbit.py @@ -0,0 +1,16 @@ +"""A module with the precisions of platform-specific `~numpy.number`s.""" + +from typing import Any + +# To-be replaced with a `npt.NBitBase` subclass by numpy's mypy plugin +_NBitByte = Any +_NBitShort = Any +_NBitIntC = Any +_NBitIntP = Any +_NBitInt = Any +_NBitLongLong = Any + +_NBitHalf = Any +_NBitSingle = Any +_NBitDouble = Any +_NBitLongDouble = Any diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_nested_sequence.py b/venv/lib/python3.10/site-packages/numpy/_typing/_nested_sequence.py new file mode 100644 index 0000000000000000000000000000000000000000..3d0d25ae5b48a7c4375364c110f05af4dd38a5eb --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_nested_sequence.py @@ -0,0 +1,86 @@ +"""A module containing the `_NestedSequence` protocol.""" + +from __future__ import annotations + +from collections.abc import Iterator +from typing import ( + Any, + TypeVar, + Protocol, + runtime_checkable, +) + +__all__ = ["_NestedSequence"] + +_T_co = TypeVar("_T_co", covariant=True) + + +@runtime_checkable +class _NestedSequence(Protocol[_T_co]): + """A protocol for representing nested sequences. + + Warning + ------- + `_NestedSequence` currently does not work in combination with typevars, + *e.g.* ``def func(a: _NestedSequnce[T]) -> T: ...``. + + See Also + -------- + collections.abc.Sequence + ABCs for read-only and mutable :term:`sequences`. + + Examples + -------- + .. code-block:: python + + >>> from __future__ import annotations + + >>> from typing import TYPE_CHECKING + >>> import numpy as np + >>> from numpy._typing import _NestedSequence + + >>> def get_dtype(seq: _NestedSequence[float]) -> np.dtype[np.float64]: + ... return np.asarray(seq).dtype + + >>> a = get_dtype([1.0]) + >>> b = get_dtype([[1.0]]) + >>> c = get_dtype([[[1.0]]]) + >>> d = get_dtype([[[[1.0]]]]) + + >>> if TYPE_CHECKING: + ... reveal_locals() + ... # note: Revealed local types are: + ... # note: a: numpy.dtype[numpy.floating[numpy._typing._64Bit]] + ... # note: b: numpy.dtype[numpy.floating[numpy._typing._64Bit]] + ... # note: c: numpy.dtype[numpy.floating[numpy._typing._64Bit]] + ... # note: d: numpy.dtype[numpy.floating[numpy._typing._64Bit]] + + """ + + def __len__(self, /) -> int: + """Implement ``len(self)``.""" + raise NotImplementedError + + def __getitem__(self, index: int, /) -> _T_co | _NestedSequence[_T_co]: + """Implement ``self[x]``.""" + raise NotImplementedError + + def __contains__(self, x: object, /) -> bool: + """Implement ``x in self``.""" + raise NotImplementedError + + def __iter__(self, /) -> Iterator[_T_co | _NestedSequence[_T_co]]: + """Implement ``iter(self)``.""" + raise NotImplementedError + + def __reversed__(self, /) -> Iterator[_T_co | _NestedSequence[_T_co]]: + """Implement ``reversed(self)``.""" + raise NotImplementedError + + def count(self, value: Any, /) -> int: + """Return the number of occurrences of `value`.""" + raise NotImplementedError + + def index(self, value: Any, /) -> int: + """Return the first index of `value`.""" + raise NotImplementedError diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_scalars.py b/venv/lib/python3.10/site-packages/numpy/_typing/_scalars.py new file mode 100644 index 0000000000000000000000000000000000000000..e46ff04a00d14dd96a8a7b8052f11484a8c85d0e --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_scalars.py @@ -0,0 +1,30 @@ +from typing import Union, Any + +import numpy as np + +# NOTE: `_StrLike_co` and `_BytesLike_co` are pointless, as `np.str_` and +# `np.bytes_` are already subclasses of their builtin counterpart + +_CharLike_co = Union[str, bytes] + +# The 6 `Like_co` type-aliases below represent all scalars that can be +# coerced into `` (with the casting rule `same_kind`) +_BoolLike_co = Union[bool, np.bool_] +_UIntLike_co = Union[_BoolLike_co, np.unsignedinteger[Any]] +_IntLike_co = Union[_BoolLike_co, int, np.integer[Any]] +_FloatLike_co = Union[_IntLike_co, float, np.floating[Any]] +_ComplexLike_co = Union[_FloatLike_co, complex, np.complexfloating[Any, Any]] +_TD64Like_co = Union[_IntLike_co, np.timedelta64] + +_NumberLike_co = Union[int, float, complex, np.number[Any], np.bool_] +_ScalarLike_co = Union[ + int, + float, + complex, + str, + bytes, + np.generic, +] + +# `_VoidLike_co` is technically not a scalar, but it's close enough +_VoidLike_co = Union[tuple[Any, ...], np.void] diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_shape.py b/venv/lib/python3.10/site-packages/numpy/_typing/_shape.py new file mode 100644 index 0000000000000000000000000000000000000000..4f1204e47c6a20012e729514fdd78424126d45b8 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_shape.py @@ -0,0 +1,7 @@ +from collections.abc import Sequence +from typing import Union, SupportsIndex + +_Shape = tuple[int, ...] + +# Anything that can be coerced to a shape tuple +_ShapeLike = Union[SupportsIndex, Sequence[SupportsIndex]] diff --git a/venv/lib/python3.10/site-packages/numpy/_typing/_ufunc.pyi b/venv/lib/python3.10/site-packages/numpy/_typing/_ufunc.pyi new file mode 100644 index 0000000000000000000000000000000000000000..9f8e0d4edbfba4b29fb9ac8743009f3073c63e40 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/_typing/_ufunc.pyi @@ -0,0 +1,445 @@ +"""A module with private type-check-only `numpy.ufunc` subclasses. + +The signatures of the ufuncs are too varied to reasonably type +with a single class. So instead, `ufunc` has been expanded into +four private subclasses, one for each combination of +`~ufunc.nin` and `~ufunc.nout`. + +""" + +from typing import ( + Any, + Generic, + overload, + TypeVar, + Literal, + SupportsIndex, + Protocol, +) + +from numpy import ufunc, _CastingKind, _OrderKACF +from numpy.typing import NDArray + +from ._shape import _ShapeLike +from ._scalars import _ScalarLike_co +from ._array_like import ArrayLike, _ArrayLikeBool_co, _ArrayLikeInt_co +from ._dtype_like import DTypeLike + +_T = TypeVar("_T") +_2Tuple = tuple[_T, _T] +_3Tuple = tuple[_T, _T, _T] +_4Tuple = tuple[_T, _T, _T, _T] + +_NTypes = TypeVar("_NTypes", bound=int) +_IDType = TypeVar("_IDType", bound=Any) +_NameType = TypeVar("_NameType", bound=str) + + +class _SupportsArrayUFunc(Protocol): + def __array_ufunc__( + self, + ufunc: ufunc, + method: Literal["__call__", "reduce", "reduceat", "accumulate", "outer", "inner"], + *inputs: Any, + **kwargs: Any, + ) -> Any: ... + + +# NOTE: In reality `extobj` should be a length of list 3 containing an +# int, an int, and a callable, but there's no way to properly express +# non-homogenous lists. +# Use `Any` over `Union` to avoid issues related to lists invariance. + +# NOTE: `reduce`, `accumulate`, `reduceat` and `outer` raise a ValueError for +# ufuncs that don't accept two input arguments and return one output argument. +# In such cases the respective methods are simply typed as `None`. + +# NOTE: Similarly, `at` won't be defined for ufuncs that return +# multiple outputs; in such cases `at` is typed as `None` + +# NOTE: If 2 output types are returned then `out` must be a +# 2-tuple of arrays. Otherwise `None` or a plain array are also acceptable + +class _UFunc_Nin1_Nout1(ufunc, Generic[_NameType, _NTypes, _IDType]): # type: ignore[misc] + @property + def __name__(self) -> _NameType: ... + @property + def ntypes(self) -> _NTypes: ... + @property + def identity(self) -> _IDType: ... + @property + def nin(self) -> Literal[1]: ... + @property + def nout(self) -> Literal[1]: ... + @property + def nargs(self) -> Literal[2]: ... + @property + def signature(self) -> None: ... + @property + def reduce(self) -> None: ... + @property + def accumulate(self) -> None: ... + @property + def reduceat(self) -> None: ... + @property + def outer(self) -> None: ... + + @overload + def __call__( + self, + __x1: _ScalarLike_co, + out: None = ..., + *, + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _2Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> Any: ... + @overload + def __call__( + self, + __x1: ArrayLike, + out: None | NDArray[Any] | tuple[NDArray[Any]] = ..., + *, + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _2Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> NDArray[Any]: ... + @overload + def __call__( + self, + __x1: _SupportsArrayUFunc, + out: None | NDArray[Any] | tuple[NDArray[Any]] = ..., + *, + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _2Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> Any: ... + + def at( + self, + a: _SupportsArrayUFunc, + indices: _ArrayLikeInt_co, + /, + ) -> None: ... + +class _UFunc_Nin2_Nout1(ufunc, Generic[_NameType, _NTypes, _IDType]): # type: ignore[misc] + @property + def __name__(self) -> _NameType: ... + @property + def ntypes(self) -> _NTypes: ... + @property + def identity(self) -> _IDType: ... + @property + def nin(self) -> Literal[2]: ... + @property + def nout(self) -> Literal[1]: ... + @property + def nargs(self) -> Literal[3]: ... + @property + def signature(self) -> None: ... + + @overload + def __call__( + self, + __x1: _ScalarLike_co, + __x2: _ScalarLike_co, + out: None = ..., + *, + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> Any: ... + @overload + def __call__( + self, + __x1: ArrayLike, + __x2: ArrayLike, + out: None | NDArray[Any] | tuple[NDArray[Any]] = ..., + *, + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> NDArray[Any]: ... + + def at( + self, + a: NDArray[Any], + indices: _ArrayLikeInt_co, + b: ArrayLike, + /, + ) -> None: ... + + def reduce( + self, + array: ArrayLike, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: None | NDArray[Any] = ..., + keepdims: bool = ..., + initial: Any = ..., + where: _ArrayLikeBool_co = ..., + ) -> Any: ... + + def accumulate( + self, + array: ArrayLike, + axis: SupportsIndex = ..., + dtype: DTypeLike = ..., + out: None | NDArray[Any] = ..., + ) -> NDArray[Any]: ... + + def reduceat( + self, + array: ArrayLike, + indices: _ArrayLikeInt_co, + axis: SupportsIndex = ..., + dtype: DTypeLike = ..., + out: None | NDArray[Any] = ..., + ) -> NDArray[Any]: ... + + # Expand `**kwargs` into explicit keyword-only arguments + @overload + def outer( + self, + A: _ScalarLike_co, + B: _ScalarLike_co, + /, *, + out: None = ..., + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> Any: ... + @overload + def outer( # type: ignore[misc] + self, + A: ArrayLike, + B: ArrayLike, + /, *, + out: None | NDArray[Any] | tuple[NDArray[Any]] = ..., + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> NDArray[Any]: ... + +class _UFunc_Nin1_Nout2(ufunc, Generic[_NameType, _NTypes, _IDType]): # type: ignore[misc] + @property + def __name__(self) -> _NameType: ... + @property + def ntypes(self) -> _NTypes: ... + @property + def identity(self) -> _IDType: ... + @property + def nin(self) -> Literal[1]: ... + @property + def nout(self) -> Literal[2]: ... + @property + def nargs(self) -> Literal[3]: ... + @property + def signature(self) -> None: ... + @property + def at(self) -> None: ... + @property + def reduce(self) -> None: ... + @property + def accumulate(self) -> None: ... + @property + def reduceat(self) -> None: ... + @property + def outer(self) -> None: ... + + @overload + def __call__( + self, + __x1: _ScalarLike_co, + __out1: None = ..., + __out2: None = ..., + *, + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> _2Tuple[Any]: ... + @overload + def __call__( + self, + __x1: ArrayLike, + __out1: None | NDArray[Any] = ..., + __out2: None | NDArray[Any] = ..., + *, + out: _2Tuple[NDArray[Any]] = ..., + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> _2Tuple[NDArray[Any]]: ... + @overload + def __call__( + self, + __x1: _SupportsArrayUFunc, + __out1: None | NDArray[Any] = ..., + __out2: None | NDArray[Any] = ..., + *, + out: _2Tuple[NDArray[Any]] = ..., + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> _2Tuple[Any]: ... + +class _UFunc_Nin2_Nout2(ufunc, Generic[_NameType, _NTypes, _IDType]): # type: ignore[misc] + @property + def __name__(self) -> _NameType: ... + @property + def ntypes(self) -> _NTypes: ... + @property + def identity(self) -> _IDType: ... + @property + def nin(self) -> Literal[2]: ... + @property + def nout(self) -> Literal[2]: ... + @property + def nargs(self) -> Literal[4]: ... + @property + def signature(self) -> None: ... + @property + def at(self) -> None: ... + @property + def reduce(self) -> None: ... + @property + def accumulate(self) -> None: ... + @property + def reduceat(self) -> None: ... + @property + def outer(self) -> None: ... + + @overload + def __call__( + self, + __x1: _ScalarLike_co, + __x2: _ScalarLike_co, + __out1: None = ..., + __out2: None = ..., + *, + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _4Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> _2Tuple[Any]: ... + @overload + def __call__( + self, + __x1: ArrayLike, + __x2: ArrayLike, + __out1: None | NDArray[Any] = ..., + __out2: None | NDArray[Any] = ..., + *, + out: _2Tuple[NDArray[Any]] = ..., + where: None | _ArrayLikeBool_co = ..., + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _4Tuple[None | str] = ..., + extobj: list[Any] = ..., + ) -> _2Tuple[NDArray[Any]]: ... + +class _GUFunc_Nin2_Nout1(ufunc, Generic[_NameType, _NTypes, _IDType]): # type: ignore[misc] + @property + def __name__(self) -> _NameType: ... + @property + def ntypes(self) -> _NTypes: ... + @property + def identity(self) -> _IDType: ... + @property + def nin(self) -> Literal[2]: ... + @property + def nout(self) -> Literal[1]: ... + @property + def nargs(self) -> Literal[3]: ... + + # NOTE: In practice the only gufunc in the main namespace is `matmul`, + # so we can use its signature here + @property + def signature(self) -> Literal["(n?,k),(k,m?)->(n?,m?)"]: ... + @property + def reduce(self) -> None: ... + @property + def accumulate(self) -> None: ... + @property + def reduceat(self) -> None: ... + @property + def outer(self) -> None: ... + @property + def at(self) -> None: ... + + # Scalar for 1D array-likes; ndarray otherwise + @overload + def __call__( + self, + __x1: ArrayLike, + __x2: ArrayLike, + out: None = ..., + *, + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + axes: list[_2Tuple[SupportsIndex]] = ..., + ) -> Any: ... + @overload + def __call__( + self, + __x1: ArrayLike, + __x2: ArrayLike, + out: NDArray[Any] | tuple[NDArray[Any]], + *, + casting: _CastingKind = ..., + order: _OrderKACF = ..., + dtype: DTypeLike = ..., + subok: bool = ..., + signature: str | _3Tuple[None | str] = ..., + extobj: list[Any] = ..., + axes: list[_2Tuple[SupportsIndex]] = ..., + ) -> NDArray[Any]: ... diff --git a/venv/lib/python3.10/site-packages/numpy/core/__init__.py b/venv/lib/python3.10/site-packages/numpy/core/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..2d59b89e6b8a0ef1addde24ffafc476b98f92d89 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/__init__.py @@ -0,0 +1,180 @@ +""" +Contains the core of NumPy: ndarray, ufuncs, dtypes, etc. + +Please note that this module is private. All functions and objects +are available in the main ``numpy`` namespace - use that instead. + +""" + +import os +import warnings + +from numpy.version import version as __version__ + + +# disables OpenBLAS affinity setting of the main thread that limits +# python threads or processes to one core +env_added = [] +for envkey in ['OPENBLAS_MAIN_FREE', 'GOTOBLAS_MAIN_FREE']: + if envkey not in os.environ: + os.environ[envkey] = '1' + env_added.append(envkey) + +try: + from . import multiarray +except ImportError as exc: + import sys + msg = """ + +IMPORTANT: PLEASE READ THIS FOR ADVICE ON HOW TO SOLVE THIS ISSUE! + +Importing the numpy C-extensions failed. This error can happen for +many reasons, often due to issues with your setup or how NumPy was +installed. + +We have compiled some common reasons and troubleshooting tips at: + + https://numpy.org/devdocs/user/troubleshooting-importerror.html + +Please note and check the following: + + * The Python version is: Python%d.%d from "%s" + * The NumPy version is: "%s" + +and make sure that they are the versions you expect. +Please carefully study the documentation linked above for further help. + +Original error was: %s +""" % (sys.version_info[0], sys.version_info[1], sys.executable, + __version__, exc) + raise ImportError(msg) +finally: + for envkey in env_added: + del os.environ[envkey] +del envkey +del env_added +del os + +from . import umath + +# Check that multiarray,umath are pure python modules wrapping +# _multiarray_umath and not either of the old c-extension modules +if not (hasattr(multiarray, '_multiarray_umath') and + hasattr(umath, '_multiarray_umath')): + import sys + path = sys.modules['numpy'].__path__ + msg = ("Something is wrong with the numpy installation. " + "While importing we detected an older version of " + "numpy in {}. One method of fixing this is to repeatedly uninstall " + "numpy until none is found, then reinstall this version.") + raise ImportError(msg.format(path)) + +from . import numerictypes as nt +multiarray.set_typeDict(nt.sctypeDict) +from . import numeric +from .numeric import * +from . import fromnumeric +from .fromnumeric import * +from . import defchararray as char +from . import records +from . import records as rec +from .records import record, recarray, format_parser +# Note: module name memmap is overwritten by a class with same name +from .memmap import * +from .defchararray import chararray +from . import function_base +from .function_base import * +from . import _machar +from . import getlimits +from .getlimits import * +from . import shape_base +from .shape_base import * +from . import einsumfunc +from .einsumfunc import * +del nt + +from .numeric import absolute as abs + +# do this after everything else, to minimize the chance of this misleadingly +# appearing in an import-time traceback +from . import _add_newdocs +from . import _add_newdocs_scalars +# add these for module-freeze analysis (like PyInstaller) +from . import _dtype_ctypes +from . import _internal +from . import _dtype +from . import _methods + +__all__ = ['char', 'rec', 'memmap'] +__all__ += numeric.__all__ +__all__ += ['record', 'recarray', 'format_parser'] +__all__ += ['chararray'] +__all__ += function_base.__all__ +__all__ += getlimits.__all__ +__all__ += shape_base.__all__ +__all__ += einsumfunc.__all__ + +# We used to use `np.core._ufunc_reconstruct` to unpickle. This is unnecessary, +# but old pickles saved before 1.20 will be using it, and there is no reason +# to break loading them. +def _ufunc_reconstruct(module, name): + # The `fromlist` kwarg is required to ensure that `mod` points to the + # inner-most module rather than the parent package when module name is + # nested. This makes it possible to pickle non-toplevel ufuncs such as + # scipy.special.expit for instance. + mod = __import__(module, fromlist=[name]) + return getattr(mod, name) + + +def _ufunc_reduce(func): + # Report the `__name__`. pickle will try to find the module. Note that + # pickle supports for this `__name__` to be a `__qualname__`. It may + # make sense to add a `__qualname__` to ufuncs, to allow this more + # explicitly (Numba has ufuncs as attributes). + # See also: https://github.com/dask/distributed/issues/3450 + return func.__name__ + + +def _DType_reconstruct(scalar_type): + # This is a work-around to pickle type(np.dtype(np.float64)), etc. + # and it should eventually be replaced with a better solution, e.g. when + # DTypes become HeapTypes. + return type(dtype(scalar_type)) + + +def _DType_reduce(DType): + # As types/classes, most DTypes can simply be pickled by their name: + if not DType._legacy or DType.__module__ == "numpy.dtypes": + return DType.__name__ + + # However, user defined legacy dtypes (like rational) do not end up in + # `numpy.dtypes` as module and do not have a public class at all. + # For these, we pickle them by reconstructing them from the scalar type: + scalar_type = DType.type + return _DType_reconstruct, (scalar_type,) + + +def __getattr__(name): + # Deprecated 2022-11-22, NumPy 1.25. + if name == "MachAr": + warnings.warn( + "The `np.core.MachAr` is considered private API (NumPy 1.24)", + DeprecationWarning, stacklevel=2, + ) + return _machar.MachAr + raise AttributeError(f"Module {__name__!r} has no attribute {name!r}") + + +import copyreg + +copyreg.pickle(ufunc, _ufunc_reduce) +copyreg.pickle(type(dtype), _DType_reduce, _DType_reconstruct) + +# Unclutter namespace (must keep _*_reconstruct for unpickling) +del copyreg +del _ufunc_reduce +del _DType_reduce + +from numpy._pytesttester import PytestTester +test = PytestTester(__name__) +del PytestTester diff --git a/venv/lib/python3.10/site-packages/numpy/core/__init__.pyi b/venv/lib/python3.10/site-packages/numpy/core/__init__.pyi new file mode 100644 index 0000000000000000000000000000000000000000..4c7a42bf3db4dd62fccf927ff0f20169bdfa5746 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/__init__.pyi @@ -0,0 +1,2 @@ +# NOTE: The `np.core` namespace is deliberately kept empty due to it +# being private (despite the lack of leading underscore) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_add_newdocs.py b/venv/lib/python3.10/site-packages/numpy/core/_add_newdocs.py new file mode 100644 index 0000000000000000000000000000000000000000..6e29fcf59f2ec14cd81f0f6fa19a5674741025ee --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_add_newdocs.py @@ -0,0 +1,7080 @@ +""" +This is only meant to add docs to objects defined in C-extension modules. +The purpose is to allow easier editing of the docstrings without +requiring a re-compile. + +NOTE: Many of the methods of ndarray have corresponding functions. + If you update these docstrings, please keep also the ones in + core/fromnumeric.py, core/defmatrix.py up-to-date. + +""" + +from numpy.core.function_base import add_newdoc +from numpy.core.overrides import array_function_like_doc + + +############################################################################### +# +# flatiter +# +# flatiter needs a toplevel description +# +############################################################################### + +add_newdoc('numpy.core', 'flatiter', + """ + Flat iterator object to iterate over arrays. + + A `flatiter` iterator is returned by ``x.flat`` for any array `x`. + It allows iterating over the array as if it were a 1-D array, + either in a for-loop or by calling its `next` method. + + Iteration is done in row-major, C-style order (the last + index varying the fastest). The iterator can also be indexed using + basic slicing or advanced indexing. + + See Also + -------- + ndarray.flat : Return a flat iterator over an array. + ndarray.flatten : Returns a flattened copy of an array. + + Notes + ----- + A `flatiter` iterator can not be constructed directly from Python code + by calling the `flatiter` constructor. + + Examples + -------- + >>> x = np.arange(6).reshape(2, 3) + >>> fl = x.flat + >>> type(fl) + + >>> for item in fl: + ... print(item) + ... + 0 + 1 + 2 + 3 + 4 + 5 + + >>> fl[2:4] + array([2, 3]) + + """) + +# flatiter attributes + +add_newdoc('numpy.core', 'flatiter', ('base', + """ + A reference to the array that is iterated over. + + Examples + -------- + >>> x = np.arange(5) + >>> fl = x.flat + >>> fl.base is x + True + + """)) + + + +add_newdoc('numpy.core', 'flatiter', ('coords', + """ + An N-dimensional tuple of current coordinates. + + Examples + -------- + >>> x = np.arange(6).reshape(2, 3) + >>> fl = x.flat + >>> fl.coords + (0, 0) + >>> next(fl) + 0 + >>> fl.coords + (0, 1) + + """)) + + + +add_newdoc('numpy.core', 'flatiter', ('index', + """ + Current flat index into the array. + + Examples + -------- + >>> x = np.arange(6).reshape(2, 3) + >>> fl = x.flat + >>> fl.index + 0 + >>> next(fl) + 0 + >>> fl.index + 1 + + """)) + +# flatiter functions + +add_newdoc('numpy.core', 'flatiter', ('__array__', + """__array__(type=None) Get array from iterator + + """)) + + +add_newdoc('numpy.core', 'flatiter', ('copy', + """ + copy() + + Get a copy of the iterator as a 1-D array. + + Examples + -------- + >>> x = np.arange(6).reshape(2, 3) + >>> x + array([[0, 1, 2], + [3, 4, 5]]) + >>> fl = x.flat + >>> fl.copy() + array([0, 1, 2, 3, 4, 5]) + + """)) + + +############################################################################### +# +# nditer +# +############################################################################### + +add_newdoc('numpy.core', 'nditer', + """ + nditer(op, flags=None, op_flags=None, op_dtypes=None, order='K', casting='safe', op_axes=None, itershape=None, buffersize=0) + + Efficient multi-dimensional iterator object to iterate over arrays. + To get started using this object, see the + :ref:`introductory guide to array iteration `. + + Parameters + ---------- + op : ndarray or sequence of array_like + The array(s) to iterate over. + + flags : sequence of str, optional + Flags to control the behavior of the iterator. + + * ``buffered`` enables buffering when required. + * ``c_index`` causes a C-order index to be tracked. + * ``f_index`` causes a Fortran-order index to be tracked. + * ``multi_index`` causes a multi-index, or a tuple of indices + with one per iteration dimension, to be tracked. + * ``common_dtype`` causes all the operands to be converted to + a common data type, with copying or buffering as necessary. + * ``copy_if_overlap`` causes the iterator to determine if read + operands have overlap with write operands, and make temporary + copies as necessary to avoid overlap. False positives (needless + copying) are possible in some cases. + * ``delay_bufalloc`` delays allocation of the buffers until + a reset() call is made. Allows ``allocate`` operands to + be initialized before their values are copied into the buffers. + * ``external_loop`` causes the ``values`` given to be + one-dimensional arrays with multiple values instead of + zero-dimensional arrays. + * ``grow_inner`` allows the ``value`` array sizes to be made + larger than the buffer size when both ``buffered`` and + ``external_loop`` is used. + * ``ranged`` allows the iterator to be restricted to a sub-range + of the iterindex values. + * ``refs_ok`` enables iteration of reference types, such as + object arrays. + * ``reduce_ok`` enables iteration of ``readwrite`` operands + which are broadcasted, also known as reduction operands. + * ``zerosize_ok`` allows `itersize` to be zero. + op_flags : list of list of str, optional + This is a list of flags for each operand. At minimum, one of + ``readonly``, ``readwrite``, or ``writeonly`` must be specified. + + * ``readonly`` indicates the operand will only be read from. + * ``readwrite`` indicates the operand will be read from and written to. + * ``writeonly`` indicates the operand will only be written to. + * ``no_broadcast`` prevents the operand from being broadcasted. + * ``contig`` forces the operand data to be contiguous. + * ``aligned`` forces the operand data to be aligned. + * ``nbo`` forces the operand data to be in native byte order. + * ``copy`` allows a temporary read-only copy if required. + * ``updateifcopy`` allows a temporary read-write copy if required. + * ``allocate`` causes the array to be allocated if it is None + in the ``op`` parameter. + * ``no_subtype`` prevents an ``allocate`` operand from using a subtype. + * ``arraymask`` indicates that this operand is the mask to use + for selecting elements when writing to operands with the + 'writemasked' flag set. The iterator does not enforce this, + but when writing from a buffer back to the array, it only + copies those elements indicated by this mask. + * ``writemasked`` indicates that only elements where the chosen + ``arraymask`` operand is True will be written to. + * ``overlap_assume_elementwise`` can be used to mark operands that are + accessed only in the iterator order, to allow less conservative + copying when ``copy_if_overlap`` is present. + op_dtypes : dtype or tuple of dtype(s), optional + The required data type(s) of the operands. If copying or buffering + is enabled, the data will be converted to/from their original types. + order : {'C', 'F', 'A', 'K'}, optional + Controls the iteration order. 'C' means C order, 'F' means + Fortran order, 'A' means 'F' order if all the arrays are Fortran + contiguous, 'C' order otherwise, and 'K' means as close to the + order the array elements appear in memory as possible. This also + affects the element memory order of ``allocate`` operands, as they + are allocated to be compatible with iteration order. + Default is 'K'. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur when making a copy + or buffering. Setting this to 'unsafe' is not recommended, + as it can adversely affect accumulations. + + * 'no' means the data types should not be cast at all. + * 'equiv' means only byte-order changes are allowed. + * 'safe' means only casts which can preserve values are allowed. + * 'same_kind' means only safe casts or casts within a kind, + like float64 to float32, are allowed. + * 'unsafe' means any data conversions may be done. + op_axes : list of list of ints, optional + If provided, is a list of ints or None for each operands. + The list of axes for an operand is a mapping from the dimensions + of the iterator to the dimensions of the operand. A value of + -1 can be placed for entries, causing that dimension to be + treated as `newaxis`. + itershape : tuple of ints, optional + The desired shape of the iterator. This allows ``allocate`` operands + with a dimension mapped by op_axes not corresponding to a dimension + of a different operand to get a value not equal to 1 for that + dimension. + buffersize : int, optional + When buffering is enabled, controls the size of the temporary + buffers. Set to 0 for the default value. + + Attributes + ---------- + dtypes : tuple of dtype(s) + The data types of the values provided in `value`. This may be + different from the operand data types if buffering is enabled. + Valid only before the iterator is closed. + finished : bool + Whether the iteration over the operands is finished or not. + has_delayed_bufalloc : bool + If True, the iterator was created with the ``delay_bufalloc`` flag, + and no reset() function was called on it yet. + has_index : bool + If True, the iterator was created with either the ``c_index`` or + the ``f_index`` flag, and the property `index` can be used to + retrieve it. + has_multi_index : bool + If True, the iterator was created with the ``multi_index`` flag, + and the property `multi_index` can be used to retrieve it. + index + When the ``c_index`` or ``f_index`` flag was used, this property + provides access to the index. Raises a ValueError if accessed + and ``has_index`` is False. + iterationneedsapi : bool + Whether iteration requires access to the Python API, for example + if one of the operands is an object array. + iterindex : int + An index which matches the order of iteration. + itersize : int + Size of the iterator. + itviews + Structured view(s) of `operands` in memory, matching the reordered + and optimized iterator access pattern. Valid only before the iterator + is closed. + multi_index + When the ``multi_index`` flag was used, this property + provides access to the index. Raises a ValueError if accessed + accessed and ``has_multi_index`` is False. + ndim : int + The dimensions of the iterator. + nop : int + The number of iterator operands. + operands : tuple of operand(s) + The array(s) to be iterated over. Valid only before the iterator is + closed. + shape : tuple of ints + Shape tuple, the shape of the iterator. + value + Value of ``operands`` at current iteration. Normally, this is a + tuple of array scalars, but if the flag ``external_loop`` is used, + it is a tuple of one dimensional arrays. + + Notes + ----- + `nditer` supersedes `flatiter`. The iterator implementation behind + `nditer` is also exposed by the NumPy C API. + + The Python exposure supplies two iteration interfaces, one which follows + the Python iterator protocol, and another which mirrors the C-style + do-while pattern. The native Python approach is better in most cases, but + if you need the coordinates or index of an iterator, use the C-style pattern. + + Examples + -------- + Here is how we might write an ``iter_add`` function, using the + Python iterator protocol: + + >>> def iter_add_py(x, y, out=None): + ... addop = np.add + ... it = np.nditer([x, y, out], [], + ... [['readonly'], ['readonly'], ['writeonly','allocate']]) + ... with it: + ... for (a, b, c) in it: + ... addop(a, b, out=c) + ... return it.operands[2] + + Here is the same function, but following the C-style pattern: + + >>> def iter_add(x, y, out=None): + ... addop = np.add + ... it = np.nditer([x, y, out], [], + ... [['readonly'], ['readonly'], ['writeonly','allocate']]) + ... with it: + ... while not it.finished: + ... addop(it[0], it[1], out=it[2]) + ... it.iternext() + ... return it.operands[2] + + Here is an example outer product function: + + >>> def outer_it(x, y, out=None): + ... mulop = np.multiply + ... it = np.nditer([x, y, out], ['external_loop'], + ... [['readonly'], ['readonly'], ['writeonly', 'allocate']], + ... op_axes=[list(range(x.ndim)) + [-1] * y.ndim, + ... [-1] * x.ndim + list(range(y.ndim)), + ... None]) + ... with it: + ... for (a, b, c) in it: + ... mulop(a, b, out=c) + ... return it.operands[2] + + >>> a = np.arange(2)+1 + >>> b = np.arange(3)+1 + >>> outer_it(a,b) + array([[1, 2, 3], + [2, 4, 6]]) + + Here is an example function which operates like a "lambda" ufunc: + + >>> def luf(lamdaexpr, *args, **kwargs): + ... '''luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)''' + ... nargs = len(args) + ... op = (kwargs.get('out',None),) + args + ... it = np.nditer(op, ['buffered','external_loop'], + ... [['writeonly','allocate','no_broadcast']] + + ... [['readonly','nbo','aligned']]*nargs, + ... order=kwargs.get('order','K'), + ... casting=kwargs.get('casting','safe'), + ... buffersize=kwargs.get('buffersize',0)) + ... while not it.finished: + ... it[0] = lamdaexpr(*it[1:]) + ... it.iternext() + ... return it.operands[0] + + >>> a = np.arange(5) + >>> b = np.ones(5) + >>> luf(lambda i,j:i*i + j/2, a, b) + array([ 0.5, 1.5, 4.5, 9.5, 16.5]) + + If operand flags ``"writeonly"`` or ``"readwrite"`` are used the + operands may be views into the original data with the + `WRITEBACKIFCOPY` flag. In this case `nditer` must be used as a + context manager or the `nditer.close` method must be called before + using the result. The temporary data will be written back to the + original data when the `__exit__` function is called but not before: + + >>> a = np.arange(6, dtype='i4')[::-2] + >>> with np.nditer(a, [], + ... [['writeonly', 'updateifcopy']], + ... casting='unsafe', + ... op_dtypes=[np.dtype('f4')]) as i: + ... x = i.operands[0] + ... x[:] = [-1, -2, -3] + ... # a still unchanged here + >>> a, x + (array([-1, -2, -3], dtype=int32), array([-1., -2., -3.], dtype=float32)) + + It is important to note that once the iterator is exited, dangling + references (like `x` in the example) may or may not share data with + the original data `a`. If writeback semantics were active, i.e. if + `x.base.flags.writebackifcopy` is `True`, then exiting the iterator + will sever the connection between `x` and `a`, writing to `x` will + no longer write to `a`. If writeback semantics are not active, then + `x.data` will still point at some part of `a.data`, and writing to + one will affect the other. + + Context management and the `close` method appeared in version 1.15.0. + + """) + +# nditer methods + +add_newdoc('numpy.core', 'nditer', ('copy', + """ + copy() + + Get a copy of the iterator in its current state. + + Examples + -------- + >>> x = np.arange(10) + >>> y = x + 1 + >>> it = np.nditer([x, y]) + >>> next(it) + (array(0), array(1)) + >>> it2 = it.copy() + >>> next(it2) + (array(1), array(2)) + + """)) + +add_newdoc('numpy.core', 'nditer', ('operands', + """ + operands[`Slice`] + + The array(s) to be iterated over. Valid only before the iterator is closed. + """)) + +add_newdoc('numpy.core', 'nditer', ('debug_print', + """ + debug_print() + + Print the current state of the `nditer` instance and debug info to stdout. + + """)) + +add_newdoc('numpy.core', 'nditer', ('enable_external_loop', + """ + enable_external_loop() + + When the "external_loop" was not used during construction, but + is desired, this modifies the iterator to behave as if the flag + was specified. + + """)) + +add_newdoc('numpy.core', 'nditer', ('iternext', + """ + iternext() + + Check whether iterations are left, and perform a single internal iteration + without returning the result. Used in the C-style pattern do-while + pattern. For an example, see `nditer`. + + Returns + ------- + iternext : bool + Whether or not there are iterations left. + + """)) + +add_newdoc('numpy.core', 'nditer', ('remove_axis', + """ + remove_axis(i, /) + + Removes axis `i` from the iterator. Requires that the flag "multi_index" + be enabled. + + """)) + +add_newdoc('numpy.core', 'nditer', ('remove_multi_index', + """ + remove_multi_index() + + When the "multi_index" flag was specified, this removes it, allowing + the internal iteration structure to be optimized further. + + """)) + +add_newdoc('numpy.core', 'nditer', ('reset', + """ + reset() + + Reset the iterator to its initial state. + + """)) + +add_newdoc('numpy.core', 'nested_iters', + """ + nested_iters(op, axes, flags=None, op_flags=None, op_dtypes=None, \ + order="K", casting="safe", buffersize=0) + + Create nditers for use in nested loops + + Create a tuple of `nditer` objects which iterate in nested loops over + different axes of the op argument. The first iterator is used in the + outermost loop, the last in the innermost loop. Advancing one will change + the subsequent iterators to point at its new element. + + Parameters + ---------- + op : ndarray or sequence of array_like + The array(s) to iterate over. + + axes : list of list of int + Each item is used as an "op_axes" argument to an nditer + + flags, op_flags, op_dtypes, order, casting, buffersize (optional) + See `nditer` parameters of the same name + + Returns + ------- + iters : tuple of nditer + An nditer for each item in `axes`, outermost first + + See Also + -------- + nditer + + Examples + -------- + + Basic usage. Note how y is the "flattened" version of + [a[:, 0, :], a[:, 1, 0], a[:, 2, :]] since we specified + the first iter's axes as [1] + + >>> a = np.arange(12).reshape(2, 3, 2) + >>> i, j = np.nested_iters(a, [[1], [0, 2]], flags=["multi_index"]) + >>> for x in i: + ... print(i.multi_index) + ... for y in j: + ... print('', j.multi_index, y) + (0,) + (0, 0) 0 + (0, 1) 1 + (1, 0) 6 + (1, 1) 7 + (1,) + (0, 0) 2 + (0, 1) 3 + (1, 0) 8 + (1, 1) 9 + (2,) + (0, 0) 4 + (0, 1) 5 + (1, 0) 10 + (1, 1) 11 + + """) + +add_newdoc('numpy.core', 'nditer', ('close', + """ + close() + + Resolve all writeback semantics in writeable operands. + + .. versionadded:: 1.15.0 + + See Also + -------- + + :ref:`nditer-context-manager` + + """)) + + +############################################################################### +# +# broadcast +# +############################################################################### + +add_newdoc('numpy.core', 'broadcast', + """ + Produce an object that mimics broadcasting. + + Parameters + ---------- + in1, in2, ... : array_like + Input parameters. + + Returns + ------- + b : broadcast object + Broadcast the input parameters against one another, and + return an object that encapsulates the result. + Amongst others, it has ``shape`` and ``nd`` properties, and + may be used as an iterator. + + See Also + -------- + broadcast_arrays + broadcast_to + broadcast_shapes + + Examples + -------- + + Manually adding two vectors, using broadcasting: + + >>> x = np.array([[1], [2], [3]]) + >>> y = np.array([4, 5, 6]) + >>> b = np.broadcast(x, y) + + >>> out = np.empty(b.shape) + >>> out.flat = [u+v for (u,v) in b] + >>> out + array([[5., 6., 7.], + [6., 7., 8.], + [7., 8., 9.]]) + + Compare against built-in broadcasting: + + >>> x + y + array([[5, 6, 7], + [6, 7, 8], + [7, 8, 9]]) + + """) + +# attributes + +add_newdoc('numpy.core', 'broadcast', ('index', + """ + current index in broadcasted result + + Examples + -------- + >>> x = np.array([[1], [2], [3]]) + >>> y = np.array([4, 5, 6]) + >>> b = np.broadcast(x, y) + >>> b.index + 0 + >>> next(b), next(b), next(b) + ((1, 4), (1, 5), (1, 6)) + >>> b.index + 3 + + """)) + +add_newdoc('numpy.core', 'broadcast', ('iters', + """ + tuple of iterators along ``self``'s "components." + + Returns a tuple of `numpy.flatiter` objects, one for each "component" + of ``self``. + + See Also + -------- + numpy.flatiter + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> y = np.array([[4], [5], [6]]) + >>> b = np.broadcast(x, y) + >>> row, col = b.iters + >>> next(row), next(col) + (1, 4) + + """)) + +add_newdoc('numpy.core', 'broadcast', ('ndim', + """ + Number of dimensions of broadcasted result. Alias for `nd`. + + .. versionadded:: 1.12.0 + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> y = np.array([[4], [5], [6]]) + >>> b = np.broadcast(x, y) + >>> b.ndim + 2 + + """)) + +add_newdoc('numpy.core', 'broadcast', ('nd', + """ + Number of dimensions of broadcasted result. For code intended for NumPy + 1.12.0 and later the more consistent `ndim` is preferred. + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> y = np.array([[4], [5], [6]]) + >>> b = np.broadcast(x, y) + >>> b.nd + 2 + + """)) + +add_newdoc('numpy.core', 'broadcast', ('numiter', + """ + Number of iterators possessed by the broadcasted result. + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> y = np.array([[4], [5], [6]]) + >>> b = np.broadcast(x, y) + >>> b.numiter + 2 + + """)) + +add_newdoc('numpy.core', 'broadcast', ('shape', + """ + Shape of broadcasted result. + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> y = np.array([[4], [5], [6]]) + >>> b = np.broadcast(x, y) + >>> b.shape + (3, 3) + + """)) + +add_newdoc('numpy.core', 'broadcast', ('size', + """ + Total size of broadcasted result. + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> y = np.array([[4], [5], [6]]) + >>> b = np.broadcast(x, y) + >>> b.size + 9 + + """)) + +add_newdoc('numpy.core', 'broadcast', ('reset', + """ + reset() + + Reset the broadcasted result's iterator(s). + + Parameters + ---------- + None + + Returns + ------- + None + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> y = np.array([[4], [5], [6]]) + >>> b = np.broadcast(x, y) + >>> b.index + 0 + >>> next(b), next(b), next(b) + ((1, 4), (2, 4), (3, 4)) + >>> b.index + 3 + >>> b.reset() + >>> b.index + 0 + + """)) + +############################################################################### +# +# numpy functions +# +############################################################################### + +add_newdoc('numpy.core.multiarray', 'array', + """ + array(object, dtype=None, *, copy=True, order='K', subok=False, ndmin=0, + like=None) + + Create an array. + + Parameters + ---------- + object : array_like + An array, any object exposing the array interface, an object whose + ``__array__`` method returns an array, or any (nested) sequence. + If object is a scalar, a 0-dimensional array containing object is + returned. + dtype : data-type, optional + The desired data-type for the array. If not given, NumPy will try to use + a default ``dtype`` that can represent the values (by applying promotion + rules when necessary.) + copy : bool, optional + If true (default), then the object is copied. Otherwise, a copy will + only be made if ``__array__`` returns a copy, if obj is a nested + sequence, or if a copy is needed to satisfy any of the other + requirements (``dtype``, ``order``, etc.). + order : {'K', 'A', 'C', 'F'}, optional + Specify the memory layout of the array. If object is not an array, the + newly created array will be in C order (row major) unless 'F' is + specified, in which case it will be in Fortran order (column major). + If object is an array the following holds. + + ===== ========= =================================================== + order no copy copy=True + ===== ========= =================================================== + 'K' unchanged F & C order preserved, otherwise most similar order + 'A' unchanged F order if input is F and not C, otherwise C order + 'C' C order C order + 'F' F order F order + ===== ========= =================================================== + + When ``copy=False`` and a copy is made for other reasons, the result is + the same as if ``copy=True``, with some exceptions for 'A', see the + Notes section. The default order is 'K'. + subok : bool, optional + If True, then sub-classes will be passed-through, otherwise + the returned array will be forced to be a base-class array (default). + ndmin : int, optional + Specifies the minimum number of dimensions that the resulting + array should have. Ones will be prepended to the shape as + needed to meet this requirement. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + An array object satisfying the specified requirements. + + See Also + -------- + empty_like : Return an empty array with shape and type of input. + ones_like : Return an array of ones with shape and type of input. + zeros_like : Return an array of zeros with shape and type of input. + full_like : Return a new array with shape of input filled with value. + empty : Return a new uninitialized array. + ones : Return a new array setting values to one. + zeros : Return a new array setting values to zero. + full : Return a new array of given shape filled with value. + + + Notes + ----- + When order is 'A' and ``object`` is an array in neither 'C' nor 'F' order, + and a copy is forced by a change in dtype, then the order of the result is + not necessarily 'C' as expected. This is likely a bug. + + Examples + -------- + >>> np.array([1, 2, 3]) + array([1, 2, 3]) + + Upcasting: + + >>> np.array([1, 2, 3.0]) + array([ 1., 2., 3.]) + + More than one dimension: + + >>> np.array([[1, 2], [3, 4]]) + array([[1, 2], + [3, 4]]) + + Minimum dimensions 2: + + >>> np.array([1, 2, 3], ndmin=2) + array([[1, 2, 3]]) + + Type provided: + + >>> np.array([1, 2, 3], dtype=complex) + array([ 1.+0.j, 2.+0.j, 3.+0.j]) + + Data-type consisting of more than one element: + + >>> x = np.array([(1,2),(3,4)],dtype=[('a','>> x['a'] + array([1, 3]) + + Creating an array from sub-classes: + + >>> np.array(np.mat('1 2; 3 4')) + array([[1, 2], + [3, 4]]) + + >>> np.array(np.mat('1 2; 3 4'), subok=True) + matrix([[1, 2], + [3, 4]]) + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'asarray', + """ + asarray(a, dtype=None, order=None, *, like=None) + + Convert the input to an array. + + Parameters + ---------- + a : array_like + Input data, in any form that can be converted to an array. This + includes lists, lists of tuples, tuples, tuples of tuples, tuples + of lists and ndarrays. + dtype : data-type, optional + By default, the data-type is inferred from the input data. + order : {'C', 'F', 'A', 'K'}, optional + Memory layout. 'A' and 'K' depend on the order of input array a. + 'C' row-major (C-style), + 'F' column-major (Fortran-style) memory representation. + 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise + 'K' (keep) preserve input order + Defaults to 'K'. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + Array interpretation of `a`. No copy is performed if the input + is already an ndarray with matching dtype and order. If `a` is a + subclass of ndarray, a base class ndarray is returned. + + See Also + -------- + asanyarray : Similar function which passes through subclasses. + ascontiguousarray : Convert input to a contiguous array. + asfarray : Convert input to a floating point ndarray. + asfortranarray : Convert input to an ndarray with column-major + memory order. + asarray_chkfinite : Similar function which checks input for NaNs and Infs. + fromiter : Create an array from an iterator. + fromfunction : Construct an array by executing a function on grid + positions. + + Examples + -------- + Convert a list into an array: + + >>> a = [1, 2] + >>> np.asarray(a) + array([1, 2]) + + Existing arrays are not copied: + + >>> a = np.array([1, 2]) + >>> np.asarray(a) is a + True + + If `dtype` is set, array is copied only if dtype does not match: + + >>> a = np.array([1, 2], dtype=np.float32) + >>> np.asarray(a, dtype=np.float32) is a + True + >>> np.asarray(a, dtype=np.float64) is a + False + + Contrary to `asanyarray`, ndarray subclasses are not passed through: + + >>> issubclass(np.recarray, np.ndarray) + True + >>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray) + >>> np.asarray(a) is a + False + >>> np.asanyarray(a) is a + True + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'asanyarray', + """ + asanyarray(a, dtype=None, order=None, *, like=None) + + Convert the input to an ndarray, but pass ndarray subclasses through. + + Parameters + ---------- + a : array_like + Input data, in any form that can be converted to an array. This + includes scalars, lists, lists of tuples, tuples, tuples of tuples, + tuples of lists, and ndarrays. + dtype : data-type, optional + By default, the data-type is inferred from the input data. + order : {'C', 'F', 'A', 'K'}, optional + Memory layout. 'A' and 'K' depend on the order of input array a. + 'C' row-major (C-style), + 'F' column-major (Fortran-style) memory representation. + 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise + 'K' (keep) preserve input order + Defaults to 'C'. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray or an ndarray subclass + Array interpretation of `a`. If `a` is an ndarray or a subclass + of ndarray, it is returned as-is and no copy is performed. + + See Also + -------- + asarray : Similar function which always returns ndarrays. + ascontiguousarray : Convert input to a contiguous array. + asfarray : Convert input to a floating point ndarray. + asfortranarray : Convert input to an ndarray with column-major + memory order. + asarray_chkfinite : Similar function which checks input for NaNs and + Infs. + fromiter : Create an array from an iterator. + fromfunction : Construct an array by executing a function on grid + positions. + + Examples + -------- + Convert a list into an array: + + >>> a = [1, 2] + >>> np.asanyarray(a) + array([1, 2]) + + Instances of `ndarray` subclasses are passed through as-is: + + >>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray) + >>> np.asanyarray(a) is a + True + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'ascontiguousarray', + """ + ascontiguousarray(a, dtype=None, *, like=None) + + Return a contiguous array (ndim >= 1) in memory (C order). + + Parameters + ---------- + a : array_like + Input array. + dtype : str or dtype object, optional + Data-type of returned array. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + Contiguous array of same shape and content as `a`, with type `dtype` + if specified. + + See Also + -------- + asfortranarray : Convert input to an ndarray with column-major + memory order. + require : Return an ndarray that satisfies requirements. + ndarray.flags : Information about the memory layout of the array. + + Examples + -------- + Starting with a Fortran-contiguous array: + + >>> x = np.ones((2, 3), order='F') + >>> x.flags['F_CONTIGUOUS'] + True + + Calling ``ascontiguousarray`` makes a C-contiguous copy: + + >>> y = np.ascontiguousarray(x) + >>> y.flags['C_CONTIGUOUS'] + True + >>> np.may_share_memory(x, y) + False + + Now, starting with a C-contiguous array: + + >>> x = np.ones((2, 3), order='C') + >>> x.flags['C_CONTIGUOUS'] + True + + Then, calling ``ascontiguousarray`` returns the same object: + + >>> y = np.ascontiguousarray(x) + >>> x is y + True + + Note: This function returns an array with at least one-dimension (1-d) + so it will not preserve 0-d arrays. + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'asfortranarray', + """ + asfortranarray(a, dtype=None, *, like=None) + + Return an array (ndim >= 1) laid out in Fortran order in memory. + + Parameters + ---------- + a : array_like + Input array. + dtype : str or dtype object, optional + By default, the data-type is inferred from the input data. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + The input `a` in Fortran, or column-major, order. + + See Also + -------- + ascontiguousarray : Convert input to a contiguous (C order) array. + asanyarray : Convert input to an ndarray with either row or + column-major memory order. + require : Return an ndarray that satisfies requirements. + ndarray.flags : Information about the memory layout of the array. + + Examples + -------- + Starting with a C-contiguous array: + + >>> x = np.ones((2, 3), order='C') + >>> x.flags['C_CONTIGUOUS'] + True + + Calling ``asfortranarray`` makes a Fortran-contiguous copy: + + >>> y = np.asfortranarray(x) + >>> y.flags['F_CONTIGUOUS'] + True + >>> np.may_share_memory(x, y) + False + + Now, starting with a Fortran-contiguous array: + + >>> x = np.ones((2, 3), order='F') + >>> x.flags['F_CONTIGUOUS'] + True + + Then, calling ``asfortranarray`` returns the same object: + + >>> y = np.asfortranarray(x) + >>> x is y + True + + Note: This function returns an array with at least one-dimension (1-d) + so it will not preserve 0-d arrays. + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'empty', + """ + empty(shape, dtype=float, order='C', *, like=None) + + Return a new array of given shape and type, without initializing entries. + + Parameters + ---------- + shape : int or tuple of int + Shape of the empty array, e.g., ``(2, 3)`` or ``2``. + dtype : data-type, optional + Desired output data-type for the array, e.g, `numpy.int8`. Default is + `numpy.float64`. + order : {'C', 'F'}, optional, default: 'C' + Whether to store multi-dimensional data in row-major + (C-style) or column-major (Fortran-style) order in + memory. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + Array of uninitialized (arbitrary) data of the given shape, dtype, and + order. Object arrays will be initialized to None. + + See Also + -------- + empty_like : Return an empty array with shape and type of input. + ones : Return a new array setting values to one. + zeros : Return a new array setting values to zero. + full : Return a new array of given shape filled with value. + + + Notes + ----- + `empty`, unlike `zeros`, does not set the array values to zero, + and may therefore be marginally faster. On the other hand, it requires + the user to manually set all the values in the array, and should be + used with caution. + + Examples + -------- + >>> np.empty([2, 2]) + array([[ -9.74499359e+001, 6.69583040e-309], + [ 2.13182611e-314, 3.06959433e-309]]) #uninitialized + + >>> np.empty([2, 2], dtype=int) + array([[-1073741821, -1067949133], + [ 496041986, 19249760]]) #uninitialized + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'scalar', + """ + scalar(dtype, obj) + + Return a new scalar array of the given type initialized with obj. + + This function is meant mainly for pickle support. `dtype` must be a + valid data-type descriptor. If `dtype` corresponds to an object + descriptor, then `obj` can be any object, otherwise `obj` must be a + string. If `obj` is not given, it will be interpreted as None for object + type and as zeros for all other types. + + """) + +add_newdoc('numpy.core.multiarray', 'zeros', + """ + zeros(shape, dtype=float, order='C', *, like=None) + + Return a new array of given shape and type, filled with zeros. + + Parameters + ---------- + shape : int or tuple of ints + Shape of the new array, e.g., ``(2, 3)`` or ``2``. + dtype : data-type, optional + The desired data-type for the array, e.g., `numpy.int8`. Default is + `numpy.float64`. + order : {'C', 'F'}, optional, default: 'C' + Whether to store multi-dimensional data in row-major + (C-style) or column-major (Fortran-style) order in + memory. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + Array of zeros with the given shape, dtype, and order. + + See Also + -------- + zeros_like : Return an array of zeros with shape and type of input. + empty : Return a new uninitialized array. + ones : Return a new array setting values to one. + full : Return a new array of given shape filled with value. + + Examples + -------- + >>> np.zeros(5) + array([ 0., 0., 0., 0., 0.]) + + >>> np.zeros((5,), dtype=int) + array([0, 0, 0, 0, 0]) + + >>> np.zeros((2, 1)) + array([[ 0.], + [ 0.]]) + + >>> s = (2,2) + >>> np.zeros(s) + array([[ 0., 0.], + [ 0., 0.]]) + + >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype + array([(0, 0), (0, 0)], + dtype=[('x', '>> np.fromstring('1 2', dtype=int, sep=' ') + array([1, 2]) + >>> np.fromstring('1, 2', dtype=int, sep=',') + array([1, 2]) + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'compare_chararrays', + """ + compare_chararrays(a1, a2, cmp, rstrip) + + Performs element-wise comparison of two string arrays using the + comparison operator specified by `cmp_op`. + + Parameters + ---------- + a1, a2 : array_like + Arrays to be compared. + cmp : {"<", "<=", "==", ">=", ">", "!="} + Type of comparison. + rstrip : Boolean + If True, the spaces at the end of Strings are removed before the comparison. + + Returns + ------- + out : ndarray + The output array of type Boolean with the same shape as a and b. + + Raises + ------ + ValueError + If `cmp_op` is not valid. + TypeError + If at least one of `a` or `b` is a non-string array + + Examples + -------- + >>> a = np.array(["a", "b", "cde"]) + >>> b = np.array(["a", "a", "dec"]) + >>> np.compare_chararrays(a, b, ">", True) + array([False, True, False]) + + """) + +add_newdoc('numpy.core.multiarray', 'fromiter', + """ + fromiter(iter, dtype, count=-1, *, like=None) + + Create a new 1-dimensional array from an iterable object. + + Parameters + ---------- + iter : iterable object + An iterable object providing data for the array. + dtype : data-type + The data-type of the returned array. + + .. versionchanged:: 1.23 + Object and subarray dtypes are now supported (note that the final + result is not 1-D for a subarray dtype). + + count : int, optional + The number of items to read from *iterable*. The default is -1, + which means all data is read. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + The output array. + + Notes + ----- + Specify `count` to improve performance. It allows ``fromiter`` to + pre-allocate the output array, instead of resizing it on demand. + + Examples + -------- + >>> iterable = (x*x for x in range(5)) + >>> np.fromiter(iterable, float) + array([ 0., 1., 4., 9., 16.]) + + A carefully constructed subarray dtype will lead to higher dimensional + results: + + >>> iterable = ((x+1, x+2) for x in range(5)) + >>> np.fromiter(iterable, dtype=np.dtype((int, 2))) + array([[1, 2], + [2, 3], + [3, 4], + [4, 5], + [5, 6]]) + + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'fromfile', + """ + fromfile(file, dtype=float, count=-1, sep='', offset=0, *, like=None) + + Construct an array from data in a text or binary file. + + A highly efficient way of reading binary data with a known data-type, + as well as parsing simply formatted text files. Data written using the + `tofile` method can be read using this function. + + Parameters + ---------- + file : file or str or Path + Open file object or filename. + + .. versionchanged:: 1.17.0 + `pathlib.Path` objects are now accepted. + + dtype : data-type + Data type of the returned array. + For binary files, it is used to determine the size and byte-order + of the items in the file. + Most builtin numeric types are supported and extension types may be supported. + + .. versionadded:: 1.18.0 + Complex dtypes. + + count : int + Number of items to read. ``-1`` means all items (i.e., the complete + file). + sep : str + Separator between items if file is a text file. + Empty ("") separator means the file should be treated as binary. + Spaces (" ") in the separator match zero or more whitespace characters. + A separator consisting only of spaces must match at least one + whitespace. + offset : int + The offset (in bytes) from the file's current position. Defaults to 0. + Only permitted for binary files. + + .. versionadded:: 1.17.0 + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + See also + -------- + load, save + ndarray.tofile + loadtxt : More flexible way of loading data from a text file. + + Notes + ----- + Do not rely on the combination of `tofile` and `fromfile` for + data storage, as the binary files generated are not platform + independent. In particular, no byte-order or data-type information is + saved. Data can be stored in the platform independent ``.npy`` format + using `save` and `load` instead. + + Examples + -------- + Construct an ndarray: + + >>> dt = np.dtype([('time', [('min', np.int64), ('sec', np.int64)]), + ... ('temp', float)]) + >>> x = np.zeros((1,), dtype=dt) + >>> x['time']['min'] = 10; x['temp'] = 98.25 + >>> x + array([((10, 0), 98.25)], + dtype=[('time', [('min', '>> import tempfile + >>> fname = tempfile.mkstemp()[1] + >>> x.tofile(fname) + + Read the raw data from disk: + + >>> np.fromfile(fname, dtype=dt) + array([((10, 0), 98.25)], + dtype=[('time', [('min', '>> np.save(fname, x) + >>> np.load(fname + '.npy') + array([((10, 0), 98.25)], + dtype=[('time', [('min', '>> dt = np.dtype(int) + >>> dt = dt.newbyteorder('>') + >>> np.frombuffer(buf, dtype=dt) # doctest: +SKIP + + The data of the resulting array will not be byteswapped, but will be + interpreted correctly. + + This function creates a view into the original object. This should be safe + in general, but it may make sense to copy the result when the original + object is mutable or untrusted. + + Examples + -------- + >>> s = b'hello world' + >>> np.frombuffer(s, dtype='S1', count=5, offset=6) + array([b'w', b'o', b'r', b'l', b'd'], dtype='|S1') + + >>> np.frombuffer(b'\\x01\\x02', dtype=np.uint8) + array([1, 2], dtype=uint8) + >>> np.frombuffer(b'\\x01\\x02\\x03\\x04\\x05', dtype=np.uint8, count=3) + array([1, 2, 3], dtype=uint8) + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', 'from_dlpack', + """ + from_dlpack(x, /) + + Create a NumPy array from an object implementing the ``__dlpack__`` + protocol. Generally, the returned NumPy array is a read-only view + of the input object. See [1]_ and [2]_ for more details. + + Parameters + ---------- + x : object + A Python object that implements the ``__dlpack__`` and + ``__dlpack_device__`` methods. + + Returns + ------- + out : ndarray + + References + ---------- + .. [1] Array API documentation, + https://data-apis.org/array-api/latest/design_topics/data_interchange.html#syntax-for-data-interchange-with-dlpack + + .. [2] Python specification for DLPack, + https://dmlc.github.io/dlpack/latest/python_spec.html + + Examples + -------- + >>> import torch + >>> x = torch.arange(10) + >>> # create a view of the torch tensor "x" in NumPy + >>> y = np.from_dlpack(x) + """) + +add_newdoc('numpy.core', 'fastCopyAndTranspose', + """ + fastCopyAndTranspose(a) + + .. deprecated:: 1.24 + + fastCopyAndTranspose is deprecated and will be removed. Use the copy and + transpose methods instead, e.g. ``arr.T.copy()`` + """) + +add_newdoc('numpy.core.multiarray', 'correlate', + """cross_correlate(a,v, mode=0)""") + +add_newdoc('numpy.core.multiarray', 'arange', + """ + arange([start,] stop[, step,], dtype=None, *, like=None) + + Return evenly spaced values within a given interval. + + ``arange`` can be called with a varying number of positional arguments: + + * ``arange(stop)``: Values are generated within the half-open interval + ``[0, stop)`` (in other words, the interval including `start` but + excluding `stop`). + * ``arange(start, stop)``: Values are generated within the half-open + interval ``[start, stop)``. + * ``arange(start, stop, step)`` Values are generated within the half-open + interval ``[start, stop)``, with spacing between values given by + ``step``. + + For integer arguments the function is roughly equivalent to the Python + built-in :py:class:`range`, but returns an ndarray rather than a ``range`` + instance. + + When using a non-integer step, such as 0.1, it is often better to use + `numpy.linspace`. + + See the Warning sections below for more information. + + Parameters + ---------- + start : integer or real, optional + Start of interval. The interval includes this value. The default + start value is 0. + stop : integer or real + End of interval. The interval does not include this value, except + in some cases where `step` is not an integer and floating point + round-off affects the length of `out`. + step : integer or real, optional + Spacing between values. For any output `out`, this is the distance + between two adjacent values, ``out[i+1] - out[i]``. The default + step size is 1. If `step` is specified as a position argument, + `start` must also be given. + dtype : dtype, optional + The type of the output array. If `dtype` is not given, infer the data + type from the other input arguments. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + arange : ndarray + Array of evenly spaced values. + + For floating point arguments, the length of the result is + ``ceil((stop - start)/step)``. Because of floating point overflow, + this rule may result in the last element of `out` being greater + than `stop`. + + Warnings + -------- + The length of the output might not be numerically stable. + + Another stability issue is due to the internal implementation of + `numpy.arange`. + The actual step value used to populate the array is + ``dtype(start + step) - dtype(start)`` and not `step`. Precision loss + can occur here, due to casting or due to using floating points when + `start` is much larger than `step`. This can lead to unexpected + behaviour. For example:: + + >>> np.arange(0, 5, 0.5, dtype=int) + array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) + >>> np.arange(-3, 3, 0.5, dtype=int) + array([-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8]) + + In such cases, the use of `numpy.linspace` should be preferred. + + The built-in :py:class:`range` generates :std:doc:`Python built-in integers + that have arbitrary size `, while `numpy.arange` + produces `numpy.int32` or `numpy.int64` numbers. This may result in + incorrect results for large integer values:: + + >>> power = 40 + >>> modulo = 10000 + >>> x1 = [(n ** power) % modulo for n in range(8)] + >>> x2 = [(n ** power) % modulo for n in np.arange(8)] + >>> print(x1) + [0, 1, 7776, 8801, 6176, 625, 6576, 4001] # correct + >>> print(x2) + [0, 1, 7776, 7185, 0, 5969, 4816, 3361] # incorrect + + See Also + -------- + numpy.linspace : Evenly spaced numbers with careful handling of endpoints. + numpy.ogrid: Arrays of evenly spaced numbers in N-dimensions. + numpy.mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions. + :ref:`how-to-partition` + + Examples + -------- + >>> np.arange(3) + array([0, 1, 2]) + >>> np.arange(3.0) + array([ 0., 1., 2.]) + >>> np.arange(3,7) + array([3, 4, 5, 6]) + >>> np.arange(3,7,2) + array([3, 5]) + + """.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + )) + +add_newdoc('numpy.core.multiarray', '_get_ndarray_c_version', + """_get_ndarray_c_version() + + Return the compile time NPY_VERSION (formerly called NDARRAY_VERSION) number. + + """) + +add_newdoc('numpy.core.multiarray', '_reconstruct', + """_reconstruct(subtype, shape, dtype) + + Construct an empty array. Used by Pickles. + + """) + + +add_newdoc('numpy.core.multiarray', 'set_string_function', + """ + set_string_function(f, repr=1) + + Internal method to set a function to be used when pretty printing arrays. + + """) + +add_newdoc('numpy.core.multiarray', 'set_numeric_ops', + """ + set_numeric_ops(op1=func1, op2=func2, ...) + + Set numerical operators for array objects. + + .. deprecated:: 1.16 + + For the general case, use :c:func:`PyUFunc_ReplaceLoopBySignature`. + For ndarray subclasses, define the ``__array_ufunc__`` method and + override the relevant ufunc. + + Parameters + ---------- + op1, op2, ... : callable + Each ``op = func`` pair describes an operator to be replaced. + For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace + addition by modulus 5 addition. + + Returns + ------- + saved_ops : list of callables + A list of all operators, stored before making replacements. + + Notes + ----- + .. warning:: + Use with care! Incorrect usage may lead to memory errors. + + A function replacing an operator cannot make use of that operator. + For example, when replacing add, you may not use ``+``. Instead, + directly call ufuncs. + + Examples + -------- + >>> def add_mod5(x, y): + ... return np.add(x, y) % 5 + ... + >>> old_funcs = np.set_numeric_ops(add=add_mod5) + + >>> x = np.arange(12).reshape((3, 4)) + >>> x + x + array([[0, 2, 4, 1], + [3, 0, 2, 4], + [1, 3, 0, 2]]) + + >>> ignore = np.set_numeric_ops(**old_funcs) # restore operators + + """) + +add_newdoc('numpy.core.multiarray', 'promote_types', + """ + promote_types(type1, type2) + + Returns the data type with the smallest size and smallest scalar + kind to which both ``type1`` and ``type2`` may be safely cast. + The returned data type is always considered "canonical", this mainly + means that the promoted dtype will always be in native byte order. + + This function is symmetric, but rarely associative. + + Parameters + ---------- + type1 : dtype or dtype specifier + First data type. + type2 : dtype or dtype specifier + Second data type. + + Returns + ------- + out : dtype + The promoted data type. + + Notes + ----- + Please see `numpy.result_type` for additional information about promotion. + + .. versionadded:: 1.6.0 + + Starting in NumPy 1.9, promote_types function now returns a valid string + length when given an integer or float dtype as one argument and a string + dtype as another argument. Previously it always returned the input string + dtype, even if it wasn't long enough to store the max integer/float value + converted to a string. + + .. versionchanged:: 1.23.0 + + NumPy now supports promotion for more structured dtypes. It will now + remove unnecessary padding from a structure dtype and promote included + fields individually. + + See Also + -------- + result_type, dtype, can_cast + + Examples + -------- + >>> np.promote_types('f4', 'f8') + dtype('float64') + + >>> np.promote_types('i8', 'f4') + dtype('float64') + + >>> np.promote_types('>i8', '>> np.promote_types('i4', 'S8') + dtype('S11') + + An example of a non-associative case: + + >>> p = np.promote_types + >>> p('S', p('i1', 'u1')) + dtype('S6') + >>> p(p('S', 'i1'), 'u1') + dtype('S4') + + """) + +add_newdoc('numpy.core.multiarray', 'c_einsum', + """ + c_einsum(subscripts, *operands, out=None, dtype=None, order='K', + casting='safe') + + *This documentation shadows that of the native python implementation of the `einsum` function, + except all references and examples related to the `optimize` argument (v 0.12.0) have been removed.* + + Evaluates the Einstein summation convention on the operands. + + Using the Einstein summation convention, many common multi-dimensional, + linear algebraic array operations can be represented in a simple fashion. + In *implicit* mode `einsum` computes these values. + + In *explicit* mode, `einsum` provides further flexibility to compute + other array operations that might not be considered classical Einstein + summation operations, by disabling, or forcing summation over specified + subscript labels. + + See the notes and examples for clarification. + + Parameters + ---------- + subscripts : str + Specifies the subscripts for summation as comma separated list of + subscript labels. An implicit (classical Einstein summation) + calculation is performed unless the explicit indicator '->' is + included as well as subscript labels of the precise output form. + operands : list of array_like + These are the arrays for the operation. + out : ndarray, optional + If provided, the calculation is done into this array. + dtype : {data-type, None}, optional + If provided, forces the calculation to use the data type specified. + Note that you may have to also give a more liberal `casting` + parameter to allow the conversions. Default is None. + order : {'C', 'F', 'A', 'K'}, optional + Controls the memory layout of the output. 'C' means it should + be C contiguous. 'F' means it should be Fortran contiguous, + 'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise. + 'K' means it should be as close to the layout of the inputs as + is possible, including arbitrarily permuted axes. + Default is 'K'. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. Setting this to + 'unsafe' is not recommended, as it can adversely affect accumulations. + + * 'no' means the data types should not be cast at all. + * 'equiv' means only byte-order changes are allowed. + * 'safe' means only casts which can preserve values are allowed. + * 'same_kind' means only safe casts or casts within a kind, + like float64 to float32, are allowed. + * 'unsafe' means any data conversions may be done. + + Default is 'safe'. + optimize : {False, True, 'greedy', 'optimal'}, optional + Controls if intermediate optimization should occur. No optimization + will occur if False and True will default to the 'greedy' algorithm. + Also accepts an explicit contraction list from the ``np.einsum_path`` + function. See ``np.einsum_path`` for more details. Defaults to False. + + Returns + ------- + output : ndarray + The calculation based on the Einstein summation convention. + + See Also + -------- + einsum_path, dot, inner, outer, tensordot, linalg.multi_dot + + Notes + ----- + .. versionadded:: 1.6.0 + + The Einstein summation convention can be used to compute + many multi-dimensional, linear algebraic array operations. `einsum` + provides a succinct way of representing these. + + A non-exhaustive list of these operations, + which can be computed by `einsum`, is shown below along with examples: + + * Trace of an array, :py:func:`numpy.trace`. + * Return a diagonal, :py:func:`numpy.diag`. + * Array axis summations, :py:func:`numpy.sum`. + * Transpositions and permutations, :py:func:`numpy.transpose`. + * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`. + * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`. + * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`. + * Tensor contractions, :py:func:`numpy.tensordot`. + * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`. + + The subscripts string is a comma-separated list of subscript labels, + where each label refers to a dimension of the corresponding operand. + Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)`` + is equivalent to :py:func:`np.inner(a,b) `. If a label + appears only once, it is not summed, so ``np.einsum('i', a)`` produces a + view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)`` + describes traditional matrix multiplication and is equivalent to + :py:func:`np.matmul(a,b) `. Repeated subscript labels in one + operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent + to :py:func:`np.trace(a) `. + + In *implicit mode*, the chosen subscripts are important + since the axes of the output are reordered alphabetically. This + means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while + ``np.einsum('ji', a)`` takes its transpose. Additionally, + ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while, + ``np.einsum('ij,jh', a, b)`` returns the transpose of the + multiplication since subscript 'h' precedes subscript 'i'. + + In *explicit mode* the output can be directly controlled by + specifying output subscript labels. This requires the + identifier '->' as well as the list of output subscript labels. + This feature increases the flexibility of the function since + summing can be disabled or forced when required. The call + ``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) `, + and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) `. + The difference is that `einsum` does not allow broadcasting by default. + Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the + order of the output subscript labels and therefore returns matrix + multiplication, unlike the example above in implicit mode. + + To enable and control broadcasting, use an ellipsis. Default + NumPy-style broadcasting is done by adding an ellipsis + to the left of each term, like ``np.einsum('...ii->...i', a)``. + To take the trace along the first and last axes, + you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix + product with the left-most indices instead of rightmost, one can do + ``np.einsum('ij...,jk...->ik...', a, b)``. + + When there is only one operand, no axes are summed, and no output + parameter is provided, a view into the operand is returned instead + of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)`` + produces a view (changed in version 1.10.0). + + `einsum` also provides an alternative way to provide the subscripts + and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``. + If the output shape is not provided in this format `einsum` will be + calculated in implicit mode, otherwise it will be performed explicitly. + The examples below have corresponding `einsum` calls with the two + parameter methods. + + .. versionadded:: 1.10.0 + + Views returned from einsum are now writeable whenever the input array + is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now + have the same effect as :py:func:`np.swapaxes(a, 0, 2) ` + and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal + of a 2D array. + + Examples + -------- + >>> a = np.arange(25).reshape(5,5) + >>> b = np.arange(5) + >>> c = np.arange(6).reshape(2,3) + + Trace of a matrix: + + >>> np.einsum('ii', a) + 60 + >>> np.einsum(a, [0,0]) + 60 + >>> np.trace(a) + 60 + + Extract the diagonal (requires explicit form): + + >>> np.einsum('ii->i', a) + array([ 0, 6, 12, 18, 24]) + >>> np.einsum(a, [0,0], [0]) + array([ 0, 6, 12, 18, 24]) + >>> np.diag(a) + array([ 0, 6, 12, 18, 24]) + + Sum over an axis (requires explicit form): + + >>> np.einsum('ij->i', a) + array([ 10, 35, 60, 85, 110]) + >>> np.einsum(a, [0,1], [0]) + array([ 10, 35, 60, 85, 110]) + >>> np.sum(a, axis=1) + array([ 10, 35, 60, 85, 110]) + + For higher dimensional arrays summing a single axis can be done with ellipsis: + + >>> np.einsum('...j->...', a) + array([ 10, 35, 60, 85, 110]) + >>> np.einsum(a, [Ellipsis,1], [Ellipsis]) + array([ 10, 35, 60, 85, 110]) + + Compute a matrix transpose, or reorder any number of axes: + + >>> np.einsum('ji', c) + array([[0, 3], + [1, 4], + [2, 5]]) + >>> np.einsum('ij->ji', c) + array([[0, 3], + [1, 4], + [2, 5]]) + >>> np.einsum(c, [1,0]) + array([[0, 3], + [1, 4], + [2, 5]]) + >>> np.transpose(c) + array([[0, 3], + [1, 4], + [2, 5]]) + + Vector inner products: + + >>> np.einsum('i,i', b, b) + 30 + >>> np.einsum(b, [0], b, [0]) + 30 + >>> np.inner(b,b) + 30 + + Matrix vector multiplication: + + >>> np.einsum('ij,j', a, b) + array([ 30, 80, 130, 180, 230]) + >>> np.einsum(a, [0,1], b, [1]) + array([ 30, 80, 130, 180, 230]) + >>> np.dot(a, b) + array([ 30, 80, 130, 180, 230]) + >>> np.einsum('...j,j', a, b) + array([ 30, 80, 130, 180, 230]) + + Broadcasting and scalar multiplication: + + >>> np.einsum('..., ...', 3, c) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + >>> np.einsum(',ij', 3, c) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + >>> np.einsum(3, [Ellipsis], c, [Ellipsis]) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + >>> np.multiply(3, c) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + + Vector outer product: + + >>> np.einsum('i,j', np.arange(2)+1, b) + array([[0, 1, 2, 3, 4], + [0, 2, 4, 6, 8]]) + >>> np.einsum(np.arange(2)+1, [0], b, [1]) + array([[0, 1, 2, 3, 4], + [0, 2, 4, 6, 8]]) + >>> np.outer(np.arange(2)+1, b) + array([[0, 1, 2, 3, 4], + [0, 2, 4, 6, 8]]) + + Tensor contraction: + + >>> a = np.arange(60.).reshape(3,4,5) + >>> b = np.arange(24.).reshape(4,3,2) + >>> np.einsum('ijk,jil->kl', a, b) + array([[ 4400., 4730.], + [ 4532., 4874.], + [ 4664., 5018.], + [ 4796., 5162.], + [ 4928., 5306.]]) + >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3]) + array([[ 4400., 4730.], + [ 4532., 4874.], + [ 4664., 5018.], + [ 4796., 5162.], + [ 4928., 5306.]]) + >>> np.tensordot(a,b, axes=([1,0],[0,1])) + array([[ 4400., 4730.], + [ 4532., 4874.], + [ 4664., 5018.], + [ 4796., 5162.], + [ 4928., 5306.]]) + + Writeable returned arrays (since version 1.10.0): + + >>> a = np.zeros((3, 3)) + >>> np.einsum('ii->i', a)[:] = 1 + >>> a + array([[ 1., 0., 0.], + [ 0., 1., 0.], + [ 0., 0., 1.]]) + + Example of ellipsis use: + + >>> a = np.arange(6).reshape((3,2)) + >>> b = np.arange(12).reshape((4,3)) + >>> np.einsum('ki,jk->ij', a, b) + array([[10, 28, 46, 64], + [13, 40, 67, 94]]) + >>> np.einsum('ki,...k->i...', a, b) + array([[10, 28, 46, 64], + [13, 40, 67, 94]]) + >>> np.einsum('k...,jk', a, b) + array([[10, 28, 46, 64], + [13, 40, 67, 94]]) + + """) + + +############################################################################## +# +# Documentation for ndarray attributes and methods +# +############################################################################## + + +############################################################################## +# +# ndarray object +# +############################################################################## + + +add_newdoc('numpy.core.multiarray', 'ndarray', + """ + ndarray(shape, dtype=float, buffer=None, offset=0, + strides=None, order=None) + + An array object represents a multidimensional, homogeneous array + of fixed-size items. An associated data-type object describes the + format of each element in the array (its byte-order, how many bytes it + occupies in memory, whether it is an integer, a floating point number, + or something else, etc.) + + Arrays should be constructed using `array`, `zeros` or `empty` (refer + to the See Also section below). The parameters given here refer to + a low-level method (`ndarray(...)`) for instantiating an array. + + For more information, refer to the `numpy` module and examine the + methods and attributes of an array. + + Parameters + ---------- + (for the __new__ method; see Notes below) + + shape : tuple of ints + Shape of created array. + dtype : data-type, optional + Any object that can be interpreted as a numpy data type. + buffer : object exposing buffer interface, optional + Used to fill the array with data. + offset : int, optional + Offset of array data in buffer. + strides : tuple of ints, optional + Strides of data in memory. + order : {'C', 'F'}, optional + Row-major (C-style) or column-major (Fortran-style) order. + + Attributes + ---------- + T : ndarray + Transpose of the array. + data : buffer + The array's elements, in memory. + dtype : dtype object + Describes the format of the elements in the array. + flags : dict + Dictionary containing information related to memory use, e.g., + 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. + flat : numpy.flatiter object + Flattened version of the array as an iterator. The iterator + allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for + assignment examples; TODO). + imag : ndarray + Imaginary part of the array. + real : ndarray + Real part of the array. + size : int + Number of elements in the array. + itemsize : int + The memory use of each array element in bytes. + nbytes : int + The total number of bytes required to store the array data, + i.e., ``itemsize * size``. + ndim : int + The array's number of dimensions. + shape : tuple of ints + Shape of the array. + strides : tuple of ints + The step-size required to move from one element to the next in + memory. For example, a contiguous ``(3, 4)`` array of type + ``int16`` in C-order has strides ``(8, 2)``. This implies that + to move from element to element in memory requires jumps of 2 bytes. + To move from row-to-row, one needs to jump 8 bytes at a time + (``2 * 4``). + ctypes : ctypes object + Class containing properties of the array needed for interaction + with ctypes. + base : ndarray + If the array is a view into another array, that array is its `base` + (unless that array is also a view). The `base` array is where the + array data is actually stored. + + See Also + -------- + array : Construct an array. + zeros : Create an array, each element of which is zero. + empty : Create an array, but leave its allocated memory unchanged (i.e., + it contains "garbage"). + dtype : Create a data-type. + numpy.typing.NDArray : An ndarray alias :term:`generic ` + w.r.t. its `dtype.type `. + + Notes + ----- + There are two modes of creating an array using ``__new__``: + + 1. If `buffer` is None, then only `shape`, `dtype`, and `order` + are used. + 2. If `buffer` is an object exposing the buffer interface, then + all keywords are interpreted. + + No ``__init__`` method is needed because the array is fully initialized + after the ``__new__`` method. + + Examples + -------- + These examples illustrate the low-level `ndarray` constructor. Refer + to the `See Also` section above for easier ways of constructing an + ndarray. + + First mode, `buffer` is None: + + >>> np.ndarray(shape=(2,2), dtype=float, order='F') + array([[0.0e+000, 0.0e+000], # random + [ nan, 2.5e-323]]) + + Second mode: + + >>> np.ndarray((2,), buffer=np.array([1,2,3]), + ... offset=np.int_().itemsize, + ... dtype=int) # offset = 1*itemsize, i.e. skip first element + array([2, 3]) + + """) + + +############################################################################## +# +# ndarray attributes +# +############################################################################## + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_interface__', + """Array protocol: Python side.""")) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_priority__', + """Array priority.""")) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_struct__', + """Array protocol: C-struct side.""")) + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__dlpack__', + """a.__dlpack__(*, stream=None) + + DLPack Protocol: Part of the Array API.""")) + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__dlpack_device__', + """a.__dlpack_device__() + + DLPack Protocol: Part of the Array API.""")) + +add_newdoc('numpy.core.multiarray', 'ndarray', ('base', + """ + Base object if memory is from some other object. + + Examples + -------- + The base of an array that owns its memory is None: + + >>> x = np.array([1,2,3,4]) + >>> x.base is None + True + + Slicing creates a view, whose memory is shared with x: + + >>> y = x[2:] + >>> y.base is x + True + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('ctypes', + """ + An object to simplify the interaction of the array with the ctypes + module. + + This attribute creates an object that makes it easier to use arrays + when calling shared libraries with the ctypes module. The returned + object has, among others, data, shape, and strides attributes (see + Notes below) which themselves return ctypes objects that can be used + as arguments to a shared library. + + Parameters + ---------- + None + + Returns + ------- + c : Python object + Possessing attributes data, shape, strides, etc. + + See Also + -------- + numpy.ctypeslib + + Notes + ----- + Below are the public attributes of this object which were documented + in "Guide to NumPy" (we have omitted undocumented public attributes, + as well as documented private attributes): + + .. autoattribute:: numpy.core._internal._ctypes.data + :noindex: + + .. autoattribute:: numpy.core._internal._ctypes.shape + :noindex: + + .. autoattribute:: numpy.core._internal._ctypes.strides + :noindex: + + .. automethod:: numpy.core._internal._ctypes.data_as + :noindex: + + .. automethod:: numpy.core._internal._ctypes.shape_as + :noindex: + + .. automethod:: numpy.core._internal._ctypes.strides_as + :noindex: + + If the ctypes module is not available, then the ctypes attribute + of array objects still returns something useful, but ctypes objects + are not returned and errors may be raised instead. In particular, + the object will still have the ``as_parameter`` attribute which will + return an integer equal to the data attribute. + + Examples + -------- + >>> import ctypes + >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) + >>> x + array([[0, 1], + [2, 3]], dtype=int32) + >>> x.ctypes.data + 31962608 # may vary + >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) + <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary + >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents + c_uint(0) + >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents + c_ulong(4294967296) + >>> x.ctypes.shape + # may vary + >>> x.ctypes.strides + # may vary + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('data', + """Python buffer object pointing to the start of the array's data.""")) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('dtype', + """ + Data-type of the array's elements. + + .. warning:: + + Setting ``arr.dtype`` is discouraged and may be deprecated in the + future. Setting will replace the ``dtype`` without modifying the + memory (see also `ndarray.view` and `ndarray.astype`). + + Parameters + ---------- + None + + Returns + ------- + d : numpy dtype object + + See Also + -------- + ndarray.astype : Cast the values contained in the array to a new data-type. + ndarray.view : Create a view of the same data but a different data-type. + numpy.dtype + + Examples + -------- + >>> x + array([[0, 1], + [2, 3]]) + >>> x.dtype + dtype('int32') + >>> type(x.dtype) + + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('imag', + """ + The imaginary part of the array. + + Examples + -------- + >>> x = np.sqrt([1+0j, 0+1j]) + >>> x.imag + array([ 0. , 0.70710678]) + >>> x.imag.dtype + dtype('float64') + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('itemsize', + """ + Length of one array element in bytes. + + Examples + -------- + >>> x = np.array([1,2,3], dtype=np.float64) + >>> x.itemsize + 8 + >>> x = np.array([1,2,3], dtype=np.complex128) + >>> x.itemsize + 16 + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('flags', + """ + Information about the memory layout of the array. + + Attributes + ---------- + C_CONTIGUOUS (C) + The data is in a single, C-style contiguous segment. + F_CONTIGUOUS (F) + The data is in a single, Fortran-style contiguous segment. + OWNDATA (O) + The array owns the memory it uses or borrows it from another object. + WRITEABLE (W) + The data area can be written to. Setting this to False locks + the data, making it read-only. A view (slice, etc.) inherits WRITEABLE + from its base array at creation time, but a view of a writeable + array may be subsequently locked while the base array remains writeable. + (The opposite is not true, in that a view of a locked array may not + be made writeable. However, currently, locking a base object does not + lock any views that already reference it, so under that circumstance it + is possible to alter the contents of a locked array via a previously + created writeable view onto it.) Attempting to change a non-writeable + array raises a RuntimeError exception. + ALIGNED (A) + The data and all elements are aligned appropriately for the hardware. + WRITEBACKIFCOPY (X) + This array is a copy of some other array. The C-API function + PyArray_ResolveWritebackIfCopy must be called before deallocating + to the base array will be updated with the contents of this array. + FNC + F_CONTIGUOUS and not C_CONTIGUOUS. + FORC + F_CONTIGUOUS or C_CONTIGUOUS (one-segment test). + BEHAVED (B) + ALIGNED and WRITEABLE. + CARRAY (CA) + BEHAVED and C_CONTIGUOUS. + FARRAY (FA) + BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS. + + Notes + ----- + The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``), + or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag + names are only supported in dictionary access. + + Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be + changed by the user, via direct assignment to the attribute or dictionary + entry, or by calling `ndarray.setflags`. + + The array flags cannot be set arbitrarily: + + - WRITEBACKIFCOPY can only be set ``False``. + - ALIGNED can only be set ``True`` if the data is truly aligned. + - WRITEABLE can only be set ``True`` if the array owns its own memory + or the ultimate owner of the memory exposes a writeable buffer + interface or is a string. + + Arrays can be both C-style and Fortran-style contiguous simultaneously. + This is clear for 1-dimensional arrays, but can also be true for higher + dimensional arrays. + + Even for contiguous arrays a stride for a given dimension + ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1`` + or the array has no elements. + It does *not* generally hold that ``self.strides[-1] == self.itemsize`` + for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for + Fortran-style contiguous arrays is true. + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('flat', + """ + A 1-D iterator over the array. + + This is a `numpy.flatiter` instance, which acts similarly to, but is not + a subclass of, Python's built-in iterator object. + + See Also + -------- + flatten : Return a copy of the array collapsed into one dimension. + + flatiter + + Examples + -------- + >>> x = np.arange(1, 7).reshape(2, 3) + >>> x + array([[1, 2, 3], + [4, 5, 6]]) + >>> x.flat[3] + 4 + >>> x.T + array([[1, 4], + [2, 5], + [3, 6]]) + >>> x.T.flat[3] + 5 + >>> type(x.flat) + + + An assignment example: + + >>> x.flat = 3; x + array([[3, 3, 3], + [3, 3, 3]]) + >>> x.flat[[1,4]] = 1; x + array([[3, 1, 3], + [3, 1, 3]]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('nbytes', + """ + Total bytes consumed by the elements of the array. + + Notes + ----- + Does not include memory consumed by non-element attributes of the + array object. + + See Also + -------- + sys.getsizeof + Memory consumed by the object itself without parents in case view. + This does include memory consumed by non-element attributes. + + Examples + -------- + >>> x = np.zeros((3,5,2), dtype=np.complex128) + >>> x.nbytes + 480 + >>> np.prod(x.shape) * x.itemsize + 480 + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('ndim', + """ + Number of array dimensions. + + Examples + -------- + >>> x = np.array([1, 2, 3]) + >>> x.ndim + 1 + >>> y = np.zeros((2, 3, 4)) + >>> y.ndim + 3 + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('real', + """ + The real part of the array. + + Examples + -------- + >>> x = np.sqrt([1+0j, 0+1j]) + >>> x.real + array([ 1. , 0.70710678]) + >>> x.real.dtype + dtype('float64') + + See Also + -------- + numpy.real : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('shape', + """ + Tuple of array dimensions. + + The shape property is usually used to get the current shape of an array, + but may also be used to reshape the array in-place by assigning a tuple of + array dimensions to it. As with `numpy.reshape`, one of the new shape + dimensions can be -1, in which case its value is inferred from the size of + the array and the remaining dimensions. Reshaping an array in-place will + fail if a copy is required. + + .. warning:: + + Setting ``arr.shape`` is discouraged and may be deprecated in the + future. Using `ndarray.reshape` is the preferred approach. + + Examples + -------- + >>> x = np.array([1, 2, 3, 4]) + >>> x.shape + (4,) + >>> y = np.zeros((2, 3, 4)) + >>> y.shape + (2, 3, 4) + >>> y.shape = (3, 8) + >>> y + array([[ 0., 0., 0., 0., 0., 0., 0., 0.], + [ 0., 0., 0., 0., 0., 0., 0., 0.], + [ 0., 0., 0., 0., 0., 0., 0., 0.]]) + >>> y.shape = (3, 6) + Traceback (most recent call last): + File "", line 1, in + ValueError: total size of new array must be unchanged + >>> np.zeros((4,2))[::2].shape = (-1,) + Traceback (most recent call last): + File "", line 1, in + AttributeError: Incompatible shape for in-place modification. Use + `.reshape()` to make a copy with the desired shape. + + See Also + -------- + numpy.shape : Equivalent getter function. + numpy.reshape : Function similar to setting ``shape``. + ndarray.reshape : Method similar to setting ``shape``. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('size', + """ + Number of elements in the array. + + Equal to ``np.prod(a.shape)``, i.e., the product of the array's + dimensions. + + Notes + ----- + `a.size` returns a standard arbitrary precision Python integer. This + may not be the case with other methods of obtaining the same value + (like the suggested ``np.prod(a.shape)``, which returns an instance + of ``np.int_``), and may be relevant if the value is used further in + calculations that may overflow a fixed size integer type. + + Examples + -------- + >>> x = np.zeros((3, 5, 2), dtype=np.complex128) + >>> x.size + 30 + >>> np.prod(x.shape) + 30 + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('strides', + """ + Tuple of bytes to step in each dimension when traversing an array. + + The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a` + is:: + + offset = sum(np.array(i) * a.strides) + + A more detailed explanation of strides can be found in the + "ndarray.rst" file in the NumPy reference guide. + + .. warning:: + + Setting ``arr.strides`` is discouraged and may be deprecated in the + future. `numpy.lib.stride_tricks.as_strided` should be preferred + to create a new view of the same data in a safer way. + + Notes + ----- + Imagine an array of 32-bit integers (each 4 bytes):: + + x = np.array([[0, 1, 2, 3, 4], + [5, 6, 7, 8, 9]], dtype=np.int32) + + This array is stored in memory as 40 bytes, one after the other + (known as a contiguous block of memory). The strides of an array tell + us how many bytes we have to skip in memory to move to the next position + along a certain axis. For example, we have to skip 4 bytes (1 value) to + move to the next column, but 20 bytes (5 values) to get to the same + position in the next row. As such, the strides for the array `x` will be + ``(20, 4)``. + + See Also + -------- + numpy.lib.stride_tricks.as_strided + + Examples + -------- + >>> y = np.reshape(np.arange(2*3*4), (2,3,4)) + >>> y + array([[[ 0, 1, 2, 3], + [ 4, 5, 6, 7], + [ 8, 9, 10, 11]], + [[12, 13, 14, 15], + [16, 17, 18, 19], + [20, 21, 22, 23]]]) + >>> y.strides + (48, 16, 4) + >>> y[1,1,1] + 17 + >>> offset=sum(y.strides * np.array((1,1,1))) + >>> offset/y.itemsize + 17 + + >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) + >>> x.strides + (32, 4, 224, 1344) + >>> i = np.array([3,5,2,2]) + >>> offset = sum(i * x.strides) + >>> x[3,5,2,2] + 813 + >>> offset / x.itemsize + 813 + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('T', + """ + View of the transposed array. + + Same as ``self.transpose()``. + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4]]) + >>> a + array([[1, 2], + [3, 4]]) + >>> a.T + array([[1, 3], + [2, 4]]) + + >>> a = np.array([1, 2, 3, 4]) + >>> a + array([1, 2, 3, 4]) + >>> a.T + array([1, 2, 3, 4]) + + See Also + -------- + transpose + + """)) + + +############################################################################## +# +# ndarray methods +# +############################################################################## + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__array__', + """ a.__array__([dtype], /) + + Returns either a new reference to self if dtype is not given or a new array + of provided data type if dtype is different from the current dtype of the + array. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_finalize__', + """a.__array_finalize__(obj, /) + + Present so subclasses can call super. Does nothing. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_prepare__', + """a.__array_prepare__(array[, context], /) + + Returns a view of `array` with the same type as self. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_wrap__', + """a.__array_wrap__(array[, context], /) + + Returns a view of `array` with the same type as self. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__copy__', + """a.__copy__() + + Used if :func:`copy.copy` is called on an array. Returns a copy of the array. + + Equivalent to ``a.copy(order='K')``. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__class_getitem__', + """a.__class_getitem__(item, /) + + Return a parametrized wrapper around the `~numpy.ndarray` type. + + .. versionadded:: 1.22 + + Returns + ------- + alias : types.GenericAlias + A parametrized `~numpy.ndarray` type. + + Examples + -------- + >>> from typing import Any + >>> import numpy as np + + >>> np.ndarray[Any, np.dtype[Any]] + numpy.ndarray[typing.Any, numpy.dtype[typing.Any]] + + See Also + -------- + :pep:`585` : Type hinting generics in standard collections. + numpy.typing.NDArray : An ndarray alias :term:`generic ` + w.r.t. its `dtype.type `. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__deepcopy__', + """a.__deepcopy__(memo, /) + + Used if :func:`copy.deepcopy` is called on an array. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__reduce__', + """a.__reduce__() + + For pickling. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('__setstate__', + """a.__setstate__(state, /) + + For unpickling. + + The `state` argument must be a sequence that contains the following + elements: + + Parameters + ---------- + version : int + optional pickle version. If omitted defaults to 0. + shape : tuple + dtype : data-type + isFortran : bool + rawdata : string or list + a binary string with the data (or a list if 'a' is an object array) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('all', + """ + a.all(axis=None, out=None, keepdims=False, *, where=True) + + Returns True if all elements evaluate to True. + + Refer to `numpy.all` for full documentation. + + See Also + -------- + numpy.all : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('any', + """ + a.any(axis=None, out=None, keepdims=False, *, where=True) + + Returns True if any of the elements of `a` evaluate to True. + + Refer to `numpy.any` for full documentation. + + See Also + -------- + numpy.any : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('argmax', + """ + a.argmax(axis=None, out=None, *, keepdims=False) + + Return indices of the maximum values along the given axis. + + Refer to `numpy.argmax` for full documentation. + + See Also + -------- + numpy.argmax : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('argmin', + """ + a.argmin(axis=None, out=None, *, keepdims=False) + + Return indices of the minimum values along the given axis. + + Refer to `numpy.argmin` for detailed documentation. + + See Also + -------- + numpy.argmin : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('argsort', + """ + a.argsort(axis=-1, kind=None, order=None) + + Returns the indices that would sort this array. + + Refer to `numpy.argsort` for full documentation. + + See Also + -------- + numpy.argsort : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('argpartition', + """ + a.argpartition(kth, axis=-1, kind='introselect', order=None) + + Returns the indices that would partition this array. + + Refer to `numpy.argpartition` for full documentation. + + .. versionadded:: 1.8.0 + + See Also + -------- + numpy.argpartition : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('astype', + """ + a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) + + Copy of the array, cast to a specified type. + + Parameters + ---------- + dtype : str or dtype + Typecode or data-type to which the array is cast. + order : {'C', 'F', 'A', 'K'}, optional + Controls the memory layout order of the result. + 'C' means C order, 'F' means Fortran order, 'A' + means 'F' order if all the arrays are Fortran contiguous, + 'C' order otherwise, and 'K' means as close to the + order the array elements appear in memory as possible. + Default is 'K'. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. Defaults to 'unsafe' + for backwards compatibility. + + * 'no' means the data types should not be cast at all. + * 'equiv' means only byte-order changes are allowed. + * 'safe' means only casts which can preserve values are allowed. + * 'same_kind' means only safe casts or casts within a kind, + like float64 to float32, are allowed. + * 'unsafe' means any data conversions may be done. + subok : bool, optional + If True, then sub-classes will be passed-through (default), otherwise + the returned array will be forced to be a base-class array. + copy : bool, optional + By default, astype always returns a newly allocated array. If this + is set to false, and the `dtype`, `order`, and `subok` + requirements are satisfied, the input array is returned instead + of a copy. + + Returns + ------- + arr_t : ndarray + Unless `copy` is False and the other conditions for returning the input + array are satisfied (see description for `copy` input parameter), `arr_t` + is a new array of the same shape as the input array, with dtype, order + given by `dtype`, `order`. + + Notes + ----- + .. versionchanged:: 1.17.0 + Casting between a simple data type and a structured one is possible only + for "unsafe" casting. Casting to multiple fields is allowed, but + casting from multiple fields is not. + + .. versionchanged:: 1.9.0 + Casting from numeric to string types in 'safe' casting mode requires + that the string dtype length is long enough to store the max + integer/float value converted. + + Raises + ------ + ComplexWarning + When casting from complex to float or int. To avoid this, + one should use ``a.real.astype(t)``. + + Examples + -------- + >>> x = np.array([1, 2, 2.5]) + >>> x + array([1. , 2. , 2.5]) + + >>> x.astype(int) + array([1, 2, 2]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('byteswap', + """ + a.byteswap(inplace=False) + + Swap the bytes of the array elements + + Toggle between low-endian and big-endian data representation by + returning a byteswapped array, optionally swapped in-place. + Arrays of byte-strings are not swapped. The real and imaginary + parts of a complex number are swapped individually. + + Parameters + ---------- + inplace : bool, optional + If ``True``, swap bytes in-place, default is ``False``. + + Returns + ------- + out : ndarray + The byteswapped array. If `inplace` is ``True``, this is + a view to self. + + Examples + -------- + >>> A = np.array([1, 256, 8755], dtype=np.int16) + >>> list(map(hex, A)) + ['0x1', '0x100', '0x2233'] + >>> A.byteswap(inplace=True) + array([ 256, 1, 13090], dtype=int16) + >>> list(map(hex, A)) + ['0x100', '0x1', '0x3322'] + + Arrays of byte-strings are not swapped + + >>> A = np.array([b'ceg', b'fac']) + >>> A.byteswap() + array([b'ceg', b'fac'], dtype='|S3') + + ``A.newbyteorder().byteswap()`` produces an array with the same values + but different representation in memory + + >>> A = np.array([1, 2, 3]) + >>> A.view(np.uint8) + array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, + 0, 0], dtype=uint8) + >>> A.newbyteorder().byteswap(inplace=True) + array([1, 2, 3]) + >>> A.view(np.uint8) + array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, + 0, 3], dtype=uint8) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('choose', + """ + a.choose(choices, out=None, mode='raise') + + Use an index array to construct a new array from a set of choices. + + Refer to `numpy.choose` for full documentation. + + See Also + -------- + numpy.choose : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('clip', + """ + a.clip(min=None, max=None, out=None, **kwargs) + + Return an array whose values are limited to ``[min, max]``. + One of max or min must be given. + + Refer to `numpy.clip` for full documentation. + + See Also + -------- + numpy.clip : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('compress', + """ + a.compress(condition, axis=None, out=None) + + Return selected slices of this array along given axis. + + Refer to `numpy.compress` for full documentation. + + See Also + -------- + numpy.compress : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('conj', + """ + a.conj() + + Complex-conjugate all elements. + + Refer to `numpy.conjugate` for full documentation. + + See Also + -------- + numpy.conjugate : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('conjugate', + """ + a.conjugate() + + Return the complex conjugate, element-wise. + + Refer to `numpy.conjugate` for full documentation. + + See Also + -------- + numpy.conjugate : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('copy', + """ + a.copy(order='C') + + Return a copy of the array. + + Parameters + ---------- + order : {'C', 'F', 'A', 'K'}, optional + Controls the memory layout of the copy. 'C' means C-order, + 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, + 'C' otherwise. 'K' means match the layout of `a` as closely + as possible. (Note that this function and :func:`numpy.copy` are very + similar but have different default values for their order= + arguments, and this function always passes sub-classes through.) + + See also + -------- + numpy.copy : Similar function with different default behavior + numpy.copyto + + Notes + ----- + This function is the preferred method for creating an array copy. The + function :func:`numpy.copy` is similar, but it defaults to using order 'K', + and will not pass sub-classes through by default. + + Examples + -------- + >>> x = np.array([[1,2,3],[4,5,6]], order='F') + + >>> y = x.copy() + + >>> x.fill(0) + + >>> x + array([[0, 0, 0], + [0, 0, 0]]) + + >>> y + array([[1, 2, 3], + [4, 5, 6]]) + + >>> y.flags['C_CONTIGUOUS'] + True + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('cumprod', + """ + a.cumprod(axis=None, dtype=None, out=None) + + Return the cumulative product of the elements along the given axis. + + Refer to `numpy.cumprod` for full documentation. + + See Also + -------- + numpy.cumprod : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('cumsum', + """ + a.cumsum(axis=None, dtype=None, out=None) + + Return the cumulative sum of the elements along the given axis. + + Refer to `numpy.cumsum` for full documentation. + + See Also + -------- + numpy.cumsum : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('diagonal', + """ + a.diagonal(offset=0, axis1=0, axis2=1) + + Return specified diagonals. In NumPy 1.9 the returned array is a + read-only view instead of a copy as in previous NumPy versions. In + a future version the read-only restriction will be removed. + + Refer to :func:`numpy.diagonal` for full documentation. + + See Also + -------- + numpy.diagonal : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('dot')) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('dump', + """a.dump(file) + + Dump a pickle of the array to the specified file. + The array can be read back with pickle.load or numpy.load. + + Parameters + ---------- + file : str or Path + A string naming the dump file. + + .. versionchanged:: 1.17.0 + `pathlib.Path` objects are now accepted. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('dumps', + """ + a.dumps() + + Returns the pickle of the array as a string. + pickle.loads will convert the string back to an array. + + Parameters + ---------- + None + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('fill', + """ + a.fill(value) + + Fill the array with a scalar value. + + Parameters + ---------- + value : scalar + All elements of `a` will be assigned this value. + + Examples + -------- + >>> a = np.array([1, 2]) + >>> a.fill(0) + >>> a + array([0, 0]) + >>> a = np.empty(2) + >>> a.fill(1) + >>> a + array([1., 1.]) + + Fill expects a scalar value and always behaves the same as assigning + to a single array element. The following is a rare example where this + distinction is important: + + >>> a = np.array([None, None], dtype=object) + >>> a[0] = np.array(3) + >>> a + array([array(3), None], dtype=object) + >>> a.fill(np.array(3)) + >>> a + array([array(3), array(3)], dtype=object) + + Where other forms of assignments will unpack the array being assigned: + + >>> a[...] = np.array(3) + >>> a + array([3, 3], dtype=object) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('flatten', + """ + a.flatten(order='C') + + Return a copy of the array collapsed into one dimension. + + Parameters + ---------- + order : {'C', 'F', 'A', 'K'}, optional + 'C' means to flatten in row-major (C-style) order. + 'F' means to flatten in column-major (Fortran- + style) order. 'A' means to flatten in column-major + order if `a` is Fortran *contiguous* in memory, + row-major order otherwise. 'K' means to flatten + `a` in the order the elements occur in memory. + The default is 'C'. + + Returns + ------- + y : ndarray + A copy of the input array, flattened to one dimension. + + See Also + -------- + ravel : Return a flattened array. + flat : A 1-D flat iterator over the array. + + Examples + -------- + >>> a = np.array([[1,2], [3,4]]) + >>> a.flatten() + array([1, 2, 3, 4]) + >>> a.flatten('F') + array([1, 3, 2, 4]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('getfield', + """ + a.getfield(dtype, offset=0) + + Returns a field of the given array as a certain type. + + A field is a view of the array data with a given data-type. The values in + the view are determined by the given type and the offset into the current + array in bytes. The offset needs to be such that the view dtype fits in the + array dtype; for example an array of dtype complex128 has 16-byte elements. + If taking a view with a 32-bit integer (4 bytes), the offset needs to be + between 0 and 12 bytes. + + Parameters + ---------- + dtype : str or dtype + The data type of the view. The dtype size of the view can not be larger + than that of the array itself. + offset : int + Number of bytes to skip before beginning the element view. + + Examples + -------- + >>> x = np.diag([1.+1.j]*2) + >>> x[1, 1] = 2 + 4.j + >>> x + array([[1.+1.j, 0.+0.j], + [0.+0.j, 2.+4.j]]) + >>> x.getfield(np.float64) + array([[1., 0.], + [0., 2.]]) + + By choosing an offset of 8 bytes we can select the complex part of the + array for our view: + + >>> x.getfield(np.float64, offset=8) + array([[1., 0.], + [0., 4.]]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('item', + """ + a.item(*args) + + Copy an element of an array to a standard Python scalar and return it. + + Parameters + ---------- + \\*args : Arguments (variable number and type) + + * none: in this case, the method only works for arrays + with one element (`a.size == 1`), which element is + copied into a standard Python scalar object and returned. + + * int_type: this argument is interpreted as a flat index into + the array, specifying which element to copy and return. + + * tuple of int_types: functions as does a single int_type argument, + except that the argument is interpreted as an nd-index into the + array. + + Returns + ------- + z : Standard Python scalar object + A copy of the specified element of the array as a suitable + Python scalar + + Notes + ----- + When the data type of `a` is longdouble or clongdouble, item() returns + a scalar array object because there is no available Python scalar that + would not lose information. Void arrays return a buffer object for item(), + unless fields are defined, in which case a tuple is returned. + + `item` is very similar to a[args], except, instead of an array scalar, + a standard Python scalar is returned. This can be useful for speeding up + access to elements of the array and doing arithmetic on elements of the + array using Python's optimized math. + + Examples + -------- + >>> np.random.seed(123) + >>> x = np.random.randint(9, size=(3, 3)) + >>> x + array([[2, 2, 6], + [1, 3, 6], + [1, 0, 1]]) + >>> x.item(3) + 1 + >>> x.item(7) + 0 + >>> x.item((0, 1)) + 2 + >>> x.item((2, 2)) + 1 + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('itemset', + """ + a.itemset(*args) + + Insert scalar into an array (scalar is cast to array's dtype, if possible) + + There must be at least 1 argument, and define the last argument + as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster + than ``a[args] = item``. The item should be a scalar value and `args` + must select a single item in the array `a`. + + Parameters + ---------- + \\*args : Arguments + If one argument: a scalar, only used in case `a` is of size 1. + If two arguments: the last argument is the value to be set + and must be a scalar, the first argument specifies a single array + element location. It is either an int or a tuple. + + Notes + ----- + Compared to indexing syntax, `itemset` provides some speed increase + for placing a scalar into a particular location in an `ndarray`, + if you must do this. However, generally this is discouraged: + among other problems, it complicates the appearance of the code. + Also, when using `itemset` (and `item`) inside a loop, be sure + to assign the methods to a local variable to avoid the attribute + look-up at each loop iteration. + + Examples + -------- + >>> np.random.seed(123) + >>> x = np.random.randint(9, size=(3, 3)) + >>> x + array([[2, 2, 6], + [1, 3, 6], + [1, 0, 1]]) + >>> x.itemset(4, 0) + >>> x.itemset((2, 2), 9) + >>> x + array([[2, 2, 6], + [1, 0, 6], + [1, 0, 9]]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('max', + """ + a.max(axis=None, out=None, keepdims=False, initial=, where=True) + + Return the maximum along a given axis. + + Refer to `numpy.amax` for full documentation. + + See Also + -------- + numpy.amax : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('mean', + """ + a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True) + + Returns the average of the array elements along given axis. + + Refer to `numpy.mean` for full documentation. + + See Also + -------- + numpy.mean : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('min', + """ + a.min(axis=None, out=None, keepdims=False, initial=, where=True) + + Return the minimum along a given axis. + + Refer to `numpy.amin` for full documentation. + + See Also + -------- + numpy.amin : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('newbyteorder', + """ + arr.newbyteorder(new_order='S', /) + + Return the array with the same data viewed with a different byte order. + + Equivalent to:: + + arr.view(arr.dtype.newbytorder(new_order)) + + Changes are also made in all fields and sub-arrays of the array data + type. + + + + Parameters + ---------- + new_order : string, optional + Byte order to force; a value from the byte order specifications + below. `new_order` codes can be any of: + + * 'S' - swap dtype from current to opposite endian + * {'<', 'little'} - little endian + * {'>', 'big'} - big endian + * {'=', 'native'} - native order, equivalent to `sys.byteorder` + * {'|', 'I'} - ignore (no change to byte order) + + The default value ('S') results in swapping the current + byte order. + + + Returns + ------- + new_arr : array + New array object with the dtype reflecting given change to the + byte order. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('nonzero', + """ + a.nonzero() + + Return the indices of the elements that are non-zero. + + Refer to `numpy.nonzero` for full documentation. + + See Also + -------- + numpy.nonzero : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('prod', + """ + a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True) + + Return the product of the array elements over the given axis + + Refer to `numpy.prod` for full documentation. + + See Also + -------- + numpy.prod : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('ptp', + """ + a.ptp(axis=None, out=None, keepdims=False) + + Peak to peak (maximum - minimum) value along a given axis. + + Refer to `numpy.ptp` for full documentation. + + See Also + -------- + numpy.ptp : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('put', + """ + a.put(indices, values, mode='raise') + + Set ``a.flat[n] = values[n]`` for all `n` in indices. + + Refer to `numpy.put` for full documentation. + + See Also + -------- + numpy.put : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('ravel', + """ + a.ravel([order]) + + Return a flattened array. + + Refer to `numpy.ravel` for full documentation. + + See Also + -------- + numpy.ravel : equivalent function + + ndarray.flat : a flat iterator on the array. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('repeat', + """ + a.repeat(repeats, axis=None) + + Repeat elements of an array. + + Refer to `numpy.repeat` for full documentation. + + See Also + -------- + numpy.repeat : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('reshape', + """ + a.reshape(shape, order='C') + + Returns an array containing the same data with a new shape. + + Refer to `numpy.reshape` for full documentation. + + See Also + -------- + numpy.reshape : equivalent function + + Notes + ----- + Unlike the free function `numpy.reshape`, this method on `ndarray` allows + the elements of the shape parameter to be passed in as separate arguments. + For example, ``a.reshape(10, 11)`` is equivalent to + ``a.reshape((10, 11))``. + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('resize', + """ + a.resize(new_shape, refcheck=True) + + Change shape and size of array in-place. + + Parameters + ---------- + new_shape : tuple of ints, or `n` ints + Shape of resized array. + refcheck : bool, optional + If False, reference count will not be checked. Default is True. + + Returns + ------- + None + + Raises + ------ + ValueError + If `a` does not own its own data or references or views to it exist, + and the data memory must be changed. + PyPy only: will always raise if the data memory must be changed, since + there is no reliable way to determine if references or views to it + exist. + + SystemError + If the `order` keyword argument is specified. This behaviour is a + bug in NumPy. + + See Also + -------- + resize : Return a new array with the specified shape. + + Notes + ----- + This reallocates space for the data area if necessary. + + Only contiguous arrays (data elements consecutive in memory) can be + resized. + + The purpose of the reference count check is to make sure you + do not use this array as a buffer for another Python object and then + reallocate the memory. However, reference counts can increase in + other ways so if you are sure that you have not shared the memory + for this array with another Python object, then you may safely set + `refcheck` to False. + + Examples + -------- + Shrinking an array: array is flattened (in the order that the data are + stored in memory), resized, and reshaped: + + >>> a = np.array([[0, 1], [2, 3]], order='C') + >>> a.resize((2, 1)) + >>> a + array([[0], + [1]]) + + >>> a = np.array([[0, 1], [2, 3]], order='F') + >>> a.resize((2, 1)) + >>> a + array([[0], + [2]]) + + Enlarging an array: as above, but missing entries are filled with zeros: + + >>> b = np.array([[0, 1], [2, 3]]) + >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple + >>> b + array([[0, 1, 2], + [3, 0, 0]]) + + Referencing an array prevents resizing... + + >>> c = a + >>> a.resize((1, 1)) + Traceback (most recent call last): + ... + ValueError: cannot resize an array that references or is referenced ... + + Unless `refcheck` is False: + + >>> a.resize((1, 1), refcheck=False) + >>> a + array([[0]]) + >>> c + array([[0]]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('round', + """ + a.round(decimals=0, out=None) + + Return `a` with each element rounded to the given number of decimals. + + Refer to `numpy.around` for full documentation. + + See Also + -------- + numpy.around : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('searchsorted', + """ + a.searchsorted(v, side='left', sorter=None) + + Find indices where elements of v should be inserted in a to maintain order. + + For full documentation, see `numpy.searchsorted` + + See Also + -------- + numpy.searchsorted : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('setfield', + """ + a.setfield(val, dtype, offset=0) + + Put a value into a specified place in a field defined by a data-type. + + Place `val` into `a`'s field defined by `dtype` and beginning `offset` + bytes into the field. + + Parameters + ---------- + val : object + Value to be placed in field. + dtype : dtype object + Data-type of the field in which to place `val`. + offset : int, optional + The number of bytes into the field at which to place `val`. + + Returns + ------- + None + + See Also + -------- + getfield + + Examples + -------- + >>> x = np.eye(3) + >>> x.getfield(np.float64) + array([[1., 0., 0.], + [0., 1., 0.], + [0., 0., 1.]]) + >>> x.setfield(3, np.int32) + >>> x.getfield(np.int32) + array([[3, 3, 3], + [3, 3, 3], + [3, 3, 3]], dtype=int32) + >>> x + array([[1.0e+000, 1.5e-323, 1.5e-323], + [1.5e-323, 1.0e+000, 1.5e-323], + [1.5e-323, 1.5e-323, 1.0e+000]]) + >>> x.setfield(np.eye(3), np.int32) + >>> x + array([[1., 0., 0.], + [0., 1., 0.], + [0., 0., 1.]]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('setflags', + """ + a.setflags(write=None, align=None, uic=None) + + Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, + respectively. + + These Boolean-valued flags affect how numpy interprets the memory + area used by `a` (see Notes below). The ALIGNED flag can only + be set to True if the data is actually aligned according to the type. + The WRITEBACKIFCOPY and flag can never be set + to True. The flag WRITEABLE can only be set to True if the array owns its + own memory, or the ultimate owner of the memory exposes a writeable buffer + interface, or is a string. (The exception for string is made so that + unpickling can be done without copying memory.) + + Parameters + ---------- + write : bool, optional + Describes whether or not `a` can be written to. + align : bool, optional + Describes whether or not `a` is aligned properly for its type. + uic : bool, optional + Describes whether or not `a` is a copy of another "base" array. + + Notes + ----- + Array flags provide information about how the memory area used + for the array is to be interpreted. There are 7 Boolean flags + in use, only four of which can be changed by the user: + WRITEBACKIFCOPY, WRITEABLE, and ALIGNED. + + WRITEABLE (W) the data area can be written to; + + ALIGNED (A) the data and strides are aligned appropriately for the hardware + (as determined by the compiler); + + WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced + by .base). When the C-API function PyArray_ResolveWritebackIfCopy is + called, the base array will be updated with the contents of this array. + + All flags can be accessed using the single (upper case) letter as well + as the full name. + + Examples + -------- + >>> y = np.array([[3, 1, 7], + ... [2, 0, 0], + ... [8, 5, 9]]) + >>> y + array([[3, 1, 7], + [2, 0, 0], + [8, 5, 9]]) + >>> y.flags + C_CONTIGUOUS : True + F_CONTIGUOUS : False + OWNDATA : True + WRITEABLE : True + ALIGNED : True + WRITEBACKIFCOPY : False + >>> y.setflags(write=0, align=0) + >>> y.flags + C_CONTIGUOUS : True + F_CONTIGUOUS : False + OWNDATA : True + WRITEABLE : False + ALIGNED : False + WRITEBACKIFCOPY : False + >>> y.setflags(uic=1) + Traceback (most recent call last): + File "", line 1, in + ValueError: cannot set WRITEBACKIFCOPY flag to True + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('sort', + """ + a.sort(axis=-1, kind=None, order=None) + + Sort an array in-place. Refer to `numpy.sort` for full documentation. + + Parameters + ---------- + axis : int, optional + Axis along which to sort. Default is -1, which means sort along the + last axis. + kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional + Sorting algorithm. The default is 'quicksort'. Note that both 'stable' + and 'mergesort' use timsort under the covers and, in general, the + actual implementation will vary with datatype. The 'mergesort' option + is retained for backwards compatibility. + + .. versionchanged:: 1.15.0 + The 'stable' option was added. + + order : str or list of str, optional + When `a` is an array with fields defined, this argument specifies + which fields to compare first, second, etc. A single field can + be specified as a string, and not all fields need be specified, + but unspecified fields will still be used, in the order in which + they come up in the dtype, to break ties. + + See Also + -------- + numpy.sort : Return a sorted copy of an array. + numpy.argsort : Indirect sort. + numpy.lexsort : Indirect stable sort on multiple keys. + numpy.searchsorted : Find elements in sorted array. + numpy.partition: Partial sort. + + Notes + ----- + See `numpy.sort` for notes on the different sorting algorithms. + + Examples + -------- + >>> a = np.array([[1,4], [3,1]]) + >>> a.sort(axis=1) + >>> a + array([[1, 4], + [1, 3]]) + >>> a.sort(axis=0) + >>> a + array([[1, 3], + [1, 4]]) + + Use the `order` keyword to specify a field to use when sorting a + structured array: + + >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) + >>> a.sort(order='y') + >>> a + array([(b'c', 1), (b'a', 2)], + dtype=[('x', 'S1'), ('y', '>> a = np.array([3, 4, 2, 1]) + >>> a.partition(3) + >>> a + array([2, 1, 3, 4]) + + >>> a.partition((1, 3)) + >>> a + array([1, 2, 3, 4]) + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('squeeze', + """ + a.squeeze(axis=None) + + Remove axes of length one from `a`. + + Refer to `numpy.squeeze` for full documentation. + + See Also + -------- + numpy.squeeze : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('std', + """ + a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True) + + Returns the standard deviation of the array elements along given axis. + + Refer to `numpy.std` for full documentation. + + See Also + -------- + numpy.std : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('sum', + """ + a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True) + + Return the sum of the array elements over the given axis. + + Refer to `numpy.sum` for full documentation. + + See Also + -------- + numpy.sum : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('swapaxes', + """ + a.swapaxes(axis1, axis2) + + Return a view of the array with `axis1` and `axis2` interchanged. + + Refer to `numpy.swapaxes` for full documentation. + + See Also + -------- + numpy.swapaxes : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('take', + """ + a.take(indices, axis=None, out=None, mode='raise') + + Return an array formed from the elements of `a` at the given indices. + + Refer to `numpy.take` for full documentation. + + See Also + -------- + numpy.take : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('tofile', + """ + a.tofile(fid, sep="", format="%s") + + Write array to a file as text or binary (default). + + Data is always written in 'C' order, independent of the order of `a`. + The data produced by this method can be recovered using the function + fromfile(). + + Parameters + ---------- + fid : file or str or Path + An open file object, or a string containing a filename. + + .. versionchanged:: 1.17.0 + `pathlib.Path` objects are now accepted. + + sep : str + Separator between array items for text output. + If "" (empty), a binary file is written, equivalent to + ``file.write(a.tobytes())``. + format : str + Format string for text file output. + Each entry in the array is formatted to text by first converting + it to the closest Python type, and then using "format" % item. + + Notes + ----- + This is a convenience function for quick storage of array data. + Information on endianness and precision is lost, so this method is not a + good choice for files intended to archive data or transport data between + machines with different endianness. Some of these problems can be overcome + by outputting the data as text files, at the expense of speed and file + size. + + When fid is a file object, array contents are directly written to the + file, bypassing the file object's ``write`` method. As a result, tofile + cannot be used with files objects supporting compression (e.g., GzipFile) + or file-like objects that do not support ``fileno()`` (e.g., BytesIO). + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('tolist', + """ + a.tolist() + + Return the array as an ``a.ndim``-levels deep nested list of Python scalars. + + Return a copy of the array data as a (nested) Python list. + Data items are converted to the nearest compatible builtin Python type, via + the `~numpy.ndarray.item` function. + + If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will + not be a list at all, but a simple Python scalar. + + Parameters + ---------- + none + + Returns + ------- + y : object, or list of object, or list of list of object, or ... + The possibly nested list of array elements. + + Notes + ----- + The array may be recreated via ``a = np.array(a.tolist())``, although this + may sometimes lose precision. + + Examples + -------- + For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``, + except that ``tolist`` changes numpy scalars to Python scalars: + + >>> a = np.uint32([1, 2]) + >>> a_list = list(a) + >>> a_list + [1, 2] + >>> type(a_list[0]) + + >>> a_tolist = a.tolist() + >>> a_tolist + [1, 2] + >>> type(a_tolist[0]) + + + Additionally, for a 2D array, ``tolist`` applies recursively: + + >>> a = np.array([[1, 2], [3, 4]]) + >>> list(a) + [array([1, 2]), array([3, 4])] + >>> a.tolist() + [[1, 2], [3, 4]] + + The base case for this recursion is a 0D array: + + >>> a = np.array(1) + >>> list(a) + Traceback (most recent call last): + ... + TypeError: iteration over a 0-d array + >>> a.tolist() + 1 + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('tobytes', """ + a.tobytes(order='C') + + Construct Python bytes containing the raw data bytes in the array. + + Constructs Python bytes showing a copy of the raw contents of + data memory. The bytes object is produced in C-order by default. + This behavior is controlled by the ``order`` parameter. + + .. versionadded:: 1.9.0 + + Parameters + ---------- + order : {'C', 'F', 'A'}, optional + Controls the memory layout of the bytes object. 'C' means C-order, + 'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is + Fortran contiguous, 'C' otherwise. Default is 'C'. + + Returns + ------- + s : bytes + Python bytes exhibiting a copy of `a`'s raw data. + + See also + -------- + frombuffer + Inverse of this operation, construct a 1-dimensional array from Python + bytes. + + Examples + -------- + >>> x = np.array([[0, 1], [2, 3]], dtype='>> x.tobytes() + b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00' + >>> x.tobytes('C') == x.tobytes() + True + >>> x.tobytes('F') + b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00' + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('tostring', r""" + a.tostring(order='C') + + A compatibility alias for `tobytes`, with exactly the same behavior. + + Despite its name, it returns `bytes` not `str`\ s. + + .. deprecated:: 1.19.0 + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('trace', + """ + a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) + + Return the sum along diagonals of the array. + + Refer to `numpy.trace` for full documentation. + + See Also + -------- + numpy.trace : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('transpose', + """ + a.transpose(*axes) + + Returns a view of the array with axes transposed. + + Refer to `numpy.transpose` for full documentation. + + Parameters + ---------- + axes : None, tuple of ints, or `n` ints + + * None or no argument: reverses the order of the axes. + + * tuple of ints: `i` in the `j`-th place in the tuple means that the + array's `i`-th axis becomes the transposed array's `j`-th axis. + + * `n` ints: same as an n-tuple of the same ints (this form is + intended simply as a "convenience" alternative to the tuple form). + + Returns + ------- + p : ndarray + View of the array with its axes suitably permuted. + + See Also + -------- + transpose : Equivalent function. + ndarray.T : Array property returning the array transposed. + ndarray.reshape : Give a new shape to an array without changing its data. + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4]]) + >>> a + array([[1, 2], + [3, 4]]) + >>> a.transpose() + array([[1, 3], + [2, 4]]) + >>> a.transpose((1, 0)) + array([[1, 3], + [2, 4]]) + >>> a.transpose(1, 0) + array([[1, 3], + [2, 4]]) + + >>> a = np.array([1, 2, 3, 4]) + >>> a + array([1, 2, 3, 4]) + >>> a.transpose() + array([1, 2, 3, 4]) + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('var', + """ + a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True) + + Returns the variance of the array elements, along given axis. + + Refer to `numpy.var` for full documentation. + + See Also + -------- + numpy.var : equivalent function + + """)) + + +add_newdoc('numpy.core.multiarray', 'ndarray', ('view', + """ + a.view([dtype][, type]) + + New view of array with the same data. + + .. note:: + Passing None for ``dtype`` is different from omitting the parameter, + since the former invokes ``dtype(None)`` which is an alias for + ``dtype('float_')``. + + Parameters + ---------- + dtype : data-type or ndarray sub-class, optional + Data-type descriptor of the returned view, e.g., float32 or int16. + Omitting it results in the view having the same data-type as `a`. + This argument can also be specified as an ndarray sub-class, which + then specifies the type of the returned object (this is equivalent to + setting the ``type`` parameter). + type : Python type, optional + Type of the returned view, e.g., ndarray or matrix. Again, omission + of the parameter results in type preservation. + + Notes + ----- + ``a.view()`` is used two different ways: + + ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view + of the array's memory with a different data-type. This can cause a + reinterpretation of the bytes of memory. + + ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just + returns an instance of `ndarray_subclass` that looks at the same array + (same shape, dtype, etc.) This does not cause a reinterpretation of the + memory. + + For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of + bytes per entry than the previous dtype (for example, converting a regular + array to a structured array), then the last axis of ``a`` must be + contiguous. This axis will be resized in the result. + + .. versionchanged:: 1.23.0 + Only the last axis needs to be contiguous. Previously, the entire array + had to be C-contiguous. + + Examples + -------- + >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) + + Viewing array data using a different type and dtype: + + >>> y = x.view(dtype=np.int16, type=np.matrix) + >>> y + matrix([[513]], dtype=int16) + >>> print(type(y)) + + + Creating a view on a structured array so it can be used in calculations + + >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) + >>> xv = x.view(dtype=np.int8).reshape(-1,2) + >>> xv + array([[1, 2], + [3, 4]], dtype=int8) + >>> xv.mean(0) + array([2., 3.]) + + Making changes to the view changes the underlying array + + >>> xv[0,1] = 20 + >>> x + array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')]) + + Using a view to convert an array to a recarray: + + >>> z = x.view(np.recarray) + >>> z.a + array([1, 3], dtype=int8) + + Views share data: + + >>> x[0] = (9, 10) + >>> z[0] + (9, 10) + + Views that change the dtype size (bytes per entry) should normally be + avoided on arrays defined by slices, transposes, fortran-ordering, etc.: + + >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16) + >>> y = x[:, ::2] + >>> y + array([[1, 3], + [4, 6]], dtype=int16) + >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) + Traceback (most recent call last): + ... + ValueError: To change to a dtype of a different size, the last axis must be contiguous + >>> z = y.copy() + >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) + array([[(1, 3)], + [(4, 6)]], dtype=[('width', '>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4) + >>> x.transpose(1, 0, 2).view(np.int16) + array([[[ 256, 770], + [3340, 3854]], + + [[1284, 1798], + [4368, 4882]], + + [[2312, 2826], + [5396, 5910]]], dtype=int16) + + """)) + + +############################################################################## +# +# umath functions +# +############################################################################## + +add_newdoc('numpy.core.umath', 'frompyfunc', + """ + frompyfunc(func, /, nin, nout, *[, identity]) + + Takes an arbitrary Python function and returns a NumPy ufunc. + + Can be used, for example, to add broadcasting to a built-in Python + function (see Examples section). + + Parameters + ---------- + func : Python function object + An arbitrary Python function. + nin : int + The number of input arguments. + nout : int + The number of objects returned by `func`. + identity : object, optional + The value to use for the `~numpy.ufunc.identity` attribute of the resulting + object. If specified, this is equivalent to setting the underlying + C ``identity`` field to ``PyUFunc_IdentityValue``. + If omitted, the identity is set to ``PyUFunc_None``. Note that this is + _not_ equivalent to setting the identity to ``None``, which implies the + operation is reorderable. + + Returns + ------- + out : ufunc + Returns a NumPy universal function (``ufunc``) object. + + See Also + -------- + vectorize : Evaluates pyfunc over input arrays using broadcasting rules of numpy. + + Notes + ----- + The returned ufunc always returns PyObject arrays. + + Examples + -------- + Use frompyfunc to add broadcasting to the Python function ``oct``: + + >>> oct_array = np.frompyfunc(oct, 1, 1) + >>> oct_array(np.array((10, 30, 100))) + array(['0o12', '0o36', '0o144'], dtype=object) + >>> np.array((oct(10), oct(30), oct(100))) # for comparison + array(['0o12', '0o36', '0o144'], dtype='>> np.geterrobj() # first get the defaults + [8192, 521, None] + + >>> def err_handler(type, flag): + ... print("Floating point error (%s), with flag %s" % (type, flag)) + ... + >>> old_bufsize = np.setbufsize(20000) + >>> old_err = np.seterr(divide='raise') + >>> old_handler = np.seterrcall(err_handler) + >>> np.geterrobj() + [8192, 521, ] + + >>> old_err = np.seterr(all='ignore') + >>> np.base_repr(np.geterrobj()[1], 8) + '0' + >>> old_err = np.seterr(divide='warn', over='log', under='call', + ... invalid='print') + >>> np.base_repr(np.geterrobj()[1], 8) + '4351' + + """) + +add_newdoc('numpy.core.umath', 'seterrobj', + """ + seterrobj(errobj, /) + + Set the object that defines floating-point error handling. + + The error object contains all information that defines the error handling + behavior in NumPy. `seterrobj` is used internally by the other + functions that set error handling behavior (`seterr`, `seterrcall`). + + Parameters + ---------- + errobj : list + The error object, a list containing three elements: + [internal numpy buffer size, error mask, error callback function]. + + The error mask is a single integer that holds the treatment information + on all four floating point errors. The information for each error type + is contained in three bits of the integer. If we print it in base 8, we + can see what treatment is set for "invalid", "under", "over", and + "divide" (in that order). The printed string can be interpreted with + + * 0 : 'ignore' + * 1 : 'warn' + * 2 : 'raise' + * 3 : 'call' + * 4 : 'print' + * 5 : 'log' + + See Also + -------- + geterrobj, seterr, geterr, seterrcall, geterrcall + getbufsize, setbufsize + + Notes + ----- + For complete documentation of the types of floating-point exceptions and + treatment options, see `seterr`. + + Examples + -------- + >>> old_errobj = np.geterrobj() # first get the defaults + >>> old_errobj + [8192, 521, None] + + >>> def err_handler(type, flag): + ... print("Floating point error (%s), with flag %s" % (type, flag)) + ... + >>> new_errobj = [20000, 12, err_handler] + >>> np.seterrobj(new_errobj) + >>> np.base_repr(12, 8) # int for divide=4 ('print') and over=1 ('warn') + '14' + >>> np.geterr() + {'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'} + >>> np.geterrcall() is err_handler + True + + """) + + +############################################################################## +# +# compiled_base functions +# +############################################################################## + +add_newdoc('numpy.core.multiarray', 'add_docstring', + """ + add_docstring(obj, docstring) + + Add a docstring to a built-in obj if possible. + If the obj already has a docstring raise a RuntimeError + If this routine does not know how to add a docstring to the object + raise a TypeError + """) + +add_newdoc('numpy.core.umath', '_add_newdoc_ufunc', + """ + add_ufunc_docstring(ufunc, new_docstring) + + Replace the docstring for a ufunc with new_docstring. + This method will only work if the current docstring for + the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.) + + Parameters + ---------- + ufunc : numpy.ufunc + A ufunc whose current doc is NULL. + new_docstring : string + The new docstring for the ufunc. + + Notes + ----- + This method allocates memory for new_docstring on + the heap. Technically this creates a mempory leak, since this + memory will not be reclaimed until the end of the program + even if the ufunc itself is removed. However this will only + be a problem if the user is repeatedly creating ufuncs with + no documentation, adding documentation via add_newdoc_ufunc, + and then throwing away the ufunc. + """) + +add_newdoc('numpy.core.multiarray', 'get_handler_name', + """ + get_handler_name(a: ndarray) -> str,None + + Return the name of the memory handler used by `a`. If not provided, return + the name of the memory handler that will be used to allocate data for the + next `ndarray` in this context. May return None if `a` does not own its + memory, in which case you can traverse ``a.base`` for a memory handler. + """) + +add_newdoc('numpy.core.multiarray', 'get_handler_version', + """ + get_handler_version(a: ndarray) -> int,None + + Return the version of the memory handler used by `a`. If not provided, + return the version of the memory handler that will be used to allocate data + for the next `ndarray` in this context. May return None if `a` does not own + its memory, in which case you can traverse ``a.base`` for a memory handler. + """) + +add_newdoc('numpy.core.multiarray', '_get_madvise_hugepage', + """ + _get_madvise_hugepage() -> bool + + Get use of ``madvise (2)`` MADV_HUGEPAGE support when + allocating the array data. Returns the currently set value. + See `global_state` for more information. + """) + +add_newdoc('numpy.core.multiarray', '_set_madvise_hugepage', + """ + _set_madvise_hugepage(enabled: bool) -> bool + + Set or unset use of ``madvise (2)`` MADV_HUGEPAGE support when + allocating the array data. Returns the previously set value. + See `global_state` for more information. + """) + +add_newdoc('numpy.core._multiarray_tests', 'format_float_OSprintf_g', + """ + format_float_OSprintf_g(val, precision) + + Print a floating point scalar using the system's printf function, + equivalent to: + + printf("%.*g", precision, val); + + for half/float/double, or replacing 'g' by 'Lg' for longdouble. This + method is designed to help cross-validate the format_float_* methods. + + Parameters + ---------- + val : python float or numpy floating scalar + Value to format. + + precision : non-negative integer, optional + Precision given to printf. + + Returns + ------- + rep : string + The string representation of the floating point value + + See Also + -------- + format_float_scientific + format_float_positional + """) + + +############################################################################## +# +# Documentation for ufunc attributes and methods +# +############################################################################## + + +############################################################################## +# +# ufunc object +# +############################################################################## + +add_newdoc('numpy.core', 'ufunc', + """ + Functions that operate element by element on whole arrays. + + To see the documentation for a specific ufunc, use `info`. For + example, ``np.info(np.sin)``. Because ufuncs are written in C + (for speed) and linked into Python with NumPy's ufunc facility, + Python's help() function finds this page whenever help() is called + on a ufunc. + + A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`. + + **Calling ufuncs:** ``op(*x[, out], where=True, **kwargs)`` + + Apply `op` to the arguments `*x` elementwise, broadcasting the arguments. + + The broadcasting rules are: + + * Dimensions of length 1 may be prepended to either array. + * Arrays may be repeated along dimensions of length 1. + + Parameters + ---------- + *x : array_like + Input arrays. + out : ndarray, None, or tuple of ndarray and None, optional + Alternate array object(s) in which to put the result; if provided, it + must have a shape that the inputs broadcast to. A tuple of arrays + (possible only as a keyword argument) must have length equal to the + number of outputs; use None for uninitialized outputs to be + allocated by the ufunc. + where : array_like, optional + This condition is broadcast over the input. At locations where the + condition is True, the `out` array will be set to the ufunc result. + Elsewhere, the `out` array will retain its original value. + Note that if an uninitialized `out` array is created via the default + ``out=None``, locations within it where the condition is False will + remain uninitialized. + **kwargs + For other keyword-only arguments, see the :ref:`ufunc docs `. + + Returns + ------- + r : ndarray or tuple of ndarray + `r` will have the shape that the arrays in `x` broadcast to; if `out` is + provided, it will be returned. If not, `r` will be allocated and + may contain uninitialized values. If the function has more than one + output, then the result will be a tuple of arrays. + + """) + + +############################################################################## +# +# ufunc attributes +# +############################################################################## + +add_newdoc('numpy.core', 'ufunc', ('identity', + """ + The identity value. + + Data attribute containing the identity element for the ufunc, if it has one. + If it does not, the attribute value is None. + + Examples + -------- + >>> np.add.identity + 0 + >>> np.multiply.identity + 1 + >>> np.power.identity + 1 + >>> print(np.exp.identity) + None + """)) + +add_newdoc('numpy.core', 'ufunc', ('nargs', + """ + The number of arguments. + + Data attribute containing the number of arguments the ufunc takes, including + optional ones. + + Notes + ----- + Typically this value will be one more than what you might expect because all + ufuncs take the optional "out" argument. + + Examples + -------- + >>> np.add.nargs + 3 + >>> np.multiply.nargs + 3 + >>> np.power.nargs + 3 + >>> np.exp.nargs + 2 + """)) + +add_newdoc('numpy.core', 'ufunc', ('nin', + """ + The number of inputs. + + Data attribute containing the number of arguments the ufunc treats as input. + + Examples + -------- + >>> np.add.nin + 2 + >>> np.multiply.nin + 2 + >>> np.power.nin + 2 + >>> np.exp.nin + 1 + """)) + +add_newdoc('numpy.core', 'ufunc', ('nout', + """ + The number of outputs. + + Data attribute containing the number of arguments the ufunc treats as output. + + Notes + ----- + Since all ufuncs can take output arguments, this will always be (at least) 1. + + Examples + -------- + >>> np.add.nout + 1 + >>> np.multiply.nout + 1 + >>> np.power.nout + 1 + >>> np.exp.nout + 1 + + """)) + +add_newdoc('numpy.core', 'ufunc', ('ntypes', + """ + The number of types. + + The number of numerical NumPy types - of which there are 18 total - on which + the ufunc can operate. + + See Also + -------- + numpy.ufunc.types + + Examples + -------- + >>> np.add.ntypes + 18 + >>> np.multiply.ntypes + 18 + >>> np.power.ntypes + 17 + >>> np.exp.ntypes + 7 + >>> np.remainder.ntypes + 14 + + """)) + +add_newdoc('numpy.core', 'ufunc', ('types', + """ + Returns a list with types grouped input->output. + + Data attribute listing the data-type "Domain-Range" groupings the ufunc can + deliver. The data-types are given using the character codes. + + See Also + -------- + numpy.ufunc.ntypes + + Examples + -------- + >>> np.add.types + ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', + 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', + 'GG->G', 'OO->O'] + + >>> np.multiply.types + ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', + 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', + 'GG->G', 'OO->O'] + + >>> np.power.types + ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', + 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G', + 'OO->O'] + + >>> np.exp.types + ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O'] + + >>> np.remainder.types + ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', + 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O'] + + """)) + +add_newdoc('numpy.core', 'ufunc', ('signature', + """ + Definition of the core elements a generalized ufunc operates on. + + The signature determines how the dimensions of each input/output array + are split into core and loop dimensions: + + 1. Each dimension in the signature is matched to a dimension of the + corresponding passed-in array, starting from the end of the shape tuple. + 2. Core dimensions assigned to the same label in the signature must have + exactly matching sizes, no broadcasting is performed. + 3. The core dimensions are removed from all inputs and the remaining + dimensions are broadcast together, defining the loop dimensions. + + Notes + ----- + Generalized ufuncs are used internally in many linalg functions, and in + the testing suite; the examples below are taken from these. + For ufuncs that operate on scalars, the signature is None, which is + equivalent to '()' for every argument. + + Examples + -------- + >>> np.core.umath_tests.matrix_multiply.signature + '(m,n),(n,p)->(m,p)' + >>> np.linalg._umath_linalg.det.signature + '(m,m)->()' + >>> np.add.signature is None + True # equivalent to '(),()->()' + """)) + +############################################################################## +# +# ufunc methods +# +############################################################################## + +add_newdoc('numpy.core', 'ufunc', ('reduce', + """ + reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=, where=True) + + Reduces `array`'s dimension by one, by applying ufunc along one axis. + + Let :math:`array.shape = (N_0, ..., N_i, ..., N_{M-1})`. Then + :math:`ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` = + the result of iterating `j` over :math:`range(N_i)`, cumulatively applying + ufunc to each :math:`array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`. + For a one-dimensional array, reduce produces results equivalent to: + :: + + r = op.identity # op = ufunc + for i in range(len(A)): + r = op(r, A[i]) + return r + + For example, add.reduce() is equivalent to sum(). + + Parameters + ---------- + array : array_like + The array to act on. + axis : None or int or tuple of ints, optional + Axis or axes along which a reduction is performed. + The default (`axis` = 0) is perform a reduction over the first + dimension of the input array. `axis` may be negative, in + which case it counts from the last to the first axis. + + .. versionadded:: 1.7.0 + + If this is None, a reduction is performed over all the axes. + If this is a tuple of ints, a reduction is performed on multiple + axes, instead of a single axis or all the axes as before. + + For operations which are either not commutative or not associative, + doing a reduction over multiple axes is not well-defined. The + ufuncs do not currently raise an exception in this case, but will + likely do so in the future. + dtype : data-type code, optional + The type used to represent the intermediate results. Defaults + to the data-type of the output array if this is provided, or + the data-type of the input array if no output array is provided. + out : ndarray, None, or tuple of ndarray and None, optional + A location into which the result is stored. If not provided or None, + a freshly-allocated array is returned. For consistency with + ``ufunc.__call__``, if given as a keyword, this may be wrapped in a + 1-element tuple. + + .. versionchanged:: 1.13.0 + Tuples are allowed for keyword argument. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the original `array`. + + .. versionadded:: 1.7.0 + initial : scalar, optional + The value with which to start the reduction. + If the ufunc has no identity or the dtype is object, this defaults + to None - otherwise it defaults to ufunc.identity. + If ``None`` is given, the first element of the reduction is used, + and an error is thrown if the reduction is empty. + + .. versionadded:: 1.15.0 + + where : array_like of bool, optional + A boolean array which is broadcasted to match the dimensions + of `array`, and selects elements to include in the reduction. Note + that for ufuncs like ``minimum`` that do not have an identity + defined, one has to pass in also ``initial``. + + .. versionadded:: 1.17.0 + + Returns + ------- + r : ndarray + The reduced array. If `out` was supplied, `r` is a reference to it. + + Examples + -------- + >>> np.multiply.reduce([2,3,5]) + 30 + + A multi-dimensional array example: + + >>> X = np.arange(8).reshape((2,2,2)) + >>> X + array([[[0, 1], + [2, 3]], + [[4, 5], + [6, 7]]]) + >>> np.add.reduce(X, 0) + array([[ 4, 6], + [ 8, 10]]) + >>> np.add.reduce(X) # confirm: default axis value is 0 + array([[ 4, 6], + [ 8, 10]]) + >>> np.add.reduce(X, 1) + array([[ 2, 4], + [10, 12]]) + >>> np.add.reduce(X, 2) + array([[ 1, 5], + [ 9, 13]]) + + You can use the ``initial`` keyword argument to initialize the reduction + with a different value, and ``where`` to select specific elements to include: + + >>> np.add.reduce([10], initial=5) + 15 + >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10) + array([14., 14.]) + >>> a = np.array([10., np.nan, 10]) + >>> np.add.reduce(a, where=~np.isnan(a)) + 20.0 + + Allows reductions of empty arrays where they would normally fail, i.e. + for ufuncs without an identity. + + >>> np.minimum.reduce([], initial=np.inf) + inf + >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False]) + array([ 1., 10.]) + >>> np.minimum.reduce([]) + Traceback (most recent call last): + ... + ValueError: zero-size array to reduction operation minimum which has no identity + """)) + +add_newdoc('numpy.core', 'ufunc', ('accumulate', + """ + accumulate(array, axis=0, dtype=None, out=None) + + Accumulate the result of applying the operator to all elements. + + For a one-dimensional array, accumulate produces results equivalent to:: + + r = np.empty(len(A)) + t = op.identity # op = the ufunc being applied to A's elements + for i in range(len(A)): + t = op(t, A[i]) + r[i] = t + return r + + For example, add.accumulate() is equivalent to np.cumsum(). + + For a multi-dimensional array, accumulate is applied along only one + axis (axis zero by default; see Examples below) so repeated use is + necessary if one wants to accumulate over multiple axes. + + Parameters + ---------- + array : array_like + The array to act on. + axis : int, optional + The axis along which to apply the accumulation; default is zero. + dtype : data-type code, optional + The data-type used to represent the intermediate results. Defaults + to the data-type of the output array if such is provided, or the + data-type of the input array if no output array is provided. + out : ndarray, None, or tuple of ndarray and None, optional + A location into which the result is stored. If not provided or None, + a freshly-allocated array is returned. For consistency with + ``ufunc.__call__``, if given as a keyword, this may be wrapped in a + 1-element tuple. + + .. versionchanged:: 1.13.0 + Tuples are allowed for keyword argument. + + Returns + ------- + r : ndarray + The accumulated values. If `out` was supplied, `r` is a reference to + `out`. + + Examples + -------- + 1-D array examples: + + >>> np.add.accumulate([2, 3, 5]) + array([ 2, 5, 10]) + >>> np.multiply.accumulate([2, 3, 5]) + array([ 2, 6, 30]) + + 2-D array examples: + + >>> I = np.eye(2) + >>> I + array([[1., 0.], + [0., 1.]]) + + Accumulate along axis 0 (rows), down columns: + + >>> np.add.accumulate(I, 0) + array([[1., 0.], + [1., 1.]]) + >>> np.add.accumulate(I) # no axis specified = axis zero + array([[1., 0.], + [1., 1.]]) + + Accumulate along axis 1 (columns), through rows: + + >>> np.add.accumulate(I, 1) + array([[1., 1.], + [0., 1.]]) + + """)) + +add_newdoc('numpy.core', 'ufunc', ('reduceat', + """ + reduceat(array, indices, axis=0, dtype=None, out=None) + + Performs a (local) reduce with specified slices over a single axis. + + For i in ``range(len(indices))``, `reduceat` computes + ``ufunc.reduce(array[indices[i]:indices[i+1]])``, which becomes the i-th + generalized "row" parallel to `axis` in the final result (i.e., in a + 2-D array, for example, if `axis = 0`, it becomes the i-th row, but if + `axis = 1`, it becomes the i-th column). There are three exceptions to this: + + * when ``i = len(indices) - 1`` (so for the last index), + ``indices[i+1] = array.shape[axis]``. + * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is + simply ``array[indices[i]]``. + * if ``indices[i] >= len(array)`` or ``indices[i] < 0``, an error is raised. + + The shape of the output depends on the size of `indices`, and may be + larger than `array` (this happens if ``len(indices) > array.shape[axis]``). + + Parameters + ---------- + array : array_like + The array to act on. + indices : array_like + Paired indices, comma separated (not colon), specifying slices to + reduce. + axis : int, optional + The axis along which to apply the reduceat. + dtype : data-type code, optional + The type used to represent the intermediate results. Defaults + to the data type of the output array if this is provided, or + the data type of the input array if no output array is provided. + out : ndarray, None, or tuple of ndarray and None, optional + A location into which the result is stored. If not provided or None, + a freshly-allocated array is returned. For consistency with + ``ufunc.__call__``, if given as a keyword, this may be wrapped in a + 1-element tuple. + + .. versionchanged:: 1.13.0 + Tuples are allowed for keyword argument. + + Returns + ------- + r : ndarray + The reduced values. If `out` was supplied, `r` is a reference to + `out`. + + Notes + ----- + A descriptive example: + + If `array` is 1-D, the function `ufunc.accumulate(array)` is the same as + ``ufunc.reduceat(array, indices)[::2]`` where `indices` is + ``range(len(array) - 1)`` with a zero placed + in every other element: + ``indices = zeros(2 * len(array) - 1)``, + ``indices[1::2] = range(1, len(array))``. + + Don't be fooled by this attribute's name: `reduceat(array)` is not + necessarily smaller than `array`. + + Examples + -------- + To take the running sum of four successive values: + + >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2] + array([ 6, 10, 14, 18]) + + A 2-D example: + + >>> x = np.linspace(0, 15, 16).reshape(4,4) + >>> x + array([[ 0., 1., 2., 3.], + [ 4., 5., 6., 7.], + [ 8., 9., 10., 11.], + [12., 13., 14., 15.]]) + + :: + + # reduce such that the result has the following five rows: + # [row1 + row2 + row3] + # [row4] + # [row2] + # [row3] + # [row1 + row2 + row3 + row4] + + >>> np.add.reduceat(x, [0, 3, 1, 2, 0]) + array([[12., 15., 18., 21.], + [12., 13., 14., 15.], + [ 4., 5., 6., 7.], + [ 8., 9., 10., 11.], + [24., 28., 32., 36.]]) + + :: + + # reduce such that result has the following two columns: + # [col1 * col2 * col3, col4] + + >>> np.multiply.reduceat(x, [0, 3], 1) + array([[ 0., 3.], + [ 120., 7.], + [ 720., 11.], + [2184., 15.]]) + + """)) + +add_newdoc('numpy.core', 'ufunc', ('outer', + r""" + outer(A, B, /, **kwargs) + + Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`. + + Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of + ``op.outer(A, B)`` is an array of dimension M + N such that: + + .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] = + op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}]) + + For `A` and `B` one-dimensional, this is equivalent to:: + + r = empty(len(A),len(B)) + for i in range(len(A)): + for j in range(len(B)): + r[i,j] = op(A[i], B[j]) # op = ufunc in question + + Parameters + ---------- + A : array_like + First array + B : array_like + Second array + kwargs : any + Arguments to pass on to the ufunc. Typically `dtype` or `out`. + See `ufunc` for a comprehensive overview of all available arguments. + + Returns + ------- + r : ndarray + Output array + + See Also + -------- + numpy.outer : A less powerful version of ``np.multiply.outer`` + that `ravel`\ s all inputs to 1D. This exists + primarily for compatibility with old code. + + tensordot : ``np.tensordot(a, b, axes=((), ()))`` and + ``np.multiply.outer(a, b)`` behave same for all + dimensions of a and b. + + Examples + -------- + >>> np.multiply.outer([1, 2, 3], [4, 5, 6]) + array([[ 4, 5, 6], + [ 8, 10, 12], + [12, 15, 18]]) + + A multi-dimensional example: + + >>> A = np.array([[1, 2, 3], [4, 5, 6]]) + >>> A.shape + (2, 3) + >>> B = np.array([[1, 2, 3, 4]]) + >>> B.shape + (1, 4) + >>> C = np.multiply.outer(A, B) + >>> C.shape; C + (2, 3, 1, 4) + array([[[[ 1, 2, 3, 4]], + [[ 2, 4, 6, 8]], + [[ 3, 6, 9, 12]]], + [[[ 4, 8, 12, 16]], + [[ 5, 10, 15, 20]], + [[ 6, 12, 18, 24]]]]) + + """)) + +add_newdoc('numpy.core', 'ufunc', ('at', + """ + at(a, indices, b=None, /) + + Performs unbuffered in place operation on operand 'a' for elements + specified by 'indices'. For addition ufunc, this method is equivalent to + ``a[indices] += b``, except that results are accumulated for elements that + are indexed more than once. For example, ``a[[0,0]] += 1`` will only + increment the first element once because of buffering, whereas + ``add.at(a, [0,0], 1)`` will increment the first element twice. + + .. versionadded:: 1.8.0 + + Parameters + ---------- + a : array_like + The array to perform in place operation on. + indices : array_like or tuple + Array like index object or slice object for indexing into first + operand. If first operand has multiple dimensions, indices can be a + tuple of array like index objects or slice objects. + b : array_like + Second operand for ufuncs requiring two operands. Operand must be + broadcastable over first operand after indexing or slicing. + + Examples + -------- + Set items 0 and 1 to their negative values: + + >>> a = np.array([1, 2, 3, 4]) + >>> np.negative.at(a, [0, 1]) + >>> a + array([-1, -2, 3, 4]) + + Increment items 0 and 1, and increment item 2 twice: + + >>> a = np.array([1, 2, 3, 4]) + >>> np.add.at(a, [0, 1, 2, 2], 1) + >>> a + array([2, 3, 5, 4]) + + Add items 0 and 1 in first array to second array, + and store results in first array: + + >>> a = np.array([1, 2, 3, 4]) + >>> b = np.array([1, 2]) + >>> np.add.at(a, [0, 1], b) + >>> a + array([2, 4, 3, 4]) + + """)) + +add_newdoc('numpy.core', 'ufunc', ('resolve_dtypes', + """ + resolve_dtypes(dtypes, *, signature=None, casting=None, reduction=False) + + Find the dtypes NumPy will use for the operation. Both input and + output dtypes are returned and may differ from those provided. + + .. note:: + + This function always applies NEP 50 rules since it is not provided + any actual values. The Python types ``int``, ``float``, and + ``complex`` thus behave weak and should be passed for "untyped" + Python input. + + Parameters + ---------- + dtypes : tuple of dtypes, None, or literal int, float, complex + The input dtypes for each operand. Output operands can be + None, indicating that the dtype must be found. + signature : tuple of DTypes or None, optional + If given, enforces exact DType (classes) of the specific operand. + The ufunc ``dtype`` argument is equivalent to passing a tuple with + only output dtypes set. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + The casting mode when casting is necessary. This is identical to + the ufunc call casting modes. + reduction : boolean + If given, the resolution assumes a reduce operation is happening + which slightly changes the promotion and type resolution rules. + `dtypes` is usually something like ``(None, np.dtype("i2"), None)`` + for reductions (first input is also the output). + + .. note:: + + The default casting mode is "same_kind", however, as of + NumPy 1.24, NumPy uses "unsafe" for reductions. + + Returns + ------- + dtypes : tuple of dtypes + The dtypes which NumPy would use for the calculation. Note that + dtypes may not match the passed in ones (casting is necessary). + + See Also + -------- + numpy.ufunc._resolve_dtypes_and_context : + Similar function to this, but returns additional information which + give access to the core C functionality of NumPy. + + Examples + -------- + This API requires passing dtypes, define them for convenience: + + >>> int32 = np.dtype("int32") + >>> float32 = np.dtype("float32") + + The typical ufunc call does not pass an output dtype. `np.add` has two + inputs and one output, so leave the output as ``None`` (not provided): + + >>> np.add.resolve_dtypes((int32, float32, None)) + (dtype('float64'), dtype('float64'), dtype('float64')) + + The loop found uses "float64" for all operands (including the output), the + first input would be cast. + + ``resolve_dtypes`` supports "weak" handling for Python scalars by passing + ``int``, ``float``, or ``complex``: + + >>> np.add.resolve_dtypes((float32, float, None)) + (dtype('float32'), dtype('float32'), dtype('float32')) + + Where the Python ``float`` behaves samilar to a Python value ``0.0`` + in a ufunc call. (See :ref:`NEP 50 ` for details.) + + """)) + +add_newdoc('numpy.core', 'ufunc', ('_resolve_dtypes_and_context', + """ + _resolve_dtypes_and_context(dtypes, *, signature=None, casting=None, reduction=False) + + See `numpy.ufunc.resolve_dtypes` for parameter information. This + function is considered *unstable*. You may use it, but the returned + information is NumPy version specific and expected to change. + Large API/ABI changes are not expected, but a new NumPy version is + expected to require updating code using this functionality. + + This function is designed to be used in conjunction with + `numpy.ufunc._get_strided_loop`. The calls are split to mirror the C API + and allow future improvements. + + Returns + ------- + dtypes : tuple of dtypes + call_info : + PyCapsule with all necessary information to get access to low level + C calls. See `numpy.ufunc._get_strided_loop` for more information. + + """)) + +add_newdoc('numpy.core', 'ufunc', ('_get_strided_loop', + """ + _get_strided_loop(call_info, /, *, fixed_strides=None) + + This function fills in the ``call_info`` capsule to include all + information necessary to call the low-level strided loop from NumPy. + + See notes for more information. + + Parameters + ---------- + call_info : PyCapsule + The PyCapsule returned by `numpy.ufunc._resolve_dtypes_and_context`. + fixed_strides : tuple of int or None, optional + A tuple with fixed byte strides of all input arrays. NumPy may use + this information to find specialized loops, so any call must follow + the given stride. Use ``None`` to indicate that the stride is not + known (or not fixed) for all calls. + + Notes + ----- + Together with `numpy.ufunc._resolve_dtypes_and_context` this function + gives low-level access to the NumPy ufunc loops. + The first function does general preparation and returns the required + information. It returns this as a C capsule with the version specific + name ``numpy_1.24_ufunc_call_info``. + The NumPy 1.24 ufunc call info capsule has the following layout:: + + typedef struct { + PyArrayMethod_StridedLoop *strided_loop; + PyArrayMethod_Context *context; + NpyAuxData *auxdata; + + /* Flag information (expected to change) */ + npy_bool requires_pyapi; /* GIL is required by loop */ + + /* Loop doesn't set FPE flags; if not set check FPE flags */ + npy_bool no_floatingpoint_errors; + } ufunc_call_info; + + Note that the first call only fills in the ``context``. The call to + ``_get_strided_loop`` fills in all other data. + Please see the ``numpy/experimental_dtype_api.h`` header for exact + call information; the main thing to note is that the new-style loops + return 0 on success, -1 on failure. They are passed context as new + first input and ``auxdata`` as (replaced) last. + + Only the ``strided_loop``signature is considered guaranteed stable + for NumPy bug-fix releases. All other API is tied to the experimental + API versioning. + + The reason for the split call is that cast information is required to + decide what the fixed-strides will be. + + NumPy ties the lifetime of the ``auxdata`` information to the capsule. + + """)) + + + +############################################################################## +# +# Documentation for dtype attributes and methods +# +############################################################################## + +############################################################################## +# +# dtype object +# +############################################################################## + +add_newdoc('numpy.core.multiarray', 'dtype', + """ + dtype(dtype, align=False, copy=False, [metadata]) + + Create a data type object. + + A numpy array is homogeneous, and contains elements described by a + dtype object. A dtype object can be constructed from different + combinations of fundamental numeric types. + + Parameters + ---------- + dtype + Object to be converted to a data type object. + align : bool, optional + Add padding to the fields to match what a C compiler would output + for a similar C-struct. Can be ``True`` only if `obj` is a dictionary + or a comma-separated string. If a struct dtype is being created, + this also sets a sticky alignment flag ``isalignedstruct``. + copy : bool, optional + Make a new copy of the data-type object. If ``False``, the result + may just be a reference to a built-in data-type object. + metadata : dict, optional + An optional dictionary with dtype metadata. + + See also + -------- + result_type + + Examples + -------- + Using array-scalar type: + + >>> np.dtype(np.int16) + dtype('int16') + + Structured type, one field name 'f1', containing int16: + + >>> np.dtype([('f1', np.int16)]) + dtype([('f1', '>> np.dtype([('f1', [('f1', np.int16)])]) + dtype([('f1', [('f1', '>> np.dtype([('f1', np.uint64), ('f2', np.int32)]) + dtype([('f1', '>> np.dtype([('a','f8'),('b','S10')]) + dtype([('a', '>> np.dtype("i4, (2,3)f8") + dtype([('f0', '>> np.dtype([('hello',(np.int64,3)),('world',np.void,10)]) + dtype([('hello', '>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)})) + dtype((numpy.int16, [('x', 'i1'), ('y', 'i1')])) + + Using dictionaries. Two fields named 'gender' and 'age': + + >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]}) + dtype([('gender', 'S1'), ('age', 'u1')]) + + Offsets in bytes, here 0 and 25: + + >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)}) + dtype([('surname', 'S25'), ('age', 'u1')]) + + """) + +############################################################################## +# +# dtype attributes +# +############################################################################## + +add_newdoc('numpy.core.multiarray', 'dtype', ('alignment', + """ + The required alignment (bytes) of this data-type according to the compiler. + + More information is available in the C-API section of the manual. + + Examples + -------- + + >>> x = np.dtype('i4') + >>> x.alignment + 4 + + >>> x = np.dtype(float) + >>> x.alignment + 8 + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('byteorder', + """ + A character indicating the byte-order of this data-type object. + + One of: + + === ============== + '=' native + '<' little-endian + '>' big-endian + '|' not applicable + === ============== + + All built-in data-type objects have byteorder either '=' or '|'. + + Examples + -------- + + >>> dt = np.dtype('i2') + >>> dt.byteorder + '=' + >>> # endian is not relevant for 8 bit numbers + >>> np.dtype('i1').byteorder + '|' + >>> # or ASCII strings + >>> np.dtype('S2').byteorder + '|' + >>> # Even if specific code is given, and it is native + >>> # '=' is the byteorder + >>> import sys + >>> sys_is_le = sys.byteorder == 'little' + >>> native_code = '<' if sys_is_le else '>' + >>> swapped_code = '>' if sys_is_le else '<' + >>> dt = np.dtype(native_code + 'i2') + >>> dt.byteorder + '=' + >>> # Swapped code shows up as itself + >>> dt = np.dtype(swapped_code + 'i2') + >>> dt.byteorder == swapped_code + True + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('char', + """A unique character code for each of the 21 different built-in types. + + Examples + -------- + + >>> x = np.dtype(float) + >>> x.char + 'd' + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('descr', + """ + `__array_interface__` description of the data-type. + + The format is that required by the 'descr' key in the + `__array_interface__` attribute. + + Warning: This attribute exists specifically for `__array_interface__`, + and passing it directly to `np.dtype` will not accurately reconstruct + some dtypes (e.g., scalar and subarray dtypes). + + Examples + -------- + + >>> x = np.dtype(float) + >>> x.descr + [('', '>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) + >>> dt.descr + [('name', '>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) + >>> print(dt.fields) + {'grades': (dtype(('float64',(2,))), 16), 'name': (dtype('|S16'), 0)} + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('flags', + """ + Bit-flags describing how this data type is to be interpreted. + + Bit-masks are in `numpy.core.multiarray` as the constants + `ITEM_HASOBJECT`, `LIST_PICKLE`, `ITEM_IS_POINTER`, `NEEDS_INIT`, + `NEEDS_PYAPI`, `USE_GETITEM`, `USE_SETITEM`. A full explanation + of these flags is in C-API documentation; they are largely useful + for user-defined data-types. + + The following example demonstrates that operations on this particular + dtype requires Python C-API. + + Examples + -------- + + >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)]) + >>> x.flags + 16 + >>> np.core.multiarray.NEEDS_PYAPI + 16 + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('hasobject', + """ + Boolean indicating whether this dtype contains any reference-counted + objects in any fields or sub-dtypes. + + Recall that what is actually in the ndarray memory representing + the Python object is the memory address of that object (a pointer). + Special handling may be required, and this attribute is useful for + distinguishing data types that may contain arbitrary Python objects + and data-types that won't. + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('isbuiltin', + """ + Integer indicating how this dtype relates to the built-in dtypes. + + Read-only. + + = ======================================================================== + 0 if this is a structured array type, with fields + 1 if this is a dtype compiled into numpy (such as ints, floats etc) + 2 if the dtype is for a user-defined numpy type + A user-defined type uses the numpy C-API machinery to extend + numpy to handle a new array type. See + :ref:`user.user-defined-data-types` in the NumPy manual. + = ======================================================================== + + Examples + -------- + >>> dt = np.dtype('i2') + >>> dt.isbuiltin + 1 + >>> dt = np.dtype('f8') + >>> dt.isbuiltin + 1 + >>> dt = np.dtype([('field1', 'f8')]) + >>> dt.isbuiltin + 0 + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('isnative', + """ + Boolean indicating whether the byte order of this dtype is native + to the platform. + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('isalignedstruct', + """ + Boolean indicating whether the dtype is a struct which maintains + field alignment. This flag is sticky, so when combining multiple + structs together, it is preserved and produces new dtypes which + are also aligned. + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('itemsize', + """ + The element size of this data-type object. + + For 18 of the 21 types this number is fixed by the data-type. + For the flexible data-types, this number can be anything. + + Examples + -------- + + >>> arr = np.array([[1, 2], [3, 4]]) + >>> arr.dtype + dtype('int64') + >>> arr.itemsize + 8 + + >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) + >>> dt.itemsize + 80 + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('kind', + """ + A character code (one of 'biufcmMOSUV') identifying the general kind of data. + + = ====================== + b boolean + i signed integer + u unsigned integer + f floating-point + c complex floating-point + m timedelta + M datetime + O object + S (byte-)string + U Unicode + V void + = ====================== + + Examples + -------- + + >>> dt = np.dtype('i4') + >>> dt.kind + 'i' + >>> dt = np.dtype('f8') + >>> dt.kind + 'f' + >>> dt = np.dtype([('field1', 'f8')]) + >>> dt.kind + 'V' + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('metadata', + """ + Either ``None`` or a readonly dictionary of metadata (mappingproxy). + + The metadata field can be set using any dictionary at data-type + creation. NumPy currently has no uniform approach to propagating + metadata; although some array operations preserve it, there is no + guarantee that others will. + + .. warning:: + + Although used in certain projects, this feature was long undocumented + and is not well supported. Some aspects of metadata propagation + are expected to change in the future. + + Examples + -------- + + >>> dt = np.dtype(float, metadata={"key": "value"}) + >>> dt.metadata["key"] + 'value' + >>> arr = np.array([1, 2, 3], dtype=dt) + >>> arr.dtype.metadata + mappingproxy({'key': 'value'}) + + Adding arrays with identical datatypes currently preserves the metadata: + + >>> (arr + arr).dtype.metadata + mappingproxy({'key': 'value'}) + + But if the arrays have different dtype metadata, the metadata may be + dropped: + + >>> dt2 = np.dtype(float, metadata={"key2": "value2"}) + >>> arr2 = np.array([3, 2, 1], dtype=dt2) + >>> (arr + arr2).dtype.metadata is None + True # The metadata field is cleared so None is returned + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('name', + """ + A bit-width name for this data-type. + + Un-sized flexible data-type objects do not have this attribute. + + Examples + -------- + + >>> x = np.dtype(float) + >>> x.name + 'float64' + >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)]) + >>> x.name + 'void640' + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('names', + """ + Ordered list of field names, or ``None`` if there are no fields. + + The names are ordered according to increasing byte offset. This can be + used, for example, to walk through all of the named fields in offset order. + + Examples + -------- + >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) + >>> dt.names + ('name', 'grades') + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('num', + """ + A unique number for each of the 21 different built-in types. + + These are roughly ordered from least-to-most precision. + + Examples + -------- + + >>> dt = np.dtype(str) + >>> dt.num + 19 + + >>> dt = np.dtype(float) + >>> dt.num + 12 + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('shape', + """ + Shape tuple of the sub-array if this data type describes a sub-array, + and ``()`` otherwise. + + Examples + -------- + + >>> dt = np.dtype(('i4', 4)) + >>> dt.shape + (4,) + + >>> dt = np.dtype(('i4', (2, 3))) + >>> dt.shape + (2, 3) + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('ndim', + """ + Number of dimensions of the sub-array if this data type describes a + sub-array, and ``0`` otherwise. + + .. versionadded:: 1.13.0 + + Examples + -------- + >>> x = np.dtype(float) + >>> x.ndim + 0 + + >>> x = np.dtype((float, 8)) + >>> x.ndim + 1 + + >>> x = np.dtype(('i4', (3, 4))) + >>> x.ndim + 2 + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('str', + """The array-protocol typestring of this data-type object.""")) + +add_newdoc('numpy.core.multiarray', 'dtype', ('subdtype', + """ + Tuple ``(item_dtype, shape)`` if this `dtype` describes a sub-array, and + None otherwise. + + The *shape* is the fixed shape of the sub-array described by this + data type, and *item_dtype* the data type of the array. + + If a field whose dtype object has this attribute is retrieved, + then the extra dimensions implied by *shape* are tacked on to + the end of the retrieved array. + + See Also + -------- + dtype.base + + Examples + -------- + >>> x = numpy.dtype('8f') + >>> x.subdtype + (dtype('float32'), (8,)) + + >>> x = numpy.dtype('i2') + >>> x.subdtype + >>> + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('base', + """ + Returns dtype for the base element of the subarrays, + regardless of their dimension or shape. + + See Also + -------- + dtype.subdtype + + Examples + -------- + >>> x = numpy.dtype('8f') + >>> x.base + dtype('float32') + + >>> x = numpy.dtype('i2') + >>> x.base + dtype('int16') + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('type', + """The type object used to instantiate a scalar of this data-type.""")) + +############################################################################## +# +# dtype methods +# +############################################################################## + +add_newdoc('numpy.core.multiarray', 'dtype', ('newbyteorder', + """ + newbyteorder(new_order='S', /) + + Return a new dtype with a different byte order. + + Changes are also made in all fields and sub-arrays of the data type. + + Parameters + ---------- + new_order : string, optional + Byte order to force; a value from the byte order specifications + below. The default value ('S') results in swapping the current + byte order. `new_order` codes can be any of: + + * 'S' - swap dtype from current to opposite endian + * {'<', 'little'} - little endian + * {'>', 'big'} - big endian + * {'=', 'native'} - native order + * {'|', 'I'} - ignore (no change to byte order) + + Returns + ------- + new_dtype : dtype + New dtype object with the given change to the byte order. + + Notes + ----- + Changes are also made in all fields and sub-arrays of the data type. + + Examples + -------- + >>> import sys + >>> sys_is_le = sys.byteorder == 'little' + >>> native_code = '<' if sys_is_le else '>' + >>> swapped_code = '>' if sys_is_le else '<' + >>> native_dt = np.dtype(native_code+'i2') + >>> swapped_dt = np.dtype(swapped_code+'i2') + >>> native_dt.newbyteorder('S') == swapped_dt + True + >>> native_dt.newbyteorder() == swapped_dt + True + >>> native_dt == swapped_dt.newbyteorder('S') + True + >>> native_dt == swapped_dt.newbyteorder('=') + True + >>> native_dt == swapped_dt.newbyteorder('N') + True + >>> native_dt == native_dt.newbyteorder('|') + True + >>> np.dtype('>> np.dtype('>> np.dtype('>i2') == native_dt.newbyteorder('>') + True + >>> np.dtype('>i2') == native_dt.newbyteorder('B') + True + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('__class_getitem__', + """ + __class_getitem__(item, /) + + Return a parametrized wrapper around the `~numpy.dtype` type. + + .. versionadded:: 1.22 + + Returns + ------- + alias : types.GenericAlias + A parametrized `~numpy.dtype` type. + + Examples + -------- + >>> import numpy as np + + >>> np.dtype[np.int64] + numpy.dtype[numpy.int64] + + See Also + -------- + :pep:`585` : Type hinting generics in standard collections. + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('__ge__', + """ + __ge__(value, /) + + Return ``self >= value``. + + Equivalent to ``np.can_cast(value, self, casting="safe")``. + + See Also + -------- + can_cast : Returns True if cast between data types can occur according to + the casting rule. + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('__le__', + """ + __le__(value, /) + + Return ``self <= value``. + + Equivalent to ``np.can_cast(self, value, casting="safe")``. + + See Also + -------- + can_cast : Returns True if cast between data types can occur according to + the casting rule. + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('__gt__', + """ + __ge__(value, /) + + Return ``self > value``. + + Equivalent to + ``self != value and np.can_cast(value, self, casting="safe")``. + + See Also + -------- + can_cast : Returns True if cast between data types can occur according to + the casting rule. + + """)) + +add_newdoc('numpy.core.multiarray', 'dtype', ('__lt__', + """ + __lt__(value, /) + + Return ``self < value``. + + Equivalent to + ``self != value and np.can_cast(self, value, casting="safe")``. + + See Also + -------- + can_cast : Returns True if cast between data types can occur according to + the casting rule. + + """)) + +############################################################################## +# +# Datetime-related Methods +# +############################################################################## + +add_newdoc('numpy.core.multiarray', 'busdaycalendar', + """ + busdaycalendar(weekmask='1111100', holidays=None) + + A business day calendar object that efficiently stores information + defining valid days for the busday family of functions. + + The default valid days are Monday through Friday ("business days"). + A busdaycalendar object can be specified with any set of weekly + valid days, plus an optional "holiday" dates that always will be invalid. + + Once a busdaycalendar object is created, the weekmask and holidays + cannot be modified. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + weekmask : str or array_like of bool, optional + A seven-element array indicating which of Monday through Sunday are + valid days. May be specified as a length-seven list or array, like + [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string + like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for + weekdays, optionally separated by white space. Valid abbreviations + are: Mon Tue Wed Thu Fri Sat Sun + holidays : array_like of datetime64[D], optional + An array of dates to consider as invalid dates, no matter which + weekday they fall upon. Holiday dates may be specified in any + order, and NaT (not-a-time) dates are ignored. This list is + saved in a normalized form that is suited for fast calculations + of valid days. + + Returns + ------- + out : busdaycalendar + A business day calendar object containing the specified + weekmask and holidays values. + + See Also + -------- + is_busday : Returns a boolean array indicating valid days. + busday_offset : Applies an offset counted in valid days. + busday_count : Counts how many valid days are in a half-open date range. + + Attributes + ---------- + Note: once a busdaycalendar object is created, you cannot modify the + weekmask or holidays. The attributes return copies of internal data. + weekmask : (copy) seven-element array of bool + holidays : (copy) sorted array of datetime64[D] + + Examples + -------- + >>> # Some important days in July + ... bdd = np.busdaycalendar( + ... holidays=['2011-07-01', '2011-07-04', '2011-07-17']) + >>> # Default is Monday to Friday weekdays + ... bdd.weekmask + array([ True, True, True, True, True, False, False]) + >>> # Any holidays already on the weekend are removed + ... bdd.holidays + array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]') + """) + +add_newdoc('numpy.core.multiarray', 'busdaycalendar', ('weekmask', + """A copy of the seven-element boolean mask indicating valid days.""")) + +add_newdoc('numpy.core.multiarray', 'busdaycalendar', ('holidays', + """A copy of the holiday array indicating additional invalid days.""")) + +add_newdoc('numpy.core.multiarray', 'normalize_axis_index', + """ + normalize_axis_index(axis, ndim, msg_prefix=None) + + Normalizes an axis index, `axis`, such that is a valid positive index into + the shape of array with `ndim` dimensions. Raises an AxisError with an + appropriate message if this is not possible. + + Used internally by all axis-checking logic. + + .. versionadded:: 1.13.0 + + Parameters + ---------- + axis : int + The un-normalized index of the axis. Can be negative + ndim : int + The number of dimensions of the array that `axis` should be normalized + against + msg_prefix : str + A prefix to put before the message, typically the name of the argument + + Returns + ------- + normalized_axis : int + The normalized axis index, such that `0 <= normalized_axis < ndim` + + Raises + ------ + AxisError + If the axis index is invalid, when `-ndim <= axis < ndim` is false. + + Examples + -------- + >>> normalize_axis_index(0, ndim=3) + 0 + >>> normalize_axis_index(1, ndim=3) + 1 + >>> normalize_axis_index(-1, ndim=3) + 2 + + >>> normalize_axis_index(3, ndim=3) + Traceback (most recent call last): + ... + AxisError: axis 3 is out of bounds for array of dimension 3 + >>> normalize_axis_index(-4, ndim=3, msg_prefix='axes_arg') + Traceback (most recent call last): + ... + AxisError: axes_arg: axis -4 is out of bounds for array of dimension 3 + """) + +add_newdoc('numpy.core.multiarray', 'datetime_data', + """ + datetime_data(dtype, /) + + Get information about the step size of a date or time type. + + The returned tuple can be passed as the second argument of `numpy.datetime64` and + `numpy.timedelta64`. + + Parameters + ---------- + dtype : dtype + The dtype object, which must be a `datetime64` or `timedelta64` type. + + Returns + ------- + unit : str + The :ref:`datetime unit ` on which this dtype + is based. + count : int + The number of base units in a step. + + Examples + -------- + >>> dt_25s = np.dtype('timedelta64[25s]') + >>> np.datetime_data(dt_25s) + ('s', 25) + >>> np.array(10, dt_25s).astype('timedelta64[s]') + array(250, dtype='timedelta64[s]') + + The result can be used to construct a datetime that uses the same units + as a timedelta + + >>> np.datetime64('2010', np.datetime_data(dt_25s)) + numpy.datetime64('2010-01-01T00:00:00','25s') + """) + + +############################################################################## +# +# Documentation for `generic` attributes and methods +# +############################################################################## + +add_newdoc('numpy.core.numerictypes', 'generic', + """ + Base class for numpy scalar types. + + Class from which most (all?) numpy scalar types are derived. For + consistency, exposes the same API as `ndarray`, despite many + consequent attributes being either "get-only," or completely irrelevant. + This is the class from which it is strongly suggested users should derive + custom scalar types. + + """) + +# Attributes + +def refer_to_array_attribute(attr, method=True): + docstring = """ + Scalar {} identical to the corresponding array attribute. + + Please see `ndarray.{}`. + """ + + return attr, docstring.format("method" if method else "attribute", attr) + + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('T', method=False)) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('base', method=False)) + +add_newdoc('numpy.core.numerictypes', 'generic', ('data', + """Pointer to start of data.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('dtype', + """Get array data-descriptor.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('flags', + """The integer value of flags.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('flat', + """A 1-D view of the scalar.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('imag', + """The imaginary part of the scalar.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('itemsize', + """The length of one element in bytes.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('nbytes', + """The length of the scalar in bytes.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('ndim', + """The number of array dimensions.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('real', + """The real part of the scalar.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('shape', + """Tuple of array dimensions.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('size', + """The number of elements in the gentype.""")) + +add_newdoc('numpy.core.numerictypes', 'generic', ('strides', + """Tuple of bytes steps in each dimension.""")) + +# Methods + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('all')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('any')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('argmax')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('argmin')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('argsort')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('astype')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('byteswap')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('choose')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('clip')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('compress')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('conjugate')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('copy')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('cumprod')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('cumsum')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('diagonal')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('dump')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('dumps')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('fill')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('flatten')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('getfield')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('item')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('itemset')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('max')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('mean')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('min')) + +add_newdoc('numpy.core.numerictypes', 'generic', ('newbyteorder', + """ + newbyteorder(new_order='S', /) + + Return a new `dtype` with a different byte order. + + Changes are also made in all fields and sub-arrays of the data type. + + The `new_order` code can be any from the following: + + * 'S' - swap dtype from current to opposite endian + * {'<', 'little'} - little endian + * {'>', 'big'} - big endian + * {'=', 'native'} - native order + * {'|', 'I'} - ignore (no change to byte order) + + Parameters + ---------- + new_order : str, optional + Byte order to force; a value from the byte order specifications + above. The default value ('S') results in swapping the current + byte order. + + + Returns + ------- + new_dtype : dtype + New `dtype` object with the given change to the byte order. + + """)) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('nonzero')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('prod')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('ptp')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('put')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('ravel')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('repeat')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('reshape')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('resize')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('round')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('searchsorted')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('setfield')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('setflags')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('sort')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('squeeze')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('std')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('sum')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('swapaxes')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('take')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('tofile')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('tolist')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('tostring')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('trace')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('transpose')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('var')) + +add_newdoc('numpy.core.numerictypes', 'generic', + refer_to_array_attribute('view')) + +add_newdoc('numpy.core.numerictypes', 'number', ('__class_getitem__', + """ + __class_getitem__(item, /) + + Return a parametrized wrapper around the `~numpy.number` type. + + .. versionadded:: 1.22 + + Returns + ------- + alias : types.GenericAlias + A parametrized `~numpy.number` type. + + Examples + -------- + >>> from typing import Any + >>> import numpy as np + + >>> np.signedinteger[Any] + numpy.signedinteger[typing.Any] + + See Also + -------- + :pep:`585` : Type hinting generics in standard collections. + + """)) + +############################################################################## +# +# Documentation for scalar type abstract base classes in type hierarchy +# +############################################################################## + + +add_newdoc('numpy.core.numerictypes', 'number', + """ + Abstract base class of all numeric scalar types. + + """) + +add_newdoc('numpy.core.numerictypes', 'integer', + """ + Abstract base class of all integer scalar types. + + """) + +add_newdoc('numpy.core.numerictypes', 'signedinteger', + """ + Abstract base class of all signed integer scalar types. + + """) + +add_newdoc('numpy.core.numerictypes', 'unsignedinteger', + """ + Abstract base class of all unsigned integer scalar types. + + """) + +add_newdoc('numpy.core.numerictypes', 'inexact', + """ + Abstract base class of all numeric scalar types with a (potentially) + inexact representation of the values in its range, such as + floating-point numbers. + + """) + +add_newdoc('numpy.core.numerictypes', 'floating', + """ + Abstract base class of all floating-point scalar types. + + """) + +add_newdoc('numpy.core.numerictypes', 'complexfloating', + """ + Abstract base class of all complex number scalar types that are made up of + floating-point numbers. + + """) + +add_newdoc('numpy.core.numerictypes', 'flexible', + """ + Abstract base class of all scalar types without predefined length. + The actual size of these types depends on the specific `np.dtype` + instantiation. + + """) + +add_newdoc('numpy.core.numerictypes', 'character', + """ + Abstract base class of all character string scalar types. + + """) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_add_newdocs_scalars.py b/venv/lib/python3.10/site-packages/numpy/core/_add_newdocs_scalars.py new file mode 100644 index 0000000000000000000000000000000000000000..f9a6ad963ec3c04d4e6c9dd57255b323e2959cfe --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_add_newdocs_scalars.py @@ -0,0 +1,372 @@ +""" +This file is separate from ``_add_newdocs.py`` so that it can be mocked out by +our sphinx ``conf.py`` during doc builds, where we want to avoid showing +platform-dependent information. +""" +import sys +import os +from numpy.core import dtype +from numpy.core import numerictypes as _numerictypes +from numpy.core.function_base import add_newdoc + +############################################################################## +# +# Documentation for concrete scalar classes +# +############################################################################## + +def numeric_type_aliases(aliases): + def type_aliases_gen(): + for alias, doc in aliases: + try: + alias_type = getattr(_numerictypes, alias) + except AttributeError: + # The set of aliases that actually exist varies between platforms + pass + else: + yield (alias_type, alias, doc) + return list(type_aliases_gen()) + + +possible_aliases = numeric_type_aliases([ + ('int8', '8-bit signed integer (``-128`` to ``127``)'), + ('int16', '16-bit signed integer (``-32_768`` to ``32_767``)'), + ('int32', '32-bit signed integer (``-2_147_483_648`` to ``2_147_483_647``)'), + ('int64', '64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``)'), + ('intp', 'Signed integer large enough to fit pointer, compatible with C ``intptr_t``'), + ('uint8', '8-bit unsigned integer (``0`` to ``255``)'), + ('uint16', '16-bit unsigned integer (``0`` to ``65_535``)'), + ('uint32', '32-bit unsigned integer (``0`` to ``4_294_967_295``)'), + ('uint64', '64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``)'), + ('uintp', 'Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``'), + ('float16', '16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa'), + ('float32', '32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa'), + ('float64', '64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa'), + ('float96', '96-bit extended-precision floating-point number type'), + ('float128', '128-bit extended-precision floating-point number type'), + ('complex64', 'Complex number type composed of 2 32-bit-precision floating-point numbers'), + ('complex128', 'Complex number type composed of 2 64-bit-precision floating-point numbers'), + ('complex192', 'Complex number type composed of 2 96-bit extended-precision floating-point numbers'), + ('complex256', 'Complex number type composed of 2 128-bit extended-precision floating-point numbers'), + ]) + + +def _get_platform_and_machine(): + try: + system, _, _, _, machine = os.uname() + except AttributeError: + system = sys.platform + if system == 'win32': + machine = os.environ.get('PROCESSOR_ARCHITEW6432', '') \ + or os.environ.get('PROCESSOR_ARCHITECTURE', '') + else: + machine = 'unknown' + return system, machine + + +_system, _machine = _get_platform_and_machine() +_doc_alias_string = f":Alias on this platform ({_system} {_machine}):" + + +def add_newdoc_for_scalar_type(obj, fixed_aliases, doc): + # note: `:field: value` is rST syntax which renders as field lists. + o = getattr(_numerictypes, obj) + + character_code = dtype(o).char + canonical_name_doc = "" if obj == o.__name__ else \ + f":Canonical name: `numpy.{obj}`\n " + if fixed_aliases: + alias_doc = ''.join(f":Alias: `numpy.{alias}`\n " + for alias in fixed_aliases) + else: + alias_doc = '' + alias_doc += ''.join(f"{_doc_alias_string} `numpy.{alias}`: {doc}.\n " + for (alias_type, alias, doc) in possible_aliases if alias_type is o) + + docstring = f""" + {doc.strip()} + + :Character code: ``'{character_code}'`` + {canonical_name_doc}{alias_doc} + """ + + add_newdoc('numpy.core.numerictypes', obj, docstring) + + +add_newdoc_for_scalar_type('bool_', [], + """ + Boolean type (True or False), stored as a byte. + + .. warning:: + + The :class:`bool_` type is not a subclass of the :class:`int_` type + (the :class:`bool_` is not even a number type). This is different + than Python's default implementation of :class:`bool` as a + sub-class of :class:`int`. + """) + +add_newdoc_for_scalar_type('byte', [], + """ + Signed integer type, compatible with C ``char``. + """) + +add_newdoc_for_scalar_type('short', [], + """ + Signed integer type, compatible with C ``short``. + """) + +add_newdoc_for_scalar_type('intc', [], + """ + Signed integer type, compatible with C ``int``. + """) + +add_newdoc_for_scalar_type('int_', [], + """ + Signed integer type, compatible with Python `int` and C ``long``. + """) + +add_newdoc_for_scalar_type('longlong', [], + """ + Signed integer type, compatible with C ``long long``. + """) + +add_newdoc_for_scalar_type('ubyte', [], + """ + Unsigned integer type, compatible with C ``unsigned char``. + """) + +add_newdoc_for_scalar_type('ushort', [], + """ + Unsigned integer type, compatible with C ``unsigned short``. + """) + +add_newdoc_for_scalar_type('uintc', [], + """ + Unsigned integer type, compatible with C ``unsigned int``. + """) + +add_newdoc_for_scalar_type('uint', [], + """ + Unsigned integer type, compatible with C ``unsigned long``. + """) + +add_newdoc_for_scalar_type('ulonglong', [], + """ + Signed integer type, compatible with C ``unsigned long long``. + """) + +add_newdoc_for_scalar_type('half', [], + """ + Half-precision floating-point number type. + """) + +add_newdoc_for_scalar_type('single', [], + """ + Single-precision floating-point number type, compatible with C ``float``. + """) + +add_newdoc_for_scalar_type('double', ['float_'], + """ + Double-precision floating-point number type, compatible with Python `float` + and C ``double``. + """) + +add_newdoc_for_scalar_type('longdouble', ['longfloat'], + """ + Extended-precision floating-point number type, compatible with C + ``long double`` but not necessarily with IEEE 754 quadruple-precision. + """) + +add_newdoc_for_scalar_type('csingle', ['singlecomplex'], + """ + Complex number type composed of two single-precision floating-point + numbers. + """) + +add_newdoc_for_scalar_type('cdouble', ['cfloat', 'complex_'], + """ + Complex number type composed of two double-precision floating-point + numbers, compatible with Python `complex`. + """) + +add_newdoc_for_scalar_type('clongdouble', ['clongfloat', 'longcomplex'], + """ + Complex number type composed of two extended-precision floating-point + numbers. + """) + +add_newdoc_for_scalar_type('object_', [], + """ + Any Python object. + """) + +add_newdoc_for_scalar_type('str_', ['unicode_'], + r""" + A unicode string. + + This type strips trailing null codepoints. + + >>> s = np.str_("abc\x00") + >>> s + 'abc' + + Unlike the builtin `str`, this supports the :ref:`python:bufferobjects`, exposing its + contents as UCS4: + + >>> m = memoryview(np.str_("abc")) + >>> m.format + '3w' + >>> m.tobytes() + b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00' + """) + +add_newdoc_for_scalar_type('bytes_', ['string_'], + r""" + A byte string. + + When used in arrays, this type strips trailing null bytes. + """) + +add_newdoc_for_scalar_type('void', [], + r""" + np.void(length_or_data, /, dtype=None) + + Create a new structured or unstructured void scalar. + + Parameters + ---------- + length_or_data : int, array-like, bytes-like, object + One of multiple meanings (see notes). The length or + bytes data of an unstructured void. Or alternatively, + the data to be stored in the new scalar when `dtype` + is provided. + This can be an array-like, in which case an array may + be returned. + dtype : dtype, optional + If provided the dtype of the new scalar. This dtype must + be "void" dtype (i.e. a structured or unstructured void, + see also :ref:`defining-structured-types`). + + ..versionadded:: 1.24 + + Notes + ----- + For historical reasons and because void scalars can represent both + arbitrary byte data and structured dtypes, the void constructor + has three calling conventions: + + 1. ``np.void(5)`` creates a ``dtype="V5"`` scalar filled with five + ``\0`` bytes. The 5 can be a Python or NumPy integer. + 2. ``np.void(b"bytes-like")`` creates a void scalar from the byte string. + The dtype itemsize will match the byte string length, here ``"V10"``. + 3. When a ``dtype=`` is passed the call is roughly the same as an + array creation. However, a void scalar rather than array is returned. + + Please see the examples which show all three different conventions. + + Examples + -------- + >>> np.void(5) + void(b'\x00\x00\x00\x00\x00') + >>> np.void(b'abcd') + void(b'\x61\x62\x63\x64') + >>> np.void((5, 3.2, "eggs"), dtype="i,d,S5") + (5, 3.2, b'eggs') # looks like a tuple, but is `np.void` + >>> np.void(3, dtype=[('x', np.int8), ('y', np.int8)]) + (3, 3) # looks like a tuple, but is `np.void` + + """) + +add_newdoc_for_scalar_type('datetime64', [], + """ + If created from a 64-bit integer, it represents an offset from + ``1970-01-01T00:00:00``. + If created from string, the string can be in ISO 8601 date + or datetime format. + + >>> np.datetime64(10, 'Y') + numpy.datetime64('1980') + >>> np.datetime64('1980', 'Y') + numpy.datetime64('1980') + >>> np.datetime64(10, 'D') + numpy.datetime64('1970-01-11') + + See :ref:`arrays.datetime` for more information. + """) + +add_newdoc_for_scalar_type('timedelta64', [], + """ + A timedelta stored as a 64-bit integer. + + See :ref:`arrays.datetime` for more information. + """) + +add_newdoc('numpy.core.numerictypes', "integer", ('is_integer', + """ + integer.is_integer() -> bool + + Return ``True`` if the number is finite with integral value. + + .. versionadded:: 1.22 + + Examples + -------- + >>> np.int64(-2).is_integer() + True + >>> np.uint32(5).is_integer() + True + """)) + +# TODO: work out how to put this on the base class, np.floating +for float_name in ('half', 'single', 'double', 'longdouble'): + add_newdoc('numpy.core.numerictypes', float_name, ('as_integer_ratio', + """ + {ftype}.as_integer_ratio() -> (int, int) + + Return a pair of integers, whose ratio is exactly equal to the original + floating point number, and with a positive denominator. + Raise `OverflowError` on infinities and a `ValueError` on NaNs. + + >>> np.{ftype}(10.0).as_integer_ratio() + (10, 1) + >>> np.{ftype}(0.0).as_integer_ratio() + (0, 1) + >>> np.{ftype}(-.25).as_integer_ratio() + (-1, 4) + """.format(ftype=float_name))) + + add_newdoc('numpy.core.numerictypes', float_name, ('is_integer', + f""" + {float_name}.is_integer() -> bool + + Return ``True`` if the floating point number is finite with integral + value, and ``False`` otherwise. + + .. versionadded:: 1.22 + + Examples + -------- + >>> np.{float_name}(-2.0).is_integer() + True + >>> np.{float_name}(3.2).is_integer() + False + """)) + +for int_name in ('int8', 'uint8', 'int16', 'uint16', 'int32', 'uint32', + 'int64', 'uint64', 'int64', 'uint64', 'int64', 'uint64'): + # Add negative examples for signed cases by checking typecode + add_newdoc('numpy.core.numerictypes', int_name, ('bit_count', + f""" + {int_name}.bit_count() -> int + + Computes the number of 1-bits in the absolute value of the input. + Analogous to the builtin `int.bit_count` or ``popcount`` in C++. + + Examples + -------- + >>> np.{int_name}(127).bit_count() + 7""" + + (f""" + >>> np.{int_name}(-127).bit_count() + 7 + """ if dtype(int_name).char.islower() else ""))) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_asarray.py b/venv/lib/python3.10/site-packages/numpy/core/_asarray.py new file mode 100644 index 0000000000000000000000000000000000000000..a9abc5a88ca38cf248996db806f789bb49b5f68b --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_asarray.py @@ -0,0 +1,134 @@ +""" +Functions in the ``as*array`` family that promote array-likes into arrays. + +`require` fits this category despite its name not matching this pattern. +""" +from .overrides import ( + array_function_dispatch, + set_array_function_like_doc, + set_module, +) +from .multiarray import array, asanyarray + + +__all__ = ["require"] + + +POSSIBLE_FLAGS = { + 'C': 'C', 'C_CONTIGUOUS': 'C', 'CONTIGUOUS': 'C', + 'F': 'F', 'F_CONTIGUOUS': 'F', 'FORTRAN': 'F', + 'A': 'A', 'ALIGNED': 'A', + 'W': 'W', 'WRITEABLE': 'W', + 'O': 'O', 'OWNDATA': 'O', + 'E': 'E', 'ENSUREARRAY': 'E' +} + + +@set_array_function_like_doc +@set_module('numpy') +def require(a, dtype=None, requirements=None, *, like=None): + """ + Return an ndarray of the provided type that satisfies requirements. + + This function is useful to be sure that an array with the correct flags + is returned for passing to compiled code (perhaps through ctypes). + + Parameters + ---------- + a : array_like + The object to be converted to a type-and-requirement-satisfying array. + dtype : data-type + The required data-type. If None preserve the current dtype. If your + application requires the data to be in native byteorder, include + a byteorder specification as a part of the dtype specification. + requirements : str or sequence of str + The requirements list can be any of the following + + * 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array + * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array + * 'ALIGNED' ('A') - ensure a data-type aligned array + * 'WRITEABLE' ('W') - ensure a writable array + * 'OWNDATA' ('O') - ensure an array that owns its own data + * 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + Array with specified requirements and type if given. + + See Also + -------- + asarray : Convert input to an ndarray. + asanyarray : Convert to an ndarray, but pass through ndarray subclasses. + ascontiguousarray : Convert input to a contiguous array. + asfortranarray : Convert input to an ndarray with column-major + memory order. + ndarray.flags : Information about the memory layout of the array. + + Notes + ----- + The returned array will be guaranteed to have the listed requirements + by making a copy if needed. + + Examples + -------- + >>> x = np.arange(6).reshape(2,3) + >>> x.flags + C_CONTIGUOUS : True + F_CONTIGUOUS : False + OWNDATA : False + WRITEABLE : True + ALIGNED : True + WRITEBACKIFCOPY : False + + >>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F']) + >>> y.flags + C_CONTIGUOUS : False + F_CONTIGUOUS : True + OWNDATA : True + WRITEABLE : True + ALIGNED : True + WRITEBACKIFCOPY : False + + """ + if like is not None: + return _require_with_like( + like, + a, + dtype=dtype, + requirements=requirements, + ) + + if not requirements: + return asanyarray(a, dtype=dtype) + + requirements = {POSSIBLE_FLAGS[x.upper()] for x in requirements} + + if 'E' in requirements: + requirements.remove('E') + subok = False + else: + subok = True + + order = 'A' + if requirements >= {'C', 'F'}: + raise ValueError('Cannot specify both "C" and "F" order') + elif 'F' in requirements: + order = 'F' + requirements.remove('F') + elif 'C' in requirements: + order = 'C' + requirements.remove('C') + + arr = array(a, dtype=dtype, order=order, copy=False, subok=subok) + + for prop in requirements: + if not arr.flags[prop]: + return arr.copy(order) + return arr + + +_require_with_like = array_function_dispatch()(require) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_dtype.py b/venv/lib/python3.10/site-packages/numpy/core/_dtype.py new file mode 100644 index 0000000000000000000000000000000000000000..ff50f5199a5c8c4d5b5b01c9335eeb6b1d06d6b2 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_dtype.py @@ -0,0 +1,369 @@ +""" +A place for code to be called from the implementation of np.dtype + +String handling is much easier to do correctly in python. +""" +import numpy as np + + +_kind_to_stem = { + 'u': 'uint', + 'i': 'int', + 'c': 'complex', + 'f': 'float', + 'b': 'bool', + 'V': 'void', + 'O': 'object', + 'M': 'datetime', + 'm': 'timedelta', + 'S': 'bytes', + 'U': 'str', +} + + +def _kind_name(dtype): + try: + return _kind_to_stem[dtype.kind] + except KeyError as e: + raise RuntimeError( + "internal dtype error, unknown kind {!r}" + .format(dtype.kind) + ) from None + + +def __str__(dtype): + if dtype.fields is not None: + return _struct_str(dtype, include_align=True) + elif dtype.subdtype: + return _subarray_str(dtype) + elif issubclass(dtype.type, np.flexible) or not dtype.isnative: + return dtype.str + else: + return dtype.name + + +def __repr__(dtype): + arg_str = _construction_repr(dtype, include_align=False) + if dtype.isalignedstruct: + arg_str = arg_str + ", align=True" + return "dtype({})".format(arg_str) + + +def _unpack_field(dtype, offset, title=None): + """ + Helper function to normalize the items in dtype.fields. + + Call as: + + dtype, offset, title = _unpack_field(*dtype.fields[name]) + """ + return dtype, offset, title + + +def _isunsized(dtype): + # PyDataType_ISUNSIZED + return dtype.itemsize == 0 + + +def _construction_repr(dtype, include_align=False, short=False): + """ + Creates a string repr of the dtype, excluding the 'dtype()' part + surrounding the object. This object may be a string, a list, or + a dict depending on the nature of the dtype. This + is the object passed as the first parameter to the dtype + constructor, and if no additional constructor parameters are + given, will reproduce the exact memory layout. + + Parameters + ---------- + short : bool + If true, this creates a shorter repr using 'kind' and 'itemsize', instead + of the longer type name. + + include_align : bool + If true, this includes the 'align=True' parameter + inside the struct dtype construction dict when needed. Use this flag + if you want a proper repr string without the 'dtype()' part around it. + + If false, this does not preserve the + 'align=True' parameter or sticky NPY_ALIGNED_STRUCT flag for + struct arrays like the regular repr does, because the 'align' + flag is not part of first dtype constructor parameter. This + mode is intended for a full 'repr', where the 'align=True' is + provided as the second parameter. + """ + if dtype.fields is not None: + return _struct_str(dtype, include_align=include_align) + elif dtype.subdtype: + return _subarray_str(dtype) + else: + return _scalar_str(dtype, short=short) + + +def _scalar_str(dtype, short): + byteorder = _byte_order_str(dtype) + + if dtype.type == np.bool_: + if short: + return "'?'" + else: + return "'bool'" + + elif dtype.type == np.object_: + # The object reference may be different sizes on different + # platforms, so it should never include the itemsize here. + return "'O'" + + elif dtype.type == np.bytes_: + if _isunsized(dtype): + return "'S'" + else: + return "'S%d'" % dtype.itemsize + + elif dtype.type == np.str_: + if _isunsized(dtype): + return "'%sU'" % byteorder + else: + return "'%sU%d'" % (byteorder, dtype.itemsize / 4) + + # unlike the other types, subclasses of void are preserved - but + # historically the repr does not actually reveal the subclass + elif issubclass(dtype.type, np.void): + if _isunsized(dtype): + return "'V'" + else: + return "'V%d'" % dtype.itemsize + + elif dtype.type == np.datetime64: + return "'%sM8%s'" % (byteorder, _datetime_metadata_str(dtype)) + + elif dtype.type == np.timedelta64: + return "'%sm8%s'" % (byteorder, _datetime_metadata_str(dtype)) + + elif np.issubdtype(dtype, np.number): + # Short repr with endianness, like '' """ + # hack to obtain the native and swapped byte order characters + swapped = np.dtype(int).newbyteorder('S') + native = swapped.newbyteorder('S') + + byteorder = dtype.byteorder + if byteorder == '=': + return native.byteorder + if byteorder == 'S': + # TODO: this path can never be reached + return swapped.byteorder + elif byteorder == '|': + return '' + else: + return byteorder + + +def _datetime_metadata_str(dtype): + # TODO: this duplicates the C metastr_to_unicode functionality + unit, count = np.datetime_data(dtype) + if unit == 'generic': + return '' + elif count == 1: + return '[{}]'.format(unit) + else: + return '[{}{}]'.format(count, unit) + + +def _struct_dict_str(dtype, includealignedflag): + # unpack the fields dictionary into ls + names = dtype.names + fld_dtypes = [] + offsets = [] + titles = [] + for name in names: + fld_dtype, offset, title = _unpack_field(*dtype.fields[name]) + fld_dtypes.append(fld_dtype) + offsets.append(offset) + titles.append(title) + + # Build up a string to make the dictionary + + if np.core.arrayprint._get_legacy_print_mode() <= 121: + colon = ":" + fieldsep = "," + else: + colon = ": " + fieldsep = ", " + + # First, the names + ret = "{'names'%s[" % colon + ret += fieldsep.join(repr(name) for name in names) + + # Second, the formats + ret += "], 'formats'%s[" % colon + ret += fieldsep.join( + _construction_repr(fld_dtype, short=True) for fld_dtype in fld_dtypes) + + # Third, the offsets + ret += "], 'offsets'%s[" % colon + ret += fieldsep.join("%d" % offset for offset in offsets) + + # Fourth, the titles + if any(title is not None for title in titles): + ret += "], 'titles'%s[" % colon + ret += fieldsep.join(repr(title) for title in titles) + + # Fifth, the itemsize + ret += "], 'itemsize'%s%d" % (colon, dtype.itemsize) + + if (includealignedflag and dtype.isalignedstruct): + # Finally, the aligned flag + ret += ", 'aligned'%sTrue}" % colon + else: + ret += "}" + + return ret + + +def _aligned_offset(offset, alignment): + # round up offset: + return - (-offset // alignment) * alignment + + +def _is_packed(dtype): + """ + Checks whether the structured data type in 'dtype' + has a simple layout, where all the fields are in order, + and follow each other with no alignment padding. + + When this returns true, the dtype can be reconstructed + from a list of the field names and dtypes with no additional + dtype parameters. + + Duplicates the C `is_dtype_struct_simple_unaligned_layout` function. + """ + align = dtype.isalignedstruct + max_alignment = 1 + total_offset = 0 + for name in dtype.names: + fld_dtype, fld_offset, title = _unpack_field(*dtype.fields[name]) + + if align: + total_offset = _aligned_offset(total_offset, fld_dtype.alignment) + max_alignment = max(max_alignment, fld_dtype.alignment) + + if fld_offset != total_offset: + return False + total_offset += fld_dtype.itemsize + + if align: + total_offset = _aligned_offset(total_offset, max_alignment) + + if total_offset != dtype.itemsize: + return False + return True + + +def _struct_list_str(dtype): + items = [] + for name in dtype.names: + fld_dtype, fld_offset, title = _unpack_field(*dtype.fields[name]) + + item = "(" + if title is not None: + item += "({!r}, {!r}), ".format(title, name) + else: + item += "{!r}, ".format(name) + # Special case subarray handling here + if fld_dtype.subdtype is not None: + base, shape = fld_dtype.subdtype + item += "{}, {}".format( + _construction_repr(base, short=True), + shape + ) + else: + item += _construction_repr(fld_dtype, short=True) + + item += ")" + items.append(item) + + return "[" + ", ".join(items) + "]" + + +def _struct_str(dtype, include_align): + # The list str representation can't include the 'align=' flag, + # so if it is requested and the struct has the aligned flag set, + # we must use the dict str instead. + if not (include_align and dtype.isalignedstruct) and _is_packed(dtype): + sub = _struct_list_str(dtype) + + else: + sub = _struct_dict_str(dtype, include_align) + + # If the data type isn't the default, void, show it + if dtype.type != np.void: + return "({t.__module__}.{t.__name__}, {f})".format(t=dtype.type, f=sub) + else: + return sub + + +def _subarray_str(dtype): + base, shape = dtype.subdtype + return "({}, {})".format( + _construction_repr(base, short=True), + shape + ) + + +def _name_includes_bit_suffix(dtype): + if dtype.type == np.object_: + # pointer size varies by system, best to omit it + return False + elif dtype.type == np.bool_: + # implied + return False + elif dtype.type is None: + return True + elif np.issubdtype(dtype, np.flexible) and _isunsized(dtype): + # unspecified + return False + else: + return True + + +def _name_get(dtype): + # provides dtype.name.__get__, documented as returning a "bit name" + + if dtype.isbuiltin == 2: + # user dtypes don't promise to do anything special + return dtype.type.__name__ + + if dtype.kind == '\x00': + name = type(dtype).__name__ + elif issubclass(dtype.type, np.void): + # historically, void subclasses preserve their name, eg `record64` + name = dtype.type.__name__ + else: + name = _kind_name(dtype) + + # append bit counts + if _name_includes_bit_suffix(dtype): + name += "{}".format(dtype.itemsize * 8) + + # append metadata to datetimes + if dtype.type in (np.datetime64, np.timedelta64): + name += _datetime_metadata_str(dtype) + + return name diff --git a/venv/lib/python3.10/site-packages/numpy/core/_dtype_ctypes.py b/venv/lib/python3.10/site-packages/numpy/core/_dtype_ctypes.py new file mode 100644 index 0000000000000000000000000000000000000000..6d7cbb244215e03b4140a679b76be46f8e724ea5 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_dtype_ctypes.py @@ -0,0 +1,117 @@ +""" +Conversion from ctypes to dtype. + +In an ideal world, we could achieve this through the PEP3118 buffer protocol, +something like:: + + def dtype_from_ctypes_type(t): + # needed to ensure that the shape of `t` is within memoryview.format + class DummyStruct(ctypes.Structure): + _fields_ = [('a', t)] + + # empty to avoid memory allocation + ctype_0 = (DummyStruct * 0)() + mv = memoryview(ctype_0) + + # convert the struct, and slice back out the field + return _dtype_from_pep3118(mv.format)['a'] + +Unfortunately, this fails because: + +* ctypes cannot handle length-0 arrays with PEP3118 (bpo-32782) +* PEP3118 cannot represent unions, but both numpy and ctypes can +* ctypes cannot handle big-endian structs with PEP3118 (bpo-32780) +""" + +# We delay-import ctypes for distributions that do not include it. +# While this module is not used unless the user passes in ctypes +# members, it is eagerly imported from numpy/core/__init__.py. +import numpy as np + + +def _from_ctypes_array(t): + return np.dtype((dtype_from_ctypes_type(t._type_), (t._length_,))) + + +def _from_ctypes_structure(t): + for item in t._fields_: + if len(item) > 2: + raise TypeError( + "ctypes bitfields have no dtype equivalent") + + if hasattr(t, "_pack_"): + import ctypes + formats = [] + offsets = [] + names = [] + current_offset = 0 + for fname, ftyp in t._fields_: + names.append(fname) + formats.append(dtype_from_ctypes_type(ftyp)) + # Each type has a default offset, this is platform dependent for some types. + effective_pack = min(t._pack_, ctypes.alignment(ftyp)) + current_offset = ((current_offset + effective_pack - 1) // effective_pack) * effective_pack + offsets.append(current_offset) + current_offset += ctypes.sizeof(ftyp) + + return np.dtype(dict( + formats=formats, + offsets=offsets, + names=names, + itemsize=ctypes.sizeof(t))) + else: + fields = [] + for fname, ftyp in t._fields_: + fields.append((fname, dtype_from_ctypes_type(ftyp))) + + # by default, ctypes structs are aligned + return np.dtype(fields, align=True) + + +def _from_ctypes_scalar(t): + """ + Return the dtype type with endianness included if it's the case + """ + if getattr(t, '__ctype_be__', None) is t: + return np.dtype('>' + t._type_) + elif getattr(t, '__ctype_le__', None) is t: + return np.dtype('<' + t._type_) + else: + return np.dtype(t._type_) + + +def _from_ctypes_union(t): + import ctypes + formats = [] + offsets = [] + names = [] + for fname, ftyp in t._fields_: + names.append(fname) + formats.append(dtype_from_ctypes_type(ftyp)) + offsets.append(0) # Union fields are offset to 0 + + return np.dtype(dict( + formats=formats, + offsets=offsets, + names=names, + itemsize=ctypes.sizeof(t))) + + +def dtype_from_ctypes_type(t): + """ + Construct a dtype object from a ctypes type + """ + import _ctypes + if issubclass(t, _ctypes.Array): + return _from_ctypes_array(t) + elif issubclass(t, _ctypes._Pointer): + raise TypeError("ctypes pointers have no dtype equivalent") + elif issubclass(t, _ctypes.Structure): + return _from_ctypes_structure(t) + elif issubclass(t, _ctypes.Union): + return _from_ctypes_union(t) + elif isinstance(getattr(t, '_type_', None), str): + return _from_ctypes_scalar(t) + else: + raise NotImplementedError( + "Unknown ctypes type {}".format(t.__name__)) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_exceptions.py b/venv/lib/python3.10/site-packages/numpy/core/_exceptions.py new file mode 100644 index 0000000000000000000000000000000000000000..87d4213a6d42cf090f8db75571244840dd68cd5a --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_exceptions.py @@ -0,0 +1,172 @@ +""" +Various richly-typed exceptions, that also help us deal with string formatting +in python where it's easier. + +By putting the formatting in `__str__`, we also avoid paying the cost for +users who silence the exceptions. +""" +from .._utils import set_module + +def _unpack_tuple(tup): + if len(tup) == 1: + return tup[0] + else: + return tup + + +def _display_as_base(cls): + """ + A decorator that makes an exception class look like its base. + + We use this to hide subclasses that are implementation details - the user + should catch the base type, which is what the traceback will show them. + + Classes decorated with this decorator are subject to removal without a + deprecation warning. + """ + assert issubclass(cls, Exception) + cls.__name__ = cls.__base__.__name__ + return cls + + +class UFuncTypeError(TypeError): + """ Base class for all ufunc exceptions """ + def __init__(self, ufunc): + self.ufunc = ufunc + + +@_display_as_base +class _UFuncNoLoopError(UFuncTypeError): + """ Thrown when a ufunc loop cannot be found """ + def __init__(self, ufunc, dtypes): + super().__init__(ufunc) + self.dtypes = tuple(dtypes) + + def __str__(self): + return ( + "ufunc {!r} did not contain a loop with signature matching types " + "{!r} -> {!r}" + ).format( + self.ufunc.__name__, + _unpack_tuple(self.dtypes[:self.ufunc.nin]), + _unpack_tuple(self.dtypes[self.ufunc.nin:]) + ) + + +@_display_as_base +class _UFuncBinaryResolutionError(_UFuncNoLoopError): + """ Thrown when a binary resolution fails """ + def __init__(self, ufunc, dtypes): + super().__init__(ufunc, dtypes) + assert len(self.dtypes) == 2 + + def __str__(self): + return ( + "ufunc {!r} cannot use operands with types {!r} and {!r}" + ).format( + self.ufunc.__name__, *self.dtypes + ) + + +@_display_as_base +class _UFuncCastingError(UFuncTypeError): + def __init__(self, ufunc, casting, from_, to): + super().__init__(ufunc) + self.casting = casting + self.from_ = from_ + self.to = to + + +@_display_as_base +class _UFuncInputCastingError(_UFuncCastingError): + """ Thrown when a ufunc input cannot be casted """ + def __init__(self, ufunc, casting, from_, to, i): + super().__init__(ufunc, casting, from_, to) + self.in_i = i + + def __str__(self): + # only show the number if more than one input exists + i_str = "{} ".format(self.in_i) if self.ufunc.nin != 1 else "" + return ( + "Cannot cast ufunc {!r} input {}from {!r} to {!r} with casting " + "rule {!r}" + ).format( + self.ufunc.__name__, i_str, self.from_, self.to, self.casting + ) + + +@_display_as_base +class _UFuncOutputCastingError(_UFuncCastingError): + """ Thrown when a ufunc output cannot be casted """ + def __init__(self, ufunc, casting, from_, to, i): + super().__init__(ufunc, casting, from_, to) + self.out_i = i + + def __str__(self): + # only show the number if more than one output exists + i_str = "{} ".format(self.out_i) if self.ufunc.nout != 1 else "" + return ( + "Cannot cast ufunc {!r} output {}from {!r} to {!r} with casting " + "rule {!r}" + ).format( + self.ufunc.__name__, i_str, self.from_, self.to, self.casting + ) + + +@_display_as_base +class _ArrayMemoryError(MemoryError): + """ Thrown when an array cannot be allocated""" + def __init__(self, shape, dtype): + self.shape = shape + self.dtype = dtype + + @property + def _total_size(self): + num_bytes = self.dtype.itemsize + for dim in self.shape: + num_bytes *= dim + return num_bytes + + @staticmethod + def _size_to_string(num_bytes): + """ Convert a number of bytes into a binary size string """ + + # https://en.wikipedia.org/wiki/Binary_prefix + LOG2_STEP = 10 + STEP = 1024 + units = ['bytes', 'KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB'] + + unit_i = max(num_bytes.bit_length() - 1, 1) // LOG2_STEP + unit_val = 1 << (unit_i * LOG2_STEP) + n_units = num_bytes / unit_val + del unit_val + + # ensure we pick a unit that is correct after rounding + if round(n_units) == STEP: + unit_i += 1 + n_units /= STEP + + # deal with sizes so large that we don't have units for them + if unit_i >= len(units): + new_unit_i = len(units) - 1 + n_units *= 1 << ((unit_i - new_unit_i) * LOG2_STEP) + unit_i = new_unit_i + + unit_name = units[unit_i] + # format with a sensible number of digits + if unit_i == 0: + # no decimal point on bytes + return '{:.0f} {}'.format(n_units, unit_name) + elif round(n_units) < 1000: + # 3 significant figures, if none are dropped to the left of the . + return '{:#.3g} {}'.format(n_units, unit_name) + else: + # just give all the digits otherwise + return '{:#.0f} {}'.format(n_units, unit_name) + + def __str__(self): + size_str = self._size_to_string(self._total_size) + return ( + "Unable to allocate {} for an array with shape {} and data type {}" + .format(size_str, self.shape, self.dtype) + ) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_internal.py b/venv/lib/python3.10/site-packages/numpy/core/_internal.py new file mode 100644 index 0000000000000000000000000000000000000000..c783858804017a30c5e7ff48586c54f9f4dcfe26 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_internal.py @@ -0,0 +1,935 @@ +""" +A place for internal code + +Some things are more easily handled Python. + +""" +import ast +import re +import sys +import warnings + +from ..exceptions import DTypePromotionError +from .multiarray import dtype, array, ndarray, promote_types +try: + import ctypes +except ImportError: + ctypes = None + +IS_PYPY = sys.implementation.name == 'pypy' + +if sys.byteorder == 'little': + _nbo = '<' +else: + _nbo = '>' + +def _makenames_list(adict, align): + allfields = [] + + for fname, obj in adict.items(): + n = len(obj) + if not isinstance(obj, tuple) or n not in (2, 3): + raise ValueError("entry not a 2- or 3- tuple") + if n > 2 and obj[2] == fname: + continue + num = int(obj[1]) + if num < 0: + raise ValueError("invalid offset.") + format = dtype(obj[0], align=align) + if n > 2: + title = obj[2] + else: + title = None + allfields.append((fname, format, num, title)) + # sort by offsets + allfields.sort(key=lambda x: x[2]) + names = [x[0] for x in allfields] + formats = [x[1] for x in allfields] + offsets = [x[2] for x in allfields] + titles = [x[3] for x in allfields] + + return names, formats, offsets, titles + +# Called in PyArray_DescrConverter function when +# a dictionary without "names" and "formats" +# fields is used as a data-type descriptor. +def _usefields(adict, align): + try: + names = adict[-1] + except KeyError: + names = None + if names is None: + names, formats, offsets, titles = _makenames_list(adict, align) + else: + formats = [] + offsets = [] + titles = [] + for name in names: + res = adict[name] + formats.append(res[0]) + offsets.append(res[1]) + if len(res) > 2: + titles.append(res[2]) + else: + titles.append(None) + + return dtype({"names": names, + "formats": formats, + "offsets": offsets, + "titles": titles}, align) + + +# construct an array_protocol descriptor list +# from the fields attribute of a descriptor +# This calls itself recursively but should eventually hit +# a descriptor that has no fields and then return +# a simple typestring + +def _array_descr(descriptor): + fields = descriptor.fields + if fields is None: + subdtype = descriptor.subdtype + if subdtype is None: + if descriptor.metadata is None: + return descriptor.str + else: + new = descriptor.metadata.copy() + if new: + return (descriptor.str, new) + else: + return descriptor.str + else: + return (_array_descr(subdtype[0]), subdtype[1]) + + names = descriptor.names + ordered_fields = [fields[x] + (x,) for x in names] + result = [] + offset = 0 + for field in ordered_fields: + if field[1] > offset: + num = field[1] - offset + result.append(('', f'|V{num}')) + offset += num + elif field[1] < offset: + raise ValueError( + "dtype.descr is not defined for types with overlapping or " + "out-of-order fields") + if len(field) > 3: + name = (field[2], field[3]) + else: + name = field[2] + if field[0].subdtype: + tup = (name, _array_descr(field[0].subdtype[0]), + field[0].subdtype[1]) + else: + tup = (name, _array_descr(field[0])) + offset += field[0].itemsize + result.append(tup) + + if descriptor.itemsize > offset: + num = descriptor.itemsize - offset + result.append(('', f'|V{num}')) + + return result + +# Build a new array from the information in a pickle. +# Note that the name numpy.core._internal._reconstruct is embedded in +# pickles of ndarrays made with NumPy before release 1.0 +# so don't remove the name here, or you'll +# break backward compatibility. +def _reconstruct(subtype, shape, dtype): + return ndarray.__new__(subtype, shape, dtype) + + +# format_re was originally from numarray by J. Todd Miller + +format_re = re.compile(r'(?P[<>|=]?)' + r'(?P *[(]?[ ,0-9]*[)]? *)' + r'(?P[<>|=]?)' + r'(?P[A-Za-z0-9.?]*(?:\[[a-zA-Z0-9,.]+\])?)') +sep_re = re.compile(r'\s*,\s*') +space_re = re.compile(r'\s+$') + +# astr is a string (perhaps comma separated) + +_convorder = {'=': _nbo} + +def _commastring(astr): + startindex = 0 + result = [] + while startindex < len(astr): + mo = format_re.match(astr, pos=startindex) + try: + (order1, repeats, order2, dtype) = mo.groups() + except (TypeError, AttributeError): + raise ValueError( + f'format number {len(result)+1} of "{astr}" is not recognized' + ) from None + startindex = mo.end() + # Separator or ending padding + if startindex < len(astr): + if space_re.match(astr, pos=startindex): + startindex = len(astr) + else: + mo = sep_re.match(astr, pos=startindex) + if not mo: + raise ValueError( + 'format number %d of "%s" is not recognized' % + (len(result)+1, astr)) + startindex = mo.end() + + if order2 == '': + order = order1 + elif order1 == '': + order = order2 + else: + order1 = _convorder.get(order1, order1) + order2 = _convorder.get(order2, order2) + if (order1 != order2): + raise ValueError( + 'inconsistent byte-order specification %s and %s' % + (order1, order2)) + order = order1 + + if order in ('|', '=', _nbo): + order = '' + dtype = order + dtype + if (repeats == ''): + newitem = dtype + else: + newitem = (dtype, ast.literal_eval(repeats)) + result.append(newitem) + + return result + +class dummy_ctype: + def __init__(self, cls): + self._cls = cls + def __mul__(self, other): + return self + def __call__(self, *other): + return self._cls(other) + def __eq__(self, other): + return self._cls == other._cls + def __ne__(self, other): + return self._cls != other._cls + +def _getintp_ctype(): + val = _getintp_ctype.cache + if val is not None: + return val + if ctypes is None: + import numpy as np + val = dummy_ctype(np.intp) + else: + char = dtype('p').char + if char == 'i': + val = ctypes.c_int + elif char == 'l': + val = ctypes.c_long + elif char == 'q': + val = ctypes.c_longlong + else: + val = ctypes.c_long + _getintp_ctype.cache = val + return val +_getintp_ctype.cache = None + +# Used for .ctypes attribute of ndarray + +class _missing_ctypes: + def cast(self, num, obj): + return num.value + + class c_void_p: + def __init__(self, ptr): + self.value = ptr + + +class _ctypes: + def __init__(self, array, ptr=None): + self._arr = array + + if ctypes: + self._ctypes = ctypes + self._data = self._ctypes.c_void_p(ptr) + else: + # fake a pointer-like object that holds onto the reference + self._ctypes = _missing_ctypes() + self._data = self._ctypes.c_void_p(ptr) + self._data._objects = array + + if self._arr.ndim == 0: + self._zerod = True + else: + self._zerod = False + + def data_as(self, obj): + """ + Return the data pointer cast to a particular c-types object. + For example, calling ``self._as_parameter_`` is equivalent to + ``self.data_as(ctypes.c_void_p)``. Perhaps you want to use the data as a + pointer to a ctypes array of floating-point data: + ``self.data_as(ctypes.POINTER(ctypes.c_double))``. + + The returned pointer will keep a reference to the array. + """ + # _ctypes.cast function causes a circular reference of self._data in + # self._data._objects. Attributes of self._data cannot be released + # until gc.collect is called. Make a copy of the pointer first then let + # it hold the array reference. This is a workaround to circumvent the + # CPython bug https://bugs.python.org/issue12836 + ptr = self._ctypes.cast(self._data, obj) + ptr._arr = self._arr + return ptr + + def shape_as(self, obj): + """ + Return the shape tuple as an array of some other c-types + type. For example: ``self.shape_as(ctypes.c_short)``. + """ + if self._zerod: + return None + return (obj*self._arr.ndim)(*self._arr.shape) + + def strides_as(self, obj): + """ + Return the strides tuple as an array of some other + c-types type. For example: ``self.strides_as(ctypes.c_longlong)``. + """ + if self._zerod: + return None + return (obj*self._arr.ndim)(*self._arr.strides) + + @property + def data(self): + """ + A pointer to the memory area of the array as a Python integer. + This memory area may contain data that is not aligned, or not in correct + byte-order. The memory area may not even be writeable. The array + flags and data-type of this array should be respected when passing this + attribute to arbitrary C-code to avoid trouble that can include Python + crashing. User Beware! The value of this attribute is exactly the same + as ``self._array_interface_['data'][0]``. + + Note that unlike ``data_as``, a reference will not be kept to the array: + code like ``ctypes.c_void_p((a + b).ctypes.data)`` will result in a + pointer to a deallocated array, and should be spelt + ``(a + b).ctypes.data_as(ctypes.c_void_p)`` + """ + return self._data.value + + @property + def shape(self): + """ + (c_intp*self.ndim): A ctypes array of length self.ndim where + the basetype is the C-integer corresponding to ``dtype('p')`` on this + platform (see `~numpy.ctypeslib.c_intp`). This base-type could be + `ctypes.c_int`, `ctypes.c_long`, or `ctypes.c_longlong` depending on + the platform. The ctypes array contains the shape of + the underlying array. + """ + return self.shape_as(_getintp_ctype()) + + @property + def strides(self): + """ + (c_intp*self.ndim): A ctypes array of length self.ndim where + the basetype is the same as for the shape attribute. This ctypes array + contains the strides information from the underlying array. This strides + information is important for showing how many bytes must be jumped to + get to the next element in the array. + """ + return self.strides_as(_getintp_ctype()) + + @property + def _as_parameter_(self): + """ + Overrides the ctypes semi-magic method + + Enables `c_func(some_array.ctypes)` + """ + return self.data_as(ctypes.c_void_p) + + # Numpy 1.21.0, 2021-05-18 + + def get_data(self): + """Deprecated getter for the `_ctypes.data` property. + + .. deprecated:: 1.21 + """ + warnings.warn('"get_data" is deprecated. Use "data" instead', + DeprecationWarning, stacklevel=2) + return self.data + + def get_shape(self): + """Deprecated getter for the `_ctypes.shape` property. + + .. deprecated:: 1.21 + """ + warnings.warn('"get_shape" is deprecated. Use "shape" instead', + DeprecationWarning, stacklevel=2) + return self.shape + + def get_strides(self): + """Deprecated getter for the `_ctypes.strides` property. + + .. deprecated:: 1.21 + """ + warnings.warn('"get_strides" is deprecated. Use "strides" instead', + DeprecationWarning, stacklevel=2) + return self.strides + + def get_as_parameter(self): + """Deprecated getter for the `_ctypes._as_parameter_` property. + + .. deprecated:: 1.21 + """ + warnings.warn( + '"get_as_parameter" is deprecated. Use "_as_parameter_" instead', + DeprecationWarning, stacklevel=2, + ) + return self._as_parameter_ + + +def _newnames(datatype, order): + """ + Given a datatype and an order object, return a new names tuple, with the + order indicated + """ + oldnames = datatype.names + nameslist = list(oldnames) + if isinstance(order, str): + order = [order] + seen = set() + if isinstance(order, (list, tuple)): + for name in order: + try: + nameslist.remove(name) + except ValueError: + if name in seen: + raise ValueError(f"duplicate field name: {name}") from None + else: + raise ValueError(f"unknown field name: {name}") from None + seen.add(name) + return tuple(list(order) + nameslist) + raise ValueError(f"unsupported order value: {order}") + +def _copy_fields(ary): + """Return copy of structured array with padding between fields removed. + + Parameters + ---------- + ary : ndarray + Structured array from which to remove padding bytes + + Returns + ------- + ary_copy : ndarray + Copy of ary with padding bytes removed + """ + dt = ary.dtype + copy_dtype = {'names': dt.names, + 'formats': [dt.fields[name][0] for name in dt.names]} + return array(ary, dtype=copy_dtype, copy=True) + +def _promote_fields(dt1, dt2): + """ Perform type promotion for two structured dtypes. + + Parameters + ---------- + dt1 : structured dtype + First dtype. + dt2 : structured dtype + Second dtype. + + Returns + ------- + out : dtype + The promoted dtype + + Notes + ----- + If one of the inputs is aligned, the result will be. The titles of + both descriptors must match (point to the same field). + """ + # Both must be structured and have the same names in the same order + if (dt1.names is None or dt2.names is None) or dt1.names != dt2.names: + raise DTypePromotionError( + f"field names `{dt1.names}` and `{dt2.names}` mismatch.") + + # if both are identical, we can (maybe!) just return the same dtype. + identical = dt1 is dt2 + new_fields = [] + for name in dt1.names: + field1 = dt1.fields[name] + field2 = dt2.fields[name] + new_descr = promote_types(field1[0], field2[0]) + identical = identical and new_descr is field1[0] + + # Check that the titles match (if given): + if field1[2:] != field2[2:]: + raise DTypePromotionError( + f"field titles of field '{name}' mismatch") + if len(field1) == 2: + new_fields.append((name, new_descr)) + else: + new_fields.append(((field1[2], name), new_descr)) + + res = dtype(new_fields, align=dt1.isalignedstruct or dt2.isalignedstruct) + + # Might as well preserve identity (and metadata) if the dtype is identical + # and the itemsize, offsets are also unmodified. This could probably be + # sped up, but also probably just be removed entirely. + if identical and res.itemsize == dt1.itemsize: + for name in dt1.names: + if dt1.fields[name][1] != res.fields[name][1]: + return res # the dtype changed. + return dt1 + + return res + + +def _getfield_is_safe(oldtype, newtype, offset): + """ Checks safety of getfield for object arrays. + + As in _view_is_safe, we need to check that memory containing objects is not + reinterpreted as a non-object datatype and vice versa. + + Parameters + ---------- + oldtype : data-type + Data type of the original ndarray. + newtype : data-type + Data type of the field being accessed by ndarray.getfield + offset : int + Offset of the field being accessed by ndarray.getfield + + Raises + ------ + TypeError + If the field access is invalid + + """ + if newtype.hasobject or oldtype.hasobject: + if offset == 0 and newtype == oldtype: + return + if oldtype.names is not None: + for name in oldtype.names: + if (oldtype.fields[name][1] == offset and + oldtype.fields[name][0] == newtype): + return + raise TypeError("Cannot get/set field of an object array") + return + +def _view_is_safe(oldtype, newtype): + """ Checks safety of a view involving object arrays, for example when + doing:: + + np.zeros(10, dtype=oldtype).view(newtype) + + Parameters + ---------- + oldtype : data-type + Data type of original ndarray + newtype : data-type + Data type of the view + + Raises + ------ + TypeError + If the new type is incompatible with the old type. + + """ + + # if the types are equivalent, there is no problem. + # for example: dtype((np.record, 'i4,i4')) == dtype((np.void, 'i4,i4')) + if oldtype == newtype: + return + + if newtype.hasobject or oldtype.hasobject: + raise TypeError("Cannot change data-type for object array.") + return + +# Given a string containing a PEP 3118 format specifier, +# construct a NumPy dtype + +_pep3118_native_map = { + '?': '?', + 'c': 'S1', + 'b': 'b', + 'B': 'B', + 'h': 'h', + 'H': 'H', + 'i': 'i', + 'I': 'I', + 'l': 'l', + 'L': 'L', + 'q': 'q', + 'Q': 'Q', + 'e': 'e', + 'f': 'f', + 'd': 'd', + 'g': 'g', + 'Zf': 'F', + 'Zd': 'D', + 'Zg': 'G', + 's': 'S', + 'w': 'U', + 'O': 'O', + 'x': 'V', # padding +} +_pep3118_native_typechars = ''.join(_pep3118_native_map.keys()) + +_pep3118_standard_map = { + '?': '?', + 'c': 'S1', + 'b': 'b', + 'B': 'B', + 'h': 'i2', + 'H': 'u2', + 'i': 'i4', + 'I': 'u4', + 'l': 'i4', + 'L': 'u4', + 'q': 'i8', + 'Q': 'u8', + 'e': 'f2', + 'f': 'f', + 'd': 'd', + 'Zf': 'F', + 'Zd': 'D', + 's': 'S', + 'w': 'U', + 'O': 'O', + 'x': 'V', # padding +} +_pep3118_standard_typechars = ''.join(_pep3118_standard_map.keys()) + +_pep3118_unsupported_map = { + 'u': 'UCS-2 strings', + '&': 'pointers', + 't': 'bitfields', + 'X': 'function pointers', +} + +class _Stream: + def __init__(self, s): + self.s = s + self.byteorder = '@' + + def advance(self, n): + res = self.s[:n] + self.s = self.s[n:] + return res + + def consume(self, c): + if self.s[:len(c)] == c: + self.advance(len(c)) + return True + return False + + def consume_until(self, c): + if callable(c): + i = 0 + while i < len(self.s) and not c(self.s[i]): + i = i + 1 + return self.advance(i) + else: + i = self.s.index(c) + res = self.advance(i) + self.advance(len(c)) + return res + + @property + def next(self): + return self.s[0] + + def __bool__(self): + return bool(self.s) + + +def _dtype_from_pep3118(spec): + stream = _Stream(spec) + dtype, align = __dtype_from_pep3118(stream, is_subdtype=False) + return dtype + +def __dtype_from_pep3118(stream, is_subdtype): + field_spec = dict( + names=[], + formats=[], + offsets=[], + itemsize=0 + ) + offset = 0 + common_alignment = 1 + is_padding = False + + # Parse spec + while stream: + value = None + + # End of structure, bail out to upper level + if stream.consume('}'): + break + + # Sub-arrays (1) + shape = None + if stream.consume('('): + shape = stream.consume_until(')') + shape = tuple(map(int, shape.split(','))) + + # Byte order + if stream.next in ('@', '=', '<', '>', '^', '!'): + byteorder = stream.advance(1) + if byteorder == '!': + byteorder = '>' + stream.byteorder = byteorder + + # Byte order characters also control native vs. standard type sizes + if stream.byteorder in ('@', '^'): + type_map = _pep3118_native_map + type_map_chars = _pep3118_native_typechars + else: + type_map = _pep3118_standard_map + type_map_chars = _pep3118_standard_typechars + + # Item sizes + itemsize_str = stream.consume_until(lambda c: not c.isdigit()) + if itemsize_str: + itemsize = int(itemsize_str) + else: + itemsize = 1 + + # Data types + is_padding = False + + if stream.consume('T{'): + value, align = __dtype_from_pep3118( + stream, is_subdtype=True) + elif stream.next in type_map_chars: + if stream.next == 'Z': + typechar = stream.advance(2) + else: + typechar = stream.advance(1) + + is_padding = (typechar == 'x') + dtypechar = type_map[typechar] + if dtypechar in 'USV': + dtypechar += '%d' % itemsize + itemsize = 1 + numpy_byteorder = {'@': '=', '^': '='}.get( + stream.byteorder, stream.byteorder) + value = dtype(numpy_byteorder + dtypechar) + align = value.alignment + elif stream.next in _pep3118_unsupported_map: + desc = _pep3118_unsupported_map[stream.next] + raise NotImplementedError( + "Unrepresentable PEP 3118 data type {!r} ({})" + .format(stream.next, desc)) + else: + raise ValueError("Unknown PEP 3118 data type specifier %r" % stream.s) + + # + # Native alignment may require padding + # + # Here we assume that the presence of a '@' character implicitly implies + # that the start of the array is *already* aligned. + # + extra_offset = 0 + if stream.byteorder == '@': + start_padding = (-offset) % align + intra_padding = (-value.itemsize) % align + + offset += start_padding + + if intra_padding != 0: + if itemsize > 1 or (shape is not None and _prod(shape) > 1): + # Inject internal padding to the end of the sub-item + value = _add_trailing_padding(value, intra_padding) + else: + # We can postpone the injection of internal padding, + # as the item appears at most once + extra_offset += intra_padding + + # Update common alignment + common_alignment = _lcm(align, common_alignment) + + # Convert itemsize to sub-array + if itemsize != 1: + value = dtype((value, (itemsize,))) + + # Sub-arrays (2) + if shape is not None: + value = dtype((value, shape)) + + # Field name + if stream.consume(':'): + name = stream.consume_until(':') + else: + name = None + + if not (is_padding and name is None): + if name is not None and name in field_spec['names']: + raise RuntimeError(f"Duplicate field name '{name}' in PEP3118 format") + field_spec['names'].append(name) + field_spec['formats'].append(value) + field_spec['offsets'].append(offset) + + offset += value.itemsize + offset += extra_offset + + field_spec['itemsize'] = offset + + # extra final padding for aligned types + if stream.byteorder == '@': + field_spec['itemsize'] += (-offset) % common_alignment + + # Check if this was a simple 1-item type, and unwrap it + if (field_spec['names'] == [None] + and field_spec['offsets'][0] == 0 + and field_spec['itemsize'] == field_spec['formats'][0].itemsize + and not is_subdtype): + ret = field_spec['formats'][0] + else: + _fix_names(field_spec) + ret = dtype(field_spec) + + # Finished + return ret, common_alignment + +def _fix_names(field_spec): + """ Replace names which are None with the next unused f%d name """ + names = field_spec['names'] + for i, name in enumerate(names): + if name is not None: + continue + + j = 0 + while True: + name = f'f{j}' + if name not in names: + break + j = j + 1 + names[i] = name + +def _add_trailing_padding(value, padding): + """Inject the specified number of padding bytes at the end of a dtype""" + if value.fields is None: + field_spec = dict( + names=['f0'], + formats=[value], + offsets=[0], + itemsize=value.itemsize + ) + else: + fields = value.fields + names = value.names + field_spec = dict( + names=names, + formats=[fields[name][0] for name in names], + offsets=[fields[name][1] for name in names], + itemsize=value.itemsize + ) + + field_spec['itemsize'] += padding + return dtype(field_spec) + +def _prod(a): + p = 1 + for x in a: + p *= x + return p + +def _gcd(a, b): + """Calculate the greatest common divisor of a and b""" + while b: + a, b = b, a % b + return a + +def _lcm(a, b): + return a // _gcd(a, b) * b + +def array_ufunc_errmsg_formatter(dummy, ufunc, method, *inputs, **kwargs): + """ Format the error message for when __array_ufunc__ gives up. """ + args_string = ', '.join(['{!r}'.format(arg) for arg in inputs] + + ['{}={!r}'.format(k, v) + for k, v in kwargs.items()]) + args = inputs + kwargs.get('out', ()) + types_string = ', '.join(repr(type(arg).__name__) for arg in args) + return ('operand type(s) all returned NotImplemented from ' + '__array_ufunc__({!r}, {!r}, {}): {}' + .format(ufunc, method, args_string, types_string)) + + +def array_function_errmsg_formatter(public_api, types): + """ Format the error message for when __array_ufunc__ gives up. """ + func_name = '{}.{}'.format(public_api.__module__, public_api.__name__) + return ("no implementation found for '{}' on types that implement " + '__array_function__: {}'.format(func_name, list(types))) + + +def _ufunc_doc_signature_formatter(ufunc): + """ + Builds a signature string which resembles PEP 457 + + This is used to construct the first line of the docstring + """ + + # input arguments are simple + if ufunc.nin == 1: + in_args = 'x' + else: + in_args = ', '.join(f'x{i+1}' for i in range(ufunc.nin)) + + # output arguments are both keyword or positional + if ufunc.nout == 0: + out_args = ', /, out=()' + elif ufunc.nout == 1: + out_args = ', /, out=None' + else: + out_args = '[, {positional}], / [, out={default}]'.format( + positional=', '.join( + 'out{}'.format(i+1) for i in range(ufunc.nout)), + default=repr((None,)*ufunc.nout) + ) + + # keyword only args depend on whether this is a gufunc + kwargs = ( + ", casting='same_kind'" + ", order='K'" + ", dtype=None" + ", subok=True" + ) + + # NOTE: gufuncs may or may not support the `axis` parameter + if ufunc.signature is None: + kwargs = f", where=True{kwargs}[, signature, extobj]" + else: + kwargs += "[, signature, extobj, axes, axis]" + + # join all the parts together + return '{name}({in_args}{out_args}, *{kwargs})'.format( + name=ufunc.__name__, + in_args=in_args, + out_args=out_args, + kwargs=kwargs + ) + + +def npy_ctypes_check(cls): + # determine if a class comes from ctypes, in order to work around + # a bug in the buffer protocol for those objects, bpo-10746 + try: + # ctypes class are new-style, so have an __mro__. This probably fails + # for ctypes classes with multiple inheritance. + if IS_PYPY: + # (..., _ctypes.basics._CData, Bufferable, object) + ctype_base = cls.__mro__[-3] + else: + # # (..., _ctypes._CData, object) + ctype_base = cls.__mro__[-2] + # right now, they're part of the _ctypes module + return '_ctypes' in ctype_base.__module__ + except Exception: + return False diff --git a/venv/lib/python3.10/site-packages/numpy/core/_internal.pyi b/venv/lib/python3.10/site-packages/numpy/core/_internal.pyi new file mode 100644 index 0000000000000000000000000000000000000000..8a25ef2cba41d33557e1a09ef630a7bb0a5d0c4c --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_internal.pyi @@ -0,0 +1,30 @@ +from typing import Any, TypeVar, overload, Generic +import ctypes as ct + +from numpy import ndarray +from numpy.ctypeslib import c_intp + +_CastT = TypeVar("_CastT", bound=ct._CanCastTo) # Copied from `ctypes.cast` +_CT = TypeVar("_CT", bound=ct._CData) +_PT = TypeVar("_PT", bound=None | int) + +# TODO: Let the likes of `shape_as` and `strides_as` return `None` +# for 0D arrays once we've got shape-support + +class _ctypes(Generic[_PT]): + @overload + def __new__(cls, array: ndarray[Any, Any], ptr: None = ...) -> _ctypes[None]: ... + @overload + def __new__(cls, array: ndarray[Any, Any], ptr: _PT) -> _ctypes[_PT]: ... + @property + def data(self) -> _PT: ... + @property + def shape(self) -> ct.Array[c_intp]: ... + @property + def strides(self) -> ct.Array[c_intp]: ... + @property + def _as_parameter_(self) -> ct.c_void_p: ... + + def data_as(self, obj: type[_CastT]) -> _CastT: ... + def shape_as(self, obj: type[_CT]) -> ct.Array[_CT]: ... + def strides_as(self, obj: type[_CT]) -> ct.Array[_CT]: ... diff --git a/venv/lib/python3.10/site-packages/numpy/core/_machar.py b/venv/lib/python3.10/site-packages/numpy/core/_machar.py new file mode 100644 index 0000000000000000000000000000000000000000..59d71014ff20053fecd69bf3448b152030842491 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_machar.py @@ -0,0 +1,356 @@ +""" +Machine arithmetic - determine the parameters of the +floating-point arithmetic system + +Author: Pearu Peterson, September 2003 + +""" +__all__ = ['MachAr'] + +from .fromnumeric import any +from ._ufunc_config import errstate +from .._utils import set_module + +# Need to speed this up...especially for longfloat + +# Deprecated 2021-10-20, NumPy 1.22 +class MachAr: + """ + Diagnosing machine parameters. + + Attributes + ---------- + ibeta : int + Radix in which numbers are represented. + it : int + Number of base-`ibeta` digits in the floating point mantissa M. + machep : int + Exponent of the smallest (most negative) power of `ibeta` that, + added to 1.0, gives something different from 1.0 + eps : float + Floating-point number ``beta**machep`` (floating point precision) + negep : int + Exponent of the smallest power of `ibeta` that, subtracted + from 1.0, gives something different from 1.0. + epsneg : float + Floating-point number ``beta**negep``. + iexp : int + Number of bits in the exponent (including its sign and bias). + minexp : int + Smallest (most negative) power of `ibeta` consistent with there + being no leading zeros in the mantissa. + xmin : float + Floating-point number ``beta**minexp`` (the smallest [in + magnitude] positive floating point number with full precision). + maxexp : int + Smallest (positive) power of `ibeta` that causes overflow. + xmax : float + ``(1-epsneg) * beta**maxexp`` (the largest [in magnitude] + usable floating value). + irnd : int + In ``range(6)``, information on what kind of rounding is done + in addition, and on how underflow is handled. + ngrd : int + Number of 'guard digits' used when truncating the product + of two mantissas to fit the representation. + epsilon : float + Same as `eps`. + tiny : float + An alias for `smallest_normal`, kept for backwards compatibility. + huge : float + Same as `xmax`. + precision : float + ``- int(-log10(eps))`` + resolution : float + ``- 10**(-precision)`` + smallest_normal : float + The smallest positive floating point number with 1 as leading bit in + the mantissa following IEEE-754. Same as `xmin`. + smallest_subnormal : float + The smallest positive floating point number with 0 as leading bit in + the mantissa following IEEE-754. + + Parameters + ---------- + float_conv : function, optional + Function that converts an integer or integer array to a float + or float array. Default is `float`. + int_conv : function, optional + Function that converts a float or float array to an integer or + integer array. Default is `int`. + float_to_float : function, optional + Function that converts a float array to float. Default is `float`. + Note that this does not seem to do anything useful in the current + implementation. + float_to_str : function, optional + Function that converts a single float to a string. Default is + ``lambda v:'%24.16e' %v``. + title : str, optional + Title that is printed in the string representation of `MachAr`. + + See Also + -------- + finfo : Machine limits for floating point types. + iinfo : Machine limits for integer types. + + References + ---------- + .. [1] Press, Teukolsky, Vetterling and Flannery, + "Numerical Recipes in C++," 2nd ed, + Cambridge University Press, 2002, p. 31. + + """ + + def __init__(self, float_conv=float,int_conv=int, + float_to_float=float, + float_to_str=lambda v:'%24.16e' % v, + title='Python floating point number'): + """ + + float_conv - convert integer to float (array) + int_conv - convert float (array) to integer + float_to_float - convert float array to float + float_to_str - convert array float to str + title - description of used floating point numbers + + """ + # We ignore all errors here because we are purposely triggering + # underflow to detect the properties of the runninng arch. + with errstate(under='ignore'): + self._do_init(float_conv, int_conv, float_to_float, float_to_str, title) + + def _do_init(self, float_conv, int_conv, float_to_float, float_to_str, title): + max_iterN = 10000 + msg = "Did not converge after %d tries with %s" + one = float_conv(1) + two = one + one + zero = one - one + + # Do we really need to do this? Aren't they 2 and 2.0? + # Determine ibeta and beta + a = one + for _ in range(max_iterN): + a = a + a + temp = a + one + temp1 = temp - a + if any(temp1 - one != zero): + break + else: + raise RuntimeError(msg % (_, one.dtype)) + b = one + for _ in range(max_iterN): + b = b + b + temp = a + b + itemp = int_conv(temp-a) + if any(itemp != 0): + break + else: + raise RuntimeError(msg % (_, one.dtype)) + ibeta = itemp + beta = float_conv(ibeta) + + # Determine it and irnd + it = -1 + b = one + for _ in range(max_iterN): + it = it + 1 + b = b * beta + temp = b + one + temp1 = temp - b + if any(temp1 - one != zero): + break + else: + raise RuntimeError(msg % (_, one.dtype)) + + betah = beta / two + a = one + for _ in range(max_iterN): + a = a + a + temp = a + one + temp1 = temp - a + if any(temp1 - one != zero): + break + else: + raise RuntimeError(msg % (_, one.dtype)) + temp = a + betah + irnd = 0 + if any(temp-a != zero): + irnd = 1 + tempa = a + beta + temp = tempa + betah + if irnd == 0 and any(temp-tempa != zero): + irnd = 2 + + # Determine negep and epsneg + negep = it + 3 + betain = one / beta + a = one + for i in range(negep): + a = a * betain + b = a + for _ in range(max_iterN): + temp = one - a + if any(temp-one != zero): + break + a = a * beta + negep = negep - 1 + # Prevent infinite loop on PPC with gcc 4.0: + if negep < 0: + raise RuntimeError("could not determine machine tolerance " + "for 'negep', locals() -> %s" % (locals())) + else: + raise RuntimeError(msg % (_, one.dtype)) + negep = -negep + epsneg = a + + # Determine machep and eps + machep = - it - 3 + a = b + + for _ in range(max_iterN): + temp = one + a + if any(temp-one != zero): + break + a = a * beta + machep = machep + 1 + else: + raise RuntimeError(msg % (_, one.dtype)) + eps = a + + # Determine ngrd + ngrd = 0 + temp = one + eps + if irnd == 0 and any(temp*one - one != zero): + ngrd = 1 + + # Determine iexp + i = 0 + k = 1 + z = betain + t = one + eps + nxres = 0 + for _ in range(max_iterN): + y = z + z = y*y + a = z*one # Check here for underflow + temp = z*t + if any(a+a == zero) or any(abs(z) >= y): + break + temp1 = temp * betain + if any(temp1*beta == z): + break + i = i + 1 + k = k + k + else: + raise RuntimeError(msg % (_, one.dtype)) + if ibeta != 10: + iexp = i + 1 + mx = k + k + else: + iexp = 2 + iz = ibeta + while k >= iz: + iz = iz * ibeta + iexp = iexp + 1 + mx = iz + iz - 1 + + # Determine minexp and xmin + for _ in range(max_iterN): + xmin = y + y = y * betain + a = y * one + temp = y * t + if any((a + a) != zero) and any(abs(y) < xmin): + k = k + 1 + temp1 = temp * betain + if any(temp1*beta == y) and any(temp != y): + nxres = 3 + xmin = y + break + else: + break + else: + raise RuntimeError(msg % (_, one.dtype)) + minexp = -k + + # Determine maxexp, xmax + if mx <= k + k - 3 and ibeta != 10: + mx = mx + mx + iexp = iexp + 1 + maxexp = mx + minexp + irnd = irnd + nxres + if irnd >= 2: + maxexp = maxexp - 2 + i = maxexp + minexp + if ibeta == 2 and not i: + maxexp = maxexp - 1 + if i > 20: + maxexp = maxexp - 1 + if any(a != y): + maxexp = maxexp - 2 + xmax = one - epsneg + if any(xmax*one != xmax): + xmax = one - beta*epsneg + xmax = xmax / (xmin*beta*beta*beta) + i = maxexp + minexp + 3 + for j in range(i): + if ibeta == 2: + xmax = xmax + xmax + else: + xmax = xmax * beta + + smallest_subnormal = abs(xmin / beta ** (it)) + + self.ibeta = ibeta + self.it = it + self.negep = negep + self.epsneg = float_to_float(epsneg) + self._str_epsneg = float_to_str(epsneg) + self.machep = machep + self.eps = float_to_float(eps) + self._str_eps = float_to_str(eps) + self.ngrd = ngrd + self.iexp = iexp + self.minexp = minexp + self.xmin = float_to_float(xmin) + self._str_xmin = float_to_str(xmin) + self.maxexp = maxexp + self.xmax = float_to_float(xmax) + self._str_xmax = float_to_str(xmax) + self.irnd = irnd + + self.title = title + # Commonly used parameters + self.epsilon = self.eps + self.tiny = self.xmin + self.huge = self.xmax + self.smallest_normal = self.xmin + self._str_smallest_normal = float_to_str(self.xmin) + self.smallest_subnormal = float_to_float(smallest_subnormal) + self._str_smallest_subnormal = float_to_str(smallest_subnormal) + + import math + self.precision = int(-math.log10(float_to_float(self.eps))) + ten = two + two + two + two + two + resolution = ten ** (-self.precision) + self.resolution = float_to_float(resolution) + self._str_resolution = float_to_str(resolution) + + def __str__(self): + fmt = ( + 'Machine parameters for %(title)s\n' + '---------------------------------------------------------------------\n' + 'ibeta=%(ibeta)s it=%(it)s iexp=%(iexp)s ngrd=%(ngrd)s irnd=%(irnd)s\n' + 'machep=%(machep)s eps=%(_str_eps)s (beta**machep == epsilon)\n' + 'negep =%(negep)s epsneg=%(_str_epsneg)s (beta**epsneg)\n' + 'minexp=%(minexp)s xmin=%(_str_xmin)s (beta**minexp == tiny)\n' + 'maxexp=%(maxexp)s xmax=%(_str_xmax)s ((1-epsneg)*beta**maxexp == huge)\n' + 'smallest_normal=%(smallest_normal)s ' + 'smallest_subnormal=%(smallest_subnormal)s\n' + '---------------------------------------------------------------------\n' + ) + return fmt % self.__dict__ + + +if __name__ == '__main__': + print(MachAr()) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_multiarray_tests.cpython-310-x86_64-linux-gnu.so b/venv/lib/python3.10/site-packages/numpy/core/_multiarray_tests.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..9dc2e476570f023136688a3ab23c95dc987cc103 Binary files /dev/null and b/venv/lib/python3.10/site-packages/numpy/core/_multiarray_tests.cpython-310-x86_64-linux-gnu.so differ diff --git a/venv/lib/python3.10/site-packages/numpy/core/_operand_flag_tests.cpython-310-x86_64-linux-gnu.so b/venv/lib/python3.10/site-packages/numpy/core/_operand_flag_tests.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..7a672f9eb4108313e7ca19ec65b1967652c5923b Binary files /dev/null and b/venv/lib/python3.10/site-packages/numpy/core/_operand_flag_tests.cpython-310-x86_64-linux-gnu.so differ diff --git a/venv/lib/python3.10/site-packages/numpy/core/_rational_tests.cpython-310-x86_64-linux-gnu.so b/venv/lib/python3.10/site-packages/numpy/core/_rational_tests.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..88ae1fbc7c171d8b69a2f46317560b1a6d86a7b2 Binary files /dev/null and b/venv/lib/python3.10/site-packages/numpy/core/_rational_tests.cpython-310-x86_64-linux-gnu.so differ diff --git a/venv/lib/python3.10/site-packages/numpy/core/_string_helpers.py b/venv/lib/python3.10/site-packages/numpy/core/_string_helpers.py new file mode 100644 index 0000000000000000000000000000000000000000..1f757cc0734fe1db9528a0ecec47731009c57c6c --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_string_helpers.py @@ -0,0 +1,100 @@ +""" +String-handling utilities to avoid locale-dependence. + +Used primarily to generate type name aliases. +""" +# "import string" is costly to import! +# Construct the translation tables directly +# "A" = chr(65), "a" = chr(97) +_all_chars = tuple(map(chr, range(256))) +_ascii_upper = _all_chars[65:65+26] +_ascii_lower = _all_chars[97:97+26] +LOWER_TABLE = "".join(_all_chars[:65] + _ascii_lower + _all_chars[65+26:]) +UPPER_TABLE = "".join(_all_chars[:97] + _ascii_upper + _all_chars[97+26:]) + + +def english_lower(s): + """ Apply English case rules to convert ASCII strings to all lower case. + + This is an internal utility function to replace calls to str.lower() such + that we can avoid changing behavior with changing locales. In particular, + Turkish has distinct dotted and dotless variants of the Latin letter "I" in + both lowercase and uppercase. Thus, "I".lower() != "i" in a "tr" locale. + + Parameters + ---------- + s : str + + Returns + ------- + lowered : str + + Examples + -------- + >>> from numpy.core.numerictypes import english_lower + >>> english_lower('ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_') + 'abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz0123456789_' + >>> english_lower('') + '' + """ + lowered = s.translate(LOWER_TABLE) + return lowered + + +def english_upper(s): + """ Apply English case rules to convert ASCII strings to all upper case. + + This is an internal utility function to replace calls to str.upper() such + that we can avoid changing behavior with changing locales. In particular, + Turkish has distinct dotted and dotless variants of the Latin letter "I" in + both lowercase and uppercase. Thus, "i".upper() != "I" in a "tr" locale. + + Parameters + ---------- + s : str + + Returns + ------- + uppered : str + + Examples + -------- + >>> from numpy.core.numerictypes import english_upper + >>> english_upper('ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_') + 'ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_' + >>> english_upper('') + '' + """ + uppered = s.translate(UPPER_TABLE) + return uppered + + +def english_capitalize(s): + """ Apply English case rules to convert the first character of an ASCII + string to upper case. + + This is an internal utility function to replace calls to str.capitalize() + such that we can avoid changing behavior with changing locales. + + Parameters + ---------- + s : str + + Returns + ------- + capitalized : str + + Examples + -------- + >>> from numpy.core.numerictypes import english_capitalize + >>> english_capitalize('int8') + 'Int8' + >>> english_capitalize('Int8') + 'Int8' + >>> english_capitalize('') + '' + """ + if s: + return english_upper(s[0]) + s[1:] + else: + return s diff --git a/venv/lib/python3.10/site-packages/numpy/core/_struct_ufunc_tests.cpython-310-x86_64-linux-gnu.so b/venv/lib/python3.10/site-packages/numpy/core/_struct_ufunc_tests.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..aeb87fa06862ff4227ad3d43c8cc14227eabb7d4 Binary files /dev/null and b/venv/lib/python3.10/site-packages/numpy/core/_struct_ufunc_tests.cpython-310-x86_64-linux-gnu.so differ diff --git a/venv/lib/python3.10/site-packages/numpy/core/_type_aliases.py b/venv/lib/python3.10/site-packages/numpy/core/_type_aliases.py new file mode 100644 index 0000000000000000000000000000000000000000..38f1a099e9e20e431cfd0ce9a80b15938d5e89d1 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_type_aliases.py @@ -0,0 +1,245 @@ +""" +Due to compatibility, numpy has a very large number of different naming +conventions for the scalar types (those subclassing from `numpy.generic`). +This file produces a convoluted set of dictionaries mapping names to types, +and sometimes other mappings too. + +.. data:: allTypes + A dictionary of names to types that will be exposed as attributes through + ``np.core.numerictypes.*`` + +.. data:: sctypeDict + Similar to `allTypes`, but maps a broader set of aliases to their types. + +.. data:: sctypes + A dictionary keyed by a "type group" string, providing a list of types + under that group. + +""" + +from numpy.compat import unicode +from numpy.core._string_helpers import english_lower +from numpy.core.multiarray import typeinfo, dtype +from numpy.core._dtype import _kind_name + + +sctypeDict = {} # Contains all leaf-node scalar types with aliases +allTypes = {} # Collect the types we will add to the module + + +# separate the actual type info from the abstract base classes +_abstract_types = {} +_concrete_typeinfo = {} +for k, v in typeinfo.items(): + # make all the keys lowercase too + k = english_lower(k) + if isinstance(v, type): + _abstract_types[k] = v + else: + _concrete_typeinfo[k] = v + +_concrete_types = {v.type for k, v in _concrete_typeinfo.items()} + + +def _bits_of(obj): + try: + info = next(v for v in _concrete_typeinfo.values() if v.type is obj) + except StopIteration: + if obj in _abstract_types.values(): + msg = "Cannot count the bits of an abstract type" + raise ValueError(msg) from None + + # some third-party type - make a best-guess + return dtype(obj).itemsize * 8 + else: + return info.bits + + +def bitname(obj): + """Return a bit-width name for a given type object""" + bits = _bits_of(obj) + dt = dtype(obj) + char = dt.kind + base = _kind_name(dt) + + if base == 'object': + bits = 0 + + if bits != 0: + char = "%s%d" % (char, bits // 8) + + return base, bits, char + + +def _add_types(): + for name, info in _concrete_typeinfo.items(): + # define C-name and insert typenum and typechar references also + allTypes[name] = info.type + sctypeDict[name] = info.type + sctypeDict[info.char] = info.type + sctypeDict[info.num] = info.type + + for name, cls in _abstract_types.items(): + allTypes[name] = cls +_add_types() + +# This is the priority order used to assign the bit-sized NPY_INTxx names, which +# must match the order in npy_common.h in order for NPY_INTxx and np.intxx to be +# consistent. +# If two C types have the same size, then the earliest one in this list is used +# as the sized name. +_int_ctypes = ['long', 'longlong', 'int', 'short', 'byte'] +_uint_ctypes = list('u' + t for t in _int_ctypes) + +def _add_aliases(): + for name, info in _concrete_typeinfo.items(): + # these are handled by _add_integer_aliases + if name in _int_ctypes or name in _uint_ctypes: + continue + + # insert bit-width version for this class (if relevant) + base, bit, char = bitname(info.type) + + myname = "%s%d" % (base, bit) + + # ensure that (c)longdouble does not overwrite the aliases assigned to + # (c)double + if name in ('longdouble', 'clongdouble') and myname in allTypes: + continue + + # Add to the main namespace if desired: + if bit != 0 and base != "bool": + allTypes[myname] = info.type + + # add forward, reverse, and string mapping to numarray + sctypeDict[char] = info.type + + # add mapping for both the bit name + sctypeDict[myname] = info.type + + +_add_aliases() + +def _add_integer_aliases(): + seen_bits = set() + for i_ctype, u_ctype in zip(_int_ctypes, _uint_ctypes): + i_info = _concrete_typeinfo[i_ctype] + u_info = _concrete_typeinfo[u_ctype] + bits = i_info.bits # same for both + + for info, charname, intname in [ + (i_info,'i%d' % (bits//8,), 'int%d' % bits), + (u_info,'u%d' % (bits//8,), 'uint%d' % bits)]: + if bits not in seen_bits: + # sometimes two different types have the same number of bits + # if so, the one iterated over first takes precedence + allTypes[intname] = info.type + sctypeDict[intname] = info.type + sctypeDict[charname] = info.type + + seen_bits.add(bits) + +_add_integer_aliases() + +# We use these later +void = allTypes['void'] + +# +# Rework the Python names (so that float and complex and int are consistent +# with Python usage) +# +def _set_up_aliases(): + type_pairs = [('complex_', 'cdouble'), + ('single', 'float'), + ('csingle', 'cfloat'), + ('singlecomplex', 'cfloat'), + ('float_', 'double'), + ('intc', 'int'), + ('uintc', 'uint'), + ('int_', 'long'), + ('uint', 'ulong'), + ('cfloat', 'cdouble'), + ('longfloat', 'longdouble'), + ('clongfloat', 'clongdouble'), + ('longcomplex', 'clongdouble'), + ('bool_', 'bool'), + ('bytes_', 'string'), + ('string_', 'string'), + ('str_', 'unicode'), + ('unicode_', 'unicode'), + ('object_', 'object')] + for alias, t in type_pairs: + allTypes[alias] = allTypes[t] + sctypeDict[alias] = sctypeDict[t] + # Remove aliases overriding python types and modules + to_remove = ['object', 'int', 'float', + 'complex', 'bool', 'string', 'datetime', 'timedelta', + 'bytes', 'str'] + + for t in to_remove: + try: + del allTypes[t] + del sctypeDict[t] + except KeyError: + pass + + # Additional aliases in sctypeDict that should not be exposed as attributes + attrs_to_remove = ['ulong'] + + for t in attrs_to_remove: + try: + del allTypes[t] + except KeyError: + pass +_set_up_aliases() + + +sctypes = {'int': [], + 'uint':[], + 'float':[], + 'complex':[], + 'others':[bool, object, bytes, unicode, void]} + +def _add_array_type(typename, bits): + try: + t = allTypes['%s%d' % (typename, bits)] + except KeyError: + pass + else: + sctypes[typename].append(t) + +def _set_array_types(): + ibytes = [1, 2, 4, 8, 16, 32, 64] + fbytes = [2, 4, 8, 10, 12, 16, 32, 64] + for bytes in ibytes: + bits = 8*bytes + _add_array_type('int', bits) + _add_array_type('uint', bits) + for bytes in fbytes: + bits = 8*bytes + _add_array_type('float', bits) + _add_array_type('complex', 2*bits) + _gi = dtype('p') + if _gi.type not in sctypes['int']: + indx = 0 + sz = _gi.itemsize + _lst = sctypes['int'] + while (indx < len(_lst) and sz >= _lst[indx](0).itemsize): + indx += 1 + sctypes['int'].insert(indx, _gi.type) + sctypes['uint'].insert(indx, dtype('P').type) +_set_array_types() + + +# Add additional strings to the sctypeDict +_toadd = ['int', 'float', 'complex', 'bool', 'object', + 'str', 'bytes', ('a', 'bytes_'), + ('int0', 'intp'), ('uint0', 'uintp')] + +for name in _toadd: + if isinstance(name, tuple): + sctypeDict[name[0]] = allTypes[name[1]] + else: + sctypeDict[name] = allTypes['%s_' % name] + +del _toadd, name diff --git a/venv/lib/python3.10/site-packages/numpy/core/_ufunc_config.py b/venv/lib/python3.10/site-packages/numpy/core/_ufunc_config.py new file mode 100644 index 0000000000000000000000000000000000000000..df821309581671a125e47f34de9289a7f481fda3 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_ufunc_config.py @@ -0,0 +1,466 @@ +""" +Functions for changing global ufunc configuration + +This provides helpers which wrap `umath.geterrobj` and `umath.seterrobj` +""" +import collections.abc +import contextlib +import contextvars + +from .._utils import set_module +from .umath import ( + UFUNC_BUFSIZE_DEFAULT, + ERR_IGNORE, ERR_WARN, ERR_RAISE, ERR_CALL, ERR_PRINT, ERR_LOG, ERR_DEFAULT, + SHIFT_DIVIDEBYZERO, SHIFT_OVERFLOW, SHIFT_UNDERFLOW, SHIFT_INVALID, +) +from . import umath + +__all__ = [ + "seterr", "geterr", "setbufsize", "getbufsize", "seterrcall", "geterrcall", + "errstate", '_no_nep50_warning' +] + +_errdict = {"ignore": ERR_IGNORE, + "warn": ERR_WARN, + "raise": ERR_RAISE, + "call": ERR_CALL, + "print": ERR_PRINT, + "log": ERR_LOG} + +_errdict_rev = {value: key for key, value in _errdict.items()} + + +@set_module('numpy') +def seterr(all=None, divide=None, over=None, under=None, invalid=None): + """ + Set how floating-point errors are handled. + + Note that operations on integer scalar types (such as `int16`) are + handled like floating point, and are affected by these settings. + + Parameters + ---------- + all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional + Set treatment for all types of floating-point errors at once: + + - ignore: Take no action when the exception occurs. + - warn: Print a `RuntimeWarning` (via the Python `warnings` module). + - raise: Raise a `FloatingPointError`. + - call: Call a function specified using the `seterrcall` function. + - print: Print a warning directly to ``stdout``. + - log: Record error in a Log object specified by `seterrcall`. + + The default is not to change the current behavior. + divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional + Treatment for division by zero. + over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional + Treatment for floating-point overflow. + under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional + Treatment for floating-point underflow. + invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional + Treatment for invalid floating-point operation. + + Returns + ------- + old_settings : dict + Dictionary containing the old settings. + + See also + -------- + seterrcall : Set a callback function for the 'call' mode. + geterr, geterrcall, errstate + + Notes + ----- + The floating-point exceptions are defined in the IEEE 754 standard [1]_: + + - Division by zero: infinite result obtained from finite numbers. + - Overflow: result too large to be expressed. + - Underflow: result so close to zero that some precision + was lost. + - Invalid operation: result is not an expressible number, typically + indicates that a NaN was produced. + + .. [1] https://en.wikipedia.org/wiki/IEEE_754 + + Examples + -------- + >>> old_settings = np.seterr(all='ignore') #seterr to known value + >>> np.seterr(over='raise') + {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'} + >>> np.seterr(**old_settings) # reset to default + {'divide': 'ignore', 'over': 'raise', 'under': 'ignore', 'invalid': 'ignore'} + + >>> np.int16(32000) * np.int16(3) + 30464 + >>> old_settings = np.seterr(all='warn', over='raise') + >>> np.int16(32000) * np.int16(3) + Traceback (most recent call last): + File "", line 1, in + FloatingPointError: overflow encountered in scalar multiply + + >>> old_settings = np.seterr(all='print') + >>> np.geterr() + {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'} + >>> np.int16(32000) * np.int16(3) + 30464 + + """ + + pyvals = umath.geterrobj() + old = geterr() + + if divide is None: + divide = all or old['divide'] + if over is None: + over = all or old['over'] + if under is None: + under = all or old['under'] + if invalid is None: + invalid = all or old['invalid'] + + maskvalue = ((_errdict[divide] << SHIFT_DIVIDEBYZERO) + + (_errdict[over] << SHIFT_OVERFLOW) + + (_errdict[under] << SHIFT_UNDERFLOW) + + (_errdict[invalid] << SHIFT_INVALID)) + + pyvals[1] = maskvalue + umath.seterrobj(pyvals) + return old + + +@set_module('numpy') +def geterr(): + """ + Get the current way of handling floating-point errors. + + Returns + ------- + res : dict + A dictionary with keys "divide", "over", "under", and "invalid", + whose values are from the strings "ignore", "print", "log", "warn", + "raise", and "call". The keys represent possible floating-point + exceptions, and the values define how these exceptions are handled. + + See Also + -------- + geterrcall, seterr, seterrcall + + Notes + ----- + For complete documentation of the types of floating-point exceptions and + treatment options, see `seterr`. + + Examples + -------- + >>> np.geterr() + {'divide': 'warn', 'over': 'warn', 'under': 'ignore', 'invalid': 'warn'} + >>> np.arange(3.) / np.arange(3.) + array([nan, 1., 1.]) + + >>> oldsettings = np.seterr(all='warn', over='raise') + >>> np.geterr() + {'divide': 'warn', 'over': 'raise', 'under': 'warn', 'invalid': 'warn'} + >>> np.arange(3.) / np.arange(3.) + array([nan, 1., 1.]) + + """ + maskvalue = umath.geterrobj()[1] + mask = 7 + res = {} + val = (maskvalue >> SHIFT_DIVIDEBYZERO) & mask + res['divide'] = _errdict_rev[val] + val = (maskvalue >> SHIFT_OVERFLOW) & mask + res['over'] = _errdict_rev[val] + val = (maskvalue >> SHIFT_UNDERFLOW) & mask + res['under'] = _errdict_rev[val] + val = (maskvalue >> SHIFT_INVALID) & mask + res['invalid'] = _errdict_rev[val] + return res + + +@set_module('numpy') +def setbufsize(size): + """ + Set the size of the buffer used in ufuncs. + + Parameters + ---------- + size : int + Size of buffer. + + """ + if size > 10e6: + raise ValueError("Buffer size, %s, is too big." % size) + if size < 5: + raise ValueError("Buffer size, %s, is too small." % size) + if size % 16 != 0: + raise ValueError("Buffer size, %s, is not a multiple of 16." % size) + + pyvals = umath.geterrobj() + old = getbufsize() + pyvals[0] = size + umath.seterrobj(pyvals) + return old + + +@set_module('numpy') +def getbufsize(): + """ + Return the size of the buffer used in ufuncs. + + Returns + ------- + getbufsize : int + Size of ufunc buffer in bytes. + + """ + return umath.geterrobj()[0] + + +@set_module('numpy') +def seterrcall(func): + """ + Set the floating-point error callback function or log object. + + There are two ways to capture floating-point error messages. The first + is to set the error-handler to 'call', using `seterr`. Then, set + the function to call using this function. + + The second is to set the error-handler to 'log', using `seterr`. + Floating-point errors then trigger a call to the 'write' method of + the provided object. + + Parameters + ---------- + func : callable f(err, flag) or object with write method + Function to call upon floating-point errors ('call'-mode) or + object whose 'write' method is used to log such message ('log'-mode). + + The call function takes two arguments. The first is a string describing + the type of error (such as "divide by zero", "overflow", "underflow", + or "invalid value"), and the second is the status flag. The flag is a + byte, whose four least-significant bits indicate the type of error, one + of "divide", "over", "under", "invalid":: + + [0 0 0 0 divide over under invalid] + + In other words, ``flags = divide + 2*over + 4*under + 8*invalid``. + + If an object is provided, its write method should take one argument, + a string. + + Returns + ------- + h : callable, log instance or None + The old error handler. + + See Also + -------- + seterr, geterr, geterrcall + + Examples + -------- + Callback upon error: + + >>> def err_handler(type, flag): + ... print("Floating point error (%s), with flag %s" % (type, flag)) + ... + + >>> saved_handler = np.seterrcall(err_handler) + >>> save_err = np.seterr(all='call') + + >>> np.array([1, 2, 3]) / 0.0 + Floating point error (divide by zero), with flag 1 + array([inf, inf, inf]) + + >>> np.seterrcall(saved_handler) + + >>> np.seterr(**save_err) + {'divide': 'call', 'over': 'call', 'under': 'call', 'invalid': 'call'} + + Log error message: + + >>> class Log: + ... def write(self, msg): + ... print("LOG: %s" % msg) + ... + + >>> log = Log() + >>> saved_handler = np.seterrcall(log) + >>> save_err = np.seterr(all='log') + + >>> np.array([1, 2, 3]) / 0.0 + LOG: Warning: divide by zero encountered in divide + array([inf, inf, inf]) + + >>> np.seterrcall(saved_handler) + + >>> np.seterr(**save_err) + {'divide': 'log', 'over': 'log', 'under': 'log', 'invalid': 'log'} + + """ + if func is not None and not isinstance(func, collections.abc.Callable): + if (not hasattr(func, 'write') or + not isinstance(func.write, collections.abc.Callable)): + raise ValueError("Only callable can be used as callback") + pyvals = umath.geterrobj() + old = geterrcall() + pyvals[2] = func + umath.seterrobj(pyvals) + return old + + +@set_module('numpy') +def geterrcall(): + """ + Return the current callback function used on floating-point errors. + + When the error handling for a floating-point error (one of "divide", + "over", "under", or "invalid") is set to 'call' or 'log', the function + that is called or the log instance that is written to is returned by + `geterrcall`. This function or log instance has been set with + `seterrcall`. + + Returns + ------- + errobj : callable, log instance or None + The current error handler. If no handler was set through `seterrcall`, + ``None`` is returned. + + See Also + -------- + seterrcall, seterr, geterr + + Notes + ----- + For complete documentation of the types of floating-point exceptions and + treatment options, see `seterr`. + + Examples + -------- + >>> np.geterrcall() # we did not yet set a handler, returns None + + >>> oldsettings = np.seterr(all='call') + >>> def err_handler(type, flag): + ... print("Floating point error (%s), with flag %s" % (type, flag)) + >>> oldhandler = np.seterrcall(err_handler) + >>> np.array([1, 2, 3]) / 0.0 + Floating point error (divide by zero), with flag 1 + array([inf, inf, inf]) + + >>> cur_handler = np.geterrcall() + >>> cur_handler is err_handler + True + + """ + return umath.geterrobj()[2] + + +class _unspecified: + pass + + +_Unspecified = _unspecified() + + +@set_module('numpy') +class errstate(contextlib.ContextDecorator): + """ + errstate(**kwargs) + + Context manager for floating-point error handling. + + Using an instance of `errstate` as a context manager allows statements in + that context to execute with a known error handling behavior. Upon entering + the context the error handling is set with `seterr` and `seterrcall`, and + upon exiting it is reset to what it was before. + + .. versionchanged:: 1.17.0 + `errstate` is also usable as a function decorator, saving + a level of indentation if an entire function is wrapped. + See :py:class:`contextlib.ContextDecorator` for more information. + + Parameters + ---------- + kwargs : {divide, over, under, invalid} + Keyword arguments. The valid keywords are the possible floating-point + exceptions. Each keyword should have a string value that defines the + treatment for the particular error. Possible values are + {'ignore', 'warn', 'raise', 'call', 'print', 'log'}. + + See Also + -------- + seterr, geterr, seterrcall, geterrcall + + Notes + ----- + For complete documentation of the types of floating-point exceptions and + treatment options, see `seterr`. + + Examples + -------- + >>> olderr = np.seterr(all='ignore') # Set error handling to known state. + + >>> np.arange(3) / 0. + array([nan, inf, inf]) + >>> with np.errstate(divide='warn'): + ... np.arange(3) / 0. + array([nan, inf, inf]) + + >>> np.sqrt(-1) + nan + >>> with np.errstate(invalid='raise'): + ... np.sqrt(-1) + Traceback (most recent call last): + File "", line 2, in + FloatingPointError: invalid value encountered in sqrt + + Outside the context the error handling behavior has not changed: + + >>> np.geterr() + {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'} + + """ + + def __init__(self, *, call=_Unspecified, **kwargs): + self.call = call + self.kwargs = kwargs + + def __enter__(self): + self.oldstate = seterr(**self.kwargs) + if self.call is not _Unspecified: + self.oldcall = seterrcall(self.call) + + def __exit__(self, *exc_info): + seterr(**self.oldstate) + if self.call is not _Unspecified: + seterrcall(self.oldcall) + + +def _setdef(): + defval = [UFUNC_BUFSIZE_DEFAULT, ERR_DEFAULT, None] + umath.seterrobj(defval) + + +# set the default values +_setdef() + + +NO_NEP50_WARNING = contextvars.ContextVar("_no_nep50_warning", default=False) + +@set_module('numpy') +@contextlib.contextmanager +def _no_nep50_warning(): + """ + Context manager to disable NEP 50 warnings. This context manager is + only relevant if the NEP 50 warnings are enabled globally (which is not + thread/context safe). + + This warning context manager itself is fully safe, however. + """ + token = NO_NEP50_WARNING.set(True) + try: + yield + finally: + NO_NEP50_WARNING.reset(token) diff --git a/venv/lib/python3.10/site-packages/numpy/core/_ufunc_config.pyi b/venv/lib/python3.10/site-packages/numpy/core/_ufunc_config.pyi new file mode 100644 index 0000000000000000000000000000000000000000..f56504507ac02995b740e49a9073e0e351b7abf5 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/_ufunc_config.pyi @@ -0,0 +1,37 @@ +from collections.abc import Callable +from typing import Any, Literal, TypedDict + +from numpy import _SupportsWrite + +_ErrKind = Literal["ignore", "warn", "raise", "call", "print", "log"] +_ErrFunc = Callable[[str, int], Any] + +class _ErrDict(TypedDict): + divide: _ErrKind + over: _ErrKind + under: _ErrKind + invalid: _ErrKind + +class _ErrDictOptional(TypedDict, total=False): + all: None | _ErrKind + divide: None | _ErrKind + over: None | _ErrKind + under: None | _ErrKind + invalid: None | _ErrKind + +def seterr( + all: None | _ErrKind = ..., + divide: None | _ErrKind = ..., + over: None | _ErrKind = ..., + under: None | _ErrKind = ..., + invalid: None | _ErrKind = ..., +) -> _ErrDict: ... +def geterr() -> _ErrDict: ... +def setbufsize(size: int) -> int: ... +def getbufsize() -> int: ... +def seterrcall( + func: None | _ErrFunc | _SupportsWrite[str] +) -> None | _ErrFunc | _SupportsWrite[str]: ... +def geterrcall() -> None | _ErrFunc | _SupportsWrite[str]: ... + +# See `numpy/__init__.pyi` for the `errstate` class and `no_nep5_warnings` diff --git a/venv/lib/python3.10/site-packages/numpy/core/_umath_tests.cpython-310-x86_64-linux-gnu.so b/venv/lib/python3.10/site-packages/numpy/core/_umath_tests.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..f422a4d759b58891dfe9abf73637b173abf22393 Binary files /dev/null and b/venv/lib/python3.10/site-packages/numpy/core/_umath_tests.cpython-310-x86_64-linux-gnu.so differ diff --git a/venv/lib/python3.10/site-packages/numpy/core/arrayprint.pyi b/venv/lib/python3.10/site-packages/numpy/core/arrayprint.pyi new file mode 100644 index 0000000000000000000000000000000000000000..d8255387a3a52635b30312d2800d02220b7ce6f2 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/arrayprint.pyi @@ -0,0 +1,142 @@ +from types import TracebackType +from collections.abc import Callable +from typing import Any, Literal, TypedDict, SupportsIndex + +# Using a private class is by no means ideal, but it is simply a consequence +# of a `contextlib.context` returning an instance of aforementioned class +from contextlib import _GeneratorContextManager + +from numpy import ( + ndarray, + generic, + bool_, + integer, + timedelta64, + datetime64, + floating, + complexfloating, + void, + str_, + bytes_, + longdouble, + clongdouble, +) +from numpy._typing import ArrayLike, _CharLike_co, _FloatLike_co + +_FloatMode = Literal["fixed", "unique", "maxprec", "maxprec_equal"] + +class _FormatDict(TypedDict, total=False): + bool: Callable[[bool_], str] + int: Callable[[integer[Any]], str] + timedelta: Callable[[timedelta64], str] + datetime: Callable[[datetime64], str] + float: Callable[[floating[Any]], str] + longfloat: Callable[[longdouble], str] + complexfloat: Callable[[complexfloating[Any, Any]], str] + longcomplexfloat: Callable[[clongdouble], str] + void: Callable[[void], str] + numpystr: Callable[[_CharLike_co], str] + object: Callable[[object], str] + all: Callable[[object], str] + int_kind: Callable[[integer[Any]], str] + float_kind: Callable[[floating[Any]], str] + complex_kind: Callable[[complexfloating[Any, Any]], str] + str_kind: Callable[[_CharLike_co], str] + +class _FormatOptions(TypedDict): + precision: int + threshold: int + edgeitems: int + linewidth: int + suppress: bool + nanstr: str + infstr: str + formatter: None | _FormatDict + sign: Literal["-", "+", " "] + floatmode: _FloatMode + legacy: Literal[False, "1.13", "1.21"] + +def set_printoptions( + precision: None | SupportsIndex = ..., + threshold: None | int = ..., + edgeitems: None | int = ..., + linewidth: None | int = ..., + suppress: None | bool = ..., + nanstr: None | str = ..., + infstr: None | str = ..., + formatter: None | _FormatDict = ..., + sign: Literal[None, "-", "+", " "] = ..., + floatmode: None | _FloatMode = ..., + *, + legacy: Literal[None, False, "1.13", "1.21"] = ... +) -> None: ... +def get_printoptions() -> _FormatOptions: ... +def array2string( + a: ndarray[Any, Any], + max_line_width: None | int = ..., + precision: None | SupportsIndex = ..., + suppress_small: None | bool = ..., + separator: str = ..., + prefix: str = ..., + # NOTE: With the `style` argument being deprecated, + # all arguments between `formatter` and `suffix` are de facto + # keyworld-only arguments + *, + formatter: None | _FormatDict = ..., + threshold: None | int = ..., + edgeitems: None | int = ..., + sign: Literal[None, "-", "+", " "] = ..., + floatmode: None | _FloatMode = ..., + suffix: str = ..., + legacy: Literal[None, False, "1.13", "1.21"] = ..., +) -> str: ... +def format_float_scientific( + x: _FloatLike_co, + precision: None | int = ..., + unique: bool = ..., + trim: Literal["k", ".", "0", "-"] = ..., + sign: bool = ..., + pad_left: None | int = ..., + exp_digits: None | int = ..., + min_digits: None | int = ..., +) -> str: ... +def format_float_positional( + x: _FloatLike_co, + precision: None | int = ..., + unique: bool = ..., + fractional: bool = ..., + trim: Literal["k", ".", "0", "-"] = ..., + sign: bool = ..., + pad_left: None | int = ..., + pad_right: None | int = ..., + min_digits: None | int = ..., +) -> str: ... +def array_repr( + arr: ndarray[Any, Any], + max_line_width: None | int = ..., + precision: None | SupportsIndex = ..., + suppress_small: None | bool = ..., +) -> str: ... +def array_str( + a: ndarray[Any, Any], + max_line_width: None | int = ..., + precision: None | SupportsIndex = ..., + suppress_small: None | bool = ..., +) -> str: ... +def set_string_function( + f: None | Callable[[ndarray[Any, Any]], str], repr: bool = ... +) -> None: ... +def printoptions( + precision: None | SupportsIndex = ..., + threshold: None | int = ..., + edgeitems: None | int = ..., + linewidth: None | int = ..., + suppress: None | bool = ..., + nanstr: None | str = ..., + infstr: None | str = ..., + formatter: None | _FormatDict = ..., + sign: Literal[None, "-", "+", " "] = ..., + floatmode: None | _FloatMode = ..., + *, + legacy: Literal[None, False, "1.13", "1.21"] = ... +) -> _GeneratorContextManager[_FormatOptions]: ... diff --git a/venv/lib/python3.10/site-packages/numpy/core/cversions.py b/venv/lib/python3.10/site-packages/numpy/core/cversions.py new file mode 100644 index 0000000000000000000000000000000000000000..00159c3a8031d8ccd44b226db42090f97014cd9f --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/cversions.py @@ -0,0 +1,13 @@ +"""Simple script to compute the api hash of the current API. + +The API has is defined by numpy_api_order and ufunc_api_order. + +""" +from os.path import dirname + +from code_generators.genapi import fullapi_hash +from code_generators.numpy_api import full_api + +if __name__ == '__main__': + curdir = dirname(__file__) + print(fullapi_hash(full_api)) diff --git a/venv/lib/python3.10/site-packages/numpy/core/defchararray.py b/venv/lib/python3.10/site-packages/numpy/core/defchararray.py new file mode 100644 index 0000000000000000000000000000000000000000..11c5a30bff70ef4edfb9fc0dd616af9d99d9da39 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/defchararray.py @@ -0,0 +1,2914 @@ +""" +This module contains a set of functions for vectorized string +operations and methods. + +.. note:: + The `chararray` class exists for backwards compatibility with + Numarray, it is not recommended for new development. Starting from numpy + 1.4, if one needs arrays of strings, it is recommended to use arrays of + `dtype` `object_`, `bytes_` or `str_`, and use the free functions + in the `numpy.char` module for fast vectorized string operations. + +Some methods will only be available if the corresponding string method is +available in your version of Python. + +The preferred alias for `defchararray` is `numpy.char`. + +""" +import functools + +from .._utils import set_module +from .numerictypes import ( + bytes_, str_, integer, int_, object_, bool_, character) +from .numeric import ndarray, compare_chararrays +from .numeric import array as narray +from numpy.core.multiarray import _vec_string +from numpy.core import overrides +from numpy.compat import asbytes +import numpy + +__all__ = [ + 'equal', 'not_equal', 'greater_equal', 'less_equal', + 'greater', 'less', 'str_len', 'add', 'multiply', 'mod', 'capitalize', + 'center', 'count', 'decode', 'encode', 'endswith', 'expandtabs', + 'find', 'index', 'isalnum', 'isalpha', 'isdigit', 'islower', 'isspace', + 'istitle', 'isupper', 'join', 'ljust', 'lower', 'lstrip', 'partition', + 'replace', 'rfind', 'rindex', 'rjust', 'rpartition', 'rsplit', + 'rstrip', 'split', 'splitlines', 'startswith', 'strip', 'swapcase', + 'title', 'translate', 'upper', 'zfill', 'isnumeric', 'isdecimal', + 'array', 'asarray' + ] + + +_globalvar = 0 + +array_function_dispatch = functools.partial( + overrides.array_function_dispatch, module='numpy.char') + + +def _is_unicode(arr): + """Returns True if arr is a string or a string array with a dtype that + represents a unicode string, otherwise returns False. + + """ + if (isinstance(arr, str) or + issubclass(numpy.asarray(arr).dtype.type, str)): + return True + return False + + +def _to_bytes_or_str_array(result, output_dtype_like=None): + """ + Helper function to cast a result back into an array + with the appropriate dtype if an object array must be used + as an intermediary. + """ + ret = numpy.asarray(result.tolist()) + dtype = getattr(output_dtype_like, 'dtype', None) + if dtype is not None: + return ret.astype(type(dtype)(_get_num_chars(ret)), copy=False) + return ret + + +def _clean_args(*args): + """ + Helper function for delegating arguments to Python string + functions. + + Many of the Python string operations that have optional arguments + do not use 'None' to indicate a default value. In these cases, + we need to remove all None arguments, and those following them. + """ + newargs = [] + for chk in args: + if chk is None: + break + newargs.append(chk) + return newargs + +def _get_num_chars(a): + """ + Helper function that returns the number of characters per field in + a string or unicode array. This is to abstract out the fact that + for a unicode array this is itemsize / 4. + """ + if issubclass(a.dtype.type, str_): + return a.itemsize // 4 + return a.itemsize + + +def _binary_op_dispatcher(x1, x2): + return (x1, x2) + + +@array_function_dispatch(_binary_op_dispatcher) +def equal(x1, x2): + """ + Return (x1 == x2) element-wise. + + Unlike `numpy.equal`, this comparison is performed by first + stripping whitespace characters from the end of the string. This + behavior is provided for backward-compatibility with numarray. + + Parameters + ---------- + x1, x2 : array_like of str or unicode + Input arrays of the same shape. + + Returns + ------- + out : ndarray + Output array of bools. + + See Also + -------- + not_equal, greater_equal, less_equal, greater, less + """ + return compare_chararrays(x1, x2, '==', True) + + +@array_function_dispatch(_binary_op_dispatcher) +def not_equal(x1, x2): + """ + Return (x1 != x2) element-wise. + + Unlike `numpy.not_equal`, this comparison is performed by first + stripping whitespace characters from the end of the string. This + behavior is provided for backward-compatibility with numarray. + + Parameters + ---------- + x1, x2 : array_like of str or unicode + Input arrays of the same shape. + + Returns + ------- + out : ndarray + Output array of bools. + + See Also + -------- + equal, greater_equal, less_equal, greater, less + """ + return compare_chararrays(x1, x2, '!=', True) + + +@array_function_dispatch(_binary_op_dispatcher) +def greater_equal(x1, x2): + """ + Return (x1 >= x2) element-wise. + + Unlike `numpy.greater_equal`, this comparison is performed by + first stripping whitespace characters from the end of the string. + This behavior is provided for backward-compatibility with + numarray. + + Parameters + ---------- + x1, x2 : array_like of str or unicode + Input arrays of the same shape. + + Returns + ------- + out : ndarray + Output array of bools. + + See Also + -------- + equal, not_equal, less_equal, greater, less + """ + return compare_chararrays(x1, x2, '>=', True) + + +@array_function_dispatch(_binary_op_dispatcher) +def less_equal(x1, x2): + """ + Return (x1 <= x2) element-wise. + + Unlike `numpy.less_equal`, this comparison is performed by first + stripping whitespace characters from the end of the string. This + behavior is provided for backward-compatibility with numarray. + + Parameters + ---------- + x1, x2 : array_like of str or unicode + Input arrays of the same shape. + + Returns + ------- + out : ndarray + Output array of bools. + + See Also + -------- + equal, not_equal, greater_equal, greater, less + """ + return compare_chararrays(x1, x2, '<=', True) + + +@array_function_dispatch(_binary_op_dispatcher) +def greater(x1, x2): + """ + Return (x1 > x2) element-wise. + + Unlike `numpy.greater`, this comparison is performed by first + stripping whitespace characters from the end of the string. This + behavior is provided for backward-compatibility with numarray. + + Parameters + ---------- + x1, x2 : array_like of str or unicode + Input arrays of the same shape. + + Returns + ------- + out : ndarray + Output array of bools. + + See Also + -------- + equal, not_equal, greater_equal, less_equal, less + """ + return compare_chararrays(x1, x2, '>', True) + + +@array_function_dispatch(_binary_op_dispatcher) +def less(x1, x2): + """ + Return (x1 < x2) element-wise. + + Unlike `numpy.greater`, this comparison is performed by first + stripping whitespace characters from the end of the string. This + behavior is provided for backward-compatibility with numarray. + + Parameters + ---------- + x1, x2 : array_like of str or unicode + Input arrays of the same shape. + + Returns + ------- + out : ndarray + Output array of bools. + + See Also + -------- + equal, not_equal, greater_equal, less_equal, greater + """ + return compare_chararrays(x1, x2, '<', True) + + +def _unary_op_dispatcher(a): + return (a,) + + +@array_function_dispatch(_unary_op_dispatcher) +def str_len(a): + """ + Return len(a) element-wise. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of integers + + See Also + -------- + len + + Examples + -------- + >>> a = np.array(['Grace Hopper Conference', 'Open Source Day']) + >>> np.char.str_len(a) + array([23, 15]) + >>> a = np.array([u'\u0420', u'\u043e']) + >>> np.char.str_len(a) + array([1, 1]) + >>> a = np.array([['hello', 'world'], [u'\u0420', u'\u043e']]) + >>> np.char.str_len(a) + array([[5, 5], [1, 1]]) + """ + # Note: __len__, etc. currently return ints, which are not C-integers. + # Generally intp would be expected for lengths, although int is sufficient + # due to the dtype itemsize limitation. + return _vec_string(a, int_, '__len__') + + +@array_function_dispatch(_binary_op_dispatcher) +def add(x1, x2): + """ + Return element-wise string concatenation for two arrays of str or unicode. + + Arrays `x1` and `x2` must have the same shape. + + Parameters + ---------- + x1 : array_like of str or unicode + Input array. + x2 : array_like of str or unicode + Input array. + + Returns + ------- + add : ndarray + Output array of `bytes_` or `str_`, depending on input types + of the same shape as `x1` and `x2`. + + """ + arr1 = numpy.asarray(x1) + arr2 = numpy.asarray(x2) + out_size = _get_num_chars(arr1) + _get_num_chars(arr2) + + if type(arr1.dtype) != type(arr2.dtype): + # Enforce this for now. The solution to it will be implement add + # as a ufunc. It never worked right on Python 3: bytes + unicode gave + # nonsense unicode + bytes errored, and unicode + object used the + # object dtype itemsize as num chars (worked on short strings). + # bytes + void worked but promoting void->bytes is dubious also. + raise TypeError( + "np.char.add() requires both arrays of the same dtype kind, but " + f"got dtypes: '{arr1.dtype}' and '{arr2.dtype}' (the few cases " + "where this used to work often lead to incorrect results).") + + return _vec_string(arr1, type(arr1.dtype)(out_size), '__add__', (arr2,)) + +def _multiply_dispatcher(a, i): + return (a,) + + +@array_function_dispatch(_multiply_dispatcher) +def multiply(a, i): + """ + Return (a * i), that is string multiple concatenation, + element-wise. + + Values in `i` of less than 0 are treated as 0 (which yields an + empty string). + + Parameters + ---------- + a : array_like of str or unicode + + i : array_like of ints + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input types + + Examples + -------- + >>> a = np.array(["a", "b", "c"]) + >>> np.char.multiply(x, 3) + array(['aaa', 'bbb', 'ccc'], dtype='>> i = np.array([1, 2, 3]) + >>> np.char.multiply(a, i) + array(['a', 'bb', 'ccc'], dtype='>> np.char.multiply(np.array(['a']), i) + array(['a', 'aa', 'aaa'], dtype='>> a = np.array(['a', 'b', 'c', 'd', 'e', 'f']).reshape((2, 3)) + >>> np.char.multiply(a, 3) + array([['aaa', 'bbb', 'ccc'], + ['ddd', 'eee', 'fff']], dtype='>> np.char.multiply(a, i) + array([['a', 'bb', 'ccc'], + ['d', 'ee', 'fff']], dtype='>> c = np.array(['a1b2','1b2a','b2a1','2a1b'],'S4'); c + array(['a1b2', '1b2a', 'b2a1', '2a1b'], + dtype='|S4') + >>> np.char.capitalize(c) + array(['A1b2', '1b2a', 'B2a1', '2a1b'], + dtype='|S4') + + """ + a_arr = numpy.asarray(a) + return _vec_string(a_arr, a_arr.dtype, 'capitalize') + + +def _center_dispatcher(a, width, fillchar=None): + return (a,) + + +@array_function_dispatch(_center_dispatcher) +def center(a, width, fillchar=' '): + """ + Return a copy of `a` with its elements centered in a string of + length `width`. + + Calls `str.center` element-wise. + + Parameters + ---------- + a : array_like of str or unicode + + width : int + The length of the resulting strings + fillchar : str or unicode, optional + The padding character to use (default is space). + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input + types + + See Also + -------- + str.center + + Notes + ----- + This function is intended to work with arrays of strings. The + fill character is not applied to numeric types. + + Examples + -------- + >>> c = np.array(['a1b2','1b2a','b2a1','2a1b']); c + array(['a1b2', '1b2a', 'b2a1', '2a1b'], dtype='>> np.char.center(c, width=9) + array([' a1b2 ', ' 1b2a ', ' b2a1 ', ' 2a1b '], dtype='>> np.char.center(c, width=9, fillchar='*') + array(['***a1b2**', '***1b2a**', '***b2a1**', '***2a1b**'], dtype='>> np.char.center(c, width=1) + array(['a', '1', 'b', '2'], dtype='>> c = np.array(['aAaAaA', ' aA ', 'abBABba']) + >>> c + array(['aAaAaA', ' aA ', 'abBABba'], dtype='>> np.char.count(c, 'A') + array([3, 1, 1]) + >>> np.char.count(c, 'aA') + array([3, 1, 0]) + >>> np.char.count(c, 'A', start=1, end=4) + array([2, 1, 1]) + >>> np.char.count(c, 'A', start=1, end=3) + array([1, 0, 0]) + + """ + return _vec_string(a, int_, 'count', [sub, start] + _clean_args(end)) + + +def _code_dispatcher(a, encoding=None, errors=None): + return (a,) + + +@array_function_dispatch(_code_dispatcher) +def decode(a, encoding=None, errors=None): + r""" + Calls ``bytes.decode`` element-wise. + + The set of available codecs comes from the Python standard library, + and may be extended at runtime. For more information, see the + :mod:`codecs` module. + + Parameters + ---------- + a : array_like of str or unicode + + encoding : str, optional + The name of an encoding + + errors : str, optional + Specifies how to handle encoding errors + + Returns + ------- + out : ndarray + + See Also + -------- + :py:meth:`bytes.decode` + + Notes + ----- + The type of the result will depend on the encoding specified. + + Examples + -------- + >>> c = np.array([b'\x81\xc1\x81\xc1\x81\xc1', b'@@\x81\xc1@@', + ... b'\x81\x82\xc2\xc1\xc2\x82\x81']) + >>> c + array([b'\x81\xc1\x81\xc1\x81\xc1', b'@@\x81\xc1@@', + ... b'\x81\x82\xc2\xc1\xc2\x82\x81'], dtype='|S7') + >>> np.char.decode(c, encoding='cp037') + array(['aAaAaA', ' aA ', 'abBABba'], dtype='>> s = np.array(['foo', 'bar']) + >>> s[0] = 'foo' + >>> s[1] = 'bar' + >>> s + array(['foo', 'bar'], dtype='>> np.char.endswith(s, 'ar') + array([False, True]) + >>> np.char.endswith(s, 'a', start=1, end=2) + array([False, True]) + + """ + return _vec_string( + a, bool_, 'endswith', [suffix, start] + _clean_args(end)) + + +def _expandtabs_dispatcher(a, tabsize=None): + return (a,) + + +@array_function_dispatch(_expandtabs_dispatcher) +def expandtabs(a, tabsize=8): + """ + Return a copy of each string element where all tab characters are + replaced by one or more spaces. + + Calls `str.expandtabs` element-wise. + + Return a copy of each string element where all tab characters are + replaced by one or more spaces, depending on the current column + and the given `tabsize`. The column number is reset to zero after + each newline occurring in the string. This doesn't understand other + non-printing characters or escape sequences. + + Parameters + ---------- + a : array_like of str or unicode + Input array + tabsize : int, optional + Replace tabs with `tabsize` number of spaces. If not given defaults + to 8 spaces. + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input type + + See Also + -------- + str.expandtabs + + """ + return _to_bytes_or_str_array( + _vec_string(a, object_, 'expandtabs', (tabsize,)), a) + + +@array_function_dispatch(_count_dispatcher) +def find(a, sub, start=0, end=None): + """ + For each element, return the lowest index in the string where + substring `sub` is found. + + Calls `str.find` element-wise. + + For each element, return the lowest index in the string where + substring `sub` is found, such that `sub` is contained in the + range [`start`, `end`]. + + Parameters + ---------- + a : array_like of str or unicode + + sub : str or unicode + + start, end : int, optional + Optional arguments `start` and `end` are interpreted as in + slice notation. + + Returns + ------- + out : ndarray or int + Output array of ints. Returns -1 if `sub` is not found. + + See Also + -------- + str.find + + Examples + -------- + >>> a = np.array(["NumPy is a Python library"]) + >>> np.char.find(a, "Python", start=0, end=None) + array([11]) + + """ + return _vec_string( + a, int_, 'find', [sub, start] + _clean_args(end)) + + +@array_function_dispatch(_count_dispatcher) +def index(a, sub, start=0, end=None): + """ + Like `find`, but raises `ValueError` when the substring is not found. + + Calls `str.index` element-wise. + + Parameters + ---------- + a : array_like of str or unicode + + sub : str or unicode + + start, end : int, optional + + Returns + ------- + out : ndarray + Output array of ints. Returns -1 if `sub` is not found. + + See Also + -------- + find, str.find + + Examples + -------- + >>> a = np.array(["Computer Science"]) + >>> np.char.index(a, "Science", start=0, end=None) + array([9]) + + """ + return _vec_string( + a, int_, 'index', [sub, start] + _clean_args(end)) + + +@array_function_dispatch(_unary_op_dispatcher) +def isalnum(a): + """ + Returns true for each element if all characters in the string are + alphanumeric and there is at least one character, false otherwise. + + Calls `str.isalnum` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input type + + See Also + -------- + str.isalnum + """ + return _vec_string(a, bool_, 'isalnum') + + +@array_function_dispatch(_unary_op_dispatcher) +def isalpha(a): + """ + Returns true for each element if all characters in the string are + alphabetic and there is at least one character, false otherwise. + + Calls `str.isalpha` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of bools + + See Also + -------- + str.isalpha + """ + return _vec_string(a, bool_, 'isalpha') + + +@array_function_dispatch(_unary_op_dispatcher) +def isdigit(a): + """ + Returns true for each element if all characters in the string are + digits and there is at least one character, false otherwise. + + Calls `str.isdigit` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of bools + + See Also + -------- + str.isdigit + + Examples + -------- + >>> a = np.array(['a', 'b', '0']) + >>> np.char.isdigit(a) + array([False, False, True]) + >>> a = np.array([['a', 'b', '0'], ['c', '1', '2']]) + >>> np.char.isdigit(a) + array([[False, False, True], [False, True, True]]) + """ + return _vec_string(a, bool_, 'isdigit') + + +@array_function_dispatch(_unary_op_dispatcher) +def islower(a): + """ + Returns true for each element if all cased characters in the + string are lowercase and there is at least one cased character, + false otherwise. + + Calls `str.islower` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of bools + + See Also + -------- + str.islower + """ + return _vec_string(a, bool_, 'islower') + + +@array_function_dispatch(_unary_op_dispatcher) +def isspace(a): + """ + Returns true for each element if there are only whitespace + characters in the string and there is at least one character, + false otherwise. + + Calls `str.isspace` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of bools + + See Also + -------- + str.isspace + """ + return _vec_string(a, bool_, 'isspace') + + +@array_function_dispatch(_unary_op_dispatcher) +def istitle(a): + """ + Returns true for each element if the element is a titlecased + string and there is at least one character, false otherwise. + + Call `str.istitle` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of bools + + See Also + -------- + str.istitle + """ + return _vec_string(a, bool_, 'istitle') + + +@array_function_dispatch(_unary_op_dispatcher) +def isupper(a): + """ + Return true for each element if all cased characters in the + string are uppercase and there is at least one character, false + otherwise. + + Call `str.isupper` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of bools + + See Also + -------- + str.isupper + + Examples + -------- + >>> str = "GHC" + >>> np.char.isupper(str) + array(True) + >>> a = np.array(["hello", "HELLO", "Hello"]) + >>> np.char.isupper(a) + array([False, True, False]) + + """ + return _vec_string(a, bool_, 'isupper') + + +def _join_dispatcher(sep, seq): + return (sep, seq) + + +@array_function_dispatch(_join_dispatcher) +def join(sep, seq): + """ + Return a string which is the concatenation of the strings in the + sequence `seq`. + + Calls `str.join` element-wise. + + Parameters + ---------- + sep : array_like of str or unicode + seq : array_like of str or unicode + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input types + + See Also + -------- + str.join + + Examples + -------- + >>> np.char.join('-', 'osd') + array('o-s-d', dtype='>> np.char.join(['-', '.'], ['ghc', 'osd']) + array(['g-h-c', 'o.s.d'], dtype='>> c = np.array(['A1B C', '1BCA', 'BCA1']); c + array(['A1B C', '1BCA', 'BCA1'], dtype='>> np.char.lower(c) + array(['a1b c', '1bca', 'bca1'], dtype='>> c = np.array(['aAaAaA', ' aA ', 'abBABba']) + >>> c + array(['aAaAaA', ' aA ', 'abBABba'], dtype='>> np.char.lstrip(c, 'a') + array(['AaAaA', ' aA ', 'bBABba'], dtype='>> np.char.lstrip(c, 'A') # leaves c unchanged + array(['aAaAaA', ' aA ', 'abBABba'], dtype='>> (np.char.lstrip(c, ' ') == np.char.lstrip(c, '')).all() + ... # XXX: is this a regression? This used to return True + ... # np.char.lstrip(c,'') does not modify c at all. + False + >>> (np.char.lstrip(c, ' ') == np.char.lstrip(c, None)).all() + True + + """ + a_arr = numpy.asarray(a) + return _vec_string(a_arr, a_arr.dtype, 'lstrip', (chars,)) + + +def _partition_dispatcher(a, sep): + return (a,) + + +@array_function_dispatch(_partition_dispatcher) +def partition(a, sep): + """ + Partition each element in `a` around `sep`. + + Calls `str.partition` element-wise. + + For each element in `a`, split the element as the first + occurrence of `sep`, and return 3 strings containing the part + before the separator, the separator itself, and the part after + the separator. If the separator is not found, return 3 strings + containing the string itself, followed by two empty strings. + + Parameters + ---------- + a : array_like, {str, unicode} + Input array + sep : {str, unicode} + Separator to split each string element in `a`. + + Returns + ------- + out : ndarray, {str, unicode} + Output array of str or unicode, depending on input type. + The output array will have an extra dimension with 3 + elements per input element. + + See Also + -------- + str.partition + + """ + return _to_bytes_or_str_array( + _vec_string(a, object_, 'partition', (sep,)), a) + + +def _replace_dispatcher(a, old, new, count=None): + return (a,) + + +@array_function_dispatch(_replace_dispatcher) +def replace(a, old, new, count=None): + """ + For each element in `a`, return a copy of the string with all + occurrences of substring `old` replaced by `new`. + + Calls `str.replace` element-wise. + + Parameters + ---------- + a : array-like of str or unicode + + old, new : str or unicode + + count : int, optional + If the optional argument `count` is given, only the first + `count` occurrences are replaced. + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input type + + See Also + -------- + str.replace + + Examples + -------- + >>> a = np.array(["That is a mango", "Monkeys eat mangos"]) + >>> np.char.replace(a, 'mango', 'banana') + array(['That is a banana', 'Monkeys eat bananas'], dtype='>> a = np.array(["The dish is fresh", "This is it"]) + >>> np.char.replace(a, 'is', 'was') + array(['The dwash was fresh', 'Thwas was it'], dtype='>> c = np.array(['aAaAaA', 'abBABba'], dtype='S7'); c + array(['aAaAaA', 'abBABba'], + dtype='|S7') + >>> np.char.rstrip(c, b'a') + array(['aAaAaA', 'abBABb'], + dtype='|S7') + >>> np.char.rstrip(c, b'A') + array(['aAaAa', 'abBABba'], + dtype='|S7') + + """ + a_arr = numpy.asarray(a) + return _vec_string(a_arr, a_arr.dtype, 'rstrip', (chars,)) + + +@array_function_dispatch(_split_dispatcher) +def split(a, sep=None, maxsplit=None): + """ + For each element in `a`, return a list of the words in the + string, using `sep` as the delimiter string. + + Calls `str.split` element-wise. + + Parameters + ---------- + a : array_like of str or unicode + + sep : str or unicode, optional + If `sep` is not specified or None, any whitespace string is a + separator. + + maxsplit : int, optional + If `maxsplit` is given, at most `maxsplit` splits are done. + + Returns + ------- + out : ndarray + Array of list objects + + See Also + -------- + str.split, rsplit + + """ + # This will return an array of lists of different sizes, so we + # leave it as an object array + return _vec_string( + a, object_, 'split', [sep] + _clean_args(maxsplit)) + + +def _splitlines_dispatcher(a, keepends=None): + return (a,) + + +@array_function_dispatch(_splitlines_dispatcher) +def splitlines(a, keepends=None): + """ + For each element in `a`, return a list of the lines in the + element, breaking at line boundaries. + + Calls `str.splitlines` element-wise. + + Parameters + ---------- + a : array_like of str or unicode + + keepends : bool, optional + Line breaks are not included in the resulting list unless + keepends is given and true. + + Returns + ------- + out : ndarray + Array of list objects + + See Also + -------- + str.splitlines + + """ + return _vec_string( + a, object_, 'splitlines', _clean_args(keepends)) + + +def _startswith_dispatcher(a, prefix, start=None, end=None): + return (a,) + + +@array_function_dispatch(_startswith_dispatcher) +def startswith(a, prefix, start=0, end=None): + """ + Returns a boolean array which is `True` where the string element + in `a` starts with `prefix`, otherwise `False`. + + Calls `str.startswith` element-wise. + + Parameters + ---------- + a : array_like of str or unicode + + prefix : str + + start, end : int, optional + With optional `start`, test beginning at that position. With + optional `end`, stop comparing at that position. + + Returns + ------- + out : ndarray + Array of booleans + + See Also + -------- + str.startswith + + """ + return _vec_string( + a, bool_, 'startswith', [prefix, start] + _clean_args(end)) + + +@array_function_dispatch(_strip_dispatcher) +def strip(a, chars=None): + """ + For each element in `a`, return a copy with the leading and + trailing characters removed. + + Calls `str.strip` element-wise. + + Parameters + ---------- + a : array-like of str or unicode + + chars : str or unicode, optional + The `chars` argument is a string specifying the set of + characters to be removed. If omitted or None, the `chars` + argument defaults to removing whitespace. The `chars` argument + is not a prefix or suffix; rather, all combinations of its + values are stripped. + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input type + + See Also + -------- + str.strip + + Examples + -------- + >>> c = np.array(['aAaAaA', ' aA ', 'abBABba']) + >>> c + array(['aAaAaA', ' aA ', 'abBABba'], dtype='>> np.char.strip(c) + array(['aAaAaA', 'aA', 'abBABba'], dtype='>> np.char.strip(c, 'a') # 'a' unstripped from c[1] because whitespace leads + array(['AaAaA', ' aA ', 'bBABb'], dtype='>> np.char.strip(c, 'A') # 'A' unstripped from c[1] because (unprinted) ws trails + array(['aAaAa', ' aA ', 'abBABba'], dtype='>> c=np.array(['a1B c','1b Ca','b Ca1','cA1b'],'S5'); c + array(['a1B c', '1b Ca', 'b Ca1', 'cA1b'], + dtype='|S5') + >>> np.char.swapcase(c) + array(['A1b C', '1B cA', 'B cA1', 'Ca1B'], + dtype='|S5') + + """ + a_arr = numpy.asarray(a) + return _vec_string(a_arr, a_arr.dtype, 'swapcase') + + +@array_function_dispatch(_unary_op_dispatcher) +def title(a): + """ + Return element-wise title cased version of string or unicode. + + Title case words start with uppercase characters, all remaining cased + characters are lowercase. + + Calls `str.title` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like, {str, unicode} + Input array. + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input type + + See Also + -------- + str.title + + Examples + -------- + >>> c=np.array(['a1b c','1b ca','b ca1','ca1b'],'S5'); c + array(['a1b c', '1b ca', 'b ca1', 'ca1b'], + dtype='|S5') + >>> np.char.title(c) + array(['A1B C', '1B Ca', 'B Ca1', 'Ca1B'], + dtype='|S5') + + """ + a_arr = numpy.asarray(a) + return _vec_string(a_arr, a_arr.dtype, 'title') + + +def _translate_dispatcher(a, table, deletechars=None): + return (a,) + + +@array_function_dispatch(_translate_dispatcher) +def translate(a, table, deletechars=None): + """ + For each element in `a`, return a copy of the string where all + characters occurring in the optional argument `deletechars` are + removed, and the remaining characters have been mapped through the + given translation table. + + Calls `str.translate` element-wise. + + Parameters + ---------- + a : array-like of str or unicode + + table : str of length 256 + + deletechars : str + + Returns + ------- + out : ndarray + Output array of str or unicode, depending on input type + + See Also + -------- + str.translate + + """ + a_arr = numpy.asarray(a) + if issubclass(a_arr.dtype.type, str_): + return _vec_string( + a_arr, a_arr.dtype, 'translate', (table,)) + else: + return _vec_string( + a_arr, a_arr.dtype, 'translate', [table] + _clean_args(deletechars)) + + +@array_function_dispatch(_unary_op_dispatcher) +def upper(a): + """ + Return an array with the elements converted to uppercase. + + Calls `str.upper` element-wise. + + For 8-bit strings, this method is locale-dependent. + + Parameters + ---------- + a : array_like, {str, unicode} + Input array. + + Returns + ------- + out : ndarray, {str, unicode} + Output array of str or unicode, depending on input type + + See Also + -------- + str.upper + + Examples + -------- + >>> c = np.array(['a1b c', '1bca', 'bca1']); c + array(['a1b c', '1bca', 'bca1'], dtype='>> np.char.upper(c) + array(['A1B C', '1BCA', 'BCA1'], dtype='>> np.char.isnumeric(['123', '123abc', '9.0', '1/4', 'VIII']) + array([ True, False, False, False, False]) + + """ + if not _is_unicode(a): + raise TypeError("isnumeric is only available for Unicode strings and arrays") + return _vec_string(a, bool_, 'isnumeric') + + +@array_function_dispatch(_unary_op_dispatcher) +def isdecimal(a): + """ + For each element, return True if there are only decimal + characters in the element. + + Calls `str.isdecimal` element-wise. + + Decimal characters include digit characters, and all characters + that can be used to form decimal-radix numbers, + e.g. ``U+0660, ARABIC-INDIC DIGIT ZERO``. + + Parameters + ---------- + a : array_like, unicode + Input array. + + Returns + ------- + out : ndarray, bool + Array of booleans identical in shape to `a`. + + See Also + -------- + str.isdecimal + + Examples + -------- + >>> np.char.isdecimal(['12345', '4.99', '123ABC', '']) + array([ True, False, False, False]) + + """ + if not _is_unicode(a): + raise TypeError( + "isdecimal is only available for Unicode strings and arrays") + return _vec_string(a, bool_, 'isdecimal') + + +@set_module('numpy') +class chararray(ndarray): + """ + chararray(shape, itemsize=1, unicode=False, buffer=None, offset=0, + strides=None, order=None) + + Provides a convenient view on arrays of string and unicode values. + + .. note:: + The `chararray` class exists for backwards compatibility with + Numarray, it is not recommended for new development. Starting from numpy + 1.4, if one needs arrays of strings, it is recommended to use arrays of + `dtype` `object_`, `bytes_` or `str_`, and use the free functions + in the `numpy.char` module for fast vectorized string operations. + + Versus a regular NumPy array of type `str` or `unicode`, this + class adds the following functionality: + + 1) values automatically have whitespace removed from the end + when indexed + + 2) comparison operators automatically remove whitespace from the + end when comparing values + + 3) vectorized string operations are provided as methods + (e.g. `.endswith`) and infix operators (e.g. ``"+", "*", "%"``) + + chararrays should be created using `numpy.char.array` or + `numpy.char.asarray`, rather than this constructor directly. + + This constructor creates the array, using `buffer` (with `offset` + and `strides`) if it is not ``None``. If `buffer` is ``None``, then + constructs a new array with `strides` in "C order", unless both + ``len(shape) >= 2`` and ``order='F'``, in which case `strides` + is in "Fortran order". + + Methods + ------- + astype + argsort + copy + count + decode + dump + dumps + encode + endswith + expandtabs + fill + find + flatten + getfield + index + isalnum + isalpha + isdecimal + isdigit + islower + isnumeric + isspace + istitle + isupper + item + join + ljust + lower + lstrip + nonzero + put + ravel + repeat + replace + reshape + resize + rfind + rindex + rjust + rsplit + rstrip + searchsorted + setfield + setflags + sort + split + splitlines + squeeze + startswith + strip + swapaxes + swapcase + take + title + tofile + tolist + tostring + translate + transpose + upper + view + zfill + + Parameters + ---------- + shape : tuple + Shape of the array. + itemsize : int, optional + Length of each array element, in number of characters. Default is 1. + unicode : bool, optional + Are the array elements of type unicode (True) or string (False). + Default is False. + buffer : object exposing the buffer interface or str, optional + Memory address of the start of the array data. Default is None, + in which case a new array is created. + offset : int, optional + Fixed stride displacement from the beginning of an axis? + Default is 0. Needs to be >=0. + strides : array_like of ints, optional + Strides for the array (see `ndarray.strides` for full description). + Default is None. + order : {'C', 'F'}, optional + The order in which the array data is stored in memory: 'C' -> + "row major" order (the default), 'F' -> "column major" + (Fortran) order. + + Examples + -------- + >>> charar = np.chararray((3, 3)) + >>> charar[:] = 'a' + >>> charar + chararray([[b'a', b'a', b'a'], + [b'a', b'a', b'a'], + [b'a', b'a', b'a']], dtype='|S1') + + >>> charar = np.chararray(charar.shape, itemsize=5) + >>> charar[:] = 'abc' + >>> charar + chararray([[b'abc', b'abc', b'abc'], + [b'abc', b'abc', b'abc'], + [b'abc', b'abc', b'abc']], dtype='|S5') + + """ + def __new__(subtype, shape, itemsize=1, unicode=False, buffer=None, + offset=0, strides=None, order='C'): + global _globalvar + + if unicode: + dtype = str_ + else: + dtype = bytes_ + + # force itemsize to be a Python int, since using NumPy integer + # types results in itemsize.itemsize being used as the size of + # strings in the new array. + itemsize = int(itemsize) + + if isinstance(buffer, str): + # unicode objects do not have the buffer interface + filler = buffer + buffer = None + else: + filler = None + + _globalvar = 1 + if buffer is None: + self = ndarray.__new__(subtype, shape, (dtype, itemsize), + order=order) + else: + self = ndarray.__new__(subtype, shape, (dtype, itemsize), + buffer=buffer, + offset=offset, strides=strides, + order=order) + if filler is not None: + self[...] = filler + _globalvar = 0 + return self + + def __array_finalize__(self, obj): + # The b is a special case because it is used for reconstructing. + if not _globalvar and self.dtype.char not in 'SUbc': + raise ValueError("Can only create a chararray from string data.") + + def __getitem__(self, obj): + val = ndarray.__getitem__(self, obj) + + if isinstance(val, character): + temp = val.rstrip() + if len(temp) == 0: + val = '' + else: + val = temp + + return val + + # IMPLEMENTATION NOTE: Most of the methods of this class are + # direct delegations to the free functions in this module. + # However, those that return an array of strings should instead + # return a chararray, so some extra wrapping is required. + + def __eq__(self, other): + """ + Return (self == other) element-wise. + + See Also + -------- + equal + """ + return equal(self, other) + + def __ne__(self, other): + """ + Return (self != other) element-wise. + + See Also + -------- + not_equal + """ + return not_equal(self, other) + + def __ge__(self, other): + """ + Return (self >= other) element-wise. + + See Also + -------- + greater_equal + """ + return greater_equal(self, other) + + def __le__(self, other): + """ + Return (self <= other) element-wise. + + See Also + -------- + less_equal + """ + return less_equal(self, other) + + def __gt__(self, other): + """ + Return (self > other) element-wise. + + See Also + -------- + greater + """ + return greater(self, other) + + def __lt__(self, other): + """ + Return (self < other) element-wise. + + See Also + -------- + less + """ + return less(self, other) + + def __add__(self, other): + """ + Return (self + other), that is string concatenation, + element-wise for a pair of array_likes of str or unicode. + + See Also + -------- + add + """ + return asarray(add(self, other)) + + def __radd__(self, other): + """ + Return (other + self), that is string concatenation, + element-wise for a pair of array_likes of `bytes_` or `str_`. + + See Also + -------- + add + """ + return asarray(add(numpy.asarray(other), self)) + + def __mul__(self, i): + """ + Return (self * i), that is string multiple concatenation, + element-wise. + + See Also + -------- + multiply + """ + return asarray(multiply(self, i)) + + def __rmul__(self, i): + """ + Return (self * i), that is string multiple concatenation, + element-wise. + + See Also + -------- + multiply + """ + return asarray(multiply(self, i)) + + def __mod__(self, i): + """ + Return (self % i), that is pre-Python 2.6 string formatting + (interpolation), element-wise for a pair of array_likes of `bytes_` + or `str_`. + + See Also + -------- + mod + """ + return asarray(mod(self, i)) + + def __rmod__(self, other): + return NotImplemented + + def argsort(self, axis=-1, kind=None, order=None): + """ + Return the indices that sort the array lexicographically. + + For full documentation see `numpy.argsort`, for which this method is + in fact merely a "thin wrapper." + + Examples + -------- + >>> c = np.array(['a1b c', '1b ca', 'b ca1', 'Ca1b'], 'S5') + >>> c = c.view(np.chararray); c + chararray(['a1b c', '1b ca', 'b ca1', 'Ca1b'], + dtype='|S5') + >>> c[c.argsort()] + chararray(['1b ca', 'Ca1b', 'a1b c', 'b ca1'], + dtype='|S5') + + """ + return self.__array__().argsort(axis, kind, order) + argsort.__doc__ = ndarray.argsort.__doc__ + + def capitalize(self): + """ + Return a copy of `self` with only the first character of each element + capitalized. + + See Also + -------- + char.capitalize + + """ + return asarray(capitalize(self)) + + def center(self, width, fillchar=' '): + """ + Return a copy of `self` with its elements centered in a + string of length `width`. + + See Also + -------- + center + """ + return asarray(center(self, width, fillchar)) + + def count(self, sub, start=0, end=None): + """ + Returns an array with the number of non-overlapping occurrences of + substring `sub` in the range [`start`, `end`]. + + See Also + -------- + char.count + + """ + return count(self, sub, start, end) + + def decode(self, encoding=None, errors=None): + """ + Calls ``bytes.decode`` element-wise. + + See Also + -------- + char.decode + + """ + return decode(self, encoding, errors) + + def encode(self, encoding=None, errors=None): + """ + Calls `str.encode` element-wise. + + See Also + -------- + char.encode + + """ + return encode(self, encoding, errors) + + def endswith(self, suffix, start=0, end=None): + """ + Returns a boolean array which is `True` where the string element + in `self` ends with `suffix`, otherwise `False`. + + See Also + -------- + char.endswith + + """ + return endswith(self, suffix, start, end) + + def expandtabs(self, tabsize=8): + """ + Return a copy of each string element where all tab characters are + replaced by one or more spaces. + + See Also + -------- + char.expandtabs + + """ + return asarray(expandtabs(self, tabsize)) + + def find(self, sub, start=0, end=None): + """ + For each element, return the lowest index in the string where + substring `sub` is found. + + See Also + -------- + char.find + + """ + return find(self, sub, start, end) + + def index(self, sub, start=0, end=None): + """ + Like `find`, but raises `ValueError` when the substring is not found. + + See Also + -------- + char.index + + """ + return index(self, sub, start, end) + + def isalnum(self): + """ + Returns true for each element if all characters in the string + are alphanumeric and there is at least one character, false + otherwise. + + See Also + -------- + char.isalnum + + """ + return isalnum(self) + + def isalpha(self): + """ + Returns true for each element if all characters in the string + are alphabetic and there is at least one character, false + otherwise. + + See Also + -------- + char.isalpha + + """ + return isalpha(self) + + def isdigit(self): + """ + Returns true for each element if all characters in the string are + digits and there is at least one character, false otherwise. + + See Also + -------- + char.isdigit + + """ + return isdigit(self) + + def islower(self): + """ + Returns true for each element if all cased characters in the + string are lowercase and there is at least one cased character, + false otherwise. + + See Also + -------- + char.islower + + """ + return islower(self) + + def isspace(self): + """ + Returns true for each element if there are only whitespace + characters in the string and there is at least one character, + false otherwise. + + See Also + -------- + char.isspace + + """ + return isspace(self) + + def istitle(self): + """ + Returns true for each element if the element is a titlecased + string and there is at least one character, false otherwise. + + See Also + -------- + char.istitle + + """ + return istitle(self) + + def isupper(self): + """ + Returns true for each element if all cased characters in the + string are uppercase and there is at least one character, false + otherwise. + + See Also + -------- + char.isupper + + """ + return isupper(self) + + def join(self, seq): + """ + Return a string which is the concatenation of the strings in the + sequence `seq`. + + See Also + -------- + char.join + + """ + return join(self, seq) + + def ljust(self, width, fillchar=' '): + """ + Return an array with the elements of `self` left-justified in a + string of length `width`. + + See Also + -------- + char.ljust + + """ + return asarray(ljust(self, width, fillchar)) + + def lower(self): + """ + Return an array with the elements of `self` converted to + lowercase. + + See Also + -------- + char.lower + + """ + return asarray(lower(self)) + + def lstrip(self, chars=None): + """ + For each element in `self`, return a copy with the leading characters + removed. + + See Also + -------- + char.lstrip + + """ + return asarray(lstrip(self, chars)) + + def partition(self, sep): + """ + Partition each element in `self` around `sep`. + + See Also + -------- + partition + """ + return asarray(partition(self, sep)) + + def replace(self, old, new, count=None): + """ + For each element in `self`, return a copy of the string with all + occurrences of substring `old` replaced by `new`. + + See Also + -------- + char.replace + + """ + return asarray(replace(self, old, new, count)) + + def rfind(self, sub, start=0, end=None): + """ + For each element in `self`, return the highest index in the string + where substring `sub` is found, such that `sub` is contained + within [`start`, `end`]. + + See Also + -------- + char.rfind + + """ + return rfind(self, sub, start, end) + + def rindex(self, sub, start=0, end=None): + """ + Like `rfind`, but raises `ValueError` when the substring `sub` is + not found. + + See Also + -------- + char.rindex + + """ + return rindex(self, sub, start, end) + + def rjust(self, width, fillchar=' '): + """ + Return an array with the elements of `self` + right-justified in a string of length `width`. + + See Also + -------- + char.rjust + + """ + return asarray(rjust(self, width, fillchar)) + + def rpartition(self, sep): + """ + Partition each element in `self` around `sep`. + + See Also + -------- + rpartition + """ + return asarray(rpartition(self, sep)) + + def rsplit(self, sep=None, maxsplit=None): + """ + For each element in `self`, return a list of the words in + the string, using `sep` as the delimiter string. + + See Also + -------- + char.rsplit + + """ + return rsplit(self, sep, maxsplit) + + def rstrip(self, chars=None): + """ + For each element in `self`, return a copy with the trailing + characters removed. + + See Also + -------- + char.rstrip + + """ + return asarray(rstrip(self, chars)) + + def split(self, sep=None, maxsplit=None): + """ + For each element in `self`, return a list of the words in the + string, using `sep` as the delimiter string. + + See Also + -------- + char.split + + """ + return split(self, sep, maxsplit) + + def splitlines(self, keepends=None): + """ + For each element in `self`, return a list of the lines in the + element, breaking at line boundaries. + + See Also + -------- + char.splitlines + + """ + return splitlines(self, keepends) + + def startswith(self, prefix, start=0, end=None): + """ + Returns a boolean array which is `True` where the string element + in `self` starts with `prefix`, otherwise `False`. + + See Also + -------- + char.startswith + + """ + return startswith(self, prefix, start, end) + + def strip(self, chars=None): + """ + For each element in `self`, return a copy with the leading and + trailing characters removed. + + See Also + -------- + char.strip + + """ + return asarray(strip(self, chars)) + + def swapcase(self): + """ + For each element in `self`, return a copy of the string with + uppercase characters converted to lowercase and vice versa. + + See Also + -------- + char.swapcase + + """ + return asarray(swapcase(self)) + + def title(self): + """ + For each element in `self`, return a titlecased version of the + string: words start with uppercase characters, all remaining cased + characters are lowercase. + + See Also + -------- + char.title + + """ + return asarray(title(self)) + + def translate(self, table, deletechars=None): + """ + For each element in `self`, return a copy of the string where + all characters occurring in the optional argument + `deletechars` are removed, and the remaining characters have + been mapped through the given translation table. + + See Also + -------- + char.translate + + """ + return asarray(translate(self, table, deletechars)) + + def upper(self): + """ + Return an array with the elements of `self` converted to + uppercase. + + See Also + -------- + char.upper + + """ + return asarray(upper(self)) + + def zfill(self, width): + """ + Return the numeric string left-filled with zeros in a string of + length `width`. + + See Also + -------- + char.zfill + + """ + return asarray(zfill(self, width)) + + def isnumeric(self): + """ + For each element in `self`, return True if there are only + numeric characters in the element. + + See Also + -------- + char.isnumeric + + """ + return isnumeric(self) + + def isdecimal(self): + """ + For each element in `self`, return True if there are only + decimal characters in the element. + + See Also + -------- + char.isdecimal + + """ + return isdecimal(self) + + +@set_module("numpy.char") +def array(obj, itemsize=None, copy=True, unicode=None, order=None): + """ + Create a `chararray`. + + .. note:: + This class is provided for numarray backward-compatibility. + New code (not concerned with numarray compatibility) should use + arrays of type `bytes_` or `str_` and use the free functions + in :mod:`numpy.char ` for fast + vectorized string operations instead. + + Versus a regular NumPy array of type `str` or `unicode`, this + class adds the following functionality: + + 1) values automatically have whitespace removed from the end + when indexed + + 2) comparison operators automatically remove whitespace from the + end when comparing values + + 3) vectorized string operations are provided as methods + (e.g. `str.endswith`) and infix operators (e.g. ``+, *, %``) + + Parameters + ---------- + obj : array of str or unicode-like + + itemsize : int, optional + `itemsize` is the number of characters per scalar in the + resulting array. If `itemsize` is None, and `obj` is an + object array or a Python list, the `itemsize` will be + automatically determined. If `itemsize` is provided and `obj` + is of type str or unicode, then the `obj` string will be + chunked into `itemsize` pieces. + + copy : bool, optional + If true (default), then the object is copied. Otherwise, a copy + will only be made if __array__ returns a copy, if obj is a + nested sequence, or if a copy is needed to satisfy any of the other + requirements (`itemsize`, unicode, `order`, etc.). + + unicode : bool, optional + When true, the resulting `chararray` can contain Unicode + characters, when false only 8-bit characters. If unicode is + None and `obj` is one of the following: + + - a `chararray`, + - an ndarray of type `str` or `unicode` + - a Python str or unicode object, + + then the unicode setting of the output array will be + automatically determined. + + order : {'C', 'F', 'A'}, optional + Specify the order of the array. If order is 'C' (default), then the + array will be in C-contiguous order (last-index varies the + fastest). If order is 'F', then the returned array + will be in Fortran-contiguous order (first-index varies the + fastest). If order is 'A', then the returned array may + be in any order (either C-, Fortran-contiguous, or even + discontiguous). + """ + if isinstance(obj, (bytes, str)): + if unicode is None: + if isinstance(obj, str): + unicode = True + else: + unicode = False + + if itemsize is None: + itemsize = len(obj) + shape = len(obj) // itemsize + + return chararray(shape, itemsize=itemsize, unicode=unicode, + buffer=obj, order=order) + + if isinstance(obj, (list, tuple)): + obj = numpy.asarray(obj) + + if isinstance(obj, ndarray) and issubclass(obj.dtype.type, character): + # If we just have a vanilla chararray, create a chararray + # view around it. + if not isinstance(obj, chararray): + obj = obj.view(chararray) + + if itemsize is None: + itemsize = obj.itemsize + # itemsize is in 8-bit chars, so for Unicode, we need + # to divide by the size of a single Unicode character, + # which for NumPy is always 4 + if issubclass(obj.dtype.type, str_): + itemsize //= 4 + + if unicode is None: + if issubclass(obj.dtype.type, str_): + unicode = True + else: + unicode = False + + if unicode: + dtype = str_ + else: + dtype = bytes_ + + if order is not None: + obj = numpy.asarray(obj, order=order) + if (copy or + (itemsize != obj.itemsize) or + (not unicode and isinstance(obj, str_)) or + (unicode and isinstance(obj, bytes_))): + obj = obj.astype((dtype, int(itemsize))) + return obj + + if isinstance(obj, ndarray) and issubclass(obj.dtype.type, object): + if itemsize is None: + # Since no itemsize was specified, convert the input array to + # a list so the ndarray constructor will automatically + # determine the itemsize for us. + obj = obj.tolist() + # Fall through to the default case + + if unicode: + dtype = str_ + else: + dtype = bytes_ + + if itemsize is None: + val = narray(obj, dtype=dtype, order=order, subok=True) + else: + val = narray(obj, dtype=(dtype, itemsize), order=order, subok=True) + return val.view(chararray) + + +@set_module("numpy.char") +def asarray(obj, itemsize=None, unicode=None, order=None): + """ + Convert the input to a `chararray`, copying the data only if + necessary. + + Versus a regular NumPy array of type `str` or `unicode`, this + class adds the following functionality: + + 1) values automatically have whitespace removed from the end + when indexed + + 2) comparison operators automatically remove whitespace from the + end when comparing values + + 3) vectorized string operations are provided as methods + (e.g. `str.endswith`) and infix operators (e.g. ``+``, ``*``,``%``) + + Parameters + ---------- + obj : array of str or unicode-like + + itemsize : int, optional + `itemsize` is the number of characters per scalar in the + resulting array. If `itemsize` is None, and `obj` is an + object array or a Python list, the `itemsize` will be + automatically determined. If `itemsize` is provided and `obj` + is of type str or unicode, then the `obj` string will be + chunked into `itemsize` pieces. + + unicode : bool, optional + When true, the resulting `chararray` can contain Unicode + characters, when false only 8-bit characters. If unicode is + None and `obj` is one of the following: + + - a `chararray`, + - an ndarray of type `str` or 'unicode` + - a Python str or unicode object, + + then the unicode setting of the output array will be + automatically determined. + + order : {'C', 'F'}, optional + Specify the order of the array. If order is 'C' (default), then the + array will be in C-contiguous order (last-index varies the + fastest). If order is 'F', then the returned array + will be in Fortran-contiguous order (first-index varies the + fastest). + """ + return array(obj, itemsize, copy=False, + unicode=unicode, order=order) diff --git a/venv/lib/python3.10/site-packages/numpy/core/einsumfunc.py b/venv/lib/python3.10/site-packages/numpy/core/einsumfunc.py new file mode 100644 index 0000000000000000000000000000000000000000..01966f0fe75b7e336a4237372e2d4cb0db0fbc84 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/einsumfunc.py @@ -0,0 +1,1443 @@ +""" +Implementation of optimized einsum. + +""" +import itertools +import operator + +from numpy.core.multiarray import c_einsum +from numpy.core.numeric import asanyarray, tensordot +from numpy.core.overrides import array_function_dispatch + +__all__ = ['einsum', 'einsum_path'] + +einsum_symbols = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ' +einsum_symbols_set = set(einsum_symbols) + + +def _flop_count(idx_contraction, inner, num_terms, size_dictionary): + """ + Computes the number of FLOPS in the contraction. + + Parameters + ---------- + idx_contraction : iterable + The indices involved in the contraction + inner : bool + Does this contraction require an inner product? + num_terms : int + The number of terms in a contraction + size_dictionary : dict + The size of each of the indices in idx_contraction + + Returns + ------- + flop_count : int + The total number of FLOPS required for the contraction. + + Examples + -------- + + >>> _flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5}) + 30 + + >>> _flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5}) + 60 + + """ + + overall_size = _compute_size_by_dict(idx_contraction, size_dictionary) + op_factor = max(1, num_terms - 1) + if inner: + op_factor += 1 + + return overall_size * op_factor + +def _compute_size_by_dict(indices, idx_dict): + """ + Computes the product of the elements in indices based on the dictionary + idx_dict. + + Parameters + ---------- + indices : iterable + Indices to base the product on. + idx_dict : dictionary + Dictionary of index sizes + + Returns + ------- + ret : int + The resulting product. + + Examples + -------- + >>> _compute_size_by_dict('abbc', {'a': 2, 'b':3, 'c':5}) + 90 + + """ + ret = 1 + for i in indices: + ret *= idx_dict[i] + return ret + + +def _find_contraction(positions, input_sets, output_set): + """ + Finds the contraction for a given set of input and output sets. + + Parameters + ---------- + positions : iterable + Integer positions of terms used in the contraction. + input_sets : list + List of sets that represent the lhs side of the einsum subscript + output_set : set + Set that represents the rhs side of the overall einsum subscript + + Returns + ------- + new_result : set + The indices of the resulting contraction + remaining : list + List of sets that have not been contracted, the new set is appended to + the end of this list + idx_removed : set + Indices removed from the entire contraction + idx_contraction : set + The indices used in the current contraction + + Examples + -------- + + # A simple dot product test case + >>> pos = (0, 1) + >>> isets = [set('ab'), set('bc')] + >>> oset = set('ac') + >>> _find_contraction(pos, isets, oset) + ({'a', 'c'}, [{'a', 'c'}], {'b'}, {'a', 'b', 'c'}) + + # A more complex case with additional terms in the contraction + >>> pos = (0, 2) + >>> isets = [set('abd'), set('ac'), set('bdc')] + >>> oset = set('ac') + >>> _find_contraction(pos, isets, oset) + ({'a', 'c'}, [{'a', 'c'}, {'a', 'c'}], {'b', 'd'}, {'a', 'b', 'c', 'd'}) + """ + + idx_contract = set() + idx_remain = output_set.copy() + remaining = [] + for ind, value in enumerate(input_sets): + if ind in positions: + idx_contract |= value + else: + remaining.append(value) + idx_remain |= value + + new_result = idx_remain & idx_contract + idx_removed = (idx_contract - new_result) + remaining.append(new_result) + + return (new_result, remaining, idx_removed, idx_contract) + + +def _optimal_path(input_sets, output_set, idx_dict, memory_limit): + """ + Computes all possible pair contractions, sieves the results based + on ``memory_limit`` and returns the lowest cost path. This algorithm + scales factorial with respect to the elements in the list ``input_sets``. + + Parameters + ---------- + input_sets : list + List of sets that represent the lhs side of the einsum subscript + output_set : set + Set that represents the rhs side of the overall einsum subscript + idx_dict : dictionary + Dictionary of index sizes + memory_limit : int + The maximum number of elements in a temporary array + + Returns + ------- + path : list + The optimal contraction order within the memory limit constraint. + + Examples + -------- + >>> isets = [set('abd'), set('ac'), set('bdc')] + >>> oset = set() + >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4} + >>> _optimal_path(isets, oset, idx_sizes, 5000) + [(0, 2), (0, 1)] + """ + + full_results = [(0, [], input_sets)] + for iteration in range(len(input_sets) - 1): + iter_results = [] + + # Compute all unique pairs + for curr in full_results: + cost, positions, remaining = curr + for con in itertools.combinations(range(len(input_sets) - iteration), 2): + + # Find the contraction + cont = _find_contraction(con, remaining, output_set) + new_result, new_input_sets, idx_removed, idx_contract = cont + + # Sieve the results based on memory_limit + new_size = _compute_size_by_dict(new_result, idx_dict) + if new_size > memory_limit: + continue + + # Build (total_cost, positions, indices_remaining) + total_cost = cost + _flop_count(idx_contract, idx_removed, len(con), idx_dict) + new_pos = positions + [con] + iter_results.append((total_cost, new_pos, new_input_sets)) + + # Update combinatorial list, if we did not find anything return best + # path + remaining contractions + if iter_results: + full_results = iter_results + else: + path = min(full_results, key=lambda x: x[0])[1] + path += [tuple(range(len(input_sets) - iteration))] + return path + + # If we have not found anything return single einsum contraction + if len(full_results) == 0: + return [tuple(range(len(input_sets)))] + + path = min(full_results, key=lambda x: x[0])[1] + return path + +def _parse_possible_contraction(positions, input_sets, output_set, idx_dict, memory_limit, path_cost, naive_cost): + """Compute the cost (removed size + flops) and resultant indices for + performing the contraction specified by ``positions``. + + Parameters + ---------- + positions : tuple of int + The locations of the proposed tensors to contract. + input_sets : list of sets + The indices found on each tensors. + output_set : set + The output indices of the expression. + idx_dict : dict + Mapping of each index to its size. + memory_limit : int + The total allowed size for an intermediary tensor. + path_cost : int + The contraction cost so far. + naive_cost : int + The cost of the unoptimized expression. + + Returns + ------- + cost : (int, int) + A tuple containing the size of any indices removed, and the flop cost. + positions : tuple of int + The locations of the proposed tensors to contract. + new_input_sets : list of sets + The resulting new list of indices if this proposed contraction is performed. + + """ + + # Find the contraction + contract = _find_contraction(positions, input_sets, output_set) + idx_result, new_input_sets, idx_removed, idx_contract = contract + + # Sieve the results based on memory_limit + new_size = _compute_size_by_dict(idx_result, idx_dict) + if new_size > memory_limit: + return None + + # Build sort tuple + old_sizes = (_compute_size_by_dict(input_sets[p], idx_dict) for p in positions) + removed_size = sum(old_sizes) - new_size + + # NB: removed_size used to be just the size of any removed indices i.e.: + # helpers.compute_size_by_dict(idx_removed, idx_dict) + cost = _flop_count(idx_contract, idx_removed, len(positions), idx_dict) + sort = (-removed_size, cost) + + # Sieve based on total cost as well + if (path_cost + cost) > naive_cost: + return None + + # Add contraction to possible choices + return [sort, positions, new_input_sets] + + +def _update_other_results(results, best): + """Update the positions and provisional input_sets of ``results`` based on + performing the contraction result ``best``. Remove any involving the tensors + contracted. + + Parameters + ---------- + results : list + List of contraction results produced by ``_parse_possible_contraction``. + best : list + The best contraction of ``results`` i.e. the one that will be performed. + + Returns + ------- + mod_results : list + The list of modified results, updated with outcome of ``best`` contraction. + """ + + best_con = best[1] + bx, by = best_con + mod_results = [] + + for cost, (x, y), con_sets in results: + + # Ignore results involving tensors just contracted + if x in best_con or y in best_con: + continue + + # Update the input_sets + del con_sets[by - int(by > x) - int(by > y)] + del con_sets[bx - int(bx > x) - int(bx > y)] + con_sets.insert(-1, best[2][-1]) + + # Update the position indices + mod_con = x - int(x > bx) - int(x > by), y - int(y > bx) - int(y > by) + mod_results.append((cost, mod_con, con_sets)) + + return mod_results + +def _greedy_path(input_sets, output_set, idx_dict, memory_limit): + """ + Finds the path by contracting the best pair until the input list is + exhausted. The best pair is found by minimizing the tuple + ``(-prod(indices_removed), cost)``. What this amounts to is prioritizing + matrix multiplication or inner product operations, then Hadamard like + operations, and finally outer operations. Outer products are limited by + ``memory_limit``. This algorithm scales cubically with respect to the + number of elements in the list ``input_sets``. + + Parameters + ---------- + input_sets : list + List of sets that represent the lhs side of the einsum subscript + output_set : set + Set that represents the rhs side of the overall einsum subscript + idx_dict : dictionary + Dictionary of index sizes + memory_limit : int + The maximum number of elements in a temporary array + + Returns + ------- + path : list + The greedy contraction order within the memory limit constraint. + + Examples + -------- + >>> isets = [set('abd'), set('ac'), set('bdc')] + >>> oset = set() + >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4} + >>> _greedy_path(isets, oset, idx_sizes, 5000) + [(0, 2), (0, 1)] + """ + + # Handle trivial cases that leaked through + if len(input_sets) == 1: + return [(0,)] + elif len(input_sets) == 2: + return [(0, 1)] + + # Build up a naive cost + contract = _find_contraction(range(len(input_sets)), input_sets, output_set) + idx_result, new_input_sets, idx_removed, idx_contract = contract + naive_cost = _flop_count(idx_contract, idx_removed, len(input_sets), idx_dict) + + # Initially iterate over all pairs + comb_iter = itertools.combinations(range(len(input_sets)), 2) + known_contractions = [] + + path_cost = 0 + path = [] + + for iteration in range(len(input_sets) - 1): + + # Iterate over all pairs on first step, only previously found pairs on subsequent steps + for positions in comb_iter: + + # Always initially ignore outer products + if input_sets[positions[0]].isdisjoint(input_sets[positions[1]]): + continue + + result = _parse_possible_contraction(positions, input_sets, output_set, idx_dict, memory_limit, path_cost, + naive_cost) + if result is not None: + known_contractions.append(result) + + # If we do not have a inner contraction, rescan pairs including outer products + if len(known_contractions) == 0: + + # Then check the outer products + for positions in itertools.combinations(range(len(input_sets)), 2): + result = _parse_possible_contraction(positions, input_sets, output_set, idx_dict, memory_limit, + path_cost, naive_cost) + if result is not None: + known_contractions.append(result) + + # If we still did not find any remaining contractions, default back to einsum like behavior + if len(known_contractions) == 0: + path.append(tuple(range(len(input_sets)))) + break + + # Sort based on first index + best = min(known_contractions, key=lambda x: x[0]) + + # Now propagate as many unused contractions as possible to next iteration + known_contractions = _update_other_results(known_contractions, best) + + # Next iteration only compute contractions with the new tensor + # All other contractions have been accounted for + input_sets = best[2] + new_tensor_pos = len(input_sets) - 1 + comb_iter = ((i, new_tensor_pos) for i in range(new_tensor_pos)) + + # Update path and total cost + path.append(best[1]) + path_cost += best[0][1] + + return path + + +def _can_dot(inputs, result, idx_removed): + """ + Checks if we can use BLAS (np.tensordot) call and its beneficial to do so. + + Parameters + ---------- + inputs : list of str + Specifies the subscripts for summation. + result : str + Resulting summation. + idx_removed : set + Indices that are removed in the summation + + + Returns + ------- + type : bool + Returns true if BLAS should and can be used, else False + + Notes + ----- + If the operations is BLAS level 1 or 2 and is not already aligned + we default back to einsum as the memory movement to copy is more + costly than the operation itself. + + + Examples + -------- + + # Standard GEMM operation + >>> _can_dot(['ij', 'jk'], 'ik', set('j')) + True + + # Can use the standard BLAS, but requires odd data movement + >>> _can_dot(['ijj', 'jk'], 'ik', set('j')) + False + + # DDOT where the memory is not aligned + >>> _can_dot(['ijk', 'ikj'], '', set('ijk')) + False + + """ + + # All `dot` calls remove indices + if len(idx_removed) == 0: + return False + + # BLAS can only handle two operands + if len(inputs) != 2: + return False + + input_left, input_right = inputs + + for c in set(input_left + input_right): + # can't deal with repeated indices on same input or more than 2 total + nl, nr = input_left.count(c), input_right.count(c) + if (nl > 1) or (nr > 1) or (nl + nr > 2): + return False + + # can't do implicit summation or dimension collapse e.g. + # "ab,bc->c" (implicitly sum over 'a') + # "ab,ca->ca" (take diagonal of 'a') + if nl + nr - 1 == int(c in result): + return False + + # Build a few temporaries + set_left = set(input_left) + set_right = set(input_right) + keep_left = set_left - idx_removed + keep_right = set_right - idx_removed + rs = len(idx_removed) + + # At this point we are a DOT, GEMV, or GEMM operation + + # Handle inner products + + # DDOT with aligned data + if input_left == input_right: + return True + + # DDOT without aligned data (better to use einsum) + if set_left == set_right: + return False + + # Handle the 4 possible (aligned) GEMV or GEMM cases + + # GEMM or GEMV no transpose + if input_left[-rs:] == input_right[:rs]: + return True + + # GEMM or GEMV transpose both + if input_left[:rs] == input_right[-rs:]: + return True + + # GEMM or GEMV transpose right + if input_left[-rs:] == input_right[-rs:]: + return True + + # GEMM or GEMV transpose left + if input_left[:rs] == input_right[:rs]: + return True + + # Einsum is faster than GEMV if we have to copy data + if not keep_left or not keep_right: + return False + + # We are a matrix-matrix product, but we need to copy data + return True + + +def _parse_einsum_input(operands): + """ + A reproduction of einsum c side einsum parsing in python. + + Returns + ------- + input_strings : str + Parsed input strings + output_string : str + Parsed output string + operands : list of array_like + The operands to use in the numpy contraction + + Examples + -------- + The operand list is simplified to reduce printing: + + >>> np.random.seed(123) + >>> a = np.random.rand(4, 4) + >>> b = np.random.rand(4, 4, 4) + >>> _parse_einsum_input(('...a,...a->...', a, b)) + ('za,xza', 'xz', [a, b]) # may vary + + >>> _parse_einsum_input((a, [Ellipsis, 0], b, [Ellipsis, 0])) + ('za,xza', 'xz', [a, b]) # may vary + """ + + if len(operands) == 0: + raise ValueError("No input operands") + + if isinstance(operands[0], str): + subscripts = operands[0].replace(" ", "") + operands = [asanyarray(v) for v in operands[1:]] + + # Ensure all characters are valid + for s in subscripts: + if s in '.,->': + continue + if s not in einsum_symbols: + raise ValueError("Character %s is not a valid symbol." % s) + + else: + tmp_operands = list(operands) + operand_list = [] + subscript_list = [] + for p in range(len(operands) // 2): + operand_list.append(tmp_operands.pop(0)) + subscript_list.append(tmp_operands.pop(0)) + + output_list = tmp_operands[-1] if len(tmp_operands) else None + operands = [asanyarray(v) for v in operand_list] + subscripts = "" + last = len(subscript_list) - 1 + for num, sub in enumerate(subscript_list): + for s in sub: + if s is Ellipsis: + subscripts += "..." + else: + try: + s = operator.index(s) + except TypeError as e: + raise TypeError("For this input type lists must contain " + "either int or Ellipsis") from e + subscripts += einsum_symbols[s] + if num != last: + subscripts += "," + + if output_list is not None: + subscripts += "->" + for s in output_list: + if s is Ellipsis: + subscripts += "..." + else: + try: + s = operator.index(s) + except TypeError as e: + raise TypeError("For this input type lists must contain " + "either int or Ellipsis") from e + subscripts += einsum_symbols[s] + # Check for proper "->" + if ("-" in subscripts) or (">" in subscripts): + invalid = (subscripts.count("-") > 1) or (subscripts.count(">") > 1) + if invalid or (subscripts.count("->") != 1): + raise ValueError("Subscripts can only contain one '->'.") + + # Parse ellipses + if "." in subscripts: + used = subscripts.replace(".", "").replace(",", "").replace("->", "") + unused = list(einsum_symbols_set - set(used)) + ellipse_inds = "".join(unused) + longest = 0 + + if "->" in subscripts: + input_tmp, output_sub = subscripts.split("->") + split_subscripts = input_tmp.split(",") + out_sub = True + else: + split_subscripts = subscripts.split(',') + out_sub = False + + for num, sub in enumerate(split_subscripts): + if "." in sub: + if (sub.count(".") != 3) or (sub.count("...") != 1): + raise ValueError("Invalid Ellipses.") + + # Take into account numerical values + if operands[num].shape == (): + ellipse_count = 0 + else: + ellipse_count = max(operands[num].ndim, 1) + ellipse_count -= (len(sub) - 3) + + if ellipse_count > longest: + longest = ellipse_count + + if ellipse_count < 0: + raise ValueError("Ellipses lengths do not match.") + elif ellipse_count == 0: + split_subscripts[num] = sub.replace('...', '') + else: + rep_inds = ellipse_inds[-ellipse_count:] + split_subscripts[num] = sub.replace('...', rep_inds) + + subscripts = ",".join(split_subscripts) + if longest == 0: + out_ellipse = "" + else: + out_ellipse = ellipse_inds[-longest:] + + if out_sub: + subscripts += "->" + output_sub.replace("...", out_ellipse) + else: + # Special care for outputless ellipses + output_subscript = "" + tmp_subscripts = subscripts.replace(",", "") + for s in sorted(set(tmp_subscripts)): + if s not in (einsum_symbols): + raise ValueError("Character %s is not a valid symbol." % s) + if tmp_subscripts.count(s) == 1: + output_subscript += s + normal_inds = ''.join(sorted(set(output_subscript) - + set(out_ellipse))) + + subscripts += "->" + out_ellipse + normal_inds + + # Build output string if does not exist + if "->" in subscripts: + input_subscripts, output_subscript = subscripts.split("->") + else: + input_subscripts = subscripts + # Build output subscripts + tmp_subscripts = subscripts.replace(",", "") + output_subscript = "" + for s in sorted(set(tmp_subscripts)): + if s not in einsum_symbols: + raise ValueError("Character %s is not a valid symbol." % s) + if tmp_subscripts.count(s) == 1: + output_subscript += s + + # Make sure output subscripts are in the input + for char in output_subscript: + if char not in input_subscripts: + raise ValueError("Output character %s did not appear in the input" + % char) + + # Make sure number operands is equivalent to the number of terms + if len(input_subscripts.split(',')) != len(operands): + raise ValueError("Number of einsum subscripts must be equal to the " + "number of operands.") + + return (input_subscripts, output_subscript, operands) + + +def _einsum_path_dispatcher(*operands, optimize=None, einsum_call=None): + # NOTE: technically, we should only dispatch on array-like arguments, not + # subscripts (given as strings). But separating operands into + # arrays/subscripts is a little tricky/slow (given einsum's two supported + # signatures), so as a practical shortcut we dispatch on everything. + # Strings will be ignored for dispatching since they don't define + # __array_function__. + return operands + + +@array_function_dispatch(_einsum_path_dispatcher, module='numpy') +def einsum_path(*operands, optimize='greedy', einsum_call=False): + """ + einsum_path(subscripts, *operands, optimize='greedy') + + Evaluates the lowest cost contraction order for an einsum expression by + considering the creation of intermediate arrays. + + Parameters + ---------- + subscripts : str + Specifies the subscripts for summation. + *operands : list of array_like + These are the arrays for the operation. + optimize : {bool, list, tuple, 'greedy', 'optimal'} + Choose the type of path. If a tuple is provided, the second argument is + assumed to be the maximum intermediate size created. If only a single + argument is provided the largest input or output array size is used + as a maximum intermediate size. + + * if a list is given that starts with ``einsum_path``, uses this as the + contraction path + * if False no optimization is taken + * if True defaults to the 'greedy' algorithm + * 'optimal' An algorithm that combinatorially explores all possible + ways of contracting the listed tensors and chooses the least costly + path. Scales exponentially with the number of terms in the + contraction. + * 'greedy' An algorithm that chooses the best pair contraction + at each step. Effectively, this algorithm searches the largest inner, + Hadamard, and then outer products at each step. Scales cubically with + the number of terms in the contraction. Equivalent to the 'optimal' + path for most contractions. + + Default is 'greedy'. + + Returns + ------- + path : list of tuples + A list representation of the einsum path. + string_repr : str + A printable representation of the einsum path. + + Notes + ----- + The resulting path indicates which terms of the input contraction should be + contracted first, the result of this contraction is then appended to the + end of the contraction list. This list can then be iterated over until all + intermediate contractions are complete. + + See Also + -------- + einsum, linalg.multi_dot + + Examples + -------- + + We can begin with a chain dot example. In this case, it is optimal to + contract the ``b`` and ``c`` tensors first as represented by the first + element of the path ``(1, 2)``. The resulting tensor is added to the end + of the contraction and the remaining contraction ``(0, 1)`` is then + completed. + + >>> np.random.seed(123) + >>> a = np.random.rand(2, 2) + >>> b = np.random.rand(2, 5) + >>> c = np.random.rand(5, 2) + >>> path_info = np.einsum_path('ij,jk,kl->il', a, b, c, optimize='greedy') + >>> print(path_info[0]) + ['einsum_path', (1, 2), (0, 1)] + >>> print(path_info[1]) + Complete contraction: ij,jk,kl->il # may vary + Naive scaling: 4 + Optimized scaling: 3 + Naive FLOP count: 1.600e+02 + Optimized FLOP count: 5.600e+01 + Theoretical speedup: 2.857 + Largest intermediate: 4.000e+00 elements + ------------------------------------------------------------------------- + scaling current remaining + ------------------------------------------------------------------------- + 3 kl,jk->jl ij,jl->il + 3 jl,ij->il il->il + + + A more complex index transformation example. + + >>> I = np.random.rand(10, 10, 10, 10) + >>> C = np.random.rand(10, 10) + >>> path_info = np.einsum_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C, + ... optimize='greedy') + + >>> print(path_info[0]) + ['einsum_path', (0, 2), (0, 3), (0, 2), (0, 1)] + >>> print(path_info[1]) + Complete contraction: ea,fb,abcd,gc,hd->efgh # may vary + Naive scaling: 8 + Optimized scaling: 5 + Naive FLOP count: 8.000e+08 + Optimized FLOP count: 8.000e+05 + Theoretical speedup: 1000.000 + Largest intermediate: 1.000e+04 elements + -------------------------------------------------------------------------- + scaling current remaining + -------------------------------------------------------------------------- + 5 abcd,ea->bcde fb,gc,hd,bcde->efgh + 5 bcde,fb->cdef gc,hd,cdef->efgh + 5 cdef,gc->defg hd,defg->efgh + 5 defg,hd->efgh efgh->efgh + """ + + # Figure out what the path really is + path_type = optimize + if path_type is True: + path_type = 'greedy' + if path_type is None: + path_type = False + + explicit_einsum_path = False + memory_limit = None + + # No optimization or a named path algorithm + if (path_type is False) or isinstance(path_type, str): + pass + + # Given an explicit path + elif len(path_type) and (path_type[0] == 'einsum_path'): + explicit_einsum_path = True + + # Path tuple with memory limit + elif ((len(path_type) == 2) and isinstance(path_type[0], str) and + isinstance(path_type[1], (int, float))): + memory_limit = int(path_type[1]) + path_type = path_type[0] + + else: + raise TypeError("Did not understand the path: %s" % str(path_type)) + + # Hidden option, only einsum should call this + einsum_call_arg = einsum_call + + # Python side parsing + input_subscripts, output_subscript, operands = _parse_einsum_input(operands) + + # Build a few useful list and sets + input_list = input_subscripts.split(',') + input_sets = [set(x) for x in input_list] + output_set = set(output_subscript) + indices = set(input_subscripts.replace(',', '')) + + # Get length of each unique dimension and ensure all dimensions are correct + dimension_dict = {} + broadcast_indices = [[] for x in range(len(input_list))] + for tnum, term in enumerate(input_list): + sh = operands[tnum].shape + if len(sh) != len(term): + raise ValueError("Einstein sum subscript %s does not contain the " + "correct number of indices for operand %d." + % (input_subscripts[tnum], tnum)) + for cnum, char in enumerate(term): + dim = sh[cnum] + + # Build out broadcast indices + if dim == 1: + broadcast_indices[tnum].append(char) + + if char in dimension_dict.keys(): + # For broadcasting cases we always want the largest dim size + if dimension_dict[char] == 1: + dimension_dict[char] = dim + elif dim not in (1, dimension_dict[char]): + raise ValueError("Size of label '%s' for operand %d (%d) " + "does not match previous terms (%d)." + % (char, tnum, dimension_dict[char], dim)) + else: + dimension_dict[char] = dim + + # Convert broadcast inds to sets + broadcast_indices = [set(x) for x in broadcast_indices] + + # Compute size of each input array plus the output array + size_list = [_compute_size_by_dict(term, dimension_dict) + for term in input_list + [output_subscript]] + max_size = max(size_list) + + if memory_limit is None: + memory_arg = max_size + else: + memory_arg = memory_limit + + # Compute naive cost + # This isn't quite right, need to look into exactly how einsum does this + inner_product = (sum(len(x) for x in input_sets) - len(indices)) > 0 + naive_cost = _flop_count(indices, inner_product, len(input_list), dimension_dict) + + # Compute the path + if explicit_einsum_path: + path = path_type[1:] + elif ( + (path_type is False) + or (len(input_list) in [1, 2]) + or (indices == output_set) + ): + # Nothing to be optimized, leave it to einsum + path = [tuple(range(len(input_list)))] + elif path_type == "greedy": + path = _greedy_path(input_sets, output_set, dimension_dict, memory_arg) + elif path_type == "optimal": + path = _optimal_path(input_sets, output_set, dimension_dict, memory_arg) + else: + raise KeyError("Path name %s not found", path_type) + + cost_list, scale_list, size_list, contraction_list = [], [], [], [] + + # Build contraction tuple (positions, gemm, einsum_str, remaining) + for cnum, contract_inds in enumerate(path): + # Make sure we remove inds from right to left + contract_inds = tuple(sorted(list(contract_inds), reverse=True)) + + contract = _find_contraction(contract_inds, input_sets, output_set) + out_inds, input_sets, idx_removed, idx_contract = contract + + cost = _flop_count(idx_contract, idx_removed, len(contract_inds), dimension_dict) + cost_list.append(cost) + scale_list.append(len(idx_contract)) + size_list.append(_compute_size_by_dict(out_inds, dimension_dict)) + + bcast = set() + tmp_inputs = [] + for x in contract_inds: + tmp_inputs.append(input_list.pop(x)) + bcast |= broadcast_indices.pop(x) + + new_bcast_inds = bcast - idx_removed + + # If we're broadcasting, nix blas + if not len(idx_removed & bcast): + do_blas = _can_dot(tmp_inputs, out_inds, idx_removed) + else: + do_blas = False + + # Last contraction + if (cnum - len(path)) == -1: + idx_result = output_subscript + else: + sort_result = [(dimension_dict[ind], ind) for ind in out_inds] + idx_result = "".join([x[1] for x in sorted(sort_result)]) + + input_list.append(idx_result) + broadcast_indices.append(new_bcast_inds) + einsum_str = ",".join(tmp_inputs) + "->" + idx_result + + contraction = (contract_inds, idx_removed, einsum_str, input_list[:], do_blas) + contraction_list.append(contraction) + + opt_cost = sum(cost_list) + 1 + + if len(input_list) != 1: + # Explicit "einsum_path" is usually trusted, but we detect this kind of + # mistake in order to prevent from returning an intermediate value. + raise RuntimeError( + "Invalid einsum_path is specified: {} more operands has to be " + "contracted.".format(len(input_list) - 1)) + + if einsum_call_arg: + return (operands, contraction_list) + + # Return the path along with a nice string representation + overall_contraction = input_subscripts + "->" + output_subscript + header = ("scaling", "current", "remaining") + + speedup = naive_cost / opt_cost + max_i = max(size_list) + + path_print = " Complete contraction: %s\n" % overall_contraction + path_print += " Naive scaling: %d\n" % len(indices) + path_print += " Optimized scaling: %d\n" % max(scale_list) + path_print += " Naive FLOP count: %.3e\n" % naive_cost + path_print += " Optimized FLOP count: %.3e\n" % opt_cost + path_print += " Theoretical speedup: %3.3f\n" % speedup + path_print += " Largest intermediate: %.3e elements\n" % max_i + path_print += "-" * 74 + "\n" + path_print += "%6s %24s %40s\n" % header + path_print += "-" * 74 + + for n, contraction in enumerate(contraction_list): + inds, idx_rm, einsum_str, remaining, blas = contraction + remaining_str = ",".join(remaining) + "->" + output_subscript + path_run = (scale_list[n], einsum_str, remaining_str) + path_print += "\n%4d %24s %40s" % path_run + + path = ['einsum_path'] + path + return (path, path_print) + + +def _einsum_dispatcher(*operands, out=None, optimize=None, **kwargs): + # Arguably we dispatch on more arguments than we really should; see note in + # _einsum_path_dispatcher for why. + yield from operands + yield out + + +# Rewrite einsum to handle different cases +@array_function_dispatch(_einsum_dispatcher, module='numpy') +def einsum(*operands, out=None, optimize=False, **kwargs): + """ + einsum(subscripts, *operands, out=None, dtype=None, order='K', + casting='safe', optimize=False) + + Evaluates the Einstein summation convention on the operands. + + Using the Einstein summation convention, many common multi-dimensional, + linear algebraic array operations can be represented in a simple fashion. + In *implicit* mode `einsum` computes these values. + + In *explicit* mode, `einsum` provides further flexibility to compute + other array operations that might not be considered classical Einstein + summation operations, by disabling, or forcing summation over specified + subscript labels. + + See the notes and examples for clarification. + + Parameters + ---------- + subscripts : str + Specifies the subscripts for summation as comma separated list of + subscript labels. An implicit (classical Einstein summation) + calculation is performed unless the explicit indicator '->' is + included as well as subscript labels of the precise output form. + operands : list of array_like + These are the arrays for the operation. + out : ndarray, optional + If provided, the calculation is done into this array. + dtype : {data-type, None}, optional + If provided, forces the calculation to use the data type specified. + Note that you may have to also give a more liberal `casting` + parameter to allow the conversions. Default is None. + order : {'C', 'F', 'A', 'K'}, optional + Controls the memory layout of the output. 'C' means it should + be C contiguous. 'F' means it should be Fortran contiguous, + 'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise. + 'K' means it should be as close to the layout as the inputs as + is possible, including arbitrarily permuted axes. + Default is 'K'. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. Setting this to + 'unsafe' is not recommended, as it can adversely affect accumulations. + + * 'no' means the data types should not be cast at all. + * 'equiv' means only byte-order changes are allowed. + * 'safe' means only casts which can preserve values are allowed. + * 'same_kind' means only safe casts or casts within a kind, + like float64 to float32, are allowed. + * 'unsafe' means any data conversions may be done. + + Default is 'safe'. + optimize : {False, True, 'greedy', 'optimal'}, optional + Controls if intermediate optimization should occur. No optimization + will occur if False and True will default to the 'greedy' algorithm. + Also accepts an explicit contraction list from the ``np.einsum_path`` + function. See ``np.einsum_path`` for more details. Defaults to False. + + Returns + ------- + output : ndarray + The calculation based on the Einstein summation convention. + + See Also + -------- + einsum_path, dot, inner, outer, tensordot, linalg.multi_dot + einops : + similar verbose interface is provided by + `einops `_ package to cover + additional operations: transpose, reshape/flatten, repeat/tile, + squeeze/unsqueeze and reductions. + opt_einsum : + `opt_einsum `_ + optimizes contraction order for einsum-like expressions + in backend-agnostic manner. + + Notes + ----- + .. versionadded:: 1.6.0 + + The Einstein summation convention can be used to compute + many multi-dimensional, linear algebraic array operations. `einsum` + provides a succinct way of representing these. + + A non-exhaustive list of these operations, + which can be computed by `einsum`, is shown below along with examples: + + * Trace of an array, :py:func:`numpy.trace`. + * Return a diagonal, :py:func:`numpy.diag`. + * Array axis summations, :py:func:`numpy.sum`. + * Transpositions and permutations, :py:func:`numpy.transpose`. + * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`. + * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`. + * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`. + * Tensor contractions, :py:func:`numpy.tensordot`. + * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`. + + The subscripts string is a comma-separated list of subscript labels, + where each label refers to a dimension of the corresponding operand. + Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)`` + is equivalent to :py:func:`np.inner(a,b) `. If a label + appears only once, it is not summed, so ``np.einsum('i', a)`` produces a + view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)`` + describes traditional matrix multiplication and is equivalent to + :py:func:`np.matmul(a,b) `. Repeated subscript labels in one + operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent + to :py:func:`np.trace(a) `. + + In *implicit mode*, the chosen subscripts are important + since the axes of the output are reordered alphabetically. This + means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while + ``np.einsum('ji', a)`` takes its transpose. Additionally, + ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while, + ``np.einsum('ij,jh', a, b)`` returns the transpose of the + multiplication since subscript 'h' precedes subscript 'i'. + + In *explicit mode* the output can be directly controlled by + specifying output subscript labels. This requires the + identifier '->' as well as the list of output subscript labels. + This feature increases the flexibility of the function since + summing can be disabled or forced when required. The call + ``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) `, + and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) `. + The difference is that `einsum` does not allow broadcasting by default. + Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the + order of the output subscript labels and therefore returns matrix + multiplication, unlike the example above in implicit mode. + + To enable and control broadcasting, use an ellipsis. Default + NumPy-style broadcasting is done by adding an ellipsis + to the left of each term, like ``np.einsum('...ii->...i', a)``. + To take the trace along the first and last axes, + you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix + product with the left-most indices instead of rightmost, one can do + ``np.einsum('ij...,jk...->ik...', a, b)``. + + When there is only one operand, no axes are summed, and no output + parameter is provided, a view into the operand is returned instead + of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)`` + produces a view (changed in version 1.10.0). + + `einsum` also provides an alternative way to provide the subscripts + and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``. + If the output shape is not provided in this format `einsum` will be + calculated in implicit mode, otherwise it will be performed explicitly. + The examples below have corresponding `einsum` calls with the two + parameter methods. + + .. versionadded:: 1.10.0 + + Views returned from einsum are now writeable whenever the input array + is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now + have the same effect as :py:func:`np.swapaxes(a, 0, 2) ` + and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal + of a 2D array. + + .. versionadded:: 1.12.0 + + Added the ``optimize`` argument which will optimize the contraction order + of an einsum expression. For a contraction with three or more operands this + can greatly increase the computational efficiency at the cost of a larger + memory footprint during computation. + + Typically a 'greedy' algorithm is applied which empirical tests have shown + returns the optimal path in the majority of cases. In some cases 'optimal' + will return the superlative path through a more expensive, exhaustive search. + For iterative calculations it may be advisable to calculate the optimal path + once and reuse that path by supplying it as an argument. An example is given + below. + + See :py:func:`numpy.einsum_path` for more details. + + Examples + -------- + >>> a = np.arange(25).reshape(5,5) + >>> b = np.arange(5) + >>> c = np.arange(6).reshape(2,3) + + Trace of a matrix: + + >>> np.einsum('ii', a) + 60 + >>> np.einsum(a, [0,0]) + 60 + >>> np.trace(a) + 60 + + Extract the diagonal (requires explicit form): + + >>> np.einsum('ii->i', a) + array([ 0, 6, 12, 18, 24]) + >>> np.einsum(a, [0,0], [0]) + array([ 0, 6, 12, 18, 24]) + >>> np.diag(a) + array([ 0, 6, 12, 18, 24]) + + Sum over an axis (requires explicit form): + + >>> np.einsum('ij->i', a) + array([ 10, 35, 60, 85, 110]) + >>> np.einsum(a, [0,1], [0]) + array([ 10, 35, 60, 85, 110]) + >>> np.sum(a, axis=1) + array([ 10, 35, 60, 85, 110]) + + For higher dimensional arrays summing a single axis can be done with ellipsis: + + >>> np.einsum('...j->...', a) + array([ 10, 35, 60, 85, 110]) + >>> np.einsum(a, [Ellipsis,1], [Ellipsis]) + array([ 10, 35, 60, 85, 110]) + + Compute a matrix transpose, or reorder any number of axes: + + >>> np.einsum('ji', c) + array([[0, 3], + [1, 4], + [2, 5]]) + >>> np.einsum('ij->ji', c) + array([[0, 3], + [1, 4], + [2, 5]]) + >>> np.einsum(c, [1,0]) + array([[0, 3], + [1, 4], + [2, 5]]) + >>> np.transpose(c) + array([[0, 3], + [1, 4], + [2, 5]]) + + Vector inner products: + + >>> np.einsum('i,i', b, b) + 30 + >>> np.einsum(b, [0], b, [0]) + 30 + >>> np.inner(b,b) + 30 + + Matrix vector multiplication: + + >>> np.einsum('ij,j', a, b) + array([ 30, 80, 130, 180, 230]) + >>> np.einsum(a, [0,1], b, [1]) + array([ 30, 80, 130, 180, 230]) + >>> np.dot(a, b) + array([ 30, 80, 130, 180, 230]) + >>> np.einsum('...j,j', a, b) + array([ 30, 80, 130, 180, 230]) + + Broadcasting and scalar multiplication: + + >>> np.einsum('..., ...', 3, c) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + >>> np.einsum(',ij', 3, c) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + >>> np.einsum(3, [Ellipsis], c, [Ellipsis]) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + >>> np.multiply(3, c) + array([[ 0, 3, 6], + [ 9, 12, 15]]) + + Vector outer product: + + >>> np.einsum('i,j', np.arange(2)+1, b) + array([[0, 1, 2, 3, 4], + [0, 2, 4, 6, 8]]) + >>> np.einsum(np.arange(2)+1, [0], b, [1]) + array([[0, 1, 2, 3, 4], + [0, 2, 4, 6, 8]]) + >>> np.outer(np.arange(2)+1, b) + array([[0, 1, 2, 3, 4], + [0, 2, 4, 6, 8]]) + + Tensor contraction: + + >>> a = np.arange(60.).reshape(3,4,5) + >>> b = np.arange(24.).reshape(4,3,2) + >>> np.einsum('ijk,jil->kl', a, b) + array([[4400., 4730.], + [4532., 4874.], + [4664., 5018.], + [4796., 5162.], + [4928., 5306.]]) + >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3]) + array([[4400., 4730.], + [4532., 4874.], + [4664., 5018.], + [4796., 5162.], + [4928., 5306.]]) + >>> np.tensordot(a,b, axes=([1,0],[0,1])) + array([[4400., 4730.], + [4532., 4874.], + [4664., 5018.], + [4796., 5162.], + [4928., 5306.]]) + + Writeable returned arrays (since version 1.10.0): + + >>> a = np.zeros((3, 3)) + >>> np.einsum('ii->i', a)[:] = 1 + >>> a + array([[1., 0., 0.], + [0., 1., 0.], + [0., 0., 1.]]) + + Example of ellipsis use: + + >>> a = np.arange(6).reshape((3,2)) + >>> b = np.arange(12).reshape((4,3)) + >>> np.einsum('ki,jk->ij', a, b) + array([[10, 28, 46, 64], + [13, 40, 67, 94]]) + >>> np.einsum('ki,...k->i...', a, b) + array([[10, 28, 46, 64], + [13, 40, 67, 94]]) + >>> np.einsum('k...,jk', a, b) + array([[10, 28, 46, 64], + [13, 40, 67, 94]]) + + Chained array operations. For more complicated contractions, speed ups + might be achieved by repeatedly computing a 'greedy' path or pre-computing the + 'optimal' path and repeatedly applying it, using an + `einsum_path` insertion (since version 1.12.0). Performance improvements can be + particularly significant with larger arrays: + + >>> a = np.ones(64).reshape(2,4,8) + + Basic `einsum`: ~1520ms (benchmarked on 3.1GHz Intel i5.) + + >>> for iteration in range(500): + ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a) + + Sub-optimal `einsum` (due to repeated path calculation time): ~330ms + + >>> for iteration in range(500): + ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal') + + Greedy `einsum` (faster optimal path approximation): ~160ms + + >>> for iteration in range(500): + ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy') + + Optimal `einsum` (best usage pattern in some use cases): ~110ms + + >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')[0] + >>> for iteration in range(500): + ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path) + + """ + # Special handling if out is specified + specified_out = out is not None + + # If no optimization, run pure einsum + if optimize is False: + if specified_out: + kwargs['out'] = out + return c_einsum(*operands, **kwargs) + + # Check the kwargs to avoid a more cryptic error later, without having to + # repeat default values here + valid_einsum_kwargs = ['dtype', 'order', 'casting'] + unknown_kwargs = [k for (k, v) in kwargs.items() if + k not in valid_einsum_kwargs] + if len(unknown_kwargs): + raise TypeError("Did not understand the following kwargs: %s" + % unknown_kwargs) + + # Build the contraction list and operand + operands, contraction_list = einsum_path(*operands, optimize=optimize, + einsum_call=True) + + # Handle order kwarg for output array, c_einsum allows mixed case + output_order = kwargs.pop('order', 'K') + if output_order.upper() == 'A': + if all(arr.flags.f_contiguous for arr in operands): + output_order = 'F' + else: + output_order = 'C' + + # Start contraction loop + for num, contraction in enumerate(contraction_list): + inds, idx_rm, einsum_str, remaining, blas = contraction + tmp_operands = [operands.pop(x) for x in inds] + + # Do we need to deal with the output? + handle_out = specified_out and ((num + 1) == len(contraction_list)) + + # Call tensordot if still possible + if blas: + # Checks have already been handled + input_str, results_index = einsum_str.split('->') + input_left, input_right = input_str.split(',') + + tensor_result = input_left + input_right + for s in idx_rm: + tensor_result = tensor_result.replace(s, "") + + # Find indices to contract over + left_pos, right_pos = [], [] + for s in sorted(idx_rm): + left_pos.append(input_left.find(s)) + right_pos.append(input_right.find(s)) + + # Contract! + new_view = tensordot(*tmp_operands, axes=(tuple(left_pos), tuple(right_pos))) + + # Build a new view if needed + if (tensor_result != results_index) or handle_out: + if handle_out: + kwargs["out"] = out + new_view = c_einsum(tensor_result + '->' + results_index, new_view, **kwargs) + + # Call einsum + else: + # If out was specified + if handle_out: + kwargs["out"] = out + + # Do the contraction + new_view = c_einsum(einsum_str, *tmp_operands, **kwargs) + + # Append new items and dereference what we can + operands.append(new_view) + del tmp_operands, new_view + + if specified_out: + return out + else: + return asanyarray(operands[0], order=output_order) diff --git a/venv/lib/python3.10/site-packages/numpy/core/einsumfunc.pyi b/venv/lib/python3.10/site-packages/numpy/core/einsumfunc.pyi new file mode 100644 index 0000000000000000000000000000000000000000..ad483bb90352000aff9708b1b75053ef39dd3196 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/einsumfunc.pyi @@ -0,0 +1,187 @@ +from collections.abc import Sequence +from typing import TypeVar, Any, overload, Union, Literal + +from numpy import ( + ndarray, + dtype, + bool_, + number, + _OrderKACF, +) +from numpy._typing import ( + _ArrayLikeBool_co, + _ArrayLikeUInt_co, + _ArrayLikeInt_co, + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, + _ArrayLikeObject_co, + _DTypeLikeBool, + _DTypeLikeUInt, + _DTypeLikeInt, + _DTypeLikeFloat, + _DTypeLikeComplex, + _DTypeLikeComplex_co, + _DTypeLikeObject, +) + +_ArrayType = TypeVar( + "_ArrayType", + bound=ndarray[Any, dtype[Union[bool_, number[Any]]]], +) + +_OptimizeKind = None | bool | Literal["greedy", "optimal"] | Sequence[Any] +_CastingSafe = Literal["no", "equiv", "safe", "same_kind"] +_CastingUnsafe = Literal["unsafe"] + +__all__: list[str] + +# TODO: Properly handle the `casting`-based combinatorics +# TODO: We need to evaluate the content `__subscripts` in order +# to identify whether or an array or scalar is returned. At a cursory +# glance this seems like something that can quite easily be done with +# a mypy plugin. +# Something like `is_scalar = bool(__subscripts.partition("->")[-1])` +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeBool_co, + out: None = ..., + dtype: None | _DTypeLikeBool = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeUInt_co, + out: None = ..., + dtype: None | _DTypeLikeUInt = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeInt_co, + out: None = ..., + dtype: None | _DTypeLikeInt = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeFloat_co, + out: None = ..., + dtype: None | _DTypeLikeFloat = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeComplex_co, + out: None = ..., + dtype: None | _DTypeLikeComplex = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: Any, + casting: _CastingUnsafe, + dtype: None | _DTypeLikeComplex_co = ..., + out: None = ..., + order: _OrderKACF = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeComplex_co, + out: _ArrayType, + dtype: None | _DTypeLikeComplex_co = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> _ArrayType: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: Any, + out: _ArrayType, + casting: _CastingUnsafe, + dtype: None | _DTypeLikeComplex_co = ..., + order: _OrderKACF = ..., + optimize: _OptimizeKind = ..., +) -> _ArrayType: ... + +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeObject_co, + out: None = ..., + dtype: None | _DTypeLikeObject = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: Any, + casting: _CastingUnsafe, + dtype: None | _DTypeLikeObject = ..., + out: None = ..., + order: _OrderKACF = ..., + optimize: _OptimizeKind = ..., +) -> Any: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeObject_co, + out: _ArrayType, + dtype: None | _DTypeLikeObject = ..., + order: _OrderKACF = ..., + casting: _CastingSafe = ..., + optimize: _OptimizeKind = ..., +) -> _ArrayType: ... +@overload +def einsum( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: Any, + out: _ArrayType, + casting: _CastingUnsafe, + dtype: None | _DTypeLikeObject = ..., + order: _OrderKACF = ..., + optimize: _OptimizeKind = ..., +) -> _ArrayType: ... + +# NOTE: `einsum_call` is a hidden kwarg unavailable for public use. +# It is therefore excluded from the signatures below. +# NOTE: In practice the list consists of a `str` (first element) +# and a variable number of integer tuples. +def einsum_path( + subscripts: str | _ArrayLikeInt_co, + /, + *operands: _ArrayLikeComplex_co | _DTypeLikeObject, + optimize: _OptimizeKind = ..., +) -> tuple[list[Any], str]: ... diff --git a/venv/lib/python3.10/site-packages/numpy/core/fromnumeric.py b/venv/lib/python3.10/site-packages/numpy/core/fromnumeric.py new file mode 100644 index 0000000000000000000000000000000000000000..69cabb33e57fd8eca0313e36b0968bfb26e4d22b --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/fromnumeric.py @@ -0,0 +1,3920 @@ +"""Module containing non-deprecated functions borrowed from Numeric. + +""" +import functools +import types +import warnings + +import numpy as np +from .._utils import set_module +from . import multiarray as mu +from . import overrides +from . import umath as um +from . import numerictypes as nt +from .multiarray import asarray, array, asanyarray, concatenate +from . import _methods + +_dt_ = nt.sctype2char + +# functions that are methods +__all__ = [ + 'all', 'alltrue', 'amax', 'amin', 'any', 'argmax', + 'argmin', 'argpartition', 'argsort', 'around', 'choose', 'clip', + 'compress', 'cumprod', 'cumproduct', 'cumsum', 'diagonal', 'mean', + 'max', 'min', + 'ndim', 'nonzero', 'partition', 'prod', 'product', 'ptp', 'put', + 'ravel', 'repeat', 'reshape', 'resize', 'round', 'round_', + 'searchsorted', 'shape', 'size', 'sometrue', 'sort', 'squeeze', + 'std', 'sum', 'swapaxes', 'take', 'trace', 'transpose', 'var', +] + +_gentype = types.GeneratorType +# save away Python sum +_sum_ = sum + +array_function_dispatch = functools.partial( + overrides.array_function_dispatch, module='numpy') + + +# functions that are now methods +def _wrapit(obj, method, *args, **kwds): + try: + wrap = obj.__array_wrap__ + except AttributeError: + wrap = None + result = getattr(asarray(obj), method)(*args, **kwds) + if wrap: + if not isinstance(result, mu.ndarray): + result = asarray(result) + result = wrap(result) + return result + + +def _wrapfunc(obj, method, *args, **kwds): + bound = getattr(obj, method, None) + if bound is None: + return _wrapit(obj, method, *args, **kwds) + + try: + return bound(*args, **kwds) + except TypeError: + # A TypeError occurs if the object does have such a method in its + # class, but its signature is not identical to that of NumPy's. This + # situation has occurred in the case of a downstream library like + # 'pandas'. + # + # Call _wrapit from within the except clause to ensure a potential + # exception has a traceback chain. + return _wrapit(obj, method, *args, **kwds) + + +def _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs): + passkwargs = {k: v for k, v in kwargs.items() + if v is not np._NoValue} + + if type(obj) is not mu.ndarray: + try: + reduction = getattr(obj, method) + except AttributeError: + pass + else: + # This branch is needed for reductions like any which don't + # support a dtype. + if dtype is not None: + return reduction(axis=axis, dtype=dtype, out=out, **passkwargs) + else: + return reduction(axis=axis, out=out, **passkwargs) + + return ufunc.reduce(obj, axis, dtype, out, **passkwargs) + + +def _take_dispatcher(a, indices, axis=None, out=None, mode=None): + return (a, out) + + +@array_function_dispatch(_take_dispatcher) +def take(a, indices, axis=None, out=None, mode='raise'): + """ + Take elements from an array along an axis. + + When axis is not None, this function does the same thing as "fancy" + indexing (indexing arrays using arrays); however, it can be easier to use + if you need elements along a given axis. A call such as + ``np.take(arr, indices, axis=3)`` is equivalent to + ``arr[:,:,:,indices,...]``. + + Explained without fancy indexing, this is equivalent to the following use + of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of + indices:: + + Ni, Nk = a.shape[:axis], a.shape[axis+1:] + Nj = indices.shape + for ii in ndindex(Ni): + for jj in ndindex(Nj): + for kk in ndindex(Nk): + out[ii + jj + kk] = a[ii + (indices[jj],) + kk] + + Parameters + ---------- + a : array_like (Ni..., M, Nk...) + The source array. + indices : array_like (Nj...) + The indices of the values to extract. + + .. versionadded:: 1.8.0 + + Also allow scalars for indices. + axis : int, optional + The axis over which to select values. By default, the flattened + input array is used. + out : ndarray, optional (Ni..., Nj..., Nk...) + If provided, the result will be placed in this array. It should + be of the appropriate shape and dtype. Note that `out` is always + buffered if `mode='raise'`; use other modes for better performance. + mode : {'raise', 'wrap', 'clip'}, optional + Specifies how out-of-bounds indices will behave. + + * 'raise' -- raise an error (default) + * 'wrap' -- wrap around + * 'clip' -- clip to the range + + 'clip' mode means that all indices that are too large are replaced + by the index that addresses the last element along that axis. Note + that this disables indexing with negative numbers. + + Returns + ------- + out : ndarray (Ni..., Nj..., Nk...) + The returned array has the same type as `a`. + + See Also + -------- + compress : Take elements using a boolean mask + ndarray.take : equivalent method + take_along_axis : Take elements by matching the array and the index arrays + + Notes + ----- + + By eliminating the inner loop in the description above, and using `s_` to + build simple slice objects, `take` can be expressed in terms of applying + fancy indexing to each 1-d slice:: + + Ni, Nk = a.shape[:axis], a.shape[axis+1:] + for ii in ndindex(Ni): + for kk in ndindex(Nj): + out[ii + s_[...,] + kk] = a[ii + s_[:,] + kk][indices] + + For this reason, it is equivalent to (but faster than) the following use + of `apply_along_axis`:: + + out = np.apply_along_axis(lambda a_1d: a_1d[indices], axis, a) + + Examples + -------- + >>> a = [4, 3, 5, 7, 6, 8] + >>> indices = [0, 1, 4] + >>> np.take(a, indices) + array([4, 3, 6]) + + In this example if `a` is an ndarray, "fancy" indexing can be used. + + >>> a = np.array(a) + >>> a[indices] + array([4, 3, 6]) + + If `indices` is not one dimensional, the output also has these dimensions. + + >>> np.take(a, [[0, 1], [2, 3]]) + array([[4, 3], + [5, 7]]) + """ + return _wrapfunc(a, 'take', indices, axis=axis, out=out, mode=mode) + + +def _reshape_dispatcher(a, newshape, order=None): + return (a,) + + +# not deprecated --- copy if necessary, view otherwise +@array_function_dispatch(_reshape_dispatcher) +def reshape(a, newshape, order='C'): + """ + Gives a new shape to an array without changing its data. + + Parameters + ---------- + a : array_like + Array to be reshaped. + newshape : int or tuple of ints + The new shape should be compatible with the original shape. If + an integer, then the result will be a 1-D array of that length. + One shape dimension can be -1. In this case, the value is + inferred from the length of the array and remaining dimensions. + order : {'C', 'F', 'A'}, optional + Read the elements of `a` using this index order, and place the + elements into the reshaped array using this index order. 'C' + means to read / write the elements using C-like index order, + with the last axis index changing fastest, back to the first + axis index changing slowest. 'F' means to read / write the + elements using Fortran-like index order, with the first index + changing fastest, and the last index changing slowest. Note that + the 'C' and 'F' options take no account of the memory layout of + the underlying array, and only refer to the order of indexing. + 'A' means to read / write the elements in Fortran-like index + order if `a` is Fortran *contiguous* in memory, C-like order + otherwise. + + Returns + ------- + reshaped_array : ndarray + This will be a new view object if possible; otherwise, it will + be a copy. Note there is no guarantee of the *memory layout* (C- or + Fortran- contiguous) of the returned array. + + See Also + -------- + ndarray.reshape : Equivalent method. + + Notes + ----- + It is not always possible to change the shape of an array without copying + the data. + + The `order` keyword gives the index ordering both for *fetching* the values + from `a`, and then *placing* the values into the output array. + For example, let's say you have an array: + + >>> a = np.arange(6).reshape((3, 2)) + >>> a + array([[0, 1], + [2, 3], + [4, 5]]) + + You can think of reshaping as first raveling the array (using the given + index order), then inserting the elements from the raveled array into the + new array using the same kind of index ordering as was used for the + raveling. + + >>> np.reshape(a, (2, 3)) # C-like index ordering + array([[0, 1, 2], + [3, 4, 5]]) + >>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape + array([[0, 1, 2], + [3, 4, 5]]) + >>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering + array([[0, 4, 3], + [2, 1, 5]]) + >>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F') + array([[0, 4, 3], + [2, 1, 5]]) + + Examples + -------- + >>> a = np.array([[1,2,3], [4,5,6]]) + >>> np.reshape(a, 6) + array([1, 2, 3, 4, 5, 6]) + >>> np.reshape(a, 6, order='F') + array([1, 4, 2, 5, 3, 6]) + + >>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2 + array([[1, 2], + [3, 4], + [5, 6]]) + """ + return _wrapfunc(a, 'reshape', newshape, order=order) + + +def _choose_dispatcher(a, choices, out=None, mode=None): + yield a + yield from choices + yield out + + +@array_function_dispatch(_choose_dispatcher) +def choose(a, choices, out=None, mode='raise'): + """ + Construct an array from an index array and a list of arrays to choose from. + + First of all, if confused or uncertain, definitely look at the Examples - + in its full generality, this function is less simple than it might + seem from the following code description (below ndi = + `numpy.lib.index_tricks`): + + ``np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])``. + + But this omits some subtleties. Here is a fully general summary: + + Given an "index" array (`a`) of integers and a sequence of ``n`` arrays + (`choices`), `a` and each choice array are first broadcast, as necessary, + to arrays of a common shape; calling these *Ba* and *Bchoices[i], i = + 0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape`` + for each ``i``. Then, a new array with shape ``Ba.shape`` is created as + follows: + + * if ``mode='raise'`` (the default), then, first of all, each element of + ``a`` (and thus ``Ba``) must be in the range ``[0, n-1]``; now, suppose + that ``i`` (in that range) is the value at the ``(j0, j1, ..., jm)`` + position in ``Ba`` - then the value at the same position in the new array + is the value in ``Bchoices[i]`` at that same position; + + * if ``mode='wrap'``, values in `a` (and thus `Ba`) may be any (signed) + integer; modular arithmetic is used to map integers outside the range + `[0, n-1]` back into that range; and then the new array is constructed + as above; + + * if ``mode='clip'``, values in `a` (and thus ``Ba``) may be any (signed) + integer; negative integers are mapped to 0; values greater than ``n-1`` + are mapped to ``n-1``; and then the new array is constructed as above. + + Parameters + ---------- + a : int array + This array must contain integers in ``[0, n-1]``, where ``n`` is the + number of choices, unless ``mode=wrap`` or ``mode=clip``, in which + cases any integers are permissible. + choices : sequence of arrays + Choice arrays. `a` and all of the choices must be broadcastable to the + same shape. If `choices` is itself an array (not recommended), then + its outermost dimension (i.e., the one corresponding to + ``choices.shape[0]``) is taken as defining the "sequence". + out : array, optional + If provided, the result will be inserted into this array. It should + be of the appropriate shape and dtype. Note that `out` is always + buffered if ``mode='raise'``; use other modes for better performance. + mode : {'raise' (default), 'wrap', 'clip'}, optional + Specifies how indices outside ``[0, n-1]`` will be treated: + + * 'raise' : an exception is raised + * 'wrap' : value becomes value mod ``n`` + * 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1 + + Returns + ------- + merged_array : array + The merged result. + + Raises + ------ + ValueError: shape mismatch + If `a` and each choice array are not all broadcastable to the same + shape. + + See Also + -------- + ndarray.choose : equivalent method + numpy.take_along_axis : Preferable if `choices` is an array + + Notes + ----- + To reduce the chance of misinterpretation, even though the following + "abuse" is nominally supported, `choices` should neither be, nor be + thought of as, a single array, i.e., the outermost sequence-like container + should be either a list or a tuple. + + Examples + -------- + + >>> choices = [[0, 1, 2, 3], [10, 11, 12, 13], + ... [20, 21, 22, 23], [30, 31, 32, 33]] + >>> np.choose([2, 3, 1, 0], choices + ... # the first element of the result will be the first element of the + ... # third (2+1) "array" in choices, namely, 20; the second element + ... # will be the second element of the fourth (3+1) choice array, i.e., + ... # 31, etc. + ... ) + array([20, 31, 12, 3]) + >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1) + array([20, 31, 12, 3]) + >>> # because there are 4 choice arrays + >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4) + array([20, 1, 12, 3]) + >>> # i.e., 0 + + A couple examples illustrating how choose broadcasts: + + >>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]] + >>> choices = [-10, 10] + >>> np.choose(a, choices) + array([[ 10, -10, 10], + [-10, 10, -10], + [ 10, -10, 10]]) + + >>> # With thanks to Anne Archibald + >>> a = np.array([0, 1]).reshape((2,1,1)) + >>> c1 = np.array([1, 2, 3]).reshape((1,3,1)) + >>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5)) + >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2 + array([[[ 1, 1, 1, 1, 1], + [ 2, 2, 2, 2, 2], + [ 3, 3, 3, 3, 3]], + [[-1, -2, -3, -4, -5], + [-1, -2, -3, -4, -5], + [-1, -2, -3, -4, -5]]]) + + """ + return _wrapfunc(a, 'choose', choices, out=out, mode=mode) + + +def _repeat_dispatcher(a, repeats, axis=None): + return (a,) + + +@array_function_dispatch(_repeat_dispatcher) +def repeat(a, repeats, axis=None): + """ + Repeat each element of an array after themselves + + Parameters + ---------- + a : array_like + Input array. + repeats : int or array of ints + The number of repetitions for each element. `repeats` is broadcasted + to fit the shape of the given axis. + axis : int, optional + The axis along which to repeat values. By default, use the + flattened input array, and return a flat output array. + + Returns + ------- + repeated_array : ndarray + Output array which has the same shape as `a`, except along + the given axis. + + See Also + -------- + tile : Tile an array. + unique : Find the unique elements of an array. + + Examples + -------- + >>> np.repeat(3, 4) + array([3, 3, 3, 3]) + >>> x = np.array([[1,2],[3,4]]) + >>> np.repeat(x, 2) + array([1, 1, 2, 2, 3, 3, 4, 4]) + >>> np.repeat(x, 3, axis=1) + array([[1, 1, 1, 2, 2, 2], + [3, 3, 3, 4, 4, 4]]) + >>> np.repeat(x, [1, 2], axis=0) + array([[1, 2], + [3, 4], + [3, 4]]) + + """ + return _wrapfunc(a, 'repeat', repeats, axis=axis) + + +def _put_dispatcher(a, ind, v, mode=None): + return (a, ind, v) + + +@array_function_dispatch(_put_dispatcher) +def put(a, ind, v, mode='raise'): + """ + Replaces specified elements of an array with given values. + + The indexing works on the flattened target array. `put` is roughly + equivalent to: + + :: + + a.flat[ind] = v + + Parameters + ---------- + a : ndarray + Target array. + ind : array_like + Target indices, interpreted as integers. + v : array_like + Values to place in `a` at target indices. If `v` is shorter than + `ind` it will be repeated as necessary. + mode : {'raise', 'wrap', 'clip'}, optional + Specifies how out-of-bounds indices will behave. + + * 'raise' -- raise an error (default) + * 'wrap' -- wrap around + * 'clip' -- clip to the range + + 'clip' mode means that all indices that are too large are replaced + by the index that addresses the last element along that axis. Note + that this disables indexing with negative numbers. In 'raise' mode, + if an exception occurs the target array may still be modified. + + See Also + -------- + putmask, place + put_along_axis : Put elements by matching the array and the index arrays + + Examples + -------- + >>> a = np.arange(5) + >>> np.put(a, [0, 2], [-44, -55]) + >>> a + array([-44, 1, -55, 3, 4]) + + >>> a = np.arange(5) + >>> np.put(a, 22, -5, mode='clip') + >>> a + array([ 0, 1, 2, 3, -5]) + + """ + try: + put = a.put + except AttributeError as e: + raise TypeError("argument 1 must be numpy.ndarray, " + "not {name}".format(name=type(a).__name__)) from e + + return put(ind, v, mode=mode) + + +def _swapaxes_dispatcher(a, axis1, axis2): + return (a,) + + +@array_function_dispatch(_swapaxes_dispatcher) +def swapaxes(a, axis1, axis2): + """ + Interchange two axes of an array. + + Parameters + ---------- + a : array_like + Input array. + axis1 : int + First axis. + axis2 : int + Second axis. + + Returns + ------- + a_swapped : ndarray + For NumPy >= 1.10.0, if `a` is an ndarray, then a view of `a` is + returned; otherwise a new array is created. For earlier NumPy + versions a view of `a` is returned only if the order of the + axes is changed, otherwise the input array is returned. + + Examples + -------- + >>> x = np.array([[1,2,3]]) + >>> np.swapaxes(x,0,1) + array([[1], + [2], + [3]]) + + >>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]]) + >>> x + array([[[0, 1], + [2, 3]], + [[4, 5], + [6, 7]]]) + + >>> np.swapaxes(x,0,2) + array([[[0, 4], + [2, 6]], + [[1, 5], + [3, 7]]]) + + """ + return _wrapfunc(a, 'swapaxes', axis1, axis2) + + +def _transpose_dispatcher(a, axes=None): + return (a,) + + +@array_function_dispatch(_transpose_dispatcher) +def transpose(a, axes=None): + """ + Returns an array with axes transposed. + + For a 1-D array, this returns an unchanged view of the original array, as a + transposed vector is simply the same vector. + To convert a 1-D array into a 2-D column vector, an additional dimension + must be added, e.g., ``np.atleast2d(a).T`` achieves this, as does + ``a[:, np.newaxis]``. + For a 2-D array, this is the standard matrix transpose. + For an n-D array, if axes are given, their order indicates how the + axes are permuted (see Examples). If axes are not provided, then + ``transpose(a).shape == a.shape[::-1]``. + + Parameters + ---------- + a : array_like + Input array. + axes : tuple or list of ints, optional + If specified, it must be a tuple or list which contains a permutation + of [0,1,...,N-1] where N is the number of axes of `a`. The `i`'th axis + of the returned array will correspond to the axis numbered ``axes[i]`` + of the input. If not specified, defaults to ``range(a.ndim)[::-1]``, + which reverses the order of the axes. + + Returns + ------- + p : ndarray + `a` with its axes permuted. A view is returned whenever possible. + + See Also + -------- + ndarray.transpose : Equivalent method. + moveaxis : Move axes of an array to new positions. + argsort : Return the indices that would sort an array. + + Notes + ----- + Use ``transpose(a, argsort(axes))`` to invert the transposition of tensors + when using the `axes` keyword argument. + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4]]) + >>> a + array([[1, 2], + [3, 4]]) + >>> np.transpose(a) + array([[1, 3], + [2, 4]]) + + >>> a = np.array([1, 2, 3, 4]) + >>> a + array([1, 2, 3, 4]) + >>> np.transpose(a) + array([1, 2, 3, 4]) + + >>> a = np.ones((1, 2, 3)) + >>> np.transpose(a, (1, 0, 2)).shape + (2, 1, 3) + + >>> a = np.ones((2, 3, 4, 5)) + >>> np.transpose(a).shape + (5, 4, 3, 2) + + """ + return _wrapfunc(a, 'transpose', axes) + + +def _partition_dispatcher(a, kth, axis=None, kind=None, order=None): + return (a,) + + +@array_function_dispatch(_partition_dispatcher) +def partition(a, kth, axis=-1, kind='introselect', order=None): + """ + Return a partitioned copy of an array. + + Creates a copy of the array with its elements rearranged in such a + way that the value of the element in k-th position is in the position + the value would be in a sorted array. In the partitioned array, all + elements before the k-th element are less than or equal to that + element, and all the elements after the k-th element are greater than + or equal to that element. The ordering of the elements in the two + partitions is undefined. + + .. versionadded:: 1.8.0 + + Parameters + ---------- + a : array_like + Array to be sorted. + kth : int or sequence of ints + Element index to partition by. The k-th value of the element + will be in its final sorted position and all smaller elements + will be moved before it and all equal or greater elements behind + it. The order of all elements in the partitions is undefined. If + provided with a sequence of k-th it will partition all elements + indexed by k-th of them into their sorted position at once. + + .. deprecated:: 1.22.0 + Passing booleans as index is deprecated. + axis : int or None, optional + Axis along which to sort. If None, the array is flattened before + sorting. The default is -1, which sorts along the last axis. + kind : {'introselect'}, optional + Selection algorithm. Default is 'introselect'. + order : str or list of str, optional + When `a` is an array with fields defined, this argument + specifies which fields to compare first, second, etc. A single + field can be specified as a string. Not all fields need be + specified, but unspecified fields will still be used, in the + order in which they come up in the dtype, to break ties. + + Returns + ------- + partitioned_array : ndarray + Array of the same type and shape as `a`. + + See Also + -------- + ndarray.partition : Method to sort an array in-place. + argpartition : Indirect partition. + sort : Full sorting + + Notes + ----- + The various selection algorithms are characterized by their average + speed, worst case performance, work space size, and whether they are + stable. A stable sort keeps items with the same key in the same + relative order. The available algorithms have the following + properties: + + ================= ======= ============= ============ ======= + kind speed worst case work space stable + ================= ======= ============= ============ ======= + 'introselect' 1 O(n) 0 no + ================= ======= ============= ============ ======= + + All the partition algorithms make temporary copies of the data when + partitioning along any but the last axis. Consequently, + partitioning along the last axis is faster and uses less space than + partitioning along any other axis. + + The sort order for complex numbers is lexicographic. If both the + real and imaginary parts are non-nan then the order is determined by + the real parts except when they are equal, in which case the order + is determined by the imaginary parts. + + Examples + -------- + >>> a = np.array([7, 1, 7, 7, 1, 5, 7, 2, 3, 2, 6, 2, 3, 0]) + >>> p = np.partition(a, 4) + >>> p + array([0, 1, 2, 1, 2, 5, 2, 3, 3, 6, 7, 7, 7, 7]) + + ``p[4]`` is 2; all elements in ``p[:4]`` are less than or equal + to ``p[4]``, and all elements in ``p[5:]`` are greater than or + equal to ``p[4]``. The partition is:: + + [0, 1, 2, 1], [2], [5, 2, 3, 3, 6, 7, 7, 7, 7] + + The next example shows the use of multiple values passed to `kth`. + + >>> p2 = np.partition(a, (4, 8)) + >>> p2 + array([0, 1, 2, 1, 2, 3, 3, 2, 5, 6, 7, 7, 7, 7]) + + ``p2[4]`` is 2 and ``p2[8]`` is 5. All elements in ``p2[:4]`` + are less than or equal to ``p2[4]``, all elements in ``p2[5:8]`` + are greater than or equal to ``p2[4]`` and less than or equal to + ``p2[8]``, and all elements in ``p2[9:]`` are greater than or + equal to ``p2[8]``. The partition is:: + + [0, 1, 2, 1], [2], [3, 3, 2], [5], [6, 7, 7, 7, 7] + """ + if axis is None: + # flatten returns (1, N) for np.matrix, so always use the last axis + a = asanyarray(a).flatten() + axis = -1 + else: + a = asanyarray(a).copy(order="K") + a.partition(kth, axis=axis, kind=kind, order=order) + return a + + +def _argpartition_dispatcher(a, kth, axis=None, kind=None, order=None): + return (a,) + + +@array_function_dispatch(_argpartition_dispatcher) +def argpartition(a, kth, axis=-1, kind='introselect', order=None): + """ + Perform an indirect partition along the given axis using the + algorithm specified by the `kind` keyword. It returns an array of + indices of the same shape as `a` that index data along the given + axis in partitioned order. + + .. versionadded:: 1.8.0 + + Parameters + ---------- + a : array_like + Array to sort. + kth : int or sequence of ints + Element index to partition by. The k-th element will be in its + final sorted position and all smaller elements will be moved + before it and all larger elements behind it. The order of all + elements in the partitions is undefined. If provided with a + sequence of k-th it will partition all of them into their sorted + position at once. + + .. deprecated:: 1.22.0 + Passing booleans as index is deprecated. + axis : int or None, optional + Axis along which to sort. The default is -1 (the last axis). If + None, the flattened array is used. + kind : {'introselect'}, optional + Selection algorithm. Default is 'introselect' + order : str or list of str, optional + When `a` is an array with fields defined, this argument + specifies which fields to compare first, second, etc. A single + field can be specified as a string, and not all fields need be + specified, but unspecified fields will still be used, in the + order in which they come up in the dtype, to break ties. + + Returns + ------- + index_array : ndarray, int + Array of indices that partition `a` along the specified axis. + If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`. + More generally, ``np.take_along_axis(a, index_array, axis=axis)`` + always yields the partitioned `a`, irrespective of dimensionality. + + See Also + -------- + partition : Describes partition algorithms used. + ndarray.partition : Inplace partition. + argsort : Full indirect sort. + take_along_axis : Apply ``index_array`` from argpartition + to an array as if by calling partition. + + Notes + ----- + See `partition` for notes on the different selection algorithms. + + Examples + -------- + One dimensional array: + + >>> x = np.array([3, 4, 2, 1]) + >>> x[np.argpartition(x, 3)] + array([2, 1, 3, 4]) + >>> x[np.argpartition(x, (1, 3))] + array([1, 2, 3, 4]) + + >>> x = [3, 4, 2, 1] + >>> np.array(x)[np.argpartition(x, 3)] + array([2, 1, 3, 4]) + + Multi-dimensional array: + + >>> x = np.array([[3, 4, 2], [1, 3, 1]]) + >>> index_array = np.argpartition(x, kth=1, axis=-1) + >>> np.take_along_axis(x, index_array, axis=-1) # same as np.partition(x, kth=1) + array([[2, 3, 4], + [1, 1, 3]]) + + """ + return _wrapfunc(a, 'argpartition', kth, axis=axis, kind=kind, order=order) + + +def _sort_dispatcher(a, axis=None, kind=None, order=None): + return (a,) + + +@array_function_dispatch(_sort_dispatcher) +def sort(a, axis=-1, kind=None, order=None): + """ + Return a sorted copy of an array. + + Parameters + ---------- + a : array_like + Array to be sorted. + axis : int or None, optional + Axis along which to sort. If None, the array is flattened before + sorting. The default is -1, which sorts along the last axis. + kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional + Sorting algorithm. The default is 'quicksort'. Note that both 'stable' + and 'mergesort' use timsort or radix sort under the covers and, in general, + the actual implementation will vary with data type. The 'mergesort' option + is retained for backwards compatibility. + + .. versionchanged:: 1.15.0. + The 'stable' option was added. + + order : str or list of str, optional + When `a` is an array with fields defined, this argument specifies + which fields to compare first, second, etc. A single field can + be specified as a string, and not all fields need be specified, + but unspecified fields will still be used, in the order in which + they come up in the dtype, to break ties. + + Returns + ------- + sorted_array : ndarray + Array of the same type and shape as `a`. + + See Also + -------- + ndarray.sort : Method to sort an array in-place. + argsort : Indirect sort. + lexsort : Indirect stable sort on multiple keys. + searchsorted : Find elements in a sorted array. + partition : Partial sort. + + Notes + ----- + The various sorting algorithms are characterized by their average speed, + worst case performance, work space size, and whether they are stable. A + stable sort keeps items with the same key in the same relative + order. The four algorithms implemented in NumPy have the following + properties: + + =========== ======= ============= ============ ======== + kind speed worst case work space stable + =========== ======= ============= ============ ======== + 'quicksort' 1 O(n^2) 0 no + 'heapsort' 3 O(n*log(n)) 0 no + 'mergesort' 2 O(n*log(n)) ~n/2 yes + 'timsort' 2 O(n*log(n)) ~n/2 yes + =========== ======= ============= ============ ======== + + .. note:: The datatype determines which of 'mergesort' or 'timsort' + is actually used, even if 'mergesort' is specified. User selection + at a finer scale is not currently available. + + All the sort algorithms make temporary copies of the data when + sorting along any but the last axis. Consequently, sorting along + the last axis is faster and uses less space than sorting along + any other axis. + + The sort order for complex numbers is lexicographic. If both the real + and imaginary parts are non-nan then the order is determined by the + real parts except when they are equal, in which case the order is + determined by the imaginary parts. + + Previous to numpy 1.4.0 sorting real and complex arrays containing nan + values led to undefined behaviour. In numpy versions >= 1.4.0 nan + values are sorted to the end. The extended sort order is: + + * Real: [R, nan] + * Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj] + + where R is a non-nan real value. Complex values with the same nan + placements are sorted according to the non-nan part if it exists. + Non-nan values are sorted as before. + + .. versionadded:: 1.12.0 + + quicksort has been changed to `introsort `_. + When sorting does not make enough progress it switches to + `heapsort `_. + This implementation makes quicksort O(n*log(n)) in the worst case. + + 'stable' automatically chooses the best stable sorting algorithm + for the data type being sorted. + It, along with 'mergesort' is currently mapped to + `timsort `_ + or `radix sort `_ + depending on the data type. + API forward compatibility currently limits the + ability to select the implementation and it is hardwired for the different + data types. + + .. versionadded:: 1.17.0 + + Timsort is added for better performance on already or nearly + sorted data. On random data timsort is almost identical to + mergesort. It is now used for stable sort while quicksort is still the + default sort if none is chosen. For timsort details, refer to + `CPython listsort.txt `_. + 'mergesort' and 'stable' are mapped to radix sort for integer data types. Radix sort is an + O(n) sort instead of O(n log n). + + .. versionchanged:: 1.18.0 + + NaT now sorts to the end of arrays for consistency with NaN. + + Examples + -------- + >>> a = np.array([[1,4],[3,1]]) + >>> np.sort(a) # sort along the last axis + array([[1, 4], + [1, 3]]) + >>> np.sort(a, axis=None) # sort the flattened array + array([1, 1, 3, 4]) + >>> np.sort(a, axis=0) # sort along the first axis + array([[1, 1], + [3, 4]]) + + Use the `order` keyword to specify a field to use when sorting a + structured array: + + >>> dtype = [('name', 'S10'), ('height', float), ('age', int)] + >>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38), + ... ('Galahad', 1.7, 38)] + >>> a = np.array(values, dtype=dtype) # create a structured array + >>> np.sort(a, order='height') # doctest: +SKIP + array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41), + ('Lancelot', 1.8999999999999999, 38)], + dtype=[('name', '|S10'), ('height', '>> np.sort(a, order=['age', 'height']) # doctest: +SKIP + array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38), + ('Arthur', 1.8, 41)], + dtype=[('name', '|S10'), ('height', '>> x = np.array([3, 1, 2]) + >>> np.argsort(x) + array([1, 2, 0]) + + Two-dimensional array: + + >>> x = np.array([[0, 3], [2, 2]]) + >>> x + array([[0, 3], + [2, 2]]) + + >>> ind = np.argsort(x, axis=0) # sorts along first axis (down) + >>> ind + array([[0, 1], + [1, 0]]) + >>> np.take_along_axis(x, ind, axis=0) # same as np.sort(x, axis=0) + array([[0, 2], + [2, 3]]) + + >>> ind = np.argsort(x, axis=1) # sorts along last axis (across) + >>> ind + array([[0, 1], + [0, 1]]) + >>> np.take_along_axis(x, ind, axis=1) # same as np.sort(x, axis=1) + array([[0, 3], + [2, 2]]) + + Indices of the sorted elements of a N-dimensional array: + + >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape) + >>> ind + (array([0, 1, 1, 0]), array([0, 0, 1, 1])) + >>> x[ind] # same as np.sort(x, axis=None) + array([0, 2, 2, 3]) + + Sorting with keys: + + >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '>> x + array([(1, 0), (0, 1)], + dtype=[('x', '>> np.argsort(x, order=('x','y')) + array([1, 0]) + + >>> np.argsort(x, order=('y','x')) + array([0, 1]) + + """ + return _wrapfunc(a, 'argsort', axis=axis, kind=kind, order=order) + + +def _argmax_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue): + return (a, out) + + +@array_function_dispatch(_argmax_dispatcher) +def argmax(a, axis=None, out=None, *, keepdims=np._NoValue): + """ + Returns the indices of the maximum values along an axis. + + Parameters + ---------- + a : array_like + Input array. + axis : int, optional + By default, the index is into the flattened array, otherwise + along the specified axis. + out : array, optional + If provided, the result will be inserted into this array. It should + be of the appropriate shape and dtype. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the array. + + .. versionadded:: 1.22.0 + + Returns + ------- + index_array : ndarray of ints + Array of indices into the array. It has the same shape as `a.shape` + with the dimension along `axis` removed. If `keepdims` is set to True, + then the size of `axis` will be 1 with the resulting array having same + shape as `a.shape`. + + See Also + -------- + ndarray.argmax, argmin + amax : The maximum value along a given axis. + unravel_index : Convert a flat index into an index tuple. + take_along_axis : Apply ``np.expand_dims(index_array, axis)`` + from argmax to an array as if by calling max. + + Notes + ----- + In case of multiple occurrences of the maximum values, the indices + corresponding to the first occurrence are returned. + + Examples + -------- + >>> a = np.arange(6).reshape(2,3) + 10 + >>> a + array([[10, 11, 12], + [13, 14, 15]]) + >>> np.argmax(a) + 5 + >>> np.argmax(a, axis=0) + array([1, 1, 1]) + >>> np.argmax(a, axis=1) + array([2, 2]) + + Indexes of the maximal elements of a N-dimensional array: + + >>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape) + >>> ind + (1, 2) + >>> a[ind] + 15 + + >>> b = np.arange(6) + >>> b[1] = 5 + >>> b + array([0, 5, 2, 3, 4, 5]) + >>> np.argmax(b) # Only the first occurrence is returned. + 1 + + >>> x = np.array([[4,2,3], [1,0,3]]) + >>> index_array = np.argmax(x, axis=-1) + >>> # Same as np.amax(x, axis=-1, keepdims=True) + >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1) + array([[4], + [3]]) + >>> # Same as np.amax(x, axis=-1) + >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1) + array([4, 3]) + + Setting `keepdims` to `True`, + + >>> x = np.arange(24).reshape((2, 3, 4)) + >>> res = np.argmax(x, axis=1, keepdims=True) + >>> res.shape + (2, 1, 4) + """ + kwds = {'keepdims': keepdims} if keepdims is not np._NoValue else {} + return _wrapfunc(a, 'argmax', axis=axis, out=out, **kwds) + + +def _argmin_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue): + return (a, out) + + +@array_function_dispatch(_argmin_dispatcher) +def argmin(a, axis=None, out=None, *, keepdims=np._NoValue): + """ + Returns the indices of the minimum values along an axis. + + Parameters + ---------- + a : array_like + Input array. + axis : int, optional + By default, the index is into the flattened array, otherwise + along the specified axis. + out : array, optional + If provided, the result will be inserted into this array. It should + be of the appropriate shape and dtype. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the array. + + .. versionadded:: 1.22.0 + + Returns + ------- + index_array : ndarray of ints + Array of indices into the array. It has the same shape as `a.shape` + with the dimension along `axis` removed. If `keepdims` is set to True, + then the size of `axis` will be 1 with the resulting array having same + shape as `a.shape`. + + See Also + -------- + ndarray.argmin, argmax + amin : The minimum value along a given axis. + unravel_index : Convert a flat index into an index tuple. + take_along_axis : Apply ``np.expand_dims(index_array, axis)`` + from argmin to an array as if by calling min. + + Notes + ----- + In case of multiple occurrences of the minimum values, the indices + corresponding to the first occurrence are returned. + + Examples + -------- + >>> a = np.arange(6).reshape(2,3) + 10 + >>> a + array([[10, 11, 12], + [13, 14, 15]]) + >>> np.argmin(a) + 0 + >>> np.argmin(a, axis=0) + array([0, 0, 0]) + >>> np.argmin(a, axis=1) + array([0, 0]) + + Indices of the minimum elements of a N-dimensional array: + + >>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape) + >>> ind + (0, 0) + >>> a[ind] + 10 + + >>> b = np.arange(6) + 10 + >>> b[4] = 10 + >>> b + array([10, 11, 12, 13, 10, 15]) + >>> np.argmin(b) # Only the first occurrence is returned. + 0 + + >>> x = np.array([[4,2,3], [1,0,3]]) + >>> index_array = np.argmin(x, axis=-1) + >>> # Same as np.amin(x, axis=-1, keepdims=True) + >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1) + array([[2], + [0]]) + >>> # Same as np.amax(x, axis=-1) + >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1) + array([2, 0]) + + Setting `keepdims` to `True`, + + >>> x = np.arange(24).reshape((2, 3, 4)) + >>> res = np.argmin(x, axis=1, keepdims=True) + >>> res.shape + (2, 1, 4) + """ + kwds = {'keepdims': keepdims} if keepdims is not np._NoValue else {} + return _wrapfunc(a, 'argmin', axis=axis, out=out, **kwds) + + +def _searchsorted_dispatcher(a, v, side=None, sorter=None): + return (a, v, sorter) + + +@array_function_dispatch(_searchsorted_dispatcher) +def searchsorted(a, v, side='left', sorter=None): + """ + Find indices where elements should be inserted to maintain order. + + Find the indices into a sorted array `a` such that, if the + corresponding elements in `v` were inserted before the indices, the + order of `a` would be preserved. + + Assuming that `a` is sorted: + + ====== ============================ + `side` returned index `i` satisfies + ====== ============================ + left ``a[i-1] < v <= a[i]`` + right ``a[i-1] <= v < a[i]`` + ====== ============================ + + Parameters + ---------- + a : 1-D array_like + Input array. If `sorter` is None, then it must be sorted in + ascending order, otherwise `sorter` must be an array of indices + that sort it. + v : array_like + Values to insert into `a`. + side : {'left', 'right'}, optional + If 'left', the index of the first suitable location found is given. + If 'right', return the last such index. If there is no suitable + index, return either 0 or N (where N is the length of `a`). + sorter : 1-D array_like, optional + Optional array of integer indices that sort array a into ascending + order. They are typically the result of argsort. + + .. versionadded:: 1.7.0 + + Returns + ------- + indices : int or array of ints + Array of insertion points with the same shape as `v`, + or an integer if `v` is a scalar. + + See Also + -------- + sort : Return a sorted copy of an array. + histogram : Produce histogram from 1-D data. + + Notes + ----- + Binary search is used to find the required insertion points. + + As of NumPy 1.4.0 `searchsorted` works with real/complex arrays containing + `nan` values. The enhanced sort order is documented in `sort`. + + This function uses the same algorithm as the builtin python `bisect.bisect_left` + (``side='left'``) and `bisect.bisect_right` (``side='right'``) functions, + which is also vectorized in the `v` argument. + + Examples + -------- + >>> np.searchsorted([1,2,3,4,5], 3) + 2 + >>> np.searchsorted([1,2,3,4,5], 3, side='right') + 3 + >>> np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3]) + array([0, 5, 1, 2]) + + """ + return _wrapfunc(a, 'searchsorted', v, side=side, sorter=sorter) + + +def _resize_dispatcher(a, new_shape): + return (a,) + + +@array_function_dispatch(_resize_dispatcher) +def resize(a, new_shape): + """ + Return a new array with the specified shape. + + If the new array is larger than the original array, then the new + array is filled with repeated copies of `a`. Note that this behavior + is different from a.resize(new_shape) which fills with zeros instead + of repeated copies of `a`. + + Parameters + ---------- + a : array_like + Array to be resized. + + new_shape : int or tuple of int + Shape of resized array. + + Returns + ------- + reshaped_array : ndarray + The new array is formed from the data in the old array, repeated + if necessary to fill out the required number of elements. The + data are repeated iterating over the array in C-order. + + See Also + -------- + numpy.reshape : Reshape an array without changing the total size. + numpy.pad : Enlarge and pad an array. + numpy.repeat : Repeat elements of an array. + ndarray.resize : resize an array in-place. + + Notes + ----- + When the total size of the array does not change `~numpy.reshape` should + be used. In most other cases either indexing (to reduce the size) + or padding (to increase the size) may be a more appropriate solution. + + Warning: This functionality does **not** consider axes separately, + i.e. it does not apply interpolation/extrapolation. + It fills the return array with the required number of elements, iterating + over `a` in C-order, disregarding axes (and cycling back from the start if + the new shape is larger). This functionality is therefore not suitable to + resize images, or data where each axis represents a separate and distinct + entity. + + Examples + -------- + >>> a=np.array([[0,1],[2,3]]) + >>> np.resize(a,(2,3)) + array([[0, 1, 2], + [3, 0, 1]]) + >>> np.resize(a,(1,4)) + array([[0, 1, 2, 3]]) + >>> np.resize(a,(2,4)) + array([[0, 1, 2, 3], + [0, 1, 2, 3]]) + + """ + if isinstance(new_shape, (int, nt.integer)): + new_shape = (new_shape,) + + a = ravel(a) + + new_size = 1 + for dim_length in new_shape: + new_size *= dim_length + if dim_length < 0: + raise ValueError('all elements of `new_shape` must be non-negative') + + if a.size == 0 or new_size == 0: + # First case must zero fill. The second would have repeats == 0. + return np.zeros_like(a, shape=new_shape) + + repeats = -(-new_size // a.size) # ceil division + a = concatenate((a,) * repeats)[:new_size] + + return reshape(a, new_shape) + + +def _squeeze_dispatcher(a, axis=None): + return (a,) + + +@array_function_dispatch(_squeeze_dispatcher) +def squeeze(a, axis=None): + """ + Remove axes of length one from `a`. + + Parameters + ---------- + a : array_like + Input data. + axis : None or int or tuple of ints, optional + .. versionadded:: 1.7.0 + + Selects a subset of the entries of length one in the + shape. If an axis is selected with shape entry greater than + one, an error is raised. + + Returns + ------- + squeezed : ndarray + The input array, but with all or a subset of the + dimensions of length 1 removed. This is always `a` itself + or a view into `a`. Note that if all axes are squeezed, + the result is a 0d array and not a scalar. + + Raises + ------ + ValueError + If `axis` is not None, and an axis being squeezed is not of length 1 + + See Also + -------- + expand_dims : The inverse operation, adding entries of length one + reshape : Insert, remove, and combine dimensions, and resize existing ones + + Examples + -------- + >>> x = np.array([[[0], [1], [2]]]) + >>> x.shape + (1, 3, 1) + >>> np.squeeze(x).shape + (3,) + >>> np.squeeze(x, axis=0).shape + (3, 1) + >>> np.squeeze(x, axis=1).shape + Traceback (most recent call last): + ... + ValueError: cannot select an axis to squeeze out which has size not equal to one + >>> np.squeeze(x, axis=2).shape + (1, 3) + >>> x = np.array([[1234]]) + >>> x.shape + (1, 1) + >>> np.squeeze(x) + array(1234) # 0d array + >>> np.squeeze(x).shape + () + >>> np.squeeze(x)[()] + 1234 + + """ + try: + squeeze = a.squeeze + except AttributeError: + return _wrapit(a, 'squeeze', axis=axis) + if axis is None: + return squeeze() + else: + return squeeze(axis=axis) + + +def _diagonal_dispatcher(a, offset=None, axis1=None, axis2=None): + return (a,) + + +@array_function_dispatch(_diagonal_dispatcher) +def diagonal(a, offset=0, axis1=0, axis2=1): + """ + Return specified diagonals. + + If `a` is 2-D, returns the diagonal of `a` with the given offset, + i.e., the collection of elements of the form ``a[i, i+offset]``. If + `a` has more than two dimensions, then the axes specified by `axis1` + and `axis2` are used to determine the 2-D sub-array whose diagonal is + returned. The shape of the resulting array can be determined by + removing `axis1` and `axis2` and appending an index to the right equal + to the size of the resulting diagonals. + + In versions of NumPy prior to 1.7, this function always returned a new, + independent array containing a copy of the values in the diagonal. + + In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal, + but depending on this fact is deprecated. Writing to the resulting + array continues to work as it used to, but a FutureWarning is issued. + + Starting in NumPy 1.9 it returns a read-only view on the original array. + Attempting to write to the resulting array will produce an error. + + In some future release, it will return a read/write view and writing to + the returned array will alter your original array. The returned array + will have the same type as the input array. + + If you don't write to the array returned by this function, then you can + just ignore all of the above. + + If you depend on the current behavior, then we suggest copying the + returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead + of just ``np.diagonal(a)``. This will work with both past and future + versions of NumPy. + + Parameters + ---------- + a : array_like + Array from which the diagonals are taken. + offset : int, optional + Offset of the diagonal from the main diagonal. Can be positive or + negative. Defaults to main diagonal (0). + axis1 : int, optional + Axis to be used as the first axis of the 2-D sub-arrays from which + the diagonals should be taken. Defaults to first axis (0). + axis2 : int, optional + Axis to be used as the second axis of the 2-D sub-arrays from + which the diagonals should be taken. Defaults to second axis (1). + + Returns + ------- + array_of_diagonals : ndarray + If `a` is 2-D, then a 1-D array containing the diagonal and of the + same type as `a` is returned unless `a` is a `matrix`, in which case + a 1-D array rather than a (2-D) `matrix` is returned in order to + maintain backward compatibility. + + If ``a.ndim > 2``, then the dimensions specified by `axis1` and `axis2` + are removed, and a new axis inserted at the end corresponding to the + diagonal. + + Raises + ------ + ValueError + If the dimension of `a` is less than 2. + + See Also + -------- + diag : MATLAB work-a-like for 1-D and 2-D arrays. + diagflat : Create diagonal arrays. + trace : Sum along diagonals. + + Examples + -------- + >>> a = np.arange(4).reshape(2,2) + >>> a + array([[0, 1], + [2, 3]]) + >>> a.diagonal() + array([0, 3]) + >>> a.diagonal(1) + array([1]) + + A 3-D example: + + >>> a = np.arange(8).reshape(2,2,2); a + array([[[0, 1], + [2, 3]], + [[4, 5], + [6, 7]]]) + >>> a.diagonal(0, # Main diagonals of two arrays created by skipping + ... 0, # across the outer(left)-most axis last and + ... 1) # the "middle" (row) axis first. + array([[0, 6], + [1, 7]]) + + The sub-arrays whose main diagonals we just obtained; note that each + corresponds to fixing the right-most (column) axis, and that the + diagonals are "packed" in rows. + + >>> a[:,:,0] # main diagonal is [0 6] + array([[0, 2], + [4, 6]]) + >>> a[:,:,1] # main diagonal is [1 7] + array([[1, 3], + [5, 7]]) + + The anti-diagonal can be obtained by reversing the order of elements + using either `numpy.flipud` or `numpy.fliplr`. + + >>> a = np.arange(9).reshape(3, 3) + >>> a + array([[0, 1, 2], + [3, 4, 5], + [6, 7, 8]]) + >>> np.fliplr(a).diagonal() # Horizontal flip + array([2, 4, 6]) + >>> np.flipud(a).diagonal() # Vertical flip + array([6, 4, 2]) + + Note that the order in which the diagonal is retrieved varies depending + on the flip function. + """ + if isinstance(a, np.matrix): + # Make diagonal of matrix 1-D to preserve backward compatibility. + return asarray(a).diagonal(offset=offset, axis1=axis1, axis2=axis2) + else: + return asanyarray(a).diagonal(offset=offset, axis1=axis1, axis2=axis2) + + +def _trace_dispatcher( + a, offset=None, axis1=None, axis2=None, dtype=None, out=None): + return (a, out) + + +@array_function_dispatch(_trace_dispatcher) +def trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None): + """ + Return the sum along diagonals of the array. + + If `a` is 2-D, the sum along its diagonal with the given offset + is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i. + + If `a` has more than two dimensions, then the axes specified by axis1 and + axis2 are used to determine the 2-D sub-arrays whose traces are returned. + The shape of the resulting array is the same as that of `a` with `axis1` + and `axis2` removed. + + Parameters + ---------- + a : array_like + Input array, from which the diagonals are taken. + offset : int, optional + Offset of the diagonal from the main diagonal. Can be both positive + and negative. Defaults to 0. + axis1, axis2 : int, optional + Axes to be used as the first and second axis of the 2-D sub-arrays + from which the diagonals should be taken. Defaults are the first two + axes of `a`. + dtype : dtype, optional + Determines the data-type of the returned array and of the accumulator + where the elements are summed. If dtype has the value None and `a` is + of integer type of precision less than the default integer + precision, then the default integer precision is used. Otherwise, + the precision is the same as that of `a`. + out : ndarray, optional + Array into which the output is placed. Its type is preserved and + it must be of the right shape to hold the output. + + Returns + ------- + sum_along_diagonals : ndarray + If `a` is 2-D, the sum along the diagonal is returned. If `a` has + larger dimensions, then an array of sums along diagonals is returned. + + See Also + -------- + diag, diagonal, diagflat + + Examples + -------- + >>> np.trace(np.eye(3)) + 3.0 + >>> a = np.arange(8).reshape((2,2,2)) + >>> np.trace(a) + array([6, 8]) + + >>> a = np.arange(24).reshape((2,2,2,3)) + >>> np.trace(a).shape + (2, 3) + + """ + if isinstance(a, np.matrix): + # Get trace of matrix via an array to preserve backward compatibility. + return asarray(a).trace(offset=offset, axis1=axis1, axis2=axis2, dtype=dtype, out=out) + else: + return asanyarray(a).trace(offset=offset, axis1=axis1, axis2=axis2, dtype=dtype, out=out) + + +def _ravel_dispatcher(a, order=None): + return (a,) + + +@array_function_dispatch(_ravel_dispatcher) +def ravel(a, order='C'): + """Return a contiguous flattened array. + + A 1-D array, containing the elements of the input, is returned. A copy is + made only if needed. + + As of NumPy 1.10, the returned array will have the same type as the input + array. (for example, a masked array will be returned for a masked array + input) + + Parameters + ---------- + a : array_like + Input array. The elements in `a` are read in the order specified by + `order`, and packed as a 1-D array. + order : {'C','F', 'A', 'K'}, optional + + The elements of `a` are read using this index order. 'C' means + to index the elements in row-major, C-style order, + with the last axis index changing fastest, back to the first + axis index changing slowest. 'F' means to index the elements + in column-major, Fortran-style order, with the + first index changing fastest, and the last index changing + slowest. Note that the 'C' and 'F' options take no account of + the memory layout of the underlying array, and only refer to + the order of axis indexing. 'A' means to read the elements in + Fortran-like index order if `a` is Fortran *contiguous* in + memory, C-like order otherwise. 'K' means to read the + elements in the order they occur in memory, except for + reversing the data when strides are negative. By default, 'C' + index order is used. + + Returns + ------- + y : array_like + y is a contiguous 1-D array of the same subtype as `a`, + with shape ``(a.size,)``. + Note that matrices are special cased for backward compatibility, + if `a` is a matrix, then y is a 1-D ndarray. + + See Also + -------- + ndarray.flat : 1-D iterator over an array. + ndarray.flatten : 1-D array copy of the elements of an array + in row-major order. + ndarray.reshape : Change the shape of an array without changing its data. + + Notes + ----- + In row-major, C-style order, in two dimensions, the row index + varies the slowest, and the column index the quickest. This can + be generalized to multiple dimensions, where row-major order + implies that the index along the first axis varies slowest, and + the index along the last quickest. The opposite holds for + column-major, Fortran-style index ordering. + + When a view is desired in as many cases as possible, ``arr.reshape(-1)`` + may be preferable. However, ``ravel`` supports ``K`` in the optional + ``order`` argument while ``reshape`` does not. + + Examples + -------- + It is equivalent to ``reshape(-1, order=order)``. + + >>> x = np.array([[1, 2, 3], [4, 5, 6]]) + >>> np.ravel(x) + array([1, 2, 3, 4, 5, 6]) + + >>> x.reshape(-1) + array([1, 2, 3, 4, 5, 6]) + + >>> np.ravel(x, order='F') + array([1, 4, 2, 5, 3, 6]) + + When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering: + + >>> np.ravel(x.T) + array([1, 4, 2, 5, 3, 6]) + >>> np.ravel(x.T, order='A') + array([1, 2, 3, 4, 5, 6]) + + When ``order`` is 'K', it will preserve orderings that are neither 'C' + nor 'F', but won't reverse axes: + + >>> a = np.arange(3)[::-1]; a + array([2, 1, 0]) + >>> a.ravel(order='C') + array([2, 1, 0]) + >>> a.ravel(order='K') + array([2, 1, 0]) + + >>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a + array([[[ 0, 2, 4], + [ 1, 3, 5]], + [[ 6, 8, 10], + [ 7, 9, 11]]]) + >>> a.ravel(order='C') + array([ 0, 2, 4, 1, 3, 5, 6, 8, 10, 7, 9, 11]) + >>> a.ravel(order='K') + array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) + + """ + if isinstance(a, np.matrix): + return asarray(a).ravel(order=order) + else: + return asanyarray(a).ravel(order=order) + + +def _nonzero_dispatcher(a): + return (a,) + + +@array_function_dispatch(_nonzero_dispatcher) +def nonzero(a): + """ + Return the indices of the elements that are non-zero. + + Returns a tuple of arrays, one for each dimension of `a`, + containing the indices of the non-zero elements in that + dimension. The values in `a` are always tested and returned in + row-major, C-style order. + + To group the indices by element, rather than dimension, use `argwhere`, + which returns a row for each non-zero element. + + .. note:: + + When called on a zero-d array or scalar, ``nonzero(a)`` is treated + as ``nonzero(atleast_1d(a))``. + + .. deprecated:: 1.17.0 + + Use `atleast_1d` explicitly if this behavior is deliberate. + + Parameters + ---------- + a : array_like + Input array. + + Returns + ------- + tuple_of_arrays : tuple + Indices of elements that are non-zero. + + See Also + -------- + flatnonzero : + Return indices that are non-zero in the flattened version of the input + array. + ndarray.nonzero : + Equivalent ndarray method. + count_nonzero : + Counts the number of non-zero elements in the input array. + + Notes + ----- + While the nonzero values can be obtained with ``a[nonzero(a)]``, it is + recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which + will correctly handle 0-d arrays. + + Examples + -------- + >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]]) + >>> x + array([[3, 0, 0], + [0, 4, 0], + [5, 6, 0]]) + >>> np.nonzero(x) + (array([0, 1, 2, 2]), array([0, 1, 0, 1])) + + >>> x[np.nonzero(x)] + array([3, 4, 5, 6]) + >>> np.transpose(np.nonzero(x)) + array([[0, 0], + [1, 1], + [2, 0], + [2, 1]]) + + A common use for ``nonzero`` is to find the indices of an array, where + a condition is True. Given an array `a`, the condition `a` > 3 is a + boolean array and since False is interpreted as 0, np.nonzero(a > 3) + yields the indices of the `a` where the condition is true. + + >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> a > 3 + array([[False, False, False], + [ True, True, True], + [ True, True, True]]) + >>> np.nonzero(a > 3) + (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2])) + + Using this result to index `a` is equivalent to using the mask directly: + + >>> a[np.nonzero(a > 3)] + array([4, 5, 6, 7, 8, 9]) + >>> a[a > 3] # prefer this spelling + array([4, 5, 6, 7, 8, 9]) + + ``nonzero`` can also be called as a method of the array. + + >>> (a > 3).nonzero() + (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2])) + + """ + return _wrapfunc(a, 'nonzero') + + +def _shape_dispatcher(a): + return (a,) + + +@array_function_dispatch(_shape_dispatcher) +def shape(a): + """ + Return the shape of an array. + + Parameters + ---------- + a : array_like + Input array. + + Returns + ------- + shape : tuple of ints + The elements of the shape tuple give the lengths of the + corresponding array dimensions. + + See Also + -------- + len : ``len(a)`` is equivalent to ``np.shape(a)[0]`` for N-D arrays with + ``N>=1``. + ndarray.shape : Equivalent array method. + + Examples + -------- + >>> np.shape(np.eye(3)) + (3, 3) + >>> np.shape([[1, 3]]) + (1, 2) + >>> np.shape([0]) + (1,) + >>> np.shape(0) + () + + >>> a = np.array([(1, 2), (3, 4), (5, 6)], + ... dtype=[('x', 'i4'), ('y', 'i4')]) + >>> np.shape(a) + (3,) + >>> a.shape + (3,) + + """ + try: + result = a.shape + except AttributeError: + result = asarray(a).shape + return result + + +def _compress_dispatcher(condition, a, axis=None, out=None): + return (condition, a, out) + + +@array_function_dispatch(_compress_dispatcher) +def compress(condition, a, axis=None, out=None): + """ + Return selected slices of an array along given axis. + + When working along a given axis, a slice along that axis is returned in + `output` for each index where `condition` evaluates to True. When + working on a 1-D array, `compress` is equivalent to `extract`. + + Parameters + ---------- + condition : 1-D array of bools + Array that selects which entries to return. If len(condition) + is less than the size of `a` along the given axis, then output is + truncated to the length of the condition array. + a : array_like + Array from which to extract a part. + axis : int, optional + Axis along which to take slices. If None (default), work on the + flattened array. + out : ndarray, optional + Output array. Its type is preserved and it must be of the right + shape to hold the output. + + Returns + ------- + compressed_array : ndarray + A copy of `a` without the slices along axis for which `condition` + is false. + + See Also + -------- + take, choose, diag, diagonal, select + ndarray.compress : Equivalent method in ndarray + extract : Equivalent method when working on 1-D arrays + :ref:`ufuncs-output-type` + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4], [5, 6]]) + >>> a + array([[1, 2], + [3, 4], + [5, 6]]) + >>> np.compress([0, 1], a, axis=0) + array([[3, 4]]) + >>> np.compress([False, True, True], a, axis=0) + array([[3, 4], + [5, 6]]) + >>> np.compress([False, True], a, axis=1) + array([[2], + [4], + [6]]) + + Working on the flattened array does not return slices along an axis but + selects elements. + + >>> np.compress([False, True], a) + array([2]) + + """ + return _wrapfunc(a, 'compress', condition, axis=axis, out=out) + + +def _clip_dispatcher(a, a_min, a_max, out=None, **kwargs): + return (a, a_min, a_max) + + +@array_function_dispatch(_clip_dispatcher) +def clip(a, a_min, a_max, out=None, **kwargs): + """ + Clip (limit) the values in an array. + + Given an interval, values outside the interval are clipped to + the interval edges. For example, if an interval of ``[0, 1]`` + is specified, values smaller than 0 become 0, and values larger + than 1 become 1. + + Equivalent to but faster than ``np.minimum(a_max, np.maximum(a, a_min))``. + + No check is performed to ensure ``a_min < a_max``. + + Parameters + ---------- + a : array_like + Array containing elements to clip. + a_min, a_max : array_like or None + Minimum and maximum value. If ``None``, clipping is not performed on + the corresponding edge. Only one of `a_min` and `a_max` may be + ``None``. Both are broadcast against `a`. + out : ndarray, optional + The results will be placed in this array. It may be the input + array for in-place clipping. `out` must be of the right shape + to hold the output. Its type is preserved. + **kwargs + For other keyword-only arguments, see the + :ref:`ufunc docs `. + + .. versionadded:: 1.17.0 + + Returns + ------- + clipped_array : ndarray + An array with the elements of `a`, but where values + < `a_min` are replaced with `a_min`, and those > `a_max` + with `a_max`. + + See Also + -------- + :ref:`ufuncs-output-type` + + Notes + ----- + When `a_min` is greater than `a_max`, `clip` returns an + array in which all values are equal to `a_max`, + as shown in the second example. + + Examples + -------- + >>> a = np.arange(10) + >>> a + array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) + >>> np.clip(a, 1, 8) + array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8]) + >>> np.clip(a, 8, 1) + array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) + >>> np.clip(a, 3, 6, out=a) + array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6]) + >>> a + array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6]) + >>> a = np.arange(10) + >>> a + array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) + >>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8) + array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8]) + + """ + return _wrapfunc(a, 'clip', a_min, a_max, out=out, **kwargs) + + +def _sum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, + initial=None, where=None): + return (a, out) + + +@array_function_dispatch(_sum_dispatcher) +def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, + initial=np._NoValue, where=np._NoValue): + """ + Sum of array elements over a given axis. + + Parameters + ---------- + a : array_like + Elements to sum. + axis : None or int or tuple of ints, optional + Axis or axes along which a sum is performed. The default, + axis=None, will sum all of the elements of the input array. If + axis is negative it counts from the last to the first axis. + + .. versionadded:: 1.7.0 + + If axis is a tuple of ints, a sum is performed on all of the axes + specified in the tuple instead of a single axis or all the axes as + before. + dtype : dtype, optional + The type of the returned array and of the accumulator in which the + elements are summed. The dtype of `a` is used by default unless `a` + has an integer dtype of less precision than the default platform + integer. In that case, if `a` is signed then the platform integer + is used while if `a` is unsigned then an unsigned integer of the + same precision as the platform integer is used. + out : ndarray, optional + Alternative output array in which to place the result. It must have + the same shape as the expected output, but the type of the output + values will be cast if necessary. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `sum` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + initial : scalar, optional + Starting value for the sum. See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.15.0 + + where : array_like of bool, optional + Elements to include in the sum. See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.17.0 + + Returns + ------- + sum_along_axis : ndarray + An array with the same shape as `a`, with the specified + axis removed. If `a` is a 0-d array, or if `axis` is None, a scalar + is returned. If an output array is specified, a reference to + `out` is returned. + + See Also + -------- + ndarray.sum : Equivalent method. + + add.reduce : Equivalent functionality of `add`. + + cumsum : Cumulative sum of array elements. + + trapz : Integration of array values using the composite trapezoidal rule. + + mean, average + + Notes + ----- + Arithmetic is modular when using integer types, and no error is + raised on overflow. + + The sum of an empty array is the neutral element 0: + + >>> np.sum([]) + 0.0 + + For floating point numbers the numerical precision of sum (and + ``np.add.reduce``) is in general limited by directly adding each number + individually to the result causing rounding errors in every step. + However, often numpy will use a numerically better approach (partial + pairwise summation) leading to improved precision in many use-cases. + This improved precision is always provided when no ``axis`` is given. + When ``axis`` is given, it will depend on which axis is summed. + Technically, to provide the best speed possible, the improved precision + is only used when the summation is along the fast axis in memory. + Note that the exact precision may vary depending on other parameters. + In contrast to NumPy, Python's ``math.fsum`` function uses a slower but + more precise approach to summation. + Especially when summing a large number of lower precision floating point + numbers, such as ``float32``, numerical errors can become significant. + In such cases it can be advisable to use `dtype="float64"` to use a higher + precision for the output. + + Examples + -------- + >>> np.sum([0.5, 1.5]) + 2.0 + >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32) + 1 + >>> np.sum([[0, 1], [0, 5]]) + 6 + >>> np.sum([[0, 1], [0, 5]], axis=0) + array([0, 6]) + >>> np.sum([[0, 1], [0, 5]], axis=1) + array([1, 5]) + >>> np.sum([[0, 1], [np.nan, 5]], where=[False, True], axis=1) + array([1., 5.]) + + If the accumulator is too small, overflow occurs: + + >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8) + -128 + + You can also start the sum with a value other than zero: + + >>> np.sum([10], initial=5) + 15 + """ + if isinstance(a, _gentype): + # 2018-02-25, 1.15.0 + warnings.warn( + "Calling np.sum(generator) is deprecated, and in the future will give a different result. " + "Use np.sum(np.fromiter(generator)) or the python sum builtin instead.", + DeprecationWarning, stacklevel=2) + + res = _sum_(a) + if out is not None: + out[...] = res + return out + return res + + return _wrapreduction(a, np.add, 'sum', axis, dtype, out, keepdims=keepdims, + initial=initial, where=where) + + +def _any_dispatcher(a, axis=None, out=None, keepdims=None, *, + where=np._NoValue): + return (a, where, out) + + +@array_function_dispatch(_any_dispatcher) +def any(a, axis=None, out=None, keepdims=np._NoValue, *, where=np._NoValue): + """ + Test whether any array element along a given axis evaluates to True. + + Returns single boolean if `axis` is ``None`` + + Parameters + ---------- + a : array_like + Input array or object that can be converted to an array. + axis : None or int or tuple of ints, optional + Axis or axes along which a logical OR reduction is performed. + The default (``axis=None``) is to perform a logical OR over all + the dimensions of the input array. `axis` may be negative, in + which case it counts from the last to the first axis. + + .. versionadded:: 1.7.0 + + If this is a tuple of ints, a reduction is performed on multiple + axes, instead of a single axis or all the axes as before. + out : ndarray, optional + Alternate output array in which to place the result. It must have + the same shape as the expected output and its type is preserved + (e.g., if it is of type float, then it will remain so, returning + 1.0 for True and 0.0 for False, regardless of the type of `a`). + See :ref:`ufuncs-output-type` for more details. + + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `any` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + where : array_like of bool, optional + Elements to include in checking for any `True` values. + See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.20.0 + + Returns + ------- + any : bool or ndarray + A new boolean or `ndarray` is returned unless `out` is specified, + in which case a reference to `out` is returned. + + See Also + -------- + ndarray.any : equivalent method + + all : Test whether all elements along a given axis evaluate to True. + + Notes + ----- + Not a Number (NaN), positive infinity and negative infinity evaluate + to `True` because these are not equal to zero. + + Examples + -------- + >>> np.any([[True, False], [True, True]]) + True + + >>> np.any([[True, False], [False, False]], axis=0) + array([ True, False]) + + >>> np.any([-1, 0, 5]) + True + + >>> np.any(np.nan) + True + + >>> np.any([[True, False], [False, False]], where=[[False], [True]]) + False + + >>> o=np.array(False) + >>> z=np.any([-1, 4, 5], out=o) + >>> z, o + (array(True), array(True)) + >>> # Check now that z is a reference to o + >>> z is o + True + >>> id(z), id(o) # identity of z and o # doctest: +SKIP + (191614240, 191614240) + + """ + return _wrapreduction(a, np.logical_or, 'any', axis, None, out, + keepdims=keepdims, where=where) + + +def _all_dispatcher(a, axis=None, out=None, keepdims=None, *, + where=None): + return (a, where, out) + + +@array_function_dispatch(_all_dispatcher) +def all(a, axis=None, out=None, keepdims=np._NoValue, *, where=np._NoValue): + """ + Test whether all array elements along a given axis evaluate to True. + + Parameters + ---------- + a : array_like + Input array or object that can be converted to an array. + axis : None or int or tuple of ints, optional + Axis or axes along which a logical AND reduction is performed. + The default (``axis=None``) is to perform a logical AND over all + the dimensions of the input array. `axis` may be negative, in + which case it counts from the last to the first axis. + + .. versionadded:: 1.7.0 + + If this is a tuple of ints, a reduction is performed on multiple + axes, instead of a single axis or all the axes as before. + out : ndarray, optional + Alternate output array in which to place the result. + It must have the same shape as the expected output and its + type is preserved (e.g., if ``dtype(out)`` is float, the result + will consist of 0.0's and 1.0's). See :ref:`ufuncs-output-type` for more + details. + + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `all` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + where : array_like of bool, optional + Elements to include in checking for all `True` values. + See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.20.0 + + Returns + ------- + all : ndarray, bool + A new boolean or array is returned unless `out` is specified, + in which case a reference to `out` is returned. + + See Also + -------- + ndarray.all : equivalent method + + any : Test whether any element along a given axis evaluates to True. + + Notes + ----- + Not a Number (NaN), positive infinity and negative infinity + evaluate to `True` because these are not equal to zero. + + Examples + -------- + >>> np.all([[True,False],[True,True]]) + False + + >>> np.all([[True,False],[True,True]], axis=0) + array([ True, False]) + + >>> np.all([-1, 4, 5]) + True + + >>> np.all([1.0, np.nan]) + True + + >>> np.all([[True, True], [False, True]], where=[[True], [False]]) + True + + >>> o=np.array(False) + >>> z=np.all([-1, 4, 5], out=o) + >>> id(z), id(o), z + (28293632, 28293632, array(True)) # may vary + + """ + return _wrapreduction(a, np.logical_and, 'all', axis, None, out, + keepdims=keepdims, where=where) + + +def _cumsum_dispatcher(a, axis=None, dtype=None, out=None): + return (a, out) + + +@array_function_dispatch(_cumsum_dispatcher) +def cumsum(a, axis=None, dtype=None, out=None): + """ + Return the cumulative sum of the elements along a given axis. + + Parameters + ---------- + a : array_like + Input array. + axis : int, optional + Axis along which the cumulative sum is computed. The default + (None) is to compute the cumsum over the flattened array. + dtype : dtype, optional + Type of the returned array and of the accumulator in which the + elements are summed. If `dtype` is not specified, it defaults + to the dtype of `a`, unless `a` has an integer dtype with a + precision less than that of the default platform integer. In + that case, the default platform integer is used. + out : ndarray, optional + Alternative output array in which to place the result. It must + have the same shape and buffer length as the expected output + but the type will be cast if necessary. See :ref:`ufuncs-output-type` for + more details. + + Returns + ------- + cumsum_along_axis : ndarray. + A new array holding the result is returned unless `out` is + specified, in which case a reference to `out` is returned. The + result has the same size as `a`, and the same shape as `a` if + `axis` is not None or `a` is a 1-d array. + + See Also + -------- + sum : Sum array elements. + trapz : Integration of array values using the composite trapezoidal rule. + diff : Calculate the n-th discrete difference along given axis. + + Notes + ----- + Arithmetic is modular when using integer types, and no error is + raised on overflow. + + ``cumsum(a)[-1]`` may not be equal to ``sum(a)`` for floating-point + values since ``sum`` may use a pairwise summation routine, reducing + the roundoff-error. See `sum` for more information. + + Examples + -------- + >>> a = np.array([[1,2,3], [4,5,6]]) + >>> a + array([[1, 2, 3], + [4, 5, 6]]) + >>> np.cumsum(a) + array([ 1, 3, 6, 10, 15, 21]) + >>> np.cumsum(a, dtype=float) # specifies type of output value(s) + array([ 1., 3., 6., 10., 15., 21.]) + + >>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns + array([[1, 2, 3], + [5, 7, 9]]) + >>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows + array([[ 1, 3, 6], + [ 4, 9, 15]]) + + ``cumsum(b)[-1]`` may not be equal to ``sum(b)`` + + >>> b = np.array([1, 2e-9, 3e-9] * 1000000) + >>> b.cumsum()[-1] + 1000000.0050045159 + >>> b.sum() + 1000000.0050000029 + + """ + return _wrapfunc(a, 'cumsum', axis=axis, dtype=dtype, out=out) + + +def _ptp_dispatcher(a, axis=None, out=None, keepdims=None): + return (a, out) + + +@array_function_dispatch(_ptp_dispatcher) +def ptp(a, axis=None, out=None, keepdims=np._NoValue): + """ + Range of values (maximum - minimum) along an axis. + + The name of the function comes from the acronym for 'peak to peak'. + + .. warning:: + `ptp` preserves the data type of the array. This means the + return value for an input of signed integers with n bits + (e.g. `np.int8`, `np.int16`, etc) is also a signed integer + with n bits. In that case, peak-to-peak values greater than + ``2**(n-1)-1`` will be returned as negative values. An example + with a work-around is shown below. + + Parameters + ---------- + a : array_like + Input values. + axis : None or int or tuple of ints, optional + Axis along which to find the peaks. By default, flatten the + array. `axis` may be negative, in + which case it counts from the last to the first axis. + + .. versionadded:: 1.15.0 + + If this is a tuple of ints, a reduction is performed on multiple + axes, instead of a single axis or all the axes as before. + out : array_like + Alternative output array in which to place the result. It must + have the same shape and buffer length as the expected output, + but the type of the output values will be cast if necessary. + + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `ptp` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + Returns + ------- + ptp : ndarray or scalar + The range of a given array - `scalar` if array is one-dimensional + or a new array holding the result along the given axis + + Examples + -------- + >>> x = np.array([[4, 9, 2, 10], + ... [6, 9, 7, 12]]) + + >>> np.ptp(x, axis=1) + array([8, 6]) + + >>> np.ptp(x, axis=0) + array([2, 0, 5, 2]) + + >>> np.ptp(x) + 10 + + This example shows that a negative value can be returned when + the input is an array of signed integers. + + >>> y = np.array([[1, 127], + ... [0, 127], + ... [-1, 127], + ... [-2, 127]], dtype=np.int8) + >>> np.ptp(y, axis=1) + array([ 126, 127, -128, -127], dtype=int8) + + A work-around is to use the `view()` method to view the result as + unsigned integers with the same bit width: + + >>> np.ptp(y, axis=1).view(np.uint8) + array([126, 127, 128, 129], dtype=uint8) + + """ + kwargs = {} + if keepdims is not np._NoValue: + kwargs['keepdims'] = keepdims + if type(a) is not mu.ndarray: + try: + ptp = a.ptp + except AttributeError: + pass + else: + return ptp(axis=axis, out=out, **kwargs) + return _methods._ptp(a, axis=axis, out=out, **kwargs) + + +def _max_dispatcher(a, axis=None, out=None, keepdims=None, initial=None, + where=None): + return (a, out) + + +@array_function_dispatch(_max_dispatcher) +@set_module('numpy') +def max(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, + where=np._NoValue): + """ + Return the maximum of an array or maximum along an axis. + + Parameters + ---------- + a : array_like + Input data. + axis : None or int or tuple of ints, optional + Axis or axes along which to operate. By default, flattened input is + used. + + .. versionadded:: 1.7.0 + + If this is a tuple of ints, the maximum is selected over multiple axes, + instead of a single axis or all the axes as before. + out : ndarray, optional + Alternative output array in which to place the result. Must + be of the same shape and buffer length as the expected output. + See :ref:`ufuncs-output-type` for more details. + + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the ``max`` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + initial : scalar, optional + The minimum value of an output element. Must be present to allow + computation on empty slice. See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.15.0 + + where : array_like of bool, optional + Elements to compare for the maximum. See `~numpy.ufunc.reduce` + for details. + + .. versionadded:: 1.17.0 + + Returns + ------- + max : ndarray or scalar + Maximum of `a`. If `axis` is None, the result is a scalar value. + If `axis` is an int, the result is an array of dimension + ``a.ndim - 1``. If `axis` is a tuple, the result is an array of + dimension ``a.ndim - len(axis)``. + + See Also + -------- + amin : + The minimum value of an array along a given axis, propagating any NaNs. + nanmax : + The maximum value of an array along a given axis, ignoring any NaNs. + maximum : + Element-wise maximum of two arrays, propagating any NaNs. + fmax : + Element-wise maximum of two arrays, ignoring any NaNs. + argmax : + Return the indices of the maximum values. + + nanmin, minimum, fmin + + Notes + ----- + NaN values are propagated, that is if at least one item is NaN, the + corresponding max value will be NaN as well. To ignore NaN values + (MATLAB behavior), please use nanmax. + + Don't use `~numpy.max` for element-wise comparison of 2 arrays; when + ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than + ``max(a, axis=0)``. + + Examples + -------- + >>> a = np.arange(4).reshape((2,2)) + >>> a + array([[0, 1], + [2, 3]]) + >>> np.max(a) # Maximum of the flattened array + 3 + >>> np.max(a, axis=0) # Maxima along the first axis + array([2, 3]) + >>> np.max(a, axis=1) # Maxima along the second axis + array([1, 3]) + >>> np.max(a, where=[False, True], initial=-1, axis=0) + array([-1, 3]) + >>> b = np.arange(5, dtype=float) + >>> b[2] = np.NaN + >>> np.max(b) + nan + >>> np.max(b, where=~np.isnan(b), initial=-1) + 4.0 + >>> np.nanmax(b) + 4.0 + + You can use an initial value to compute the maximum of an empty slice, or + to initialize it to a different value: + + >>> np.max([[-50], [10]], axis=-1, initial=0) + array([ 0, 10]) + + Notice that the initial value is used as one of the elements for which the + maximum is determined, unlike for the default argument Python's max + function, which is only used for empty iterables. + + >>> np.max([5], initial=6) + 6 + >>> max([5], default=6) + 5 + """ + return _wrapreduction(a, np.maximum, 'max', axis, None, out, + keepdims=keepdims, initial=initial, where=where) + + +@array_function_dispatch(_max_dispatcher) +def amax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, + where=np._NoValue): + """ + Return the maximum of an array or maximum along an axis. + + `amax` is an alias of `~numpy.max`. + + See Also + -------- + max : alias of this function + ndarray.max : equivalent method + """ + return _wrapreduction(a, np.maximum, 'max', axis, None, out, + keepdims=keepdims, initial=initial, where=where) + + +def _min_dispatcher(a, axis=None, out=None, keepdims=None, initial=None, + where=None): + return (a, out) + + +@array_function_dispatch(_min_dispatcher) +def min(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, + where=np._NoValue): + """ + Return the minimum of an array or minimum along an axis. + + Parameters + ---------- + a : array_like + Input data. + axis : None or int or tuple of ints, optional + Axis or axes along which to operate. By default, flattened input is + used. + + .. versionadded:: 1.7.0 + + If this is a tuple of ints, the minimum is selected over multiple axes, + instead of a single axis or all the axes as before. + out : ndarray, optional + Alternative output array in which to place the result. Must + be of the same shape and buffer length as the expected output. + See :ref:`ufuncs-output-type` for more details. + + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the ``min`` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + initial : scalar, optional + The maximum value of an output element. Must be present to allow + computation on empty slice. See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.15.0 + + where : array_like of bool, optional + Elements to compare for the minimum. See `~numpy.ufunc.reduce` + for details. + + .. versionadded:: 1.17.0 + + Returns + ------- + min : ndarray or scalar + Minimum of `a`. If `axis` is None, the result is a scalar value. + If `axis` is an int, the result is an array of dimension + ``a.ndim - 1``. If `axis` is a tuple, the result is an array of + dimension ``a.ndim - len(axis)``. + + See Also + -------- + amax : + The maximum value of an array along a given axis, propagating any NaNs. + nanmin : + The minimum value of an array along a given axis, ignoring any NaNs. + minimum : + Element-wise minimum of two arrays, propagating any NaNs. + fmin : + Element-wise minimum of two arrays, ignoring any NaNs. + argmin : + Return the indices of the minimum values. + + nanmax, maximum, fmax + + Notes + ----- + NaN values are propagated, that is if at least one item is NaN, the + corresponding min value will be NaN as well. To ignore NaN values + (MATLAB behavior), please use nanmin. + + Don't use `~numpy.min` for element-wise comparison of 2 arrays; when + ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than + ``min(a, axis=0)``. + + Examples + -------- + >>> a = np.arange(4).reshape((2,2)) + >>> a + array([[0, 1], + [2, 3]]) + >>> np.min(a) # Minimum of the flattened array + 0 + >>> np.min(a, axis=0) # Minima along the first axis + array([0, 1]) + >>> np.min(a, axis=1) # Minima along the second axis + array([0, 2]) + >>> np.min(a, where=[False, True], initial=10, axis=0) + array([10, 1]) + + >>> b = np.arange(5, dtype=float) + >>> b[2] = np.NaN + >>> np.min(b) + nan + >>> np.min(b, where=~np.isnan(b), initial=10) + 0.0 + >>> np.nanmin(b) + 0.0 + + >>> np.min([[-50], [10]], axis=-1, initial=0) + array([-50, 0]) + + Notice that the initial value is used as one of the elements for which the + minimum is determined, unlike for the default argument Python's max + function, which is only used for empty iterables. + + Notice that this isn't the same as Python's ``default`` argument. + + >>> np.min([6], initial=5) + 5 + >>> min([6], default=5) + 6 + """ + return _wrapreduction(a, np.minimum, 'min', axis, None, out, + keepdims=keepdims, initial=initial, where=where) + + +@array_function_dispatch(_min_dispatcher) +def amin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, + where=np._NoValue): + """ + Return the minimum of an array or minimum along an axis. + + `amin` is an alias of `~numpy.min`. + + See Also + -------- + min : alias of this function + ndarray.min : equivalent method + """ + return _wrapreduction(a, np.minimum, 'min', axis, None, out, + keepdims=keepdims, initial=initial, where=where) + + +def _prod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, + initial=None, where=None): + return (a, out) + + +@array_function_dispatch(_prod_dispatcher) +def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, + initial=np._NoValue, where=np._NoValue): + """ + Return the product of array elements over a given axis. + + Parameters + ---------- + a : array_like + Input data. + axis : None or int or tuple of ints, optional + Axis or axes along which a product is performed. The default, + axis=None, will calculate the product of all the elements in the + input array. If axis is negative it counts from the last to the + first axis. + + .. versionadded:: 1.7.0 + + If axis is a tuple of ints, a product is performed on all of the + axes specified in the tuple instead of a single axis or all the + axes as before. + dtype : dtype, optional + The type of the returned array, as well as of the accumulator in + which the elements are multiplied. The dtype of `a` is used by + default unless `a` has an integer dtype of less precision than the + default platform integer. In that case, if `a` is signed then the + platform integer is used while if `a` is unsigned then an unsigned + integer of the same precision as the platform integer is used. + out : ndarray, optional + Alternative output array in which to place the result. It must have + the same shape as the expected output, but the type of the output + values will be cast if necessary. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left in the + result as dimensions with size one. With this option, the result + will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `prod` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + initial : scalar, optional + The starting value for this product. See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.15.0 + + where : array_like of bool, optional + Elements to include in the product. See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.17.0 + + Returns + ------- + product_along_axis : ndarray, see `dtype` parameter above. + An array shaped as `a` but with the specified axis removed. + Returns a reference to `out` if specified. + + See Also + -------- + ndarray.prod : equivalent method + :ref:`ufuncs-output-type` + + Notes + ----- + Arithmetic is modular when using integer types, and no error is + raised on overflow. That means that, on a 32-bit platform: + + >>> x = np.array([536870910, 536870910, 536870910, 536870910]) + >>> np.prod(x) + 16 # may vary + + The product of an empty array is the neutral element 1: + + >>> np.prod([]) + 1.0 + + Examples + -------- + By default, calculate the product of all elements: + + >>> np.prod([1.,2.]) + 2.0 + + Even when the input array is two-dimensional: + + >>> a = np.array([[1., 2.], [3., 4.]]) + >>> np.prod(a) + 24.0 + + But we can also specify the axis over which to multiply: + + >>> np.prod(a, axis=1) + array([ 2., 12.]) + >>> np.prod(a, axis=0) + array([3., 8.]) + + Or select specific elements to include: + + >>> np.prod([1., np.nan, 3.], where=[True, False, True]) + 3.0 + + If the type of `x` is unsigned, then the output type is + the unsigned platform integer: + + >>> x = np.array([1, 2, 3], dtype=np.uint8) + >>> np.prod(x).dtype == np.uint + True + + If `x` is of a signed integer type, then the output type + is the default platform integer: + + >>> x = np.array([1, 2, 3], dtype=np.int8) + >>> np.prod(x).dtype == int + True + + You can also start the product with a value other than one: + + >>> np.prod([1, 2], initial=5) + 10 + """ + return _wrapreduction(a, np.multiply, 'prod', axis, dtype, out, + keepdims=keepdims, initial=initial, where=where) + + +def _cumprod_dispatcher(a, axis=None, dtype=None, out=None): + return (a, out) + + +@array_function_dispatch(_cumprod_dispatcher) +def cumprod(a, axis=None, dtype=None, out=None): + """ + Return the cumulative product of elements along a given axis. + + Parameters + ---------- + a : array_like + Input array. + axis : int, optional + Axis along which the cumulative product is computed. By default + the input is flattened. + dtype : dtype, optional + Type of the returned array, as well as of the accumulator in which + the elements are multiplied. If *dtype* is not specified, it + defaults to the dtype of `a`, unless `a` has an integer dtype with + a precision less than that of the default platform integer. In + that case, the default platform integer is used instead. + out : ndarray, optional + Alternative output array in which to place the result. It must + have the same shape and buffer length as the expected output + but the type of the resulting values will be cast if necessary. + + Returns + ------- + cumprod : ndarray + A new array holding the result is returned unless `out` is + specified, in which case a reference to out is returned. + + See Also + -------- + :ref:`ufuncs-output-type` + + Notes + ----- + Arithmetic is modular when using integer types, and no error is + raised on overflow. + + Examples + -------- + >>> a = np.array([1,2,3]) + >>> np.cumprod(a) # intermediate results 1, 1*2 + ... # total product 1*2*3 = 6 + array([1, 2, 6]) + >>> a = np.array([[1, 2, 3], [4, 5, 6]]) + >>> np.cumprod(a, dtype=float) # specify type of output + array([ 1., 2., 6., 24., 120., 720.]) + + The cumulative product for each column (i.e., over the rows) of `a`: + + >>> np.cumprod(a, axis=0) + array([[ 1, 2, 3], + [ 4, 10, 18]]) + + The cumulative product for each row (i.e. over the columns) of `a`: + + >>> np.cumprod(a,axis=1) + array([[ 1, 2, 6], + [ 4, 20, 120]]) + + """ + return _wrapfunc(a, 'cumprod', axis=axis, dtype=dtype, out=out) + + +def _ndim_dispatcher(a): + return (a,) + + +@array_function_dispatch(_ndim_dispatcher) +def ndim(a): + """ + Return the number of dimensions of an array. + + Parameters + ---------- + a : array_like + Input array. If it is not already an ndarray, a conversion is + attempted. + + Returns + ------- + number_of_dimensions : int + The number of dimensions in `a`. Scalars are zero-dimensional. + + See Also + -------- + ndarray.ndim : equivalent method + shape : dimensions of array + ndarray.shape : dimensions of array + + Examples + -------- + >>> np.ndim([[1,2,3],[4,5,6]]) + 2 + >>> np.ndim(np.array([[1,2,3],[4,5,6]])) + 2 + >>> np.ndim(1) + 0 + + """ + try: + return a.ndim + except AttributeError: + return asarray(a).ndim + + +def _size_dispatcher(a, axis=None): + return (a,) + + +@array_function_dispatch(_size_dispatcher) +def size(a, axis=None): + """ + Return the number of elements along a given axis. + + Parameters + ---------- + a : array_like + Input data. + axis : int, optional + Axis along which the elements are counted. By default, give + the total number of elements. + + Returns + ------- + element_count : int + Number of elements along the specified axis. + + See Also + -------- + shape : dimensions of array + ndarray.shape : dimensions of array + ndarray.size : number of elements in array + + Examples + -------- + >>> a = np.array([[1,2,3],[4,5,6]]) + >>> np.size(a) + 6 + >>> np.size(a,1) + 3 + >>> np.size(a,0) + 2 + + """ + if axis is None: + try: + return a.size + except AttributeError: + return asarray(a).size + else: + try: + return a.shape[axis] + except AttributeError: + return asarray(a).shape[axis] + + +def _round_dispatcher(a, decimals=None, out=None): + return (a, out) + + +@array_function_dispatch(_round_dispatcher) +def round(a, decimals=0, out=None): + """ + Evenly round to the given number of decimals. + + Parameters + ---------- + a : array_like + Input data. + decimals : int, optional + Number of decimal places to round to (default: 0). If + decimals is negative, it specifies the number of positions to + the left of the decimal point. + out : ndarray, optional + Alternative output array in which to place the result. It must have + the same shape as the expected output, but the type of the output + values will be cast if necessary. See :ref:`ufuncs-output-type` for more + details. + + Returns + ------- + rounded_array : ndarray + An array of the same type as `a`, containing the rounded values. + Unless `out` was specified, a new array is created. A reference to + the result is returned. + + The real and imaginary parts of complex numbers are rounded + separately. The result of rounding a float is a float. + + See Also + -------- + ndarray.round : equivalent method + around : an alias for this function + ceil, fix, floor, rint, trunc + + + Notes + ----- + For values exactly halfway between rounded decimal values, NumPy + rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, + -0.5 and 0.5 round to 0.0, etc. + + ``np.round`` uses a fast but sometimes inexact algorithm to round + floating-point datatypes. For positive `decimals` it is equivalent to + ``np.true_divide(np.rint(a * 10**decimals), 10**decimals)``, which has + error due to the inexact representation of decimal fractions in the IEEE + floating point standard [1]_ and errors introduced when scaling by powers + of ten. For instance, note the extra "1" in the following: + + >>> np.round(56294995342131.5, 3) + 56294995342131.51 + + If your goal is to print such values with a fixed number of decimals, it is + preferable to use numpy's float printing routines to limit the number of + printed decimals: + + >>> np.format_float_positional(56294995342131.5, precision=3) + '56294995342131.5' + + The float printing routines use an accurate but much more computationally + demanding algorithm to compute the number of digits after the decimal + point. + + Alternatively, Python's builtin `round` function uses a more accurate + but slower algorithm for 64-bit floating point values: + + >>> round(56294995342131.5, 3) + 56294995342131.5 + >>> np.round(16.055, 2), round(16.055, 2) # equals 16.0549999999999997 + (16.06, 16.05) + + + References + ---------- + .. [1] "Lecture Notes on the Status of IEEE 754", William Kahan, + https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF + + Examples + -------- + >>> np.round([0.37, 1.64]) + array([0., 2.]) + >>> np.round([0.37, 1.64], decimals=1) + array([0.4, 1.6]) + >>> np.round([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value + array([0., 2., 2., 4., 4.]) + >>> np.round([1,2,3,11], decimals=1) # ndarray of ints is returned + array([ 1, 2, 3, 11]) + >>> np.round([1,2,3,11], decimals=-1) + array([ 0, 0, 0, 10]) + + """ + return _wrapfunc(a, 'round', decimals=decimals, out=out) + + +@array_function_dispatch(_round_dispatcher) +def around(a, decimals=0, out=None): + """ + Round an array to the given number of decimals. + + `around` is an alias of `~numpy.round`. + + See Also + -------- + ndarray.round : equivalent method + round : alias for this function + ceil, fix, floor, rint, trunc + + """ + return _wrapfunc(a, 'round', decimals=decimals, out=out) + + +def _mean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, *, + where=None): + return (a, where, out) + + +@array_function_dispatch(_mean_dispatcher) +def mean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, *, + where=np._NoValue): + """ + Compute the arithmetic mean along the specified axis. + + Returns the average of the array elements. The average is taken over + the flattened array by default, otherwise over the specified axis. + `float64` intermediate and return values are used for integer inputs. + + Parameters + ---------- + a : array_like + Array containing numbers whose mean is desired. If `a` is not an + array, a conversion is attempted. + axis : None or int or tuple of ints, optional + Axis or axes along which the means are computed. The default is to + compute the mean of the flattened array. + + .. versionadded:: 1.7.0 + + If this is a tuple of ints, a mean is performed over multiple axes, + instead of a single axis or all the axes as before. + dtype : data-type, optional + Type to use in computing the mean. For integer inputs, the default + is `float64`; for floating point inputs, it is the same as the + input dtype. + out : ndarray, optional + Alternate output array in which to place the result. The default + is ``None``; if provided, it must have the same shape as the + expected output, but the type will be cast if necessary. + See :ref:`ufuncs-output-type` for more details. + + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `mean` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + where : array_like of bool, optional + Elements to include in the mean. See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.20.0 + + Returns + ------- + m : ndarray, see dtype parameter above + If `out=None`, returns a new array containing the mean values, + otherwise a reference to the output array is returned. + + See Also + -------- + average : Weighted average + std, var, nanmean, nanstd, nanvar + + Notes + ----- + The arithmetic mean is the sum of the elements along the axis divided + by the number of elements. + + Note that for floating-point input, the mean is computed using the + same precision the input has. Depending on the input data, this can + cause the results to be inaccurate, especially for `float32` (see + example below). Specifying a higher-precision accumulator using the + `dtype` keyword can alleviate this issue. + + By default, `float16` results are computed using `float32` intermediates + for extra precision. + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4]]) + >>> np.mean(a) + 2.5 + >>> np.mean(a, axis=0) + array([2., 3.]) + >>> np.mean(a, axis=1) + array([1.5, 3.5]) + + In single precision, `mean` can be inaccurate: + + >>> a = np.zeros((2, 512*512), dtype=np.float32) + >>> a[0, :] = 1.0 + >>> a[1, :] = 0.1 + >>> np.mean(a) + 0.54999924 + + Computing the mean in float64 is more accurate: + + >>> np.mean(a, dtype=np.float64) + 0.55000000074505806 # may vary + + Specifying a where argument: + + >>> a = np.array([[5, 9, 13], [14, 10, 12], [11, 15, 19]]) + >>> np.mean(a) + 12.0 + >>> np.mean(a, where=[[True], [False], [False]]) + 9.0 + + """ + kwargs = {} + if keepdims is not np._NoValue: + kwargs['keepdims'] = keepdims + if where is not np._NoValue: + kwargs['where'] = where + if type(a) is not mu.ndarray: + try: + mean = a.mean + except AttributeError: + pass + else: + return mean(axis=axis, dtype=dtype, out=out, **kwargs) + + return _methods._mean(a, axis=axis, dtype=dtype, + out=out, **kwargs) + + +def _std_dispatcher(a, axis=None, dtype=None, out=None, ddof=None, + keepdims=None, *, where=None): + return (a, where, out) + + +@array_function_dispatch(_std_dispatcher) +def std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *, + where=np._NoValue): + """ + Compute the standard deviation along the specified axis. + + Returns the standard deviation, a measure of the spread of a distribution, + of the array elements. The standard deviation is computed for the + flattened array by default, otherwise over the specified axis. + + Parameters + ---------- + a : array_like + Calculate the standard deviation of these values. + axis : None or int or tuple of ints, optional + Axis or axes along which the standard deviation is computed. The + default is to compute the standard deviation of the flattened array. + + .. versionadded:: 1.7.0 + + If this is a tuple of ints, a standard deviation is performed over + multiple axes, instead of a single axis or all the axes as before. + dtype : dtype, optional + Type to use in computing the standard deviation. For arrays of + integer type the default is float64, for arrays of float types it is + the same as the array type. + out : ndarray, optional + Alternative output array in which to place the result. It must have + the same shape as the expected output but the type (of the calculated + values) will be cast if necessary. + ddof : int, optional + Means Delta Degrees of Freedom. The divisor used in calculations + is ``N - ddof``, where ``N`` represents the number of elements. + By default `ddof` is zero. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `std` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + where : array_like of bool, optional + Elements to include in the standard deviation. + See `~numpy.ufunc.reduce` for details. + + .. versionadded:: 1.20.0 + + Returns + ------- + standard_deviation : ndarray, see dtype parameter above. + If `out` is None, return a new array containing the standard deviation, + otherwise return a reference to the output array. + + See Also + -------- + var, mean, nanmean, nanstd, nanvar + :ref:`ufuncs-output-type` + + Notes + ----- + The standard deviation is the square root of the average of the squared + deviations from the mean, i.e., ``std = sqrt(mean(x))``, where + ``x = abs(a - a.mean())**2``. + + The average squared deviation is typically calculated as ``x.sum() / N``, + where ``N = len(x)``. If, however, `ddof` is specified, the divisor + ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` + provides an unbiased estimator of the variance of the infinite population. + ``ddof=0`` provides a maximum likelihood estimate of the variance for + normally distributed variables. The standard deviation computed in this + function is the square root of the estimated variance, so even with + ``ddof=1``, it will not be an unbiased estimate of the standard deviation + per se. + + Note that, for complex numbers, `std` takes the absolute + value before squaring, so that the result is always real and nonnegative. + + For floating-point input, the *std* is computed using the same + precision the input has. Depending on the input data, this can cause + the results to be inaccurate, especially for float32 (see example below). + Specifying a higher-accuracy accumulator using the `dtype` keyword can + alleviate this issue. + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4]]) + >>> np.std(a) + 1.1180339887498949 # may vary + >>> np.std(a, axis=0) + array([1., 1.]) + >>> np.std(a, axis=1) + array([0.5, 0.5]) + + In single precision, std() can be inaccurate: + + >>> a = np.zeros((2, 512*512), dtype=np.float32) + >>> a[0, :] = 1.0 + >>> a[1, :] = 0.1 + >>> np.std(a) + 0.45000005 + + Computing the standard deviation in float64 is more accurate: + + >>> np.std(a, dtype=np.float64) + 0.44999999925494177 # may vary + + Specifying a where argument: + + >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]]) + >>> np.std(a) + 2.614064523559687 # may vary + >>> np.std(a, where=[[True], [True], [False]]) + 2.0 + + """ + kwargs = {} + if keepdims is not np._NoValue: + kwargs['keepdims'] = keepdims + if where is not np._NoValue: + kwargs['where'] = where + if type(a) is not mu.ndarray: + try: + std = a.std + except AttributeError: + pass + else: + return std(axis=axis, dtype=dtype, out=out, ddof=ddof, **kwargs) + + return _methods._std(a, axis=axis, dtype=dtype, out=out, ddof=ddof, + **kwargs) + + +def _var_dispatcher(a, axis=None, dtype=None, out=None, ddof=None, + keepdims=None, *, where=None): + return (a, where, out) + + +@array_function_dispatch(_var_dispatcher) +def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *, + where=np._NoValue): + """ + Compute the variance along the specified axis. + + Returns the variance of the array elements, a measure of the spread of a + distribution. The variance is computed for the flattened array by + default, otherwise over the specified axis. + + Parameters + ---------- + a : array_like + Array containing numbers whose variance is desired. If `a` is not an + array, a conversion is attempted. + axis : None or int or tuple of ints, optional + Axis or axes along which the variance is computed. The default is to + compute the variance of the flattened array. + + .. versionadded:: 1.7.0 + + If this is a tuple of ints, a variance is performed over multiple axes, + instead of a single axis or all the axes as before. + dtype : data-type, optional + Type to use in computing the variance. For arrays of integer type + the default is `float64`; for arrays of float types it is the same as + the array type. + out : ndarray, optional + Alternate output array in which to place the result. It must have + the same shape as the expected output, but the type is cast if + necessary. + ddof : int, optional + "Delta Degrees of Freedom": the divisor used in the calculation is + ``N - ddof``, where ``N`` represents the number of elements. By + default `ddof` is zero. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + If the default value is passed, then `keepdims` will not be + passed through to the `var` method of sub-classes of + `ndarray`, however any non-default value will be. If the + sub-class' method does not implement `keepdims` any + exceptions will be raised. + + where : array_like of bool, optional + Elements to include in the variance. See `~numpy.ufunc.reduce` for + details. + + .. versionadded:: 1.20.0 + + Returns + ------- + variance : ndarray, see dtype parameter above + If ``out=None``, returns a new array containing the variance; + otherwise, a reference to the output array is returned. + + See Also + -------- + std, mean, nanmean, nanstd, nanvar + :ref:`ufuncs-output-type` + + Notes + ----- + The variance is the average of the squared deviations from the mean, + i.e., ``var = mean(x)``, where ``x = abs(a - a.mean())**2``. + + The mean is typically calculated as ``x.sum() / N``, where ``N = len(x)``. + If, however, `ddof` is specified, the divisor ``N - ddof`` is used + instead. In standard statistical practice, ``ddof=1`` provides an + unbiased estimator of the variance of a hypothetical infinite population. + ``ddof=0`` provides a maximum likelihood estimate of the variance for + normally distributed variables. + + Note that for complex numbers, the absolute value is taken before + squaring, so that the result is always real and nonnegative. + + For floating-point input, the variance is computed using the same + precision the input has. Depending on the input data, this can cause + the results to be inaccurate, especially for `float32` (see example + below). Specifying a higher-accuracy accumulator using the ``dtype`` + keyword can alleviate this issue. + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4]]) + >>> np.var(a) + 1.25 + >>> np.var(a, axis=0) + array([1., 1.]) + >>> np.var(a, axis=1) + array([0.25, 0.25]) + + In single precision, var() can be inaccurate: + + >>> a = np.zeros((2, 512*512), dtype=np.float32) + >>> a[0, :] = 1.0 + >>> a[1, :] = 0.1 + >>> np.var(a) + 0.20250003 + + Computing the variance in float64 is more accurate: + + >>> np.var(a, dtype=np.float64) + 0.20249999932944759 # may vary + >>> ((1-0.55)**2 + (0.1-0.55)**2)/2 + 0.2025 + + Specifying a where argument: + + >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]]) + >>> np.var(a) + 6.833333333333333 # may vary + >>> np.var(a, where=[[True], [True], [False]]) + 4.0 + + """ + kwargs = {} + if keepdims is not np._NoValue: + kwargs['keepdims'] = keepdims + if where is not np._NoValue: + kwargs['where'] = where + + if type(a) is not mu.ndarray: + try: + var = a.var + + except AttributeError: + pass + else: + return var(axis=axis, dtype=dtype, out=out, ddof=ddof, **kwargs) + + return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof, + **kwargs) + + +# Aliases of other functions. Provided unique docstrings +# are for reference purposes only. Wherever possible, +# avoid using them. + + +def _round__dispatcher(a, decimals=None, out=None): + # 2023-02-28, 1.25.0 + warnings.warn("`round_` is deprecated as of NumPy 1.25.0, and will be " + "removed in NumPy 2.0. Please use `round` instead.", + DeprecationWarning, stacklevel=3) + return (a, out) + + +@array_function_dispatch(_round__dispatcher) +def round_(a, decimals=0, out=None): + """ + Round an array to the given number of decimals. + + `~numpy.round_` is a disrecommended backwards-compatibility + alias of `~numpy.around` and `~numpy.round`. + + .. deprecated:: 1.25.0 + ``round_`` is deprecated as of NumPy 1.25.0, and will be + removed in NumPy 2.0. Please use `round` instead. + + See Also + -------- + around : equivalent function; see for details. + """ + return around(a, decimals=decimals, out=out) + + +def _product_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, + initial=None, where=None): + # 2023-03-02, 1.25.0 + warnings.warn("`product` is deprecated as of NumPy 1.25.0, and will be " + "removed in NumPy 2.0. Please use `prod` instead.", + DeprecationWarning, stacklevel=3) + return (a, out) + + +@array_function_dispatch(_product_dispatcher, verify=False) +def product(*args, **kwargs): + """ + Return the product of array elements over a given axis. + + .. deprecated:: 1.25.0 + ``product`` is deprecated as of NumPy 1.25.0, and will be + removed in NumPy 2.0. Please use `prod` instead. + + See Also + -------- + prod : equivalent function; see for details. + """ + return prod(*args, **kwargs) + + +def _cumproduct_dispatcher(a, axis=None, dtype=None, out=None): + # 2023-03-02, 1.25.0 + warnings.warn("`cumproduct` is deprecated as of NumPy 1.25.0, and will be " + "removed in NumPy 2.0. Please use `cumprod` instead.", + DeprecationWarning, stacklevel=3) + return (a, out) + + +@array_function_dispatch(_cumproduct_dispatcher, verify=False) +def cumproduct(*args, **kwargs): + """ + Return the cumulative product over the given axis. + + .. deprecated:: 1.25.0 + ``cumproduct`` is deprecated as of NumPy 1.25.0, and will be + removed in NumPy 2.0. Please use `cumprod` instead. + + See Also + -------- + cumprod : equivalent function; see for details. + """ + return cumprod(*args, **kwargs) + + +def _sometrue_dispatcher(a, axis=None, out=None, keepdims=None, *, + where=np._NoValue): + # 2023-03-02, 1.25.0 + warnings.warn("`sometrue` is deprecated as of NumPy 1.25.0, and will be " + "removed in NumPy 2.0. Please use `any` instead.", + DeprecationWarning, stacklevel=3) + return (a, where, out) + + +@array_function_dispatch(_sometrue_dispatcher, verify=False) +def sometrue(*args, **kwargs): + """ + Check whether some values are true. + + Refer to `any` for full documentation. + + .. deprecated:: 1.25.0 + ``sometrue`` is deprecated as of NumPy 1.25.0, and will be + removed in NumPy 2.0. Please use `any` instead. + + See Also + -------- + any : equivalent function; see for details. + """ + return any(*args, **kwargs) + + +def _alltrue_dispatcher(a, axis=None, out=None, keepdims=None, *, where=None): + # 2023-03-02, 1.25.0 + warnings.warn("`alltrue` is deprecated as of NumPy 1.25.0, and will be " + "removed in NumPy 2.0. Please use `all` instead.", + DeprecationWarning, stacklevel=3) + return (a, where, out) + + +@array_function_dispatch(_alltrue_dispatcher, verify=False) +def alltrue(*args, **kwargs): + """ + Check if all elements of input array are true. + + .. deprecated:: 1.25.0 + ``alltrue`` is deprecated as of NumPy 1.25.0, and will be + removed in NumPy 2.0. Please use `all` instead. + + See Also + -------- + numpy.all : Equivalent function; see for details. + """ + return all(*args, **kwargs) diff --git a/venv/lib/python3.10/site-packages/numpy/core/fromnumeric.pyi b/venv/lib/python3.10/site-packages/numpy/core/fromnumeric.pyi new file mode 100644 index 0000000000000000000000000000000000000000..5438b2700bd56cb404a319c2d9880d448cdb857c --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/fromnumeric.pyi @@ -0,0 +1,1060 @@ +import datetime as dt +from collections.abc import Sequence +from typing import Union, Any, overload, TypeVar, Literal, SupportsIndex + +from numpy import ( + ndarray, + number, + uint64, + int_, + int64, + intp, + float16, + bool_, + floating, + complexfloating, + object_, + generic, + _OrderKACF, + _OrderACF, + _ModeKind, + _PartitionKind, + _SortKind, + _SortSide, + _CastingKind, +) +from numpy._typing import ( + DTypeLike, + _DTypeLike, + ArrayLike, + _ArrayLike, + NDArray, + _ShapeLike, + _Shape, + _ArrayLikeBool_co, + _ArrayLikeUInt_co, + _ArrayLikeInt_co, + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, + _ArrayLikeObject_co, + _IntLike_co, + _BoolLike_co, + _ComplexLike_co, + _NumberLike_co, + _ScalarLike_co, +) + +_SCT = TypeVar("_SCT", bound=generic) +_SCT_uifcO = TypeVar("_SCT_uifcO", bound=number[Any] | object_) +_ArrayType = TypeVar("_ArrayType", bound=NDArray[Any]) + +__all__: list[str] + +@overload +def take( + a: _ArrayLike[_SCT], + indices: _IntLike_co, + axis: None = ..., + out: None = ..., + mode: _ModeKind = ..., +) -> _SCT: ... +@overload +def take( + a: ArrayLike, + indices: _IntLike_co, + axis: None | SupportsIndex = ..., + out: None = ..., + mode: _ModeKind = ..., +) -> Any: ... +@overload +def take( + a: _ArrayLike[_SCT], + indices: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., + out: None = ..., + mode: _ModeKind = ..., +) -> NDArray[_SCT]: ... +@overload +def take( + a: ArrayLike, + indices: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., + out: None = ..., + mode: _ModeKind = ..., +) -> NDArray[Any]: ... +@overload +def take( + a: ArrayLike, + indices: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., + out: _ArrayType = ..., + mode: _ModeKind = ..., +) -> _ArrayType: ... + +@overload +def reshape( + a: _ArrayLike[_SCT], + newshape: _ShapeLike, + order: _OrderACF = ..., +) -> NDArray[_SCT]: ... +@overload +def reshape( + a: ArrayLike, + newshape: _ShapeLike, + order: _OrderACF = ..., +) -> NDArray[Any]: ... + +@overload +def choose( + a: _IntLike_co, + choices: ArrayLike, + out: None = ..., + mode: _ModeKind = ..., +) -> Any: ... +@overload +def choose( + a: _ArrayLikeInt_co, + choices: _ArrayLike[_SCT], + out: None = ..., + mode: _ModeKind = ..., +) -> NDArray[_SCT]: ... +@overload +def choose( + a: _ArrayLikeInt_co, + choices: ArrayLike, + out: None = ..., + mode: _ModeKind = ..., +) -> NDArray[Any]: ... +@overload +def choose( + a: _ArrayLikeInt_co, + choices: ArrayLike, + out: _ArrayType = ..., + mode: _ModeKind = ..., +) -> _ArrayType: ... + +@overload +def repeat( + a: _ArrayLike[_SCT], + repeats: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., +) -> NDArray[_SCT]: ... +@overload +def repeat( + a: ArrayLike, + repeats: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., +) -> NDArray[Any]: ... + +def put( + a: NDArray[Any], + ind: _ArrayLikeInt_co, + v: ArrayLike, + mode: _ModeKind = ..., +) -> None: ... + +@overload +def swapaxes( + a: _ArrayLike[_SCT], + axis1: SupportsIndex, + axis2: SupportsIndex, +) -> NDArray[_SCT]: ... +@overload +def swapaxes( + a: ArrayLike, + axis1: SupportsIndex, + axis2: SupportsIndex, +) -> NDArray[Any]: ... + +@overload +def transpose( + a: _ArrayLike[_SCT], + axes: None | _ShapeLike = ... +) -> NDArray[_SCT]: ... +@overload +def transpose( + a: ArrayLike, + axes: None | _ShapeLike = ... +) -> NDArray[Any]: ... + +@overload +def partition( + a: _ArrayLike[_SCT], + kth: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., + kind: _PartitionKind = ..., + order: None | str | Sequence[str] = ..., +) -> NDArray[_SCT]: ... +@overload +def partition( + a: ArrayLike, + kth: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., + kind: _PartitionKind = ..., + order: None | str | Sequence[str] = ..., +) -> NDArray[Any]: ... + +def argpartition( + a: ArrayLike, + kth: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., + kind: _PartitionKind = ..., + order: None | str | Sequence[str] = ..., +) -> NDArray[intp]: ... + +@overload +def sort( + a: _ArrayLike[_SCT], + axis: None | SupportsIndex = ..., + kind: None | _SortKind = ..., + order: None | str | Sequence[str] = ..., +) -> NDArray[_SCT]: ... +@overload +def sort( + a: ArrayLike, + axis: None | SupportsIndex = ..., + kind: None | _SortKind = ..., + order: None | str | Sequence[str] = ..., +) -> NDArray[Any]: ... + +def argsort( + a: ArrayLike, + axis: None | SupportsIndex = ..., + kind: None | _SortKind = ..., + order: None | str | Sequence[str] = ..., +) -> NDArray[intp]: ... + +@overload +def argmax( + a: ArrayLike, + axis: None = ..., + out: None = ..., + *, + keepdims: Literal[False] = ..., +) -> intp: ... +@overload +def argmax( + a: ArrayLike, + axis: None | SupportsIndex = ..., + out: None = ..., + *, + keepdims: bool = ..., +) -> Any: ... +@overload +def argmax( + a: ArrayLike, + axis: None | SupportsIndex = ..., + out: _ArrayType = ..., + *, + keepdims: bool = ..., +) -> _ArrayType: ... + +@overload +def argmin( + a: ArrayLike, + axis: None = ..., + out: None = ..., + *, + keepdims: Literal[False] = ..., +) -> intp: ... +@overload +def argmin( + a: ArrayLike, + axis: None | SupportsIndex = ..., + out: None = ..., + *, + keepdims: bool = ..., +) -> Any: ... +@overload +def argmin( + a: ArrayLike, + axis: None | SupportsIndex = ..., + out: _ArrayType = ..., + *, + keepdims: bool = ..., +) -> _ArrayType: ... + +@overload +def searchsorted( + a: ArrayLike, + v: _ScalarLike_co, + side: _SortSide = ..., + sorter: None | _ArrayLikeInt_co = ..., # 1D int array +) -> intp: ... +@overload +def searchsorted( + a: ArrayLike, + v: ArrayLike, + side: _SortSide = ..., + sorter: None | _ArrayLikeInt_co = ..., # 1D int array +) -> NDArray[intp]: ... + +@overload +def resize( + a: _ArrayLike[_SCT], + new_shape: _ShapeLike, +) -> NDArray[_SCT]: ... +@overload +def resize( + a: ArrayLike, + new_shape: _ShapeLike, +) -> NDArray[Any]: ... + +@overload +def squeeze( + a: _SCT, + axis: None | _ShapeLike = ..., +) -> _SCT: ... +@overload +def squeeze( + a: _ArrayLike[_SCT], + axis: None | _ShapeLike = ..., +) -> NDArray[_SCT]: ... +@overload +def squeeze( + a: ArrayLike, + axis: None | _ShapeLike = ..., +) -> NDArray[Any]: ... + +@overload +def diagonal( + a: _ArrayLike[_SCT], + offset: SupportsIndex = ..., + axis1: SupportsIndex = ..., + axis2: SupportsIndex = ..., # >= 2D array +) -> NDArray[_SCT]: ... +@overload +def diagonal( + a: ArrayLike, + offset: SupportsIndex = ..., + axis1: SupportsIndex = ..., + axis2: SupportsIndex = ..., # >= 2D array +) -> NDArray[Any]: ... + +@overload +def trace( + a: ArrayLike, # >= 2D array + offset: SupportsIndex = ..., + axis1: SupportsIndex = ..., + axis2: SupportsIndex = ..., + dtype: DTypeLike = ..., + out: None = ..., +) -> Any: ... +@overload +def trace( + a: ArrayLike, # >= 2D array + offset: SupportsIndex = ..., + axis1: SupportsIndex = ..., + axis2: SupportsIndex = ..., + dtype: DTypeLike = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +@overload +def ravel(a: _ArrayLike[_SCT], order: _OrderKACF = ...) -> NDArray[_SCT]: ... +@overload +def ravel(a: ArrayLike, order: _OrderKACF = ...) -> NDArray[Any]: ... + +def nonzero(a: ArrayLike) -> tuple[NDArray[intp], ...]: ... + +def shape(a: ArrayLike) -> _Shape: ... + +@overload +def compress( + condition: _ArrayLikeBool_co, # 1D bool array + a: _ArrayLike[_SCT], + axis: None | SupportsIndex = ..., + out: None = ..., +) -> NDArray[_SCT]: ... +@overload +def compress( + condition: _ArrayLikeBool_co, # 1D bool array + a: ArrayLike, + axis: None | SupportsIndex = ..., + out: None = ..., +) -> NDArray[Any]: ... +@overload +def compress( + condition: _ArrayLikeBool_co, # 1D bool array + a: ArrayLike, + axis: None | SupportsIndex = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +@overload +def clip( + a: _SCT, + a_min: None | ArrayLike, + a_max: None | ArrayLike, + out: None = ..., + *, + dtype: None = ..., + where: None | _ArrayLikeBool_co = ..., + order: _OrderKACF = ..., + subok: bool = ..., + signature: str | tuple[None | str, ...] = ..., + extobj: list[Any] = ..., + casting: _CastingKind = ..., +) -> _SCT: ... +@overload +def clip( + a: _ScalarLike_co, + a_min: None | ArrayLike, + a_max: None | ArrayLike, + out: None = ..., + *, + dtype: None = ..., + where: None | _ArrayLikeBool_co = ..., + order: _OrderKACF = ..., + subok: bool = ..., + signature: str | tuple[None | str, ...] = ..., + extobj: list[Any] = ..., + casting: _CastingKind = ..., +) -> Any: ... +@overload +def clip( + a: _ArrayLike[_SCT], + a_min: None | ArrayLike, + a_max: None | ArrayLike, + out: None = ..., + *, + dtype: None = ..., + where: None | _ArrayLikeBool_co = ..., + order: _OrderKACF = ..., + subok: bool = ..., + signature: str | tuple[None | str, ...] = ..., + extobj: list[Any] = ..., + casting: _CastingKind = ..., +) -> NDArray[_SCT]: ... +@overload +def clip( + a: ArrayLike, + a_min: None | ArrayLike, + a_max: None | ArrayLike, + out: None = ..., + *, + dtype: None = ..., + where: None | _ArrayLikeBool_co = ..., + order: _OrderKACF = ..., + subok: bool = ..., + signature: str | tuple[None | str, ...] = ..., + extobj: list[Any] = ..., + casting: _CastingKind = ..., +) -> NDArray[Any]: ... +@overload +def clip( + a: ArrayLike, + a_min: None | ArrayLike, + a_max: None | ArrayLike, + out: _ArrayType = ..., + *, + dtype: DTypeLike, + where: None | _ArrayLikeBool_co = ..., + order: _OrderKACF = ..., + subok: bool = ..., + signature: str | tuple[None | str, ...] = ..., + extobj: list[Any] = ..., + casting: _CastingKind = ..., +) -> Any: ... +@overload +def clip( + a: ArrayLike, + a_min: None | ArrayLike, + a_max: None | ArrayLike, + out: _ArrayType, + *, + dtype: DTypeLike = ..., + where: None | _ArrayLikeBool_co = ..., + order: _OrderKACF = ..., + subok: bool = ..., + signature: str | tuple[None | str, ...] = ..., + extobj: list[Any] = ..., + casting: _CastingKind = ..., +) -> _ArrayType: ... + +@overload +def sum( + a: _ArrayLike[_SCT], + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _SCT: ... +@overload +def sum( + a: ArrayLike, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: None = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def sum( + a: ArrayLike, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +@overload +def all( + a: ArrayLike, + axis: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> bool_: ... +@overload +def all( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: None = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def all( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +@overload +def any( + a: ArrayLike, + axis: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> bool_: ... +@overload +def any( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: None = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def any( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +@overload +def cumsum( + a: _ArrayLike[_SCT], + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[_SCT]: ... +@overload +def cumsum( + a: ArrayLike, + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[Any]: ... +@overload +def cumsum( + a: ArrayLike, + axis: None | SupportsIndex = ..., + dtype: _DTypeLike[_SCT] = ..., + out: None = ..., +) -> NDArray[_SCT]: ... +@overload +def cumsum( + a: ArrayLike, + axis: None | SupportsIndex = ..., + dtype: DTypeLike = ..., + out: None = ..., +) -> NDArray[Any]: ... +@overload +def cumsum( + a: ArrayLike, + axis: None | SupportsIndex = ..., + dtype: DTypeLike = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +@overload +def ptp( + a: _ArrayLike[_SCT], + axis: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., +) -> _SCT: ... +@overload +def ptp( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: None = ..., + keepdims: bool = ..., +) -> Any: ... +@overload +def ptp( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., +) -> _ArrayType: ... + +@overload +def amax( + a: _ArrayLike[_SCT], + axis: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _SCT: ... +@overload +def amax( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: None = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def amax( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +@overload +def amin( + a: _ArrayLike[_SCT], + axis: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _SCT: ... +@overload +def amin( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: None = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def amin( + a: ArrayLike, + axis: None | _ShapeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +# TODO: `np.prod()``: For object arrays `initial` does not necessarily +# have to be a numerical scalar. +# The only requirement is that it is compatible +# with the `.__mul__()` method(s) of the passed array's elements. + +# Note that the same situation holds for all wrappers around +# `np.ufunc.reduce`, e.g. `np.sum()` (`.__add__()`). +@overload +def prod( + a: _ArrayLikeBool_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> int_: ... +@overload +def prod( + a: _ArrayLikeUInt_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> uint64: ... +@overload +def prod( + a: _ArrayLikeInt_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> int64: ... +@overload +def prod( + a: _ArrayLikeFloat_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> floating[Any]: ... +@overload +def prod( + a: _ArrayLikeComplex_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> complexfloating[Any, Any]: ... +@overload +def prod( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: None = ..., + out: None = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def prod( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None = ..., + dtype: _DTypeLike[_SCT] = ..., + out: None = ..., + keepdims: Literal[False] = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _SCT: ... +@overload +def prod( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: None | DTypeLike = ..., + out: None = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def prod( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: None | DTypeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., + initial: _NumberLike_co = ..., + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +@overload +def cumprod( + a: _ArrayLikeBool_co, + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[int_]: ... +@overload +def cumprod( + a: _ArrayLikeUInt_co, + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[uint64]: ... +@overload +def cumprod( + a: _ArrayLikeInt_co, + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[int64]: ... +@overload +def cumprod( + a: _ArrayLikeFloat_co, + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[floating[Any]]: ... +@overload +def cumprod( + a: _ArrayLikeComplex_co, + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def cumprod( + a: _ArrayLikeObject_co, + axis: None | SupportsIndex = ..., + dtype: None = ..., + out: None = ..., +) -> NDArray[object_]: ... +@overload +def cumprod( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | SupportsIndex = ..., + dtype: _DTypeLike[_SCT] = ..., + out: None = ..., +) -> NDArray[_SCT]: ... +@overload +def cumprod( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | SupportsIndex = ..., + dtype: DTypeLike = ..., + out: None = ..., +) -> NDArray[Any]: ... +@overload +def cumprod( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | SupportsIndex = ..., + dtype: DTypeLike = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +def ndim(a: ArrayLike) -> int: ... + +def size(a: ArrayLike, axis: None | int = ...) -> int: ... + +@overload +def around( + a: _BoolLike_co, + decimals: SupportsIndex = ..., + out: None = ..., +) -> float16: ... +@overload +def around( + a: _SCT_uifcO, + decimals: SupportsIndex = ..., + out: None = ..., +) -> _SCT_uifcO: ... +@overload +def around( + a: _ComplexLike_co | object_, + decimals: SupportsIndex = ..., + out: None = ..., +) -> Any: ... +@overload +def around( + a: _ArrayLikeBool_co, + decimals: SupportsIndex = ..., + out: None = ..., +) -> NDArray[float16]: ... +@overload +def around( + a: _ArrayLike[_SCT_uifcO], + decimals: SupportsIndex = ..., + out: None = ..., +) -> NDArray[_SCT_uifcO]: ... +@overload +def around( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + decimals: SupportsIndex = ..., + out: None = ..., +) -> NDArray[Any]: ... +@overload +def around( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + decimals: SupportsIndex = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +@overload +def mean( + a: _ArrayLikeFloat_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> floating[Any]: ... +@overload +def mean( + a: _ArrayLikeComplex_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> complexfloating[Any, Any]: ... +@overload +def mean( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: None = ..., + out: None = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def mean( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None = ..., + dtype: _DTypeLike[_SCT] = ..., + out: None = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _SCT: ... +@overload +def mean( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: None = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def mean( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: _ArrayType = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +@overload +def std( + a: _ArrayLikeComplex_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + ddof: float = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> floating[Any]: ... +@overload +def std( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: None = ..., + out: None = ..., + ddof: float = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def std( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None = ..., + dtype: _DTypeLike[_SCT] = ..., + out: None = ..., + ddof: float = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _SCT: ... +@overload +def std( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: None = ..., + ddof: float = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def std( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: _ArrayType = ..., + ddof: float = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +@overload +def var( + a: _ArrayLikeComplex_co, + axis: None = ..., + dtype: None = ..., + out: None = ..., + ddof: float = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> floating[Any]: ... +@overload +def var( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: None = ..., + out: None = ..., + ddof: float = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def var( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None = ..., + dtype: _DTypeLike[_SCT] = ..., + out: None = ..., + ddof: float = ..., + keepdims: Literal[False] = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _SCT: ... +@overload +def var( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: None = ..., + ddof: float = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> Any: ... +@overload +def var( + a: _ArrayLikeComplex_co | _ArrayLikeObject_co, + axis: None | _ShapeLike = ..., + dtype: DTypeLike = ..., + out: _ArrayType = ..., + ddof: float = ..., + keepdims: bool = ..., + *, + where: _ArrayLikeBool_co = ..., +) -> _ArrayType: ... + +max = amax +min = amin +round = around diff --git a/venv/lib/python3.10/site-packages/numpy/core/function_base.py b/venv/lib/python3.10/site-packages/numpy/core/function_base.py new file mode 100644 index 0000000000000000000000000000000000000000..00e4e6b0ea843fc5fde7a82f16a1e4c31bb65959 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/function_base.py @@ -0,0 +1,551 @@ +import functools +import warnings +import operator +import types + +import numpy as np +from . import numeric as _nx +from .numeric import result_type, NaN, asanyarray, ndim +from numpy.core.multiarray import add_docstring +from numpy.core import overrides + +__all__ = ['logspace', 'linspace', 'geomspace'] + + +array_function_dispatch = functools.partial( + overrides.array_function_dispatch, module='numpy') + + +def _linspace_dispatcher(start, stop, num=None, endpoint=None, retstep=None, + dtype=None, axis=None): + return (start, stop) + + +@array_function_dispatch(_linspace_dispatcher) +def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, + axis=0): + """ + Return evenly spaced numbers over a specified interval. + + Returns `num` evenly spaced samples, calculated over the + interval [`start`, `stop`]. + + The endpoint of the interval can optionally be excluded. + + .. versionchanged:: 1.16.0 + Non-scalar `start` and `stop` are now supported. + + .. versionchanged:: 1.20.0 + Values are rounded towards ``-inf`` instead of ``0`` when an + integer ``dtype`` is specified. The old behavior can + still be obtained with ``np.linspace(start, stop, num).astype(int)`` + + Parameters + ---------- + start : array_like + The starting value of the sequence. + stop : array_like + The end value of the sequence, unless `endpoint` is set to False. + In that case, the sequence consists of all but the last of ``num + 1`` + evenly spaced samples, so that `stop` is excluded. Note that the step + size changes when `endpoint` is False. + num : int, optional + Number of samples to generate. Default is 50. Must be non-negative. + endpoint : bool, optional + If True, `stop` is the last sample. Otherwise, it is not included. + Default is True. + retstep : bool, optional + If True, return (`samples`, `step`), where `step` is the spacing + between samples. + dtype : dtype, optional + The type of the output array. If `dtype` is not given, the data type + is inferred from `start` and `stop`. The inferred dtype will never be + an integer; `float` is chosen even if the arguments would produce an + array of integers. + + .. versionadded:: 1.9.0 + + axis : int, optional + The axis in the result to store the samples. Relevant only if start + or stop are array-like. By default (0), the samples will be along a + new axis inserted at the beginning. Use -1 to get an axis at the end. + + .. versionadded:: 1.16.0 + + Returns + ------- + samples : ndarray + There are `num` equally spaced samples in the closed interval + ``[start, stop]`` or the half-open interval ``[start, stop)`` + (depending on whether `endpoint` is True or False). + step : float, optional + Only returned if `retstep` is True + + Size of spacing between samples. + + + See Also + -------- + arange : Similar to `linspace`, but uses a step size (instead of the + number of samples). + geomspace : Similar to `linspace`, but with numbers spaced evenly on a log + scale (a geometric progression). + logspace : Similar to `geomspace`, but with the end points specified as + logarithms. + :ref:`how-to-partition` + + Examples + -------- + >>> np.linspace(2.0, 3.0, num=5) + array([2. , 2.25, 2.5 , 2.75, 3. ]) + >>> np.linspace(2.0, 3.0, num=5, endpoint=False) + array([2. , 2.2, 2.4, 2.6, 2.8]) + >>> np.linspace(2.0, 3.0, num=5, retstep=True) + (array([2. , 2.25, 2.5 , 2.75, 3. ]), 0.25) + + Graphical illustration: + + >>> import matplotlib.pyplot as plt + >>> N = 8 + >>> y = np.zeros(N) + >>> x1 = np.linspace(0, 10, N, endpoint=True) + >>> x2 = np.linspace(0, 10, N, endpoint=False) + >>> plt.plot(x1, y, 'o') + [] + >>> plt.plot(x2, y + 0.5, 'o') + [] + >>> plt.ylim([-0.5, 1]) + (-0.5, 1) + >>> plt.show() + + """ + num = operator.index(num) + if num < 0: + raise ValueError("Number of samples, %s, must be non-negative." % num) + div = (num - 1) if endpoint else num + + # Convert float/complex array scalars to float, gh-3504 + # and make sure one can use variables that have an __array_interface__, gh-6634 + start = asanyarray(start) * 1.0 + stop = asanyarray(stop) * 1.0 + + dt = result_type(start, stop, float(num)) + if dtype is None: + dtype = dt + integer_dtype = False + else: + integer_dtype = _nx.issubdtype(dtype, _nx.integer) + + delta = stop - start + y = _nx.arange(0, num, dtype=dt).reshape((-1,) + (1,) * ndim(delta)) + # In-place multiplication y *= delta/div is faster, but prevents the multiplicant + # from overriding what class is produced, and thus prevents, e.g. use of Quantities, + # see gh-7142. Hence, we multiply in place only for standard scalar types. + if div > 0: + _mult_inplace = _nx.isscalar(delta) + step = delta / div + any_step_zero = ( + step == 0 if _mult_inplace else _nx.asanyarray(step == 0).any()) + if any_step_zero: + # Special handling for denormal numbers, gh-5437 + y /= div + if _mult_inplace: + y *= delta + else: + y = y * delta + else: + if _mult_inplace: + y *= step + else: + y = y * step + else: + # sequences with 0 items or 1 item with endpoint=True (i.e. div <= 0) + # have an undefined step + step = NaN + # Multiply with delta to allow possible override of output class. + y = y * delta + + y += start + + if endpoint and num > 1: + y[-1, ...] = stop + + if axis != 0: + y = _nx.moveaxis(y, 0, axis) + + if integer_dtype: + _nx.floor(y, out=y) + + if retstep: + return y.astype(dtype, copy=False), step + else: + return y.astype(dtype, copy=False) + + +def _logspace_dispatcher(start, stop, num=None, endpoint=None, base=None, + dtype=None, axis=None): + return (start, stop, base) + + +@array_function_dispatch(_logspace_dispatcher) +def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, + axis=0): + """ + Return numbers spaced evenly on a log scale. + + In linear space, the sequence starts at ``base ** start`` + (`base` to the power of `start`) and ends with ``base ** stop`` + (see `endpoint` below). + + .. versionchanged:: 1.16.0 + Non-scalar `start` and `stop` are now supported. + + .. versionchanged:: 1.25.0 + Non-scalar 'base` is now supported + + Parameters + ---------- + start : array_like + ``base ** start`` is the starting value of the sequence. + stop : array_like + ``base ** stop`` is the final value of the sequence, unless `endpoint` + is False. In that case, ``num + 1`` values are spaced over the + interval in log-space, of which all but the last (a sequence of + length `num`) are returned. + num : integer, optional + Number of samples to generate. Default is 50. + endpoint : boolean, optional + If true, `stop` is the last sample. Otherwise, it is not included. + Default is True. + base : array_like, optional + The base of the log space. The step size between the elements in + ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform. + Default is 10.0. + dtype : dtype + The type of the output array. If `dtype` is not given, the data type + is inferred from `start` and `stop`. The inferred type will never be + an integer; `float` is chosen even if the arguments would produce an + array of integers. + axis : int, optional + The axis in the result to store the samples. Relevant only if start, + stop, or base are array-like. By default (0), the samples will be + along a new axis inserted at the beginning. Use -1 to get an axis at + the end. + + .. versionadded:: 1.16.0 + + + Returns + ------- + samples : ndarray + `num` samples, equally spaced on a log scale. + + See Also + -------- + arange : Similar to linspace, with the step size specified instead of the + number of samples. Note that, when used with a float endpoint, the + endpoint may or may not be included. + linspace : Similar to logspace, but with the samples uniformly distributed + in linear space, instead of log space. + geomspace : Similar to logspace, but with endpoints specified directly. + :ref:`how-to-partition` + + Notes + ----- + If base is a scalar, logspace is equivalent to the code + + >>> y = np.linspace(start, stop, num=num, endpoint=endpoint) + ... # doctest: +SKIP + >>> power(base, y).astype(dtype) + ... # doctest: +SKIP + + Examples + -------- + >>> np.logspace(2.0, 3.0, num=4) + array([ 100. , 215.443469 , 464.15888336, 1000. ]) + >>> np.logspace(2.0, 3.0, num=4, endpoint=False) + array([100. , 177.827941 , 316.22776602, 562.34132519]) + >>> np.logspace(2.0, 3.0, num=4, base=2.0) + array([4. , 5.0396842 , 6.34960421, 8. ]) + >>> np.logspace(2.0, 3.0, num=4, base=[2.0, 3.0], axis=-1) + array([[ 4. , 5.0396842 , 6.34960421, 8. ], + [ 9. , 12.98024613, 18.72075441, 27. ]]) + + Graphical illustration: + + >>> import matplotlib.pyplot as plt + >>> N = 10 + >>> x1 = np.logspace(0.1, 1, N, endpoint=True) + >>> x2 = np.logspace(0.1, 1, N, endpoint=False) + >>> y = np.zeros(N) + >>> plt.plot(x1, y, 'o') + [] + >>> plt.plot(x2, y + 0.5, 'o') + [] + >>> plt.ylim([-0.5, 1]) + (-0.5, 1) + >>> plt.show() + + """ + ndmax = np.broadcast(start, stop, base).ndim + start, stop, base = ( + np.array(a, copy=False, subok=True, ndmin=ndmax) + for a in (start, stop, base) + ) + y = linspace(start, stop, num=num, endpoint=endpoint, axis=axis) + base = np.expand_dims(base, axis=axis) + if dtype is None: + return _nx.power(base, y) + return _nx.power(base, y).astype(dtype, copy=False) + + +def _geomspace_dispatcher(start, stop, num=None, endpoint=None, dtype=None, + axis=None): + return (start, stop) + + +@array_function_dispatch(_geomspace_dispatcher) +def geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0): + """ + Return numbers spaced evenly on a log scale (a geometric progression). + + This is similar to `logspace`, but with endpoints specified directly. + Each output sample is a constant multiple of the previous. + + .. versionchanged:: 1.16.0 + Non-scalar `start` and `stop` are now supported. + + Parameters + ---------- + start : array_like + The starting value of the sequence. + stop : array_like + The final value of the sequence, unless `endpoint` is False. + In that case, ``num + 1`` values are spaced over the + interval in log-space, of which all but the last (a sequence of + length `num`) are returned. + num : integer, optional + Number of samples to generate. Default is 50. + endpoint : boolean, optional + If true, `stop` is the last sample. Otherwise, it is not included. + Default is True. + dtype : dtype + The type of the output array. If `dtype` is not given, the data type + is inferred from `start` and `stop`. The inferred dtype will never be + an integer; `float` is chosen even if the arguments would produce an + array of integers. + axis : int, optional + The axis in the result to store the samples. Relevant only if start + or stop are array-like. By default (0), the samples will be along a + new axis inserted at the beginning. Use -1 to get an axis at the end. + + .. versionadded:: 1.16.0 + + Returns + ------- + samples : ndarray + `num` samples, equally spaced on a log scale. + + See Also + -------- + logspace : Similar to geomspace, but with endpoints specified using log + and base. + linspace : Similar to geomspace, but with arithmetic instead of geometric + progression. + arange : Similar to linspace, with the step size specified instead of the + number of samples. + :ref:`how-to-partition` + + Notes + ----- + If the inputs or dtype are complex, the output will follow a logarithmic + spiral in the complex plane. (There are an infinite number of spirals + passing through two points; the output will follow the shortest such path.) + + Examples + -------- + >>> np.geomspace(1, 1000, num=4) + array([ 1., 10., 100., 1000.]) + >>> np.geomspace(1, 1000, num=3, endpoint=False) + array([ 1., 10., 100.]) + >>> np.geomspace(1, 1000, num=4, endpoint=False) + array([ 1. , 5.62341325, 31.6227766 , 177.827941 ]) + >>> np.geomspace(1, 256, num=9) + array([ 1., 2., 4., 8., 16., 32., 64., 128., 256.]) + + Note that the above may not produce exact integers: + + >>> np.geomspace(1, 256, num=9, dtype=int) + array([ 1, 2, 4, 7, 16, 32, 63, 127, 256]) + >>> np.around(np.geomspace(1, 256, num=9)).astype(int) + array([ 1, 2, 4, 8, 16, 32, 64, 128, 256]) + + Negative, decreasing, and complex inputs are allowed: + + >>> np.geomspace(1000, 1, num=4) + array([1000., 100., 10., 1.]) + >>> np.geomspace(-1000, -1, num=4) + array([-1000., -100., -10., -1.]) + >>> np.geomspace(1j, 1000j, num=4) # Straight line + array([0. +1.j, 0. +10.j, 0. +100.j, 0.+1000.j]) + >>> np.geomspace(-1+0j, 1+0j, num=5) # Circle + array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j, + 6.12323400e-17+1.00000000e+00j, 7.07106781e-01+7.07106781e-01j, + 1.00000000e+00+0.00000000e+00j]) + + Graphical illustration of `endpoint` parameter: + + >>> import matplotlib.pyplot as plt + >>> N = 10 + >>> y = np.zeros(N) + >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o') + [] + >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o') + [] + >>> plt.axis([0.5, 2000, 0, 3]) + [0.5, 2000, 0, 3] + >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both') + >>> plt.show() + + """ + start = asanyarray(start) + stop = asanyarray(stop) + if _nx.any(start == 0) or _nx.any(stop == 0): + raise ValueError('Geometric sequence cannot include zero') + + dt = result_type(start, stop, float(num), _nx.zeros((), dtype)) + if dtype is None: + dtype = dt + else: + # complex to dtype('complex128'), for instance + dtype = _nx.dtype(dtype) + + # Promote both arguments to the same dtype in case, for instance, one is + # complex and another is negative and log would produce NaN otherwise. + # Copy since we may change things in-place further down. + start = start.astype(dt, copy=True) + stop = stop.astype(dt, copy=True) + + out_sign = _nx.ones(_nx.broadcast(start, stop).shape, dt) + # Avoid negligible real or imaginary parts in output by rotating to + # positive real, calculating, then undoing rotation + if _nx.issubdtype(dt, _nx.complexfloating): + all_imag = (start.real == 0.) & (stop.real == 0.) + if _nx.any(all_imag): + start[all_imag] = start[all_imag].imag + stop[all_imag] = stop[all_imag].imag + out_sign[all_imag] = 1j + + both_negative = (_nx.sign(start) == -1) & (_nx.sign(stop) == -1) + if _nx.any(both_negative): + _nx.negative(start, out=start, where=both_negative) + _nx.negative(stop, out=stop, where=both_negative) + _nx.negative(out_sign, out=out_sign, where=both_negative) + + log_start = _nx.log10(start) + log_stop = _nx.log10(stop) + result = logspace(log_start, log_stop, num=num, + endpoint=endpoint, base=10.0, dtype=dtype) + + # Make sure the endpoints match the start and stop arguments. This is + # necessary because np.exp(np.log(x)) is not necessarily equal to x. + if num > 0: + result[0] = start + if num > 1 and endpoint: + result[-1] = stop + + result = out_sign * result + + if axis != 0: + result = _nx.moveaxis(result, 0, axis) + + return result.astype(dtype, copy=False) + + +def _needs_add_docstring(obj): + """ + Returns true if the only way to set the docstring of `obj` from python is + via add_docstring. + + This function errs on the side of being overly conservative. + """ + Py_TPFLAGS_HEAPTYPE = 1 << 9 + + if isinstance(obj, (types.FunctionType, types.MethodType, property)): + return False + + if isinstance(obj, type) and obj.__flags__ & Py_TPFLAGS_HEAPTYPE: + return False + + return True + + +def _add_docstring(obj, doc, warn_on_python): + if warn_on_python and not _needs_add_docstring(obj): + warnings.warn( + "add_newdoc was used on a pure-python object {}. " + "Prefer to attach it directly to the source." + .format(obj), + UserWarning, + stacklevel=3) + try: + add_docstring(obj, doc) + except Exception: + pass + + +def add_newdoc(place, obj, doc, warn_on_python=True): + """ + Add documentation to an existing object, typically one defined in C + + The purpose is to allow easier editing of the docstrings without requiring + a re-compile. This exists primarily for internal use within numpy itself. + + Parameters + ---------- + place : str + The absolute name of the module to import from + obj : str + The name of the object to add documentation to, typically a class or + function name + doc : {str, Tuple[str, str], List[Tuple[str, str]]} + If a string, the documentation to apply to `obj` + + If a tuple, then the first element is interpreted as an attribute of + `obj` and the second as the docstring to apply - ``(method, docstring)`` + + If a list, then each element of the list should be a tuple of length + two - ``[(method1, docstring1), (method2, docstring2), ...]`` + warn_on_python : bool + If True, the default, emit `UserWarning` if this is used to attach + documentation to a pure-python object. + + Notes + ----- + This routine never raises an error if the docstring can't be written, but + will raise an error if the object being documented does not exist. + + This routine cannot modify read-only docstrings, as appear + in new-style classes or built-in functions. Because this + routine never raises an error the caller must check manually + that the docstrings were changed. + + Since this function grabs the ``char *`` from a c-level str object and puts + it into the ``tp_doc`` slot of the type of `obj`, it violates a number of + C-API best-practices, by: + + - modifying a `PyTypeObject` after calling `PyType_Ready` + - calling `Py_INCREF` on the str and losing the reference, so the str + will never be released + + If possible it should be avoided. + """ + new = getattr(__import__(place, globals(), {}, [obj]), obj) + if isinstance(doc, str): + _add_docstring(new, doc.strip(), warn_on_python) + elif isinstance(doc, tuple): + attr, docstring = doc + _add_docstring(getattr(new, attr), docstring.strip(), warn_on_python) + elif isinstance(doc, list): + for attr, docstring in doc: + _add_docstring(getattr(new, attr), docstring.strip(), warn_on_python) diff --git a/venv/lib/python3.10/site-packages/numpy/core/function_base.pyi b/venv/lib/python3.10/site-packages/numpy/core/function_base.pyi new file mode 100644 index 0000000000000000000000000000000000000000..2c2a277b1b1b0d180bc13473ce11e637fe946fdb --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/function_base.pyi @@ -0,0 +1,187 @@ +from typing import ( + Literal as L, + overload, + Any, + SupportsIndex, + TypeVar, +) + +from numpy import floating, complexfloating, generic +from numpy._typing import ( + NDArray, + DTypeLike, + _DTypeLike, + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, +) + +_SCT = TypeVar("_SCT", bound=generic) + +__all__: list[str] + +@overload +def linspace( + start: _ArrayLikeFloat_co, + stop: _ArrayLikeFloat_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[False] = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> NDArray[floating[Any]]: ... +@overload +def linspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[False] = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def linspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[False] = ..., + dtype: _DTypeLike[_SCT] = ..., + axis: SupportsIndex = ..., +) -> NDArray[_SCT]: ... +@overload +def linspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[False] = ..., + dtype: DTypeLike = ..., + axis: SupportsIndex = ..., +) -> NDArray[Any]: ... +@overload +def linspace( + start: _ArrayLikeFloat_co, + stop: _ArrayLikeFloat_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[True] = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> tuple[NDArray[floating[Any]], floating[Any]]: ... +@overload +def linspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[True] = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> tuple[NDArray[complexfloating[Any, Any]], complexfloating[Any, Any]]: ... +@overload +def linspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[True] = ..., + dtype: _DTypeLike[_SCT] = ..., + axis: SupportsIndex = ..., +) -> tuple[NDArray[_SCT], _SCT]: ... +@overload +def linspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + retstep: L[True] = ..., + dtype: DTypeLike = ..., + axis: SupportsIndex = ..., +) -> tuple[NDArray[Any], Any]: ... + +@overload +def logspace( + start: _ArrayLikeFloat_co, + stop: _ArrayLikeFloat_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + base: _ArrayLikeFloat_co = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> NDArray[floating[Any]]: ... +@overload +def logspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + base: _ArrayLikeComplex_co = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def logspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + base: _ArrayLikeComplex_co = ..., + dtype: _DTypeLike[_SCT] = ..., + axis: SupportsIndex = ..., +) -> NDArray[_SCT]: ... +@overload +def logspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + base: _ArrayLikeComplex_co = ..., + dtype: DTypeLike = ..., + axis: SupportsIndex = ..., +) -> NDArray[Any]: ... + +@overload +def geomspace( + start: _ArrayLikeFloat_co, + stop: _ArrayLikeFloat_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> NDArray[floating[Any]]: ... +@overload +def geomspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + dtype: None = ..., + axis: SupportsIndex = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def geomspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + dtype: _DTypeLike[_SCT] = ..., + axis: SupportsIndex = ..., +) -> NDArray[_SCT]: ... +@overload +def geomspace( + start: _ArrayLikeComplex_co, + stop: _ArrayLikeComplex_co, + num: SupportsIndex = ..., + endpoint: bool = ..., + dtype: DTypeLike = ..., + axis: SupportsIndex = ..., +) -> NDArray[Any]: ... + +# Re-exported to `np.lib.function_base` +def add_newdoc( + place: str, + obj: str, + doc: str | tuple[str, str] | list[tuple[str, str]], + warn_on_python: bool = ..., +) -> None: ... diff --git a/venv/lib/python3.10/site-packages/numpy/core/getlimits.py b/venv/lib/python3.10/site-packages/numpy/core/getlimits.py new file mode 100644 index 0000000000000000000000000000000000000000..13414c2a64d688aa96c9cece79bc187210e19589 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/getlimits.py @@ -0,0 +1,735 @@ +"""Machine limits for Float32 and Float64 and (long double) if available... + +""" +__all__ = ['finfo', 'iinfo'] + +import warnings + +from .._utils import set_module +from ._machar import MachAr +from . import numeric +from . import numerictypes as ntypes +from .numeric import array, inf, NaN +from .umath import log10, exp2, nextafter, isnan + + +def _fr0(a): + """fix rank-0 --> rank-1""" + if a.ndim == 0: + a = a.copy() + a.shape = (1,) + return a + + +def _fr1(a): + """fix rank > 0 --> rank-0""" + if a.size == 1: + a = a.copy() + a.shape = () + return a + + +class MachArLike: + """ Object to simulate MachAr instance """ + def __init__(self, ftype, *, eps, epsneg, huge, tiny, + ibeta, smallest_subnormal=None, **kwargs): + self.params = _MACHAR_PARAMS[ftype] + self.ftype = ftype + self.title = self.params['title'] + # Parameter types same as for discovered MachAr object. + if not smallest_subnormal: + self._smallest_subnormal = nextafter( + self.ftype(0), self.ftype(1), dtype=self.ftype) + else: + self._smallest_subnormal = smallest_subnormal + self.epsilon = self.eps = self._float_to_float(eps) + self.epsneg = self._float_to_float(epsneg) + self.xmax = self.huge = self._float_to_float(huge) + self.xmin = self._float_to_float(tiny) + self.smallest_normal = self.tiny = self._float_to_float(tiny) + self.ibeta = self.params['itype'](ibeta) + self.__dict__.update(kwargs) + self.precision = int(-log10(self.eps)) + self.resolution = self._float_to_float( + self._float_conv(10) ** (-self.precision)) + self._str_eps = self._float_to_str(self.eps) + self._str_epsneg = self._float_to_str(self.epsneg) + self._str_xmin = self._float_to_str(self.xmin) + self._str_xmax = self._float_to_str(self.xmax) + self._str_resolution = self._float_to_str(self.resolution) + self._str_smallest_normal = self._float_to_str(self.xmin) + + @property + def smallest_subnormal(self): + """Return the value for the smallest subnormal. + + Returns + ------- + smallest_subnormal : float + value for the smallest subnormal. + + Warns + ----- + UserWarning + If the calculated value for the smallest subnormal is zero. + """ + # Check that the calculated value is not zero, in case it raises a + # warning. + value = self._smallest_subnormal + if self.ftype(0) == value: + warnings.warn( + 'The value of the smallest subnormal for {} type ' + 'is zero.'.format(self.ftype), UserWarning, stacklevel=2) + + return self._float_to_float(value) + + @property + def _str_smallest_subnormal(self): + """Return the string representation of the smallest subnormal.""" + return self._float_to_str(self.smallest_subnormal) + + def _float_to_float(self, value): + """Converts float to float. + + Parameters + ---------- + value : float + value to be converted. + """ + return _fr1(self._float_conv(value)) + + def _float_conv(self, value): + """Converts float to conv. + + Parameters + ---------- + value : float + value to be converted. + """ + return array([value], self.ftype) + + def _float_to_str(self, value): + """Converts float to str. + + Parameters + ---------- + value : float + value to be converted. + """ + return self.params['fmt'] % array(_fr0(value)[0], self.ftype) + + +_convert_to_float = { + ntypes.csingle: ntypes.single, + ntypes.complex_: ntypes.float_, + ntypes.clongfloat: ntypes.longfloat + } + +# Parameters for creating MachAr / MachAr-like objects +_title_fmt = 'numpy {} precision floating point number' +_MACHAR_PARAMS = { + ntypes.double: dict( + itype = ntypes.int64, + fmt = '%24.16e', + title = _title_fmt.format('double')), + ntypes.single: dict( + itype = ntypes.int32, + fmt = '%15.7e', + title = _title_fmt.format('single')), + ntypes.longdouble: dict( + itype = ntypes.longlong, + fmt = '%s', + title = _title_fmt.format('long double')), + ntypes.half: dict( + itype = ntypes.int16, + fmt = '%12.5e', + title = _title_fmt.format('half'))} + +# Key to identify the floating point type. Key is result of +# ftype('-0.1').newbyteorder('<').tobytes() +# +# 20230201 - use (ftype(-1.0) / ftype(10.0)).newbyteorder('<').tobytes() +# instead because stold may have deficiencies on some platforms. +# See: +# https://perl5.git.perl.org/perl.git/blob/3118d7d684b56cbeb702af874f4326683c45f045:/Configure + +_KNOWN_TYPES = {} +def _register_type(machar, bytepat): + _KNOWN_TYPES[bytepat] = machar +_float_ma = {} + + +def _register_known_types(): + # Known parameters for float16 + # See docstring of MachAr class for description of parameters. + f16 = ntypes.float16 + float16_ma = MachArLike(f16, + machep=-10, + negep=-11, + minexp=-14, + maxexp=16, + it=10, + iexp=5, + ibeta=2, + irnd=5, + ngrd=0, + eps=exp2(f16(-10)), + epsneg=exp2(f16(-11)), + huge=f16(65504), + tiny=f16(2 ** -14)) + _register_type(float16_ma, b'f\xae') + _float_ma[16] = float16_ma + + # Known parameters for float32 + f32 = ntypes.float32 + float32_ma = MachArLike(f32, + machep=-23, + negep=-24, + minexp=-126, + maxexp=128, + it=23, + iexp=8, + ibeta=2, + irnd=5, + ngrd=0, + eps=exp2(f32(-23)), + epsneg=exp2(f32(-24)), + huge=f32((1 - 2 ** -24) * 2**128), + tiny=exp2(f32(-126))) + _register_type(float32_ma, b'\xcd\xcc\xcc\xbd') + _float_ma[32] = float32_ma + + # Known parameters for float64 + f64 = ntypes.float64 + epsneg_f64 = 2.0 ** -53.0 + tiny_f64 = 2.0 ** -1022.0 + float64_ma = MachArLike(f64, + machep=-52, + negep=-53, + minexp=-1022, + maxexp=1024, + it=52, + iexp=11, + ibeta=2, + irnd=5, + ngrd=0, + eps=2.0 ** -52.0, + epsneg=epsneg_f64, + huge=(1.0 - epsneg_f64) / tiny_f64 * f64(4), + tiny=tiny_f64) + _register_type(float64_ma, b'\x9a\x99\x99\x99\x99\x99\xb9\xbf') + _float_ma[64] = float64_ma + + # Known parameters for IEEE 754 128-bit binary float + ld = ntypes.longdouble + epsneg_f128 = exp2(ld(-113)) + tiny_f128 = exp2(ld(-16382)) + # Ignore runtime error when this is not f128 + with numeric.errstate(all='ignore'): + huge_f128 = (ld(1) - epsneg_f128) / tiny_f128 * ld(4) + float128_ma = MachArLike(ld, + machep=-112, + negep=-113, + minexp=-16382, + maxexp=16384, + it=112, + iexp=15, + ibeta=2, + irnd=5, + ngrd=0, + eps=exp2(ld(-112)), + epsneg=epsneg_f128, + huge=huge_f128, + tiny=tiny_f128) + # IEEE 754 128-bit binary float + _register_type(float128_ma, + b'\x9a\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\xfb\xbf') + _float_ma[128] = float128_ma + + # Known parameters for float80 (Intel 80-bit extended precision) + epsneg_f80 = exp2(ld(-64)) + tiny_f80 = exp2(ld(-16382)) + # Ignore runtime error when this is not f80 + with numeric.errstate(all='ignore'): + huge_f80 = (ld(1) - epsneg_f80) / tiny_f80 * ld(4) + float80_ma = MachArLike(ld, + machep=-63, + negep=-64, + minexp=-16382, + maxexp=16384, + it=63, + iexp=15, + ibeta=2, + irnd=5, + ngrd=0, + eps=exp2(ld(-63)), + epsneg=epsneg_f80, + huge=huge_f80, + tiny=tiny_f80) + # float80, first 10 bytes containing actual storage + _register_type(float80_ma, b'\xcd\xcc\xcc\xcc\xcc\xcc\xcc\xcc\xfb\xbf') + _float_ma[80] = float80_ma + + # Guessed / known parameters for double double; see: + # https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format#Double-double_arithmetic + # These numbers have the same exponent range as float64, but extended number of + # digits in the significand. + huge_dd = nextafter(ld(inf), ld(0), dtype=ld) + # As the smallest_normal in double double is so hard to calculate we set + # it to NaN. + smallest_normal_dd = NaN + # Leave the same value for the smallest subnormal as double + smallest_subnormal_dd = ld(nextafter(0., 1.)) + float_dd_ma = MachArLike(ld, + machep=-105, + negep=-106, + minexp=-1022, + maxexp=1024, + it=105, + iexp=11, + ibeta=2, + irnd=5, + ngrd=0, + eps=exp2(ld(-105)), + epsneg=exp2(ld(-106)), + huge=huge_dd, + tiny=smallest_normal_dd, + smallest_subnormal=smallest_subnormal_dd) + # double double; low, high order (e.g. PPC 64) + _register_type(float_dd_ma, + b'\x9a\x99\x99\x99\x99\x99Y<\x9a\x99\x99\x99\x99\x99\xb9\xbf') + # double double; high, low order (e.g. PPC 64 le) + _register_type(float_dd_ma, + b'\x9a\x99\x99\x99\x99\x99\xb9\xbf\x9a\x99\x99\x99\x99\x99Y<') + _float_ma['dd'] = float_dd_ma + + +def _get_machar(ftype): + """ Get MachAr instance or MachAr-like instance + + Get parameters for floating point type, by first trying signatures of + various known floating point types, then, if none match, attempting to + identify parameters by analysis. + + Parameters + ---------- + ftype : class + Numpy floating point type class (e.g. ``np.float64``) + + Returns + ------- + ma_like : instance of :class:`MachAr` or :class:`MachArLike` + Object giving floating point parameters for `ftype`. + + Warns + ----- + UserWarning + If the binary signature of the float type is not in the dictionary of + known float types. + """ + params = _MACHAR_PARAMS.get(ftype) + if params is None: + raise ValueError(repr(ftype)) + # Detect known / suspected types + # ftype(-1.0) / ftype(10.0) is better than ftype('-0.1') because stold + # may be deficient + key = (ftype(-1.0) / ftype(10.)).newbyteorder('<').tobytes() + ma_like = None + if ftype == ntypes.longdouble: + # Could be 80 bit == 10 byte extended precision, where last bytes can + # be random garbage. + # Comparing first 10 bytes to pattern first to avoid branching on the + # random garbage. + ma_like = _KNOWN_TYPES.get(key[:10]) + if ma_like is None: + # see if the full key is known. + ma_like = _KNOWN_TYPES.get(key) + if ma_like is None and len(key) == 16: + # machine limits could be f80 masquerading as np.float128, + # find all keys with length 16 and make new dict, but make the keys + # only 10 bytes long, the last bytes can be random garbage + _kt = {k[:10]: v for k, v in _KNOWN_TYPES.items() if len(k) == 16} + ma_like = _kt.get(key[:10]) + if ma_like is not None: + return ma_like + # Fall back to parameter discovery + warnings.warn( + f'Signature {key} for {ftype} does not match any known type: ' + 'falling back to type probe function.\n' + 'This warnings indicates broken support for the dtype!', + UserWarning, stacklevel=2) + return _discovered_machar(ftype) + + +def _discovered_machar(ftype): + """ Create MachAr instance with found information on float types + + TODO: MachAr should be retired completely ideally. We currently only + ever use it system with broken longdouble (valgrind, WSL). + """ + params = _MACHAR_PARAMS[ftype] + return MachAr(lambda v: array([v], ftype), + lambda v:_fr0(v.astype(params['itype']))[0], + lambda v:array(_fr0(v)[0], ftype), + lambda v: params['fmt'] % array(_fr0(v)[0], ftype), + params['title']) + + +@set_module('numpy') +class finfo: + """ + finfo(dtype) + + Machine limits for floating point types. + + Attributes + ---------- + bits : int + The number of bits occupied by the type. + dtype : dtype + Returns the dtype for which `finfo` returns information. For complex + input, the returned dtype is the associated ``float*`` dtype for its + real and complex components. + eps : float + The difference between 1.0 and the next smallest representable float + larger than 1.0. For example, for 64-bit binary floats in the IEEE-754 + standard, ``eps = 2**-52``, approximately 2.22e-16. + epsneg : float + The difference between 1.0 and the next smallest representable float + less than 1.0. For example, for 64-bit binary floats in the IEEE-754 + standard, ``epsneg = 2**-53``, approximately 1.11e-16. + iexp : int + The number of bits in the exponent portion of the floating point + representation. + machep : int + The exponent that yields `eps`. + max : floating point number of the appropriate type + The largest representable number. + maxexp : int + The smallest positive power of the base (2) that causes overflow. + min : floating point number of the appropriate type + The smallest representable number, typically ``-max``. + minexp : int + The most negative power of the base (2) consistent with there + being no leading 0's in the mantissa. + negep : int + The exponent that yields `epsneg`. + nexp : int + The number of bits in the exponent including its sign and bias. + nmant : int + The number of bits in the mantissa. + precision : int + The approximate number of decimal digits to which this kind of + float is precise. + resolution : floating point number of the appropriate type + The approximate decimal resolution of this type, i.e., + ``10**-precision``. + tiny : float + An alias for `smallest_normal`, kept for backwards compatibility. + smallest_normal : float + The smallest positive floating point number with 1 as leading bit in + the mantissa following IEEE-754 (see Notes). + smallest_subnormal : float + The smallest positive floating point number with 0 as leading bit in + the mantissa following IEEE-754. + + Parameters + ---------- + dtype : float, dtype, or instance + Kind of floating point or complex floating point + data-type about which to get information. + + See Also + -------- + iinfo : The equivalent for integer data types. + spacing : The distance between a value and the nearest adjacent number + nextafter : The next floating point value after x1 towards x2 + + Notes + ----- + For developers of NumPy: do not instantiate this at the module level. + The initial calculation of these parameters is expensive and negatively + impacts import times. These objects are cached, so calling ``finfo()`` + repeatedly inside your functions is not a problem. + + Note that ``smallest_normal`` is not actually the smallest positive + representable value in a NumPy floating point type. As in the IEEE-754 + standard [1]_, NumPy floating point types make use of subnormal numbers to + fill the gap between 0 and ``smallest_normal``. However, subnormal numbers + may have significantly reduced precision [2]_. + + This function can also be used for complex data types as well. If used, + the output will be the same as the corresponding real float type + (e.g. numpy.finfo(numpy.csingle) is the same as numpy.finfo(numpy.single)). + However, the output is true for the real and imaginary components. + + References + ---------- + .. [1] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008, + pp.1-70, 2008, http://www.doi.org/10.1109/IEEESTD.2008.4610935 + .. [2] Wikipedia, "Denormal Numbers", + https://en.wikipedia.org/wiki/Denormal_number + + Examples + -------- + >>> np.finfo(np.float64).dtype + dtype('float64') + >>> np.finfo(np.complex64).dtype + dtype('float32') + + """ + + _finfo_cache = {} + + def __new__(cls, dtype): + try: + obj = cls._finfo_cache.get(dtype) # most common path + if obj is not None: + return obj + except TypeError: + pass + + if dtype is None: + # Deprecated in NumPy 1.25, 2023-01-16 + warnings.warn( + "finfo() dtype cannot be None. This behavior will " + "raise an error in the future. (Deprecated in NumPy 1.25)", + DeprecationWarning, + stacklevel=2 + ) + + try: + dtype = numeric.dtype(dtype) + except TypeError: + # In case a float instance was given + dtype = numeric.dtype(type(dtype)) + + obj = cls._finfo_cache.get(dtype) + if obj is not None: + return obj + dtypes = [dtype] + newdtype = numeric.obj2sctype(dtype) + if newdtype is not dtype: + dtypes.append(newdtype) + dtype = newdtype + if not issubclass(dtype, numeric.inexact): + raise ValueError("data type %r not inexact" % (dtype)) + obj = cls._finfo_cache.get(dtype) + if obj is not None: + return obj + if not issubclass(dtype, numeric.floating): + newdtype = _convert_to_float[dtype] + if newdtype is not dtype: + # dtype changed, for example from complex128 to float64 + dtypes.append(newdtype) + dtype = newdtype + + obj = cls._finfo_cache.get(dtype, None) + if obj is not None: + # the original dtype was not in the cache, but the new + # dtype is in the cache. we add the original dtypes to + # the cache and return the result + for dt in dtypes: + cls._finfo_cache[dt] = obj + return obj + obj = object.__new__(cls)._init(dtype) + for dt in dtypes: + cls._finfo_cache[dt] = obj + return obj + + def _init(self, dtype): + self.dtype = numeric.dtype(dtype) + machar = _get_machar(dtype) + + for word in ['precision', 'iexp', + 'maxexp', 'minexp', 'negep', + 'machep']: + setattr(self, word, getattr(machar, word)) + for word in ['resolution', 'epsneg', 'smallest_subnormal']: + setattr(self, word, getattr(machar, word).flat[0]) + self.bits = self.dtype.itemsize * 8 + self.max = machar.huge.flat[0] + self.min = -self.max + self.eps = machar.eps.flat[0] + self.nexp = machar.iexp + self.nmant = machar.it + self._machar = machar + self._str_tiny = machar._str_xmin.strip() + self._str_max = machar._str_xmax.strip() + self._str_epsneg = machar._str_epsneg.strip() + self._str_eps = machar._str_eps.strip() + self._str_resolution = machar._str_resolution.strip() + self._str_smallest_normal = machar._str_smallest_normal.strip() + self._str_smallest_subnormal = machar._str_smallest_subnormal.strip() + return self + + def __str__(self): + fmt = ( + 'Machine parameters for %(dtype)s\n' + '---------------------------------------------------------------\n' + 'precision = %(precision)3s resolution = %(_str_resolution)s\n' + 'machep = %(machep)6s eps = %(_str_eps)s\n' + 'negep = %(negep)6s epsneg = %(_str_epsneg)s\n' + 'minexp = %(minexp)6s tiny = %(_str_tiny)s\n' + 'maxexp = %(maxexp)6s max = %(_str_max)s\n' + 'nexp = %(nexp)6s min = -max\n' + 'smallest_normal = %(_str_smallest_normal)s ' + 'smallest_subnormal = %(_str_smallest_subnormal)s\n' + '---------------------------------------------------------------\n' + ) + return fmt % self.__dict__ + + def __repr__(self): + c = self.__class__.__name__ + d = self.__dict__.copy() + d['klass'] = c + return (("%(klass)s(resolution=%(resolution)s, min=-%(_str_max)s," + " max=%(_str_max)s, dtype=%(dtype)s)") % d) + + @property + def smallest_normal(self): + """Return the value for the smallest normal. + + Returns + ------- + smallest_normal : float + Value for the smallest normal. + + Warns + ----- + UserWarning + If the calculated value for the smallest normal is requested for + double-double. + """ + # This check is necessary because the value for smallest_normal is + # platform dependent for longdouble types. + if isnan(self._machar.smallest_normal.flat[0]): + warnings.warn( + 'The value of smallest normal is undefined for double double', + UserWarning, stacklevel=2) + return self._machar.smallest_normal.flat[0] + + @property + def tiny(self): + """Return the value for tiny, alias of smallest_normal. + + Returns + ------- + tiny : float + Value for the smallest normal, alias of smallest_normal. + + Warns + ----- + UserWarning + If the calculated value for the smallest normal is requested for + double-double. + """ + return self.smallest_normal + + +@set_module('numpy') +class iinfo: + """ + iinfo(type) + + Machine limits for integer types. + + Attributes + ---------- + bits : int + The number of bits occupied by the type. + dtype : dtype + Returns the dtype for which `iinfo` returns information. + min : int + The smallest integer expressible by the type. + max : int + The largest integer expressible by the type. + + Parameters + ---------- + int_type : integer type, dtype, or instance + The kind of integer data type to get information about. + + See Also + -------- + finfo : The equivalent for floating point data types. + + Examples + -------- + With types: + + >>> ii16 = np.iinfo(np.int16) + >>> ii16.min + -32768 + >>> ii16.max + 32767 + >>> ii32 = np.iinfo(np.int32) + >>> ii32.min + -2147483648 + >>> ii32.max + 2147483647 + + With instances: + + >>> ii32 = np.iinfo(np.int32(10)) + >>> ii32.min + -2147483648 + >>> ii32.max + 2147483647 + + """ + + _min_vals = {} + _max_vals = {} + + def __init__(self, int_type): + try: + self.dtype = numeric.dtype(int_type) + except TypeError: + self.dtype = numeric.dtype(type(int_type)) + self.kind = self.dtype.kind + self.bits = self.dtype.itemsize * 8 + self.key = "%s%d" % (self.kind, self.bits) + if self.kind not in 'iu': + raise ValueError("Invalid integer data type %r." % (self.kind,)) + + @property + def min(self): + """Minimum value of given dtype.""" + if self.kind == 'u': + return 0 + else: + try: + val = iinfo._min_vals[self.key] + except KeyError: + val = int(-(1 << (self.bits-1))) + iinfo._min_vals[self.key] = val + return val + + @property + def max(self): + """Maximum value of given dtype.""" + try: + val = iinfo._max_vals[self.key] + except KeyError: + if self.kind == 'u': + val = int((1 << self.bits) - 1) + else: + val = int((1 << (self.bits-1)) - 1) + iinfo._max_vals[self.key] = val + return val + + def __str__(self): + """String representation.""" + fmt = ( + 'Machine parameters for %(dtype)s\n' + '---------------------------------------------------------------\n' + 'min = %(min)s\n' + 'max = %(max)s\n' + '---------------------------------------------------------------\n' + ) + return fmt % {'dtype': self.dtype, 'min': self.min, 'max': self.max} + + def __repr__(self): + return "%s(min=%s, max=%s, dtype=%s)" % (self.__class__.__name__, + self.min, self.max, self.dtype) diff --git a/venv/lib/python3.10/site-packages/numpy/core/getlimits.pyi b/venv/lib/python3.10/site-packages/numpy/core/getlimits.pyi new file mode 100644 index 0000000000000000000000000000000000000000..da5e3c23ea724bfeca0d83ff2550febe1aade2f0 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/getlimits.pyi @@ -0,0 +1,6 @@ +from numpy import ( + finfo as finfo, + iinfo as iinfo, +) + +__all__: list[str] diff --git a/venv/lib/python3.10/site-packages/numpy/core/lib/libnpymath.a b/venv/lib/python3.10/site-packages/numpy/core/lib/libnpymath.a new file mode 100644 index 0000000000000000000000000000000000000000..96a955e032495a2f05c094967ca015d489ea6457 Binary files /dev/null and b/venv/lib/python3.10/site-packages/numpy/core/lib/libnpymath.a differ diff --git a/venv/lib/python3.10/site-packages/numpy/core/lib/npy-pkg-config/mlib.ini b/venv/lib/python3.10/site-packages/numpy/core/lib/npy-pkg-config/mlib.ini new file mode 100644 index 0000000000000000000000000000000000000000..5840f5e1bc167f50ebc9fc98d60b60ee21ecbeec --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/lib/npy-pkg-config/mlib.ini @@ -0,0 +1,12 @@ +[meta] +Name = mlib +Description = Math library used with this version of numpy +Version = 1.0 + +[default] +Libs=-lm +Cflags= + +[msvc] +Libs=m.lib +Cflags= diff --git a/venv/lib/python3.10/site-packages/numpy/core/lib/npy-pkg-config/npymath.ini b/venv/lib/python3.10/site-packages/numpy/core/lib/npy-pkg-config/npymath.ini new file mode 100644 index 0000000000000000000000000000000000000000..3e465ad2aceafd52f512d279e0de93e271e330b0 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/lib/npy-pkg-config/npymath.ini @@ -0,0 +1,20 @@ +[meta] +Name=npymath +Description=Portable, core math library implementing C99 standard +Version=0.1 + +[variables] +pkgname=numpy.core +prefix=${pkgdir} +libdir=${prefix}/lib +includedir=${prefix}/include + +[default] +Libs=-L${libdir} -lnpymath +Cflags=-I${includedir} +Requires=mlib + +[msvc] +Libs=/LIBPATH:${libdir} npymath.lib +Cflags=/INCLUDE:${includedir} +Requires=mlib diff --git a/venv/lib/python3.10/site-packages/numpy/core/memmap.pyi b/venv/lib/python3.10/site-packages/numpy/core/memmap.pyi new file mode 100644 index 0000000000000000000000000000000000000000..03c6b772dcd52c87bb958329f5acecd0ed8c1092 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/memmap.pyi @@ -0,0 +1,3 @@ +from numpy import memmap as memmap + +__all__: list[str] diff --git a/venv/lib/python3.10/site-packages/numpy/core/multiarray.py b/venv/lib/python3.10/site-packages/numpy/core/multiarray.py new file mode 100644 index 0000000000000000000000000000000000000000..d11283345952d4302ee67bcb700cd325854f6414 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/multiarray.py @@ -0,0 +1,1715 @@ +""" +Create the numpy.core.multiarray namespace for backward compatibility. In v1.16 +the multiarray and umath c-extension modules were merged into a single +_multiarray_umath extension module. So we replicate the old namespace +by importing from the extension module. + +""" + +import functools +from . import overrides +from . import _multiarray_umath +from ._multiarray_umath import * # noqa: F403 +# These imports are needed for backward compatibility, +# do not change them. issue gh-15518 +# _get_ndarray_c_version is semi-public, on purpose not added to __all__ +from ._multiarray_umath import ( + fastCopyAndTranspose, _flagdict, from_dlpack, _place, _reconstruct, + _vec_string, _ARRAY_API, _monotonicity, _get_ndarray_c_version, + _get_madvise_hugepage, _set_madvise_hugepage, + _get_promotion_state, _set_promotion_state, _using_numpy2_behavior + ) + +__all__ = [ + '_ARRAY_API', 'ALLOW_THREADS', 'BUFSIZE', 'CLIP', 'DATETIMEUNITS', + 'ITEM_HASOBJECT', 'ITEM_IS_POINTER', 'LIST_PICKLE', 'MAXDIMS', + 'MAY_SHARE_BOUNDS', 'MAY_SHARE_EXACT', 'NEEDS_INIT', 'NEEDS_PYAPI', + 'RAISE', 'USE_GETITEM', 'USE_SETITEM', 'WRAP', + '_flagdict', 'from_dlpack', '_place', '_reconstruct', '_vec_string', + '_monotonicity', 'add_docstring', 'arange', 'array', 'asarray', + 'asanyarray', 'ascontiguousarray', 'asfortranarray', 'bincount', + 'broadcast', 'busday_count', 'busday_offset', 'busdaycalendar', 'can_cast', + 'compare_chararrays', 'concatenate', 'copyto', 'correlate', 'correlate2', + 'count_nonzero', 'c_einsum', 'datetime_as_string', 'datetime_data', + 'dot', 'dragon4_positional', 'dragon4_scientific', 'dtype', + 'empty', 'empty_like', 'error', 'flagsobj', 'flatiter', 'format_longfloat', + 'frombuffer', 'fromfile', 'fromiter', 'fromstring', + 'get_handler_name', 'get_handler_version', 'inner', 'interp', + 'interp_complex', 'is_busday', 'lexsort', 'matmul', 'may_share_memory', + 'min_scalar_type', 'ndarray', 'nditer', 'nested_iters', + 'normalize_axis_index', 'packbits', 'promote_types', 'putmask', + 'ravel_multi_index', 'result_type', 'scalar', 'set_datetimeparse_function', + 'set_legacy_print_mode', 'set_numeric_ops', 'set_string_function', + 'set_typeDict', 'shares_memory', 'tracemalloc_domain', 'typeinfo', + 'unpackbits', 'unravel_index', 'vdot', 'where', 'zeros', + '_get_promotion_state', '_set_promotion_state', '_using_numpy2_behavior'] + +# For backward compatibility, make sure pickle imports these functions from here +_reconstruct.__module__ = 'numpy.core.multiarray' +scalar.__module__ = 'numpy.core.multiarray' + + +from_dlpack.__module__ = 'numpy' +arange.__module__ = 'numpy' +array.__module__ = 'numpy' +asarray.__module__ = 'numpy' +asanyarray.__module__ = 'numpy' +ascontiguousarray.__module__ = 'numpy' +asfortranarray.__module__ = 'numpy' +datetime_data.__module__ = 'numpy' +empty.__module__ = 'numpy' +frombuffer.__module__ = 'numpy' +fromfile.__module__ = 'numpy' +fromiter.__module__ = 'numpy' +frompyfunc.__module__ = 'numpy' +fromstring.__module__ = 'numpy' +geterrobj.__module__ = 'numpy' +may_share_memory.__module__ = 'numpy' +nested_iters.__module__ = 'numpy' +promote_types.__module__ = 'numpy' +set_numeric_ops.__module__ = 'numpy' +seterrobj.__module__ = 'numpy' +zeros.__module__ = 'numpy' +_get_promotion_state.__module__ = 'numpy' +_set_promotion_state.__module__ = 'numpy' +_using_numpy2_behavior.__module__ = 'numpy' + + +# We can't verify dispatcher signatures because NumPy's C functions don't +# support introspection. +array_function_from_c_func_and_dispatcher = functools.partial( + overrides.array_function_from_dispatcher, + module='numpy', docs_from_dispatcher=True, verify=False) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.empty_like) +def empty_like(prototype, dtype=None, order=None, subok=None, shape=None): + """ + empty_like(prototype, dtype=None, order='K', subok=True, shape=None) + + Return a new array with the same shape and type as a given array. + + Parameters + ---------- + prototype : array_like + The shape and data-type of `prototype` define these same attributes + of the returned array. + dtype : data-type, optional + Overrides the data type of the result. + + .. versionadded:: 1.6.0 + order : {'C', 'F', 'A', or 'K'}, optional + Overrides the memory layout of the result. 'C' means C-order, + 'F' means F-order, 'A' means 'F' if `prototype` is Fortran + contiguous, 'C' otherwise. 'K' means match the layout of `prototype` + as closely as possible. + + .. versionadded:: 1.6.0 + subok : bool, optional. + If True, then the newly created array will use the sub-class + type of `prototype`, otherwise it will be a base-class array. Defaults + to True. + shape : int or sequence of ints, optional. + Overrides the shape of the result. If order='K' and the number of + dimensions is unchanged, will try to keep order, otherwise, + order='C' is implied. + + .. versionadded:: 1.17.0 + + Returns + ------- + out : ndarray + Array of uninitialized (arbitrary) data with the same + shape and type as `prototype`. + + See Also + -------- + ones_like : Return an array of ones with shape and type of input. + zeros_like : Return an array of zeros with shape and type of input. + full_like : Return a new array with shape of input filled with value. + empty : Return a new uninitialized array. + + Notes + ----- + This function does *not* initialize the returned array; to do that use + `zeros_like` or `ones_like` instead. It may be marginally faster than + the functions that do set the array values. + + Examples + -------- + >>> a = ([1,2,3], [4,5,6]) # a is array-like + >>> np.empty_like(a) + array([[-1073741821, -1073741821, 3], # uninitialized + [ 0, 0, -1073741821]]) + >>> a = np.array([[1., 2., 3.],[4.,5.,6.]]) + >>> np.empty_like(a) + array([[ -2.00000715e+000, 1.48219694e-323, -2.00000572e+000], # uninitialized + [ 4.38791518e-305, -2.00000715e+000, 4.17269252e-309]]) + + """ + return (prototype,) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.concatenate) +def concatenate(arrays, axis=None, out=None, *, dtype=None, casting=None): + """ + concatenate((a1, a2, ...), axis=0, out=None, dtype=None, casting="same_kind") + + Join a sequence of arrays along an existing axis. + + Parameters + ---------- + a1, a2, ... : sequence of array_like + The arrays must have the same shape, except in the dimension + corresponding to `axis` (the first, by default). + axis : int, optional + The axis along which the arrays will be joined. If axis is None, + arrays are flattened before use. Default is 0. + out : ndarray, optional + If provided, the destination to place the result. The shape must be + correct, matching that of what concatenate would have returned if no + out argument were specified. + dtype : str or dtype + If provided, the destination array will have this dtype. Cannot be + provided together with `out`. + + .. versionadded:: 1.20.0 + + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. Defaults to 'same_kind'. + + .. versionadded:: 1.20.0 + + Returns + ------- + res : ndarray + The concatenated array. + + See Also + -------- + ma.concatenate : Concatenate function that preserves input masks. + array_split : Split an array into multiple sub-arrays of equal or + near-equal size. + split : Split array into a list of multiple sub-arrays of equal size. + hsplit : Split array into multiple sub-arrays horizontally (column wise). + vsplit : Split array into multiple sub-arrays vertically (row wise). + dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). + stack : Stack a sequence of arrays along a new axis. + block : Assemble arrays from blocks. + hstack : Stack arrays in sequence horizontally (column wise). + vstack : Stack arrays in sequence vertically (row wise). + dstack : Stack arrays in sequence depth wise (along third dimension). + column_stack : Stack 1-D arrays as columns into a 2-D array. + + Notes + ----- + When one or more of the arrays to be concatenated is a MaskedArray, + this function will return a MaskedArray object instead of an ndarray, + but the input masks are *not* preserved. In cases where a MaskedArray + is expected as input, use the ma.concatenate function from the masked + array module instead. + + Examples + -------- + >>> a = np.array([[1, 2], [3, 4]]) + >>> b = np.array([[5, 6]]) + >>> np.concatenate((a, b), axis=0) + array([[1, 2], + [3, 4], + [5, 6]]) + >>> np.concatenate((a, b.T), axis=1) + array([[1, 2, 5], + [3, 4, 6]]) + >>> np.concatenate((a, b), axis=None) + array([1, 2, 3, 4, 5, 6]) + + This function will not preserve masking of MaskedArray inputs. + + >>> a = np.ma.arange(3) + >>> a[1] = np.ma.masked + >>> b = np.arange(2, 5) + >>> a + masked_array(data=[0, --, 2], + mask=[False, True, False], + fill_value=999999) + >>> b + array([2, 3, 4]) + >>> np.concatenate([a, b]) + masked_array(data=[0, 1, 2, 2, 3, 4], + mask=False, + fill_value=999999) + >>> np.ma.concatenate([a, b]) + masked_array(data=[0, --, 2, 2, 3, 4], + mask=[False, True, False, False, False, False], + fill_value=999999) + + """ + if out is not None: + # optimize for the typical case where only arrays is provided + arrays = list(arrays) + arrays.append(out) + return arrays + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.inner) +def inner(a, b): + """ + inner(a, b, /) + + Inner product of two arrays. + + Ordinary inner product of vectors for 1-D arrays (without complex + conjugation), in higher dimensions a sum product over the last axes. + + Parameters + ---------- + a, b : array_like + If `a` and `b` are nonscalar, their last dimensions must match. + + Returns + ------- + out : ndarray + If `a` and `b` are both + scalars or both 1-D arrays then a scalar is returned; otherwise + an array is returned. + ``out.shape = (*a.shape[:-1], *b.shape[:-1])`` + + Raises + ------ + ValueError + If both `a` and `b` are nonscalar and their last dimensions have + different sizes. + + See Also + -------- + tensordot : Sum products over arbitrary axes. + dot : Generalised matrix product, using second last dimension of `b`. + einsum : Einstein summation convention. + + Notes + ----- + For vectors (1-D arrays) it computes the ordinary inner-product:: + + np.inner(a, b) = sum(a[:]*b[:]) + + More generally, if ``ndim(a) = r > 0`` and ``ndim(b) = s > 0``:: + + np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1)) + + or explicitly:: + + np.inner(a, b)[i0,...,ir-2,j0,...,js-2] + = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:]) + + In addition `a` or `b` may be scalars, in which case:: + + np.inner(a,b) = a*b + + Examples + -------- + Ordinary inner product for vectors: + + >>> a = np.array([1,2,3]) + >>> b = np.array([0,1,0]) + >>> np.inner(a, b) + 2 + + Some multidimensional examples: + + >>> a = np.arange(24).reshape((2,3,4)) + >>> b = np.arange(4) + >>> c = np.inner(a, b) + >>> c.shape + (2, 3) + >>> c + array([[ 14, 38, 62], + [ 86, 110, 134]]) + + >>> a = np.arange(2).reshape((1,1,2)) + >>> b = np.arange(6).reshape((3,2)) + >>> c = np.inner(a, b) + >>> c.shape + (1, 1, 3) + >>> c + array([[[1, 3, 5]]]) + + An example where `b` is a scalar: + + >>> np.inner(np.eye(2), 7) + array([[7., 0.], + [0., 7.]]) + + """ + return (a, b) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.where) +def where(condition, x=None, y=None): + """ + where(condition, [x, y], /) + + Return elements chosen from `x` or `y` depending on `condition`. + + .. note:: + When only `condition` is provided, this function is a shorthand for + ``np.asarray(condition).nonzero()``. Using `nonzero` directly should be + preferred, as it behaves correctly for subclasses. The rest of this + documentation covers only the case where all three arguments are + provided. + + Parameters + ---------- + condition : array_like, bool + Where True, yield `x`, otherwise yield `y`. + x, y : array_like + Values from which to choose. `x`, `y` and `condition` need to be + broadcastable to some shape. + + Returns + ------- + out : ndarray + An array with elements from `x` where `condition` is True, and elements + from `y` elsewhere. + + See Also + -------- + choose + nonzero : The function that is called when x and y are omitted + + Notes + ----- + If all the arrays are 1-D, `where` is equivalent to:: + + [xv if c else yv + for c, xv, yv in zip(condition, x, y)] + + Examples + -------- + >>> a = np.arange(10) + >>> a + array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) + >>> np.where(a < 5, a, 10*a) + array([ 0, 1, 2, 3, 4, 50, 60, 70, 80, 90]) + + This can be used on multidimensional arrays too: + + >>> np.where([[True, False], [True, True]], + ... [[1, 2], [3, 4]], + ... [[9, 8], [7, 6]]) + array([[1, 8], + [3, 4]]) + + The shapes of x, y, and the condition are broadcast together: + + >>> x, y = np.ogrid[:3, :4] + >>> np.where(x < y, x, 10 + y) # both x and 10+y are broadcast + array([[10, 0, 0, 0], + [10, 11, 1, 1], + [10, 11, 12, 2]]) + + >>> a = np.array([[0, 1, 2], + ... [0, 2, 4], + ... [0, 3, 6]]) + >>> np.where(a < 4, a, -1) # -1 is broadcast + array([[ 0, 1, 2], + [ 0, 2, -1], + [ 0, 3, -1]]) + """ + return (condition, x, y) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.lexsort) +def lexsort(keys, axis=None): + """ + lexsort(keys, axis=-1) + + Perform an indirect stable sort using a sequence of keys. + + Given multiple sorting keys, which can be interpreted as columns in a + spreadsheet, lexsort returns an array of integer indices that describes + the sort order by multiple columns. The last key in the sequence is used + for the primary sort order, the second-to-last key for the secondary sort + order, and so on. The keys argument must be a sequence of objects that + can be converted to arrays of the same shape. If a 2D array is provided + for the keys argument, its rows are interpreted as the sorting keys and + sorting is according to the last row, second last row etc. + + Parameters + ---------- + keys : (k, N) array or tuple containing k (N,)-shaped sequences + The `k` different "columns" to be sorted. The last column (or row if + `keys` is a 2D array) is the primary sort key. + axis : int, optional + Axis to be indirectly sorted. By default, sort over the last axis. + + Returns + ------- + indices : (N,) ndarray of ints + Array of indices that sort the keys along the specified axis. + + See Also + -------- + argsort : Indirect sort. + ndarray.sort : In-place sort. + sort : Return a sorted copy of an array. + + Examples + -------- + Sort names: first by surname, then by name. + + >>> surnames = ('Hertz', 'Galilei', 'Hertz') + >>> first_names = ('Heinrich', 'Galileo', 'Gustav') + >>> ind = np.lexsort((first_names, surnames)) + >>> ind + array([1, 2, 0]) + + >>> [surnames[i] + ", " + first_names[i] for i in ind] + ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich'] + + Sort two columns of numbers: + + >>> a = [1,5,1,4,3,4,4] # First column + >>> b = [9,4,0,4,0,2,1] # Second column + >>> ind = np.lexsort((b,a)) # Sort by a, then by b + >>> ind + array([2, 0, 4, 6, 5, 3, 1]) + + >>> [(a[i],b[i]) for i in ind] + [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)] + + Note that sorting is first according to the elements of ``a``. + Secondary sorting is according to the elements of ``b``. + + A normal ``argsort`` would have yielded: + + >>> [(a[i],b[i]) for i in np.argsort(a)] + [(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)] + + Structured arrays are sorted lexically by ``argsort``: + + >>> x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)], + ... dtype=np.dtype([('x', int), ('y', int)])) + + >>> np.argsort(x) # or np.argsort(x, order=('x', 'y')) + array([2, 0, 4, 6, 5, 3, 1]) + + """ + if isinstance(keys, tuple): + return keys + else: + return (keys,) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.can_cast) +def can_cast(from_, to, casting=None): + """ + can_cast(from_, to, casting='safe') + + Returns True if cast between data types can occur according to the + casting rule. If from is a scalar or array scalar, also returns + True if the scalar value can be cast without overflow or truncation + to an integer. + + Parameters + ---------- + from_ : dtype, dtype specifier, scalar, or array + Data type, scalar, or array to cast from. + to : dtype or dtype specifier + Data type to cast to. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. + + * 'no' means the data types should not be cast at all. + * 'equiv' means only byte-order changes are allowed. + * 'safe' means only casts which can preserve values are allowed. + * 'same_kind' means only safe casts or casts within a kind, + like float64 to float32, are allowed. + * 'unsafe' means any data conversions may be done. + + Returns + ------- + out : bool + True if cast can occur according to the casting rule. + + Notes + ----- + .. versionchanged:: 1.17.0 + Casting between a simple data type and a structured one is possible only + for "unsafe" casting. Casting to multiple fields is allowed, but + casting from multiple fields is not. + + .. versionchanged:: 1.9.0 + Casting from numeric to string types in 'safe' casting mode requires + that the string dtype length is long enough to store the maximum + integer/float value converted. + + See also + -------- + dtype, result_type + + Examples + -------- + Basic examples + + >>> np.can_cast(np.int32, np.int64) + True + >>> np.can_cast(np.float64, complex) + True + >>> np.can_cast(complex, float) + False + + >>> np.can_cast('i8', 'f8') + True + >>> np.can_cast('i8', 'f4') + False + >>> np.can_cast('i4', 'S4') + False + + Casting scalars + + >>> np.can_cast(100, 'i1') + True + >>> np.can_cast(150, 'i1') + False + >>> np.can_cast(150, 'u1') + True + + >>> np.can_cast(3.5e100, np.float32) + False + >>> np.can_cast(1000.0, np.float32) + True + + Array scalar checks the value, array does not + + >>> np.can_cast(np.array(1000.0), np.float32) + True + >>> np.can_cast(np.array([1000.0]), np.float32) + False + + Using the casting rules + + >>> np.can_cast('i8', 'i8', 'no') + True + >>> np.can_cast('i8', 'no') + False + + >>> np.can_cast('i8', 'equiv') + True + >>> np.can_cast('i8', 'equiv') + False + + >>> np.can_cast('i8', 'safe') + True + >>> np.can_cast('i4', 'safe') + False + + >>> np.can_cast('i4', 'same_kind') + True + >>> np.can_cast('u4', 'same_kind') + False + + >>> np.can_cast('u4', 'unsafe') + True + + """ + return (from_,) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.min_scalar_type) +def min_scalar_type(a): + """ + min_scalar_type(a, /) + + For scalar ``a``, returns the data type with the smallest size + and smallest scalar kind which can hold its value. For non-scalar + array ``a``, returns the vector's dtype unmodified. + + Floating point values are not demoted to integers, + and complex values are not demoted to floats. + + Parameters + ---------- + a : scalar or array_like + The value whose minimal data type is to be found. + + Returns + ------- + out : dtype + The minimal data type. + + Notes + ----- + .. versionadded:: 1.6.0 + + See Also + -------- + result_type, promote_types, dtype, can_cast + + Examples + -------- + >>> np.min_scalar_type(10) + dtype('uint8') + + >>> np.min_scalar_type(-260) + dtype('int16') + + >>> np.min_scalar_type(3.1) + dtype('float16') + + >>> np.min_scalar_type(1e50) + dtype('float64') + + >>> np.min_scalar_type(np.arange(4,dtype='f8')) + dtype('float64') + + """ + return (a,) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.result_type) +def result_type(*arrays_and_dtypes): + """ + result_type(*arrays_and_dtypes) + + Returns the type that results from applying the NumPy + type promotion rules to the arguments. + + Type promotion in NumPy works similarly to the rules in languages + like C++, with some slight differences. When both scalars and + arrays are used, the array's type takes precedence and the actual value + of the scalar is taken into account. + + For example, calculating 3*a, where a is an array of 32-bit floats, + intuitively should result in a 32-bit float output. If the 3 is a + 32-bit integer, the NumPy rules indicate it can't convert losslessly + into a 32-bit float, so a 64-bit float should be the result type. + By examining the value of the constant, '3', we see that it fits in + an 8-bit integer, which can be cast losslessly into the 32-bit float. + + Parameters + ---------- + arrays_and_dtypes : list of arrays and dtypes + The operands of some operation whose result type is needed. + + Returns + ------- + out : dtype + The result type. + + See also + -------- + dtype, promote_types, min_scalar_type, can_cast + + Notes + ----- + .. versionadded:: 1.6.0 + + The specific algorithm used is as follows. + + Categories are determined by first checking which of boolean, + integer (int/uint), or floating point (float/complex) the maximum + kind of all the arrays and the scalars are. + + If there are only scalars or the maximum category of the scalars + is higher than the maximum category of the arrays, + the data types are combined with :func:`promote_types` + to produce the return value. + + Otherwise, `min_scalar_type` is called on each scalar, and + the resulting data types are all combined with :func:`promote_types` + to produce the return value. + + The set of int values is not a subset of the uint values for types + with the same number of bits, something not reflected in + :func:`min_scalar_type`, but handled as a special case in `result_type`. + + Examples + -------- + >>> np.result_type(3, np.arange(7, dtype='i1')) + dtype('int8') + + >>> np.result_type('i4', 'c8') + dtype('complex128') + + >>> np.result_type(3.0, -2) + dtype('float64') + + """ + return arrays_and_dtypes + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.dot) +def dot(a, b, out=None): + """ + dot(a, b, out=None) + + Dot product of two arrays. Specifically, + + - If both `a` and `b` are 1-D arrays, it is inner product of vectors + (without complex conjugation). + + - If both `a` and `b` are 2-D arrays, it is matrix multiplication, + but using :func:`matmul` or ``a @ b`` is preferred. + + - If either `a` or `b` is 0-D (scalar), it is equivalent to + :func:`multiply` and using ``numpy.multiply(a, b)`` or ``a * b`` is + preferred. + + - If `a` is an N-D array and `b` is a 1-D array, it is a sum product over + the last axis of `a` and `b`. + + - If `a` is an N-D array and `b` is an M-D array (where ``M>=2``), it is a + sum product over the last axis of `a` and the second-to-last axis of + `b`:: + + dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m]) + + It uses an optimized BLAS library when possible (see `numpy.linalg`). + + Parameters + ---------- + a : array_like + First argument. + b : array_like + Second argument. + out : ndarray, optional + Output argument. This must have the exact kind that would be returned + if it was not used. In particular, it must have the right type, must be + C-contiguous, and its dtype must be the dtype that would be returned + for `dot(a,b)`. This is a performance feature. Therefore, if these + conditions are not met, an exception is raised, instead of attempting + to be flexible. + + Returns + ------- + output : ndarray + Returns the dot product of `a` and `b`. If `a` and `b` are both + scalars or both 1-D arrays then a scalar is returned; otherwise + an array is returned. + If `out` is given, then it is returned. + + Raises + ------ + ValueError + If the last dimension of `a` is not the same size as + the second-to-last dimension of `b`. + + See Also + -------- + vdot : Complex-conjugating dot product. + tensordot : Sum products over arbitrary axes. + einsum : Einstein summation convention. + matmul : '@' operator as method with out parameter. + linalg.multi_dot : Chained dot product. + + Examples + -------- + >>> np.dot(3, 4) + 12 + + Neither argument is complex-conjugated: + + >>> np.dot([2j, 3j], [2j, 3j]) + (-13+0j) + + For 2-D arrays it is the matrix product: + + >>> a = [[1, 0], [0, 1]] + >>> b = [[4, 1], [2, 2]] + >>> np.dot(a, b) + array([[4, 1], + [2, 2]]) + + >>> a = np.arange(3*4*5*6).reshape((3,4,5,6)) + >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3)) + >>> np.dot(a, b)[2,3,2,1,2,2] + 499128 + >>> sum(a[2,3,2,:] * b[1,2,:,2]) + 499128 + + """ + return (a, b, out) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.vdot) +def vdot(a, b): + """ + vdot(a, b, /) + + Return the dot product of two vectors. + + The vdot(`a`, `b`) function handles complex numbers differently than + dot(`a`, `b`). If the first argument is complex the complex conjugate + of the first argument is used for the calculation of the dot product. + + Note that `vdot` handles multidimensional arrays differently than `dot`: + it does *not* perform a matrix product, but flattens input arguments + to 1-D vectors first. Consequently, it should only be used for vectors. + + Parameters + ---------- + a : array_like + If `a` is complex the complex conjugate is taken before calculation + of the dot product. + b : array_like + Second argument to the dot product. + + Returns + ------- + output : ndarray + Dot product of `a` and `b`. Can be an int, float, or + complex depending on the types of `a` and `b`. + + See Also + -------- + dot : Return the dot product without using the complex conjugate of the + first argument. + + Examples + -------- + >>> a = np.array([1+2j,3+4j]) + >>> b = np.array([5+6j,7+8j]) + >>> np.vdot(a, b) + (70-8j) + >>> np.vdot(b, a) + (70+8j) + + Note that higher-dimensional arrays are flattened! + + >>> a = np.array([[1, 4], [5, 6]]) + >>> b = np.array([[4, 1], [2, 2]]) + >>> np.vdot(a, b) + 30 + >>> np.vdot(b, a) + 30 + >>> 1*4 + 4*1 + 5*2 + 6*2 + 30 + + """ + return (a, b) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.bincount) +def bincount(x, weights=None, minlength=None): + """ + bincount(x, /, weights=None, minlength=0) + + Count number of occurrences of each value in array of non-negative ints. + + The number of bins (of size 1) is one larger than the largest value in + `x`. If `minlength` is specified, there will be at least this number + of bins in the output array (though it will be longer if necessary, + depending on the contents of `x`). + Each bin gives the number of occurrences of its index value in `x`. + If `weights` is specified the input array is weighted by it, i.e. if a + value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead + of ``out[n] += 1``. + + Parameters + ---------- + x : array_like, 1 dimension, nonnegative ints + Input array. + weights : array_like, optional + Weights, array of the same shape as `x`. + minlength : int, optional + A minimum number of bins for the output array. + + .. versionadded:: 1.6.0 + + Returns + ------- + out : ndarray of ints + The result of binning the input array. + The length of `out` is equal to ``np.amax(x)+1``. + + Raises + ------ + ValueError + If the input is not 1-dimensional, or contains elements with negative + values, or if `minlength` is negative. + TypeError + If the type of the input is float or complex. + + See Also + -------- + histogram, digitize, unique + + Examples + -------- + >>> np.bincount(np.arange(5)) + array([1, 1, 1, 1, 1]) + >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7])) + array([1, 3, 1, 1, 0, 0, 0, 1]) + + >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23]) + >>> np.bincount(x).size == np.amax(x)+1 + True + + The input array needs to be of integer dtype, otherwise a + TypeError is raised: + + >>> np.bincount(np.arange(5, dtype=float)) + Traceback (most recent call last): + ... + TypeError: Cannot cast array data from dtype('float64') to dtype('int64') + according to the rule 'safe' + + A possible use of ``bincount`` is to perform sums over + variable-size chunks of an array, using the ``weights`` keyword. + + >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights + >>> x = np.array([0, 1, 1, 2, 2, 2]) + >>> np.bincount(x, weights=w) + array([ 0.3, 0.7, 1.1]) + + """ + return (x, weights) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.ravel_multi_index) +def ravel_multi_index(multi_index, dims, mode=None, order=None): + """ + ravel_multi_index(multi_index, dims, mode='raise', order='C') + + Converts a tuple of index arrays into an array of flat + indices, applying boundary modes to the multi-index. + + Parameters + ---------- + multi_index : tuple of array_like + A tuple of integer arrays, one array for each dimension. + dims : tuple of ints + The shape of array into which the indices from ``multi_index`` apply. + mode : {'raise', 'wrap', 'clip'}, optional + Specifies how out-of-bounds indices are handled. Can specify + either one mode or a tuple of modes, one mode per index. + + * 'raise' -- raise an error (default) + * 'wrap' -- wrap around + * 'clip' -- clip to the range + + In 'clip' mode, a negative index which would normally + wrap will clip to 0 instead. + order : {'C', 'F'}, optional + Determines whether the multi-index should be viewed as + indexing in row-major (C-style) or column-major + (Fortran-style) order. + + Returns + ------- + raveled_indices : ndarray + An array of indices into the flattened version of an array + of dimensions ``dims``. + + See Also + -------- + unravel_index + + Notes + ----- + .. versionadded:: 1.6.0 + + Examples + -------- + >>> arr = np.array([[3,6,6],[4,5,1]]) + >>> np.ravel_multi_index(arr, (7,6)) + array([22, 41, 37]) + >>> np.ravel_multi_index(arr, (7,6), order='F') + array([31, 41, 13]) + >>> np.ravel_multi_index(arr, (4,6), mode='clip') + array([22, 23, 19]) + >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap')) + array([12, 13, 13]) + + >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9)) + 1621 + """ + return multi_index + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.unravel_index) +def unravel_index(indices, shape=None, order=None): + """ + unravel_index(indices, shape, order='C') + + Converts a flat index or array of flat indices into a tuple + of coordinate arrays. + + Parameters + ---------- + indices : array_like + An integer array whose elements are indices into the flattened + version of an array of dimensions ``shape``. Before version 1.6.0, + this function accepted just one index value. + shape : tuple of ints + The shape of the array to use for unraveling ``indices``. + + .. versionchanged:: 1.16.0 + Renamed from ``dims`` to ``shape``. + + order : {'C', 'F'}, optional + Determines whether the indices should be viewed as indexing in + row-major (C-style) or column-major (Fortran-style) order. + + .. versionadded:: 1.6.0 + + Returns + ------- + unraveled_coords : tuple of ndarray + Each array in the tuple has the same shape as the ``indices`` + array. + + See Also + -------- + ravel_multi_index + + Examples + -------- + >>> np.unravel_index([22, 41, 37], (7,6)) + (array([3, 6, 6]), array([4, 5, 1])) + >>> np.unravel_index([31, 41, 13], (7,6), order='F') + (array([3, 6, 6]), array([4, 5, 1])) + + >>> np.unravel_index(1621, (6,7,8,9)) + (3, 1, 4, 1) + + """ + return (indices,) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.copyto) +def copyto(dst, src, casting=None, where=None): + """ + copyto(dst, src, casting='same_kind', where=True) + + Copies values from one array to another, broadcasting as necessary. + + Raises a TypeError if the `casting` rule is violated, and if + `where` is provided, it selects which elements to copy. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + dst : ndarray + The array into which values are copied. + src : array_like + The array from which values are copied. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur when copying. + + * 'no' means the data types should not be cast at all. + * 'equiv' means only byte-order changes are allowed. + * 'safe' means only casts which can preserve values are allowed. + * 'same_kind' means only safe casts or casts within a kind, + like float64 to float32, are allowed. + * 'unsafe' means any data conversions may be done. + where : array_like of bool, optional + A boolean array which is broadcasted to match the dimensions + of `dst`, and selects elements to copy from `src` to `dst` + wherever it contains the value True. + + Examples + -------- + >>> A = np.array([4, 5, 6]) + >>> B = [1, 2, 3] + >>> np.copyto(A, B) + >>> A + array([1, 2, 3]) + + >>> A = np.array([[1, 2, 3], [4, 5, 6]]) + >>> B = [[4, 5, 6], [7, 8, 9]] + >>> np.copyto(A, B) + >>> A + array([[4, 5, 6], + [7, 8, 9]]) + + """ + return (dst, src, where) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.putmask) +def putmask(a, /, mask, values): + """ + putmask(a, mask, values) + + Changes elements of an array based on conditional and input values. + + Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``. + + If `values` is not the same size as `a` and `mask` then it will repeat. + This gives behavior different from ``a[mask] = values``. + + Parameters + ---------- + a : ndarray + Target array. + mask : array_like + Boolean mask array. It has to be the same shape as `a`. + values : array_like + Values to put into `a` where `mask` is True. If `values` is smaller + than `a` it will be repeated. + + See Also + -------- + place, put, take, copyto + + Examples + -------- + >>> x = np.arange(6).reshape(2, 3) + >>> np.putmask(x, x>2, x**2) + >>> x + array([[ 0, 1, 2], + [ 9, 16, 25]]) + + If `values` is smaller than `a` it is repeated: + + >>> x = np.arange(5) + >>> np.putmask(x, x>1, [-33, -44]) + >>> x + array([ 0, 1, -33, -44, -33]) + + """ + return (a, mask, values) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.packbits) +def packbits(a, axis=None, bitorder='big'): + """ + packbits(a, /, axis=None, bitorder='big') + + Packs the elements of a binary-valued array into bits in a uint8 array. + + The result is padded to full bytes by inserting zero bits at the end. + + Parameters + ---------- + a : array_like + An array of integers or booleans whose elements should be packed to + bits. + axis : int, optional + The dimension over which bit-packing is done. + ``None`` implies packing the flattened array. + bitorder : {'big', 'little'}, optional + The order of the input bits. 'big' will mimic bin(val), + ``[0, 0, 0, 0, 0, 0, 1, 1] => 3 = 0b00000011``, 'little' will + reverse the order so ``[1, 1, 0, 0, 0, 0, 0, 0] => 3``. + Defaults to 'big'. + + .. versionadded:: 1.17.0 + + Returns + ------- + packed : ndarray + Array of type uint8 whose elements represent bits corresponding to the + logical (0 or nonzero) value of the input elements. The shape of + `packed` has the same number of dimensions as the input (unless `axis` + is None, in which case the output is 1-D). + + See Also + -------- + unpackbits: Unpacks elements of a uint8 array into a binary-valued output + array. + + Examples + -------- + >>> a = np.array([[[1,0,1], + ... [0,1,0]], + ... [[1,1,0], + ... [0,0,1]]]) + >>> b = np.packbits(a, axis=-1) + >>> b + array([[[160], + [ 64]], + [[192], + [ 32]]], dtype=uint8) + + Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000, + and 32 = 0010 0000. + + """ + return (a,) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.unpackbits) +def unpackbits(a, axis=None, count=None, bitorder='big'): + """ + unpackbits(a, /, axis=None, count=None, bitorder='big') + + Unpacks elements of a uint8 array into a binary-valued output array. + + Each element of `a` represents a bit-field that should be unpacked + into a binary-valued output array. The shape of the output array is + either 1-D (if `axis` is ``None``) or the same shape as the input + array with unpacking done along the axis specified. + + Parameters + ---------- + a : ndarray, uint8 type + Input array. + axis : int, optional + The dimension over which bit-unpacking is done. + ``None`` implies unpacking the flattened array. + count : int or None, optional + The number of elements to unpack along `axis`, provided as a way + of undoing the effect of packing a size that is not a multiple + of eight. A non-negative number means to only unpack `count` + bits. A negative number means to trim off that many bits from + the end. ``None`` means to unpack the entire array (the + default). Counts larger than the available number of bits will + add zero padding to the output. Negative counts must not + exceed the available number of bits. + + .. versionadded:: 1.17.0 + + bitorder : {'big', 'little'}, optional + The order of the returned bits. 'big' will mimic bin(val), + ``3 = 0b00000011 => [0, 0, 0, 0, 0, 0, 1, 1]``, 'little' will reverse + the order to ``[1, 1, 0, 0, 0, 0, 0, 0]``. + Defaults to 'big'. + + .. versionadded:: 1.17.0 + + Returns + ------- + unpacked : ndarray, uint8 type + The elements are binary-valued (0 or 1). + + See Also + -------- + packbits : Packs the elements of a binary-valued array into bits in + a uint8 array. + + Examples + -------- + >>> a = np.array([[2], [7], [23]], dtype=np.uint8) + >>> a + array([[ 2], + [ 7], + [23]], dtype=uint8) + >>> b = np.unpackbits(a, axis=1) + >>> b + array([[0, 0, 0, 0, 0, 0, 1, 0], + [0, 0, 0, 0, 0, 1, 1, 1], + [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8) + >>> c = np.unpackbits(a, axis=1, count=-3) + >>> c + array([[0, 0, 0, 0, 0], + [0, 0, 0, 0, 0], + [0, 0, 0, 1, 0]], dtype=uint8) + + >>> p = np.packbits(b, axis=0) + >>> np.unpackbits(p, axis=0) + array([[0, 0, 0, 0, 0, 0, 1, 0], + [0, 0, 0, 0, 0, 1, 1, 1], + [0, 0, 0, 1, 0, 1, 1, 1], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8) + >>> np.array_equal(b, np.unpackbits(p, axis=0, count=b.shape[0])) + True + + """ + return (a,) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.shares_memory) +def shares_memory(a, b, max_work=None): + """ + shares_memory(a, b, /, max_work=None) + + Determine if two arrays share memory. + + .. warning:: + + This function can be exponentially slow for some inputs, unless + `max_work` is set to a finite number or ``MAY_SHARE_BOUNDS``. + If in doubt, use `numpy.may_share_memory` instead. + + Parameters + ---------- + a, b : ndarray + Input arrays + max_work : int, optional + Effort to spend on solving the overlap problem (maximum number + of candidate solutions to consider). The following special + values are recognized: + + max_work=MAY_SHARE_EXACT (default) + The problem is solved exactly. In this case, the function returns + True only if there is an element shared between the arrays. Finding + the exact solution may take extremely long in some cases. + max_work=MAY_SHARE_BOUNDS + Only the memory bounds of a and b are checked. + + Raises + ------ + numpy.exceptions.TooHardError + Exceeded max_work. + + Returns + ------- + out : bool + + See Also + -------- + may_share_memory + + Examples + -------- + >>> x = np.array([1, 2, 3, 4]) + >>> np.shares_memory(x, np.array([5, 6, 7])) + False + >>> np.shares_memory(x[::2], x) + True + >>> np.shares_memory(x[::2], x[1::2]) + False + + Checking whether two arrays share memory is NP-complete, and + runtime may increase exponentially in the number of + dimensions. Hence, `max_work` should generally be set to a finite + number, as it is possible to construct examples that take + extremely long to run: + + >>> from numpy.lib.stride_tricks import as_strided + >>> x = np.zeros([192163377], dtype=np.int8) + >>> x1 = as_strided(x, strides=(36674, 61119, 85569), shape=(1049, 1049, 1049)) + >>> x2 = as_strided(x[64023025:], strides=(12223, 12224, 1), shape=(1049, 1049, 1)) + >>> np.shares_memory(x1, x2, max_work=1000) + Traceback (most recent call last): + ... + numpy.exceptions.TooHardError: Exceeded max_work + + Running ``np.shares_memory(x1, x2)`` without `max_work` set takes + around 1 minute for this case. It is possible to find problems + that take still significantly longer. + + """ + return (a, b) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.may_share_memory) +def may_share_memory(a, b, max_work=None): + """ + may_share_memory(a, b, /, max_work=None) + + Determine if two arrays might share memory + + A return of True does not necessarily mean that the two arrays + share any element. It just means that they *might*. + + Only the memory bounds of a and b are checked by default. + + Parameters + ---------- + a, b : ndarray + Input arrays + max_work : int, optional + Effort to spend on solving the overlap problem. See + `shares_memory` for details. Default for ``may_share_memory`` + is to do a bounds check. + + Returns + ------- + out : bool + + See Also + -------- + shares_memory + + Examples + -------- + >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9])) + False + >>> x = np.zeros([3, 4]) + >>> np.may_share_memory(x[:,0], x[:,1]) + True + + """ + return (a, b) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.is_busday) +def is_busday(dates, weekmask=None, holidays=None, busdaycal=None, out=None): + """ + is_busday(dates, weekmask='1111100', holidays=None, busdaycal=None, out=None) + + Calculates which of the given dates are valid days, and which are not. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + dates : array_like of datetime64[D] + The array of dates to process. + weekmask : str or array_like of bool, optional + A seven-element array indicating which of Monday through Sunday are + valid days. May be specified as a length-seven list or array, like + [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string + like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for + weekdays, optionally separated by white space. Valid abbreviations + are: Mon Tue Wed Thu Fri Sat Sun + holidays : array_like of datetime64[D], optional + An array of dates to consider as invalid dates. They may be + specified in any order, and NaT (not-a-time) dates are ignored. + This list is saved in a normalized form that is suited for + fast calculations of valid days. + busdaycal : busdaycalendar, optional + A `busdaycalendar` object which specifies the valid days. If this + parameter is provided, neither weekmask nor holidays may be + provided. + out : array of bool, optional + If provided, this array is filled with the result. + + Returns + ------- + out : array of bool + An array with the same shape as ``dates``, containing True for + each valid day, and False for each invalid day. + + See Also + -------- + busdaycalendar : An object that specifies a custom set of valid days. + busday_offset : Applies an offset counted in valid days. + busday_count : Counts how many valid days are in a half-open date range. + + Examples + -------- + >>> # The weekdays are Friday, Saturday, and Monday + ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'], + ... holidays=['2011-07-01', '2011-07-04', '2011-07-17']) + array([False, False, True]) + """ + return (dates, weekmask, holidays, out) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.busday_offset) +def busday_offset(dates, offsets, roll=None, weekmask=None, holidays=None, + busdaycal=None, out=None): + """ + busday_offset(dates, offsets, roll='raise', weekmask='1111100', holidays=None, busdaycal=None, out=None) + + First adjusts the date to fall on a valid day according to + the ``roll`` rule, then applies offsets to the given dates + counted in valid days. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + dates : array_like of datetime64[D] + The array of dates to process. + offsets : array_like of int + The array of offsets, which is broadcast with ``dates``. + roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', 'modifiedfollowing', 'modifiedpreceding'}, optional + How to treat dates that do not fall on a valid day. The default + is 'raise'. + + * 'raise' means to raise an exception for an invalid day. + * 'nat' means to return a NaT (not-a-time) for an invalid day. + * 'forward' and 'following' mean to take the first valid day + later in time. + * 'backward' and 'preceding' mean to take the first valid day + earlier in time. + * 'modifiedfollowing' means to take the first valid day + later in time unless it is across a Month boundary, in which + case to take the first valid day earlier in time. + * 'modifiedpreceding' means to take the first valid day + earlier in time unless it is across a Month boundary, in which + case to take the first valid day later in time. + weekmask : str or array_like of bool, optional + A seven-element array indicating which of Monday through Sunday are + valid days. May be specified as a length-seven list or array, like + [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string + like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for + weekdays, optionally separated by white space. Valid abbreviations + are: Mon Tue Wed Thu Fri Sat Sun + holidays : array_like of datetime64[D], optional + An array of dates to consider as invalid dates. They may be + specified in any order, and NaT (not-a-time) dates are ignored. + This list is saved in a normalized form that is suited for + fast calculations of valid days. + busdaycal : busdaycalendar, optional + A `busdaycalendar` object which specifies the valid days. If this + parameter is provided, neither weekmask nor holidays may be + provided. + out : array of datetime64[D], optional + If provided, this array is filled with the result. + + Returns + ------- + out : array of datetime64[D] + An array with a shape from broadcasting ``dates`` and ``offsets`` + together, containing the dates with offsets applied. + + See Also + -------- + busdaycalendar : An object that specifies a custom set of valid days. + is_busday : Returns a boolean array indicating valid days. + busday_count : Counts how many valid days are in a half-open date range. + + Examples + -------- + >>> # First business day in October 2011 (not accounting for holidays) + ... np.busday_offset('2011-10', 0, roll='forward') + numpy.datetime64('2011-10-03') + >>> # Last business day in February 2012 (not accounting for holidays) + ... np.busday_offset('2012-03', -1, roll='forward') + numpy.datetime64('2012-02-29') + >>> # Third Wednesday in January 2011 + ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed') + numpy.datetime64('2011-01-19') + >>> # 2012 Mother's Day in Canada and the U.S. + ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun') + numpy.datetime64('2012-05-13') + + >>> # First business day on or after a date + ... np.busday_offset('2011-03-20', 0, roll='forward') + numpy.datetime64('2011-03-21') + >>> np.busday_offset('2011-03-22', 0, roll='forward') + numpy.datetime64('2011-03-22') + >>> # First business day after a date + ... np.busday_offset('2011-03-20', 1, roll='backward') + numpy.datetime64('2011-03-21') + >>> np.busday_offset('2011-03-22', 1, roll='backward') + numpy.datetime64('2011-03-23') + """ + return (dates, offsets, weekmask, holidays, out) + + +@array_function_from_c_func_and_dispatcher(_multiarray_umath.busday_count) +def busday_count(begindates, enddates, weekmask=None, holidays=None, + busdaycal=None, out=None): + """ + busday_count(begindates, enddates, weekmask='1111100', holidays=[], busdaycal=None, out=None) + + Counts the number of valid days between `begindates` and + `enddates`, not including the day of `enddates`. + + If ``enddates`` specifies a date value that is earlier than the + corresponding ``begindates`` date value, the count will be negative. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + begindates : array_like of datetime64[D] + The array of the first dates for counting. + enddates : array_like of datetime64[D] + The array of the end dates for counting, which are excluded + from the count themselves. + weekmask : str or array_like of bool, optional + A seven-element array indicating which of Monday through Sunday are + valid days. May be specified as a length-seven list or array, like + [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string + like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for + weekdays, optionally separated by white space. Valid abbreviations + are: Mon Tue Wed Thu Fri Sat Sun + holidays : array_like of datetime64[D], optional + An array of dates to consider as invalid dates. They may be + specified in any order, and NaT (not-a-time) dates are ignored. + This list is saved in a normalized form that is suited for + fast calculations of valid days. + busdaycal : busdaycalendar, optional + A `busdaycalendar` object which specifies the valid days. If this + parameter is provided, neither weekmask nor holidays may be + provided. + out : array of int, optional + If provided, this array is filled with the result. + + Returns + ------- + out : array of int + An array with a shape from broadcasting ``begindates`` and ``enddates`` + together, containing the number of valid days between + the begin and end dates. + + See Also + -------- + busdaycalendar : An object that specifies a custom set of valid days. + is_busday : Returns a boolean array indicating valid days. + busday_offset : Applies an offset counted in valid days. + + Examples + -------- + >>> # Number of weekdays in January 2011 + ... np.busday_count('2011-01', '2011-02') + 21 + >>> # Number of weekdays in 2011 + >>> np.busday_count('2011', '2012') + 260 + >>> # Number of Saturdays in 2011 + ... np.busday_count('2011', '2012', weekmask='Sat') + 53 + """ + return (begindates, enddates, weekmask, holidays, out) + + +@array_function_from_c_func_and_dispatcher( + _multiarray_umath.datetime_as_string) +def datetime_as_string(arr, unit=None, timezone=None, casting=None): + """ + datetime_as_string(arr, unit=None, timezone='naive', casting='same_kind') + + Convert an array of datetimes into an array of strings. + + Parameters + ---------- + arr : array_like of datetime64 + The array of UTC timestamps to format. + unit : str + One of None, 'auto', or a :ref:`datetime unit `. + timezone : {'naive', 'UTC', 'local'} or tzinfo + Timezone information to use when displaying the datetime. If 'UTC', end + with a Z to indicate UTC time. If 'local', convert to the local timezone + first, and suffix with a +-#### timezone offset. If a tzinfo object, + then do as with 'local', but use the specified timezone. + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'} + Casting to allow when changing between datetime units. + + Returns + ------- + str_arr : ndarray + An array of strings the same shape as `arr`. + + Examples + -------- + >>> import pytz + >>> d = np.arange('2002-10-27T04:30', 4*60, 60, dtype='M8[m]') + >>> d + array(['2002-10-27T04:30', '2002-10-27T05:30', '2002-10-27T06:30', + '2002-10-27T07:30'], dtype='datetime64[m]') + + Setting the timezone to UTC shows the same information, but with a Z suffix + + >>> np.datetime_as_string(d, timezone='UTC') + array(['2002-10-27T04:30Z', '2002-10-27T05:30Z', '2002-10-27T06:30Z', + '2002-10-27T07:30Z'], dtype='>> np.datetime_as_string(d, timezone=pytz.timezone('US/Eastern')) + array(['2002-10-27T00:30-0400', '2002-10-27T01:30-0400', + '2002-10-27T01:30-0500', '2002-10-27T02:30-0500'], dtype='>> np.datetime_as_string(d, unit='h') + array(['2002-10-27T04', '2002-10-27T05', '2002-10-27T06', '2002-10-27T07'], + dtype='>> np.datetime_as_string(d, unit='s') + array(['2002-10-27T04:30:00', '2002-10-27T05:30:00', '2002-10-27T06:30:00', + '2002-10-27T07:30:00'], dtype='>> np.datetime_as_string(d, unit='h', casting='safe') + Traceback (most recent call last): + ... + TypeError: Cannot create a datetime string as units 'h' from a NumPy + datetime with units 'm' according to the rule 'safe' + """ + return (arr,) diff --git a/venv/lib/python3.10/site-packages/numpy/core/multiarray.pyi b/venv/lib/python3.10/site-packages/numpy/core/multiarray.pyi new file mode 100644 index 0000000000000000000000000000000000000000..dc05f8126ba892683b0bbcaa75e978396fd5bc1f --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/multiarray.pyi @@ -0,0 +1,1022 @@ +# TODO: Sort out any and all missing functions in this namespace + +import os +import datetime as dt +from collections.abc import Sequence, Callable, Iterable +from typing import ( + Literal as L, + Any, + overload, + TypeVar, + SupportsIndex, + final, + Final, + Protocol, + ClassVar, +) + +from numpy import ( + # Re-exports + busdaycalendar as busdaycalendar, + broadcast as broadcast, + dtype as dtype, + ndarray as ndarray, + nditer as nditer, + + # The rest + ufunc, + str_, + bool_, + uint8, + intp, + int_, + float64, + timedelta64, + datetime64, + generic, + unsignedinteger, + signedinteger, + floating, + complexfloating, + _OrderKACF, + _OrderCF, + _CastingKind, + _ModeKind, + _SupportsBuffer, + _IOProtocol, + _CopyMode, + _NDIterFlagsKind, + _NDIterOpFlagsKind, +) + +from numpy._typing import ( + # Shapes + _ShapeLike, + + # DTypes + DTypeLike, + _DTypeLike, + + # Arrays + NDArray, + ArrayLike, + _ArrayLike, + _SupportsArrayFunc, + _NestedSequence, + _ArrayLikeBool_co, + _ArrayLikeUInt_co, + _ArrayLikeInt_co, + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, + _ArrayLikeTD64_co, + _ArrayLikeDT64_co, + _ArrayLikeObject_co, + _ArrayLikeStr_co, + _ArrayLikeBytes_co, + _ScalarLike_co, + _IntLike_co, + _FloatLike_co, + _TD64Like_co, +) + +_T_co = TypeVar("_T_co", covariant=True) +_T_contra = TypeVar("_T_contra", contravariant=True) +_SCT = TypeVar("_SCT", bound=generic) +_ArrayType = TypeVar("_ArrayType", bound=NDArray[Any]) + +# Valid time units +_UnitKind = L[ + "Y", + "M", + "D", + "h", + "m", + "s", + "ms", + "us", "μs", + "ns", + "ps", + "fs", + "as", +] +_RollKind = L[ # `raise` is deliberately excluded + "nat", + "forward", + "following", + "backward", + "preceding", + "modifiedfollowing", + "modifiedpreceding", +] + +class _SupportsLenAndGetItem(Protocol[_T_contra, _T_co]): + def __len__(self) -> int: ... + def __getitem__(self, key: _T_contra, /) -> _T_co: ... + +__all__: list[str] + +ALLOW_THREADS: Final[int] # 0 or 1 (system-specific) +BUFSIZE: L[8192] +CLIP: L[0] +WRAP: L[1] +RAISE: L[2] +MAXDIMS: L[32] +MAY_SHARE_BOUNDS: L[0] +MAY_SHARE_EXACT: L[-1] +tracemalloc_domain: L[389047] + +@overload +def empty_like( + prototype: _ArrayType, + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> _ArrayType: ... +@overload +def empty_like( + prototype: _ArrayLike[_SCT], + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> NDArray[_SCT]: ... +@overload +def empty_like( + prototype: object, + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> NDArray[Any]: ... +@overload +def empty_like( + prototype: Any, + dtype: _DTypeLike[_SCT], + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> NDArray[_SCT]: ... +@overload +def empty_like( + prototype: Any, + dtype: DTypeLike, + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> NDArray[Any]: ... + +@overload +def array( + object: _ArrayType, + dtype: None = ..., + *, + copy: bool | _CopyMode = ..., + order: _OrderKACF = ..., + subok: L[True], + ndmin: int = ..., + like: None | _SupportsArrayFunc = ..., +) -> _ArrayType: ... +@overload +def array( + object: _ArrayLike[_SCT], + dtype: None = ..., + *, + copy: bool | _CopyMode = ..., + order: _OrderKACF = ..., + subok: bool = ..., + ndmin: int = ..., + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def array( + object: object, + dtype: None = ..., + *, + copy: bool | _CopyMode = ..., + order: _OrderKACF = ..., + subok: bool = ..., + ndmin: int = ..., + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... +@overload +def array( + object: Any, + dtype: _DTypeLike[_SCT], + *, + copy: bool | _CopyMode = ..., + order: _OrderKACF = ..., + subok: bool = ..., + ndmin: int = ..., + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def array( + object: Any, + dtype: DTypeLike, + *, + copy: bool | _CopyMode = ..., + order: _OrderKACF = ..., + subok: bool = ..., + ndmin: int = ..., + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def zeros( + shape: _ShapeLike, + dtype: None = ..., + order: _OrderCF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[float64]: ... +@overload +def zeros( + shape: _ShapeLike, + dtype: _DTypeLike[_SCT], + order: _OrderCF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def zeros( + shape: _ShapeLike, + dtype: DTypeLike, + order: _OrderCF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def empty( + shape: _ShapeLike, + dtype: None = ..., + order: _OrderCF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[float64]: ... +@overload +def empty( + shape: _ShapeLike, + dtype: _DTypeLike[_SCT], + order: _OrderCF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def empty( + shape: _ShapeLike, + dtype: DTypeLike, + order: _OrderCF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def unravel_index( # type: ignore[misc] + indices: _IntLike_co, + shape: _ShapeLike, + order: _OrderCF = ..., +) -> tuple[intp, ...]: ... +@overload +def unravel_index( + indices: _ArrayLikeInt_co, + shape: _ShapeLike, + order: _OrderCF = ..., +) -> tuple[NDArray[intp], ...]: ... + +@overload +def ravel_multi_index( # type: ignore[misc] + multi_index: Sequence[_IntLike_co], + dims: Sequence[SupportsIndex], + mode: _ModeKind | tuple[_ModeKind, ...] = ..., + order: _OrderCF = ..., +) -> intp: ... +@overload +def ravel_multi_index( + multi_index: Sequence[_ArrayLikeInt_co], + dims: Sequence[SupportsIndex], + mode: _ModeKind | tuple[_ModeKind, ...] = ..., + order: _OrderCF = ..., +) -> NDArray[intp]: ... + +# NOTE: Allow any sequence of array-like objects +@overload +def concatenate( # type: ignore[misc] + arrays: _ArrayLike[_SCT], + /, + axis: None | SupportsIndex = ..., + out: None = ..., + *, + dtype: None = ..., + casting: None | _CastingKind = ... +) -> NDArray[_SCT]: ... +@overload +def concatenate( # type: ignore[misc] + arrays: _SupportsLenAndGetItem[int, ArrayLike], + /, + axis: None | SupportsIndex = ..., + out: None = ..., + *, + dtype: None = ..., + casting: None | _CastingKind = ... +) -> NDArray[Any]: ... +@overload +def concatenate( # type: ignore[misc] + arrays: _SupportsLenAndGetItem[int, ArrayLike], + /, + axis: None | SupportsIndex = ..., + out: None = ..., + *, + dtype: _DTypeLike[_SCT], + casting: None | _CastingKind = ... +) -> NDArray[_SCT]: ... +@overload +def concatenate( # type: ignore[misc] + arrays: _SupportsLenAndGetItem[int, ArrayLike], + /, + axis: None | SupportsIndex = ..., + out: None = ..., + *, + dtype: DTypeLike, + casting: None | _CastingKind = ... +) -> NDArray[Any]: ... +@overload +def concatenate( + arrays: _SupportsLenAndGetItem[int, ArrayLike], + /, + axis: None | SupportsIndex = ..., + out: _ArrayType = ..., + *, + dtype: DTypeLike = ..., + casting: None | _CastingKind = ... +) -> _ArrayType: ... + +def inner( + a: ArrayLike, + b: ArrayLike, + /, +) -> Any: ... + +@overload +def where( + condition: ArrayLike, + /, +) -> tuple[NDArray[intp], ...]: ... +@overload +def where( + condition: ArrayLike, + x: ArrayLike, + y: ArrayLike, + /, +) -> NDArray[Any]: ... + +def lexsort( + keys: ArrayLike, + axis: None | SupportsIndex = ..., +) -> Any: ... + +def can_cast( + from_: ArrayLike | DTypeLike, + to: DTypeLike, + casting: None | _CastingKind = ..., +) -> bool: ... + +def min_scalar_type( + a: ArrayLike, /, +) -> dtype[Any]: ... + +def result_type( + *arrays_and_dtypes: ArrayLike | DTypeLike, +) -> dtype[Any]: ... + +@overload +def dot(a: ArrayLike, b: ArrayLike, out: None = ...) -> Any: ... +@overload +def dot(a: ArrayLike, b: ArrayLike, out: _ArrayType) -> _ArrayType: ... + +@overload +def vdot(a: _ArrayLikeBool_co, b: _ArrayLikeBool_co, /) -> bool_: ... # type: ignore[misc] +@overload +def vdot(a: _ArrayLikeUInt_co, b: _ArrayLikeUInt_co, /) -> unsignedinteger[Any]: ... # type: ignore[misc] +@overload +def vdot(a: _ArrayLikeInt_co, b: _ArrayLikeInt_co, /) -> signedinteger[Any]: ... # type: ignore[misc] +@overload +def vdot(a: _ArrayLikeFloat_co, b: _ArrayLikeFloat_co, /) -> floating[Any]: ... # type: ignore[misc] +@overload +def vdot(a: _ArrayLikeComplex_co, b: _ArrayLikeComplex_co, /) -> complexfloating[Any, Any]: ... # type: ignore[misc] +@overload +def vdot(a: _ArrayLikeTD64_co, b: _ArrayLikeTD64_co, /) -> timedelta64: ... +@overload +def vdot(a: _ArrayLikeObject_co, b: Any, /) -> Any: ... +@overload +def vdot(a: Any, b: _ArrayLikeObject_co, /) -> Any: ... + +def bincount( + x: ArrayLike, + /, + weights: None | ArrayLike = ..., + minlength: SupportsIndex = ..., +) -> NDArray[intp]: ... + +def copyto( + dst: NDArray[Any], + src: ArrayLike, + casting: None | _CastingKind = ..., + where: None | _ArrayLikeBool_co = ..., +) -> None: ... + +def putmask( + a: NDArray[Any], + /, + mask: _ArrayLikeBool_co, + values: ArrayLike, +) -> None: ... + +def packbits( + a: _ArrayLikeInt_co, + /, + axis: None | SupportsIndex = ..., + bitorder: L["big", "little"] = ..., +) -> NDArray[uint8]: ... + +def unpackbits( + a: _ArrayLike[uint8], + /, + axis: None | SupportsIndex = ..., + count: None | SupportsIndex = ..., + bitorder: L["big", "little"] = ..., +) -> NDArray[uint8]: ... + +def shares_memory( + a: object, + b: object, + /, + max_work: None | int = ..., +) -> bool: ... + +def may_share_memory( + a: object, + b: object, + /, + max_work: None | int = ..., +) -> bool: ... + +@overload +def asarray( + a: _ArrayLike[_SCT], + dtype: None = ..., + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def asarray( + a: object, + dtype: None = ..., + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... +@overload +def asarray( + a: Any, + dtype: _DTypeLike[_SCT], + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def asarray( + a: Any, + dtype: DTypeLike, + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def asanyarray( + a: _ArrayType, # Preserve subclass-information + dtype: None = ..., + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> _ArrayType: ... +@overload +def asanyarray( + a: _ArrayLike[_SCT], + dtype: None = ..., + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def asanyarray( + a: object, + dtype: None = ..., + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... +@overload +def asanyarray( + a: Any, + dtype: _DTypeLike[_SCT], + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def asanyarray( + a: Any, + dtype: DTypeLike, + order: _OrderKACF = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def ascontiguousarray( + a: _ArrayLike[_SCT], + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def ascontiguousarray( + a: object, + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... +@overload +def ascontiguousarray( + a: Any, + dtype: _DTypeLike[_SCT], + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def ascontiguousarray( + a: Any, + dtype: DTypeLike, + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def asfortranarray( + a: _ArrayLike[_SCT], + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def asfortranarray( + a: object, + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... +@overload +def asfortranarray( + a: Any, + dtype: _DTypeLike[_SCT], + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def asfortranarray( + a: Any, + dtype: DTypeLike, + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +# In practice `list[Any]` is list with an int, int and a valid +# `np.seterrcall()` object +def geterrobj() -> list[Any]: ... +def seterrobj(errobj: list[Any], /) -> None: ... + +def promote_types(__type1: DTypeLike, __type2: DTypeLike) -> dtype[Any]: ... + +# `sep` is a de facto mandatory argument, as its default value is deprecated +@overload +def fromstring( + string: str | bytes, + dtype: None = ..., + count: SupportsIndex = ..., + *, + sep: str, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[float64]: ... +@overload +def fromstring( + string: str | bytes, + dtype: _DTypeLike[_SCT], + count: SupportsIndex = ..., + *, + sep: str, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def fromstring( + string: str | bytes, + dtype: DTypeLike, + count: SupportsIndex = ..., + *, + sep: str, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +def frompyfunc( + func: Callable[..., Any], /, + nin: SupportsIndex, + nout: SupportsIndex, + *, + identity: Any = ..., +) -> ufunc: ... + +@overload +def fromfile( + file: str | bytes | os.PathLike[Any] | _IOProtocol, + dtype: None = ..., + count: SupportsIndex = ..., + sep: str = ..., + offset: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[float64]: ... +@overload +def fromfile( + file: str | bytes | os.PathLike[Any] | _IOProtocol, + dtype: _DTypeLike[_SCT], + count: SupportsIndex = ..., + sep: str = ..., + offset: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def fromfile( + file: str | bytes | os.PathLike[Any] | _IOProtocol, + dtype: DTypeLike, + count: SupportsIndex = ..., + sep: str = ..., + offset: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def fromiter( + iter: Iterable[Any], + dtype: _DTypeLike[_SCT], + count: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def fromiter( + iter: Iterable[Any], + dtype: DTypeLike, + count: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def frombuffer( + buffer: _SupportsBuffer, + dtype: None = ..., + count: SupportsIndex = ..., + offset: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[float64]: ... +@overload +def frombuffer( + buffer: _SupportsBuffer, + dtype: _DTypeLike[_SCT], + count: SupportsIndex = ..., + offset: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def frombuffer( + buffer: _SupportsBuffer, + dtype: DTypeLike, + count: SupportsIndex = ..., + offset: SupportsIndex = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def arange( # type: ignore[misc] + stop: _IntLike_co, + /, *, + dtype: None = ..., + like: None | _SupportsArrayFunc = ..., +) -> NDArray[signedinteger[Any]]: ... +@overload +def arange( # type: ignore[misc] + start: _IntLike_co, + stop: _IntLike_co, + step: _IntLike_co = ..., + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[signedinteger[Any]]: ... +@overload +def arange( # type: ignore[misc] + stop: _FloatLike_co, + /, *, + dtype: None = ..., + like: None | _SupportsArrayFunc = ..., +) -> NDArray[floating[Any]]: ... +@overload +def arange( # type: ignore[misc] + start: _FloatLike_co, + stop: _FloatLike_co, + step: _FloatLike_co = ..., + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[floating[Any]]: ... +@overload +def arange( + stop: _TD64Like_co, + /, *, + dtype: None = ..., + like: None | _SupportsArrayFunc = ..., +) -> NDArray[timedelta64]: ... +@overload +def arange( + start: _TD64Like_co, + stop: _TD64Like_co, + step: _TD64Like_co = ..., + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[timedelta64]: ... +@overload +def arange( # both start and stop must always be specified for datetime64 + start: datetime64, + stop: datetime64, + step: datetime64 = ..., + dtype: None = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[datetime64]: ... +@overload +def arange( + stop: Any, + /, *, + dtype: _DTypeLike[_SCT], + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def arange( + start: Any, + stop: Any, + step: Any = ..., + dtype: _DTypeLike[_SCT] = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def arange( + stop: Any, /, + *, + dtype: DTypeLike, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... +@overload +def arange( + start: Any, + stop: Any, + step: Any = ..., + dtype: DTypeLike = ..., + *, + like: None | _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +def datetime_data( + dtype: str | _DTypeLike[datetime64] | _DTypeLike[timedelta64], /, +) -> tuple[str, int]: ... + +# The datetime functions perform unsafe casts to `datetime64[D]`, +# so a lot of different argument types are allowed here + +@overload +def busday_count( # type: ignore[misc] + begindates: _ScalarLike_co | dt.date, + enddates: _ScalarLike_co | dt.date, + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> int_: ... +@overload +def busday_count( # type: ignore[misc] + begindates: ArrayLike | dt.date | _NestedSequence[dt.date], + enddates: ArrayLike | dt.date | _NestedSequence[dt.date], + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> NDArray[int_]: ... +@overload +def busday_count( + begindates: ArrayLike | dt.date | _NestedSequence[dt.date], + enddates: ArrayLike | dt.date | _NestedSequence[dt.date], + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +# `roll="raise"` is (more or less?) equivalent to `casting="safe"` +@overload +def busday_offset( # type: ignore[misc] + dates: datetime64 | dt.date, + offsets: _TD64Like_co | dt.timedelta, + roll: L["raise"] = ..., + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> datetime64: ... +@overload +def busday_offset( # type: ignore[misc] + dates: _ArrayLike[datetime64] | dt.date | _NestedSequence[dt.date], + offsets: _ArrayLikeTD64_co | dt.timedelta | _NestedSequence[dt.timedelta], + roll: L["raise"] = ..., + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> NDArray[datetime64]: ... +@overload +def busday_offset( # type: ignore[misc] + dates: _ArrayLike[datetime64] | dt.date | _NestedSequence[dt.date], + offsets: _ArrayLikeTD64_co | dt.timedelta | _NestedSequence[dt.timedelta], + roll: L["raise"] = ..., + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... +@overload +def busday_offset( # type: ignore[misc] + dates: _ScalarLike_co | dt.date, + offsets: _ScalarLike_co | dt.timedelta, + roll: _RollKind, + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> datetime64: ... +@overload +def busday_offset( # type: ignore[misc] + dates: ArrayLike | dt.date | _NestedSequence[dt.date], + offsets: ArrayLike | dt.timedelta | _NestedSequence[dt.timedelta], + roll: _RollKind, + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> NDArray[datetime64]: ... +@overload +def busday_offset( + dates: ArrayLike | dt.date | _NestedSequence[dt.date], + offsets: ArrayLike | dt.timedelta | _NestedSequence[dt.timedelta], + roll: _RollKind, + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +@overload +def is_busday( # type: ignore[misc] + dates: _ScalarLike_co | dt.date, + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> bool_: ... +@overload +def is_busday( # type: ignore[misc] + dates: ArrayLike | _NestedSequence[dt.date], + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: None = ..., +) -> NDArray[bool_]: ... +@overload +def is_busday( + dates: ArrayLike | _NestedSequence[dt.date], + weekmask: ArrayLike = ..., + holidays: None | ArrayLike | dt.date | _NestedSequence[dt.date] = ..., + busdaycal: None | busdaycalendar = ..., + out: _ArrayType = ..., +) -> _ArrayType: ... + +@overload +def datetime_as_string( # type: ignore[misc] + arr: datetime64 | dt.date, + unit: None | L["auto"] | _UnitKind = ..., + timezone: L["naive", "UTC", "local"] | dt.tzinfo = ..., + casting: _CastingKind = ..., +) -> str_: ... +@overload +def datetime_as_string( + arr: _ArrayLikeDT64_co | _NestedSequence[dt.date], + unit: None | L["auto"] | _UnitKind = ..., + timezone: L["naive", "UTC", "local"] | dt.tzinfo = ..., + casting: _CastingKind = ..., +) -> NDArray[str_]: ... + +@overload +def compare_chararrays( + a1: _ArrayLikeStr_co, + a2: _ArrayLikeStr_co, + cmp: L["<", "<=", "==", ">=", ">", "!="], + rstrip: bool, +) -> NDArray[bool_]: ... +@overload +def compare_chararrays( + a1: _ArrayLikeBytes_co, + a2: _ArrayLikeBytes_co, + cmp: L["<", "<=", "==", ">=", ">", "!="], + rstrip: bool, +) -> NDArray[bool_]: ... + +def add_docstring(obj: Callable[..., Any], docstring: str, /) -> None: ... + +_GetItemKeys = L[ + "C", "CONTIGUOUS", "C_CONTIGUOUS", + "F", "FORTRAN", "F_CONTIGUOUS", + "W", "WRITEABLE", + "B", "BEHAVED", + "O", "OWNDATA", + "A", "ALIGNED", + "X", "WRITEBACKIFCOPY", + "CA", "CARRAY", + "FA", "FARRAY", + "FNC", + "FORC", +] +_SetItemKeys = L[ + "A", "ALIGNED", + "W", "WRITEABLE", + "X", "WRITEBACKIFCOPY", +] + +@final +class flagsobj: + __hash__: ClassVar[None] # type: ignore[assignment] + aligned: bool + # NOTE: deprecated + # updateifcopy: bool + writeable: bool + writebackifcopy: bool + @property + def behaved(self) -> bool: ... + @property + def c_contiguous(self) -> bool: ... + @property + def carray(self) -> bool: ... + @property + def contiguous(self) -> bool: ... + @property + def f_contiguous(self) -> bool: ... + @property + def farray(self) -> bool: ... + @property + def fnc(self) -> bool: ... + @property + def forc(self) -> bool: ... + @property + def fortran(self) -> bool: ... + @property + def num(self) -> int: ... + @property + def owndata(self) -> bool: ... + def __getitem__(self, key: _GetItemKeys) -> bool: ... + def __setitem__(self, key: _SetItemKeys, value: bool) -> None: ... + +def nested_iters( + op: ArrayLike | Sequence[ArrayLike], + axes: Sequence[Sequence[SupportsIndex]], + flags: None | Sequence[_NDIterFlagsKind] = ..., + op_flags: None | Sequence[Sequence[_NDIterOpFlagsKind]] = ..., + op_dtypes: DTypeLike | Sequence[DTypeLike] = ..., + order: _OrderKACF = ..., + casting: _CastingKind = ..., + buffersize: SupportsIndex = ..., +) -> tuple[nditer, ...]: ... diff --git a/venv/lib/python3.10/site-packages/numpy/core/numeric.py b/venv/lib/python3.10/site-packages/numpy/core/numeric.py new file mode 100644 index 0000000000000000000000000000000000000000..91ac3f8606fedbf9c57edf5b1ec64693a9c3edd7 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/numeric.py @@ -0,0 +1,2530 @@ +import functools +import itertools +import operator +import sys +import warnings +import numbers +import builtins + +import numpy as np +from . import multiarray +from .multiarray import ( + fastCopyAndTranspose, ALLOW_THREADS, + BUFSIZE, CLIP, MAXDIMS, MAY_SHARE_BOUNDS, MAY_SHARE_EXACT, RAISE, + WRAP, arange, array, asarray, asanyarray, ascontiguousarray, + asfortranarray, broadcast, can_cast, compare_chararrays, + concatenate, copyto, dot, dtype, empty, + empty_like, flatiter, frombuffer, from_dlpack, fromfile, fromiter, + fromstring, inner, lexsort, matmul, may_share_memory, + min_scalar_type, ndarray, nditer, nested_iters, promote_types, + putmask, result_type, set_numeric_ops, shares_memory, vdot, where, + zeros, normalize_axis_index, _get_promotion_state, _set_promotion_state, + _using_numpy2_behavior) + +from . import overrides +from . import umath +from . import shape_base +from .overrides import set_array_function_like_doc, set_module +from .umath import (multiply, invert, sin, PINF, NAN) +from . import numerictypes +from .numerictypes import longlong, intc, int_, float_, complex_, bool_ +from ..exceptions import ComplexWarning, TooHardError, AxisError +from ._ufunc_config import errstate, _no_nep50_warning + +bitwise_not = invert +ufunc = type(sin) +newaxis = None + +array_function_dispatch = functools.partial( + overrides.array_function_dispatch, module='numpy') + + +__all__ = [ + 'newaxis', 'ndarray', 'flatiter', 'nditer', 'nested_iters', 'ufunc', + 'arange', 'array', 'asarray', 'asanyarray', 'ascontiguousarray', + 'asfortranarray', 'zeros', 'count_nonzero', 'empty', 'broadcast', 'dtype', + 'fromstring', 'fromfile', 'frombuffer', 'from_dlpack', 'where', + 'argwhere', 'copyto', 'concatenate', 'fastCopyAndTranspose', 'lexsort', + 'set_numeric_ops', 'can_cast', 'promote_types', 'min_scalar_type', + 'result_type', 'isfortran', 'empty_like', 'zeros_like', 'ones_like', + 'correlate', 'convolve', 'inner', 'dot', 'outer', 'vdot', 'roll', + 'rollaxis', 'moveaxis', 'cross', 'tensordot', 'little_endian', + 'fromiter', 'array_equal', 'array_equiv', 'indices', 'fromfunction', + 'isclose', 'isscalar', 'binary_repr', 'base_repr', 'ones', + 'identity', 'allclose', 'compare_chararrays', 'putmask', + 'flatnonzero', 'Inf', 'inf', 'infty', 'Infinity', 'nan', 'NaN', + 'False_', 'True_', 'bitwise_not', 'CLIP', 'RAISE', 'WRAP', 'MAXDIMS', + 'BUFSIZE', 'ALLOW_THREADS', 'full', 'full_like', + 'matmul', 'shares_memory', 'may_share_memory', 'MAY_SHARE_BOUNDS', + 'MAY_SHARE_EXACT', '_get_promotion_state', '_set_promotion_state', + '_using_numpy2_behavior'] + + +def _zeros_like_dispatcher(a, dtype=None, order=None, subok=None, shape=None): + return (a,) + + +@array_function_dispatch(_zeros_like_dispatcher) +def zeros_like(a, dtype=None, order='K', subok=True, shape=None): + """ + Return an array of zeros with the same shape and type as a given array. + + Parameters + ---------- + a : array_like + The shape and data-type of `a` define these same attributes of + the returned array. + dtype : data-type, optional + Overrides the data type of the result. + + .. versionadded:: 1.6.0 + order : {'C', 'F', 'A', or 'K'}, optional + Overrides the memory layout of the result. 'C' means C-order, + 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, + 'C' otherwise. 'K' means match the layout of `a` as closely + as possible. + + .. versionadded:: 1.6.0 + subok : bool, optional. + If True, then the newly created array will use the sub-class + type of `a`, otherwise it will be a base-class array. Defaults + to True. + shape : int or sequence of ints, optional. + Overrides the shape of the result. If order='K' and the number of + dimensions is unchanged, will try to keep order, otherwise, + order='C' is implied. + + .. versionadded:: 1.17.0 + + Returns + ------- + out : ndarray + Array of zeros with the same shape and type as `a`. + + See Also + -------- + empty_like : Return an empty array with shape and type of input. + ones_like : Return an array of ones with shape and type of input. + full_like : Return a new array with shape of input filled with value. + zeros : Return a new array setting values to zero. + + Examples + -------- + >>> x = np.arange(6) + >>> x = x.reshape((2, 3)) + >>> x + array([[0, 1, 2], + [3, 4, 5]]) + >>> np.zeros_like(x) + array([[0, 0, 0], + [0, 0, 0]]) + + >>> y = np.arange(3, dtype=float) + >>> y + array([0., 1., 2.]) + >>> np.zeros_like(y) + array([0., 0., 0.]) + + """ + res = empty_like(a, dtype=dtype, order=order, subok=subok, shape=shape) + # needed instead of a 0 to get same result as zeros for string dtypes + z = zeros(1, dtype=res.dtype) + multiarray.copyto(res, z, casting='unsafe') + return res + + +@set_array_function_like_doc +@set_module('numpy') +def ones(shape, dtype=None, order='C', *, like=None): + """ + Return a new array of given shape and type, filled with ones. + + Parameters + ---------- + shape : int or sequence of ints + Shape of the new array, e.g., ``(2, 3)`` or ``2``. + dtype : data-type, optional + The desired data-type for the array, e.g., `numpy.int8`. Default is + `numpy.float64`. + order : {'C', 'F'}, optional, default: C + Whether to store multi-dimensional data in row-major + (C-style) or column-major (Fortran-style) order in + memory. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + Array of ones with the given shape, dtype, and order. + + See Also + -------- + ones_like : Return an array of ones with shape and type of input. + empty : Return a new uninitialized array. + zeros : Return a new array setting values to zero. + full : Return a new array of given shape filled with value. + + + Examples + -------- + >>> np.ones(5) + array([1., 1., 1., 1., 1.]) + + >>> np.ones((5,), dtype=int) + array([1, 1, 1, 1, 1]) + + >>> np.ones((2, 1)) + array([[1.], + [1.]]) + + >>> s = (2,2) + >>> np.ones(s) + array([[1., 1.], + [1., 1.]]) + + """ + if like is not None: + return _ones_with_like(like, shape, dtype=dtype, order=order) + + a = empty(shape, dtype, order) + multiarray.copyto(a, 1, casting='unsafe') + return a + + +_ones_with_like = array_function_dispatch()(ones) + + +def _ones_like_dispatcher(a, dtype=None, order=None, subok=None, shape=None): + return (a,) + + +@array_function_dispatch(_ones_like_dispatcher) +def ones_like(a, dtype=None, order='K', subok=True, shape=None): + """ + Return an array of ones with the same shape and type as a given array. + + Parameters + ---------- + a : array_like + The shape and data-type of `a` define these same attributes of + the returned array. + dtype : data-type, optional + Overrides the data type of the result. + + .. versionadded:: 1.6.0 + order : {'C', 'F', 'A', or 'K'}, optional + Overrides the memory layout of the result. 'C' means C-order, + 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, + 'C' otherwise. 'K' means match the layout of `a` as closely + as possible. + + .. versionadded:: 1.6.0 + subok : bool, optional. + If True, then the newly created array will use the sub-class + type of `a`, otherwise it will be a base-class array. Defaults + to True. + shape : int or sequence of ints, optional. + Overrides the shape of the result. If order='K' and the number of + dimensions is unchanged, will try to keep order, otherwise, + order='C' is implied. + + .. versionadded:: 1.17.0 + + Returns + ------- + out : ndarray + Array of ones with the same shape and type as `a`. + + See Also + -------- + empty_like : Return an empty array with shape and type of input. + zeros_like : Return an array of zeros with shape and type of input. + full_like : Return a new array with shape of input filled with value. + ones : Return a new array setting values to one. + + Examples + -------- + >>> x = np.arange(6) + >>> x = x.reshape((2, 3)) + >>> x + array([[0, 1, 2], + [3, 4, 5]]) + >>> np.ones_like(x) + array([[1, 1, 1], + [1, 1, 1]]) + + >>> y = np.arange(3, dtype=float) + >>> y + array([0., 1., 2.]) + >>> np.ones_like(y) + array([1., 1., 1.]) + + """ + res = empty_like(a, dtype=dtype, order=order, subok=subok, shape=shape) + multiarray.copyto(res, 1, casting='unsafe') + return res + + +def _full_dispatcher(shape, fill_value, dtype=None, order=None, *, like=None): + return(like,) + + +@set_array_function_like_doc +@set_module('numpy') +def full(shape, fill_value, dtype=None, order='C', *, like=None): + """ + Return a new array of given shape and type, filled with `fill_value`. + + Parameters + ---------- + shape : int or sequence of ints + Shape of the new array, e.g., ``(2, 3)`` or ``2``. + fill_value : scalar or array_like + Fill value. + dtype : data-type, optional + The desired data-type for the array The default, None, means + ``np.array(fill_value).dtype``. + order : {'C', 'F'}, optional + Whether to store multidimensional data in C- or Fortran-contiguous + (row- or column-wise) order in memory. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + Array of `fill_value` with the given shape, dtype, and order. + + See Also + -------- + full_like : Return a new array with shape of input filled with value. + empty : Return a new uninitialized array. + ones : Return a new array setting values to one. + zeros : Return a new array setting values to zero. + + Examples + -------- + >>> np.full((2, 2), np.inf) + array([[inf, inf], + [inf, inf]]) + >>> np.full((2, 2), 10) + array([[10, 10], + [10, 10]]) + + >>> np.full((2, 2), [1, 2]) + array([[1, 2], + [1, 2]]) + + """ + if like is not None: + return _full_with_like( + like, shape, fill_value, dtype=dtype, order=order) + + if dtype is None: + fill_value = asarray(fill_value) + dtype = fill_value.dtype + a = empty(shape, dtype, order) + multiarray.copyto(a, fill_value, casting='unsafe') + return a + + +_full_with_like = array_function_dispatch()(full) + + +def _full_like_dispatcher(a, fill_value, dtype=None, order=None, subok=None, shape=None): + return (a,) + + +@array_function_dispatch(_full_like_dispatcher) +def full_like(a, fill_value, dtype=None, order='K', subok=True, shape=None): + """ + Return a full array with the same shape and type as a given array. + + Parameters + ---------- + a : array_like + The shape and data-type of `a` define these same attributes of + the returned array. + fill_value : array_like + Fill value. + dtype : data-type, optional + Overrides the data type of the result. + order : {'C', 'F', 'A', or 'K'}, optional + Overrides the memory layout of the result. 'C' means C-order, + 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, + 'C' otherwise. 'K' means match the layout of `a` as closely + as possible. + subok : bool, optional. + If True, then the newly created array will use the sub-class + type of `a`, otherwise it will be a base-class array. Defaults + to True. + shape : int or sequence of ints, optional. + Overrides the shape of the result. If order='K' and the number of + dimensions is unchanged, will try to keep order, otherwise, + order='C' is implied. + + .. versionadded:: 1.17.0 + + Returns + ------- + out : ndarray + Array of `fill_value` with the same shape and type as `a`. + + See Also + -------- + empty_like : Return an empty array with shape and type of input. + ones_like : Return an array of ones with shape and type of input. + zeros_like : Return an array of zeros with shape and type of input. + full : Return a new array of given shape filled with value. + + Examples + -------- + >>> x = np.arange(6, dtype=int) + >>> np.full_like(x, 1) + array([1, 1, 1, 1, 1, 1]) + >>> np.full_like(x, 0.1) + array([0, 0, 0, 0, 0, 0]) + >>> np.full_like(x, 0.1, dtype=np.double) + array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) + >>> np.full_like(x, np.nan, dtype=np.double) + array([nan, nan, nan, nan, nan, nan]) + + >>> y = np.arange(6, dtype=np.double) + >>> np.full_like(y, 0.1) + array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) + + >>> y = np.zeros([2, 2, 3], dtype=int) + >>> np.full_like(y, [0, 0, 255]) + array([[[ 0, 0, 255], + [ 0, 0, 255]], + [[ 0, 0, 255], + [ 0, 0, 255]]]) + """ + res = empty_like(a, dtype=dtype, order=order, subok=subok, shape=shape) + multiarray.copyto(res, fill_value, casting='unsafe') + return res + + +def _count_nonzero_dispatcher(a, axis=None, *, keepdims=None): + return (a,) + + +@array_function_dispatch(_count_nonzero_dispatcher) +def count_nonzero(a, axis=None, *, keepdims=False): + """ + Counts the number of non-zero values in the array ``a``. + + The word "non-zero" is in reference to the Python 2.x + built-in method ``__nonzero__()`` (renamed ``__bool__()`` + in Python 3.x) of Python objects that tests an object's + "truthfulness". For example, any number is considered + truthful if it is nonzero, whereas any string is considered + truthful if it is not the empty string. Thus, this function + (recursively) counts how many elements in ``a`` (and in + sub-arrays thereof) have their ``__nonzero__()`` or ``__bool__()`` + method evaluated to ``True``. + + Parameters + ---------- + a : array_like + The array for which to count non-zeros. + axis : int or tuple, optional + Axis or tuple of axes along which to count non-zeros. + Default is None, meaning that non-zeros will be counted + along a flattened version of ``a``. + + .. versionadded:: 1.12.0 + + keepdims : bool, optional + If this is set to True, the axes that are counted are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + .. versionadded:: 1.19.0 + + Returns + ------- + count : int or array of int + Number of non-zero values in the array along a given axis. + Otherwise, the total number of non-zero values in the array + is returned. + + See Also + -------- + nonzero : Return the coordinates of all the non-zero values. + + Examples + -------- + >>> np.count_nonzero(np.eye(4)) + 4 + >>> a = np.array([[0, 1, 7, 0], + ... [3, 0, 2, 19]]) + >>> np.count_nonzero(a) + 5 + >>> np.count_nonzero(a, axis=0) + array([1, 1, 2, 1]) + >>> np.count_nonzero(a, axis=1) + array([2, 3]) + >>> np.count_nonzero(a, axis=1, keepdims=True) + array([[2], + [3]]) + """ + if axis is None and not keepdims: + return multiarray.count_nonzero(a) + + a = asanyarray(a) + + # TODO: this works around .astype(bool) not working properly (gh-9847) + if np.issubdtype(a.dtype, np.character): + a_bool = a != a.dtype.type() + else: + a_bool = a.astype(np.bool_, copy=False) + + return a_bool.sum(axis=axis, dtype=np.intp, keepdims=keepdims) + + +@set_module('numpy') +def isfortran(a): + """ + Check if the array is Fortran contiguous but *not* C contiguous. + + This function is obsolete and, because of changes due to relaxed stride + checking, its return value for the same array may differ for versions + of NumPy >= 1.10.0 and previous versions. If you only want to check if an + array is Fortran contiguous use ``a.flags.f_contiguous`` instead. + + Parameters + ---------- + a : ndarray + Input array. + + Returns + ------- + isfortran : bool + Returns True if the array is Fortran contiguous but *not* C contiguous. + + + Examples + -------- + + np.array allows to specify whether the array is written in C-contiguous + order (last index varies the fastest), or FORTRAN-contiguous order in + memory (first index varies the fastest). + + >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') + >>> a + array([[1, 2, 3], + [4, 5, 6]]) + >>> np.isfortran(a) + False + + >>> b = np.array([[1, 2, 3], [4, 5, 6]], order='F') + >>> b + array([[1, 2, 3], + [4, 5, 6]]) + >>> np.isfortran(b) + True + + + The transpose of a C-ordered array is a FORTRAN-ordered array. + + >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') + >>> a + array([[1, 2, 3], + [4, 5, 6]]) + >>> np.isfortran(a) + False + >>> b = a.T + >>> b + array([[1, 4], + [2, 5], + [3, 6]]) + >>> np.isfortran(b) + True + + C-ordered arrays evaluate as False even if they are also FORTRAN-ordered. + + >>> np.isfortran(np.array([1, 2], order='F')) + False + + """ + return a.flags.fnc + + +def _argwhere_dispatcher(a): + return (a,) + + +@array_function_dispatch(_argwhere_dispatcher) +def argwhere(a): + """ + Find the indices of array elements that are non-zero, grouped by element. + + Parameters + ---------- + a : array_like + Input data. + + Returns + ------- + index_array : (N, a.ndim) ndarray + Indices of elements that are non-zero. Indices are grouped by element. + This array will have shape ``(N, a.ndim)`` where ``N`` is the number of + non-zero items. + + See Also + -------- + where, nonzero + + Notes + ----- + ``np.argwhere(a)`` is almost the same as ``np.transpose(np.nonzero(a))``, + but produces a result of the correct shape for a 0D array. + + The output of ``argwhere`` is not suitable for indexing arrays. + For this purpose use ``nonzero(a)`` instead. + + Examples + -------- + >>> x = np.arange(6).reshape(2,3) + >>> x + array([[0, 1, 2], + [3, 4, 5]]) + >>> np.argwhere(x>1) + array([[0, 2], + [1, 0], + [1, 1], + [1, 2]]) + + """ + # nonzero does not behave well on 0d, so promote to 1d + if np.ndim(a) == 0: + a = shape_base.atleast_1d(a) + # then remove the added dimension + return argwhere(a)[:,:0] + return transpose(nonzero(a)) + + +def _flatnonzero_dispatcher(a): + return (a,) + + +@array_function_dispatch(_flatnonzero_dispatcher) +def flatnonzero(a): + """ + Return indices that are non-zero in the flattened version of a. + + This is equivalent to ``np.nonzero(np.ravel(a))[0]``. + + Parameters + ---------- + a : array_like + Input data. + + Returns + ------- + res : ndarray + Output array, containing the indices of the elements of ``a.ravel()`` + that are non-zero. + + See Also + -------- + nonzero : Return the indices of the non-zero elements of the input array. + ravel : Return a 1-D array containing the elements of the input array. + + Examples + -------- + >>> x = np.arange(-2, 3) + >>> x + array([-2, -1, 0, 1, 2]) + >>> np.flatnonzero(x) + array([0, 1, 3, 4]) + + Use the indices of the non-zero elements as an index array to extract + these elements: + + >>> x.ravel()[np.flatnonzero(x)] + array([-2, -1, 1, 2]) + + """ + return np.nonzero(np.ravel(a))[0] + + +def _correlate_dispatcher(a, v, mode=None): + return (a, v) + + +@array_function_dispatch(_correlate_dispatcher) +def correlate(a, v, mode='valid'): + r""" + Cross-correlation of two 1-dimensional sequences. + + This function computes the correlation as generally defined in signal + processing texts: + + .. math:: c_k = \sum_n a_{n+k} \cdot \overline{v}_n + + with a and v sequences being zero-padded where necessary and + :math:`\overline x` denoting complex conjugation. + + Parameters + ---------- + a, v : array_like + Input sequences. + mode : {'valid', 'same', 'full'}, optional + Refer to the `convolve` docstring. Note that the default + is 'valid', unlike `convolve`, which uses 'full'. + old_behavior : bool + `old_behavior` was removed in NumPy 1.10. If you need the old + behavior, use `multiarray.correlate`. + + Returns + ------- + out : ndarray + Discrete cross-correlation of `a` and `v`. + + See Also + -------- + convolve : Discrete, linear convolution of two one-dimensional sequences. + multiarray.correlate : Old, no conjugate, version of correlate. + scipy.signal.correlate : uses FFT which has superior performance on large arrays. + + Notes + ----- + The definition of correlation above is not unique and sometimes correlation + may be defined differently. Another common definition is: + + .. math:: c'_k = \sum_n a_{n} \cdot \overline{v_{n+k}} + + which is related to :math:`c_k` by :math:`c'_k = c_{-k}`. + + `numpy.correlate` may perform slowly in large arrays (i.e. n = 1e5) because it does + not use the FFT to compute the convolution; in that case, `scipy.signal.correlate` might + be preferable. + + + Examples + -------- + >>> np.correlate([1, 2, 3], [0, 1, 0.5]) + array([3.5]) + >>> np.correlate([1, 2, 3], [0, 1, 0.5], "same") + array([2. , 3.5, 3. ]) + >>> np.correlate([1, 2, 3], [0, 1, 0.5], "full") + array([0.5, 2. , 3.5, 3. , 0. ]) + + Using complex sequences: + + >>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full') + array([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ]) + + Note that you get the time reversed, complex conjugated result + (:math:`\overline{c_{-k}}`) when the two input sequences a and v change + places: + + >>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full') + array([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j]) + + """ + return multiarray.correlate2(a, v, mode) + + +def _convolve_dispatcher(a, v, mode=None): + return (a, v) + + +@array_function_dispatch(_convolve_dispatcher) +def convolve(a, v, mode='full'): + """ + Returns the discrete, linear convolution of two one-dimensional sequences. + + The convolution operator is often seen in signal processing, where it + models the effect of a linear time-invariant system on a signal [1]_. In + probability theory, the sum of two independent random variables is + distributed according to the convolution of their individual + distributions. + + If `v` is longer than `a`, the arrays are swapped before computation. + + Parameters + ---------- + a : (N,) array_like + First one-dimensional input array. + v : (M,) array_like + Second one-dimensional input array. + mode : {'full', 'valid', 'same'}, optional + 'full': + By default, mode is 'full'. This returns the convolution + at each point of overlap, with an output shape of (N+M-1,). At + the end-points of the convolution, the signals do not overlap + completely, and boundary effects may be seen. + + 'same': + Mode 'same' returns output of length ``max(M, N)``. Boundary + effects are still visible. + + 'valid': + Mode 'valid' returns output of length + ``max(M, N) - min(M, N) + 1``. The convolution product is only given + for points where the signals overlap completely. Values outside + the signal boundary have no effect. + + Returns + ------- + out : ndarray + Discrete, linear convolution of `a` and `v`. + + See Also + -------- + scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier + Transform. + scipy.linalg.toeplitz : Used to construct the convolution operator. + polymul : Polynomial multiplication. Same output as convolve, but also + accepts poly1d objects as input. + + Notes + ----- + The discrete convolution operation is defined as + + .. math:: (a * v)_n = \\sum_{m = -\\infty}^{\\infty} a_m v_{n - m} + + It can be shown that a convolution :math:`x(t) * y(t)` in time/space + is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier + domain, after appropriate padding (padding is necessary to prevent + circular convolution). Since multiplication is more efficient (faster) + than convolution, the function `scipy.signal.fftconvolve` exploits the + FFT to calculate the convolution of large data-sets. + + References + ---------- + .. [1] Wikipedia, "Convolution", + https://en.wikipedia.org/wiki/Convolution + + Examples + -------- + Note how the convolution operator flips the second array + before "sliding" the two across one another: + + >>> np.convolve([1, 2, 3], [0, 1, 0.5]) + array([0. , 1. , 2.5, 4. , 1.5]) + + Only return the middle values of the convolution. + Contains boundary effects, where zeros are taken + into account: + + >>> np.convolve([1,2,3],[0,1,0.5], 'same') + array([1. , 2.5, 4. ]) + + The two arrays are of the same length, so there + is only one position where they completely overlap: + + >>> np.convolve([1,2,3],[0,1,0.5], 'valid') + array([2.5]) + + """ + a, v = array(a, copy=False, ndmin=1), array(v, copy=False, ndmin=1) + if (len(v) > len(a)): + a, v = v, a + if len(a) == 0: + raise ValueError('a cannot be empty') + if len(v) == 0: + raise ValueError('v cannot be empty') + return multiarray.correlate(a, v[::-1], mode) + + +def _outer_dispatcher(a, b, out=None): + return (a, b, out) + + +@array_function_dispatch(_outer_dispatcher) +def outer(a, b, out=None): + """ + Compute the outer product of two vectors. + + Given two vectors `a` and `b` of length ``M`` and ``N``, repsectively, + the outer product [1]_ is:: + + [[a_0*b_0 a_0*b_1 ... a_0*b_{N-1} ] + [a_1*b_0 . + [ ... . + [a_{M-1}*b_0 a_{M-1}*b_{N-1} ]] + + Parameters + ---------- + a : (M,) array_like + First input vector. Input is flattened if + not already 1-dimensional. + b : (N,) array_like + Second input vector. Input is flattened if + not already 1-dimensional. + out : (M, N) ndarray, optional + A location where the result is stored + + .. versionadded:: 1.9.0 + + Returns + ------- + out : (M, N) ndarray + ``out[i, j] = a[i] * b[j]`` + + See also + -------- + inner + einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent. + ufunc.outer : A generalization to dimensions other than 1D and other + operations. ``np.multiply.outer(a.ravel(), b.ravel())`` + is the equivalent. + tensordot : ``np.tensordot(a.ravel(), b.ravel(), axes=((), ()))`` + is the equivalent. + + References + ---------- + .. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd + ed., Baltimore, MD, Johns Hopkins University Press, 1996, + pg. 8. + + Examples + -------- + Make a (*very* coarse) grid for computing a Mandelbrot set: + + >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5)) + >>> rl + array([[-2., -1., 0., 1., 2.], + [-2., -1., 0., 1., 2.], + [-2., -1., 0., 1., 2.], + [-2., -1., 0., 1., 2.], + [-2., -1., 0., 1., 2.]]) + >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,))) + >>> im + array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j], + [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j], + [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], + [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j], + [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]]) + >>> grid = rl + im + >>> grid + array([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j], + [-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j], + [-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j], + [-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j], + [-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]]) + + An example using a "vector" of letters: + + >>> x = np.array(['a', 'b', 'c'], dtype=object) + >>> np.outer(x, [1, 2, 3]) + array([['a', 'aa', 'aaa'], + ['b', 'bb', 'bbb'], + ['c', 'cc', 'ccc']], dtype=object) + + """ + a = asarray(a) + b = asarray(b) + return multiply(a.ravel()[:, newaxis], b.ravel()[newaxis, :], out) + + +def _tensordot_dispatcher(a, b, axes=None): + return (a, b) + + +@array_function_dispatch(_tensordot_dispatcher) +def tensordot(a, b, axes=2): + """ + Compute tensor dot product along specified axes. + + Given two tensors, `a` and `b`, and an array_like object containing + two array_like objects, ``(a_axes, b_axes)``, sum the products of + `a`'s and `b`'s elements (components) over the axes specified by + ``a_axes`` and ``b_axes``. The third argument can be a single non-negative + integer_like scalar, ``N``; if it is such, then the last ``N`` dimensions + of `a` and the first ``N`` dimensions of `b` are summed over. + + Parameters + ---------- + a, b : array_like + Tensors to "dot". + + axes : int or (2,) array_like + * integer_like + If an int N, sum over the last N axes of `a` and the first N axes + of `b` in order. The sizes of the corresponding axes must match. + * (2,) array_like + Or, a list of axes to be summed over, first sequence applying to `a`, + second to `b`. Both elements array_like must be of the same length. + + Returns + ------- + output : ndarray + The tensor dot product of the input. + + See Also + -------- + dot, einsum + + Notes + ----- + Three common use cases are: + * ``axes = 0`` : tensor product :math:`a\\otimes b` + * ``axes = 1`` : tensor dot product :math:`a\\cdot b` + * ``axes = 2`` : (default) tensor double contraction :math:`a:b` + + When `axes` is integer_like, the sequence for evaluation will be: first + the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and + Nth axis in `b` last. + + When there is more than one axis to sum over - and they are not the last + (first) axes of `a` (`b`) - the argument `axes` should consist of + two sequences of the same length, with the first axis to sum over given + first in both sequences, the second axis second, and so forth. + + The shape of the result consists of the non-contracted axes of the + first tensor, followed by the non-contracted axes of the second. + + Examples + -------- + A "traditional" example: + + >>> a = np.arange(60.).reshape(3,4,5) + >>> b = np.arange(24.).reshape(4,3,2) + >>> c = np.tensordot(a,b, axes=([1,0],[0,1])) + >>> c.shape + (5, 2) + >>> c + array([[4400., 4730.], + [4532., 4874.], + [4664., 5018.], + [4796., 5162.], + [4928., 5306.]]) + >>> # A slower but equivalent way of computing the same... + >>> d = np.zeros((5,2)) + >>> for i in range(5): + ... for j in range(2): + ... for k in range(3): + ... for n in range(4): + ... d[i,j] += a[k,n,i] * b[n,k,j] + >>> c == d + array([[ True, True], + [ True, True], + [ True, True], + [ True, True], + [ True, True]]) + + An extended example taking advantage of the overloading of + and \\*: + + >>> a = np.array(range(1, 9)) + >>> a.shape = (2, 2, 2) + >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object) + >>> A.shape = (2, 2) + >>> a; A + array([[[1, 2], + [3, 4]], + [[5, 6], + [7, 8]]]) + array([['a', 'b'], + ['c', 'd']], dtype=object) + + >>> np.tensordot(a, A) # third argument default is 2 for double-contraction + array(['abbcccdddd', 'aaaaabbbbbbcccccccdddddddd'], dtype=object) + + >>> np.tensordot(a, A, 1) + array([[['acc', 'bdd'], + ['aaacccc', 'bbbdddd']], + [['aaaaacccccc', 'bbbbbdddddd'], + ['aaaaaaacccccccc', 'bbbbbbbdddddddd']]], dtype=object) + + >>> np.tensordot(a, A, 0) # tensor product (result too long to incl.) + array([[[[['a', 'b'], + ['c', 'd']], + ... + + >>> np.tensordot(a, A, (0, 1)) + array([[['abbbbb', 'cddddd'], + ['aabbbbbb', 'ccdddddd']], + [['aaabbbbbbb', 'cccddddddd'], + ['aaaabbbbbbbb', 'ccccdddddddd']]], dtype=object) + + >>> np.tensordot(a, A, (2, 1)) + array([[['abb', 'cdd'], + ['aaabbbb', 'cccdddd']], + [['aaaaabbbbbb', 'cccccdddddd'], + ['aaaaaaabbbbbbbb', 'cccccccdddddddd']]], dtype=object) + + >>> np.tensordot(a, A, ((0, 1), (0, 1))) + array(['abbbcccccddddddd', 'aabbbbccccccdddddddd'], dtype=object) + + >>> np.tensordot(a, A, ((2, 1), (1, 0))) + array(['acccbbdddd', 'aaaaacccccccbbbbbbdddddddd'], dtype=object) + + """ + try: + iter(axes) + except Exception: + axes_a = list(range(-axes, 0)) + axes_b = list(range(0, axes)) + else: + axes_a, axes_b = axes + try: + na = len(axes_a) + axes_a = list(axes_a) + except TypeError: + axes_a = [axes_a] + na = 1 + try: + nb = len(axes_b) + axes_b = list(axes_b) + except TypeError: + axes_b = [axes_b] + nb = 1 + + a, b = asarray(a), asarray(b) + as_ = a.shape + nda = a.ndim + bs = b.shape + ndb = b.ndim + equal = True + if na != nb: + equal = False + else: + for k in range(na): + if as_[axes_a[k]] != bs[axes_b[k]]: + equal = False + break + if axes_a[k] < 0: + axes_a[k] += nda + if axes_b[k] < 0: + axes_b[k] += ndb + if not equal: + raise ValueError("shape-mismatch for sum") + + # Move the axes to sum over to the end of "a" + # and to the front of "b" + notin = [k for k in range(nda) if k not in axes_a] + newaxes_a = notin + axes_a + N2 = 1 + for axis in axes_a: + N2 *= as_[axis] + newshape_a = (int(multiply.reduce([as_[ax] for ax in notin])), N2) + olda = [as_[axis] for axis in notin] + + notin = [k for k in range(ndb) if k not in axes_b] + newaxes_b = axes_b + notin + N2 = 1 + for axis in axes_b: + N2 *= bs[axis] + newshape_b = (N2, int(multiply.reduce([bs[ax] for ax in notin]))) + oldb = [bs[axis] for axis in notin] + + at = a.transpose(newaxes_a).reshape(newshape_a) + bt = b.transpose(newaxes_b).reshape(newshape_b) + res = dot(at, bt) + return res.reshape(olda + oldb) + + +def _roll_dispatcher(a, shift, axis=None): + return (a,) + + +@array_function_dispatch(_roll_dispatcher) +def roll(a, shift, axis=None): + """ + Roll array elements along a given axis. + + Elements that roll beyond the last position are re-introduced at + the first. + + Parameters + ---------- + a : array_like + Input array. + shift : int or tuple of ints + The number of places by which elements are shifted. If a tuple, + then `axis` must be a tuple of the same size, and each of the + given axes is shifted by the corresponding number. If an int + while `axis` is a tuple of ints, then the same value is used for + all given axes. + axis : int or tuple of ints, optional + Axis or axes along which elements are shifted. By default, the + array is flattened before shifting, after which the original + shape is restored. + + Returns + ------- + res : ndarray + Output array, with the same shape as `a`. + + See Also + -------- + rollaxis : Roll the specified axis backwards, until it lies in a + given position. + + Notes + ----- + .. versionadded:: 1.12.0 + + Supports rolling over multiple dimensions simultaneously. + + Examples + -------- + >>> x = np.arange(10) + >>> np.roll(x, 2) + array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]) + >>> np.roll(x, -2) + array([2, 3, 4, 5, 6, 7, 8, 9, 0, 1]) + + >>> x2 = np.reshape(x, (2, 5)) + >>> x2 + array([[0, 1, 2, 3, 4], + [5, 6, 7, 8, 9]]) + >>> np.roll(x2, 1) + array([[9, 0, 1, 2, 3], + [4, 5, 6, 7, 8]]) + >>> np.roll(x2, -1) + array([[1, 2, 3, 4, 5], + [6, 7, 8, 9, 0]]) + >>> np.roll(x2, 1, axis=0) + array([[5, 6, 7, 8, 9], + [0, 1, 2, 3, 4]]) + >>> np.roll(x2, -1, axis=0) + array([[5, 6, 7, 8, 9], + [0, 1, 2, 3, 4]]) + >>> np.roll(x2, 1, axis=1) + array([[4, 0, 1, 2, 3], + [9, 5, 6, 7, 8]]) + >>> np.roll(x2, -1, axis=1) + array([[1, 2, 3, 4, 0], + [6, 7, 8, 9, 5]]) + >>> np.roll(x2, (1, 1), axis=(1, 0)) + array([[9, 5, 6, 7, 8], + [4, 0, 1, 2, 3]]) + >>> np.roll(x2, (2, 1), axis=(1, 0)) + array([[8, 9, 5, 6, 7], + [3, 4, 0, 1, 2]]) + + """ + a = asanyarray(a) + if axis is None: + return roll(a.ravel(), shift, 0).reshape(a.shape) + + else: + axis = normalize_axis_tuple(axis, a.ndim, allow_duplicate=True) + broadcasted = broadcast(shift, axis) + if broadcasted.ndim > 1: + raise ValueError( + "'shift' and 'axis' should be scalars or 1D sequences") + shifts = {ax: 0 for ax in range(a.ndim)} + for sh, ax in broadcasted: + shifts[ax] += sh + + rolls = [((slice(None), slice(None)),)] * a.ndim + for ax, offset in shifts.items(): + offset %= a.shape[ax] or 1 # If `a` is empty, nothing matters. + if offset: + # (original, result), (original, result) + rolls[ax] = ((slice(None, -offset), slice(offset, None)), + (slice(-offset, None), slice(None, offset))) + + result = empty_like(a) + for indices in itertools.product(*rolls): + arr_index, res_index = zip(*indices) + result[res_index] = a[arr_index] + + return result + + +def _rollaxis_dispatcher(a, axis, start=None): + return (a,) + + +@array_function_dispatch(_rollaxis_dispatcher) +def rollaxis(a, axis, start=0): + """ + Roll the specified axis backwards, until it lies in a given position. + + This function continues to be supported for backward compatibility, but you + should prefer `moveaxis`. The `moveaxis` function was added in NumPy + 1.11. + + Parameters + ---------- + a : ndarray + Input array. + axis : int + The axis to be rolled. The positions of the other axes do not + change relative to one another. + start : int, optional + When ``start <= axis``, the axis is rolled back until it lies in + this position. When ``start > axis``, the axis is rolled until it + lies before this position. The default, 0, results in a "complete" + roll. The following table describes how negative values of ``start`` + are interpreted: + + .. table:: + :align: left + + +-------------------+----------------------+ + | ``start`` | Normalized ``start`` | + +===================+======================+ + | ``-(arr.ndim+1)`` | raise ``AxisError`` | + +-------------------+----------------------+ + | ``-arr.ndim`` | 0 | + +-------------------+----------------------+ + | |vdots| | |vdots| | + +-------------------+----------------------+ + | ``-1`` | ``arr.ndim-1`` | + +-------------------+----------------------+ + | ``0`` | ``0`` | + +-------------------+----------------------+ + | |vdots| | |vdots| | + +-------------------+----------------------+ + | ``arr.ndim`` | ``arr.ndim`` | + +-------------------+----------------------+ + | ``arr.ndim + 1`` | raise ``AxisError`` | + +-------------------+----------------------+ + + .. |vdots| unicode:: U+22EE .. Vertical Ellipsis + + Returns + ------- + res : ndarray + For NumPy >= 1.10.0 a view of `a` is always returned. For earlier + NumPy versions a view of `a` is returned only if the order of the + axes is changed, otherwise the input array is returned. + + See Also + -------- + moveaxis : Move array axes to new positions. + roll : Roll the elements of an array by a number of positions along a + given axis. + + Examples + -------- + >>> a = np.ones((3,4,5,6)) + >>> np.rollaxis(a, 3, 1).shape + (3, 6, 4, 5) + >>> np.rollaxis(a, 2).shape + (5, 3, 4, 6) + >>> np.rollaxis(a, 1, 4).shape + (3, 5, 6, 4) + + """ + n = a.ndim + axis = normalize_axis_index(axis, n) + if start < 0: + start += n + msg = "'%s' arg requires %d <= %s < %d, but %d was passed in" + if not (0 <= start < n + 1): + raise AxisError(msg % ('start', -n, 'start', n + 1, start)) + if axis < start: + # it's been removed + start -= 1 + if axis == start: + return a[...] + axes = list(range(0, n)) + axes.remove(axis) + axes.insert(start, axis) + return a.transpose(axes) + + +def normalize_axis_tuple(axis, ndim, argname=None, allow_duplicate=False): + """ + Normalizes an axis argument into a tuple of non-negative integer axes. + + This handles shorthands such as ``1`` and converts them to ``(1,)``, + as well as performing the handling of negative indices covered by + `normalize_axis_index`. + + By default, this forbids axes from being specified multiple times. + + Used internally by multi-axis-checking logic. + + .. versionadded:: 1.13.0 + + Parameters + ---------- + axis : int, iterable of int + The un-normalized index or indices of the axis. + ndim : int + The number of dimensions of the array that `axis` should be normalized + against. + argname : str, optional + A prefix to put before the error message, typically the name of the + argument. + allow_duplicate : bool, optional + If False, the default, disallow an axis from being specified twice. + + Returns + ------- + normalized_axes : tuple of int + The normalized axis index, such that `0 <= normalized_axis < ndim` + + Raises + ------ + AxisError + If any axis provided is out of range + ValueError + If an axis is repeated + + See also + -------- + normalize_axis_index : normalizing a single scalar axis + """ + # Optimization to speed-up the most common cases. + if type(axis) not in (tuple, list): + try: + axis = [operator.index(axis)] + except TypeError: + pass + # Going via an iterator directly is slower than via list comprehension. + axis = tuple([normalize_axis_index(ax, ndim, argname) for ax in axis]) + if not allow_duplicate and len(set(axis)) != len(axis): + if argname: + raise ValueError('repeated axis in `{}` argument'.format(argname)) + else: + raise ValueError('repeated axis') + return axis + + +def _moveaxis_dispatcher(a, source, destination): + return (a,) + + +@array_function_dispatch(_moveaxis_dispatcher) +def moveaxis(a, source, destination): + """ + Move axes of an array to new positions. + + Other axes remain in their original order. + + .. versionadded:: 1.11.0 + + Parameters + ---------- + a : np.ndarray + The array whose axes should be reordered. + source : int or sequence of int + Original positions of the axes to move. These must be unique. + destination : int or sequence of int + Destination positions for each of the original axes. These must also be + unique. + + Returns + ------- + result : np.ndarray + Array with moved axes. This array is a view of the input array. + + See Also + -------- + transpose : Permute the dimensions of an array. + swapaxes : Interchange two axes of an array. + + Examples + -------- + >>> x = np.zeros((3, 4, 5)) + >>> np.moveaxis(x, 0, -1).shape + (4, 5, 3) + >>> np.moveaxis(x, -1, 0).shape + (5, 3, 4) + + These all achieve the same result: + + >>> np.transpose(x).shape + (5, 4, 3) + >>> np.swapaxes(x, 0, -1).shape + (5, 4, 3) + >>> np.moveaxis(x, [0, 1], [-1, -2]).shape + (5, 4, 3) + >>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape + (5, 4, 3) + + """ + try: + # allow duck-array types if they define transpose + transpose = a.transpose + except AttributeError: + a = asarray(a) + transpose = a.transpose + + source = normalize_axis_tuple(source, a.ndim, 'source') + destination = normalize_axis_tuple(destination, a.ndim, 'destination') + if len(source) != len(destination): + raise ValueError('`source` and `destination` arguments must have ' + 'the same number of elements') + + order = [n for n in range(a.ndim) if n not in source] + + for dest, src in sorted(zip(destination, source)): + order.insert(dest, src) + + result = transpose(order) + return result + + +def _cross_dispatcher(a, b, axisa=None, axisb=None, axisc=None, axis=None): + return (a, b) + + +@array_function_dispatch(_cross_dispatcher) +def cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None): + """ + Return the cross product of two (arrays of) vectors. + + The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular + to both `a` and `b`. If `a` and `b` are arrays of vectors, the vectors + are defined by the last axis of `a` and `b` by default, and these axes + can have dimensions 2 or 3. Where the dimension of either `a` or `b` is + 2, the third component of the input vector is assumed to be zero and the + cross product calculated accordingly. In cases where both input vectors + have dimension 2, the z-component of the cross product is returned. + + Parameters + ---------- + a : array_like + Components of the first vector(s). + b : array_like + Components of the second vector(s). + axisa : int, optional + Axis of `a` that defines the vector(s). By default, the last axis. + axisb : int, optional + Axis of `b` that defines the vector(s). By default, the last axis. + axisc : int, optional + Axis of `c` containing the cross product vector(s). Ignored if + both input vectors have dimension 2, as the return is scalar. + By default, the last axis. + axis : int, optional + If defined, the axis of `a`, `b` and `c` that defines the vector(s) + and cross product(s). Overrides `axisa`, `axisb` and `axisc`. + + Returns + ------- + c : ndarray + Vector cross product(s). + + Raises + ------ + ValueError + When the dimension of the vector(s) in `a` and/or `b` does not + equal 2 or 3. + + See Also + -------- + inner : Inner product + outer : Outer product. + ix_ : Construct index arrays. + + Notes + ----- + .. versionadded:: 1.9.0 + + Supports full broadcasting of the inputs. + + Examples + -------- + Vector cross-product. + + >>> x = [1, 2, 3] + >>> y = [4, 5, 6] + >>> np.cross(x, y) + array([-3, 6, -3]) + + One vector with dimension 2. + + >>> x = [1, 2] + >>> y = [4, 5, 6] + >>> np.cross(x, y) + array([12, -6, -3]) + + Equivalently: + + >>> x = [1, 2, 0] + >>> y = [4, 5, 6] + >>> np.cross(x, y) + array([12, -6, -3]) + + Both vectors with dimension 2. + + >>> x = [1,2] + >>> y = [4,5] + >>> np.cross(x, y) + array(-3) + + Multiple vector cross-products. Note that the direction of the cross + product vector is defined by the *right-hand rule*. + + >>> x = np.array([[1,2,3], [4,5,6]]) + >>> y = np.array([[4,5,6], [1,2,3]]) + >>> np.cross(x, y) + array([[-3, 6, -3], + [ 3, -6, 3]]) + + The orientation of `c` can be changed using the `axisc` keyword. + + >>> np.cross(x, y, axisc=0) + array([[-3, 3], + [ 6, -6], + [-3, 3]]) + + Change the vector definition of `x` and `y` using `axisa` and `axisb`. + + >>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]]) + >>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]]) + >>> np.cross(x, y) + array([[ -6, 12, -6], + [ 0, 0, 0], + [ 6, -12, 6]]) + >>> np.cross(x, y, axisa=0, axisb=0) + array([[-24, 48, -24], + [-30, 60, -30], + [-36, 72, -36]]) + + """ + if axis is not None: + axisa, axisb, axisc = (axis,) * 3 + a = asarray(a) + b = asarray(b) + # Check axisa and axisb are within bounds + axisa = normalize_axis_index(axisa, a.ndim, msg_prefix='axisa') + axisb = normalize_axis_index(axisb, b.ndim, msg_prefix='axisb') + + # Move working axis to the end of the shape + a = moveaxis(a, axisa, -1) + b = moveaxis(b, axisb, -1) + msg = ("incompatible dimensions for cross product\n" + "(dimension must be 2 or 3)") + if a.shape[-1] not in (2, 3) or b.shape[-1] not in (2, 3): + raise ValueError(msg) + + # Create the output array + shape = broadcast(a[..., 0], b[..., 0]).shape + if a.shape[-1] == 3 or b.shape[-1] == 3: + shape += (3,) + # Check axisc is within bounds + axisc = normalize_axis_index(axisc, len(shape), msg_prefix='axisc') + dtype = promote_types(a.dtype, b.dtype) + cp = empty(shape, dtype) + + # recast arrays as dtype + a = a.astype(dtype) + b = b.astype(dtype) + + # create local aliases for readability + a0 = a[..., 0] + a1 = a[..., 1] + if a.shape[-1] == 3: + a2 = a[..., 2] + b0 = b[..., 0] + b1 = b[..., 1] + if b.shape[-1] == 3: + b2 = b[..., 2] + if cp.ndim != 0 and cp.shape[-1] == 3: + cp0 = cp[..., 0] + cp1 = cp[..., 1] + cp2 = cp[..., 2] + + if a.shape[-1] == 2: + if b.shape[-1] == 2: + # a0 * b1 - a1 * b0 + multiply(a0, b1, out=cp) + cp -= a1 * b0 + return cp + else: + assert b.shape[-1] == 3 + # cp0 = a1 * b2 - 0 (a2 = 0) + # cp1 = 0 - a0 * b2 (a2 = 0) + # cp2 = a0 * b1 - a1 * b0 + multiply(a1, b2, out=cp0) + multiply(a0, b2, out=cp1) + negative(cp1, out=cp1) + multiply(a0, b1, out=cp2) + cp2 -= a1 * b0 + else: + assert a.shape[-1] == 3 + if b.shape[-1] == 3: + # cp0 = a1 * b2 - a2 * b1 + # cp1 = a2 * b0 - a0 * b2 + # cp2 = a0 * b1 - a1 * b0 + multiply(a1, b2, out=cp0) + tmp = array(a2 * b1) + cp0 -= tmp + multiply(a2, b0, out=cp1) + multiply(a0, b2, out=tmp) + cp1 -= tmp + multiply(a0, b1, out=cp2) + multiply(a1, b0, out=tmp) + cp2 -= tmp + else: + assert b.shape[-1] == 2 + # cp0 = 0 - a2 * b1 (b2 = 0) + # cp1 = a2 * b0 - 0 (b2 = 0) + # cp2 = a0 * b1 - a1 * b0 + multiply(a2, b1, out=cp0) + negative(cp0, out=cp0) + multiply(a2, b0, out=cp1) + multiply(a0, b1, out=cp2) + cp2 -= a1 * b0 + + return moveaxis(cp, -1, axisc) + + +little_endian = (sys.byteorder == 'little') + + +@set_module('numpy') +def indices(dimensions, dtype=int, sparse=False): + """ + Return an array representing the indices of a grid. + + Compute an array where the subarrays contain index values 0, 1, ... + varying only along the corresponding axis. + + Parameters + ---------- + dimensions : sequence of ints + The shape of the grid. + dtype : dtype, optional + Data type of the result. + sparse : boolean, optional + Return a sparse representation of the grid instead of a dense + representation. Default is False. + + .. versionadded:: 1.17 + + Returns + ------- + grid : one ndarray or tuple of ndarrays + If sparse is False: + Returns one array of grid indices, + ``grid.shape = (len(dimensions),) + tuple(dimensions)``. + If sparse is True: + Returns a tuple of arrays, with + ``grid[i].shape = (1, ..., 1, dimensions[i], 1, ..., 1)`` with + dimensions[i] in the ith place + + See Also + -------- + mgrid, ogrid, meshgrid + + Notes + ----- + The output shape in the dense case is obtained by prepending the number + of dimensions in front of the tuple of dimensions, i.e. if `dimensions` + is a tuple ``(r0, ..., rN-1)`` of length ``N``, the output shape is + ``(N, r0, ..., rN-1)``. + + The subarrays ``grid[k]`` contains the N-D array of indices along the + ``k-th`` axis. Explicitly:: + + grid[k, i0, i1, ..., iN-1] = ik + + Examples + -------- + >>> grid = np.indices((2, 3)) + >>> grid.shape + (2, 2, 3) + >>> grid[0] # row indices + array([[0, 0, 0], + [1, 1, 1]]) + >>> grid[1] # column indices + array([[0, 1, 2], + [0, 1, 2]]) + + The indices can be used as an index into an array. + + >>> x = np.arange(20).reshape(5, 4) + >>> row, col = np.indices((2, 3)) + >>> x[row, col] + array([[0, 1, 2], + [4, 5, 6]]) + + Note that it would be more straightforward in the above example to + extract the required elements directly with ``x[:2, :3]``. + + If sparse is set to true, the grid will be returned in a sparse + representation. + + >>> i, j = np.indices((2, 3), sparse=True) + >>> i.shape + (2, 1) + >>> j.shape + (1, 3) + >>> i # row indices + array([[0], + [1]]) + >>> j # column indices + array([[0, 1, 2]]) + + """ + dimensions = tuple(dimensions) + N = len(dimensions) + shape = (1,)*N + if sparse: + res = tuple() + else: + res = empty((N,)+dimensions, dtype=dtype) + for i, dim in enumerate(dimensions): + idx = arange(dim, dtype=dtype).reshape( + shape[:i] + (dim,) + shape[i+1:] + ) + if sparse: + res = res + (idx,) + else: + res[i] = idx + return res + + +@set_array_function_like_doc +@set_module('numpy') +def fromfunction(function, shape, *, dtype=float, like=None, **kwargs): + """ + Construct an array by executing a function over each coordinate. + + The resulting array therefore has a value ``fn(x, y, z)`` at + coordinate ``(x, y, z)``. + + Parameters + ---------- + function : callable + The function is called with N parameters, where N is the rank of + `shape`. Each parameter represents the coordinates of the array + varying along a specific axis. For example, if `shape` + were ``(2, 2)``, then the parameters would be + ``array([[0, 0], [1, 1]])`` and ``array([[0, 1], [0, 1]])`` + shape : (N,) tuple of ints + Shape of the output array, which also determines the shape of + the coordinate arrays passed to `function`. + dtype : data-type, optional + Data-type of the coordinate arrays passed to `function`. + By default, `dtype` is float. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + fromfunction : any + The result of the call to `function` is passed back directly. + Therefore the shape of `fromfunction` is completely determined by + `function`. If `function` returns a scalar value, the shape of + `fromfunction` would not match the `shape` parameter. + + See Also + -------- + indices, meshgrid + + Notes + ----- + Keywords other than `dtype` and `like` are passed to `function`. + + Examples + -------- + >>> np.fromfunction(lambda i, j: i, (2, 2), dtype=float) + array([[0., 0.], + [1., 1.]]) + + >>> np.fromfunction(lambda i, j: j, (2, 2), dtype=float) + array([[0., 1.], + [0., 1.]]) + + >>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int) + array([[ True, False, False], + [False, True, False], + [False, False, True]]) + + >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int) + array([[0, 1, 2], + [1, 2, 3], + [2, 3, 4]]) + + """ + if like is not None: + return _fromfunction_with_like( + like, function, shape, dtype=dtype, **kwargs) + + args = indices(shape, dtype=dtype) + return function(*args, **kwargs) + + +_fromfunction_with_like = array_function_dispatch()(fromfunction) + + +def _frombuffer(buf, dtype, shape, order): + return frombuffer(buf, dtype=dtype).reshape(shape, order=order) + + +@set_module('numpy') +def isscalar(element): + """ + Returns True if the type of `element` is a scalar type. + + Parameters + ---------- + element : any + Input argument, can be of any type and shape. + + Returns + ------- + val : bool + True if `element` is a scalar type, False if it is not. + + See Also + -------- + ndim : Get the number of dimensions of an array + + Notes + ----- + If you need a stricter way to identify a *numerical* scalar, use + ``isinstance(x, numbers.Number)``, as that returns ``False`` for most + non-numerical elements such as strings. + + In most cases ``np.ndim(x) == 0`` should be used instead of this function, + as that will also return true for 0d arrays. This is how numpy overloads + functions in the style of the ``dx`` arguments to `gradient` and the ``bins`` + argument to `histogram`. Some key differences: + + +--------------------------------------+---------------+-------------------+ + | x |``isscalar(x)``|``np.ndim(x) == 0``| + +======================================+===============+===================+ + | PEP 3141 numeric objects (including | ``True`` | ``True`` | + | builtins) | | | + +--------------------------------------+---------------+-------------------+ + | builtin string and buffer objects | ``True`` | ``True`` | + +--------------------------------------+---------------+-------------------+ + | other builtin objects, like | ``False`` | ``True`` | + | `pathlib.Path`, `Exception`, | | | + | the result of `re.compile` | | | + +--------------------------------------+---------------+-------------------+ + | third-party objects like | ``False`` | ``True`` | + | `matplotlib.figure.Figure` | | | + +--------------------------------------+---------------+-------------------+ + | zero-dimensional numpy arrays | ``False`` | ``True`` | + +--------------------------------------+---------------+-------------------+ + | other numpy arrays | ``False`` | ``False`` | + +--------------------------------------+---------------+-------------------+ + | `list`, `tuple`, and other sequence | ``False`` | ``False`` | + | objects | | | + +--------------------------------------+---------------+-------------------+ + + Examples + -------- + >>> np.isscalar(3.1) + True + >>> np.isscalar(np.array(3.1)) + False + >>> np.isscalar([3.1]) + False + >>> np.isscalar(False) + True + >>> np.isscalar('numpy') + True + + NumPy supports PEP 3141 numbers: + + >>> from fractions import Fraction + >>> np.isscalar(Fraction(5, 17)) + True + >>> from numbers import Number + >>> np.isscalar(Number()) + True + + """ + return (isinstance(element, generic) + or type(element) in ScalarType + or isinstance(element, numbers.Number)) + + +@set_module('numpy') +def binary_repr(num, width=None): + """ + Return the binary representation of the input number as a string. + + For negative numbers, if width is not given, a minus sign is added to the + front. If width is given, the two's complement of the number is + returned, with respect to that width. + + In a two's-complement system negative numbers are represented by the two's + complement of the absolute value. This is the most common method of + representing signed integers on computers [1]_. A N-bit two's-complement + system can represent every integer in the range + :math:`-2^{N-1}` to :math:`+2^{N-1}-1`. + + Parameters + ---------- + num : int + Only an integer decimal number can be used. + width : int, optional + The length of the returned string if `num` is positive, or the length + of the two's complement if `num` is negative, provided that `width` is + at least a sufficient number of bits for `num` to be represented in the + designated form. + + If the `width` value is insufficient, it will be ignored, and `num` will + be returned in binary (`num` > 0) or two's complement (`num` < 0) form + with its width equal to the minimum number of bits needed to represent + the number in the designated form. This behavior is deprecated and will + later raise an error. + + .. deprecated:: 1.12.0 + + Returns + ------- + bin : str + Binary representation of `num` or two's complement of `num`. + + See Also + -------- + base_repr: Return a string representation of a number in the given base + system. + bin: Python's built-in binary representation generator of an integer. + + Notes + ----- + `binary_repr` is equivalent to using `base_repr` with base 2, but about 25x + faster. + + References + ---------- + .. [1] Wikipedia, "Two's complement", + https://en.wikipedia.org/wiki/Two's_complement + + Examples + -------- + >>> np.binary_repr(3) + '11' + >>> np.binary_repr(-3) + '-11' + >>> np.binary_repr(3, width=4) + '0011' + + The two's complement is returned when the input number is negative and + width is specified: + + >>> np.binary_repr(-3, width=3) + '101' + >>> np.binary_repr(-3, width=5) + '11101' + + """ + def warn_if_insufficient(width, binwidth): + if width is not None and width < binwidth: + warnings.warn( + "Insufficient bit width provided. This behavior " + "will raise an error in the future.", DeprecationWarning, + stacklevel=3) + + # Ensure that num is a Python integer to avoid overflow or unwanted + # casts to floating point. + num = operator.index(num) + + if num == 0: + return '0' * (width or 1) + + elif num > 0: + binary = bin(num)[2:] + binwidth = len(binary) + outwidth = (binwidth if width is None + else builtins.max(binwidth, width)) + warn_if_insufficient(width, binwidth) + return binary.zfill(outwidth) + + else: + if width is None: + return '-' + bin(-num)[2:] + + else: + poswidth = len(bin(-num)[2:]) + + # See gh-8679: remove extra digit + # for numbers at boundaries. + if 2**(poswidth - 1) == -num: + poswidth -= 1 + + twocomp = 2**(poswidth + 1) + num + binary = bin(twocomp)[2:] + binwidth = len(binary) + + outwidth = builtins.max(binwidth, width) + warn_if_insufficient(width, binwidth) + return '1' * (outwidth - binwidth) + binary + + +@set_module('numpy') +def base_repr(number, base=2, padding=0): + """ + Return a string representation of a number in the given base system. + + Parameters + ---------- + number : int + The value to convert. Positive and negative values are handled. + base : int, optional + Convert `number` to the `base` number system. The valid range is 2-36, + the default value is 2. + padding : int, optional + Number of zeros padded on the left. Default is 0 (no padding). + + Returns + ------- + out : str + String representation of `number` in `base` system. + + See Also + -------- + binary_repr : Faster version of `base_repr` for base 2. + + Examples + -------- + >>> np.base_repr(5) + '101' + >>> np.base_repr(6, 5) + '11' + >>> np.base_repr(7, base=5, padding=3) + '00012' + + >>> np.base_repr(10, base=16) + 'A' + >>> np.base_repr(32, base=16) + '20' + + """ + digits = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ' + if base > len(digits): + raise ValueError("Bases greater than 36 not handled in base_repr.") + elif base < 2: + raise ValueError("Bases less than 2 not handled in base_repr.") + + num = abs(number) + res = [] + while num: + res.append(digits[num % base]) + num //= base + if padding: + res.append('0' * padding) + if number < 0: + res.append('-') + return ''.join(reversed(res or '0')) + + +# These are all essentially abbreviations +# These might wind up in a special abbreviations module + + +def _maketup(descr, val): + dt = dtype(descr) + # Place val in all scalar tuples: + fields = dt.fields + if fields is None: + return val + else: + res = [_maketup(fields[name][0], val) for name in dt.names] + return tuple(res) + + +@set_array_function_like_doc +@set_module('numpy') +def identity(n, dtype=None, *, like=None): + """ + Return the identity array. + + The identity array is a square array with ones on + the main diagonal. + + Parameters + ---------- + n : int + Number of rows (and columns) in `n` x `n` output. + dtype : data-type, optional + Data-type of the output. Defaults to ``float``. + ${ARRAY_FUNCTION_LIKE} + + .. versionadded:: 1.20.0 + + Returns + ------- + out : ndarray + `n` x `n` array with its main diagonal set to one, + and all other elements 0. + + Examples + -------- + >>> np.identity(3) + array([[1., 0., 0.], + [0., 1., 0.], + [0., 0., 1.]]) + + """ + if like is not None: + return _identity_with_like(like, n, dtype=dtype) + + from numpy import eye + return eye(n, dtype=dtype, like=like) + + +_identity_with_like = array_function_dispatch()(identity) + + +def _allclose_dispatcher(a, b, rtol=None, atol=None, equal_nan=None): + return (a, b) + + +@array_function_dispatch(_allclose_dispatcher) +def allclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False): + """ + Returns True if two arrays are element-wise equal within a tolerance. + + The tolerance values are positive, typically very small numbers. The + relative difference (`rtol` * abs(`b`)) and the absolute difference + `atol` are added together to compare against the absolute difference + between `a` and `b`. + + NaNs are treated as equal if they are in the same place and if + ``equal_nan=True``. Infs are treated as equal if they are in the same + place and of the same sign in both arrays. + + Parameters + ---------- + a, b : array_like + Input arrays to compare. + rtol : float + The relative tolerance parameter (see Notes). + atol : float + The absolute tolerance parameter (see Notes). + equal_nan : bool + Whether to compare NaN's as equal. If True, NaN's in `a` will be + considered equal to NaN's in `b` in the output array. + + .. versionadded:: 1.10.0 + + Returns + ------- + allclose : bool + Returns True if the two arrays are equal within the given + tolerance; False otherwise. + + See Also + -------- + isclose, all, any, equal + + Notes + ----- + If the following equation is element-wise True, then allclose returns + True. + + absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`)) + + The above equation is not symmetric in `a` and `b`, so that + ``allclose(a, b)`` might be different from ``allclose(b, a)`` in + some rare cases. + + The comparison of `a` and `b` uses standard broadcasting, which + means that `a` and `b` need not have the same shape in order for + ``allclose(a, b)`` to evaluate to True. The same is true for + `equal` but not `array_equal`. + + `allclose` is not defined for non-numeric data types. + `bool` is considered a numeric data-type for this purpose. + + Examples + -------- + >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8]) + False + >>> np.allclose([1e10,1e-8], [1.00001e10,1e-9]) + True + >>> np.allclose([1e10,1e-8], [1.0001e10,1e-9]) + False + >>> np.allclose([1.0, np.nan], [1.0, np.nan]) + False + >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) + True + + """ + res = all(isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)) + return bool(res) + + +def _isclose_dispatcher(a, b, rtol=None, atol=None, equal_nan=None): + return (a, b) + + +@array_function_dispatch(_isclose_dispatcher) +def isclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False): + """ + Returns a boolean array where two arrays are element-wise equal within a + tolerance. + + The tolerance values are positive, typically very small numbers. The + relative difference (`rtol` * abs(`b`)) and the absolute difference + `atol` are added together to compare against the absolute difference + between `a` and `b`. + + .. warning:: The default `atol` is not appropriate for comparing numbers + that are much smaller than one (see Notes). + + Parameters + ---------- + a, b : array_like + Input arrays to compare. + rtol : float + The relative tolerance parameter (see Notes). + atol : float + The absolute tolerance parameter (see Notes). + equal_nan : bool + Whether to compare NaN's as equal. If True, NaN's in `a` will be + considered equal to NaN's in `b` in the output array. + + Returns + ------- + y : array_like + Returns a boolean array of where `a` and `b` are equal within the + given tolerance. If both `a` and `b` are scalars, returns a single + boolean value. + + See Also + -------- + allclose + math.isclose + + Notes + ----- + .. versionadded:: 1.7.0 + + For finite values, isclose uses the following equation to test whether + two floating point values are equivalent. + + absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`)) + + Unlike the built-in `math.isclose`, the above equation is not symmetric + in `a` and `b` -- it assumes `b` is the reference value -- so that + `isclose(a, b)` might be different from `isclose(b, a)`. Furthermore, + the default value of atol is not zero, and is used to determine what + small values should be considered close to zero. The default value is + appropriate for expected values of order unity: if the expected values + are significantly smaller than one, it can result in false positives. + `atol` should be carefully selected for the use case at hand. A zero value + for `atol` will result in `False` if either `a` or `b` is zero. + + `isclose` is not defined for non-numeric data types. + `bool` is considered a numeric data-type for this purpose. + + Examples + -------- + >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8]) + array([ True, False]) + >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9]) + array([ True, True]) + >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9]) + array([False, True]) + >>> np.isclose([1.0, np.nan], [1.0, np.nan]) + array([ True, False]) + >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) + array([ True, True]) + >>> np.isclose([1e-8, 1e-7], [0.0, 0.0]) + array([ True, False]) + >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0) + array([False, False]) + >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0]) + array([ True, True]) + >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0) + array([False, True]) + """ + def within_tol(x, y, atol, rtol): + with errstate(invalid='ignore'), _no_nep50_warning(): + return less_equal(abs(x-y), atol + rtol * abs(y)) + + x = asanyarray(a) + y = asanyarray(b) + + # Make sure y is an inexact type to avoid bad behavior on abs(MIN_INT). + # This will cause casting of x later. Also, make sure to allow subclasses + # (e.g., for numpy.ma). + # NOTE: We explicitly allow timedelta, which used to work. This could + # possibly be deprecated. See also gh-18286. + # timedelta works if `atol` is an integer or also a timedelta. + # Although, the default tolerances are unlikely to be useful + if y.dtype.kind != "m": + dt = multiarray.result_type(y, 1.) + y = asanyarray(y, dtype=dt) + + xfin = isfinite(x) + yfin = isfinite(y) + if all(xfin) and all(yfin): + return within_tol(x, y, atol, rtol) + else: + finite = xfin & yfin + cond = zeros_like(finite, subok=True) + # Because we're using boolean indexing, x & y must be the same shape. + # Ideally, we'd just do x, y = broadcast_arrays(x, y). It's in + # lib.stride_tricks, though, so we can't import it here. + x = x * ones_like(cond) + y = y * ones_like(cond) + # Avoid subtraction with infinite/nan values... + cond[finite] = within_tol(x[finite], y[finite], atol, rtol) + # Check for equality of infinite values... + cond[~finite] = (x[~finite] == y[~finite]) + if equal_nan: + # Make NaN == NaN + both_nan = isnan(x) & isnan(y) + + # Needed to treat masked arrays correctly. = True would not work. + cond[both_nan] = both_nan[both_nan] + + return cond[()] # Flatten 0d arrays to scalars + + +def _array_equal_dispatcher(a1, a2, equal_nan=None): + return (a1, a2) + + +@array_function_dispatch(_array_equal_dispatcher) +def array_equal(a1, a2, equal_nan=False): + """ + True if two arrays have the same shape and elements, False otherwise. + + Parameters + ---------- + a1, a2 : array_like + Input arrays. + equal_nan : bool + Whether to compare NaN's as equal. If the dtype of a1 and a2 is + complex, values will be considered equal if either the real or the + imaginary component of a given value is ``nan``. + + .. versionadded:: 1.19.0 + + Returns + ------- + b : bool + Returns True if the arrays are equal. + + See Also + -------- + allclose: Returns True if two arrays are element-wise equal within a + tolerance. + array_equiv: Returns True if input arrays are shape consistent and all + elements equal. + + Examples + -------- + >>> np.array_equal([1, 2], [1, 2]) + True + >>> np.array_equal(np.array([1, 2]), np.array([1, 2])) + True + >>> np.array_equal([1, 2], [1, 2, 3]) + False + >>> np.array_equal([1, 2], [1, 4]) + False + >>> a = np.array([1, np.nan]) + >>> np.array_equal(a, a) + False + >>> np.array_equal(a, a, equal_nan=True) + True + + When ``equal_nan`` is True, complex values with nan components are + considered equal if either the real *or* the imaginary components are nan. + + >>> a = np.array([1 + 1j]) + >>> b = a.copy() + >>> a.real = np.nan + >>> b.imag = np.nan + >>> np.array_equal(a, b, equal_nan=True) + True + """ + try: + a1, a2 = asarray(a1), asarray(a2) + except Exception: + return False + if a1.shape != a2.shape: + return False + if not equal_nan: + return bool(asarray(a1 == a2).all()) + # Handling NaN values if equal_nan is True + a1nan, a2nan = isnan(a1), isnan(a2) + # NaN's occur at different locations + if not (a1nan == a2nan).all(): + return False + # Shapes of a1, a2 and masks are guaranteed to be consistent by this point + return bool(asarray(a1[~a1nan] == a2[~a1nan]).all()) + + +def _array_equiv_dispatcher(a1, a2): + return (a1, a2) + + +@array_function_dispatch(_array_equiv_dispatcher) +def array_equiv(a1, a2): + """ + Returns True if input arrays are shape consistent and all elements equal. + + Shape consistent means they are either the same shape, or one input array + can be broadcasted to create the same shape as the other one. + + Parameters + ---------- + a1, a2 : array_like + Input arrays. + + Returns + ------- + out : bool + True if equivalent, False otherwise. + + Examples + -------- + >>> np.array_equiv([1, 2], [1, 2]) + True + >>> np.array_equiv([1, 2], [1, 3]) + False + + Showing the shape equivalence: + + >>> np.array_equiv([1, 2], [[1, 2], [1, 2]]) + True + >>> np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]]) + False + + >>> np.array_equiv([1, 2], [[1, 2], [1, 3]]) + False + + """ + try: + a1, a2 = asarray(a1), asarray(a2) + except Exception: + return False + try: + multiarray.broadcast(a1, a2) + except Exception: + return False + + return bool(asarray(a1 == a2).all()) + + +Inf = inf = infty = Infinity = PINF +nan = NaN = NAN +False_ = bool_(False) +True_ = bool_(True) + + +def extend_all(module): + existing = set(__all__) + mall = getattr(module, '__all__') + for a in mall: + if a not in existing: + __all__.append(a) + + +from .umath import * +from .numerictypes import * +from . import fromnumeric +from .fromnumeric import * +from . import arrayprint +from .arrayprint import * +from . import _asarray +from ._asarray import * +from . import _ufunc_config +from ._ufunc_config import * +extend_all(fromnumeric) +extend_all(umath) +extend_all(numerictypes) +extend_all(arrayprint) +extend_all(_asarray) +extend_all(_ufunc_config) diff --git a/venv/lib/python3.10/site-packages/numpy/core/numeric.pyi b/venv/lib/python3.10/site-packages/numpy/core/numeric.pyi new file mode 100644 index 0000000000000000000000000000000000000000..fc10bb88f54a1737e77db5d45e3df0579d6f84da --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/numeric.pyi @@ -0,0 +1,660 @@ +from collections.abc import Callable, Sequence +from typing import ( + Any, + overload, + TypeVar, + Literal, + SupportsAbs, + SupportsIndex, + NoReturn, +) +if sys.version_info >= (3, 10): + from typing import TypeGuard +else: + from typing_extensions import TypeGuard + +from numpy import ( + ComplexWarning as ComplexWarning, + generic, + unsignedinteger, + signedinteger, + floating, + complexfloating, + bool_, + int_, + intp, + float64, + timedelta64, + object_, + _OrderKACF, + _OrderCF, +) + +from numpy._typing import ( + ArrayLike, + NDArray, + DTypeLike, + _ShapeLike, + _DTypeLike, + _ArrayLike, + _SupportsArrayFunc, + _ScalarLike_co, + _ArrayLikeBool_co, + _ArrayLikeUInt_co, + _ArrayLikeInt_co, + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, + _ArrayLikeTD64_co, + _ArrayLikeObject_co, + _ArrayLikeUnknown, +) + +_T = TypeVar("_T") +_SCT = TypeVar("_SCT", bound=generic) +_ArrayType = TypeVar("_ArrayType", bound=NDArray[Any]) + +_CorrelateMode = Literal["valid", "same", "full"] + +__all__: list[str] + +@overload +def zeros_like( + a: _ArrayType, + dtype: None = ..., + order: _OrderKACF = ..., + subok: Literal[True] = ..., + shape: None = ..., +) -> _ArrayType: ... +@overload +def zeros_like( + a: _ArrayLike[_SCT], + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> NDArray[_SCT]: ... +@overload +def zeros_like( + a: object, + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[Any]: ... +@overload +def zeros_like( + a: Any, + dtype: _DTypeLike[_SCT], + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[_SCT]: ... +@overload +def zeros_like( + a: Any, + dtype: DTypeLike, + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[Any]: ... + +@overload +def ones( + shape: _ShapeLike, + dtype: None = ..., + order: _OrderCF = ..., + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[float64]: ... +@overload +def ones( + shape: _ShapeLike, + dtype: _DTypeLike[_SCT], + order: _OrderCF = ..., + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def ones( + shape: _ShapeLike, + dtype: DTypeLike, + order: _OrderCF = ..., + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def ones_like( + a: _ArrayType, + dtype: None = ..., + order: _OrderKACF = ..., + subok: Literal[True] = ..., + shape: None = ..., +) -> _ArrayType: ... +@overload +def ones_like( + a: _ArrayLike[_SCT], + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> NDArray[_SCT]: ... +@overload +def ones_like( + a: object, + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[Any]: ... +@overload +def ones_like( + a: Any, + dtype: _DTypeLike[_SCT], + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[_SCT]: ... +@overload +def ones_like( + a: Any, + dtype: DTypeLike, + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[Any]: ... + +@overload +def full( + shape: _ShapeLike, + fill_value: Any, + dtype: None = ..., + order: _OrderCF = ..., + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... +@overload +def full( + shape: _ShapeLike, + fill_value: Any, + dtype: _DTypeLike[_SCT], + order: _OrderCF = ..., + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def full( + shape: _ShapeLike, + fill_value: Any, + dtype: DTypeLike, + order: _OrderCF = ..., + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +@overload +def full_like( + a: _ArrayType, + fill_value: Any, + dtype: None = ..., + order: _OrderKACF = ..., + subok: Literal[True] = ..., + shape: None = ..., +) -> _ArrayType: ... +@overload +def full_like( + a: _ArrayLike[_SCT], + fill_value: Any, + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike = ..., +) -> NDArray[_SCT]: ... +@overload +def full_like( + a: object, + fill_value: Any, + dtype: None = ..., + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[Any]: ... +@overload +def full_like( + a: Any, + fill_value: Any, + dtype: _DTypeLike[_SCT], + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[_SCT]: ... +@overload +def full_like( + a: Any, + fill_value: Any, + dtype: DTypeLike, + order: _OrderKACF = ..., + subok: bool = ..., + shape: None | _ShapeLike= ..., +) -> NDArray[Any]: ... + +@overload +def count_nonzero( + a: ArrayLike, + axis: None = ..., + *, + keepdims: Literal[False] = ..., +) -> int: ... +@overload +def count_nonzero( + a: ArrayLike, + axis: _ShapeLike = ..., + *, + keepdims: bool = ..., +) -> Any: ... # TODO: np.intp or ndarray[np.intp] + +def isfortran(a: NDArray[Any] | generic) -> bool: ... + +def argwhere(a: ArrayLike) -> NDArray[intp]: ... + +def flatnonzero(a: ArrayLike) -> NDArray[intp]: ... + +@overload +def correlate( + a: _ArrayLikeUnknown, + v: _ArrayLikeUnknown, + mode: _CorrelateMode = ..., +) -> NDArray[Any]: ... +@overload +def correlate( + a: _ArrayLikeBool_co, + v: _ArrayLikeBool_co, + mode: _CorrelateMode = ..., +) -> NDArray[bool_]: ... +@overload +def correlate( + a: _ArrayLikeUInt_co, + v: _ArrayLikeUInt_co, + mode: _CorrelateMode = ..., +) -> NDArray[unsignedinteger[Any]]: ... +@overload +def correlate( + a: _ArrayLikeInt_co, + v: _ArrayLikeInt_co, + mode: _CorrelateMode = ..., +) -> NDArray[signedinteger[Any]]: ... +@overload +def correlate( + a: _ArrayLikeFloat_co, + v: _ArrayLikeFloat_co, + mode: _CorrelateMode = ..., +) -> NDArray[floating[Any]]: ... +@overload +def correlate( + a: _ArrayLikeComplex_co, + v: _ArrayLikeComplex_co, + mode: _CorrelateMode = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def correlate( + a: _ArrayLikeTD64_co, + v: _ArrayLikeTD64_co, + mode: _CorrelateMode = ..., +) -> NDArray[timedelta64]: ... +@overload +def correlate( + a: _ArrayLikeObject_co, + v: _ArrayLikeObject_co, + mode: _CorrelateMode = ..., +) -> NDArray[object_]: ... + +@overload +def convolve( + a: _ArrayLikeUnknown, + v: _ArrayLikeUnknown, + mode: _CorrelateMode = ..., +) -> NDArray[Any]: ... +@overload +def convolve( + a: _ArrayLikeBool_co, + v: _ArrayLikeBool_co, + mode: _CorrelateMode = ..., +) -> NDArray[bool_]: ... +@overload +def convolve( + a: _ArrayLikeUInt_co, + v: _ArrayLikeUInt_co, + mode: _CorrelateMode = ..., +) -> NDArray[unsignedinteger[Any]]: ... +@overload +def convolve( + a: _ArrayLikeInt_co, + v: _ArrayLikeInt_co, + mode: _CorrelateMode = ..., +) -> NDArray[signedinteger[Any]]: ... +@overload +def convolve( + a: _ArrayLikeFloat_co, + v: _ArrayLikeFloat_co, + mode: _CorrelateMode = ..., +) -> NDArray[floating[Any]]: ... +@overload +def convolve( + a: _ArrayLikeComplex_co, + v: _ArrayLikeComplex_co, + mode: _CorrelateMode = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def convolve( + a: _ArrayLikeTD64_co, + v: _ArrayLikeTD64_co, + mode: _CorrelateMode = ..., +) -> NDArray[timedelta64]: ... +@overload +def convolve( + a: _ArrayLikeObject_co, + v: _ArrayLikeObject_co, + mode: _CorrelateMode = ..., +) -> NDArray[object_]: ... + +@overload +def outer( + a: _ArrayLikeUnknown, + b: _ArrayLikeUnknown, + out: None = ..., +) -> NDArray[Any]: ... +@overload +def outer( + a: _ArrayLikeBool_co, + b: _ArrayLikeBool_co, + out: None = ..., +) -> NDArray[bool_]: ... +@overload +def outer( + a: _ArrayLikeUInt_co, + b: _ArrayLikeUInt_co, + out: None = ..., +) -> NDArray[unsignedinteger[Any]]: ... +@overload +def outer( + a: _ArrayLikeInt_co, + b: _ArrayLikeInt_co, + out: None = ..., +) -> NDArray[signedinteger[Any]]: ... +@overload +def outer( + a: _ArrayLikeFloat_co, + b: _ArrayLikeFloat_co, + out: None = ..., +) -> NDArray[floating[Any]]: ... +@overload +def outer( + a: _ArrayLikeComplex_co, + b: _ArrayLikeComplex_co, + out: None = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def outer( + a: _ArrayLikeTD64_co, + b: _ArrayLikeTD64_co, + out: None = ..., +) -> NDArray[timedelta64]: ... +@overload +def outer( + a: _ArrayLikeObject_co, + b: _ArrayLikeObject_co, + out: None = ..., +) -> NDArray[object_]: ... +@overload +def outer( + a: _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co, + b: _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co, + out: _ArrayType, +) -> _ArrayType: ... + +@overload +def tensordot( + a: _ArrayLikeUnknown, + b: _ArrayLikeUnknown, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[Any]: ... +@overload +def tensordot( + a: _ArrayLikeBool_co, + b: _ArrayLikeBool_co, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[bool_]: ... +@overload +def tensordot( + a: _ArrayLikeUInt_co, + b: _ArrayLikeUInt_co, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[unsignedinteger[Any]]: ... +@overload +def tensordot( + a: _ArrayLikeInt_co, + b: _ArrayLikeInt_co, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[signedinteger[Any]]: ... +@overload +def tensordot( + a: _ArrayLikeFloat_co, + b: _ArrayLikeFloat_co, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[floating[Any]]: ... +@overload +def tensordot( + a: _ArrayLikeComplex_co, + b: _ArrayLikeComplex_co, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def tensordot( + a: _ArrayLikeTD64_co, + b: _ArrayLikeTD64_co, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[timedelta64]: ... +@overload +def tensordot( + a: _ArrayLikeObject_co, + b: _ArrayLikeObject_co, + axes: int | tuple[_ShapeLike, _ShapeLike] = ..., +) -> NDArray[object_]: ... + +@overload +def roll( + a: _ArrayLike[_SCT], + shift: _ShapeLike, + axis: None | _ShapeLike = ..., +) -> NDArray[_SCT]: ... +@overload +def roll( + a: ArrayLike, + shift: _ShapeLike, + axis: None | _ShapeLike = ..., +) -> NDArray[Any]: ... + +def rollaxis( + a: NDArray[_SCT], + axis: int, + start: int = ..., +) -> NDArray[_SCT]: ... + +def moveaxis( + a: NDArray[_SCT], + source: _ShapeLike, + destination: _ShapeLike, +) -> NDArray[_SCT]: ... + +@overload +def cross( + a: _ArrayLikeUnknown, + b: _ArrayLikeUnknown, + axisa: int = ..., + axisb: int = ..., + axisc: int = ..., + axis: None | int = ..., +) -> NDArray[Any]: ... +@overload +def cross( + a: _ArrayLikeBool_co, + b: _ArrayLikeBool_co, + axisa: int = ..., + axisb: int = ..., + axisc: int = ..., + axis: None | int = ..., +) -> NoReturn: ... +@overload +def cross( + a: _ArrayLikeUInt_co, + b: _ArrayLikeUInt_co, + axisa: int = ..., + axisb: int = ..., + axisc: int = ..., + axis: None | int = ..., +) -> NDArray[unsignedinteger[Any]]: ... +@overload +def cross( + a: _ArrayLikeInt_co, + b: _ArrayLikeInt_co, + axisa: int = ..., + axisb: int = ..., + axisc: int = ..., + axis: None | int = ..., +) -> NDArray[signedinteger[Any]]: ... +@overload +def cross( + a: _ArrayLikeFloat_co, + b: _ArrayLikeFloat_co, + axisa: int = ..., + axisb: int = ..., + axisc: int = ..., + axis: None | int = ..., +) -> NDArray[floating[Any]]: ... +@overload +def cross( + a: _ArrayLikeComplex_co, + b: _ArrayLikeComplex_co, + axisa: int = ..., + axisb: int = ..., + axisc: int = ..., + axis: None | int = ..., +) -> NDArray[complexfloating[Any, Any]]: ... +@overload +def cross( + a: _ArrayLikeObject_co, + b: _ArrayLikeObject_co, + axisa: int = ..., + axisb: int = ..., + axisc: int = ..., + axis: None | int = ..., +) -> NDArray[object_]: ... + +@overload +def indices( + dimensions: Sequence[int], + dtype: type[int] = ..., + sparse: Literal[False] = ..., +) -> NDArray[int_]: ... +@overload +def indices( + dimensions: Sequence[int], + dtype: type[int] = ..., + sparse: Literal[True] = ..., +) -> tuple[NDArray[int_], ...]: ... +@overload +def indices( + dimensions: Sequence[int], + dtype: _DTypeLike[_SCT], + sparse: Literal[False] = ..., +) -> NDArray[_SCT]: ... +@overload +def indices( + dimensions: Sequence[int], + dtype: _DTypeLike[_SCT], + sparse: Literal[True], +) -> tuple[NDArray[_SCT], ...]: ... +@overload +def indices( + dimensions: Sequence[int], + dtype: DTypeLike, + sparse: Literal[False] = ..., +) -> NDArray[Any]: ... +@overload +def indices( + dimensions: Sequence[int], + dtype: DTypeLike, + sparse: Literal[True], +) -> tuple[NDArray[Any], ...]: ... + +def fromfunction( + function: Callable[..., _T], + shape: Sequence[int], + *, + dtype: DTypeLike = ..., + like: _SupportsArrayFunc = ..., + **kwargs: Any, +) -> _T: ... + +def isscalar(element: object) -> TypeGuard[ + generic | bool | int | float | complex | str | bytes | memoryview +]: ... + +def binary_repr(num: SupportsIndex, width: None | int = ...) -> str: ... + +def base_repr( + number: SupportsAbs[float], + base: float = ..., + padding: SupportsIndex = ..., +) -> str: ... + +@overload +def identity( + n: int, + dtype: None = ..., + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[float64]: ... +@overload +def identity( + n: int, + dtype: _DTypeLike[_SCT], + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[_SCT]: ... +@overload +def identity( + n: int, + dtype: DTypeLike, + *, + like: _SupportsArrayFunc = ..., +) -> NDArray[Any]: ... + +def allclose( + a: ArrayLike, + b: ArrayLike, + rtol: float = ..., + atol: float = ..., + equal_nan: bool = ..., +) -> bool: ... + +@overload +def isclose( + a: _ScalarLike_co, + b: _ScalarLike_co, + rtol: float = ..., + atol: float = ..., + equal_nan: bool = ..., +) -> bool_: ... +@overload +def isclose( + a: ArrayLike, + b: ArrayLike, + rtol: float = ..., + atol: float = ..., + equal_nan: bool = ..., +) -> NDArray[bool_]: ... + +def array_equal(a1: ArrayLike, a2: ArrayLike, equal_nan: bool = ...) -> bool: ... + +def array_equiv(a1: ArrayLike, a2: ArrayLike) -> bool: ... diff --git a/venv/lib/python3.10/site-packages/numpy/core/overrides.py b/venv/lib/python3.10/site-packages/numpy/core/overrides.py new file mode 100644 index 0000000000000000000000000000000000000000..6403e65b02b8a34fe49717ca3d4e9a592082f68d --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/overrides.py @@ -0,0 +1,181 @@ +"""Implementation of __array_function__ overrides from NEP-18.""" +import collections +import functools +import os + +from .._utils import set_module +from .._utils._inspect import getargspec +from numpy.core._multiarray_umath import ( + add_docstring, _get_implementing_args, _ArrayFunctionDispatcher) + + +ARRAY_FUNCTIONS = set() + +array_function_like_doc = ( + """like : array_like, optional + Reference object to allow the creation of arrays which are not + NumPy arrays. If an array-like passed in as ``like`` supports + the ``__array_function__`` protocol, the result will be defined + by it. In this case, it ensures the creation of an array object + compatible with that passed in via this argument.""" +) + +def set_array_function_like_doc(public_api): + if public_api.__doc__ is not None: + public_api.__doc__ = public_api.__doc__.replace( + "${ARRAY_FUNCTION_LIKE}", + array_function_like_doc, + ) + return public_api + + +add_docstring( + _ArrayFunctionDispatcher, + """ + Class to wrap functions with checks for __array_function__ overrides. + + All arguments are required, and can only be passed by position. + + Parameters + ---------- + dispatcher : function or None + The dispatcher function that returns a single sequence-like object + of all arguments relevant. It must have the same signature (except + the default values) as the actual implementation. + If ``None``, this is a ``like=`` dispatcher and the + ``_ArrayFunctionDispatcher`` must be called with ``like`` as the + first (additional and positional) argument. + implementation : function + Function that implements the operation on NumPy arrays without + overrides. Arguments passed calling the ``_ArrayFunctionDispatcher`` + will be forwarded to this (and the ``dispatcher``) as if using + ``*args, **kwargs``. + + Attributes + ---------- + _implementation : function + The original implementation passed in. + """) + + +# exposed for testing purposes; used internally by _ArrayFunctionDispatcher +add_docstring( + _get_implementing_args, + """ + Collect arguments on which to call __array_function__. + + Parameters + ---------- + relevant_args : iterable of array-like + Iterable of possibly array-like arguments to check for + __array_function__ methods. + + Returns + ------- + Sequence of arguments with __array_function__ methods, in the order in + which they should be called. + """) + + +ArgSpec = collections.namedtuple('ArgSpec', 'args varargs keywords defaults') + + +def verify_matching_signatures(implementation, dispatcher): + """Verify that a dispatcher function has the right signature.""" + implementation_spec = ArgSpec(*getargspec(implementation)) + dispatcher_spec = ArgSpec(*getargspec(dispatcher)) + + if (implementation_spec.args != dispatcher_spec.args or + implementation_spec.varargs != dispatcher_spec.varargs or + implementation_spec.keywords != dispatcher_spec.keywords or + (bool(implementation_spec.defaults) != + bool(dispatcher_spec.defaults)) or + (implementation_spec.defaults is not None and + len(implementation_spec.defaults) != + len(dispatcher_spec.defaults))): + raise RuntimeError('implementation and dispatcher for %s have ' + 'different function signatures' % implementation) + + if implementation_spec.defaults is not None: + if dispatcher_spec.defaults != (None,) * len(dispatcher_spec.defaults): + raise RuntimeError('dispatcher functions can only use None for ' + 'default argument values') + + +def array_function_dispatch(dispatcher=None, module=None, verify=True, + docs_from_dispatcher=False): + """Decorator for adding dispatch with the __array_function__ protocol. + + See NEP-18 for example usage. + + Parameters + ---------- + dispatcher : callable or None + Function that when called like ``dispatcher(*args, **kwargs)`` with + arguments from the NumPy function call returns an iterable of + array-like arguments to check for ``__array_function__``. + + If `None`, the first argument is used as the single `like=` argument + and not passed on. A function implementing `like=` must call its + dispatcher with `like` as the first non-keyword argument. + module : str, optional + __module__ attribute to set on new function, e.g., ``module='numpy'``. + By default, module is copied from the decorated function. + verify : bool, optional + If True, verify the that the signature of the dispatcher and decorated + function signatures match exactly: all required and optional arguments + should appear in order with the same names, but the default values for + all optional arguments should be ``None``. Only disable verification + if the dispatcher's signature needs to deviate for some particular + reason, e.g., because the function has a signature like + ``func(*args, **kwargs)``. + docs_from_dispatcher : bool, optional + If True, copy docs from the dispatcher function onto the dispatched + function, rather than from the implementation. This is useful for + functions defined in C, which otherwise don't have docstrings. + + Returns + ------- + Function suitable for decorating the implementation of a NumPy function. + + """ + def decorator(implementation): + if verify: + if dispatcher is not None: + verify_matching_signatures(implementation, dispatcher) + else: + # Using __code__ directly similar to verify_matching_signature + co = implementation.__code__ + last_arg = co.co_argcount + co.co_kwonlyargcount - 1 + last_arg = co.co_varnames[last_arg] + if last_arg != "like" or co.co_kwonlyargcount == 0: + raise RuntimeError( + "__array_function__ expects `like=` to be the last " + "argument and a keyword-only argument. " + f"{implementation} does not seem to comply.") + + if docs_from_dispatcher: + add_docstring(implementation, dispatcher.__doc__) + + public_api = _ArrayFunctionDispatcher(dispatcher, implementation) + public_api = functools.wraps(implementation)(public_api) + + if module is not None: + public_api.__module__ = module + + ARRAY_FUNCTIONS.add(public_api) + + return public_api + + return decorator + + +def array_function_from_dispatcher( + implementation, module=None, verify=True, docs_from_dispatcher=True): + """Like array_function_dispatcher, but with function arguments flipped.""" + + def decorator(dispatcher): + return array_function_dispatch( + dispatcher, module, verify=verify, + docs_from_dispatcher=docs_from_dispatcher)(implementation) + return decorator diff --git a/venv/lib/python3.10/site-packages/numpy/core/records.py b/venv/lib/python3.10/site-packages/numpy/core/records.py new file mode 100644 index 0000000000000000000000000000000000000000..0fb49e8f70f122e578649ea7fe38d96e30e59802 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/records.py @@ -0,0 +1,1099 @@ +""" +Record Arrays +============= +Record arrays expose the fields of structured arrays as properties. + +Most commonly, ndarrays contain elements of a single type, e.g. floats, +integers, bools etc. However, it is possible for elements to be combinations +of these using structured types, such as:: + + >>> a = np.array([(1, 2.0), (1, 2.0)], dtype=[('x', np.int64), ('y', np.float64)]) + >>> a + array([(1, 2.), (1, 2.)], dtype=[('x', '>> a['x'] + array([1, 1]) + + >>> a['y'] + array([2., 2.]) + +Record arrays allow us to access fields as properties:: + + >>> ar = np.rec.array(a) + + >>> ar.x + array([1, 1]) + + >>> ar.y + array([2., 2.]) + +""" +import warnings +from collections import Counter +from contextlib import nullcontext + +from .._utils import set_module +from . import numeric as sb +from . import numerictypes as nt +from numpy.compat import os_fspath +from .arrayprint import _get_legacy_print_mode + +# All of the functions allow formats to be a dtype +__all__ = [ + 'record', 'recarray', 'format_parser', + 'fromarrays', 'fromrecords', 'fromstring', 'fromfile', 'array', +] + + +ndarray = sb.ndarray + +_byteorderconv = {'b':'>', + 'l':'<', + 'n':'=', + 'B':'>', + 'L':'<', + 'N':'=', + 'S':'s', + 's':'s', + '>':'>', + '<':'<', + '=':'=', + '|':'|', + 'I':'|', + 'i':'|'} + +# formats regular expression +# allows multidimensional spec with a tuple syntax in front +# of the letter code '(2,3)f4' and ' ( 2 , 3 ) f4 ' +# are equally allowed + +numfmt = nt.sctypeDict + + +def find_duplicate(list): + """Find duplication in a list, return a list of duplicated elements""" + return [ + item + for item, counts in Counter(list).items() + if counts > 1 + ] + + +@set_module('numpy') +class format_parser: + """ + Class to convert formats, names, titles description to a dtype. + + After constructing the format_parser object, the dtype attribute is + the converted data-type: + ``dtype = format_parser(formats, names, titles).dtype`` + + Attributes + ---------- + dtype : dtype + The converted data-type. + + Parameters + ---------- + formats : str or list of str + The format description, either specified as a string with + comma-separated format descriptions in the form ``'f8, i4, a5'``, or + a list of format description strings in the form + ``['f8', 'i4', 'a5']``. + names : str or list/tuple of str + The field names, either specified as a comma-separated string in the + form ``'col1, col2, col3'``, or as a list or tuple of strings in the + form ``['col1', 'col2', 'col3']``. + An empty list can be used, in that case default field names + ('f0', 'f1', ...) are used. + titles : sequence + Sequence of title strings. An empty list can be used to leave titles + out. + aligned : bool, optional + If True, align the fields by padding as the C-compiler would. + Default is False. + byteorder : str, optional + If specified, all the fields will be changed to the + provided byte-order. Otherwise, the default byte-order is + used. For all available string specifiers, see `dtype.newbyteorder`. + + See Also + -------- + dtype, typename, sctype2char + + Examples + -------- + >>> np.format_parser(['>> np.format_parser(['f8', 'i4', 'a5'], ['col1', 'col2', 'col3'], + ... []).dtype + dtype([('col1', '>> np.format_parser([' len(titles): + self._titles += [None] * (self._nfields - len(titles)) + + def _createdtype(self, byteorder): + dtype = sb.dtype({ + 'names': self._names, + 'formats': self._f_formats, + 'offsets': self._offsets, + 'titles': self._titles, + }) + if byteorder is not None: + byteorder = _byteorderconv[byteorder[0]] + dtype = dtype.newbyteorder(byteorder) + + self.dtype = dtype + + +class record(nt.void): + """A data-type scalar that allows field access as attribute lookup. + """ + + # manually set name and module so that this class's type shows up + # as numpy.record when printed + __name__ = 'record' + __module__ = 'numpy' + + def __repr__(self): + if _get_legacy_print_mode() <= 113: + return self.__str__() + return super().__repr__() + + def __str__(self): + if _get_legacy_print_mode() <= 113: + return str(self.item()) + return super().__str__() + + def __getattribute__(self, attr): + if attr in ('setfield', 'getfield', 'dtype'): + return nt.void.__getattribute__(self, attr) + try: + return nt.void.__getattribute__(self, attr) + except AttributeError: + pass + fielddict = nt.void.__getattribute__(self, 'dtype').fields + res = fielddict.get(attr, None) + if res: + obj = self.getfield(*res[:2]) + # if it has fields return a record, + # otherwise return the object + try: + dt = obj.dtype + except AttributeError: + #happens if field is Object type + return obj + if dt.names is not None: + return obj.view((self.__class__, obj.dtype)) + return obj + else: + raise AttributeError("'record' object has no " + "attribute '%s'" % attr) + + def __setattr__(self, attr, val): + if attr in ('setfield', 'getfield', 'dtype'): + raise AttributeError("Cannot set '%s' attribute" % attr) + fielddict = nt.void.__getattribute__(self, 'dtype').fields + res = fielddict.get(attr, None) + if res: + return self.setfield(val, *res[:2]) + else: + if getattr(self, attr, None): + return nt.void.__setattr__(self, attr, val) + else: + raise AttributeError("'record' object has no " + "attribute '%s'" % attr) + + def __getitem__(self, indx): + obj = nt.void.__getitem__(self, indx) + + # copy behavior of record.__getattribute__, + if isinstance(obj, nt.void) and obj.dtype.names is not None: + return obj.view((self.__class__, obj.dtype)) + else: + # return a single element + return obj + + def pprint(self): + """Pretty-print all fields.""" + # pretty-print all fields + names = self.dtype.names + maxlen = max(len(name) for name in names) + fmt = '%% %ds: %%s' % maxlen + rows = [fmt % (name, getattr(self, name)) for name in names] + return "\n".join(rows) + +# The recarray is almost identical to a standard array (which supports +# named fields already) The biggest difference is that it can use +# attribute-lookup to find the fields and it is constructed using +# a record. + +# If byteorder is given it forces a particular byteorder on all +# the fields (and any subfields) + +class recarray(ndarray): + """Construct an ndarray that allows field access using attributes. + + Arrays may have a data-types containing fields, analogous + to columns in a spread sheet. An example is ``[(x, int), (y, float)]``, + where each entry in the array is a pair of ``(int, float)``. Normally, + these attributes are accessed using dictionary lookups such as ``arr['x']`` + and ``arr['y']``. Record arrays allow the fields to be accessed as members + of the array, using ``arr.x`` and ``arr.y``. + + Parameters + ---------- + shape : tuple + Shape of output array. + dtype : data-type, optional + The desired data-type. By default, the data-type is determined + from `formats`, `names`, `titles`, `aligned` and `byteorder`. + formats : list of data-types, optional + A list containing the data-types for the different columns, e.g. + ``['i4', 'f8', 'i4']``. `formats` does *not* support the new + convention of using types directly, i.e. ``(int, float, int)``. + Note that `formats` must be a list, not a tuple. + Given that `formats` is somewhat limited, we recommend specifying + `dtype` instead. + names : tuple of str, optional + The name of each column, e.g. ``('x', 'y', 'z')``. + buf : buffer, optional + By default, a new array is created of the given shape and data-type. + If `buf` is specified and is an object exposing the buffer interface, + the array will use the memory from the existing buffer. In this case, + the `offset` and `strides` keywords are available. + + Other Parameters + ---------------- + titles : tuple of str, optional + Aliases for column names. For example, if `names` were + ``('x', 'y', 'z')`` and `titles` is + ``('x_coordinate', 'y_coordinate', 'z_coordinate')``, then + ``arr['x']`` is equivalent to both ``arr.x`` and ``arr.x_coordinate``. + byteorder : {'<', '>', '='}, optional + Byte-order for all fields. + aligned : bool, optional + Align the fields in memory as the C-compiler would. + strides : tuple of ints, optional + Buffer (`buf`) is interpreted according to these strides (strides + define how many bytes each array element, row, column, etc. + occupy in memory). + offset : int, optional + Start reading buffer (`buf`) from this offset onwards. + order : {'C', 'F'}, optional + Row-major (C-style) or column-major (Fortran-style) order. + + Returns + ------- + rec : recarray + Empty array of the given shape and type. + + See Also + -------- + core.records.fromrecords : Construct a record array from data. + record : fundamental data-type for `recarray`. + format_parser : determine a data-type from formats, names, titles. + + Notes + ----- + This constructor can be compared to ``empty``: it creates a new record + array but does not fill it with data. To create a record array from data, + use one of the following methods: + + 1. Create a standard ndarray and convert it to a record array, + using ``arr.view(np.recarray)`` + 2. Use the `buf` keyword. + 3. Use `np.rec.fromrecords`. + + Examples + -------- + Create an array with two fields, ``x`` and ``y``: + + >>> x = np.array([(1.0, 2), (3.0, 4)], dtype=[('x', '>> x + array([(1., 2), (3., 4)], dtype=[('x', '>> x['x'] + array([1., 3.]) + + View the array as a record array: + + >>> x = x.view(np.recarray) + + >>> x.x + array([1., 3.]) + + >>> x.y + array([2, 4]) + + Create a new, empty record array: + + >>> np.recarray((2,), + ... dtype=[('x', int), ('y', float), ('z', int)]) #doctest: +SKIP + rec.array([(-1073741821, 1.2249118382103472e-301, 24547520), + (3471280, 1.2134086255804012e-316, 0)], + dtype=[('x', ' 0 or self.shape == (0,): + lst = sb.array2string( + self, separator=', ', prefix=prefix, suffix=',') + else: + # show zero-length shape unless it is (0,) + lst = "[], shape=%s" % (repr(self.shape),) + + lf = '\n'+' '*len(prefix) + if _get_legacy_print_mode() <= 113: + lf = ' ' + lf # trailing space + return fmt % (lst, lf, repr_dtype) + + def field(self, attr, val=None): + if isinstance(attr, int): + names = ndarray.__getattribute__(self, 'dtype').names + attr = names[attr] + + fielddict = ndarray.__getattribute__(self, 'dtype').fields + + res = fielddict[attr][:2] + + if val is None: + obj = self.getfield(*res) + if obj.dtype.names is not None: + return obj + return obj.view(ndarray) + else: + return self.setfield(val, *res) + + +def _deprecate_shape_0_as_None(shape): + if shape == 0: + warnings.warn( + "Passing `shape=0` to have the shape be inferred is deprecated, " + "and in future will be equivalent to `shape=(0,)`. To infer " + "the shape and suppress this warning, pass `shape=None` instead.", + FutureWarning, stacklevel=3) + return None + else: + return shape + + +@set_module("numpy.rec") +def fromarrays(arrayList, dtype=None, shape=None, formats=None, + names=None, titles=None, aligned=False, byteorder=None): + """Create a record array from a (flat) list of arrays + + Parameters + ---------- + arrayList : list or tuple + List of array-like objects (such as lists, tuples, + and ndarrays). + dtype : data-type, optional + valid dtype for all arrays + shape : int or tuple of ints, optional + Shape of the resulting array. If not provided, inferred from + ``arrayList[0]``. + formats, names, titles, aligned, byteorder : + If `dtype` is ``None``, these arguments are passed to + `numpy.format_parser` to construct a dtype. See that function for + detailed documentation. + + Returns + ------- + np.recarray + Record array consisting of given arrayList columns. + + Examples + -------- + >>> x1=np.array([1,2,3,4]) + >>> x2=np.array(['a','dd','xyz','12']) + >>> x3=np.array([1.1,2,3,4]) + >>> r = np.core.records.fromarrays([x1,x2,x3],names='a,b,c') + >>> print(r[1]) + (2, 'dd', 2.0) # may vary + >>> x1[1]=34 + >>> r.a + array([1, 2, 3, 4]) + + >>> x1 = np.array([1, 2, 3, 4]) + >>> x2 = np.array(['a', 'dd', 'xyz', '12']) + >>> x3 = np.array([1.1, 2, 3,4]) + >>> r = np.core.records.fromarrays( + ... [x1, x2, x3], + ... dtype=np.dtype([('a', np.int32), ('b', 'S3'), ('c', np.float32)])) + >>> r + rec.array([(1, b'a', 1.1), (2, b'dd', 2. ), (3, b'xyz', 3. ), + (4, b'12', 4. )], + dtype=[('a', ' 0: + shape = shape[:-nn] + + _array = recarray(shape, descr) + + # populate the record array (makes a copy) + for k, obj in enumerate(arrayList): + nn = descr[k].ndim + testshape = obj.shape[:obj.ndim - nn] + name = _names[k] + if testshape != shape: + raise ValueError(f'array-shape mismatch in array {k} ("{name}")') + + _array[name] = obj + + return _array + + +@set_module("numpy.rec") +def fromrecords(recList, dtype=None, shape=None, formats=None, names=None, + titles=None, aligned=False, byteorder=None): + """Create a recarray from a list of records in text form. + + Parameters + ---------- + recList : sequence + data in the same field may be heterogeneous - they will be promoted + to the highest data type. + dtype : data-type, optional + valid dtype for all arrays + shape : int or tuple of ints, optional + shape of each array. + formats, names, titles, aligned, byteorder : + If `dtype` is ``None``, these arguments are passed to + `numpy.format_parser` to construct a dtype. See that function for + detailed documentation. + + If both `formats` and `dtype` are None, then this will auto-detect + formats. Use list of tuples rather than list of lists for faster + processing. + + Returns + ------- + np.recarray + record array consisting of given recList rows. + + Examples + -------- + >>> r=np.core.records.fromrecords([(456,'dbe',1.2),(2,'de',1.3)], + ... names='col1,col2,col3') + >>> print(r[0]) + (456, 'dbe', 1.2) + >>> r.col1 + array([456, 2]) + >>> r.col2 + array(['dbe', 'de'], dtype='>> import pickle + >>> pickle.loads(pickle.dumps(r)) + rec.array([(456, 'dbe', 1.2), ( 2, 'de', 1.3)], + dtype=[('col1', ' 1: + raise ValueError("Can only deal with 1-d array.") + _array = recarray(shape, descr) + for k in range(_array.size): + _array[k] = tuple(recList[k]) + # list of lists instead of list of tuples ? + # 2018-02-07, 1.14.1 + warnings.warn( + "fromrecords expected a list of tuples, may have received a list " + "of lists instead. In the future that will raise an error", + FutureWarning, stacklevel=2) + return _array + else: + if shape is not None and retval.shape != shape: + retval.shape = shape + + res = retval.view(recarray) + + return res + + +@set_module("numpy.rec") +def fromstring(datastring, dtype=None, shape=None, offset=0, formats=None, + names=None, titles=None, aligned=False, byteorder=None): + r"""Create a record array from binary data + + Note that despite the name of this function it does not accept `str` + instances. + + Parameters + ---------- + datastring : bytes-like + Buffer of binary data + dtype : data-type, optional + Valid dtype for all arrays + shape : int or tuple of ints, optional + Shape of each array. + offset : int, optional + Position in the buffer to start reading from. + formats, names, titles, aligned, byteorder : + If `dtype` is ``None``, these arguments are passed to + `numpy.format_parser` to construct a dtype. See that function for + detailed documentation. + + + Returns + ------- + np.recarray + Record array view into the data in datastring. This will be readonly + if `datastring` is readonly. + + See Also + -------- + numpy.frombuffer + + Examples + -------- + >>> a = b'\x01\x02\x03abc' + >>> np.core.records.fromstring(a, dtype='u1,u1,u1,S3') + rec.array([(1, 2, 3, b'abc')], + dtype=[('f0', 'u1'), ('f1', 'u1'), ('f2', 'u1'), ('f3', 'S3')]) + + >>> grades_dtype = [('Name', (np.str_, 10)), ('Marks', np.float64), + ... ('GradeLevel', np.int32)] + >>> grades_array = np.array([('Sam', 33.3, 3), ('Mike', 44.4, 5), + ... ('Aadi', 66.6, 6)], dtype=grades_dtype) + >>> np.core.records.fromstring(grades_array.tobytes(), dtype=grades_dtype) + rec.array([('Sam', 33.3, 3), ('Mike', 44.4, 5), ('Aadi', 66.6, 6)], + dtype=[('Name', '>> s = '\x01\x02\x03abc' + >>> np.core.records.fromstring(s, dtype='u1,u1,u1,S3') + Traceback (most recent call last) + ... + TypeError: a bytes-like object is required, not 'str' + """ + + if dtype is None and formats is None: + raise TypeError("fromstring() needs a 'dtype' or 'formats' argument") + + if dtype is not None: + descr = sb.dtype(dtype) + else: + descr = format_parser(formats, names, titles, aligned, byteorder).dtype + + itemsize = descr.itemsize + + # NumPy 1.19.0, 2020-01-01 + shape = _deprecate_shape_0_as_None(shape) + + if shape in (None, -1): + shape = (len(datastring) - offset) // itemsize + + _array = recarray(shape, descr, buf=datastring, offset=offset) + return _array + +def get_remaining_size(fd): + pos = fd.tell() + try: + fd.seek(0, 2) + return fd.tell() - pos + finally: + fd.seek(pos, 0) + + +@set_module("numpy.rec") +def fromfile(fd, dtype=None, shape=None, offset=0, formats=None, + names=None, titles=None, aligned=False, byteorder=None): + """Create an array from binary file data + + Parameters + ---------- + fd : str or file type + If file is a string or a path-like object then that file is opened, + else it is assumed to be a file object. The file object must + support random access (i.e. it must have tell and seek methods). + dtype : data-type, optional + valid dtype for all arrays + shape : int or tuple of ints, optional + shape of each array. + offset : int, optional + Position in the file to start reading from. + formats, names, titles, aligned, byteorder : + If `dtype` is ``None``, these arguments are passed to + `numpy.format_parser` to construct a dtype. See that function for + detailed documentation + + Returns + ------- + np.recarray + record array consisting of data enclosed in file. + + Examples + -------- + >>> from tempfile import TemporaryFile + >>> a = np.empty(10,dtype='f8,i4,a5') + >>> a[5] = (0.5,10,'abcde') + >>> + >>> fd=TemporaryFile() + >>> a = a.newbyteorder('<') + >>> a.tofile(fd) + >>> + >>> _ = fd.seek(0) + >>> r=np.core.records.fromfile(fd, formats='f8,i4,a5', shape=10, + ... byteorder='<') + >>> print(r[5]) + (0.5, 10, 'abcde') + >>> r.shape + (10,) + """ + + if dtype is None and formats is None: + raise TypeError("fromfile() needs a 'dtype' or 'formats' argument") + + # NumPy 1.19.0, 2020-01-01 + shape = _deprecate_shape_0_as_None(shape) + + if shape is None: + shape = (-1,) + elif isinstance(shape, int): + shape = (shape,) + + if hasattr(fd, 'readinto'): + # GH issue 2504. fd supports io.RawIOBase or io.BufferedIOBase interface. + # Example of fd: gzip, BytesIO, BufferedReader + # file already opened + ctx = nullcontext(fd) + else: + # open file + ctx = open(os_fspath(fd), 'rb') + + with ctx as fd: + if offset > 0: + fd.seek(offset, 1) + size = get_remaining_size(fd) + + if dtype is not None: + descr = sb.dtype(dtype) + else: + descr = format_parser(formats, names, titles, aligned, byteorder).dtype + + itemsize = descr.itemsize + + shapeprod = sb.array(shape).prod(dtype=nt.intp) + shapesize = shapeprod * itemsize + if shapesize < 0: + shape = list(shape) + shape[shape.index(-1)] = size // -shapesize + shape = tuple(shape) + shapeprod = sb.array(shape).prod(dtype=nt.intp) + + nbytes = shapeprod * itemsize + + if nbytes > size: + raise ValueError( + "Not enough bytes left in file for specified shape and type") + + # create the array + _array = recarray(shape, descr) + nbytesread = fd.readinto(_array.data) + if nbytesread != nbytes: + raise OSError("Didn't read as many bytes as expected") + + return _array + + +@set_module("numpy.rec") +def array(obj, dtype=None, shape=None, offset=0, strides=None, formats=None, + names=None, titles=None, aligned=False, byteorder=None, copy=True): + """ + Construct a record array from a wide-variety of objects. + + A general-purpose record array constructor that dispatches to the + appropriate `recarray` creation function based on the inputs (see Notes). + + Parameters + ---------- + obj : any + Input object. See Notes for details on how various input types are + treated. + dtype : data-type, optional + Valid dtype for array. + shape : int or tuple of ints, optional + Shape of each array. + offset : int, optional + Position in the file or buffer to start reading from. + strides : tuple of ints, optional + Buffer (`buf`) is interpreted according to these strides (strides + define how many bytes each array element, row, column, etc. + occupy in memory). + formats, names, titles, aligned, byteorder : + If `dtype` is ``None``, these arguments are passed to + `numpy.format_parser` to construct a dtype. See that function for + detailed documentation. + copy : bool, optional + Whether to copy the input object (True), or to use a reference instead. + This option only applies when the input is an ndarray or recarray. + Defaults to True. + + Returns + ------- + np.recarray + Record array created from the specified object. + + Notes + ----- + If `obj` is ``None``, then call the `~numpy.recarray` constructor. If + `obj` is a string, then call the `fromstring` constructor. If `obj` is a + list or a tuple, then if the first object is an `~numpy.ndarray`, call + `fromarrays`, otherwise call `fromrecords`. If `obj` is a + `~numpy.recarray`, then make a copy of the data in the recarray + (if ``copy=True``) and use the new formats, names, and titles. If `obj` + is a file, then call `fromfile`. Finally, if obj is an `ndarray`, then + return ``obj.view(recarray)``, making a copy of the data if ``copy=True``. + + Examples + -------- + >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9]]) + + >>> np.core.records.array(a) + rec.array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9]], + dtype=int32) + + >>> b = [(1, 1), (2, 4), (3, 9)] + >>> c = np.core.records.array(b, formats = ['i2', 'f2'], names = ('x', 'y')) + >>> c + rec.array([(1, 1.0), (2, 4.0), (3, 9.0)], + dtype=[('x', '>> c.x + rec.array([1, 2, 3], dtype=int16) + + >>> c.y + rec.array([ 1.0, 4.0, 9.0], dtype=float16) + + >>> r = np.rec.array(['abc','def'], names=['col1','col2']) + >>> print(r.col1) + abc + + >>> r.col1 + array('abc', dtype='>> r.col2 + array('def', dtype='= 1``. + Copies are made only if necessary. + + See Also + -------- + atleast_2d, atleast_3d + + Examples + -------- + >>> np.atleast_1d(1.0) + array([1.]) + + >>> x = np.arange(9.0).reshape(3,3) + >>> np.atleast_1d(x) + array([[0., 1., 2.], + [3., 4., 5.], + [6., 7., 8.]]) + >>> np.atleast_1d(x) is x + True + + >>> np.atleast_1d(1, [3, 4]) + [array([1]), array([3, 4])] + + """ + res = [] + for ary in arys: + ary = asanyarray(ary) + if ary.ndim == 0: + result = ary.reshape(1) + else: + result = ary + res.append(result) + if len(res) == 1: + return res[0] + else: + return res + + +def _atleast_2d_dispatcher(*arys): + return arys + + +@array_function_dispatch(_atleast_2d_dispatcher) +def atleast_2d(*arys): + """ + View inputs as arrays with at least two dimensions. + + Parameters + ---------- + arys1, arys2, ... : array_like + One or more array-like sequences. Non-array inputs are converted + to arrays. Arrays that already have two or more dimensions are + preserved. + + Returns + ------- + res, res2, ... : ndarray + An array, or list of arrays, each with ``a.ndim >= 2``. + Copies are avoided where possible, and views with two or more + dimensions are returned. + + See Also + -------- + atleast_1d, atleast_3d + + Examples + -------- + >>> np.atleast_2d(3.0) + array([[3.]]) + + >>> x = np.arange(3.0) + >>> np.atleast_2d(x) + array([[0., 1., 2.]]) + >>> np.atleast_2d(x).base is x + True + + >>> np.atleast_2d(1, [1, 2], [[1, 2]]) + [array([[1]]), array([[1, 2]]), array([[1, 2]])] + + """ + res = [] + for ary in arys: + ary = asanyarray(ary) + if ary.ndim == 0: + result = ary.reshape(1, 1) + elif ary.ndim == 1: + result = ary[_nx.newaxis, :] + else: + result = ary + res.append(result) + if len(res) == 1: + return res[0] + else: + return res + + +def _atleast_3d_dispatcher(*arys): + return arys + + +@array_function_dispatch(_atleast_3d_dispatcher) +def atleast_3d(*arys): + """ + View inputs as arrays with at least three dimensions. + + Parameters + ---------- + arys1, arys2, ... : array_like + One or more array-like sequences. Non-array inputs are converted to + arrays. Arrays that already have three or more dimensions are + preserved. + + Returns + ------- + res1, res2, ... : ndarray + An array, or list of arrays, each with ``a.ndim >= 3``. Copies are + avoided where possible, and views with three or more dimensions are + returned. For example, a 1-D array of shape ``(N,)`` becomes a view + of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a + view of shape ``(M, N, 1)``. + + See Also + -------- + atleast_1d, atleast_2d + + Examples + -------- + >>> np.atleast_3d(3.0) + array([[[3.]]]) + + >>> x = np.arange(3.0) + >>> np.atleast_3d(x).shape + (1, 3, 1) + + >>> x = np.arange(12.0).reshape(4,3) + >>> np.atleast_3d(x).shape + (4, 3, 1) + >>> np.atleast_3d(x).base is x.base # x is a reshape, so not base itself + True + + >>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]): + ... print(arr, arr.shape) # doctest: +SKIP + ... + [[[1] + [2]]] (1, 2, 1) + [[[1] + [2]]] (1, 2, 1) + [[[1 2]]] (1, 1, 2) + + """ + res = [] + for ary in arys: + ary = asanyarray(ary) + if ary.ndim == 0: + result = ary.reshape(1, 1, 1) + elif ary.ndim == 1: + result = ary[_nx.newaxis, :, _nx.newaxis] + elif ary.ndim == 2: + result = ary[:, :, _nx.newaxis] + else: + result = ary + res.append(result) + if len(res) == 1: + return res[0] + else: + return res + + +def _arrays_for_stack_dispatcher(arrays): + if not hasattr(arrays, "__getitem__"): + raise TypeError('arrays to stack must be passed as a "sequence" type ' + 'such as list or tuple.') + + return tuple(arrays) + + +def _vhstack_dispatcher(tup, *, dtype=None, casting=None): + return _arrays_for_stack_dispatcher(tup) + + +@array_function_dispatch(_vhstack_dispatcher) +def vstack(tup, *, dtype=None, casting="same_kind"): + """ + Stack arrays in sequence vertically (row wise). + + This is equivalent to concatenation along the first axis after 1-D arrays + of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by + `vsplit`. + + This function makes most sense for arrays with up to 3 dimensions. For + instance, for pixel-data with a height (first axis), width (second axis), + and r/g/b channels (third axis). The functions `concatenate`, `stack` and + `block` provide more general stacking and concatenation operations. + + ``np.row_stack`` is an alias for `vstack`. They are the same function. + + Parameters + ---------- + tup : sequence of ndarrays + The arrays must have the same shape along all but the first axis. + 1-D arrays must have the same length. + + dtype : str or dtype + If provided, the destination array will have this dtype. Cannot be + provided together with `out`. + + .. versionadded:: 1.24 + + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. Defaults to 'same_kind'. + + .. versionadded:: 1.24 + + Returns + ------- + stacked : ndarray + The array formed by stacking the given arrays, will be at least 2-D. + + See Also + -------- + concatenate : Join a sequence of arrays along an existing axis. + stack : Join a sequence of arrays along a new axis. + block : Assemble an nd-array from nested lists of blocks. + hstack : Stack arrays in sequence horizontally (column wise). + dstack : Stack arrays in sequence depth wise (along third axis). + column_stack : Stack 1-D arrays as columns into a 2-D array. + vsplit : Split an array into multiple sub-arrays vertically (row-wise). + + Examples + -------- + >>> a = np.array([1, 2, 3]) + >>> b = np.array([4, 5, 6]) + >>> np.vstack((a,b)) + array([[1, 2, 3], + [4, 5, 6]]) + + >>> a = np.array([[1], [2], [3]]) + >>> b = np.array([[4], [5], [6]]) + >>> np.vstack((a,b)) + array([[1], + [2], + [3], + [4], + [5], + [6]]) + + """ + arrs = atleast_2d(*tup) + if not isinstance(arrs, list): + arrs = [arrs] + return _nx.concatenate(arrs, 0, dtype=dtype, casting=casting) + + +@array_function_dispatch(_vhstack_dispatcher) +def hstack(tup, *, dtype=None, casting="same_kind"): + """ + Stack arrays in sequence horizontally (column wise). + + This is equivalent to concatenation along the second axis, except for 1-D + arrays where it concatenates along the first axis. Rebuilds arrays divided + by `hsplit`. + + This function makes most sense for arrays with up to 3 dimensions. For + instance, for pixel-data with a height (first axis), width (second axis), + and r/g/b channels (third axis). The functions `concatenate`, `stack` and + `block` provide more general stacking and concatenation operations. + + Parameters + ---------- + tup : sequence of ndarrays + The arrays must have the same shape along all but the second axis, + except 1-D arrays which can be any length. + + dtype : str or dtype + If provided, the destination array will have this dtype. Cannot be + provided together with `out`. + + .. versionadded:: 1.24 + + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. Defaults to 'same_kind'. + + .. versionadded:: 1.24 + + Returns + ------- + stacked : ndarray + The array formed by stacking the given arrays. + + See Also + -------- + concatenate : Join a sequence of arrays along an existing axis. + stack : Join a sequence of arrays along a new axis. + block : Assemble an nd-array from nested lists of blocks. + vstack : Stack arrays in sequence vertically (row wise). + dstack : Stack arrays in sequence depth wise (along third axis). + column_stack : Stack 1-D arrays as columns into a 2-D array. + hsplit : Split an array into multiple sub-arrays horizontally (column-wise). + + Examples + -------- + >>> a = np.array((1,2,3)) + >>> b = np.array((4,5,6)) + >>> np.hstack((a,b)) + array([1, 2, 3, 4, 5, 6]) + >>> a = np.array([[1],[2],[3]]) + >>> b = np.array([[4],[5],[6]]) + >>> np.hstack((a,b)) + array([[1, 4], + [2, 5], + [3, 6]]) + + """ + arrs = atleast_1d(*tup) + if not isinstance(arrs, list): + arrs = [arrs] + # As a special case, dimension 0 of 1-dimensional arrays is "horizontal" + if arrs and arrs[0].ndim == 1: + return _nx.concatenate(arrs, 0, dtype=dtype, casting=casting) + else: + return _nx.concatenate(arrs, 1, dtype=dtype, casting=casting) + + +def _stack_dispatcher(arrays, axis=None, out=None, *, + dtype=None, casting=None): + arrays = _arrays_for_stack_dispatcher(arrays) + if out is not None: + # optimize for the typical case where only arrays is provided + arrays = list(arrays) + arrays.append(out) + return arrays + + +@array_function_dispatch(_stack_dispatcher) +def stack(arrays, axis=0, out=None, *, dtype=None, casting="same_kind"): + """ + Join a sequence of arrays along a new axis. + + The ``axis`` parameter specifies the index of the new axis in the + dimensions of the result. For example, if ``axis=0`` it will be the first + dimension and if ``axis=-1`` it will be the last dimension. + + .. versionadded:: 1.10.0 + + Parameters + ---------- + arrays : sequence of array_like + Each array must have the same shape. + + axis : int, optional + The axis in the result array along which the input arrays are stacked. + + out : ndarray, optional + If provided, the destination to place the result. The shape must be + correct, matching that of what stack would have returned if no + out argument were specified. + + dtype : str or dtype + If provided, the destination array will have this dtype. Cannot be + provided together with `out`. + + .. versionadded:: 1.24 + + casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional + Controls what kind of data casting may occur. Defaults to 'same_kind'. + + .. versionadded:: 1.24 + + + Returns + ------- + stacked : ndarray + The stacked array has one more dimension than the input arrays. + + See Also + -------- + concatenate : Join a sequence of arrays along an existing axis. + block : Assemble an nd-array from nested lists of blocks. + split : Split array into a list of multiple sub-arrays of equal size. + + Examples + -------- + >>> arrays = [np.random.randn(3, 4) for _ in range(10)] + >>> np.stack(arrays, axis=0).shape + (10, 3, 4) + + >>> np.stack(arrays, axis=1).shape + (3, 10, 4) + + >>> np.stack(arrays, axis=2).shape + (3, 4, 10) + + >>> a = np.array([1, 2, 3]) + >>> b = np.array([4, 5, 6]) + >>> np.stack((a, b)) + array([[1, 2, 3], + [4, 5, 6]]) + + >>> np.stack((a, b), axis=-1) + array([[1, 4], + [2, 5], + [3, 6]]) + + """ + arrays = [asanyarray(arr) for arr in arrays] + if not arrays: + raise ValueError('need at least one array to stack') + + shapes = {arr.shape for arr in arrays} + if len(shapes) != 1: + raise ValueError('all input arrays must have the same shape') + + result_ndim = arrays[0].ndim + 1 + axis = normalize_axis_index(axis, result_ndim) + + sl = (slice(None),) * axis + (_nx.newaxis,) + expanded_arrays = [arr[sl] for arr in arrays] + return _nx.concatenate(expanded_arrays, axis=axis, out=out, + dtype=dtype, casting=casting) + + +# Internal functions to eliminate the overhead of repeated dispatch in one of +# the two possible paths inside np.block. +# Use getattr to protect against __array_function__ being disabled. +_size = getattr(_from_nx.size, '__wrapped__', _from_nx.size) +_ndim = getattr(_from_nx.ndim, '__wrapped__', _from_nx.ndim) +_concatenate = getattr(_from_nx.concatenate, + '__wrapped__', _from_nx.concatenate) + + +def _block_format_index(index): + """ + Convert a list of indices ``[0, 1, 2]`` into ``"arrays[0][1][2]"``. + """ + idx_str = ''.join('[{}]'.format(i) for i in index if i is not None) + return 'arrays' + idx_str + + +def _block_check_depths_match(arrays, parent_index=[]): + """ + Recursive function checking that the depths of nested lists in `arrays` + all match. Mismatch raises a ValueError as described in the block + docstring below. + + The entire index (rather than just the depth) needs to be calculated + for each innermost list, in case an error needs to be raised, so that + the index of the offending list can be printed as part of the error. + + Parameters + ---------- + arrays : nested list of arrays + The arrays to check + parent_index : list of int + The full index of `arrays` within the nested lists passed to + `_block_check_depths_match` at the top of the recursion. + + Returns + ------- + first_index : list of int + The full index of an element from the bottom of the nesting in + `arrays`. If any element at the bottom is an empty list, this will + refer to it, and the last index along the empty axis will be None. + max_arr_ndim : int + The maximum of the ndims of the arrays nested in `arrays`. + final_size: int + The number of elements in the final array. This is used the motivate + the choice of algorithm used using benchmarking wisdom. + + """ + if type(arrays) is tuple: + # not strictly necessary, but saves us from: + # - more than one way to do things - no point treating tuples like + # lists + # - horribly confusing behaviour that results when tuples are + # treated like ndarray + raise TypeError( + '{} is a tuple. ' + 'Only lists can be used to arrange blocks, and np.block does ' + 'not allow implicit conversion from tuple to ndarray.'.format( + _block_format_index(parent_index) + ) + ) + elif type(arrays) is list and len(arrays) > 0: + idxs_ndims = (_block_check_depths_match(arr, parent_index + [i]) + for i, arr in enumerate(arrays)) + + first_index, max_arr_ndim, final_size = next(idxs_ndims) + for index, ndim, size in idxs_ndims: + final_size += size + if ndim > max_arr_ndim: + max_arr_ndim = ndim + if len(index) != len(first_index): + raise ValueError( + "List depths are mismatched. First element was at depth " + "{}, but there is an element at depth {} ({})".format( + len(first_index), + len(index), + _block_format_index(index) + ) + ) + # propagate our flag that indicates an empty list at the bottom + if index[-1] is None: + first_index = index + + return first_index, max_arr_ndim, final_size + elif type(arrays) is list and len(arrays) == 0: + # We've 'bottomed out' on an empty list + return parent_index + [None], 0, 0 + else: + # We've 'bottomed out' - arrays is either a scalar or an array + size = _size(arrays) + return parent_index, _ndim(arrays), size + + +def _atleast_nd(a, ndim): + # Ensures `a` has at least `ndim` dimensions by prepending + # ones to `a.shape` as necessary + return array(a, ndmin=ndim, copy=False, subok=True) + + +def _accumulate(values): + return list(itertools.accumulate(values)) + + +def _concatenate_shapes(shapes, axis): + """Given array shapes, return the resulting shape and slices prefixes. + + These help in nested concatenation. + + Returns + ------- + shape: tuple of int + This tuple satisfies:: + + shape, _ = _concatenate_shapes([arr.shape for shape in arrs], axis) + shape == concatenate(arrs, axis).shape + + slice_prefixes: tuple of (slice(start, end), ) + For a list of arrays being concatenated, this returns the slice + in the larger array at axis that needs to be sliced into. + + For example, the following holds:: + + ret = concatenate([a, b, c], axis) + _, (sl_a, sl_b, sl_c) = concatenate_slices([a, b, c], axis) + + ret[(slice(None),) * axis + sl_a] == a + ret[(slice(None),) * axis + sl_b] == b + ret[(slice(None),) * axis + sl_c] == c + + These are called slice prefixes since they are used in the recursive + blocking algorithm to compute the left-most slices during the + recursion. Therefore, they must be prepended to rest of the slice + that was computed deeper in the recursion. + + These are returned as tuples to ensure that they can quickly be added + to existing slice tuple without creating a new tuple every time. + + """ + # Cache a result that will be reused. + shape_at_axis = [shape[axis] for shape in shapes] + + # Take a shape, any shape + first_shape = shapes[0] + first_shape_pre = first_shape[:axis] + first_shape_post = first_shape[axis+1:] + + if any(shape[:axis] != first_shape_pre or + shape[axis+1:] != first_shape_post for shape in shapes): + raise ValueError( + 'Mismatched array shapes in block along axis {}.'.format(axis)) + + shape = (first_shape_pre + (sum(shape_at_axis),) + first_shape[axis+1:]) + + offsets_at_axis = _accumulate(shape_at_axis) + slice_prefixes = [(slice(start, end),) + for start, end in zip([0] + offsets_at_axis, + offsets_at_axis)] + return shape, slice_prefixes + + +def _block_info_recursion(arrays, max_depth, result_ndim, depth=0): + """ + Returns the shape of the final array, along with a list + of slices and a list of arrays that can be used for assignment inside the + new array + + Parameters + ---------- + arrays : nested list of arrays + The arrays to check + max_depth : list of int + The number of nested lists + result_ndim : int + The number of dimensions in thefinal array. + + Returns + ------- + shape : tuple of int + The shape that the final array will take on. + slices: list of tuple of slices + The slices into the full array required for assignment. These are + required to be prepended with ``(Ellipsis, )`` to obtain to correct + final index. + arrays: list of ndarray + The data to assign to each slice of the full array + + """ + if depth < max_depth: + shapes, slices, arrays = zip( + *[_block_info_recursion(arr, max_depth, result_ndim, depth+1) + for arr in arrays]) + + axis = result_ndim - max_depth + depth + shape, slice_prefixes = _concatenate_shapes(shapes, axis) + + # Prepend the slice prefix and flatten the slices + slices = [slice_prefix + the_slice + for slice_prefix, inner_slices in zip(slice_prefixes, slices) + for the_slice in inner_slices] + + # Flatten the array list + arrays = functools.reduce(operator.add, arrays) + + return shape, slices, arrays + else: + # We've 'bottomed out' - arrays is either a scalar or an array + # type(arrays) is not list + # Return the slice and the array inside a list to be consistent with + # the recursive case. + arr = _atleast_nd(arrays, result_ndim) + return arr.shape, [()], [arr] + + +def _block(arrays, max_depth, result_ndim, depth=0): + """ + Internal implementation of block based on repeated concatenation. + `arrays` is the argument passed to + block. `max_depth` is the depth of nested lists within `arrays` and + `result_ndim` is the greatest of the dimensions of the arrays in + `arrays` and the depth of the lists in `arrays` (see block docstring + for details). + """ + if depth < max_depth: + arrs = [_block(arr, max_depth, result_ndim, depth+1) + for arr in arrays] + return _concatenate(arrs, axis=-(max_depth-depth)) + else: + # We've 'bottomed out' - arrays is either a scalar or an array + # type(arrays) is not list + return _atleast_nd(arrays, result_ndim) + + +def _block_dispatcher(arrays): + # Use type(...) is list to match the behavior of np.block(), which special + # cases list specifically rather than allowing for generic iterables or + # tuple. Also, we know that list.__array_function__ will never exist. + if type(arrays) is list: + for subarrays in arrays: + yield from _block_dispatcher(subarrays) + else: + yield arrays + + +@array_function_dispatch(_block_dispatcher) +def block(arrays): + """ + Assemble an nd-array from nested lists of blocks. + + Blocks in the innermost lists are concatenated (see `concatenate`) along + the last dimension (-1), then these are concatenated along the + second-last dimension (-2), and so on until the outermost list is reached. + + Blocks can be of any dimension, but will not be broadcasted using the normal + rules. Instead, leading axes of size 1 are inserted, to make ``block.ndim`` + the same for all blocks. This is primarily useful for working with scalars, + and means that code like ``np.block([v, 1])`` is valid, where + ``v.ndim == 1``. + + When the nested list is two levels deep, this allows block matrices to be + constructed from their components. + + .. versionadded:: 1.13.0 + + Parameters + ---------- + arrays : nested list of array_like or scalars (but not tuples) + If passed a single ndarray or scalar (a nested list of depth 0), this + is returned unmodified (and not copied). + + Elements shapes must match along the appropriate axes (without + broadcasting), but leading 1s will be prepended to the shape as + necessary to make the dimensions match. + + Returns + ------- + block_array : ndarray + The array assembled from the given blocks. + + The dimensionality of the output is equal to the greatest of: + * the dimensionality of all the inputs + * the depth to which the input list is nested + + Raises + ------ + ValueError + * If list depths are mismatched - for instance, ``[[a, b], c]`` is + illegal, and should be spelt ``[[a, b], [c]]`` + * If lists are empty - for instance, ``[[a, b], []]`` + + See Also + -------- + concatenate : Join a sequence of arrays along an existing axis. + stack : Join a sequence of arrays along a new axis. + vstack : Stack arrays in sequence vertically (row wise). + hstack : Stack arrays in sequence horizontally (column wise). + dstack : Stack arrays in sequence depth wise (along third axis). + column_stack : Stack 1-D arrays as columns into a 2-D array. + vsplit : Split an array into multiple sub-arrays vertically (row-wise). + + Notes + ----- + + When called with only scalars, ``np.block`` is equivalent to an ndarray + call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to + ``np.array([[1, 2], [3, 4]])``. + + This function does not enforce that the blocks lie on a fixed grid. + ``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form:: + + AAAbb + AAAbb + cccDD + + But is also allowed to produce, for some ``a, b, c, d``:: + + AAAbb + AAAbb + cDDDD + + Since concatenation happens along the last axis first, `block` is _not_ + capable of producing the following directly:: + + AAAbb + cccbb + cccDD + + Matlab's "square bracket stacking", ``[A, B, ...; p, q, ...]``, is + equivalent to ``np.block([[A, B, ...], [p, q, ...]])``. + + Examples + -------- + The most common use of this function is to build a block matrix + + >>> A = np.eye(2) * 2 + >>> B = np.eye(3) * 3 + >>> np.block([ + ... [A, np.zeros((2, 3))], + ... [np.ones((3, 2)), B ] + ... ]) + array([[2., 0., 0., 0., 0.], + [0., 2., 0., 0., 0.], + [1., 1., 3., 0., 0.], + [1., 1., 0., 3., 0.], + [1., 1., 0., 0., 3.]]) + + With a list of depth 1, `block` can be used as `hstack` + + >>> np.block([1, 2, 3]) # hstack([1, 2, 3]) + array([1, 2, 3]) + + >>> a = np.array([1, 2, 3]) + >>> b = np.array([4, 5, 6]) + >>> np.block([a, b, 10]) # hstack([a, b, 10]) + array([ 1, 2, 3, 4, 5, 6, 10]) + + >>> A = np.ones((2, 2), int) + >>> B = 2 * A + >>> np.block([A, B]) # hstack([A, B]) + array([[1, 1, 2, 2], + [1, 1, 2, 2]]) + + With a list of depth 2, `block` can be used in place of `vstack`: + + >>> a = np.array([1, 2, 3]) + >>> b = np.array([4, 5, 6]) + >>> np.block([[a], [b]]) # vstack([a, b]) + array([[1, 2, 3], + [4, 5, 6]]) + + >>> A = np.ones((2, 2), int) + >>> B = 2 * A + >>> np.block([[A], [B]]) # vstack([A, B]) + array([[1, 1], + [1, 1], + [2, 2], + [2, 2]]) + + It can also be used in places of `atleast_1d` and `atleast_2d` + + >>> a = np.array(0) + >>> b = np.array([1]) + >>> np.block([a]) # atleast_1d(a) + array([0]) + >>> np.block([b]) # atleast_1d(b) + array([1]) + + >>> np.block([[a]]) # atleast_2d(a) + array([[0]]) + >>> np.block([[b]]) # atleast_2d(b) + array([[1]]) + + + """ + arrays, list_ndim, result_ndim, final_size = _block_setup(arrays) + + # It was found through benchmarking that making an array of final size + # around 256x256 was faster by straight concatenation on a + # i7-7700HQ processor and dual channel ram 2400MHz. + # It didn't seem to matter heavily on the dtype used. + # + # A 2D array using repeated concatenation requires 2 copies of the array. + # + # The fastest algorithm will depend on the ratio of CPU power to memory + # speed. + # One can monitor the results of the benchmark + # https://pv.github.io/numpy-bench/#bench_shape_base.Block2D.time_block2d + # to tune this parameter until a C version of the `_block_info_recursion` + # algorithm is implemented which would likely be faster than the python + # version. + if list_ndim * final_size > (2 * 512 * 512): + return _block_slicing(arrays, list_ndim, result_ndim) + else: + return _block_concatenate(arrays, list_ndim, result_ndim) + + +# These helper functions are mostly used for testing. +# They allow us to write tests that directly call `_block_slicing` +# or `_block_concatenate` without blocking large arrays to force the wisdom +# to trigger the desired path. +def _block_setup(arrays): + """ + Returns + (`arrays`, list_ndim, result_ndim, final_size) + """ + bottom_index, arr_ndim, final_size = _block_check_depths_match(arrays) + list_ndim = len(bottom_index) + if bottom_index and bottom_index[-1] is None: + raise ValueError( + 'List at {} cannot be empty'.format( + _block_format_index(bottom_index) + ) + ) + result_ndim = max(arr_ndim, list_ndim) + return arrays, list_ndim, result_ndim, final_size + + +def _block_slicing(arrays, list_ndim, result_ndim): + shape, slices, arrays = _block_info_recursion( + arrays, list_ndim, result_ndim) + dtype = _nx.result_type(*[arr.dtype for arr in arrays]) + + # Test preferring F only in the case that all input arrays are F + F_order = all(arr.flags['F_CONTIGUOUS'] for arr in arrays) + C_order = all(arr.flags['C_CONTIGUOUS'] for arr in arrays) + order = 'F' if F_order and not C_order else 'C' + result = _nx.empty(shape=shape, dtype=dtype, order=order) + # Note: In a c implementation, the function + # PyArray_CreateMultiSortedStridePerm could be used for more advanced + # guessing of the desired order. + + for the_slice, arr in zip(slices, arrays): + result[(Ellipsis,) + the_slice] = arr + return result + + +def _block_concatenate(arrays, list_ndim, result_ndim): + result = _block(arrays, list_ndim, result_ndim) + if list_ndim == 0: + # Catch an edge case where _block returns a view because + # `arrays` is a single numpy array and not a list of numpy arrays. + # This might copy scalars or lists twice, but this isn't a likely + # usecase for those interested in performance + result = result.copy() + return result diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_argparse.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_argparse.py new file mode 100644 index 0000000000000000000000000000000000000000..fae22702710916b52f99f7024d4d07410c148ede --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_argparse.py @@ -0,0 +1,62 @@ +""" +Tests for the private NumPy argument parsing functionality. +They mainly exists to ensure good test coverage without having to try the +weirder cases on actual numpy functions but test them in one place. + +The test function is defined in C to be equivalent to (errors may not always +match exactly, and could be adjusted): + + def func(arg1, /, arg2, *, arg3): + i = integer(arg1) # reproducing the 'i' parsing in Python. + return None +""" + +import pytest + +import numpy as np +from numpy.core._multiarray_tests import argparse_example_function as func + + +def test_invalid_integers(): + with pytest.raises(TypeError, + match="integer argument expected, got float"): + func(1.) + with pytest.raises(OverflowError): + func(2**100) + + +def test_missing_arguments(): + with pytest.raises(TypeError, + match="missing required positional argument 0"): + func() + with pytest.raises(TypeError, + match="missing required positional argument 0"): + func(arg2=1, arg3=4) + with pytest.raises(TypeError, + match=r"missing required argument \'arg2\' \(pos 1\)"): + func(1, arg3=5) + + +def test_too_many_positional(): + # the second argument is positional but can be passed as keyword. + with pytest.raises(TypeError, + match="takes from 2 to 3 positional arguments but 4 were given"): + func(1, 2, 3, 4) + + +def test_multiple_values(): + with pytest.raises(TypeError, + match=r"given by name \('arg2'\) and position \(position 1\)"): + func(1, 2, arg2=3) + + +def test_string_fallbacks(): + # We can (currently?) use numpy strings to test the "slow" fallbacks + # that should normally not be taken due to string interning. + arg2 = np.str_("arg2") + missing_arg = np.str_("missing_arg") + func(1, **{arg2: 3}) + with pytest.raises(TypeError, + match="got an unexpected keyword argument 'missing_arg'"): + func(2, **{missing_arg: 3}) + diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_dlpack.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_dlpack.py new file mode 100644 index 0000000000000000000000000000000000000000..49249bc6a8b48383d0a318f7a6a45403ad1b095f --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_dlpack.py @@ -0,0 +1,124 @@ +import sys +import pytest + +import numpy as np +from numpy.testing import assert_array_equal, IS_PYPY + + +class TestDLPack: + @pytest.mark.skipif(IS_PYPY, reason="PyPy can't get refcounts.") + def test_dunder_dlpack_refcount(self): + x = np.arange(5) + y = x.__dlpack__() + assert sys.getrefcount(x) == 3 + del y + assert sys.getrefcount(x) == 2 + + def test_dunder_dlpack_stream(self): + x = np.arange(5) + x.__dlpack__(stream=None) + + with pytest.raises(RuntimeError): + x.__dlpack__(stream=1) + + def test_strides_not_multiple_of_itemsize(self): + dt = np.dtype([('int', np.int32), ('char', np.int8)]) + y = np.zeros((5,), dtype=dt) + z = y['int'] + + with pytest.raises(BufferError): + np.from_dlpack(z) + + @pytest.mark.skipif(IS_PYPY, reason="PyPy can't get refcounts.") + def test_from_dlpack_refcount(self): + x = np.arange(5) + y = np.from_dlpack(x) + assert sys.getrefcount(x) == 3 + del y + assert sys.getrefcount(x) == 2 + + @pytest.mark.parametrize("dtype", [ + np.bool_, + np.int8, np.int16, np.int32, np.int64, + np.uint8, np.uint16, np.uint32, np.uint64, + np.float16, np.float32, np.float64, + np.complex64, np.complex128 + ]) + def test_dtype_passthrough(self, dtype): + x = np.arange(5).astype(dtype) + y = np.from_dlpack(x) + + assert y.dtype == x.dtype + assert_array_equal(x, y) + + def test_invalid_dtype(self): + x = np.asarray(np.datetime64('2021-05-27')) + + with pytest.raises(BufferError): + np.from_dlpack(x) + + def test_invalid_byte_swapping(self): + dt = np.dtype('=i8').newbyteorder() + x = np.arange(5, dtype=dt) + + with pytest.raises(BufferError): + np.from_dlpack(x) + + def test_non_contiguous(self): + x = np.arange(25).reshape((5, 5)) + + y1 = x[0] + assert_array_equal(y1, np.from_dlpack(y1)) + + y2 = x[:, 0] + assert_array_equal(y2, np.from_dlpack(y2)) + + y3 = x[1, :] + assert_array_equal(y3, np.from_dlpack(y3)) + + y4 = x[1] + assert_array_equal(y4, np.from_dlpack(y4)) + + y5 = np.diagonal(x).copy() + assert_array_equal(y5, np.from_dlpack(y5)) + + @pytest.mark.parametrize("ndim", range(33)) + def test_higher_dims(self, ndim): + shape = (1,) * ndim + x = np.zeros(shape, dtype=np.float64) + + assert shape == np.from_dlpack(x).shape + + def test_dlpack_device(self): + x = np.arange(5) + assert x.__dlpack_device__() == (1, 0) + y = np.from_dlpack(x) + assert y.__dlpack_device__() == (1, 0) + z = y[::2] + assert z.__dlpack_device__() == (1, 0) + + def dlpack_deleter_exception(self): + x = np.arange(5) + _ = x.__dlpack__() + raise RuntimeError + + def test_dlpack_destructor_exception(self): + with pytest.raises(RuntimeError): + self.dlpack_deleter_exception() + + def test_readonly(self): + x = np.arange(5) + x.flags.writeable = False + with pytest.raises(BufferError): + x.__dlpack__() + + def test_ndim0(self): + x = np.array(1.0) + y = np.from_dlpack(x) + assert_array_equal(x, y) + + def test_size1dims_arrays(self): + x = np.ndarray(dtype='f8', shape=(10, 5, 1), strides=(8, 80, 4), + buffer=np.ones(1000, dtype=np.uint8), order='F') + y = np.from_dlpack(x) + assert_array_equal(x, y) diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_einsum.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_einsum.py new file mode 100644 index 0000000000000000000000000000000000000000..702be2486515402d835e44d361d8642211919487 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_einsum.py @@ -0,0 +1,1248 @@ +import itertools +import sys +import platform + +import pytest + +import numpy as np +from numpy.testing import ( + assert_, assert_equal, assert_array_equal, assert_almost_equal, + assert_raises, suppress_warnings, assert_raises_regex, assert_allclose + ) + +try: + COMPILERS = np.show_config(mode="dicts")["Compilers"] + USING_CLANG_CL = COMPILERS["c"]["name"] == "clang-cl" +except TypeError: + USING_CLANG_CL = False + +# Setup for optimize einsum +chars = 'abcdefghij' +sizes = np.array([2, 3, 4, 5, 4, 3, 2, 6, 5, 4, 3]) +global_size_dict = dict(zip(chars, sizes)) + + +class TestEinsum: + def test_einsum_errors(self): + for do_opt in [True, False]: + # Need enough arguments + assert_raises(ValueError, np.einsum, optimize=do_opt) + assert_raises(ValueError, np.einsum, "", optimize=do_opt) + + # subscripts must be a string + assert_raises(TypeError, np.einsum, 0, 0, optimize=do_opt) + + # out parameter must be an array + assert_raises(TypeError, np.einsum, "", 0, out='test', + optimize=do_opt) + + # order parameter must be a valid order + assert_raises(ValueError, np.einsum, "", 0, order='W', + optimize=do_opt) + + # casting parameter must be a valid casting + assert_raises(ValueError, np.einsum, "", 0, casting='blah', + optimize=do_opt) + + # dtype parameter must be a valid dtype + assert_raises(TypeError, np.einsum, "", 0, dtype='bad_data_type', + optimize=do_opt) + + # other keyword arguments are rejected + assert_raises(TypeError, np.einsum, "", 0, bad_arg=0, + optimize=do_opt) + + # issue 4528 revealed a segfault with this call + assert_raises(TypeError, np.einsum, *(None,)*63, optimize=do_opt) + + # number of operands must match count in subscripts string + assert_raises(ValueError, np.einsum, "", 0, 0, optimize=do_opt) + assert_raises(ValueError, np.einsum, ",", 0, [0], [0], + optimize=do_opt) + assert_raises(ValueError, np.einsum, ",", [0], optimize=do_opt) + + # can't have more subscripts than dimensions in the operand + assert_raises(ValueError, np.einsum, "i", 0, optimize=do_opt) + assert_raises(ValueError, np.einsum, "ij", [0, 0], optimize=do_opt) + assert_raises(ValueError, np.einsum, "...i", 0, optimize=do_opt) + assert_raises(ValueError, np.einsum, "i...j", [0, 0], optimize=do_opt) + assert_raises(ValueError, np.einsum, "i...", 0, optimize=do_opt) + assert_raises(ValueError, np.einsum, "ij...", [0, 0], optimize=do_opt) + + # invalid ellipsis + assert_raises(ValueError, np.einsum, "i..", [0, 0], optimize=do_opt) + assert_raises(ValueError, np.einsum, ".i...", [0, 0], optimize=do_opt) + assert_raises(ValueError, np.einsum, "j->..j", [0, 0], optimize=do_opt) + assert_raises(ValueError, np.einsum, "j->.j...", [0, 0], optimize=do_opt) + + # invalid subscript character + assert_raises(ValueError, np.einsum, "i%...", [0, 0], optimize=do_opt) + assert_raises(ValueError, np.einsum, "...j$", [0, 0], optimize=do_opt) + assert_raises(ValueError, np.einsum, "i->&", [0, 0], optimize=do_opt) + + # output subscripts must appear in input + assert_raises(ValueError, np.einsum, "i->ij", [0, 0], optimize=do_opt) + + # output subscripts may only be specified once + assert_raises(ValueError, np.einsum, "ij->jij", [[0, 0], [0, 0]], + optimize=do_opt) + + # dimensions much match when being collapsed + assert_raises(ValueError, np.einsum, "ii", + np.arange(6).reshape(2, 3), optimize=do_opt) + assert_raises(ValueError, np.einsum, "ii->i", + np.arange(6).reshape(2, 3), optimize=do_opt) + + # broadcasting to new dimensions must be enabled explicitly + assert_raises(ValueError, np.einsum, "i", np.arange(6).reshape(2, 3), + optimize=do_opt) + assert_raises(ValueError, np.einsum, "i->i", [[0, 1], [0, 1]], + out=np.arange(4).reshape(2, 2), optimize=do_opt) + with assert_raises_regex(ValueError, "'b'"): + # gh-11221 - 'c' erroneously appeared in the error message + a = np.ones((3, 3, 4, 5, 6)) + b = np.ones((3, 4, 5)) + np.einsum('aabcb,abc', a, b) + + # Check order kwarg, asanyarray allows 1d to pass through + assert_raises(ValueError, np.einsum, "i->i", np.arange(6).reshape(-1, 1), + optimize=do_opt, order='d') + + def test_einsum_object_errors(self): + # Exceptions created by object arithmetic should + # successfully propagate + + class CustomException(Exception): + pass + + class DestructoBox: + + def __init__(self, value, destruct): + self._val = value + self._destruct = destruct + + def __add__(self, other): + tmp = self._val + other._val + if tmp >= self._destruct: + raise CustomException + else: + self._val = tmp + return self + + def __radd__(self, other): + if other == 0: + return self + else: + return self.__add__(other) + + def __mul__(self, other): + tmp = self._val * other._val + if tmp >= self._destruct: + raise CustomException + else: + self._val = tmp + return self + + def __rmul__(self, other): + if other == 0: + return self + else: + return self.__mul__(other) + + a = np.array([DestructoBox(i, 5) for i in range(1, 10)], + dtype='object').reshape(3, 3) + + # raised from unbuffered_loop_nop1_ndim2 + assert_raises(CustomException, np.einsum, "ij->i", a) + + # raised from unbuffered_loop_nop1_ndim3 + b = np.array([DestructoBox(i, 100) for i in range(0, 27)], + dtype='object').reshape(3, 3, 3) + assert_raises(CustomException, np.einsum, "i...k->...", b) + + # raised from unbuffered_loop_nop2_ndim2 + b = np.array([DestructoBox(i, 55) for i in range(1, 4)], + dtype='object') + assert_raises(CustomException, np.einsum, "ij, j", a, b) + + # raised from unbuffered_loop_nop2_ndim3 + assert_raises(CustomException, np.einsum, "ij, jh", a, a) + + # raised from PyArray_EinsteinSum + assert_raises(CustomException, np.einsum, "ij->", a) + + def test_einsum_views(self): + # pass-through + for do_opt in [True, False]: + a = np.arange(6) + a.shape = (2, 3) + + b = np.einsum("...", a, optimize=do_opt) + assert_(b.base is a) + + b = np.einsum(a, [Ellipsis], optimize=do_opt) + assert_(b.base is a) + + b = np.einsum("ij", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, a) + + b = np.einsum(a, [0, 1], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, a) + + # output is writeable whenever input is writeable + b = np.einsum("...", a, optimize=do_opt) + assert_(b.flags['WRITEABLE']) + a.flags['WRITEABLE'] = False + b = np.einsum("...", a, optimize=do_opt) + assert_(not b.flags['WRITEABLE']) + + # transpose + a = np.arange(6) + a.shape = (2, 3) + + b = np.einsum("ji", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, a.T) + + b = np.einsum(a, [1, 0], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, a.T) + + # diagonal + a = np.arange(9) + a.shape = (3, 3) + + b = np.einsum("ii->i", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[i, i] for i in range(3)]) + + b = np.einsum(a, [0, 0], [0], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[i, i] for i in range(3)]) + + # diagonal with various ways of broadcasting an additional dimension + a = np.arange(27) + a.shape = (3, 3, 3) + + b = np.einsum("...ii->...i", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [[x[i, i] for i in range(3)] for x in a]) + + b = np.einsum(a, [Ellipsis, 0, 0], [Ellipsis, 0], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [[x[i, i] for i in range(3)] for x in a]) + + b = np.einsum("ii...->...i", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [[x[i, i] for i in range(3)] + for x in a.transpose(2, 0, 1)]) + + b = np.einsum(a, [0, 0, Ellipsis], [Ellipsis, 0], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [[x[i, i] for i in range(3)] + for x in a.transpose(2, 0, 1)]) + + b = np.einsum("...ii->i...", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[:, i, i] for i in range(3)]) + + b = np.einsum(a, [Ellipsis, 0, 0], [0, Ellipsis], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[:, i, i] for i in range(3)]) + + b = np.einsum("jii->ij", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[:, i, i] for i in range(3)]) + + b = np.einsum(a, [1, 0, 0], [0, 1], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[:, i, i] for i in range(3)]) + + b = np.einsum("ii...->i...", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a.transpose(2, 0, 1)[:, i, i] for i in range(3)]) + + b = np.einsum(a, [0, 0, Ellipsis], [0, Ellipsis], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a.transpose(2, 0, 1)[:, i, i] for i in range(3)]) + + b = np.einsum("i...i->i...", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a.transpose(1, 0, 2)[:, i, i] for i in range(3)]) + + b = np.einsum(a, [0, Ellipsis, 0], [0, Ellipsis], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a.transpose(1, 0, 2)[:, i, i] for i in range(3)]) + + b = np.einsum("i...i->...i", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [[x[i, i] for i in range(3)] + for x in a.transpose(1, 0, 2)]) + + b = np.einsum(a, [0, Ellipsis, 0], [Ellipsis, 0], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [[x[i, i] for i in range(3)] + for x in a.transpose(1, 0, 2)]) + + # triple diagonal + a = np.arange(27) + a.shape = (3, 3, 3) + + b = np.einsum("iii->i", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[i, i, i] for i in range(3)]) + + b = np.einsum(a, [0, 0, 0], [0], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, [a[i, i, i] for i in range(3)]) + + # swap axes + a = np.arange(24) + a.shape = (2, 3, 4) + + b = np.einsum("ijk->jik", a, optimize=do_opt) + assert_(b.base is a) + assert_equal(b, a.swapaxes(0, 1)) + + b = np.einsum(a, [0, 1, 2], [1, 0, 2], optimize=do_opt) + assert_(b.base is a) + assert_equal(b, a.swapaxes(0, 1)) + + @np._no_nep50_warning() + def check_einsum_sums(self, dtype, do_opt=False): + dtype = np.dtype(dtype) + # Check various sums. Does many sizes to exercise unrolled loops. + + # sum(a, axis=-1) + for n in range(1, 17): + a = np.arange(n, dtype=dtype) + b = np.sum(a, axis=-1) + if hasattr(b, 'astype'): + b = b.astype(dtype) + assert_equal(np.einsum("i->", a, optimize=do_opt), b) + assert_equal(np.einsum(a, [0], [], optimize=do_opt), b) + + for n in range(1, 17): + a = np.arange(2*3*n, dtype=dtype).reshape(2, 3, n) + b = np.sum(a, axis=-1) + if hasattr(b, 'astype'): + b = b.astype(dtype) + assert_equal(np.einsum("...i->...", a, optimize=do_opt), b) + assert_equal(np.einsum(a, [Ellipsis, 0], [Ellipsis], optimize=do_opt), b) + + # sum(a, axis=0) + for n in range(1, 17): + a = np.arange(2*n, dtype=dtype).reshape(2, n) + b = np.sum(a, axis=0) + if hasattr(b, 'astype'): + b = b.astype(dtype) + assert_equal(np.einsum("i...->...", a, optimize=do_opt), b) + assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt), b) + + for n in range(1, 17): + a = np.arange(2*3*n, dtype=dtype).reshape(2, 3, n) + b = np.sum(a, axis=0) + if hasattr(b, 'astype'): + b = b.astype(dtype) + assert_equal(np.einsum("i...->...", a, optimize=do_opt), b) + assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt), b) + + # trace(a) + for n in range(1, 17): + a = np.arange(n*n, dtype=dtype).reshape(n, n) + b = np.trace(a) + if hasattr(b, 'astype'): + b = b.astype(dtype) + assert_equal(np.einsum("ii", a, optimize=do_opt), b) + assert_equal(np.einsum(a, [0, 0], optimize=do_opt), b) + + # gh-15961: should accept numpy int64 type in subscript list + np_array = np.asarray([0, 0]) + assert_equal(np.einsum(a, np_array, optimize=do_opt), b) + assert_equal(np.einsum(a, list(np_array), optimize=do_opt), b) + + # multiply(a, b) + assert_equal(np.einsum("..., ...", 3, 4), 12) # scalar case + for n in range(1, 17): + a = np.arange(3 * n, dtype=dtype).reshape(3, n) + b = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n) + assert_equal(np.einsum("..., ...", a, b, optimize=do_opt), + np.multiply(a, b)) + assert_equal(np.einsum(a, [Ellipsis], b, [Ellipsis], optimize=do_opt), + np.multiply(a, b)) + + # inner(a,b) + for n in range(1, 17): + a = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n) + b = np.arange(n, dtype=dtype) + assert_equal(np.einsum("...i, ...i", a, b, optimize=do_opt), np.inner(a, b)) + assert_equal(np.einsum(a, [Ellipsis, 0], b, [Ellipsis, 0], optimize=do_opt), + np.inner(a, b)) + + for n in range(1, 11): + a = np.arange(n * 3 * 2, dtype=dtype).reshape(n, 3, 2) + b = np.arange(n, dtype=dtype) + assert_equal(np.einsum("i..., i...", a, b, optimize=do_opt), + np.inner(a.T, b.T).T) + assert_equal(np.einsum(a, [0, Ellipsis], b, [0, Ellipsis], optimize=do_opt), + np.inner(a.T, b.T).T) + + # outer(a,b) + for n in range(1, 17): + a = np.arange(3, dtype=dtype)+1 + b = np.arange(n, dtype=dtype)+1 + assert_equal(np.einsum("i,j", a, b, optimize=do_opt), + np.outer(a, b)) + assert_equal(np.einsum(a, [0], b, [1], optimize=do_opt), + np.outer(a, b)) + + # Suppress the complex warnings for the 'as f8' tests + with suppress_warnings() as sup: + sup.filter(np.ComplexWarning) + + # matvec(a,b) / a.dot(b) where a is matrix, b is vector + for n in range(1, 17): + a = np.arange(4*n, dtype=dtype).reshape(4, n) + b = np.arange(n, dtype=dtype) + assert_equal(np.einsum("ij, j", a, b, optimize=do_opt), + np.dot(a, b)) + assert_equal(np.einsum(a, [0, 1], b, [1], optimize=do_opt), + np.dot(a, b)) + + c = np.arange(4, dtype=dtype) + np.einsum("ij,j", a, b, out=c, + dtype='f8', casting='unsafe', optimize=do_opt) + assert_equal(c, + np.dot(a.astype('f8'), + b.astype('f8')).astype(dtype)) + c[...] = 0 + np.einsum(a, [0, 1], b, [1], out=c, + dtype='f8', casting='unsafe', optimize=do_opt) + assert_equal(c, + np.dot(a.astype('f8'), + b.astype('f8')).astype(dtype)) + + for n in range(1, 17): + a = np.arange(4*n, dtype=dtype).reshape(4, n) + b = np.arange(n, dtype=dtype) + assert_equal(np.einsum("ji,j", a.T, b.T, optimize=do_opt), + np.dot(b.T, a.T)) + assert_equal(np.einsum(a.T, [1, 0], b.T, [1], optimize=do_opt), + np.dot(b.T, a.T)) + + c = np.arange(4, dtype=dtype) + np.einsum("ji,j", a.T, b.T, out=c, + dtype='f8', casting='unsafe', optimize=do_opt) + assert_equal(c, + np.dot(b.T.astype('f8'), + a.T.astype('f8')).astype(dtype)) + c[...] = 0 + np.einsum(a.T, [1, 0], b.T, [1], out=c, + dtype='f8', casting='unsafe', optimize=do_opt) + assert_equal(c, + np.dot(b.T.astype('f8'), + a.T.astype('f8')).astype(dtype)) + + # matmat(a,b) / a.dot(b) where a is matrix, b is matrix + for n in range(1, 17): + if n < 8 or dtype != 'f2': + a = np.arange(4*n, dtype=dtype).reshape(4, n) + b = np.arange(n*6, dtype=dtype).reshape(n, 6) + assert_equal(np.einsum("ij,jk", a, b, optimize=do_opt), + np.dot(a, b)) + assert_equal(np.einsum(a, [0, 1], b, [1, 2], optimize=do_opt), + np.dot(a, b)) + + for n in range(1, 17): + a = np.arange(4*n, dtype=dtype).reshape(4, n) + b = np.arange(n*6, dtype=dtype).reshape(n, 6) + c = np.arange(24, dtype=dtype).reshape(4, 6) + np.einsum("ij,jk", a, b, out=c, dtype='f8', casting='unsafe', + optimize=do_opt) + assert_equal(c, + np.dot(a.astype('f8'), + b.astype('f8')).astype(dtype)) + c[...] = 0 + np.einsum(a, [0, 1], b, [1, 2], out=c, + dtype='f8', casting='unsafe', optimize=do_opt) + assert_equal(c, + np.dot(a.astype('f8'), + b.astype('f8')).astype(dtype)) + + # matrix triple product (note this is not currently an efficient + # way to multiply 3 matrices) + a = np.arange(12, dtype=dtype).reshape(3, 4) + b = np.arange(20, dtype=dtype).reshape(4, 5) + c = np.arange(30, dtype=dtype).reshape(5, 6) + if dtype != 'f2': + assert_equal(np.einsum("ij,jk,kl", a, b, c, optimize=do_opt), + a.dot(b).dot(c)) + assert_equal(np.einsum(a, [0, 1], b, [1, 2], c, [2, 3], + optimize=do_opt), a.dot(b).dot(c)) + + d = np.arange(18, dtype=dtype).reshape(3, 6) + np.einsum("ij,jk,kl", a, b, c, out=d, + dtype='f8', casting='unsafe', optimize=do_opt) + tgt = a.astype('f8').dot(b.astype('f8')) + tgt = tgt.dot(c.astype('f8')).astype(dtype) + assert_equal(d, tgt) + + d[...] = 0 + np.einsum(a, [0, 1], b, [1, 2], c, [2, 3], out=d, + dtype='f8', casting='unsafe', optimize=do_opt) + tgt = a.astype('f8').dot(b.astype('f8')) + tgt = tgt.dot(c.astype('f8')).astype(dtype) + assert_equal(d, tgt) + + # tensordot(a, b) + if np.dtype(dtype) != np.dtype('f2'): + a = np.arange(60, dtype=dtype).reshape(3, 4, 5) + b = np.arange(24, dtype=dtype).reshape(4, 3, 2) + assert_equal(np.einsum("ijk, jil -> kl", a, b), + np.tensordot(a, b, axes=([1, 0], [0, 1]))) + assert_equal(np.einsum(a, [0, 1, 2], b, [1, 0, 3], [2, 3]), + np.tensordot(a, b, axes=([1, 0], [0, 1]))) + + c = np.arange(10, dtype=dtype).reshape(5, 2) + np.einsum("ijk,jil->kl", a, b, out=c, + dtype='f8', casting='unsafe', optimize=do_opt) + assert_equal(c, np.tensordot(a.astype('f8'), b.astype('f8'), + axes=([1, 0], [0, 1])).astype(dtype)) + c[...] = 0 + np.einsum(a, [0, 1, 2], b, [1, 0, 3], [2, 3], out=c, + dtype='f8', casting='unsafe', optimize=do_opt) + assert_equal(c, np.tensordot(a.astype('f8'), b.astype('f8'), + axes=([1, 0], [0, 1])).astype(dtype)) + + # logical_and(logical_and(a!=0, b!=0), c!=0) + neg_val = -2 if dtype.kind != "u" else np.iinfo(dtype).max - 1 + a = np.array([1, 3, neg_val, 0, 12, 13, 0, 1], dtype=dtype) + b = np.array([0, 3.5, 0., neg_val, 0, 1, 3, 12], dtype=dtype) + c = np.array([True, True, False, True, True, False, True, True]) + + assert_equal(np.einsum("i,i,i->i", a, b, c, + dtype='?', casting='unsafe', optimize=do_opt), + np.logical_and(np.logical_and(a != 0, b != 0), c != 0)) + assert_equal(np.einsum(a, [0], b, [0], c, [0], [0], + dtype='?', casting='unsafe'), + np.logical_and(np.logical_and(a != 0, b != 0), c != 0)) + + a = np.arange(9, dtype=dtype) + assert_equal(np.einsum(",i->", 3, a), 3*np.sum(a)) + assert_equal(np.einsum(3, [], a, [0], []), 3*np.sum(a)) + assert_equal(np.einsum("i,->", a, 3), 3*np.sum(a)) + assert_equal(np.einsum(a, [0], 3, [], []), 3*np.sum(a)) + + # Various stride0, contiguous, and SSE aligned variants + for n in range(1, 25): + a = np.arange(n, dtype=dtype) + if np.dtype(dtype).itemsize > 1: + assert_equal(np.einsum("...,...", a, a, optimize=do_opt), + np.multiply(a, a)) + assert_equal(np.einsum("i,i", a, a, optimize=do_opt), np.dot(a, a)) + assert_equal(np.einsum("i,->i", a, 2, optimize=do_opt), 2*a) + assert_equal(np.einsum(",i->i", 2, a, optimize=do_opt), 2*a) + assert_equal(np.einsum("i,->", a, 2, optimize=do_opt), 2*np.sum(a)) + assert_equal(np.einsum(",i->", 2, a, optimize=do_opt), 2*np.sum(a)) + + assert_equal(np.einsum("...,...", a[1:], a[:-1], optimize=do_opt), + np.multiply(a[1:], a[:-1])) + assert_equal(np.einsum("i,i", a[1:], a[:-1], optimize=do_opt), + np.dot(a[1:], a[:-1])) + assert_equal(np.einsum("i,->i", a[1:], 2, optimize=do_opt), 2*a[1:]) + assert_equal(np.einsum(",i->i", 2, a[1:], optimize=do_opt), 2*a[1:]) + assert_equal(np.einsum("i,->", a[1:], 2, optimize=do_opt), + 2*np.sum(a[1:])) + assert_equal(np.einsum(",i->", 2, a[1:], optimize=do_opt), + 2*np.sum(a[1:])) + + # An object array, summed as the data type + a = np.arange(9, dtype=object) + + b = np.einsum("i->", a, dtype=dtype, casting='unsafe') + assert_equal(b, np.sum(a)) + if hasattr(b, "dtype"): + # Can be a python object when dtype is object + assert_equal(b.dtype, np.dtype(dtype)) + + b = np.einsum(a, [0], [], dtype=dtype, casting='unsafe') + assert_equal(b, np.sum(a)) + if hasattr(b, "dtype"): + # Can be a python object when dtype is object + assert_equal(b.dtype, np.dtype(dtype)) + + # A case which was failing (ticket #1885) + p = np.arange(2) + 1 + q = np.arange(4).reshape(2, 2) + 3 + r = np.arange(4).reshape(2, 2) + 7 + assert_equal(np.einsum('z,mz,zm->', p, q, r), 253) + + # singleton dimensions broadcast (gh-10343) + p = np.ones((10,2)) + q = np.ones((1,2)) + assert_array_equal(np.einsum('ij,ij->j', p, q, optimize=True), + np.einsum('ij,ij->j', p, q, optimize=False)) + assert_array_equal(np.einsum('ij,ij->j', p, q, optimize=True), + [10.] * 2) + + # a blas-compatible contraction broadcasting case which was failing + # for optimize=True (ticket #10930) + x = np.array([2., 3.]) + y = np.array([4.]) + assert_array_equal(np.einsum("i, i", x, y, optimize=False), 20.) + assert_array_equal(np.einsum("i, i", x, y, optimize=True), 20.) + + # all-ones array was bypassing bug (ticket #10930) + p = np.ones((1, 5)) / 2 + q = np.ones((5, 5)) / 2 + for optimize in (True, False): + assert_array_equal(np.einsum("...ij,...jk->...ik", p, p, + optimize=optimize), + np.einsum("...ij,...jk->...ik", p, q, + optimize=optimize)) + assert_array_equal(np.einsum("...ij,...jk->...ik", p, q, + optimize=optimize), + np.full((1, 5), 1.25)) + + # Cases which were failing (gh-10899) + x = np.eye(2, dtype=dtype) + y = np.ones(2, dtype=dtype) + assert_array_equal(np.einsum("ji,i->", x, y, optimize=optimize), + [2.]) # contig_contig_outstride0_two + assert_array_equal(np.einsum("i,ij->", y, x, optimize=optimize), + [2.]) # stride0_contig_outstride0_two + assert_array_equal(np.einsum("ij,i->", x, y, optimize=optimize), + [2.]) # contig_stride0_outstride0_two + + def test_einsum_sums_int8(self): + if ( + (sys.platform == 'darwin' and platform.machine() == 'x86_64') + or + USING_CLANG_CL + ): + pytest.xfail('Fails on macOS x86-64 and when using clang-cl ' + 'with Meson, see gh-23838') + self.check_einsum_sums('i1') + + def test_einsum_sums_uint8(self): + if ( + (sys.platform == 'darwin' and platform.machine() == 'x86_64') + or + USING_CLANG_CL + ): + pytest.xfail('Fails on macOS x86-64 and when using clang-cl ' + 'with Meson, see gh-23838') + self.check_einsum_sums('u1') + + def test_einsum_sums_int16(self): + self.check_einsum_sums('i2') + + def test_einsum_sums_uint16(self): + self.check_einsum_sums('u2') + + def test_einsum_sums_int32(self): + self.check_einsum_sums('i4') + self.check_einsum_sums('i4', True) + + def test_einsum_sums_uint32(self): + self.check_einsum_sums('u4') + self.check_einsum_sums('u4', True) + + def test_einsum_sums_int64(self): + self.check_einsum_sums('i8') + + def test_einsum_sums_uint64(self): + self.check_einsum_sums('u8') + + def test_einsum_sums_float16(self): + self.check_einsum_sums('f2') + + def test_einsum_sums_float32(self): + self.check_einsum_sums('f4') + + def test_einsum_sums_float64(self): + self.check_einsum_sums('f8') + self.check_einsum_sums('f8', True) + + def test_einsum_sums_longdouble(self): + self.check_einsum_sums(np.longdouble) + + def test_einsum_sums_cfloat64(self): + self.check_einsum_sums('c8') + self.check_einsum_sums('c8', True) + + def test_einsum_sums_cfloat128(self): + self.check_einsum_sums('c16') + + def test_einsum_sums_clongdouble(self): + self.check_einsum_sums(np.clongdouble) + + def test_einsum_sums_object(self): + self.check_einsum_sums('object') + self.check_einsum_sums('object', True) + + def test_einsum_misc(self): + # This call used to crash because of a bug in + # PyArray_AssignZero + a = np.ones((1, 2)) + b = np.ones((2, 2, 1)) + assert_equal(np.einsum('ij...,j...->i...', a, b), [[[2], [2]]]) + assert_equal(np.einsum('ij...,j...->i...', a, b, optimize=True), [[[2], [2]]]) + + # Regression test for issue #10369 (test unicode inputs with Python 2) + assert_equal(np.einsum('ij...,j...->i...', a, b), [[[2], [2]]]) + assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4]), 20) + assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4], + optimize='greedy'), 20) + + # The iterator had an issue with buffering this reduction + a = np.ones((5, 12, 4, 2, 3), np.int64) + b = np.ones((5, 12, 11), np.int64) + assert_equal(np.einsum('ijklm,ijn,ijn->', a, b, b), + np.einsum('ijklm,ijn->', a, b)) + assert_equal(np.einsum('ijklm,ijn,ijn->', a, b, b, optimize=True), + np.einsum('ijklm,ijn->', a, b, optimize=True)) + + # Issue #2027, was a problem in the contiguous 3-argument + # inner loop implementation + a = np.arange(1, 3) + b = np.arange(1, 5).reshape(2, 2) + c = np.arange(1, 9).reshape(4, 2) + assert_equal(np.einsum('x,yx,zx->xzy', a, b, c), + [[[1, 3], [3, 9], [5, 15], [7, 21]], + [[8, 16], [16, 32], [24, 48], [32, 64]]]) + assert_equal(np.einsum('x,yx,zx->xzy', a, b, c, optimize=True), + [[[1, 3], [3, 9], [5, 15], [7, 21]], + [[8, 16], [16, 32], [24, 48], [32, 64]]]) + + # Ensure explicitly setting out=None does not cause an error + # see issue gh-15776 and issue gh-15256 + assert_equal(np.einsum('i,j', [1], [2], out=None), [[2]]) + + def test_object_loop(self): + + class Mult: + def __mul__(self, other): + return 42 + + objMult = np.array([Mult()]) + objNULL = np.ndarray(buffer = b'\0' * np.intp(0).itemsize, shape=1, dtype=object) + + with pytest.raises(TypeError): + np.einsum("i,j", [1], objNULL) + with pytest.raises(TypeError): + np.einsum("i,j", objNULL, [1]) + assert np.einsum("i,j", objMult, objMult) == 42 + + def test_subscript_range(self): + # Issue #7741, make sure that all letters of Latin alphabet (both uppercase & lowercase) can be used + # when creating a subscript from arrays + a = np.ones((2, 3)) + b = np.ones((3, 4)) + np.einsum(a, [0, 20], b, [20, 2], [0, 2], optimize=False) + np.einsum(a, [0, 27], b, [27, 2], [0, 2], optimize=False) + np.einsum(a, [0, 51], b, [51, 2], [0, 2], optimize=False) + assert_raises(ValueError, lambda: np.einsum(a, [0, 52], b, [52, 2], [0, 2], optimize=False)) + assert_raises(ValueError, lambda: np.einsum(a, [-1, 5], b, [5, 2], [-1, 2], optimize=False)) + + def test_einsum_broadcast(self): + # Issue #2455 change in handling ellipsis + # remove the 'middle broadcast' error + # only use the 'RIGHT' iteration in prepare_op_axes + # adds auto broadcast on left where it belongs + # broadcast on right has to be explicit + # We need to test the optimized parsing as well + + A = np.arange(2 * 3 * 4).reshape(2, 3, 4) + B = np.arange(3) + ref = np.einsum('ijk,j->ijk', A, B, optimize=False) + for opt in [True, False]: + assert_equal(np.einsum('ij...,j...->ij...', A, B, optimize=opt), ref) + assert_equal(np.einsum('ij...,...j->ij...', A, B, optimize=opt), ref) + assert_equal(np.einsum('ij...,j->ij...', A, B, optimize=opt), ref) # used to raise error + + A = np.arange(12).reshape((4, 3)) + B = np.arange(6).reshape((3, 2)) + ref = np.einsum('ik,kj->ij', A, B, optimize=False) + for opt in [True, False]: + assert_equal(np.einsum('ik...,k...->i...', A, B, optimize=opt), ref) + assert_equal(np.einsum('ik...,...kj->i...j', A, B, optimize=opt), ref) + assert_equal(np.einsum('...k,kj', A, B, optimize=opt), ref) # used to raise error + assert_equal(np.einsum('ik,k...->i...', A, B, optimize=opt), ref) # used to raise error + + dims = [2, 3, 4, 5] + a = np.arange(np.prod(dims)).reshape(dims) + v = np.arange(dims[2]) + ref = np.einsum('ijkl,k->ijl', a, v, optimize=False) + for opt in [True, False]: + assert_equal(np.einsum('ijkl,k', a, v, optimize=opt), ref) + assert_equal(np.einsum('...kl,k', a, v, optimize=opt), ref) # used to raise error + assert_equal(np.einsum('...kl,k...', a, v, optimize=opt), ref) + + J, K, M = 160, 160, 120 + A = np.arange(J * K * M).reshape(1, 1, 1, J, K, M) + B = np.arange(J * K * M * 3).reshape(J, K, M, 3) + ref = np.einsum('...lmn,...lmno->...o', A, B, optimize=False) + for opt in [True, False]: + assert_equal(np.einsum('...lmn,lmno->...o', A, B, + optimize=opt), ref) # used to raise error + + def test_einsum_fixedstridebug(self): + # Issue #4485 obscure einsum bug + # This case revealed a bug in nditer where it reported a stride + # as 'fixed' (0) when it was in fact not fixed during processing + # (0 or 4). The reason for the bug was that the check for a fixed + # stride was using the information from the 2D inner loop reuse + # to restrict the iteration dimensions it had to validate to be + # the same, but that 2D inner loop reuse logic is only triggered + # during the buffer copying step, and hence it was invalid to + # rely on those values. The fix is to check all the dimensions + # of the stride in question, which in the test case reveals that + # the stride is not fixed. + # + # NOTE: This test is triggered by the fact that the default buffersize, + # used by einsum, is 8192, and 3*2731 = 8193, is larger than that + # and results in a mismatch between the buffering and the + # striding for operand A. + A = np.arange(2 * 3).reshape(2, 3).astype(np.float32) + B = np.arange(2 * 3 * 2731).reshape(2, 3, 2731).astype(np.int16) + es = np.einsum('cl, cpx->lpx', A, B) + tp = np.tensordot(A, B, axes=(0, 0)) + assert_equal(es, tp) + # The following is the original test case from the bug report, + # made repeatable by changing random arrays to aranges. + A = np.arange(3 * 3).reshape(3, 3).astype(np.float64) + B = np.arange(3 * 3 * 64 * 64).reshape(3, 3, 64, 64).astype(np.float32) + es = np.einsum('cl, cpxy->lpxy', A, B) + tp = np.tensordot(A, B, axes=(0, 0)) + assert_equal(es, tp) + + def test_einsum_fixed_collapsingbug(self): + # Issue #5147. + # The bug only occurred when output argument of einssum was used. + x = np.random.normal(0, 1, (5, 5, 5, 5)) + y1 = np.zeros((5, 5)) + np.einsum('aabb->ab', x, out=y1) + idx = np.arange(5) + y2 = x[idx[:, None], idx[:, None], idx, idx] + assert_equal(y1, y2) + + def test_einsum_failed_on_p9_and_s390x(self): + # Issues gh-14692 and gh-12689 + # Bug with signed vs unsigned char errored on power9 and s390x Linux + tensor = np.random.random_sample((10, 10, 10, 10)) + x = np.einsum('ijij->', tensor) + y = tensor.trace(axis1=0, axis2=2).trace() + assert_allclose(x, y) + + def test_einsum_all_contig_non_contig_output(self): + # Issue gh-5907, tests that the all contiguous special case + # actually checks the contiguity of the output + x = np.ones((5, 5)) + out = np.ones(10)[::2] + correct_base = np.ones(10) + correct_base[::2] = 5 + # Always worked (inner iteration is done with 0-stride): + np.einsum('mi,mi,mi->m', x, x, x, out=out) + assert_array_equal(out.base, correct_base) + # Example 1: + out = np.ones(10)[::2] + np.einsum('im,im,im->m', x, x, x, out=out) + assert_array_equal(out.base, correct_base) + # Example 2, buffering causes x to be contiguous but + # special cases do not catch the operation before: + out = np.ones((2, 2, 2))[..., 0] + correct_base = np.ones((2, 2, 2)) + correct_base[..., 0] = 2 + x = np.ones((2, 2), np.float32) + np.einsum('ij,jk->ik', x, x, out=out) + assert_array_equal(out.base, correct_base) + + @pytest.mark.parametrize("dtype", + np.typecodes["AllFloat"] + np.typecodes["AllInteger"]) + def test_different_paths(self, dtype): + # Test originally added to cover broken float16 path: gh-20305 + # Likely most are covered elsewhere, at least partially. + dtype = np.dtype(dtype) + # Simple test, designed to exercise most specialized code paths, + # note the +0.5 for floats. This makes sure we use a float value + # where the results must be exact. + arr = (np.arange(7) + 0.5).astype(dtype) + scalar = np.array(2, dtype=dtype) + + # contig -> scalar: + res = np.einsum('i->', arr) + assert res == arr.sum() + # contig, contig -> contig: + res = np.einsum('i,i->i', arr, arr) + assert_array_equal(res, arr * arr) + # noncontig, noncontig -> contig: + res = np.einsum('i,i->i', arr.repeat(2)[::2], arr.repeat(2)[::2]) + assert_array_equal(res, arr * arr) + # contig + contig -> scalar + assert np.einsum('i,i->', arr, arr) == (arr * arr).sum() + # contig + scalar -> contig (with out) + out = np.ones(7, dtype=dtype) + res = np.einsum('i,->i', arr, dtype.type(2), out=out) + assert_array_equal(res, arr * dtype.type(2)) + # scalar + contig -> contig (with out) + res = np.einsum(',i->i', scalar, arr) + assert_array_equal(res, arr * dtype.type(2)) + # scalar + contig -> scalar + res = np.einsum(',i->', scalar, arr) + # Use einsum to compare to not have difference due to sum round-offs: + assert res == np.einsum('i->', scalar * arr) + # contig + scalar -> scalar + res = np.einsum('i,->', arr, scalar) + # Use einsum to compare to not have difference due to sum round-offs: + assert res == np.einsum('i->', scalar * arr) + # contig + contig + contig -> scalar + arr = np.array([0.5, 0.5, 0.25, 4.5, 3.], dtype=dtype) + res = np.einsum('i,i,i->', arr, arr, arr) + assert_array_equal(res, (arr * arr * arr).sum()) + # four arrays: + res = np.einsum('i,i,i,i->', arr, arr, arr, arr) + assert_array_equal(res, (arr * arr * arr * arr).sum()) + + def test_small_boolean_arrays(self): + # See gh-5946. + # Use array of True embedded in False. + a = np.zeros((16, 1, 1), dtype=np.bool_)[:2] + a[...] = True + out = np.zeros((16, 1, 1), dtype=np.bool_)[:2] + tgt = np.ones((2, 1, 1), dtype=np.bool_) + res = np.einsum('...ij,...jk->...ik', a, a, out=out) + assert_equal(res, tgt) + + def test_out_is_res(self): + a = np.arange(9).reshape(3, 3) + res = np.einsum('...ij,...jk->...ik', a, a, out=a) + assert res is a + + def optimize_compare(self, subscripts, operands=None): + # Tests all paths of the optimization function against + # conventional einsum + if operands is None: + args = [subscripts] + terms = subscripts.split('->')[0].split(',') + for term in terms: + dims = [global_size_dict[x] for x in term] + args.append(np.random.rand(*dims)) + else: + args = [subscripts] + operands + + noopt = np.einsum(*args, optimize=False) + opt = np.einsum(*args, optimize='greedy') + assert_almost_equal(opt, noopt) + opt = np.einsum(*args, optimize='optimal') + assert_almost_equal(opt, noopt) + + def test_hadamard_like_products(self): + # Hadamard outer products + self.optimize_compare('a,ab,abc->abc') + self.optimize_compare('a,b,ab->ab') + + def test_index_transformations(self): + # Simple index transformation cases + self.optimize_compare('ea,fb,gc,hd,abcd->efgh') + self.optimize_compare('ea,fb,abcd,gc,hd->efgh') + self.optimize_compare('abcd,ea,fb,gc,hd->efgh') + + def test_complex(self): + # Long test cases + self.optimize_compare('acdf,jbje,gihb,hfac,gfac,gifabc,hfac') + self.optimize_compare('acdf,jbje,gihb,hfac,gfac,gifabc,hfac') + self.optimize_compare('cd,bdhe,aidb,hgca,gc,hgibcd,hgac') + self.optimize_compare('abhe,hidj,jgba,hiab,gab') + self.optimize_compare('bde,cdh,agdb,hica,ibd,hgicd,hiac') + self.optimize_compare('chd,bde,agbc,hiad,hgc,hgi,hiad') + self.optimize_compare('chd,bde,agbc,hiad,bdi,cgh,agdb') + self.optimize_compare('bdhe,acad,hiab,agac,hibd') + + def test_collapse(self): + # Inner products + self.optimize_compare('ab,ab,c->') + self.optimize_compare('ab,ab,c->c') + self.optimize_compare('ab,ab,cd,cd->') + self.optimize_compare('ab,ab,cd,cd->ac') + self.optimize_compare('ab,ab,cd,cd->cd') + self.optimize_compare('ab,ab,cd,cd,ef,ef->') + + def test_expand(self): + # Outer products + self.optimize_compare('ab,cd,ef->abcdef') + self.optimize_compare('ab,cd,ef->acdf') + self.optimize_compare('ab,cd,de->abcde') + self.optimize_compare('ab,cd,de->be') + self.optimize_compare('ab,bcd,cd->abcd') + self.optimize_compare('ab,bcd,cd->abd') + + def test_edge_cases(self): + # Difficult edge cases for optimization + self.optimize_compare('eb,cb,fb->cef') + self.optimize_compare('dd,fb,be,cdb->cef') + self.optimize_compare('bca,cdb,dbf,afc->') + self.optimize_compare('dcc,fce,ea,dbf->ab') + self.optimize_compare('fdf,cdd,ccd,afe->ae') + self.optimize_compare('abcd,ad') + self.optimize_compare('ed,fcd,ff,bcf->be') + self.optimize_compare('baa,dcf,af,cde->be') + self.optimize_compare('bd,db,eac->ace') + self.optimize_compare('fff,fae,bef,def->abd') + self.optimize_compare('efc,dbc,acf,fd->abe') + self.optimize_compare('ba,ac,da->bcd') + + def test_inner_product(self): + # Inner products + self.optimize_compare('ab,ab') + self.optimize_compare('ab,ba') + self.optimize_compare('abc,abc') + self.optimize_compare('abc,bac') + self.optimize_compare('abc,cba') + + def test_random_cases(self): + # Randomly built test cases + self.optimize_compare('aab,fa,df,ecc->bde') + self.optimize_compare('ecb,fef,bad,ed->ac') + self.optimize_compare('bcf,bbb,fbf,fc->') + self.optimize_compare('bb,ff,be->e') + self.optimize_compare('bcb,bb,fc,fff->') + self.optimize_compare('fbb,dfd,fc,fc->') + self.optimize_compare('afd,ba,cc,dc->bf') + self.optimize_compare('adb,bc,fa,cfc->d') + self.optimize_compare('bbd,bda,fc,db->acf') + self.optimize_compare('dba,ead,cad->bce') + self.optimize_compare('aef,fbc,dca->bde') + + def test_combined_views_mapping(self): + # gh-10792 + a = np.arange(9).reshape(1, 1, 3, 1, 3) + b = np.einsum('bbcdc->d', a) + assert_equal(b, [12]) + + def test_broadcasting_dot_cases(self): + # Ensures broadcasting cases are not mistaken for GEMM + + a = np.random.rand(1, 5, 4) + b = np.random.rand(4, 6) + c = np.random.rand(5, 6) + d = np.random.rand(10) + + self.optimize_compare('ijk,kl,jl', operands=[a, b, c]) + self.optimize_compare('ijk,kl,jl,i->i', operands=[a, b, c, d]) + + e = np.random.rand(1, 1, 5, 4) + f = np.random.rand(7, 7) + self.optimize_compare('abjk,kl,jl', operands=[e, b, c]) + self.optimize_compare('abjk,kl,jl,ab->ab', operands=[e, b, c, f]) + + # Edge case found in gh-11308 + g = np.arange(64).reshape(2, 4, 8) + self.optimize_compare('obk,ijk->ioj', operands=[g, g]) + + def test_output_order(self): + # Ensure output order is respected for optimize cases, the below + # conraction should yield a reshaped tensor view + # gh-16415 + + a = np.ones((2, 3, 5), order='F') + b = np.ones((4, 3), order='F') + + for opt in [True, False]: + tmp = np.einsum('...ft,mf->...mt', a, b, order='a', optimize=opt) + assert_(tmp.flags.f_contiguous) + + tmp = np.einsum('...ft,mf->...mt', a, b, order='f', optimize=opt) + assert_(tmp.flags.f_contiguous) + + tmp = np.einsum('...ft,mf->...mt', a, b, order='c', optimize=opt) + assert_(tmp.flags.c_contiguous) + + tmp = np.einsum('...ft,mf->...mt', a, b, order='k', optimize=opt) + assert_(tmp.flags.c_contiguous is False) + assert_(tmp.flags.f_contiguous is False) + + tmp = np.einsum('...ft,mf->...mt', a, b, optimize=opt) + assert_(tmp.flags.c_contiguous is False) + assert_(tmp.flags.f_contiguous is False) + + c = np.ones((4, 3), order='C') + for opt in [True, False]: + tmp = np.einsum('...ft,mf->...mt', a, c, order='a', optimize=opt) + assert_(tmp.flags.c_contiguous) + + d = np.ones((2, 3, 5), order='C') + for opt in [True, False]: + tmp = np.einsum('...ft,mf->...mt', d, c, order='a', optimize=opt) + assert_(tmp.flags.c_contiguous) + +class TestEinsumPath: + def build_operands(self, string, size_dict=global_size_dict): + + # Builds views based off initial operands + operands = [string] + terms = string.split('->')[0].split(',') + for term in terms: + dims = [size_dict[x] for x in term] + operands.append(np.random.rand(*dims)) + + return operands + + def assert_path_equal(self, comp, benchmark): + # Checks if list of tuples are equivalent + ret = (len(comp) == len(benchmark)) + assert_(ret) + for pos in range(len(comp) - 1): + ret &= isinstance(comp[pos + 1], tuple) + ret &= (comp[pos + 1] == benchmark[pos + 1]) + assert_(ret) + + def test_memory_contraints(self): + # Ensure memory constraints are satisfied + + outer_test = self.build_operands('a,b,c->abc') + + path, path_str = np.einsum_path(*outer_test, optimize=('greedy', 0)) + self.assert_path_equal(path, ['einsum_path', (0, 1, 2)]) + + path, path_str = np.einsum_path(*outer_test, optimize=('optimal', 0)) + self.assert_path_equal(path, ['einsum_path', (0, 1, 2)]) + + long_test = self.build_operands('acdf,jbje,gihb,hfac') + path, path_str = np.einsum_path(*long_test, optimize=('greedy', 0)) + self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)]) + + path, path_str = np.einsum_path(*long_test, optimize=('optimal', 0)) + self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)]) + + def test_long_paths(self): + # Long complex cases + + # Long test 1 + long_test1 = self.build_operands('acdf,jbje,gihb,hfac,gfac,gifabc,hfac') + path, path_str = np.einsum_path(*long_test1, optimize='greedy') + self.assert_path_equal(path, ['einsum_path', + (3, 6), (3, 4), (2, 4), (2, 3), (0, 2), (0, 1)]) + + path, path_str = np.einsum_path(*long_test1, optimize='optimal') + self.assert_path_equal(path, ['einsum_path', + (3, 6), (3, 4), (2, 4), (2, 3), (0, 2), (0, 1)]) + + # Long test 2 + long_test2 = self.build_operands('chd,bde,agbc,hiad,bdi,cgh,agdb') + path, path_str = np.einsum_path(*long_test2, optimize='greedy') + self.assert_path_equal(path, ['einsum_path', + (3, 4), (0, 3), (3, 4), (1, 3), (1, 2), (0, 1)]) + + path, path_str = np.einsum_path(*long_test2, optimize='optimal') + self.assert_path_equal(path, ['einsum_path', + (0, 5), (1, 4), (3, 4), (1, 3), (1, 2), (0, 1)]) + + def test_edge_paths(self): + # Difficult edge cases + + # Edge test1 + edge_test1 = self.build_operands('eb,cb,fb->cef') + path, path_str = np.einsum_path(*edge_test1, optimize='greedy') + self.assert_path_equal(path, ['einsum_path', (0, 2), (0, 1)]) + + path, path_str = np.einsum_path(*edge_test1, optimize='optimal') + self.assert_path_equal(path, ['einsum_path', (0, 2), (0, 1)]) + + # Edge test2 + edge_test2 = self.build_operands('dd,fb,be,cdb->cef') + path, path_str = np.einsum_path(*edge_test2, optimize='greedy') + self.assert_path_equal(path, ['einsum_path', (0, 3), (0, 1), (0, 1)]) + + path, path_str = np.einsum_path(*edge_test2, optimize='optimal') + self.assert_path_equal(path, ['einsum_path', (0, 3), (0, 1), (0, 1)]) + + # Edge test3 + edge_test3 = self.build_operands('bca,cdb,dbf,afc->') + path, path_str = np.einsum_path(*edge_test3, optimize='greedy') + self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)]) + + path, path_str = np.einsum_path(*edge_test3, optimize='optimal') + self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)]) + + # Edge test4 + edge_test4 = self.build_operands('dcc,fce,ea,dbf->ab') + path, path_str = np.einsum_path(*edge_test4, optimize='greedy') + self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 1), (0, 1)]) + + path, path_str = np.einsum_path(*edge_test4, optimize='optimal') + self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)]) + + # Edge test5 + edge_test4 = self.build_operands('a,ac,ab,ad,cd,bd,bc->', + size_dict={"a": 20, "b": 20, "c": 20, "d": 20}) + path, path_str = np.einsum_path(*edge_test4, optimize='greedy') + self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)]) + + path, path_str = np.einsum_path(*edge_test4, optimize='optimal') + self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)]) + + def test_path_type_input(self): + # Test explicit path handling + path_test = self.build_operands('dcc,fce,ea,dbf->ab') + + path, path_str = np.einsum_path(*path_test, optimize=False) + self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)]) + + path, path_str = np.einsum_path(*path_test, optimize=True) + self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 1), (0, 1)]) + + exp_path = ['einsum_path', (0, 2), (0, 2), (0, 1)] + path, path_str = np.einsum_path(*path_test, optimize=exp_path) + self.assert_path_equal(path, exp_path) + + # Double check einsum works on the input path + noopt = np.einsum(*path_test, optimize=False) + opt = np.einsum(*path_test, optimize=exp_path) + assert_almost_equal(noopt, opt) + + def test_path_type_input_internal_trace(self): + #gh-20962 + path_test = self.build_operands('cab,cdd->ab') + exp_path = ['einsum_path', (1,), (0, 1)] + + path, path_str = np.einsum_path(*path_test, optimize=exp_path) + self.assert_path_equal(path, exp_path) + + # Double check einsum works on the input path + noopt = np.einsum(*path_test, optimize=False) + opt = np.einsum(*path_test, optimize=exp_path) + assert_almost_equal(noopt, opt) + + def test_path_type_input_invalid(self): + path_test = self.build_operands('ab,bc,cd,de->ae') + exp_path = ['einsum_path', (2, 3), (0, 1)] + assert_raises(RuntimeError, np.einsum, *path_test, optimize=exp_path) + assert_raises( + RuntimeError, np.einsum_path, *path_test, optimize=exp_path) + + path_test = self.build_operands('a,a,a->a') + exp_path = ['einsum_path', (1,), (0, 1)] + assert_raises(RuntimeError, np.einsum, *path_test, optimize=exp_path) + assert_raises( + RuntimeError, np.einsum_path, *path_test, optimize=exp_path) + + def test_spaces(self): + #gh-10794 + arr = np.array([[1]]) + for sp in itertools.product(['', ' '], repeat=4): + # no error for any spacing + np.einsum('{}...a{}->{}...a{}'.format(*sp), arr) + +def test_overlap(): + a = np.arange(9, dtype=int).reshape(3, 3) + b = np.arange(9, dtype=int).reshape(3, 3) + d = np.dot(a, b) + # sanity check + c = np.einsum('ij,jk->ik', a, b) + assert_equal(c, d) + #gh-10080, out overlaps one of the operands + c = np.einsum('ij,jk->ik', a, b, out=b) + assert_equal(c, d) diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_longdouble.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_longdouble.py new file mode 100644 index 0000000000000000000000000000000000000000..45721950c0f19685d9c1075f95f7f126a43831aa --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_longdouble.py @@ -0,0 +1,395 @@ +import warnings +import platform +import pytest + +import numpy as np +from numpy.testing import ( + assert_, assert_equal, assert_raises, assert_warns, assert_array_equal, + temppath, IS_MUSL + ) +from numpy.core.tests._locales import CommaDecimalPointLocale + + +LD_INFO = np.finfo(np.longdouble) +longdouble_longer_than_double = (LD_INFO.eps < np.finfo(np.double).eps) + + +_o = 1 + LD_INFO.eps +string_to_longdouble_inaccurate = (_o != np.longdouble(repr(_o))) +del _o + + +def test_scalar_extraction(): + """Confirm that extracting a value doesn't convert to python float""" + o = 1 + LD_INFO.eps + a = np.array([o, o, o]) + assert_equal(a[1], o) + + +# Conversions string -> long double + +# 0.1 not exactly representable in base 2 floating point. +repr_precision = len(repr(np.longdouble(0.1))) +# +2 from macro block starting around line 842 in scalartypes.c.src. + + +@pytest.mark.skipif(IS_MUSL, + reason="test flaky on musllinux") +@pytest.mark.skipif(LD_INFO.precision + 2 >= repr_precision, + reason="repr precision not enough to show eps") +def test_repr_roundtrip(): + # We will only see eps in repr if within printing precision. + o = 1 + LD_INFO.eps + assert_equal(np.longdouble(repr(o)), o, "repr was %s" % repr(o)) + + +@pytest.mark.skipif(string_to_longdouble_inaccurate, reason="Need strtold_l") +def test_repr_roundtrip_bytes(): + o = 1 + LD_INFO.eps + assert_equal(np.longdouble(repr(o).encode("ascii")), o) + + +@pytest.mark.skipif(string_to_longdouble_inaccurate, reason="Need strtold_l") +@pytest.mark.parametrize("strtype", (np.str_, np.bytes_, str, bytes)) +def test_array_and_stringlike_roundtrip(strtype): + """ + Test that string representations of long-double roundtrip both + for array casting and scalar coercion, see also gh-15608. + """ + o = 1 + LD_INFO.eps + + if strtype in (np.bytes_, bytes): + o_str = strtype(repr(o).encode("ascii")) + else: + o_str = strtype(repr(o)) + + # Test that `o` is correctly coerced from the string-like + assert o == np.longdouble(o_str) + + # Test that arrays also roundtrip correctly: + o_strarr = np.asarray([o] * 3, dtype=strtype) + assert (o == o_strarr.astype(np.longdouble)).all() + + # And array coercion and casting to string give the same as scalar repr: + assert (o_strarr == o_str).all() + assert (np.asarray([o] * 3).astype(strtype) == o_str).all() + + +def test_bogus_string(): + assert_raises(ValueError, np.longdouble, "spam") + assert_raises(ValueError, np.longdouble, "1.0 flub") + + +@pytest.mark.skipif(string_to_longdouble_inaccurate, reason="Need strtold_l") +def test_fromstring(): + o = 1 + LD_INFO.eps + s = (" " + repr(o))*5 + a = np.array([o]*5) + assert_equal(np.fromstring(s, sep=" ", dtype=np.longdouble), a, + err_msg="reading '%s'" % s) + + +def test_fromstring_complex(): + for ctype in ["complex", "cdouble", "cfloat"]: + # Check spacing between separator + assert_equal(np.fromstring("1, 2 , 3 ,4", sep=",", dtype=ctype), + np.array([1., 2., 3., 4.])) + # Real component not specified + assert_equal(np.fromstring("1j, -2j, 3j, 4e1j", sep=",", dtype=ctype), + np.array([1.j, -2.j, 3.j, 40.j])) + # Both components specified + assert_equal(np.fromstring("1+1j,2-2j, -3+3j, -4e1+4j", sep=",", dtype=ctype), + np.array([1. + 1.j, 2. - 2.j, - 3. + 3.j, - 40. + 4j])) + # Spaces at wrong places + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1+2 j,3", dtype=ctype, sep=","), + np.array([1.])) + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1+ 2j,3", dtype=ctype, sep=","), + np.array([1.])) + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1 +2j,3", dtype=ctype, sep=","), + np.array([1.])) + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1+j", dtype=ctype, sep=","), + np.array([1.])) + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1+", dtype=ctype, sep=","), + np.array([1.])) + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1j+1", dtype=ctype, sep=","), + np.array([1j])) + + +def test_fromstring_bogus(): + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1. 2. 3. flop 4.", dtype=float, sep=" "), + np.array([1., 2., 3.])) + + +def test_fromstring_empty(): + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("xxxxx", sep="x"), + np.array([])) + + +def test_fromstring_missing(): + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1xx3x4x5x6", sep="x"), + np.array([1])) + + +class TestFileBased: + + ldbl = 1 + LD_INFO.eps + tgt = np.array([ldbl]*5) + out = ''.join([repr(t) + '\n' for t in tgt]) + + def test_fromfile_bogus(self): + with temppath() as path: + with open(path, 'w') as f: + f.write("1. 2. 3. flop 4.\n") + + with assert_warns(DeprecationWarning): + res = np.fromfile(path, dtype=float, sep=" ") + assert_equal(res, np.array([1., 2., 3.])) + + def test_fromfile_complex(self): + for ctype in ["complex", "cdouble", "cfloat"]: + # Check spacing between separator and only real component specified + with temppath() as path: + with open(path, 'w') as f: + f.write("1, 2 , 3 ,4\n") + + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1., 2., 3., 4.])) + + # Real component not specified + with temppath() as path: + with open(path, 'w') as f: + f.write("1j, -2j, 3j, 4e1j\n") + + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1.j, -2.j, 3.j, 40.j])) + + # Both components specified + with temppath() as path: + with open(path, 'w') as f: + f.write("1+1j,2-2j, -3+3j, -4e1+4j\n") + + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1. + 1.j, 2. - 2.j, - 3. + 3.j, - 40. + 4j])) + + # Spaces at wrong places + with temppath() as path: + with open(path, 'w') as f: + f.write("1+2 j,3\n") + + with assert_warns(DeprecationWarning): + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1.])) + + # Spaces at wrong places + with temppath() as path: + with open(path, 'w') as f: + f.write("1+ 2j,3\n") + + with assert_warns(DeprecationWarning): + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1.])) + + # Spaces at wrong places + with temppath() as path: + with open(path, 'w') as f: + f.write("1 +2j,3\n") + + with assert_warns(DeprecationWarning): + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1.])) + + # Spaces at wrong places + with temppath() as path: + with open(path, 'w') as f: + f.write("1+j\n") + + with assert_warns(DeprecationWarning): + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1.])) + + # Spaces at wrong places + with temppath() as path: + with open(path, 'w') as f: + f.write("1+\n") + + with assert_warns(DeprecationWarning): + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1.])) + + # Spaces at wrong places + with temppath() as path: + with open(path, 'w') as f: + f.write("1j+1\n") + + with assert_warns(DeprecationWarning): + res = np.fromfile(path, dtype=ctype, sep=",") + assert_equal(res, np.array([1.j])) + + + + @pytest.mark.skipif(string_to_longdouble_inaccurate, + reason="Need strtold_l") + def test_fromfile(self): + with temppath() as path: + with open(path, 'w') as f: + f.write(self.out) + res = np.fromfile(path, dtype=np.longdouble, sep="\n") + assert_equal(res, self.tgt) + + @pytest.mark.skipif(string_to_longdouble_inaccurate, + reason="Need strtold_l") + def test_genfromtxt(self): + with temppath() as path: + with open(path, 'w') as f: + f.write(self.out) + res = np.genfromtxt(path, dtype=np.longdouble) + assert_equal(res, self.tgt) + + @pytest.mark.skipif(string_to_longdouble_inaccurate, + reason="Need strtold_l") + def test_loadtxt(self): + with temppath() as path: + with open(path, 'w') as f: + f.write(self.out) + res = np.loadtxt(path, dtype=np.longdouble) + assert_equal(res, self.tgt) + + @pytest.mark.skipif(string_to_longdouble_inaccurate, + reason="Need strtold_l") + def test_tofile_roundtrip(self): + with temppath() as path: + self.tgt.tofile(path, sep=" ") + res = np.fromfile(path, dtype=np.longdouble, sep=" ") + assert_equal(res, self.tgt) + + +# Conversions long double -> string + + +def test_repr_exact(): + o = 1 + LD_INFO.eps + assert_(repr(o) != '1') + + +@pytest.mark.skipif(longdouble_longer_than_double, reason="BUG #2376") +@pytest.mark.skipif(string_to_longdouble_inaccurate, + reason="Need strtold_l") +def test_format(): + o = 1 + LD_INFO.eps + assert_("{0:.40g}".format(o) != '1') + + +@pytest.mark.skipif(longdouble_longer_than_double, reason="BUG #2376") +@pytest.mark.skipif(string_to_longdouble_inaccurate, + reason="Need strtold_l") +def test_percent(): + o = 1 + LD_INFO.eps + assert_("%.40g" % o != '1') + + +@pytest.mark.skipif(longdouble_longer_than_double, + reason="array repr problem") +@pytest.mark.skipif(string_to_longdouble_inaccurate, + reason="Need strtold_l") +def test_array_repr(): + o = 1 + LD_INFO.eps + a = np.array([o]) + b = np.array([1], dtype=np.longdouble) + if not np.all(a != b): + raise ValueError("precision loss creating arrays") + assert_(repr(a) != repr(b)) + +# +# Locale tests: scalar types formatting should be independent of the locale +# + +class TestCommaDecimalPointLocale(CommaDecimalPointLocale): + + def test_repr_roundtrip_foreign(self): + o = 1.5 + assert_equal(o, np.longdouble(repr(o))) + + def test_fromstring_foreign_repr(self): + f = 1.234 + a = np.fromstring(repr(f), dtype=float, sep=" ") + assert_equal(a[0], f) + + def test_fromstring_best_effort_float(self): + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1,234", dtype=float, sep=" "), + np.array([1.])) + + def test_fromstring_best_effort(self): + with assert_warns(DeprecationWarning): + assert_equal(np.fromstring("1,234", dtype=np.longdouble, sep=" "), + np.array([1.])) + + def test_fromstring_foreign(self): + s = "1.234" + a = np.fromstring(s, dtype=np.longdouble, sep=" ") + assert_equal(a[0], np.longdouble(s)) + + def test_fromstring_foreign_sep(self): + a = np.array([1, 2, 3, 4]) + b = np.fromstring("1,2,3,4,", dtype=np.longdouble, sep=",") + assert_array_equal(a, b) + + def test_fromstring_foreign_value(self): + with assert_warns(DeprecationWarning): + b = np.fromstring("1,234", dtype=np.longdouble, sep=" ") + assert_array_equal(b[0], 1) + + +@pytest.mark.parametrize("int_val", [ + # cases discussed in gh-10723 + # and gh-9968 + 2 ** 1024, 0]) +def test_longdouble_from_int(int_val): + # for issue gh-9968 + str_val = str(int_val) + # we'll expect a RuntimeWarning on platforms + # with np.longdouble equivalent to np.double + # for large integer input + with warnings.catch_warnings(record=True) as w: + warnings.filterwarnings('always', '', RuntimeWarning) + # can be inf==inf on some platforms + assert np.longdouble(int_val) == np.longdouble(str_val) + # we can't directly compare the int and + # max longdouble value on all platforms + if np.allclose(np.finfo(np.longdouble).max, + np.finfo(np.double).max) and w: + assert w[0].category is RuntimeWarning + +@pytest.mark.parametrize("bool_val", [ + True, False]) +def test_longdouble_from_bool(bool_val): + assert np.longdouble(bool_val) == np.longdouble(int(bool_val)) + + +@pytest.mark.skipif( + not (IS_MUSL and platform.machine() == "x86_64"), + reason="only need to run on musllinux_x86_64" +) +def test_musllinux_x86_64_signature(): + # this test may fail if you're emulating musllinux_x86_64 on a different + # architecture, but should pass natively. + known_sigs = [b'\xcd\xcc\xcc\xcc\xcc\xcc\xcc\xcc\xfb\xbf'] + sig = (np.longdouble(-1.0) / np.longdouble(10.0) + ).newbyteorder('<').tobytes()[:10] + assert sig in known_sigs + + +def test_eps_positive(): + # np.finfo('g').eps should be positive on all platforms. If this isn't true + # then something may have gone wrong with the MachArLike, e.g. if + # np.core.getlimits._discovered_machar didn't work properly + assert np.finfo(np.longdouble).eps > 0. diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_machar.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_machar.py new file mode 100644 index 0000000000000000000000000000000000000000..3a66ec51fd5860a546b917af3b83d21ac55540ad --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_machar.py @@ -0,0 +1,30 @@ +""" +Test machar. Given recent changes to hardcode type data, we might want to get +rid of both MachAr and this test at some point. + +""" +from numpy.core._machar import MachAr +import numpy.core.numerictypes as ntypes +from numpy import errstate, array + + +class TestMachAr: + def _run_machar_highprec(self): + # Instantiate MachAr instance with high enough precision to cause + # underflow + try: + hiprec = ntypes.float96 + MachAr(lambda v: array(v, hiprec)) + except AttributeError: + # Fixme, this needs to raise a 'skip' exception. + "Skipping test: no ntypes.float96 available on this platform." + + def test_underlow(self): + # Regression test for #759: + # instantiating MachAr for dtype = np.float96 raises spurious warning. + with errstate(all='raise'): + try: + self._run_machar_highprec() + except FloatingPointError as e: + msg = "Caught %s exception, should not have been raised." % e + raise AssertionError(msg) diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_numeric.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_numeric.py new file mode 100644 index 0000000000000000000000000000000000000000..e5edd3efce5a71cdb48f0fef0ad792f9da61b374 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_numeric.py @@ -0,0 +1,3593 @@ +import sys +import warnings +import itertools +import platform +import pytest +import math +from decimal import Decimal + +import numpy as np +from numpy.core import umath +from numpy.random import rand, randint, randn +from numpy.testing import ( + assert_, assert_equal, assert_raises, assert_raises_regex, + assert_array_equal, assert_almost_equal, assert_array_almost_equal, + assert_warns, assert_array_max_ulp, HAS_REFCOUNT, IS_WASM + ) +from numpy.core._rational_tests import rational + +from hypothesis import given, strategies as st +from hypothesis.extra import numpy as hynp + + +class TestResize: + def test_copies(self): + A = np.array([[1, 2], [3, 4]]) + Ar1 = np.array([[1, 2, 3, 4], [1, 2, 3, 4]]) + assert_equal(np.resize(A, (2, 4)), Ar1) + + Ar2 = np.array([[1, 2], [3, 4], [1, 2], [3, 4]]) + assert_equal(np.resize(A, (4, 2)), Ar2) + + Ar3 = np.array([[1, 2, 3], [4, 1, 2], [3, 4, 1], [2, 3, 4]]) + assert_equal(np.resize(A, (4, 3)), Ar3) + + def test_repeats(self): + A = np.array([1, 2, 3]) + Ar1 = np.array([[1, 2, 3, 1], [2, 3, 1, 2]]) + assert_equal(np.resize(A, (2, 4)), Ar1) + + Ar2 = np.array([[1, 2], [3, 1], [2, 3], [1, 2]]) + assert_equal(np.resize(A, (4, 2)), Ar2) + + Ar3 = np.array([[1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3]]) + assert_equal(np.resize(A, (4, 3)), Ar3) + + def test_zeroresize(self): + A = np.array([[1, 2], [3, 4]]) + Ar = np.resize(A, (0,)) + assert_array_equal(Ar, np.array([])) + assert_equal(A.dtype, Ar.dtype) + + Ar = np.resize(A, (0, 2)) + assert_equal(Ar.shape, (0, 2)) + + Ar = np.resize(A, (2, 0)) + assert_equal(Ar.shape, (2, 0)) + + def test_reshape_from_zero(self): + # See also gh-6740 + A = np.zeros(0, dtype=[('a', np.float32)]) + Ar = np.resize(A, (2, 1)) + assert_array_equal(Ar, np.zeros((2, 1), Ar.dtype)) + assert_equal(A.dtype, Ar.dtype) + + def test_negative_resize(self): + A = np.arange(0, 10, dtype=np.float32) + new_shape = (-10, -1) + with pytest.raises(ValueError, match=r"negative"): + np.resize(A, new_shape=new_shape) + + def test_subclass(self): + class MyArray(np.ndarray): + __array_priority__ = 1. + + my_arr = np.array([1]).view(MyArray) + assert type(np.resize(my_arr, 5)) is MyArray + assert type(np.resize(my_arr, 0)) is MyArray + + my_arr = np.array([]).view(MyArray) + assert type(np.resize(my_arr, 5)) is MyArray + + +class TestNonarrayArgs: + # check that non-array arguments to functions wrap them in arrays + def test_choose(self): + choices = [[0, 1, 2], + [3, 4, 5], + [5, 6, 7]] + tgt = [5, 1, 5] + a = [2, 0, 1] + + out = np.choose(a, choices) + assert_equal(out, tgt) + + def test_clip(self): + arr = [-1, 5, 2, 3, 10, -4, -9] + out = np.clip(arr, 2, 7) + tgt = [2, 5, 2, 3, 7, 2, 2] + assert_equal(out, tgt) + + def test_compress(self): + arr = [[0, 1, 2, 3, 4], + [5, 6, 7, 8, 9]] + tgt = [[5, 6, 7, 8, 9]] + out = np.compress([0, 1], arr, axis=0) + assert_equal(out, tgt) + + def test_count_nonzero(self): + arr = [[0, 1, 7, 0, 0], + [3, 0, 0, 2, 19]] + tgt = np.array([2, 3]) + out = np.count_nonzero(arr, axis=1) + assert_equal(out, tgt) + + def test_cumproduct(self): + A = [[1, 2, 3], [4, 5, 6]] + with assert_warns(DeprecationWarning): + expected = np.array([1, 2, 6, 24, 120, 720]) + assert_(np.all(np.cumproduct(A) == expected)) + + def test_diagonal(self): + a = [[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11]] + out = np.diagonal(a) + tgt = [0, 5, 10] + + assert_equal(out, tgt) + + def test_mean(self): + A = [[1, 2, 3], [4, 5, 6]] + assert_(np.mean(A) == 3.5) + assert_(np.all(np.mean(A, 0) == np.array([2.5, 3.5, 4.5]))) + assert_(np.all(np.mean(A, 1) == np.array([2., 5.]))) + + with warnings.catch_warnings(record=True) as w: + warnings.filterwarnings('always', '', RuntimeWarning) + assert_(np.isnan(np.mean([]))) + assert_(w[0].category is RuntimeWarning) + + def test_ptp(self): + a = [3, 4, 5, 10, -3, -5, 6.0] + assert_equal(np.ptp(a, axis=0), 15.0) + + def test_prod(self): + arr = [[1, 2, 3, 4], + [5, 6, 7, 9], + [10, 3, 4, 5]] + tgt = [24, 1890, 600] + + assert_equal(np.prod(arr, axis=-1), tgt) + + def test_ravel(self): + a = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]] + tgt = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] + assert_equal(np.ravel(a), tgt) + + def test_repeat(self): + a = [1, 2, 3] + tgt = [1, 1, 2, 2, 3, 3] + + out = np.repeat(a, 2) + assert_equal(out, tgt) + + def test_reshape(self): + arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]] + tgt = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]] + assert_equal(np.reshape(arr, (2, 6)), tgt) + + def test_round(self): + arr = [1.56, 72.54, 6.35, 3.25] + tgt = [1.6, 72.5, 6.4, 3.2] + assert_equal(np.around(arr, decimals=1), tgt) + s = np.float64(1.) + assert_(isinstance(s.round(), np.float64)) + assert_equal(s.round(), 1.) + + @pytest.mark.parametrize('dtype', [ + np.int8, np.int16, np.int32, np.int64, + np.uint8, np.uint16, np.uint32, np.uint64, + np.float16, np.float32, np.float64, + ]) + def test_dunder_round(self, dtype): + s = dtype(1) + assert_(isinstance(round(s), int)) + assert_(isinstance(round(s, None), int)) + assert_(isinstance(round(s, ndigits=None), int)) + assert_equal(round(s), 1) + assert_equal(round(s, None), 1) + assert_equal(round(s, ndigits=None), 1) + + @pytest.mark.parametrize('val, ndigits', [ + pytest.param(2**31 - 1, -1, + marks=pytest.mark.xfail(reason="Out of range of int32") + ), + (2**31 - 1, 1-math.ceil(math.log10(2**31 - 1))), + (2**31 - 1, -math.ceil(math.log10(2**31 - 1))) + ]) + def test_dunder_round_edgecases(self, val, ndigits): + assert_equal(round(val, ndigits), round(np.int32(val), ndigits)) + + def test_dunder_round_accuracy(self): + f = np.float64(5.1 * 10**73) + assert_(isinstance(round(f, -73), np.float64)) + assert_array_max_ulp(round(f, -73), 5.0 * 10**73) + assert_(isinstance(round(f, ndigits=-73), np.float64)) + assert_array_max_ulp(round(f, ndigits=-73), 5.0 * 10**73) + + i = np.int64(501) + assert_(isinstance(round(i, -2), np.int64)) + assert_array_max_ulp(round(i, -2), 500) + assert_(isinstance(round(i, ndigits=-2), np.int64)) + assert_array_max_ulp(round(i, ndigits=-2), 500) + + @pytest.mark.xfail(raises=AssertionError, reason="gh-15896") + def test_round_py_consistency(self): + f = 5.1 * 10**73 + assert_equal(round(np.float64(f), -73), round(f, -73)) + + def test_searchsorted(self): + arr = [-8, -5, -1, 3, 6, 10] + out = np.searchsorted(arr, 0) + assert_equal(out, 3) + + def test_size(self): + A = [[1, 2, 3], [4, 5, 6]] + assert_(np.size(A) == 6) + assert_(np.size(A, 0) == 2) + assert_(np.size(A, 1) == 3) + + def test_squeeze(self): + A = [[[1, 1, 1], [2, 2, 2], [3, 3, 3]]] + assert_equal(np.squeeze(A).shape, (3, 3)) + assert_equal(np.squeeze(np.zeros((1, 3, 1))).shape, (3,)) + assert_equal(np.squeeze(np.zeros((1, 3, 1)), axis=0).shape, (3, 1)) + assert_equal(np.squeeze(np.zeros((1, 3, 1)), axis=-1).shape, (1, 3)) + assert_equal(np.squeeze(np.zeros((1, 3, 1)), axis=2).shape, (1, 3)) + assert_equal(np.squeeze([np.zeros((3, 1))]).shape, (3,)) + assert_equal(np.squeeze([np.zeros((3, 1))], axis=0).shape, (3, 1)) + assert_equal(np.squeeze([np.zeros((3, 1))], axis=2).shape, (1, 3)) + assert_equal(np.squeeze([np.zeros((3, 1))], axis=-1).shape, (1, 3)) + + def test_std(self): + A = [[1, 2, 3], [4, 5, 6]] + assert_almost_equal(np.std(A), 1.707825127659933) + assert_almost_equal(np.std(A, 0), np.array([1.5, 1.5, 1.5])) + assert_almost_equal(np.std(A, 1), np.array([0.81649658, 0.81649658])) + + with warnings.catch_warnings(record=True) as w: + warnings.filterwarnings('always', '', RuntimeWarning) + assert_(np.isnan(np.std([]))) + assert_(w[0].category is RuntimeWarning) + + def test_swapaxes(self): + tgt = [[[0, 4], [2, 6]], [[1, 5], [3, 7]]] + a = [[[0, 1], [2, 3]], [[4, 5], [6, 7]]] + out = np.swapaxes(a, 0, 2) + assert_equal(out, tgt) + + def test_sum(self): + m = [[1, 2, 3], + [4, 5, 6], + [7, 8, 9]] + tgt = [[6], [15], [24]] + out = np.sum(m, axis=1, keepdims=True) + + assert_equal(tgt, out) + + def test_take(self): + tgt = [2, 3, 5] + indices = [1, 2, 4] + a = [1, 2, 3, 4, 5] + + out = np.take(a, indices) + assert_equal(out, tgt) + + def test_trace(self): + c = [[1, 2], [3, 4], [5, 6]] + assert_equal(np.trace(c), 5) + + def test_transpose(self): + arr = [[1, 2], [3, 4], [5, 6]] + tgt = [[1, 3, 5], [2, 4, 6]] + assert_equal(np.transpose(arr, (1, 0)), tgt) + + def test_var(self): + A = [[1, 2, 3], [4, 5, 6]] + assert_almost_equal(np.var(A), 2.9166666666666665) + assert_almost_equal(np.var(A, 0), np.array([2.25, 2.25, 2.25])) + assert_almost_equal(np.var(A, 1), np.array([0.66666667, 0.66666667])) + + with warnings.catch_warnings(record=True) as w: + warnings.filterwarnings('always', '', RuntimeWarning) + assert_(np.isnan(np.var([]))) + assert_(w[0].category is RuntimeWarning) + + B = np.array([None, 0]) + B[0] = 1j + assert_almost_equal(np.var(B), 0.25) + + +class TestIsscalar: + def test_isscalar(self): + assert_(np.isscalar(3.1)) + assert_(np.isscalar(np.int16(12345))) + assert_(np.isscalar(False)) + assert_(np.isscalar('numpy')) + assert_(not np.isscalar([3.1])) + assert_(not np.isscalar(None)) + + # PEP 3141 + from fractions import Fraction + assert_(np.isscalar(Fraction(5, 17))) + from numbers import Number + assert_(np.isscalar(Number())) + + +class TestBoolScalar: + def test_logical(self): + f = np.False_ + t = np.True_ + s = "xyz" + assert_((t and s) is s) + assert_((f and s) is f) + + def test_bitwise_or(self): + f = np.False_ + t = np.True_ + assert_((t | t) is t) + assert_((f | t) is t) + assert_((t | f) is t) + assert_((f | f) is f) + + def test_bitwise_and(self): + f = np.False_ + t = np.True_ + assert_((t & t) is t) + assert_((f & t) is f) + assert_((t & f) is f) + assert_((f & f) is f) + + def test_bitwise_xor(self): + f = np.False_ + t = np.True_ + assert_((t ^ t) is f) + assert_((f ^ t) is t) + assert_((t ^ f) is t) + assert_((f ^ f) is f) + + +class TestBoolArray: + def setup_method(self): + # offset for simd tests + self.t = np.array([True] * 41, dtype=bool)[1::] + self.f = np.array([False] * 41, dtype=bool)[1::] + self.o = np.array([False] * 42, dtype=bool)[2::] + self.nm = self.f.copy() + self.im = self.t.copy() + self.nm[3] = True + self.nm[-2] = True + self.im[3] = False + self.im[-2] = False + + def test_all_any(self): + assert_(self.t.all()) + assert_(self.t.any()) + assert_(not self.f.all()) + assert_(not self.f.any()) + assert_(self.nm.any()) + assert_(self.im.any()) + assert_(not self.nm.all()) + assert_(not self.im.all()) + # check bad element in all positions + for i in range(256 - 7): + d = np.array([False] * 256, dtype=bool)[7::] + d[i] = True + assert_(np.any(d)) + e = np.array([True] * 256, dtype=bool)[7::] + e[i] = False + assert_(not np.all(e)) + assert_array_equal(e, ~d) + # big array test for blocked libc loops + for i in list(range(9, 6000, 507)) + [7764, 90021, -10]: + d = np.array([False] * 100043, dtype=bool) + d[i] = True + assert_(np.any(d), msg="%r" % i) + e = np.array([True] * 100043, dtype=bool) + e[i] = False + assert_(not np.all(e), msg="%r" % i) + + def test_logical_not_abs(self): + assert_array_equal(~self.t, self.f) + assert_array_equal(np.abs(~self.t), self.f) + assert_array_equal(np.abs(~self.f), self.t) + assert_array_equal(np.abs(self.f), self.f) + assert_array_equal(~np.abs(self.f), self.t) + assert_array_equal(~np.abs(self.t), self.f) + assert_array_equal(np.abs(~self.nm), self.im) + np.logical_not(self.t, out=self.o) + assert_array_equal(self.o, self.f) + np.abs(self.t, out=self.o) + assert_array_equal(self.o, self.t) + + def test_logical_and_or_xor(self): + assert_array_equal(self.t | self.t, self.t) + assert_array_equal(self.f | self.f, self.f) + assert_array_equal(self.t | self.f, self.t) + assert_array_equal(self.f | self.t, self.t) + np.logical_or(self.t, self.t, out=self.o) + assert_array_equal(self.o, self.t) + assert_array_equal(self.t & self.t, self.t) + assert_array_equal(self.f & self.f, self.f) + assert_array_equal(self.t & self.f, self.f) + assert_array_equal(self.f & self.t, self.f) + np.logical_and(self.t, self.t, out=self.o) + assert_array_equal(self.o, self.t) + assert_array_equal(self.t ^ self.t, self.f) + assert_array_equal(self.f ^ self.f, self.f) + assert_array_equal(self.t ^ self.f, self.t) + assert_array_equal(self.f ^ self.t, self.t) + np.logical_xor(self.t, self.t, out=self.o) + assert_array_equal(self.o, self.f) + + assert_array_equal(self.nm & self.t, self.nm) + assert_array_equal(self.im & self.f, False) + assert_array_equal(self.nm & True, self.nm) + assert_array_equal(self.im & False, self.f) + assert_array_equal(self.nm | self.t, self.t) + assert_array_equal(self.im | self.f, self.im) + assert_array_equal(self.nm | True, self.t) + assert_array_equal(self.im | False, self.im) + assert_array_equal(self.nm ^ self.t, self.im) + assert_array_equal(self.im ^ self.f, self.im) + assert_array_equal(self.nm ^ True, self.im) + assert_array_equal(self.im ^ False, self.im) + + +class TestBoolCmp: + def setup_method(self): + self.f = np.ones(256, dtype=np.float32) + self.ef = np.ones(self.f.size, dtype=bool) + self.d = np.ones(128, dtype=np.float64) + self.ed = np.ones(self.d.size, dtype=bool) + # generate values for all permutation of 256bit simd vectors + s = 0 + for i in range(32): + self.f[s:s+8] = [i & 2**x for x in range(8)] + self.ef[s:s+8] = [(i & 2**x) != 0 for x in range(8)] + s += 8 + s = 0 + for i in range(16): + self.d[s:s+4] = [i & 2**x for x in range(4)] + self.ed[s:s+4] = [(i & 2**x) != 0 for x in range(4)] + s += 4 + + self.nf = self.f.copy() + self.nd = self.d.copy() + self.nf[self.ef] = np.nan + self.nd[self.ed] = np.nan + + self.inff = self.f.copy() + self.infd = self.d.copy() + self.inff[::3][self.ef[::3]] = np.inf + self.infd[::3][self.ed[::3]] = np.inf + self.inff[1::3][self.ef[1::3]] = -np.inf + self.infd[1::3][self.ed[1::3]] = -np.inf + self.inff[2::3][self.ef[2::3]] = np.nan + self.infd[2::3][self.ed[2::3]] = np.nan + self.efnonan = self.ef.copy() + self.efnonan[2::3] = False + self.ednonan = self.ed.copy() + self.ednonan[2::3] = False + + self.signf = self.f.copy() + self.signd = self.d.copy() + self.signf[self.ef] *= -1. + self.signd[self.ed] *= -1. + self.signf[1::6][self.ef[1::6]] = -np.inf + self.signd[1::6][self.ed[1::6]] = -np.inf + # On RISC-V, many operations that produce NaNs, such as converting + # a -NaN from f64 to f32, return a canonical NaN. The canonical + # NaNs are always positive. See section 11.3 NaN Generation and + # Propagation of the RISC-V Unprivileged ISA for more details. + # We disable the float32 sign test on riscv64 for -np.nan as the sign + # of the NaN will be lost when it's converted to a float32. + if platform.processor() != 'riscv64': + self.signf[3::6][self.ef[3::6]] = -np.nan + self.signd[3::6][self.ed[3::6]] = -np.nan + self.signf[4::6][self.ef[4::6]] = -0. + self.signd[4::6][self.ed[4::6]] = -0. + + def test_float(self): + # offset for alignment test + for i in range(4): + assert_array_equal(self.f[i:] > 0, self.ef[i:]) + assert_array_equal(self.f[i:] - 1 >= 0, self.ef[i:]) + assert_array_equal(self.f[i:] == 0, ~self.ef[i:]) + assert_array_equal(-self.f[i:] < 0, self.ef[i:]) + assert_array_equal(-self.f[i:] + 1 <= 0, self.ef[i:]) + r = self.f[i:] != 0 + assert_array_equal(r, self.ef[i:]) + r2 = self.f[i:] != np.zeros_like(self.f[i:]) + r3 = 0 != self.f[i:] + assert_array_equal(r, r2) + assert_array_equal(r, r3) + # check bool == 0x1 + assert_array_equal(r.view(np.int8), r.astype(np.int8)) + assert_array_equal(r2.view(np.int8), r2.astype(np.int8)) + assert_array_equal(r3.view(np.int8), r3.astype(np.int8)) + + # isnan on amd64 takes the same code path + assert_array_equal(np.isnan(self.nf[i:]), self.ef[i:]) + assert_array_equal(np.isfinite(self.nf[i:]), ~self.ef[i:]) + assert_array_equal(np.isfinite(self.inff[i:]), ~self.ef[i:]) + assert_array_equal(np.isinf(self.inff[i:]), self.efnonan[i:]) + assert_array_equal(np.signbit(self.signf[i:]), self.ef[i:]) + + def test_double(self): + # offset for alignment test + for i in range(2): + assert_array_equal(self.d[i:] > 0, self.ed[i:]) + assert_array_equal(self.d[i:] - 1 >= 0, self.ed[i:]) + assert_array_equal(self.d[i:] == 0, ~self.ed[i:]) + assert_array_equal(-self.d[i:] < 0, self.ed[i:]) + assert_array_equal(-self.d[i:] + 1 <= 0, self.ed[i:]) + r = self.d[i:] != 0 + assert_array_equal(r, self.ed[i:]) + r2 = self.d[i:] != np.zeros_like(self.d[i:]) + r3 = 0 != self.d[i:] + assert_array_equal(r, r2) + assert_array_equal(r, r3) + # check bool == 0x1 + assert_array_equal(r.view(np.int8), r.astype(np.int8)) + assert_array_equal(r2.view(np.int8), r2.astype(np.int8)) + assert_array_equal(r3.view(np.int8), r3.astype(np.int8)) + + # isnan on amd64 takes the same code path + assert_array_equal(np.isnan(self.nd[i:]), self.ed[i:]) + assert_array_equal(np.isfinite(self.nd[i:]), ~self.ed[i:]) + assert_array_equal(np.isfinite(self.infd[i:]), ~self.ed[i:]) + assert_array_equal(np.isinf(self.infd[i:]), self.ednonan[i:]) + assert_array_equal(np.signbit(self.signd[i:]), self.ed[i:]) + + +class TestSeterr: + def test_default(self): + err = np.geterr() + assert_equal(err, + dict(divide='warn', + invalid='warn', + over='warn', + under='ignore') + ) + + def test_set(self): + with np.errstate(): + err = np.seterr() + old = np.seterr(divide='print') + assert_(err == old) + new = np.seterr() + assert_(new['divide'] == 'print') + np.seterr(over='raise') + assert_(np.geterr()['over'] == 'raise') + assert_(new['divide'] == 'print') + np.seterr(**old) + assert_(np.geterr() == old) + + @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support") + @pytest.mark.skipif(platform.machine() == "armv5tel", reason="See gh-413.") + def test_divide_err(self): + with np.errstate(divide='raise'): + with assert_raises(FloatingPointError): + np.array([1.]) / np.array([0.]) + + np.seterr(divide='ignore') + np.array([1.]) / np.array([0.]) + + @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support") + def test_errobj(self): + olderrobj = np.geterrobj() + self.called = 0 + try: + with warnings.catch_warnings(record=True) as w: + warnings.simplefilter("always") + with np.errstate(divide='warn'): + np.seterrobj([20000, 1, None]) + np.array([1.]) / np.array([0.]) + assert_equal(len(w), 1) + + def log_err(*args): + self.called += 1 + extobj_err = args + assert_(len(extobj_err) == 2) + assert_("divide" in extobj_err[0]) + + with np.errstate(divide='ignore'): + np.seterrobj([20000, 3, log_err]) + np.array([1.]) / np.array([0.]) + assert_equal(self.called, 1) + + np.seterrobj(olderrobj) + with np.errstate(divide='ignore'): + np.divide(1., 0., extobj=[20000, 3, log_err]) + assert_equal(self.called, 2) + finally: + np.seterrobj(olderrobj) + del self.called + + def test_errobj_noerrmask(self): + # errmask = 0 has a special code path for the default + olderrobj = np.geterrobj() + try: + # set errobj to something non default + np.seterrobj([umath.UFUNC_BUFSIZE_DEFAULT, + umath.ERR_DEFAULT + 1, None]) + # call a ufunc + np.isnan(np.array([6])) + # same with the default, lots of times to get rid of possible + # pre-existing stack in the code + for i in range(10000): + np.seterrobj([umath.UFUNC_BUFSIZE_DEFAULT, umath.ERR_DEFAULT, + None]) + np.isnan(np.array([6])) + finally: + np.seterrobj(olderrobj) + + +class TestFloatExceptions: + def assert_raises_fpe(self, fpeerr, flop, x, y): + ftype = type(x) + try: + flop(x, y) + assert_(False, + "Type %s did not raise fpe error '%s'." % (ftype, fpeerr)) + except FloatingPointError as exc: + assert_(str(exc).find(fpeerr) >= 0, + "Type %s raised wrong fpe error '%s'." % (ftype, exc)) + + def assert_op_raises_fpe(self, fpeerr, flop, sc1, sc2): + # Check that fpe exception is raised. + # + # Given a floating operation `flop` and two scalar values, check that + # the operation raises the floating point exception specified by + # `fpeerr`. Tests all variants with 0-d array scalars as well. + + self.assert_raises_fpe(fpeerr, flop, sc1, sc2) + self.assert_raises_fpe(fpeerr, flop, sc1[()], sc2) + self.assert_raises_fpe(fpeerr, flop, sc1, sc2[()]) + self.assert_raises_fpe(fpeerr, flop, sc1[()], sc2[()]) + + # Test for all real and complex float types + @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support") + @pytest.mark.parametrize("typecode", np.typecodes["AllFloat"]) + def test_floating_exceptions(self, typecode): + if 'bsd' in sys.platform and typecode in 'gG': + pytest.skip(reason="Fallback impl for (c)longdouble may not raise " + "FPE errors as expected on BSD OSes, " + "see gh-24876, gh-23379") + + # Test basic arithmetic function errors + with np.errstate(all='raise'): + ftype = np.obj2sctype(typecode) + if np.dtype(ftype).kind == 'f': + # Get some extreme values for the type + fi = np.finfo(ftype) + ft_tiny = fi._machar.tiny + ft_max = fi.max + ft_eps = fi.eps + underflow = 'underflow' + divbyzero = 'divide by zero' + else: + # 'c', complex, corresponding real dtype + rtype = type(ftype(0).real) + fi = np.finfo(rtype) + ft_tiny = ftype(fi._machar.tiny) + ft_max = ftype(fi.max) + ft_eps = ftype(fi.eps) + # The complex types raise different exceptions + underflow = '' + divbyzero = '' + overflow = 'overflow' + invalid = 'invalid' + + # The value of tiny for double double is NaN, so we need to + # pass the assert + if not np.isnan(ft_tiny): + self.assert_raises_fpe(underflow, + lambda a, b: a/b, ft_tiny, ft_max) + self.assert_raises_fpe(underflow, + lambda a, b: a*b, ft_tiny, ft_tiny) + self.assert_raises_fpe(overflow, + lambda a, b: a*b, ft_max, ftype(2)) + self.assert_raises_fpe(overflow, + lambda a, b: a/b, ft_max, ftype(0.5)) + self.assert_raises_fpe(overflow, + lambda a, b: a+b, ft_max, ft_max*ft_eps) + self.assert_raises_fpe(overflow, + lambda a, b: a-b, -ft_max, ft_max*ft_eps) + self.assert_raises_fpe(overflow, + np.power, ftype(2), ftype(2**fi.nexp)) + self.assert_raises_fpe(divbyzero, + lambda a, b: a/b, ftype(1), ftype(0)) + self.assert_raises_fpe( + invalid, lambda a, b: a/b, ftype(np.inf), ftype(np.inf) + ) + self.assert_raises_fpe(invalid, + lambda a, b: a/b, ftype(0), ftype(0)) + self.assert_raises_fpe( + invalid, lambda a, b: a-b, ftype(np.inf), ftype(np.inf) + ) + self.assert_raises_fpe( + invalid, lambda a, b: a+b, ftype(np.inf), ftype(-np.inf) + ) + self.assert_raises_fpe(invalid, + lambda a, b: a*b, ftype(0), ftype(np.inf)) + + @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support") + def test_warnings(self): + # test warning code path + with warnings.catch_warnings(record=True) as w: + warnings.simplefilter("always") + with np.errstate(all="warn"): + np.divide(1, 0.) + assert_equal(len(w), 1) + assert_("divide by zero" in str(w[0].message)) + np.array(1e300) * np.array(1e300) + assert_equal(len(w), 2) + assert_("overflow" in str(w[-1].message)) + np.array(np.inf) - np.array(np.inf) + assert_equal(len(w), 3) + assert_("invalid value" in str(w[-1].message)) + np.array(1e-300) * np.array(1e-300) + assert_equal(len(w), 4) + assert_("underflow" in str(w[-1].message)) + + +class TestTypes: + def check_promotion_cases(self, promote_func): + # tests that the scalars get coerced correctly. + b = np.bool_(0) + i8, i16, i32, i64 = np.int8(0), np.int16(0), np.int32(0), np.int64(0) + u8, u16, u32, u64 = np.uint8(0), np.uint16(0), np.uint32(0), np.uint64(0) + f32, f64, fld = np.float32(0), np.float64(0), np.longdouble(0) + c64, c128, cld = np.complex64(0), np.complex128(0), np.clongdouble(0) + + # coercion within the same kind + assert_equal(promote_func(i8, i16), np.dtype(np.int16)) + assert_equal(promote_func(i32, i8), np.dtype(np.int32)) + assert_equal(promote_func(i16, i64), np.dtype(np.int64)) + assert_equal(promote_func(u8, u32), np.dtype(np.uint32)) + assert_equal(promote_func(f32, f64), np.dtype(np.float64)) + assert_equal(promote_func(fld, f32), np.dtype(np.longdouble)) + assert_equal(promote_func(f64, fld), np.dtype(np.longdouble)) + assert_equal(promote_func(c128, c64), np.dtype(np.complex128)) + assert_equal(promote_func(cld, c128), np.dtype(np.clongdouble)) + assert_equal(promote_func(c64, fld), np.dtype(np.clongdouble)) + + # coercion between kinds + assert_equal(promote_func(b, i32), np.dtype(np.int32)) + assert_equal(promote_func(b, u8), np.dtype(np.uint8)) + assert_equal(promote_func(i8, u8), np.dtype(np.int16)) + assert_equal(promote_func(u8, i32), np.dtype(np.int32)) + assert_equal(promote_func(i64, u32), np.dtype(np.int64)) + assert_equal(promote_func(u64, i32), np.dtype(np.float64)) + assert_equal(promote_func(i32, f32), np.dtype(np.float64)) + assert_equal(promote_func(i64, f32), np.dtype(np.float64)) + assert_equal(promote_func(f32, i16), np.dtype(np.float32)) + assert_equal(promote_func(f32, u32), np.dtype(np.float64)) + assert_equal(promote_func(f32, c64), np.dtype(np.complex64)) + assert_equal(promote_func(c128, f32), np.dtype(np.complex128)) + assert_equal(promote_func(cld, f64), np.dtype(np.clongdouble)) + + # coercion between scalars and 1-D arrays + assert_equal(promote_func(np.array([b]), i8), np.dtype(np.int8)) + assert_equal(promote_func(np.array([b]), u8), np.dtype(np.uint8)) + assert_equal(promote_func(np.array([b]), i32), np.dtype(np.int32)) + assert_equal(promote_func(np.array([b]), u32), np.dtype(np.uint32)) + assert_equal(promote_func(np.array([i8]), i64), np.dtype(np.int8)) + assert_equal(promote_func(u64, np.array([i32])), np.dtype(np.int32)) + assert_equal(promote_func(i64, np.array([u32])), np.dtype(np.uint32)) + assert_equal(promote_func(np.int32(-1), np.array([u64])), + np.dtype(np.float64)) + assert_equal(promote_func(f64, np.array([f32])), np.dtype(np.float32)) + assert_equal(promote_func(fld, np.array([f32])), np.dtype(np.float32)) + assert_equal(promote_func(np.array([f64]), fld), np.dtype(np.float64)) + assert_equal(promote_func(fld, np.array([c64])), + np.dtype(np.complex64)) + assert_equal(promote_func(c64, np.array([f64])), + np.dtype(np.complex128)) + assert_equal(promote_func(np.complex64(3j), np.array([f64])), + np.dtype(np.complex128)) + + # coercion between scalars and 1-D arrays, where + # the scalar has greater kind than the array + assert_equal(promote_func(np.array([b]), f64), np.dtype(np.float64)) + assert_equal(promote_func(np.array([b]), i64), np.dtype(np.int64)) + assert_equal(promote_func(np.array([b]), u64), np.dtype(np.uint64)) + assert_equal(promote_func(np.array([i8]), f64), np.dtype(np.float64)) + assert_equal(promote_func(np.array([u16]), f64), np.dtype(np.float64)) + + # uint and int are treated as the same "kind" for + # the purposes of array-scalar promotion. + assert_equal(promote_func(np.array([u16]), i32), np.dtype(np.uint16)) + + # float and complex are treated as the same "kind" for + # the purposes of array-scalar promotion, so that you can do + # (0j + float32array) to get a complex64 array instead of + # a complex128 array. + assert_equal(promote_func(np.array([f32]), c128), + np.dtype(np.complex64)) + + def test_coercion(self): + def res_type(a, b): + return np.add(a, b).dtype + + self.check_promotion_cases(res_type) + + # Use-case: float/complex scalar * bool/int8 array + # shouldn't narrow the float/complex type + for a in [np.array([True, False]), np.array([-3, 12], dtype=np.int8)]: + b = 1.234 * a + assert_equal(b.dtype, np.dtype('f8'), "array type %s" % a.dtype) + b = np.longdouble(1.234) * a + assert_equal(b.dtype, np.dtype(np.longdouble), + "array type %s" % a.dtype) + b = np.float64(1.234) * a + assert_equal(b.dtype, np.dtype('f8'), "array type %s" % a.dtype) + b = np.float32(1.234) * a + assert_equal(b.dtype, np.dtype('f4'), "array type %s" % a.dtype) + b = np.float16(1.234) * a + assert_equal(b.dtype, np.dtype('f2'), "array type %s" % a.dtype) + + b = 1.234j * a + assert_equal(b.dtype, np.dtype('c16'), "array type %s" % a.dtype) + b = np.clongdouble(1.234j) * a + assert_equal(b.dtype, np.dtype(np.clongdouble), + "array type %s" % a.dtype) + b = np.complex128(1.234j) * a + assert_equal(b.dtype, np.dtype('c16'), "array type %s" % a.dtype) + b = np.complex64(1.234j) * a + assert_equal(b.dtype, np.dtype('c8'), "array type %s" % a.dtype) + + # The following use-case is problematic, and to resolve its + # tricky side-effects requires more changes. + # + # Use-case: (1-t)*a, where 't' is a boolean array and 'a' is + # a float32, shouldn't promote to float64 + # + # a = np.array([1.0, 1.5], dtype=np.float32) + # t = np.array([True, False]) + # b = t*a + # assert_equal(b, [1.0, 0.0]) + # assert_equal(b.dtype, np.dtype('f4')) + # b = (1-t)*a + # assert_equal(b, [0.0, 1.5]) + # assert_equal(b.dtype, np.dtype('f4')) + # + # Probably ~t (bitwise negation) is more proper to use here, + # but this is arguably less intuitive to understand at a glance, and + # would fail if 't' is actually an integer array instead of boolean: + # + # b = (~t)*a + # assert_equal(b, [0.0, 1.5]) + # assert_equal(b.dtype, np.dtype('f4')) + + def test_result_type(self): + self.check_promotion_cases(np.result_type) + assert_(np.result_type(None) == np.dtype(None)) + + def test_promote_types_endian(self): + # promote_types should always return native-endian types + assert_equal(np.promote_types('i8', '>i8'), np.dtype('i8')) + + assert_equal(np.promote_types('>i8', '>U16'), np.dtype('U21')) + assert_equal(np.promote_types('U16', '>i8'), np.dtype('U21')) + assert_equal(np.promote_types('S5', '>U8'), np.dtype('U8')) + assert_equal(np.promote_types('U8', '>S5'), np.dtype('U8')) + assert_equal(np.promote_types('U8', '>U5'), np.dtype('U8')) + + assert_equal(np.promote_types('M8', '>M8'), np.dtype('M8')) + assert_equal(np.promote_types('m8', '>m8'), np.dtype('m8')) + + def test_can_cast_and_promote_usertypes(self): + # The rational type defines safe casting for signed integers, + # boolean. Rational itself *does* cast safely to double. + # (rational does not actually cast to all signed integers, e.g. + # int64 can be both long and longlong and it registers only the first) + valid_types = ["int8", "int16", "int32", "int64", "bool"] + invalid_types = "BHILQP" + "FDG" + "mM" + "f" + "V" + + rational_dt = np.dtype(rational) + for numpy_dtype in valid_types: + numpy_dtype = np.dtype(numpy_dtype) + assert np.can_cast(numpy_dtype, rational_dt) + assert np.promote_types(numpy_dtype, rational_dt) is rational_dt + + for numpy_dtype in invalid_types: + numpy_dtype = np.dtype(numpy_dtype) + assert not np.can_cast(numpy_dtype, rational_dt) + with pytest.raises(TypeError): + np.promote_types(numpy_dtype, rational_dt) + + double_dt = np.dtype("double") + assert np.can_cast(rational_dt, double_dt) + assert np.promote_types(double_dt, rational_dt) is double_dt + + @pytest.mark.parametrize("swap", ["", "swap"]) + @pytest.mark.parametrize("string_dtype", ["U", "S"]) + def test_promote_types_strings(self, swap, string_dtype): + if swap == "swap": + promote_types = lambda a, b: np.promote_types(b, a) + else: + promote_types = np.promote_types + + S = string_dtype + + # Promote numeric with unsized string: + assert_equal(promote_types('bool', S), np.dtype(S+'5')) + assert_equal(promote_types('b', S), np.dtype(S+'4')) + assert_equal(promote_types('u1', S), np.dtype(S+'3')) + assert_equal(promote_types('u2', S), np.dtype(S+'5')) + assert_equal(promote_types('u4', S), np.dtype(S+'10')) + assert_equal(promote_types('u8', S), np.dtype(S+'20')) + assert_equal(promote_types('i1', S), np.dtype(S+'4')) + assert_equal(promote_types('i2', S), np.dtype(S+'6')) + assert_equal(promote_types('i4', S), np.dtype(S+'11')) + assert_equal(promote_types('i8', S), np.dtype(S+'21')) + # Promote numeric with sized string: + assert_equal(promote_types('bool', S+'1'), np.dtype(S+'5')) + assert_equal(promote_types('bool', S+'30'), np.dtype(S+'30')) + assert_equal(promote_types('b', S+'1'), np.dtype(S+'4')) + assert_equal(promote_types('b', S+'30'), np.dtype(S+'30')) + assert_equal(promote_types('u1', S+'1'), np.dtype(S+'3')) + assert_equal(promote_types('u1', S+'30'), np.dtype(S+'30')) + assert_equal(promote_types('u2', S+'1'), np.dtype(S+'5')) + assert_equal(promote_types('u2', S+'30'), np.dtype(S+'30')) + assert_equal(promote_types('u4', S+'1'), np.dtype(S+'10')) + assert_equal(promote_types('u4', S+'30'), np.dtype(S+'30')) + assert_equal(promote_types('u8', S+'1'), np.dtype(S+'20')) + assert_equal(promote_types('u8', S+'30'), np.dtype(S+'30')) + # Promote with object: + assert_equal(promote_types('O', S+'30'), np.dtype('O')) + + @pytest.mark.parametrize(["dtype1", "dtype2"], + [[np.dtype("V6"), np.dtype("V10")], # mismatch shape + # Mismatching names: + [np.dtype([("name1", "i8")]), np.dtype([("name2", "i8")])], + ]) + def test_invalid_void_promotion(self, dtype1, dtype2): + with pytest.raises(TypeError): + np.promote_types(dtype1, dtype2) + + @pytest.mark.parametrize(["dtype1", "dtype2"], + [[np.dtype("V10"), np.dtype("V10")], + [np.dtype([("name1", "i8")]), + np.dtype([("name1", np.dtype("i8").newbyteorder())])], + [np.dtype("i8,i8"), np.dtype("i8,>i8")], + [np.dtype("i8,i8"), np.dtype("i4,i4")], + ]) + def test_valid_void_promotion(self, dtype1, dtype2): + assert np.promote_types(dtype1, dtype2) == dtype1 + + @pytest.mark.parametrize("dtype", + list(np.typecodes["All"]) + + ["i,i", "10i", "S3", "S100", "U3", "U100", rational]) + def test_promote_identical_types_metadata(self, dtype): + # The same type passed in twice to promote types always + # preserves metadata + metadata = {1: 1} + dtype = np.dtype(dtype, metadata=metadata) + + res = np.promote_types(dtype, dtype) + assert res.metadata == dtype.metadata + + # byte-swapping preserves and makes the dtype native: + dtype = dtype.newbyteorder() + if dtype.isnative: + # The type does not have byte swapping + return + + res = np.promote_types(dtype, dtype) + + # Metadata is (currently) generally lost on byte-swapping (except for + # unicode. + if dtype.char != "U": + assert res.metadata is None + else: + assert res.metadata == metadata + assert res.isnative + + @pytest.mark.slow + @pytest.mark.filterwarnings('ignore:Promotion of numbers:FutureWarning') + @pytest.mark.parametrize(["dtype1", "dtype2"], + itertools.product( + list(np.typecodes["All"]) + + ["i,i", "S3", "S100", "U3", "U100", rational], + repeat=2)) + def test_promote_types_metadata(self, dtype1, dtype2): + """Metadata handling in promotion does not appear formalized + right now in NumPy. This test should thus be considered to + document behaviour, rather than test the correct definition of it. + + This test is very ugly, it was useful for rewriting part of the + promotion, but probably should eventually be replaced/deleted + (i.e. when metadata handling in promotion is better defined). + """ + metadata1 = {1: 1} + metadata2 = {2: 2} + dtype1 = np.dtype(dtype1, metadata=metadata1) + dtype2 = np.dtype(dtype2, metadata=metadata2) + + try: + res = np.promote_types(dtype1, dtype2) + except TypeError: + # Promotion failed, this test only checks metadata + return + + if res.char not in "USV" or res.names is not None or res.shape != (): + # All except string dtypes (and unstructured void) lose metadata + # on promotion (unless both dtypes are identical). + # At some point structured ones did not, but were restrictive. + assert res.metadata is None + elif res == dtype1: + # If one result is the result, it is usually returned unchanged: + assert res is dtype1 + elif res == dtype2: + # dtype1 may have been cast to the same type/kind as dtype2. + # If the resulting dtype is identical we currently pick the cast + # version of dtype1, which lost the metadata: + if np.promote_types(dtype1, dtype2.kind) == dtype2: + res.metadata is None + else: + res.metadata == metadata2 + else: + assert res.metadata is None + + # Try again for byteswapped version + dtype1 = dtype1.newbyteorder() + assert dtype1.metadata == metadata1 + res_bs = np.promote_types(dtype1, dtype2) + assert res_bs == res + assert res_bs.metadata == res.metadata + + def test_can_cast(self): + assert_(np.can_cast(np.int32, np.int64)) + assert_(np.can_cast(np.float64, complex)) + assert_(not np.can_cast(complex, float)) + + assert_(np.can_cast('i8', 'f8')) + assert_(not np.can_cast('i8', 'f4')) + assert_(np.can_cast('i4', 'S11')) + + assert_(np.can_cast('i8', 'i8', 'no')) + assert_(not np.can_cast('i8', 'no')) + + assert_(np.can_cast('i8', 'equiv')) + assert_(not np.can_cast('i8', 'equiv')) + + assert_(np.can_cast('i8', 'safe')) + assert_(not np.can_cast('i4', 'safe')) + + assert_(np.can_cast('i4', 'same_kind')) + assert_(not np.can_cast('u4', 'same_kind')) + + assert_(np.can_cast('u4', 'unsafe')) + + assert_(np.can_cast('bool', 'S5')) + assert_(not np.can_cast('bool', 'S4')) + + assert_(np.can_cast('b', 'S4')) + assert_(not np.can_cast('b', 'S3')) + + assert_(np.can_cast('u1', 'S3')) + assert_(not np.can_cast('u1', 'S2')) + assert_(np.can_cast('u2', 'S5')) + assert_(not np.can_cast('u2', 'S4')) + assert_(np.can_cast('u4', 'S10')) + assert_(not np.can_cast('u4', 'S9')) + assert_(np.can_cast('u8', 'S20')) + assert_(not np.can_cast('u8', 'S19')) + + assert_(np.can_cast('i1', 'S4')) + assert_(not np.can_cast('i1', 'S3')) + assert_(np.can_cast('i2', 'S6')) + assert_(not np.can_cast('i2', 'S5')) + assert_(np.can_cast('i4', 'S11')) + assert_(not np.can_cast('i4', 'S10')) + assert_(np.can_cast('i8', 'S21')) + assert_(not np.can_cast('i8', 'S20')) + + assert_(np.can_cast('bool', 'S5')) + assert_(not np.can_cast('bool', 'S4')) + + assert_(np.can_cast('b', 'U4')) + assert_(not np.can_cast('b', 'U3')) + + assert_(np.can_cast('u1', 'U3')) + assert_(not np.can_cast('u1', 'U2')) + assert_(np.can_cast('u2', 'U5')) + assert_(not np.can_cast('u2', 'U4')) + assert_(np.can_cast('u4', 'U10')) + assert_(not np.can_cast('u4', 'U9')) + assert_(np.can_cast('u8', 'U20')) + assert_(not np.can_cast('u8', 'U19')) + + assert_(np.can_cast('i1', 'U4')) + assert_(not np.can_cast('i1', 'U3')) + assert_(np.can_cast('i2', 'U6')) + assert_(not np.can_cast('i2', 'U5')) + assert_(np.can_cast('i4', 'U11')) + assert_(not np.can_cast('i4', 'U10')) + assert_(np.can_cast('i8', 'U21')) + assert_(not np.can_cast('i8', 'U20')) + + assert_raises(TypeError, np.can_cast, 'i4', None) + assert_raises(TypeError, np.can_cast, None, 'i4') + + # Also test keyword arguments + assert_(np.can_cast(from_=np.int32, to=np.int64)) + + def test_can_cast_simple_to_structured(self): + # Non-structured can only be cast to structured in 'unsafe' mode. + assert_(not np.can_cast('i4', 'i4,i4')) + assert_(not np.can_cast('i4', 'i4,i2')) + assert_(np.can_cast('i4', 'i4,i4', casting='unsafe')) + assert_(np.can_cast('i4', 'i4,i2', casting='unsafe')) + # Even if there is just a single field which is OK. + assert_(not np.can_cast('i2', [('f1', 'i4')])) + assert_(not np.can_cast('i2', [('f1', 'i4')], casting='same_kind')) + assert_(np.can_cast('i2', [('f1', 'i4')], casting='unsafe')) + # It should be the same for recursive structured or subarrays. + assert_(not np.can_cast('i2', [('f1', 'i4,i4')])) + assert_(np.can_cast('i2', [('f1', 'i4,i4')], casting='unsafe')) + assert_(not np.can_cast('i2', [('f1', '(2,3)i4')])) + assert_(np.can_cast('i2', [('f1', '(2,3)i4')], casting='unsafe')) + + def test_can_cast_structured_to_simple(self): + # Need unsafe casting for structured to simple. + assert_(not np.can_cast([('f1', 'i4')], 'i4')) + assert_(np.can_cast([('f1', 'i4')], 'i4', casting='unsafe')) + assert_(np.can_cast([('f1', 'i4')], 'i2', casting='unsafe')) + # Since it is unclear what is being cast, multiple fields to + # single should not work even for unsafe casting. + assert_(not np.can_cast('i4,i4', 'i4', casting='unsafe')) + # But a single field inside a single field is OK. + assert_(not np.can_cast([('f1', [('x', 'i4')])], 'i4')) + assert_(np.can_cast([('f1', [('x', 'i4')])], 'i4', casting='unsafe')) + # And a subarray is fine too - it will just take the first element + # (arguably not very consistently; might also take the first field). + assert_(not np.can_cast([('f0', '(3,)i4')], 'i4')) + assert_(np.can_cast([('f0', '(3,)i4')], 'i4', casting='unsafe')) + # But a structured subarray with multiple fields should fail. + assert_(not np.can_cast([('f0', ('i4,i4'), (2,))], 'i4', + casting='unsafe')) + + def test_can_cast_values(self): + # gh-5917 + for dt in np.sctypes['int'] + np.sctypes['uint']: + ii = np.iinfo(dt) + assert_(np.can_cast(ii.min, dt)) + assert_(np.can_cast(ii.max, dt)) + assert_(not np.can_cast(ii.min - 1, dt)) + assert_(not np.can_cast(ii.max + 1, dt)) + + for dt in np.sctypes['float']: + fi = np.finfo(dt) + assert_(np.can_cast(fi.min, dt)) + assert_(np.can_cast(fi.max, dt)) + + +# Custom exception class to test exception propagation in fromiter +class NIterError(Exception): + pass + + +class TestFromiter: + def makegen(self): + return (x**2 for x in range(24)) + + def test_types(self): + ai32 = np.fromiter(self.makegen(), np.int32) + ai64 = np.fromiter(self.makegen(), np.int64) + af = np.fromiter(self.makegen(), float) + assert_(ai32.dtype == np.dtype(np.int32)) + assert_(ai64.dtype == np.dtype(np.int64)) + assert_(af.dtype == np.dtype(float)) + + def test_lengths(self): + expected = np.array(list(self.makegen())) + a = np.fromiter(self.makegen(), int) + a20 = np.fromiter(self.makegen(), int, 20) + assert_(len(a) == len(expected)) + assert_(len(a20) == 20) + assert_raises(ValueError, np.fromiter, + self.makegen(), int, len(expected) + 10) + + def test_values(self): + expected = np.array(list(self.makegen())) + a = np.fromiter(self.makegen(), int) + a20 = np.fromiter(self.makegen(), int, 20) + assert_(np.all(a == expected, axis=0)) + assert_(np.all(a20 == expected[:20], axis=0)) + + def load_data(self, n, eindex): + # Utility method for the issue 2592 tests. + # Raise an exception at the desired index in the iterator. + for e in range(n): + if e == eindex: + raise NIterError('error at index %s' % eindex) + yield e + + @pytest.mark.parametrize("dtype", [int, object]) + @pytest.mark.parametrize(["count", "error_index"], [(10, 5), (10, 9)]) + def test_2592(self, count, error_index, dtype): + # Test iteration exceptions are correctly raised. The data/generator + # has `count` elements but errors at `error_index` + iterable = self.load_data(count, error_index) + with pytest.raises(NIterError): + np.fromiter(iterable, dtype=dtype, count=count) + + @pytest.mark.parametrize("dtype", ["S", "S0", "V0", "U0"]) + def test_empty_not_structured(self, dtype): + # Note, "S0" could be allowed at some point, so long "S" (without + # any length) is rejected. + with pytest.raises(ValueError, match="Must specify length"): + np.fromiter([], dtype=dtype) + + @pytest.mark.parametrize(["dtype", "data"], + [("d", [1, 2, 3, 4, 5, 6, 7, 8, 9]), + ("O", [1, 2, 3, 4, 5, 6, 7, 8, 9]), + ("i,O", [(1, 2), (5, 4), (2, 3), (9, 8), (6, 7)]), + # subarray dtypes (important because their dimensions end up + # in the result arrays dimension: + ("2i", [(1, 2), (5, 4), (2, 3), (9, 8), (6, 7)]), + (np.dtype(("O", (2, 3))), + [((1, 2, 3), (3, 4, 5)), ((3, 2, 1), (5, 4, 3))])]) + @pytest.mark.parametrize("length_hint", [0, 1]) + def test_growth_and_complicated_dtypes(self, dtype, data, length_hint): + dtype = np.dtype(dtype) + + data = data * 100 # make sure we realloc a bit + + class MyIter: + # Class/example from gh-15789 + def __length_hint__(self): + # only required to be an estimate, this is legal + return length_hint # 0 or 1 + + def __iter__(self): + return iter(data) + + res = np.fromiter(MyIter(), dtype=dtype) + expected = np.array(data, dtype=dtype) + + assert_array_equal(res, expected) + + def test_empty_result(self): + class MyIter: + def __length_hint__(self): + return 10 + + def __iter__(self): + return iter([]) # actual iterator is empty. + + res = np.fromiter(MyIter(), dtype="d") + assert res.shape == (0,) + assert res.dtype == "d" + + def test_too_few_items(self): + msg = "iterator too short: Expected 10 but iterator had only 3 items." + with pytest.raises(ValueError, match=msg): + np.fromiter([1, 2, 3], count=10, dtype=int) + + def test_failed_itemsetting(self): + with pytest.raises(TypeError): + np.fromiter([1, None, 3], dtype=int) + + # The following manages to hit somewhat trickier code paths: + iterable = ((2, 3, 4) for i in range(5)) + with pytest.raises(ValueError): + np.fromiter(iterable, dtype=np.dtype((int, 2))) + +class TestNonzero: + def test_nonzero_trivial(self): + assert_equal(np.count_nonzero(np.array([])), 0) + assert_equal(np.count_nonzero(np.array([], dtype='?')), 0) + assert_equal(np.nonzero(np.array([])), ([],)) + + assert_equal(np.count_nonzero(np.array([0])), 0) + assert_equal(np.count_nonzero(np.array([0], dtype='?')), 0) + assert_equal(np.nonzero(np.array([0])), ([],)) + + assert_equal(np.count_nonzero(np.array([1])), 1) + assert_equal(np.count_nonzero(np.array([1], dtype='?')), 1) + assert_equal(np.nonzero(np.array([1])), ([0],)) + + def test_nonzero_zerod(self): + assert_equal(np.count_nonzero(np.array(0)), 0) + assert_equal(np.count_nonzero(np.array(0, dtype='?')), 0) + with assert_warns(DeprecationWarning): + assert_equal(np.nonzero(np.array(0)), ([],)) + + assert_equal(np.count_nonzero(np.array(1)), 1) + assert_equal(np.count_nonzero(np.array(1, dtype='?')), 1) + with assert_warns(DeprecationWarning): + assert_equal(np.nonzero(np.array(1)), ([0],)) + + def test_nonzero_onedim(self): + x = np.array([1, 0, 2, -1, 0, 0, 8]) + assert_equal(np.count_nonzero(x), 4) + assert_equal(np.count_nonzero(x), 4) + assert_equal(np.nonzero(x), ([0, 2, 3, 6],)) + + # x = np.array([(1, 2), (0, 0), (1, 1), (-1, 3), (0, 7)], + # dtype=[('a', 'i4'), ('b', 'i2')]) + x = np.array([(1, 2, -5, -3), (0, 0, 2, 7), (1, 1, 0, 1), (-1, 3, 1, 0), (0, 7, 0, 4)], + dtype=[('a', 'i4'), ('b', 'i2'), ('c', 'i1'), ('d', 'i8')]) + assert_equal(np.count_nonzero(x['a']), 3) + assert_equal(np.count_nonzero(x['b']), 4) + assert_equal(np.count_nonzero(x['c']), 3) + assert_equal(np.count_nonzero(x['d']), 4) + assert_equal(np.nonzero(x['a']), ([0, 2, 3],)) + assert_equal(np.nonzero(x['b']), ([0, 2, 3, 4],)) + + def test_nonzero_twodim(self): + x = np.array([[0, 1, 0], [2, 0, 3]]) + assert_equal(np.count_nonzero(x.astype('i1')), 3) + assert_equal(np.count_nonzero(x.astype('i2')), 3) + assert_equal(np.count_nonzero(x.astype('i4')), 3) + assert_equal(np.count_nonzero(x.astype('i8')), 3) + assert_equal(np.nonzero(x), ([0, 1, 1], [1, 0, 2])) + + x = np.eye(3) + assert_equal(np.count_nonzero(x.astype('i1')), 3) + assert_equal(np.count_nonzero(x.astype('i2')), 3) + assert_equal(np.count_nonzero(x.astype('i4')), 3) + assert_equal(np.count_nonzero(x.astype('i8')), 3) + assert_equal(np.nonzero(x), ([0, 1, 2], [0, 1, 2])) + + x = np.array([[(0, 1), (0, 0), (1, 11)], + [(1, 1), (1, 0), (0, 0)], + [(0, 0), (1, 5), (0, 1)]], dtype=[('a', 'f4'), ('b', 'u1')]) + assert_equal(np.count_nonzero(x['a']), 4) + assert_equal(np.count_nonzero(x['b']), 5) + assert_equal(np.nonzero(x['a']), ([0, 1, 1, 2], [2, 0, 1, 1])) + assert_equal(np.nonzero(x['b']), ([0, 0, 1, 2, 2], [0, 2, 0, 1, 2])) + + assert_(not x['a'].T.flags.aligned) + assert_equal(np.count_nonzero(x['a'].T), 4) + assert_equal(np.count_nonzero(x['b'].T), 5) + assert_equal(np.nonzero(x['a'].T), ([0, 1, 1, 2], [1, 1, 2, 0])) + assert_equal(np.nonzero(x['b'].T), ([0, 0, 1, 2, 2], [0, 1, 2, 0, 2])) + + def test_sparse(self): + # test special sparse condition boolean code path + for i in range(20): + c = np.zeros(200, dtype=bool) + c[i::20] = True + assert_equal(np.nonzero(c)[0], np.arange(i, 200 + i, 20)) + + c = np.zeros(400, dtype=bool) + c[10 + i:20 + i] = True + c[20 + i*2] = True + assert_equal(np.nonzero(c)[0], + np.concatenate((np.arange(10 + i, 20 + i), [20 + i*2]))) + + def test_return_type(self): + class C(np.ndarray): + pass + + for view in (C, np.ndarray): + for nd in range(1, 4): + shape = tuple(range(2, 2+nd)) + x = np.arange(np.prod(shape)).reshape(shape).view(view) + for nzx in (np.nonzero(x), x.nonzero()): + for nzx_i in nzx: + assert_(type(nzx_i) is np.ndarray) + assert_(nzx_i.flags.writeable) + + def test_count_nonzero_axis(self): + # Basic check of functionality + m = np.array([[0, 1, 7, 0, 0], [3, 0, 0, 2, 19]]) + + expected = np.array([1, 1, 1, 1, 1]) + assert_equal(np.count_nonzero(m, axis=0), expected) + + expected = np.array([2, 3]) + assert_equal(np.count_nonzero(m, axis=1), expected) + + assert_raises(ValueError, np.count_nonzero, m, axis=(1, 1)) + assert_raises(TypeError, np.count_nonzero, m, axis='foo') + assert_raises(np.AxisError, np.count_nonzero, m, axis=3) + assert_raises(TypeError, np.count_nonzero, + m, axis=np.array([[1], [2]])) + + def test_count_nonzero_axis_all_dtypes(self): + # More thorough test that the axis argument is respected + # for all dtypes and responds correctly when presented with + # either integer or tuple arguments for axis + msg = "Mismatch for dtype: %s" + + def assert_equal_w_dt(a, b, err_msg): + assert_equal(a.dtype, b.dtype, err_msg=err_msg) + assert_equal(a, b, err_msg=err_msg) + + for dt in np.typecodes['All']: + err_msg = msg % (np.dtype(dt).name,) + + if dt != 'V': + if dt != 'M': + m = np.zeros((3, 3), dtype=dt) + n = np.ones(1, dtype=dt) + + m[0, 0] = n[0] + m[1, 0] = n[0] + + else: # np.zeros doesn't work for np.datetime64 + m = np.array(['1970-01-01'] * 9) + m = m.reshape((3, 3)) + + m[0, 0] = '1970-01-12' + m[1, 0] = '1970-01-12' + m = m.astype(dt) + + expected = np.array([2, 0, 0], dtype=np.intp) + assert_equal_w_dt(np.count_nonzero(m, axis=0), + expected, err_msg=err_msg) + + expected = np.array([1, 1, 0], dtype=np.intp) + assert_equal_w_dt(np.count_nonzero(m, axis=1), + expected, err_msg=err_msg) + + expected = np.array(2) + assert_equal(np.count_nonzero(m, axis=(0, 1)), + expected, err_msg=err_msg) + assert_equal(np.count_nonzero(m, axis=None), + expected, err_msg=err_msg) + assert_equal(np.count_nonzero(m), + expected, err_msg=err_msg) + + if dt == 'V': + # There are no 'nonzero' objects for np.void, so the testing + # setup is slightly different for this dtype + m = np.array([np.void(1)] * 6).reshape((2, 3)) + + expected = np.array([0, 0, 0], dtype=np.intp) + assert_equal_w_dt(np.count_nonzero(m, axis=0), + expected, err_msg=err_msg) + + expected = np.array([0, 0], dtype=np.intp) + assert_equal_w_dt(np.count_nonzero(m, axis=1), + expected, err_msg=err_msg) + + expected = np.array(0) + assert_equal(np.count_nonzero(m, axis=(0, 1)), + expected, err_msg=err_msg) + assert_equal(np.count_nonzero(m, axis=None), + expected, err_msg=err_msg) + assert_equal(np.count_nonzero(m), + expected, err_msg=err_msg) + + def test_count_nonzero_axis_consistent(self): + # Check that the axis behaviour for valid axes in + # non-special cases is consistent (and therefore + # correct) by checking it against an integer array + # that is then casted to the generic object dtype + from itertools import combinations, permutations + + axis = (0, 1, 2, 3) + size = (5, 5, 5, 5) + msg = "Mismatch for axis: %s" + + rng = np.random.RandomState(1234) + m = rng.randint(-100, 100, size=size) + n = m.astype(object) + + for length in range(len(axis)): + for combo in combinations(axis, length): + for perm in permutations(combo): + assert_equal( + np.count_nonzero(m, axis=perm), + np.count_nonzero(n, axis=perm), + err_msg=msg % (perm,)) + + def test_countnonzero_axis_empty(self): + a = np.array([[0, 0, 1], [1, 0, 1]]) + assert_equal(np.count_nonzero(a, axis=()), a.astype(bool)) + + def test_countnonzero_keepdims(self): + a = np.array([[0, 0, 1, 0], + [0, 3, 5, 0], + [7, 9, 2, 0]]) + assert_equal(np.count_nonzero(a, axis=0, keepdims=True), + [[1, 2, 3, 0]]) + assert_equal(np.count_nonzero(a, axis=1, keepdims=True), + [[1], [2], [3]]) + assert_equal(np.count_nonzero(a, keepdims=True), + [[6]]) + + def test_array_method(self): + # Tests that the array method + # call to nonzero works + m = np.array([[1, 0, 0], [4, 0, 6]]) + tgt = [[0, 1, 1], [0, 0, 2]] + + assert_equal(m.nonzero(), tgt) + + def test_nonzero_invalid_object(self): + # gh-9295 + a = np.array([np.array([1, 2]), 3], dtype=object) + assert_raises(ValueError, np.nonzero, a) + + class BoolErrors: + def __bool__(self): + raise ValueError("Not allowed") + + assert_raises(ValueError, np.nonzero, np.array([BoolErrors()])) + + def test_nonzero_sideeffect_safety(self): + # gh-13631 + class FalseThenTrue: + _val = False + def __bool__(self): + try: + return self._val + finally: + self._val = True + + class TrueThenFalse: + _val = True + def __bool__(self): + try: + return self._val + finally: + self._val = False + + # result grows on the second pass + a = np.array([True, FalseThenTrue()]) + assert_raises(RuntimeError, np.nonzero, a) + + a = np.array([[True], [FalseThenTrue()]]) + assert_raises(RuntimeError, np.nonzero, a) + + # result shrinks on the second pass + a = np.array([False, TrueThenFalse()]) + assert_raises(RuntimeError, np.nonzero, a) + + a = np.array([[False], [TrueThenFalse()]]) + assert_raises(RuntimeError, np.nonzero, a) + + def test_nonzero_sideffects_structured_void(self): + # Checks that structured void does not mutate alignment flag of + # original array. + arr = np.zeros(5, dtype="i1,i8,i8") # `ones` may short-circuit + assert arr.flags.aligned # structs are considered "aligned" + assert not arr["f2"].flags.aligned + # make sure that nonzero/count_nonzero do not flip the flag: + np.nonzero(arr) + assert arr.flags.aligned + np.count_nonzero(arr) + assert arr.flags.aligned + + def test_nonzero_exception_safe(self): + # gh-13930 + + class ThrowsAfter: + def __init__(self, iters): + self.iters_left = iters + + def __bool__(self): + if self.iters_left == 0: + raise ValueError("called `iters` times") + + self.iters_left -= 1 + return True + + """ + Test that a ValueError is raised instead of a SystemError + + If the __bool__ function is called after the error state is set, + Python (cpython) will raise a SystemError. + """ + + # assert that an exception in first pass is handled correctly + a = np.array([ThrowsAfter(5)]*10) + assert_raises(ValueError, np.nonzero, a) + + # raise exception in second pass for 1-dimensional loop + a = np.array([ThrowsAfter(15)]*10) + assert_raises(ValueError, np.nonzero, a) + + # raise exception in second pass for n-dimensional loop + a = np.array([[ThrowsAfter(15)]]*10) + assert_raises(ValueError, np.nonzero, a) + + @pytest.mark.skipif(IS_WASM, reason="wasm doesn't have threads") + def test_structured_threadsafety(self): + # Nonzero (and some other functions) should be threadsafe for + # structured datatypes, see gh-15387. This test can behave randomly. + from concurrent.futures import ThreadPoolExecutor + + # Create a deeply nested dtype to make a failure more likely: + dt = np.dtype([("", "f8")]) + dt = np.dtype([("", dt)]) + dt = np.dtype([("", dt)] * 2) + # The array should be large enough to likely run into threading issues + arr = np.random.uniform(size=(5000, 4)).view(dt)[:, 0] + def func(arr): + arr.nonzero() + + tpe = ThreadPoolExecutor(max_workers=8) + futures = [tpe.submit(func, arr) for _ in range(10)] + for f in futures: + f.result() + + assert arr.dtype is dt + + +class TestIndex: + def test_boolean(self): + a = rand(3, 5, 8) + V = rand(5, 8) + g1 = randint(0, 5, size=15) + g2 = randint(0, 8, size=15) + V[g1, g2] = -V[g1, g2] + assert_((np.array([a[0][V > 0], a[1][V > 0], a[2][V > 0]]) == a[:, V > 0]).all()) + + def test_boolean_edgecase(self): + a = np.array([], dtype='int32') + b = np.array([], dtype='bool') + c = a[b] + assert_equal(c, []) + assert_equal(c.dtype, np.dtype('int32')) + + +class TestBinaryRepr: + def test_zero(self): + assert_equal(np.binary_repr(0), '0') + + def test_positive(self): + assert_equal(np.binary_repr(10), '1010') + assert_equal(np.binary_repr(12522), + '11000011101010') + assert_equal(np.binary_repr(10736848), + '101000111101010011010000') + + def test_negative(self): + assert_equal(np.binary_repr(-1), '-1') + assert_equal(np.binary_repr(-10), '-1010') + assert_equal(np.binary_repr(-12522), + '-11000011101010') + assert_equal(np.binary_repr(-10736848), + '-101000111101010011010000') + + def test_sufficient_width(self): + assert_equal(np.binary_repr(0, width=5), '00000') + assert_equal(np.binary_repr(10, width=7), '0001010') + assert_equal(np.binary_repr(-5, width=7), '1111011') + + def test_neg_width_boundaries(self): + # see gh-8670 + + # Ensure that the example in the issue does not + # break before proceeding to a more thorough test. + assert_equal(np.binary_repr(-128, width=8), '10000000') + + for width in range(1, 11): + num = -2**(width - 1) + exp = '1' + (width - 1) * '0' + assert_equal(np.binary_repr(num, width=width), exp) + + def test_large_neg_int64(self): + # See gh-14289. + assert_equal(np.binary_repr(np.int64(-2**62), width=64), + '11' + '0'*62) + + +class TestBaseRepr: + def test_base3(self): + assert_equal(np.base_repr(3**5, 3), '100000') + + def test_positive(self): + assert_equal(np.base_repr(12, 10), '12') + assert_equal(np.base_repr(12, 10, 4), '000012') + assert_equal(np.base_repr(12, 4), '30') + assert_equal(np.base_repr(3731624803700888, 36), '10QR0ROFCEW') + + def test_negative(self): + assert_equal(np.base_repr(-12, 10), '-12') + assert_equal(np.base_repr(-12, 10, 4), '-000012') + assert_equal(np.base_repr(-12, 4), '-30') + + def test_base_range(self): + with assert_raises(ValueError): + np.base_repr(1, 1) + with assert_raises(ValueError): + np.base_repr(1, 37) + + +class TestArrayComparisons: + def test_array_equal(self): + res = np.array_equal(np.array([1, 2]), np.array([1, 2])) + assert_(res) + assert_(type(res) is bool) + res = np.array_equal(np.array([1, 2]), np.array([1, 2, 3])) + assert_(not res) + assert_(type(res) is bool) + res = np.array_equal(np.array([1, 2]), np.array([3, 4])) + assert_(not res) + assert_(type(res) is bool) + res = np.array_equal(np.array([1, 2]), np.array([1, 3])) + assert_(not res) + assert_(type(res) is bool) + res = np.array_equal(np.array(['a'], dtype='S1'), np.array(['a'], dtype='S1')) + assert_(res) + assert_(type(res) is bool) + res = np.array_equal(np.array([('a', 1)], dtype='S1,u4'), + np.array([('a', 1)], dtype='S1,u4')) + assert_(res) + assert_(type(res) is bool) + + def test_array_equal_equal_nan(self): + # Test array_equal with equal_nan kwarg + a1 = np.array([1, 2, np.nan]) + a2 = np.array([1, np.nan, 2]) + a3 = np.array([1, 2, np.inf]) + + # equal_nan=False by default + assert_(not np.array_equal(a1, a1)) + assert_(np.array_equal(a1, a1, equal_nan=True)) + assert_(not np.array_equal(a1, a2, equal_nan=True)) + # nan's not conflated with inf's + assert_(not np.array_equal(a1, a3, equal_nan=True)) + # 0-D arrays + a = np.array(np.nan) + assert_(not np.array_equal(a, a)) + assert_(np.array_equal(a, a, equal_nan=True)) + # Non-float dtype - equal_nan should have no effect + a = np.array([1, 2, 3], dtype=int) + assert_(np.array_equal(a, a)) + assert_(np.array_equal(a, a, equal_nan=True)) + # Multi-dimensional array + a = np.array([[0, 1], [np.nan, 1]]) + assert_(not np.array_equal(a, a)) + assert_(np.array_equal(a, a, equal_nan=True)) + # Complex values + a, b = [np.array([1 + 1j])]*2 + a.real, b.imag = np.nan, np.nan + assert_(not np.array_equal(a, b, equal_nan=False)) + assert_(np.array_equal(a, b, equal_nan=True)) + + def test_none_compares_elementwise(self): + a = np.array([None, 1, None], dtype=object) + assert_equal(a == None, [True, False, True]) + assert_equal(a != None, [False, True, False]) + + a = np.ones(3) + assert_equal(a == None, [False, False, False]) + assert_equal(a != None, [True, True, True]) + + def test_array_equiv(self): + res = np.array_equiv(np.array([1, 2]), np.array([1, 2])) + assert_(res) + assert_(type(res) is bool) + res = np.array_equiv(np.array([1, 2]), np.array([1, 2, 3])) + assert_(not res) + assert_(type(res) is bool) + res = np.array_equiv(np.array([1, 2]), np.array([3, 4])) + assert_(not res) + assert_(type(res) is bool) + res = np.array_equiv(np.array([1, 2]), np.array([1, 3])) + assert_(not res) + assert_(type(res) is bool) + + res = np.array_equiv(np.array([1, 1]), np.array([1])) + assert_(res) + assert_(type(res) is bool) + res = np.array_equiv(np.array([1, 1]), np.array([[1], [1]])) + assert_(res) + assert_(type(res) is bool) + res = np.array_equiv(np.array([1, 2]), np.array([2])) + assert_(not res) + assert_(type(res) is bool) + res = np.array_equiv(np.array([1, 2]), np.array([[1], [2]])) + assert_(not res) + assert_(type(res) is bool) + res = np.array_equiv(np.array([1, 2]), np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])) + assert_(not res) + assert_(type(res) is bool) + + @pytest.mark.parametrize("dtype", ["V0", "V3", "V10"]) + def test_compare_unstructured_voids(self, dtype): + zeros = np.zeros(3, dtype=dtype) + + assert_array_equal(zeros, zeros) + assert not (zeros != zeros).any() + + if dtype == "V0": + # Can't test != of actually different data + return + + nonzeros = np.array([b"1", b"2", b"3"], dtype=dtype) + + assert not (zeros == nonzeros).any() + assert (zeros != nonzeros).all() + + +def assert_array_strict_equal(x, y): + assert_array_equal(x, y) + # Check flags, 32 bit arches typically don't provide 16 byte alignment + if ((x.dtype.alignment <= 8 or + np.intp().dtype.itemsize != 4) and + sys.platform != 'win32'): + assert_(x.flags == y.flags) + else: + assert_(x.flags.owndata == y.flags.owndata) + assert_(x.flags.writeable == y.flags.writeable) + assert_(x.flags.c_contiguous == y.flags.c_contiguous) + assert_(x.flags.f_contiguous == y.flags.f_contiguous) + assert_(x.flags.writebackifcopy == y.flags.writebackifcopy) + # check endianness + assert_(x.dtype.isnative == y.dtype.isnative) + + +class TestClip: + def setup_method(self): + self.nr = 5 + self.nc = 3 + + def fastclip(self, a, m, M, out=None, **kwargs): + return a.clip(m, M, out=out, **kwargs) + + def clip(self, a, m, M, out=None): + # use a.choose to verify fastclip result + selector = np.less(a, m) + 2*np.greater(a, M) + return selector.choose((a, m, M), out=out) + + # Handy functions + def _generate_data(self, n, m): + return randn(n, m) + + def _generate_data_complex(self, n, m): + return randn(n, m) + 1.j * rand(n, m) + + def _generate_flt_data(self, n, m): + return (randn(n, m)).astype(np.float32) + + def _neg_byteorder(self, a): + a = np.asarray(a) + if sys.byteorder == 'little': + a = a.astype(a.dtype.newbyteorder('>')) + else: + a = a.astype(a.dtype.newbyteorder('<')) + return a + + def _generate_non_native_data(self, n, m): + data = randn(n, m) + data = self._neg_byteorder(data) + assert_(not data.dtype.isnative) + return data + + def _generate_int_data(self, n, m): + return (10 * rand(n, m)).astype(np.int64) + + def _generate_int32_data(self, n, m): + return (10 * rand(n, m)).astype(np.int32) + + # Now the real test cases + + @pytest.mark.parametrize("dtype", '?bhilqpBHILQPefdgFDGO') + def test_ones_pathological(self, dtype): + # for preservation of behavior described in + # gh-12519; amin > amax behavior may still change + # in the future + arr = np.ones(10, dtype=dtype) + expected = np.zeros(10, dtype=dtype) + actual = np.clip(arr, 1, 0) + if dtype == 'O': + assert actual.tolist() == expected.tolist() + else: + assert_equal(actual, expected) + + def test_simple_double(self): + # Test native double input with scalar min/max. + a = self._generate_data(self.nr, self.nc) + m = 0.1 + M = 0.6 + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + def test_simple_int(self): + # Test native int input with scalar min/max. + a = self._generate_int_data(self.nr, self.nc) + a = a.astype(int) + m = -2 + M = 4 + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + def test_array_double(self): + # Test native double input with array min/max. + a = self._generate_data(self.nr, self.nc) + m = np.zeros(a.shape) + M = m + 0.5 + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + def test_simple_nonnative(self): + # Test non native double input with scalar min/max. + # Test native double input with non native double scalar min/max. + a = self._generate_non_native_data(self.nr, self.nc) + m = -0.5 + M = 0.6 + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_equal(ac, act) + + # Test native double input with non native double scalar min/max. + a = self._generate_data(self.nr, self.nc) + m = -0.5 + M = self._neg_byteorder(0.6) + assert_(not M.dtype.isnative) + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_equal(ac, act) + + def test_simple_complex(self): + # Test native complex input with native double scalar min/max. + # Test native input with complex double scalar min/max. + a = 3 * self._generate_data_complex(self.nr, self.nc) + m = -0.5 + M = 1. + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + # Test native input with complex double scalar min/max. + a = 3 * self._generate_data(self.nr, self.nc) + m = -0.5 + 1.j + M = 1. + 2.j + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + def test_clip_complex(self): + # Address Issue gh-5354 for clipping complex arrays + # Test native complex input without explicit min/max + # ie, either min=None or max=None + a = np.ones(10, dtype=complex) + m = a.min() + M = a.max() + am = self.fastclip(a, m, None) + aM = self.fastclip(a, None, M) + assert_array_strict_equal(am, a) + assert_array_strict_equal(aM, a) + + def test_clip_non_contig(self): + # Test clip for non contiguous native input and native scalar min/max. + a = self._generate_data(self.nr * 2, self.nc * 3) + a = a[::2, ::3] + assert_(not a.flags['F_CONTIGUOUS']) + assert_(not a.flags['C_CONTIGUOUS']) + ac = self.fastclip(a, -1.6, 1.7) + act = self.clip(a, -1.6, 1.7) + assert_array_strict_equal(ac, act) + + def test_simple_out(self): + # Test native double input with scalar min/max. + a = self._generate_data(self.nr, self.nc) + m = -0.5 + M = 0.6 + ac = np.zeros(a.shape) + act = np.zeros(a.shape) + self.fastclip(a, m, M, ac) + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + @pytest.mark.parametrize("casting", [None, "unsafe"]) + def test_simple_int32_inout(self, casting): + # Test native int32 input with double min/max and int32 out. + a = self._generate_int32_data(self.nr, self.nc) + m = np.float64(0) + M = np.float64(2) + ac = np.zeros(a.shape, dtype=np.int32) + act = ac.copy() + if casting is None: + with pytest.raises(TypeError): + self.fastclip(a, m, M, ac, casting=casting) + else: + # explicitly passing "unsafe" will silence warning + self.fastclip(a, m, M, ac, casting=casting) + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_simple_int64_out(self): + # Test native int32 input with int32 scalar min/max and int64 out. + a = self._generate_int32_data(self.nr, self.nc) + m = np.int32(-1) + M = np.int32(1) + ac = np.zeros(a.shape, dtype=np.int64) + act = ac.copy() + self.fastclip(a, m, M, ac) + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_simple_int64_inout(self): + # Test native int32 input with double array min/max and int32 out. + a = self._generate_int32_data(self.nr, self.nc) + m = np.zeros(a.shape, np.float64) + M = np.float64(1) + ac = np.zeros(a.shape, dtype=np.int32) + act = ac.copy() + self.fastclip(a, m, M, out=ac, casting="unsafe") + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_simple_int32_out(self): + # Test native double input with scalar min/max and int out. + a = self._generate_data(self.nr, self.nc) + m = -1.0 + M = 2.0 + ac = np.zeros(a.shape, dtype=np.int32) + act = ac.copy() + self.fastclip(a, m, M, out=ac, casting="unsafe") + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_simple_inplace_01(self): + # Test native double input with array min/max in-place. + a = self._generate_data(self.nr, self.nc) + ac = a.copy() + m = np.zeros(a.shape) + M = 1.0 + self.fastclip(a, m, M, a) + self.clip(a, m, M, ac) + assert_array_strict_equal(a, ac) + + def test_simple_inplace_02(self): + # Test native double input with scalar min/max in-place. + a = self._generate_data(self.nr, self.nc) + ac = a.copy() + m = -0.5 + M = 0.6 + self.fastclip(a, m, M, a) + self.clip(ac, m, M, ac) + assert_array_strict_equal(a, ac) + + def test_noncontig_inplace(self): + # Test non contiguous double input with double scalar min/max in-place. + a = self._generate_data(self.nr * 2, self.nc * 3) + a = a[::2, ::3] + assert_(not a.flags['F_CONTIGUOUS']) + assert_(not a.flags['C_CONTIGUOUS']) + ac = a.copy() + m = -0.5 + M = 0.6 + self.fastclip(a, m, M, a) + self.clip(ac, m, M, ac) + assert_array_equal(a, ac) + + def test_type_cast_01(self): + # Test native double input with scalar min/max. + a = self._generate_data(self.nr, self.nc) + m = -0.5 + M = 0.6 + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + def test_type_cast_02(self): + # Test native int32 input with int32 scalar min/max. + a = self._generate_int_data(self.nr, self.nc) + a = a.astype(np.int32) + m = -2 + M = 4 + ac = self.fastclip(a, m, M) + act = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + def test_type_cast_03(self): + # Test native int32 input with float64 scalar min/max. + a = self._generate_int32_data(self.nr, self.nc) + m = -2 + M = 4 + ac = self.fastclip(a, np.float64(m), np.float64(M)) + act = self.clip(a, np.float64(m), np.float64(M)) + assert_array_strict_equal(ac, act) + + def test_type_cast_04(self): + # Test native int32 input with float32 scalar min/max. + a = self._generate_int32_data(self.nr, self.nc) + m = np.float32(-2) + M = np.float32(4) + act = self.fastclip(a, m, M) + ac = self.clip(a, m, M) + assert_array_strict_equal(ac, act) + + def test_type_cast_05(self): + # Test native int32 with double arrays min/max. + a = self._generate_int_data(self.nr, self.nc) + m = -0.5 + M = 1. + ac = self.fastclip(a, m * np.zeros(a.shape), M) + act = self.clip(a, m * np.zeros(a.shape), M) + assert_array_strict_equal(ac, act) + + def test_type_cast_06(self): + # Test native with NON native scalar min/max. + a = self._generate_data(self.nr, self.nc) + m = 0.5 + m_s = self._neg_byteorder(m) + M = 1. + act = self.clip(a, m_s, M) + ac = self.fastclip(a, m_s, M) + assert_array_strict_equal(ac, act) + + def test_type_cast_07(self): + # Test NON native with native array min/max. + a = self._generate_data(self.nr, self.nc) + m = -0.5 * np.ones(a.shape) + M = 1. + a_s = self._neg_byteorder(a) + assert_(not a_s.dtype.isnative) + act = a_s.clip(m, M) + ac = self.fastclip(a_s, m, M) + assert_array_strict_equal(ac, act) + + def test_type_cast_08(self): + # Test NON native with native scalar min/max. + a = self._generate_data(self.nr, self.nc) + m = -0.5 + M = 1. + a_s = self._neg_byteorder(a) + assert_(not a_s.dtype.isnative) + ac = self.fastclip(a_s, m, M) + act = a_s.clip(m, M) + assert_array_strict_equal(ac, act) + + def test_type_cast_09(self): + # Test native with NON native array min/max. + a = self._generate_data(self.nr, self.nc) + m = -0.5 * np.ones(a.shape) + M = 1. + m_s = self._neg_byteorder(m) + assert_(not m_s.dtype.isnative) + ac = self.fastclip(a, m_s, M) + act = self.clip(a, m_s, M) + assert_array_strict_equal(ac, act) + + def test_type_cast_10(self): + # Test native int32 with float min/max and float out for output argument. + a = self._generate_int_data(self.nr, self.nc) + b = np.zeros(a.shape, dtype=np.float32) + m = np.float32(-0.5) + M = np.float32(1) + act = self.clip(a, m, M, out=b) + ac = self.fastclip(a, m, M, out=b) + assert_array_strict_equal(ac, act) + + def test_type_cast_11(self): + # Test non native with native scalar, min/max, out non native + a = self._generate_non_native_data(self.nr, self.nc) + b = a.copy() + b = b.astype(b.dtype.newbyteorder('>')) + bt = b.copy() + m = -0.5 + M = 1. + self.fastclip(a, m, M, out=b) + self.clip(a, m, M, out=bt) + assert_array_strict_equal(b, bt) + + def test_type_cast_12(self): + # Test native int32 input and min/max and float out + a = self._generate_int_data(self.nr, self.nc) + b = np.zeros(a.shape, dtype=np.float32) + m = np.int32(0) + M = np.int32(1) + act = self.clip(a, m, M, out=b) + ac = self.fastclip(a, m, M, out=b) + assert_array_strict_equal(ac, act) + + def test_clip_with_out_simple(self): + # Test native double input with scalar min/max + a = self._generate_data(self.nr, self.nc) + m = -0.5 + M = 0.6 + ac = np.zeros(a.shape) + act = np.zeros(a.shape) + self.fastclip(a, m, M, ac) + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_clip_with_out_simple2(self): + # Test native int32 input with double min/max and int32 out + a = self._generate_int32_data(self.nr, self.nc) + m = np.float64(0) + M = np.float64(2) + ac = np.zeros(a.shape, dtype=np.int32) + act = ac.copy() + self.fastclip(a, m, M, out=ac, casting="unsafe") + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_clip_with_out_simple_int32(self): + # Test native int32 input with int32 scalar min/max and int64 out + a = self._generate_int32_data(self.nr, self.nc) + m = np.int32(-1) + M = np.int32(1) + ac = np.zeros(a.shape, dtype=np.int64) + act = ac.copy() + self.fastclip(a, m, M, ac) + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_clip_with_out_array_int32(self): + # Test native int32 input with double array min/max and int32 out + a = self._generate_int32_data(self.nr, self.nc) + m = np.zeros(a.shape, np.float64) + M = np.float64(1) + ac = np.zeros(a.shape, dtype=np.int32) + act = ac.copy() + self.fastclip(a, m, M, out=ac, casting="unsafe") + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_clip_with_out_array_outint32(self): + # Test native double input with scalar min/max and int out + a = self._generate_data(self.nr, self.nc) + m = -1.0 + M = 2.0 + ac = np.zeros(a.shape, dtype=np.int32) + act = ac.copy() + self.fastclip(a, m, M, out=ac, casting="unsafe") + self.clip(a, m, M, act) + assert_array_strict_equal(ac, act) + + def test_clip_with_out_transposed(self): + # Test that the out argument works when transposed + a = np.arange(16).reshape(4, 4) + out = np.empty_like(a).T + a.clip(4, 10, out=out) + expected = self.clip(a, 4, 10) + assert_array_equal(out, expected) + + def test_clip_with_out_memory_overlap(self): + # Test that the out argument works when it has memory overlap + a = np.arange(16).reshape(4, 4) + ac = a.copy() + a[:-1].clip(4, 10, out=a[1:]) + expected = self.clip(ac[:-1], 4, 10) + assert_array_equal(a[1:], expected) + + def test_clip_inplace_array(self): + # Test native double input with array min/max + a = self._generate_data(self.nr, self.nc) + ac = a.copy() + m = np.zeros(a.shape) + M = 1.0 + self.fastclip(a, m, M, a) + self.clip(a, m, M, ac) + assert_array_strict_equal(a, ac) + + def test_clip_inplace_simple(self): + # Test native double input with scalar min/max + a = self._generate_data(self.nr, self.nc) + ac = a.copy() + m = -0.5 + M = 0.6 + self.fastclip(a, m, M, a) + self.clip(a, m, M, ac) + assert_array_strict_equal(a, ac) + + def test_clip_func_takes_out(self): + # Ensure that the clip() function takes an out=argument. + a = self._generate_data(self.nr, self.nc) + ac = a.copy() + m = -0.5 + M = 0.6 + a2 = np.clip(a, m, M, out=a) + self.clip(a, m, M, ac) + assert_array_strict_equal(a2, ac) + assert_(a2 is a) + + def test_clip_nan(self): + d = np.arange(7.) + assert_equal(d.clip(min=np.nan), np.nan) + assert_equal(d.clip(max=np.nan), np.nan) + assert_equal(d.clip(min=np.nan, max=np.nan), np.nan) + assert_equal(d.clip(min=-2, max=np.nan), np.nan) + assert_equal(d.clip(min=np.nan, max=10), np.nan) + + def test_object_clip(self): + a = np.arange(10, dtype=object) + actual = np.clip(a, 1, 5) + expected = np.array([1, 1, 2, 3, 4, 5, 5, 5, 5, 5]) + assert actual.tolist() == expected.tolist() + + def test_clip_all_none(self): + a = np.arange(10, dtype=object) + with assert_raises_regex(ValueError, 'max or min'): + np.clip(a, None, None) + + def test_clip_invalid_casting(self): + a = np.arange(10, dtype=object) + with assert_raises_regex(ValueError, + 'casting must be one of'): + self.fastclip(a, 1, 8, casting="garbage") + + @pytest.mark.parametrize("amin, amax", [ + # two scalars + (1, 0), + # mix scalar and array + (1, np.zeros(10)), + # two arrays + (np.ones(10), np.zeros(10)), + ]) + def test_clip_value_min_max_flip(self, amin, amax): + a = np.arange(10, dtype=np.int64) + # requirement from ufunc_docstrings.py + expected = np.minimum(np.maximum(a, amin), amax) + actual = np.clip(a, amin, amax) + assert_equal(actual, expected) + + @pytest.mark.parametrize("arr, amin, amax, exp", [ + # for a bug in npy_ObjectClip, based on a + # case produced by hypothesis + (np.zeros(10, dtype=np.int64), + 0, + -2**64+1, + np.full(10, -2**64+1, dtype=object)), + # for bugs in NPY_TIMEDELTA_MAX, based on a case + # produced by hypothesis + (np.zeros(10, dtype='m8') - 1, + 0, + 0, + np.zeros(10, dtype='m8')), + ]) + def test_clip_problem_cases(self, arr, amin, amax, exp): + actual = np.clip(arr, amin, amax) + assert_equal(actual, exp) + + @pytest.mark.parametrize("arr, amin, amax", [ + # problematic scalar nan case from hypothesis + (np.zeros(10, dtype=np.int64), + np.array(np.nan), + np.zeros(10, dtype=np.int32)), + ]) + def test_clip_scalar_nan_propagation(self, arr, amin, amax): + # enforcement of scalar nan propagation for comparisons + # called through clip() + expected = np.minimum(np.maximum(arr, amin), amax) + actual = np.clip(arr, amin, amax) + assert_equal(actual, expected) + + @pytest.mark.xfail(reason="propagation doesn't match spec") + @pytest.mark.parametrize("arr, amin, amax", [ + (np.array([1] * 10, dtype='m8'), + np.timedelta64('NaT'), + np.zeros(10, dtype=np.int32)), + ]) + @pytest.mark.filterwarnings("ignore::DeprecationWarning") + def test_NaT_propagation(self, arr, amin, amax): + # NOTE: the expected function spec doesn't + # propagate NaT, but clip() now does + expected = np.minimum(np.maximum(arr, amin), amax) + actual = np.clip(arr, amin, amax) + assert_equal(actual, expected) + + @given( + data=st.data(), + arr=hynp.arrays( + dtype=hynp.integer_dtypes() | hynp.floating_dtypes(), + shape=hynp.array_shapes() + ) + ) + def test_clip_property(self, data, arr): + """A property-based test using Hypothesis. + + This aims for maximum generality: it could in principle generate *any* + valid inputs to np.clip, and in practice generates much more varied + inputs than human testers come up with. + + Because many of the inputs have tricky dependencies - compatible dtypes + and mutually-broadcastable shapes - we use `st.data()` strategy draw + values *inside* the test function, from strategies we construct based + on previous values. An alternative would be to define a custom strategy + with `@st.composite`, but until we have duplicated code inline is fine. + + That accounts for most of the function; the actual test is just three + lines to calculate and compare actual vs expected results! + """ + numeric_dtypes = hynp.integer_dtypes() | hynp.floating_dtypes() + # Generate shapes for the bounds which can be broadcast with each other + # and with the base shape. Below, we might decide to use scalar bounds, + # but it's clearer to generate these shapes unconditionally in advance. + in_shapes, result_shape = data.draw( + hynp.mutually_broadcastable_shapes( + num_shapes=2, base_shape=arr.shape + ) + ) + # Scalar `nan` is deprecated due to the differing behaviour it shows. + s = numeric_dtypes.flatmap( + lambda x: hynp.from_dtype(x, allow_nan=False)) + amin = data.draw(s | hynp.arrays(dtype=numeric_dtypes, + shape=in_shapes[0], elements={"allow_nan": False})) + amax = data.draw(s | hynp.arrays(dtype=numeric_dtypes, + shape=in_shapes[1], elements={"allow_nan": False})) + + # Then calculate our result and expected result and check that they're + # equal! See gh-12519 and gh-19457 for discussion deciding on this + # property and the result_type argument. + result = np.clip(arr, amin, amax) + t = np.result_type(arr, amin, amax) + expected = np.minimum(amax, np.maximum(arr, amin, dtype=t), dtype=t) + assert result.dtype == t + assert_array_equal(result, expected) + + +class TestAllclose: + rtol = 1e-5 + atol = 1e-8 + + def setup_method(self): + self.olderr = np.seterr(invalid='ignore') + + def teardown_method(self): + np.seterr(**self.olderr) + + def tst_allclose(self, x, y): + assert_(np.allclose(x, y), "%s and %s not close" % (x, y)) + + def tst_not_allclose(self, x, y): + assert_(not np.allclose(x, y), "%s and %s shouldn't be close" % (x, y)) + + def test_ip_allclose(self): + # Parametric test factory. + arr = np.array([100, 1000]) + aran = np.arange(125).reshape((5, 5, 5)) + + atol = self.atol + rtol = self.rtol + + data = [([1, 0], [1, 0]), + ([atol], [0]), + ([1], [1+rtol+atol]), + (arr, arr + arr*rtol), + (arr, arr + arr*rtol + atol*2), + (aran, aran + aran*rtol), + (np.inf, np.inf), + (np.inf, [np.inf])] + + for (x, y) in data: + self.tst_allclose(x, y) + + def test_ip_not_allclose(self): + # Parametric test factory. + aran = np.arange(125).reshape((5, 5, 5)) + + atol = self.atol + rtol = self.rtol + + data = [([np.inf, 0], [1, np.inf]), + ([np.inf, 0], [1, 0]), + ([np.inf, np.inf], [1, np.inf]), + ([np.inf, np.inf], [1, 0]), + ([-np.inf, 0], [np.inf, 0]), + ([np.nan, 0], [np.nan, 0]), + ([atol*2], [0]), + ([1], [1+rtol+atol*2]), + (aran, aran + aran*atol + atol*2), + (np.array([np.inf, 1]), np.array([0, np.inf]))] + + for (x, y) in data: + self.tst_not_allclose(x, y) + + def test_no_parameter_modification(self): + x = np.array([np.inf, 1]) + y = np.array([0, np.inf]) + np.allclose(x, y) + assert_array_equal(x, np.array([np.inf, 1])) + assert_array_equal(y, np.array([0, np.inf])) + + def test_min_int(self): + # Could make problems because of abs(min_int) == min_int + min_int = np.iinfo(np.int_).min + a = np.array([min_int], dtype=np.int_) + assert_(np.allclose(a, a)) + + def test_equalnan(self): + x = np.array([1.0, np.nan]) + assert_(np.allclose(x, x, equal_nan=True)) + + def test_return_class_is_ndarray(self): + # Issue gh-6475 + # Check that allclose does not preserve subtypes + class Foo(np.ndarray): + def __new__(cls, *args, **kwargs): + return np.array(*args, **kwargs).view(cls) + + a = Foo([1]) + assert_(type(np.allclose(a, a)) is bool) + + +class TestIsclose: + rtol = 1e-5 + atol = 1e-8 + + def _setup(self): + atol = self.atol + rtol = self.rtol + arr = np.array([100, 1000]) + aran = np.arange(125).reshape((5, 5, 5)) + + self.all_close_tests = [ + ([1, 0], [1, 0]), + ([atol], [0]), + ([1], [1 + rtol + atol]), + (arr, arr + arr*rtol), + (arr, arr + arr*rtol + atol), + (aran, aran + aran*rtol), + (np.inf, np.inf), + (np.inf, [np.inf]), + ([np.inf, -np.inf], [np.inf, -np.inf]), + ] + self.none_close_tests = [ + ([np.inf, 0], [1, np.inf]), + ([np.inf, -np.inf], [1, 0]), + ([np.inf, np.inf], [1, -np.inf]), + ([np.inf, np.inf], [1, 0]), + ([np.nan, 0], [np.nan, -np.inf]), + ([atol*2], [0]), + ([1], [1 + rtol + atol*2]), + (aran, aran + rtol*1.1*aran + atol*1.1), + (np.array([np.inf, 1]), np.array([0, np.inf])), + ] + self.some_close_tests = [ + ([np.inf, 0], [np.inf, atol*2]), + ([atol, 1, 1e6*(1 + 2*rtol) + atol], [0, np.nan, 1e6]), + (np.arange(3), [0, 1, 2.1]), + (np.nan, [np.nan, np.nan, np.nan]), + ([0], [atol, np.inf, -np.inf, np.nan]), + (0, [atol, np.inf, -np.inf, np.nan]), + ] + self.some_close_results = [ + [True, False], + [True, False, False], + [True, True, False], + [False, False, False], + [True, False, False, False], + [True, False, False, False], + ] + + def test_ip_isclose(self): + self._setup() + tests = self.some_close_tests + results = self.some_close_results + for (x, y), result in zip(tests, results): + assert_array_equal(np.isclose(x, y), result) + + def tst_all_isclose(self, x, y): + assert_(np.all(np.isclose(x, y)), "%s and %s not close" % (x, y)) + + def tst_none_isclose(self, x, y): + msg = "%s and %s shouldn't be close" + assert_(not np.any(np.isclose(x, y)), msg % (x, y)) + + def tst_isclose_allclose(self, x, y): + msg = "isclose.all() and allclose aren't same for %s and %s" + msg2 = "isclose and allclose aren't same for %s and %s" + if np.isscalar(x) and np.isscalar(y): + assert_(np.isclose(x, y) == np.allclose(x, y), msg=msg2 % (x, y)) + else: + assert_array_equal(np.isclose(x, y).all(), np.allclose(x, y), msg % (x, y)) + + def test_ip_all_isclose(self): + self._setup() + for (x, y) in self.all_close_tests: + self.tst_all_isclose(x, y) + + def test_ip_none_isclose(self): + self._setup() + for (x, y) in self.none_close_tests: + self.tst_none_isclose(x, y) + + def test_ip_isclose_allclose(self): + self._setup() + tests = (self.all_close_tests + self.none_close_tests + + self.some_close_tests) + for (x, y) in tests: + self.tst_isclose_allclose(x, y) + + def test_equal_nan(self): + assert_array_equal(np.isclose(np.nan, np.nan, equal_nan=True), [True]) + arr = np.array([1.0, np.nan]) + assert_array_equal(np.isclose(arr, arr, equal_nan=True), [True, True]) + + def test_masked_arrays(self): + # Make sure to test the output type when arguments are interchanged. + + x = np.ma.masked_where([True, True, False], np.arange(3)) + assert_(type(x) is type(np.isclose(2, x))) + assert_(type(x) is type(np.isclose(x, 2))) + + x = np.ma.masked_where([True, True, False], [np.nan, np.inf, np.nan]) + assert_(type(x) is type(np.isclose(np.inf, x))) + assert_(type(x) is type(np.isclose(x, np.inf))) + + x = np.ma.masked_where([True, True, False], [np.nan, np.nan, np.nan]) + y = np.isclose(np.nan, x, equal_nan=True) + assert_(type(x) is type(y)) + # Ensure that the mask isn't modified... + assert_array_equal([True, True, False], y.mask) + y = np.isclose(x, np.nan, equal_nan=True) + assert_(type(x) is type(y)) + # Ensure that the mask isn't modified... + assert_array_equal([True, True, False], y.mask) + + x = np.ma.masked_where([True, True, False], [np.nan, np.nan, np.nan]) + y = np.isclose(x, x, equal_nan=True) + assert_(type(x) is type(y)) + # Ensure that the mask isn't modified... + assert_array_equal([True, True, False], y.mask) + + def test_scalar_return(self): + assert_(np.isscalar(np.isclose(1, 1))) + + def test_no_parameter_modification(self): + x = np.array([np.inf, 1]) + y = np.array([0, np.inf]) + np.isclose(x, y) + assert_array_equal(x, np.array([np.inf, 1])) + assert_array_equal(y, np.array([0, np.inf])) + + def test_non_finite_scalar(self): + # GH7014, when two scalars are compared the output should also be a + # scalar + assert_(np.isclose(np.inf, -np.inf) is np.False_) + assert_(np.isclose(0, np.inf) is np.False_) + assert_(type(np.isclose(0, np.inf)) is np.bool_) + + def test_timedelta(self): + # Allclose currently works for timedelta64 as long as `atol` is + # an integer or also a timedelta64 + a = np.array([[1, 2, 3, "NaT"]], dtype="m8[ns]") + assert np.isclose(a, a, atol=0, equal_nan=True).all() + assert np.isclose(a, a, atol=np.timedelta64(1, "ns"), equal_nan=True).all() + assert np.allclose(a, a, atol=0, equal_nan=True) + assert np.allclose(a, a, atol=np.timedelta64(1, "ns"), equal_nan=True) + + +class TestStdVar: + def setup_method(self): + self.A = np.array([1, -1, 1, -1]) + self.real_var = 1 + + def test_basic(self): + assert_almost_equal(np.var(self.A), self.real_var) + assert_almost_equal(np.std(self.A)**2, self.real_var) + + def test_scalars(self): + assert_equal(np.var(1), 0) + assert_equal(np.std(1), 0) + + def test_ddof1(self): + assert_almost_equal(np.var(self.A, ddof=1), + self.real_var * len(self.A) / (len(self.A) - 1)) + assert_almost_equal(np.std(self.A, ddof=1)**2, + self.real_var*len(self.A) / (len(self.A) - 1)) + + def test_ddof2(self): + assert_almost_equal(np.var(self.A, ddof=2), + self.real_var * len(self.A) / (len(self.A) - 2)) + assert_almost_equal(np.std(self.A, ddof=2)**2, + self.real_var * len(self.A) / (len(self.A) - 2)) + + def test_out_scalar(self): + d = np.arange(10) + out = np.array(0.) + r = np.std(d, out=out) + assert_(r is out) + assert_array_equal(r, out) + r = np.var(d, out=out) + assert_(r is out) + assert_array_equal(r, out) + r = np.mean(d, out=out) + assert_(r is out) + assert_array_equal(r, out) + + +class TestStdVarComplex: + def test_basic(self): + A = np.array([1, 1.j, -1, -1.j]) + real_var = 1 + assert_almost_equal(np.var(A), real_var) + assert_almost_equal(np.std(A)**2, real_var) + + def test_scalars(self): + assert_equal(np.var(1j), 0) + assert_equal(np.std(1j), 0) + + +class TestCreationFuncs: + # Test ones, zeros, empty and full. + + def setup_method(self): + dtypes = {np.dtype(tp) for tp in itertools.chain(*np.sctypes.values())} + # void, bytes, str + variable_sized = {tp for tp in dtypes if tp.str.endswith('0')} + self.dtypes = sorted(dtypes - variable_sized | + {np.dtype(tp.str.replace("0", str(i))) + for tp in variable_sized for i in range(1, 10)}, + key=lambda dtype: dtype.str) + self.orders = {'C': 'c_contiguous', 'F': 'f_contiguous'} + self.ndims = 10 + + def check_function(self, func, fill_value=None): + par = ((0, 1, 2), + range(self.ndims), + self.orders, + self.dtypes) + fill_kwarg = {} + if fill_value is not None: + fill_kwarg = {'fill_value': fill_value} + + for size, ndims, order, dtype in itertools.product(*par): + shape = ndims * [size] + + # do not fill void type + if fill_kwarg and dtype.str.startswith('|V'): + continue + + arr = func(shape, order=order, dtype=dtype, + **fill_kwarg) + + assert_equal(arr.dtype, dtype) + assert_(getattr(arr.flags, self.orders[order])) + + if fill_value is not None: + if dtype.str.startswith('|S'): + val = str(fill_value) + else: + val = fill_value + assert_equal(arr, dtype.type(val)) + + def test_zeros(self): + self.check_function(np.zeros) + + def test_ones(self): + self.check_function(np.ones) + + def test_empty(self): + self.check_function(np.empty) + + def test_full(self): + self.check_function(np.full, 0) + self.check_function(np.full, 1) + + @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts") + def test_for_reference_leak(self): + # Make sure we have an object for reference + dim = 1 + beg = sys.getrefcount(dim) + np.zeros([dim]*10) + assert_(sys.getrefcount(dim) == beg) + np.ones([dim]*10) + assert_(sys.getrefcount(dim) == beg) + np.empty([dim]*10) + assert_(sys.getrefcount(dim) == beg) + np.full([dim]*10, 0) + assert_(sys.getrefcount(dim) == beg) + + +class TestLikeFuncs: + '''Test ones_like, zeros_like, empty_like and full_like''' + + def setup_method(self): + self.data = [ + # Array scalars + (np.array(3.), None), + (np.array(3), 'f8'), + # 1D arrays + (np.arange(6, dtype='f4'), None), + (np.arange(6), 'c16'), + # 2D C-layout arrays + (np.arange(6).reshape(2, 3), None), + (np.arange(6).reshape(3, 2), 'i1'), + # 2D F-layout arrays + (np.arange(6).reshape((2, 3), order='F'), None), + (np.arange(6).reshape((3, 2), order='F'), 'i1'), + # 3D C-layout arrays + (np.arange(24).reshape(2, 3, 4), None), + (np.arange(24).reshape(4, 3, 2), 'f4'), + # 3D F-layout arrays + (np.arange(24).reshape((2, 3, 4), order='F'), None), + (np.arange(24).reshape((4, 3, 2), order='F'), 'f4'), + # 3D non-C/F-layout arrays + (np.arange(24).reshape(2, 3, 4).swapaxes(0, 1), None), + (np.arange(24).reshape(4, 3, 2).swapaxes(0, 1), '?'), + ] + self.shapes = [(), (5,), (5,6,), (5,6,7,)] + + def compare_array_value(self, dz, value, fill_value): + if value is not None: + if fill_value: + # Conversion is close to what np.full_like uses + # but we may want to convert directly in the future + # which may result in errors (where this does not). + z = np.array(value).astype(dz.dtype) + assert_(np.all(dz == z)) + else: + assert_(np.all(dz == value)) + + def check_like_function(self, like_function, value, fill_value=False): + if fill_value: + fill_kwarg = {'fill_value': value} + else: + fill_kwarg = {} + for d, dtype in self.data: + # default (K) order, dtype + dz = like_function(d, dtype=dtype, **fill_kwarg) + assert_equal(dz.shape, d.shape) + assert_equal(np.array(dz.strides)*d.dtype.itemsize, + np.array(d.strides)*dz.dtype.itemsize) + assert_equal(d.flags.c_contiguous, dz.flags.c_contiguous) + assert_equal(d.flags.f_contiguous, dz.flags.f_contiguous) + if dtype is None: + assert_equal(dz.dtype, d.dtype) + else: + assert_equal(dz.dtype, np.dtype(dtype)) + self.compare_array_value(dz, value, fill_value) + + # C order, default dtype + dz = like_function(d, order='C', dtype=dtype, **fill_kwarg) + assert_equal(dz.shape, d.shape) + assert_(dz.flags.c_contiguous) + if dtype is None: + assert_equal(dz.dtype, d.dtype) + else: + assert_equal(dz.dtype, np.dtype(dtype)) + self.compare_array_value(dz, value, fill_value) + + # F order, default dtype + dz = like_function(d, order='F', dtype=dtype, **fill_kwarg) + assert_equal(dz.shape, d.shape) + assert_(dz.flags.f_contiguous) + if dtype is None: + assert_equal(dz.dtype, d.dtype) + else: + assert_equal(dz.dtype, np.dtype(dtype)) + self.compare_array_value(dz, value, fill_value) + + # A order + dz = like_function(d, order='A', dtype=dtype, **fill_kwarg) + assert_equal(dz.shape, d.shape) + if d.flags.f_contiguous: + assert_(dz.flags.f_contiguous) + else: + assert_(dz.flags.c_contiguous) + if dtype is None: + assert_equal(dz.dtype, d.dtype) + else: + assert_equal(dz.dtype, np.dtype(dtype)) + self.compare_array_value(dz, value, fill_value) + + # Test the 'shape' parameter + for s in self.shapes: + for o in 'CFA': + sz = like_function(d, dtype=dtype, shape=s, order=o, + **fill_kwarg) + assert_equal(sz.shape, s) + if dtype is None: + assert_equal(sz.dtype, d.dtype) + else: + assert_equal(sz.dtype, np.dtype(dtype)) + if o == 'C' or (o == 'A' and d.flags.c_contiguous): + assert_(sz.flags.c_contiguous) + elif o == 'F' or (o == 'A' and d.flags.f_contiguous): + assert_(sz.flags.f_contiguous) + self.compare_array_value(sz, value, fill_value) + + if (d.ndim != len(s)): + assert_equal(np.argsort(like_function(d, dtype=dtype, + shape=s, order='K', + **fill_kwarg).strides), + np.argsort(np.empty(s, dtype=dtype, + order='C').strides)) + else: + assert_equal(np.argsort(like_function(d, dtype=dtype, + shape=s, order='K', + **fill_kwarg).strides), + np.argsort(d.strides)) + + # Test the 'subok' parameter + class MyNDArray(np.ndarray): + pass + + a = np.array([[1, 2], [3, 4]]).view(MyNDArray) + + b = like_function(a, **fill_kwarg) + assert_(type(b) is MyNDArray) + + b = like_function(a, subok=False, **fill_kwarg) + assert_(type(b) is not MyNDArray) + + def test_ones_like(self): + self.check_like_function(np.ones_like, 1) + + def test_zeros_like(self): + self.check_like_function(np.zeros_like, 0) + + def test_empty_like(self): + self.check_like_function(np.empty_like, None) + + def test_filled_like(self): + self.check_like_function(np.full_like, 0, True) + self.check_like_function(np.full_like, 1, True) + self.check_like_function(np.full_like, 1000, True) + self.check_like_function(np.full_like, 123.456, True) + # Inf to integer casts cause invalid-value errors: ignore them. + with np.errstate(invalid="ignore"): + self.check_like_function(np.full_like, np.inf, True) + + @pytest.mark.parametrize('likefunc', [np.empty_like, np.full_like, + np.zeros_like, np.ones_like]) + @pytest.mark.parametrize('dtype', [str, bytes]) + def test_dtype_str_bytes(self, likefunc, dtype): + # Regression test for gh-19860 + a = np.arange(16).reshape(2, 8) + b = a[:, ::2] # Ensure b is not contiguous. + kwargs = {'fill_value': ''} if likefunc == np.full_like else {} + result = likefunc(b, dtype=dtype, **kwargs) + if dtype == str: + assert result.strides == (16, 4) + else: + # dtype is bytes + assert result.strides == (4, 1) + + +class TestCorrelate: + def _setup(self, dt): + self.x = np.array([1, 2, 3, 4, 5], dtype=dt) + self.xs = np.arange(1, 20)[::3] + self.y = np.array([-1, -2, -3], dtype=dt) + self.z1 = np.array([-3., -8., -14., -20., -26., -14., -5.], dtype=dt) + self.z1_4 = np.array([-2., -5., -8., -11., -14., -5.], dtype=dt) + self.z1r = np.array([-15., -22., -22., -16., -10., -4., -1.], dtype=dt) + self.z2 = np.array([-5., -14., -26., -20., -14., -8., -3.], dtype=dt) + self.z2r = np.array([-1., -4., -10., -16., -22., -22., -15.], dtype=dt) + self.zs = np.array([-3., -14., -30., -48., -66., -84., + -102., -54., -19.], dtype=dt) + + def test_float(self): + self._setup(float) + z = np.correlate(self.x, self.y, 'full') + assert_array_almost_equal(z, self.z1) + z = np.correlate(self.x, self.y[:-1], 'full') + assert_array_almost_equal(z, self.z1_4) + z = np.correlate(self.y, self.x, 'full') + assert_array_almost_equal(z, self.z2) + z = np.correlate(self.x[::-1], self.y, 'full') + assert_array_almost_equal(z, self.z1r) + z = np.correlate(self.y, self.x[::-1], 'full') + assert_array_almost_equal(z, self.z2r) + z = np.correlate(self.xs, self.y, 'full') + assert_array_almost_equal(z, self.zs) + + def test_object(self): + self._setup(Decimal) + z = np.correlate(self.x, self.y, 'full') + assert_array_almost_equal(z, self.z1) + z = np.correlate(self.y, self.x, 'full') + assert_array_almost_equal(z, self.z2) + + def test_no_overwrite(self): + d = np.ones(100) + k = np.ones(3) + np.correlate(d, k) + assert_array_equal(d, np.ones(100)) + assert_array_equal(k, np.ones(3)) + + def test_complex(self): + x = np.array([1, 2, 3, 4+1j], dtype=complex) + y = np.array([-1, -2j, 3+1j], dtype=complex) + r_z = np.array([3-1j, 6, 8+1j, 11+5j, -5+8j, -4-1j], dtype=complex) + r_z = r_z[::-1].conjugate() + z = np.correlate(y, x, mode='full') + assert_array_almost_equal(z, r_z) + + def test_zero_size(self): + with pytest.raises(ValueError): + np.correlate(np.array([]), np.ones(1000), mode='full') + with pytest.raises(ValueError): + np.correlate(np.ones(1000), np.array([]), mode='full') + + def test_mode(self): + d = np.ones(100) + k = np.ones(3) + default_mode = np.correlate(d, k, mode='valid') + with assert_warns(DeprecationWarning): + valid_mode = np.correlate(d, k, mode='v') + assert_array_equal(valid_mode, default_mode) + # integer mode + with assert_raises(ValueError): + np.correlate(d, k, mode=-1) + assert_array_equal(np.correlate(d, k, mode=0), valid_mode) + # illegal arguments + with assert_raises(TypeError): + np.correlate(d, k, mode=None) + + +class TestConvolve: + def test_object(self): + d = [1.] * 100 + k = [1.] * 3 + assert_array_almost_equal(np.convolve(d, k)[2:-2], np.full(98, 3)) + + def test_no_overwrite(self): + d = np.ones(100) + k = np.ones(3) + np.convolve(d, k) + assert_array_equal(d, np.ones(100)) + assert_array_equal(k, np.ones(3)) + + def test_mode(self): + d = np.ones(100) + k = np.ones(3) + default_mode = np.convolve(d, k, mode='full') + with assert_warns(DeprecationWarning): + full_mode = np.convolve(d, k, mode='f') + assert_array_equal(full_mode, default_mode) + # integer mode + with assert_raises(ValueError): + np.convolve(d, k, mode=-1) + assert_array_equal(np.convolve(d, k, mode=2), full_mode) + # illegal arguments + with assert_raises(TypeError): + np.convolve(d, k, mode=None) + + +class TestArgwhere: + + @pytest.mark.parametrize('nd', [0, 1, 2]) + def test_nd(self, nd): + # get an nd array with multiple elements in every dimension + x = np.empty((2,)*nd, bool) + + # none + x[...] = False + assert_equal(np.argwhere(x).shape, (0, nd)) + + # only one + x[...] = False + x.flat[0] = True + assert_equal(np.argwhere(x).shape, (1, nd)) + + # all but one + x[...] = True + x.flat[0] = False + assert_equal(np.argwhere(x).shape, (x.size - 1, nd)) + + # all + x[...] = True + assert_equal(np.argwhere(x).shape, (x.size, nd)) + + def test_2D(self): + x = np.arange(6).reshape((2, 3)) + assert_array_equal(np.argwhere(x > 1), + [[0, 2], + [1, 0], + [1, 1], + [1, 2]]) + + def test_list(self): + assert_equal(np.argwhere([4, 0, 2, 1, 3]), [[0], [2], [3], [4]]) + + +class TestStringFunction: + + def test_set_string_function(self): + a = np.array([1]) + np.set_string_function(lambda x: "FOO", repr=True) + assert_equal(repr(a), "FOO") + np.set_string_function(None, repr=True) + assert_equal(repr(a), "array([1])") + + np.set_string_function(lambda x: "FOO", repr=False) + assert_equal(str(a), "FOO") + np.set_string_function(None, repr=False) + assert_equal(str(a), "[1]") + + +class TestRoll: + def test_roll1d(self): + x = np.arange(10) + xr = np.roll(x, 2) + assert_equal(xr, np.array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7])) + + def test_roll2d(self): + x2 = np.reshape(np.arange(10), (2, 5)) + x2r = np.roll(x2, 1) + assert_equal(x2r, np.array([[9, 0, 1, 2, 3], [4, 5, 6, 7, 8]])) + + x2r = np.roll(x2, 1, axis=0) + assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]])) + + x2r = np.roll(x2, 1, axis=1) + assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]])) + + # Roll multiple axes at once. + x2r = np.roll(x2, 1, axis=(0, 1)) + assert_equal(x2r, np.array([[9, 5, 6, 7, 8], [4, 0, 1, 2, 3]])) + + x2r = np.roll(x2, (1, 0), axis=(0, 1)) + assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]])) + + x2r = np.roll(x2, (-1, 0), axis=(0, 1)) + assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]])) + + x2r = np.roll(x2, (0, 1), axis=(0, 1)) + assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]])) + + x2r = np.roll(x2, (0, -1), axis=(0, 1)) + assert_equal(x2r, np.array([[1, 2, 3, 4, 0], [6, 7, 8, 9, 5]])) + + x2r = np.roll(x2, (1, 1), axis=(0, 1)) + assert_equal(x2r, np.array([[9, 5, 6, 7, 8], [4, 0, 1, 2, 3]])) + + x2r = np.roll(x2, (-1, -1), axis=(0, 1)) + assert_equal(x2r, np.array([[6, 7, 8, 9, 5], [1, 2, 3, 4, 0]])) + + # Roll the same axis multiple times. + x2r = np.roll(x2, 1, axis=(0, 0)) + assert_equal(x2r, np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]])) + + x2r = np.roll(x2, 1, axis=(1, 1)) + assert_equal(x2r, np.array([[3, 4, 0, 1, 2], [8, 9, 5, 6, 7]])) + + # Roll more than one turn in either direction. + x2r = np.roll(x2, 6, axis=1) + assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]])) + + x2r = np.roll(x2, -4, axis=1) + assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]])) + + def test_roll_empty(self): + x = np.array([]) + assert_equal(np.roll(x, 1), np.array([])) + + +class TestRollaxis: + + # expected shape indexed by (axis, start) for array of + # shape (1, 2, 3, 4) + tgtshape = {(0, 0): (1, 2, 3, 4), (0, 1): (1, 2, 3, 4), + (0, 2): (2, 1, 3, 4), (0, 3): (2, 3, 1, 4), + (0, 4): (2, 3, 4, 1), + (1, 0): (2, 1, 3, 4), (1, 1): (1, 2, 3, 4), + (1, 2): (1, 2, 3, 4), (1, 3): (1, 3, 2, 4), + (1, 4): (1, 3, 4, 2), + (2, 0): (3, 1, 2, 4), (2, 1): (1, 3, 2, 4), + (2, 2): (1, 2, 3, 4), (2, 3): (1, 2, 3, 4), + (2, 4): (1, 2, 4, 3), + (3, 0): (4, 1, 2, 3), (3, 1): (1, 4, 2, 3), + (3, 2): (1, 2, 4, 3), (3, 3): (1, 2, 3, 4), + (3, 4): (1, 2, 3, 4)} + + def test_exceptions(self): + a = np.arange(1*2*3*4).reshape(1, 2, 3, 4) + assert_raises(np.AxisError, np.rollaxis, a, -5, 0) + assert_raises(np.AxisError, np.rollaxis, a, 0, -5) + assert_raises(np.AxisError, np.rollaxis, a, 4, 0) + assert_raises(np.AxisError, np.rollaxis, a, 0, 5) + + def test_results(self): + a = np.arange(1*2*3*4).reshape(1, 2, 3, 4).copy() + aind = np.indices(a.shape) + assert_(a.flags['OWNDATA']) + for (i, j) in self.tgtshape: + # positive axis, positive start + res = np.rollaxis(a, axis=i, start=j) + i0, i1, i2, i3 = aind[np.array(res.shape) - 1] + assert_(np.all(res[i0, i1, i2, i3] == a)) + assert_(res.shape == self.tgtshape[(i, j)], str((i,j))) + assert_(not res.flags['OWNDATA']) + + # negative axis, positive start + ip = i + 1 + res = np.rollaxis(a, axis=-ip, start=j) + i0, i1, i2, i3 = aind[np.array(res.shape) - 1] + assert_(np.all(res[i0, i1, i2, i3] == a)) + assert_(res.shape == self.tgtshape[(4 - ip, j)]) + assert_(not res.flags['OWNDATA']) + + # positive axis, negative start + jp = j + 1 if j < 4 else j + res = np.rollaxis(a, axis=i, start=-jp) + i0, i1, i2, i3 = aind[np.array(res.shape) - 1] + assert_(np.all(res[i0, i1, i2, i3] == a)) + assert_(res.shape == self.tgtshape[(i, 4 - jp)]) + assert_(not res.flags['OWNDATA']) + + # negative axis, negative start + ip = i + 1 + jp = j + 1 if j < 4 else j + res = np.rollaxis(a, axis=-ip, start=-jp) + i0, i1, i2, i3 = aind[np.array(res.shape) - 1] + assert_(np.all(res[i0, i1, i2, i3] == a)) + assert_(res.shape == self.tgtshape[(4 - ip, 4 - jp)]) + assert_(not res.flags['OWNDATA']) + + +class TestMoveaxis: + def test_move_to_end(self): + x = np.random.randn(5, 6, 7) + for source, expected in [(0, (6, 7, 5)), + (1, (5, 7, 6)), + (2, (5, 6, 7)), + (-1, (5, 6, 7))]: + actual = np.moveaxis(x, source, -1).shape + assert_(actual, expected) + + def test_move_new_position(self): + x = np.random.randn(1, 2, 3, 4) + for source, destination, expected in [ + (0, 1, (2, 1, 3, 4)), + (1, 2, (1, 3, 2, 4)), + (1, -1, (1, 3, 4, 2)), + ]: + actual = np.moveaxis(x, source, destination).shape + assert_(actual, expected) + + def test_preserve_order(self): + x = np.zeros((1, 2, 3, 4)) + for source, destination in [ + (0, 0), + (3, -1), + (-1, 3), + ([0, -1], [0, -1]), + ([2, 0], [2, 0]), + (range(4), range(4)), + ]: + actual = np.moveaxis(x, source, destination).shape + assert_(actual, (1, 2, 3, 4)) + + def test_move_multiples(self): + x = np.zeros((0, 1, 2, 3)) + for source, destination, expected in [ + ([0, 1], [2, 3], (2, 3, 0, 1)), + ([2, 3], [0, 1], (2, 3, 0, 1)), + ([0, 1, 2], [2, 3, 0], (2, 3, 0, 1)), + ([3, 0], [1, 0], (0, 3, 1, 2)), + ([0, 3], [0, 1], (0, 3, 1, 2)), + ]: + actual = np.moveaxis(x, source, destination).shape + assert_(actual, expected) + + def test_errors(self): + x = np.random.randn(1, 2, 3) + assert_raises_regex(np.AxisError, 'source.*out of bounds', + np.moveaxis, x, 3, 0) + assert_raises_regex(np.AxisError, 'source.*out of bounds', + np.moveaxis, x, -4, 0) + assert_raises_regex(np.AxisError, 'destination.*out of bounds', + np.moveaxis, x, 0, 5) + assert_raises_regex(ValueError, 'repeated axis in `source`', + np.moveaxis, x, [0, 0], [0, 1]) + assert_raises_regex(ValueError, 'repeated axis in `destination`', + np.moveaxis, x, [0, 1], [1, 1]) + assert_raises_regex(ValueError, 'must have the same number', + np.moveaxis, x, 0, [0, 1]) + assert_raises_regex(ValueError, 'must have the same number', + np.moveaxis, x, [0, 1], [0]) + + def test_array_likes(self): + x = np.ma.zeros((1, 2, 3)) + result = np.moveaxis(x, 0, 0) + assert_(x.shape, result.shape) + assert_(isinstance(result, np.ma.MaskedArray)) + + x = [1, 2, 3] + result = np.moveaxis(x, 0, 0) + assert_(x, list(result)) + assert_(isinstance(result, np.ndarray)) + + +class TestCross: + def test_2x2(self): + u = [1, 2] + v = [3, 4] + z = -2 + cp = np.cross(u, v) + assert_equal(cp, z) + cp = np.cross(v, u) + assert_equal(cp, -z) + + def test_2x3(self): + u = [1, 2] + v = [3, 4, 5] + z = np.array([10, -5, -2]) + cp = np.cross(u, v) + assert_equal(cp, z) + cp = np.cross(v, u) + assert_equal(cp, -z) + + def test_3x3(self): + u = [1, 2, 3] + v = [4, 5, 6] + z = np.array([-3, 6, -3]) + cp = np.cross(u, v) + assert_equal(cp, z) + cp = np.cross(v, u) + assert_equal(cp, -z) + + def test_broadcasting(self): + # Ticket #2624 (Trac #2032) + u = np.tile([1, 2], (11, 1)) + v = np.tile([3, 4], (11, 1)) + z = -2 + assert_equal(np.cross(u, v), z) + assert_equal(np.cross(v, u), -z) + assert_equal(np.cross(u, u), 0) + + u = np.tile([1, 2], (11, 1)).T + v = np.tile([3, 4, 5], (11, 1)) + z = np.tile([10, -5, -2], (11, 1)) + assert_equal(np.cross(u, v, axisa=0), z) + assert_equal(np.cross(v, u.T), -z) + assert_equal(np.cross(v, v), 0) + + u = np.tile([1, 2, 3], (11, 1)).T + v = np.tile([3, 4], (11, 1)).T + z = np.tile([-12, 9, -2], (11, 1)) + assert_equal(np.cross(u, v, axisa=0, axisb=0), z) + assert_equal(np.cross(v.T, u.T), -z) + assert_equal(np.cross(u.T, u.T), 0) + + u = np.tile([1, 2, 3], (5, 1)) + v = np.tile([4, 5, 6], (5, 1)).T + z = np.tile([-3, 6, -3], (5, 1)) + assert_equal(np.cross(u, v, axisb=0), z) + assert_equal(np.cross(v.T, u), -z) + assert_equal(np.cross(u, u), 0) + + def test_broadcasting_shapes(self): + u = np.ones((2, 1, 3)) + v = np.ones((5, 3)) + assert_equal(np.cross(u, v).shape, (2, 5, 3)) + u = np.ones((10, 3, 5)) + v = np.ones((2, 5)) + assert_equal(np.cross(u, v, axisa=1, axisb=0).shape, (10, 5, 3)) + assert_raises(np.AxisError, np.cross, u, v, axisa=1, axisb=2) + assert_raises(np.AxisError, np.cross, u, v, axisa=3, axisb=0) + u = np.ones((10, 3, 5, 7)) + v = np.ones((5, 7, 2)) + assert_equal(np.cross(u, v, axisa=1, axisc=2).shape, (10, 5, 3, 7)) + assert_raises(np.AxisError, np.cross, u, v, axisa=-5, axisb=2) + assert_raises(np.AxisError, np.cross, u, v, axisa=1, axisb=-4) + # gh-5885 + u = np.ones((3, 4, 2)) + for axisc in range(-2, 2): + assert_equal(np.cross(u, u, axisc=axisc).shape, (3, 4)) + + def test_uint8_int32_mixed_dtypes(self): + # regression test for gh-19138 + u = np.array([[195, 8, 9]], np.uint8) + v = np.array([250, 166, 68], np.int32) + z = np.array([[950, 11010, -30370]], dtype=np.int32) + assert_equal(np.cross(v, u), z) + assert_equal(np.cross(u, v), -z) + + +def test_outer_out_param(): + arr1 = np.ones((5,)) + arr2 = np.ones((2,)) + arr3 = np.linspace(-2, 2, 5) + out1 = np.ndarray(shape=(5,5)) + out2 = np.ndarray(shape=(2, 5)) + res1 = np.outer(arr1, arr3, out1) + assert_equal(res1, out1) + assert_equal(np.outer(arr2, arr3, out2), out2) + + +class TestIndices: + + def test_simple(self): + [x, y] = np.indices((4, 3)) + assert_array_equal(x, np.array([[0, 0, 0], + [1, 1, 1], + [2, 2, 2], + [3, 3, 3]])) + assert_array_equal(y, np.array([[0, 1, 2], + [0, 1, 2], + [0, 1, 2], + [0, 1, 2]])) + + def test_single_input(self): + [x] = np.indices((4,)) + assert_array_equal(x, np.array([0, 1, 2, 3])) + + [x] = np.indices((4,), sparse=True) + assert_array_equal(x, np.array([0, 1, 2, 3])) + + def test_scalar_input(self): + assert_array_equal([], np.indices(())) + assert_array_equal([], np.indices((), sparse=True)) + assert_array_equal([[]], np.indices((0,))) + assert_array_equal([[]], np.indices((0,), sparse=True)) + + def test_sparse(self): + [x, y] = np.indices((4,3), sparse=True) + assert_array_equal(x, np.array([[0], [1], [2], [3]])) + assert_array_equal(y, np.array([[0, 1, 2]])) + + @pytest.mark.parametrize("dtype", [np.int32, np.int64, np.float32, np.float64]) + @pytest.mark.parametrize("dims", [(), (0,), (4, 3)]) + def test_return_type(self, dtype, dims): + inds = np.indices(dims, dtype=dtype) + assert_(inds.dtype == dtype) + + for arr in np.indices(dims, dtype=dtype, sparse=True): + assert_(arr.dtype == dtype) + + +class TestRequire: + flag_names = ['C', 'C_CONTIGUOUS', 'CONTIGUOUS', + 'F', 'F_CONTIGUOUS', 'FORTRAN', + 'A', 'ALIGNED', + 'W', 'WRITEABLE', + 'O', 'OWNDATA'] + + def generate_all_false(self, dtype): + arr = np.zeros((2, 2), [('junk', 'i1'), ('a', dtype)]) + arr.setflags(write=False) + a = arr['a'] + assert_(not a.flags['C']) + assert_(not a.flags['F']) + assert_(not a.flags['O']) + assert_(not a.flags['W']) + assert_(not a.flags['A']) + return a + + def set_and_check_flag(self, flag, dtype, arr): + if dtype is None: + dtype = arr.dtype + b = np.require(arr, dtype, [flag]) + assert_(b.flags[flag]) + assert_(b.dtype == dtype) + + # a further call to np.require ought to return the same array + # unless OWNDATA is specified. + c = np.require(b, None, [flag]) + if flag[0] != 'O': + assert_(c is b) + else: + assert_(c.flags[flag]) + + def test_require_each(self): + + id = ['f8', 'i4'] + fd = [None, 'f8', 'c16'] + for idtype, fdtype, flag in itertools.product(id, fd, self.flag_names): + a = self.generate_all_false(idtype) + self.set_and_check_flag(flag, fdtype, a) + + def test_unknown_requirement(self): + a = self.generate_all_false('f8') + assert_raises(KeyError, np.require, a, None, 'Q') + + def test_non_array_input(self): + a = np.require([1, 2, 3, 4], 'i4', ['C', 'A', 'O']) + assert_(a.flags['O']) + assert_(a.flags['C']) + assert_(a.flags['A']) + assert_(a.dtype == 'i4') + assert_equal(a, [1, 2, 3, 4]) + + def test_C_and_F_simul(self): + a = self.generate_all_false('f8') + assert_raises(ValueError, np.require, a, None, ['C', 'F']) + + def test_ensure_array(self): + class ArraySubclass(np.ndarray): + pass + + a = ArraySubclass((2, 2)) + b = np.require(a, None, ['E']) + assert_(type(b) is np.ndarray) + + def test_preserve_subtype(self): + class ArraySubclass(np.ndarray): + pass + + for flag in self.flag_names: + a = ArraySubclass((2, 2)) + self.set_and_check_flag(flag, None, a) + + +class TestBroadcast: + def test_broadcast_in_args(self): + # gh-5881 + arrs = [np.empty((6, 7)), np.empty((5, 6, 1)), np.empty((7,)), + np.empty((5, 1, 7))] + mits = [np.broadcast(*arrs), + np.broadcast(np.broadcast(*arrs[:0]), np.broadcast(*arrs[0:])), + np.broadcast(np.broadcast(*arrs[:1]), np.broadcast(*arrs[1:])), + np.broadcast(np.broadcast(*arrs[:2]), np.broadcast(*arrs[2:])), + np.broadcast(arrs[0], np.broadcast(*arrs[1:-1]), arrs[-1])] + for mit in mits: + assert_equal(mit.shape, (5, 6, 7)) + assert_equal(mit.ndim, 3) + assert_equal(mit.nd, 3) + assert_equal(mit.numiter, 4) + for a, ia in zip(arrs, mit.iters): + assert_(a is ia.base) + + def test_broadcast_single_arg(self): + # gh-6899 + arrs = [np.empty((5, 6, 7))] + mit = np.broadcast(*arrs) + assert_equal(mit.shape, (5, 6, 7)) + assert_equal(mit.ndim, 3) + assert_equal(mit.nd, 3) + assert_equal(mit.numiter, 1) + assert_(arrs[0] is mit.iters[0].base) + + def test_number_of_arguments(self): + arr = np.empty((5,)) + for j in range(35): + arrs = [arr] * j + if j > 32: + assert_raises(ValueError, np.broadcast, *arrs) + else: + mit = np.broadcast(*arrs) + assert_equal(mit.numiter, j) + + def test_broadcast_error_kwargs(self): + #gh-13455 + arrs = [np.empty((5, 6, 7))] + mit = np.broadcast(*arrs) + mit2 = np.broadcast(*arrs, **{}) + assert_equal(mit.shape, mit2.shape) + assert_equal(mit.ndim, mit2.ndim) + assert_equal(mit.nd, mit2.nd) + assert_equal(mit.numiter, mit2.numiter) + assert_(mit.iters[0].base is mit2.iters[0].base) + + assert_raises(ValueError, np.broadcast, 1, **{'x': 1}) + + def test_shape_mismatch_error_message(self): + with pytest.raises(ValueError, match=r"arg 0 with shape \(1, 3\) and " + r"arg 2 with shape \(2,\)"): + np.broadcast([[1, 2, 3]], [[4], [5]], [6, 7]) + + +class TestKeepdims: + + class sub_array(np.ndarray): + def sum(self, axis=None, dtype=None, out=None): + return np.ndarray.sum(self, axis, dtype, out, keepdims=True) + + def test_raise(self): + sub_class = self.sub_array + x = np.arange(30).view(sub_class) + assert_raises(TypeError, np.sum, x, keepdims=True) + + +class TestTensordot: + + def test_zero_dimension(self): + # Test resolution to issue #5663 + a = np.ndarray((3,0)) + b = np.ndarray((0,4)) + td = np.tensordot(a, b, (1, 0)) + assert_array_equal(td, np.dot(a, b)) + assert_array_equal(td, np.einsum('ij,jk', a, b)) + + def test_zero_dimensional(self): + # gh-12130 + arr_0d = np.array(1) + ret = np.tensordot(arr_0d, arr_0d, ([], [])) # contracting no axes is well defined + assert_array_equal(ret, arr_0d) diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_scalarbuffer.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_scalarbuffer.py new file mode 100644 index 0000000000000000000000000000000000000000..31b0494cf00b76d718e97d984e0de81f63e15017 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_scalarbuffer.py @@ -0,0 +1,153 @@ +""" +Test scalar buffer interface adheres to PEP 3118 +""" +import numpy as np +from numpy.core._rational_tests import rational +from numpy.core._multiarray_tests import get_buffer_info +import pytest + +from numpy.testing import assert_, assert_equal, assert_raises + +# PEP3118 format strings for native (standard alignment and byteorder) types +scalars_and_codes = [ + (np.bool_, '?'), + (np.byte, 'b'), + (np.short, 'h'), + (np.intc, 'i'), + (np.int_, 'l'), + (np.longlong, 'q'), + (np.ubyte, 'B'), + (np.ushort, 'H'), + (np.uintc, 'I'), + (np.uint, 'L'), + (np.ulonglong, 'Q'), + (np.half, 'e'), + (np.single, 'f'), + (np.double, 'd'), + (np.longdouble, 'g'), + (np.csingle, 'Zf'), + (np.cdouble, 'Zd'), + (np.clongdouble, 'Zg'), +] +scalars_only, codes_only = zip(*scalars_and_codes) + + +class TestScalarPEP3118: + + @pytest.mark.parametrize('scalar', scalars_only, ids=codes_only) + def test_scalar_match_array(self, scalar): + x = scalar() + a = np.array([], dtype=np.dtype(scalar)) + mv_x = memoryview(x) + mv_a = memoryview(a) + assert_equal(mv_x.format, mv_a.format) + + @pytest.mark.parametrize('scalar', scalars_only, ids=codes_only) + def test_scalar_dim(self, scalar): + x = scalar() + mv_x = memoryview(x) + assert_equal(mv_x.itemsize, np.dtype(scalar).itemsize) + assert_equal(mv_x.ndim, 0) + assert_equal(mv_x.shape, ()) + assert_equal(mv_x.strides, ()) + assert_equal(mv_x.suboffsets, ()) + + @pytest.mark.parametrize('scalar, code', scalars_and_codes, ids=codes_only) + def test_scalar_code_and_properties(self, scalar, code): + x = scalar() + expected = dict(strides=(), itemsize=x.dtype.itemsize, ndim=0, + shape=(), format=code, readonly=True) + + mv_x = memoryview(x) + assert self._as_dict(mv_x) == expected + + @pytest.mark.parametrize('scalar', scalars_only, ids=codes_only) + def test_scalar_buffers_readonly(self, scalar): + x = scalar() + with pytest.raises(BufferError, match="scalar buffer is readonly"): + get_buffer_info(x, ["WRITABLE"]) + + def test_void_scalar_structured_data(self): + dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) + x = np.array(('ndarray_scalar', (1.2, 3.0)), dtype=dt)[()] + assert_(isinstance(x, np.void)) + mv_x = memoryview(x) + expected_size = 16 * np.dtype((np.str_, 1)).itemsize + expected_size += 2 * np.dtype(np.float64).itemsize + assert_equal(mv_x.itemsize, expected_size) + assert_equal(mv_x.ndim, 0) + assert_equal(mv_x.shape, ()) + assert_equal(mv_x.strides, ()) + assert_equal(mv_x.suboffsets, ()) + + # check scalar format string against ndarray format string + a = np.array([('Sarah', (8.0, 7.0)), ('John', (6.0, 7.0))], dtype=dt) + assert_(isinstance(a, np.ndarray)) + mv_a = memoryview(a) + assert_equal(mv_x.itemsize, mv_a.itemsize) + assert_equal(mv_x.format, mv_a.format) + + # Check that we do not allow writeable buffer export (technically + # we could allow it sometimes here...) + with pytest.raises(BufferError, match="scalar buffer is readonly"): + get_buffer_info(x, ["WRITABLE"]) + + def _as_dict(self, m): + return dict(strides=m.strides, shape=m.shape, itemsize=m.itemsize, + ndim=m.ndim, format=m.format, readonly=m.readonly) + + def test_datetime_memoryview(self): + # gh-11656 + # Values verified with v1.13.3, shape is not () as in test_scalar_dim + + dt1 = np.datetime64('2016-01-01') + dt2 = np.datetime64('2017-01-01') + expected = dict(strides=(1,), itemsize=1, ndim=1, shape=(8,), + format='B', readonly=True) + v = memoryview(dt1) + assert self._as_dict(v) == expected + + v = memoryview(dt2 - dt1) + assert self._as_dict(v) == expected + + dt = np.dtype([('a', 'uint16'), ('b', 'M8[s]')]) + a = np.empty(1, dt) + # Fails to create a PEP 3118 valid buffer + assert_raises((ValueError, BufferError), memoryview, a[0]) + + # Check that we do not allow writeable buffer export + with pytest.raises(BufferError, match="scalar buffer is readonly"): + get_buffer_info(dt1, ["WRITABLE"]) + + @pytest.mark.parametrize('s', [ + pytest.param("\x32\x32", id="ascii"), + pytest.param("\uFE0F\uFE0F", id="basic multilingual"), + pytest.param("\U0001f4bb\U0001f4bb", id="non-BMP"), + ]) + def test_str_ucs4(self, s): + s = np.str_(s) # only our subclass implements the buffer protocol + + # all the same, characters always encode as ucs4 + expected = dict(strides=(), itemsize=8, ndim=0, shape=(), format='2w', + readonly=True) + + v = memoryview(s) + assert self._as_dict(v) == expected + + # integers of the paltform-appropriate endianness + code_points = np.frombuffer(v, dtype='i4') + + assert_equal(code_points, [ord(c) for c in s]) + + # Check that we do not allow writeable buffer export + with pytest.raises(BufferError, match="scalar buffer is readonly"): + get_buffer_info(s, ["WRITABLE"]) + + def test_user_scalar_fails_buffer(self): + r = rational(1) + with assert_raises(TypeError): + memoryview(r) + + # Check that we do not allow writeable buffer export + with pytest.raises(BufferError, match="scalar buffer is readonly"): + get_buffer_info(r, ["WRITABLE"]) diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_scalarprint.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_scalarprint.py new file mode 100644 index 0000000000000000000000000000000000000000..98d1f4aa11f7a2d4ca1125fe19124eb63c561ac5 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_scalarprint.py @@ -0,0 +1,382 @@ +""" Test printing of scalar types. + +""" +import code +import platform +import pytest +import sys + +from tempfile import TemporaryFile +import numpy as np +from numpy.testing import assert_, assert_equal, assert_raises, IS_MUSL + +class TestRealScalars: + def test_str(self): + svals = [0.0, -0.0, 1, -1, np.inf, -np.inf, np.nan] + styps = [np.float16, np.float32, np.float64, np.longdouble] + wanted = [ + ['0.0', '0.0', '0.0', '0.0' ], + ['-0.0', '-0.0', '-0.0', '-0.0'], + ['1.0', '1.0', '1.0', '1.0' ], + ['-1.0', '-1.0', '-1.0', '-1.0'], + ['inf', 'inf', 'inf', 'inf' ], + ['-inf', '-inf', '-inf', '-inf'], + ['nan', 'nan', 'nan', 'nan']] + + for wants, val in zip(wanted, svals): + for want, styp in zip(wants, styps): + msg = 'for str({}({}))'.format(np.dtype(styp).name, repr(val)) + assert_equal(str(styp(val)), want, err_msg=msg) + + def test_scalar_cutoffs(self): + # test that both the str and repr of np.float64 behaves + # like python floats in python3. + def check(v): + assert_equal(str(np.float64(v)), str(v)) + assert_equal(str(np.float64(v)), repr(v)) + assert_equal(repr(np.float64(v)), repr(v)) + assert_equal(repr(np.float64(v)), str(v)) + + # check we use the same number of significant digits + check(1.12345678901234567890) + check(0.0112345678901234567890) + + # check switch from scientific output to positional and back + check(1e-5) + check(1e-4) + check(1e15) + check(1e16) + + def test_py2_float_print(self): + # gh-10753 + # In python2, the python float type implements an obsolete method + # tp_print, which overrides tp_repr and tp_str when using "print" to + # output to a "real file" (ie, not a StringIO). Make sure we don't + # inherit it. + x = np.double(0.1999999999999) + with TemporaryFile('r+t') as f: + print(x, file=f) + f.seek(0) + output = f.read() + assert_equal(output, str(x) + '\n') + # In python2 the value float('0.1999999999999') prints with reduced + # precision as '0.2', but we want numpy's np.double('0.1999999999999') + # to print the unique value, '0.1999999999999'. + + # gh-11031 + # Only in the python2 interactive shell and when stdout is a "real" + # file, the output of the last command is printed to stdout without + # Py_PRINT_RAW (unlike the print statement) so `>>> x` and `>>> print + # x` are potentially different. Make sure they are the same. The only + # way I found to get prompt-like output is using an actual prompt from + # the 'code' module. Again, must use tempfile to get a "real" file. + + # dummy user-input which enters one line and then ctrl-Ds. + def userinput(): + yield 'np.sqrt(2)' + raise EOFError + gen = userinput() + input_func = lambda prompt="": next(gen) + + with TemporaryFile('r+t') as fo, TemporaryFile('r+t') as fe: + orig_stdout, orig_stderr = sys.stdout, sys.stderr + sys.stdout, sys.stderr = fo, fe + + code.interact(local={'np': np}, readfunc=input_func, banner='') + + sys.stdout, sys.stderr = orig_stdout, orig_stderr + + fo.seek(0) + capture = fo.read().strip() + + assert_equal(capture, repr(np.sqrt(2))) + + def test_dragon4(self): + # these tests are adapted from Ryan Juckett's dragon4 implementation, + # see dragon4.c for details. + + fpos32 = lambda x, **k: np.format_float_positional(np.float32(x), **k) + fsci32 = lambda x, **k: np.format_float_scientific(np.float32(x), **k) + fpos64 = lambda x, **k: np.format_float_positional(np.float64(x), **k) + fsci64 = lambda x, **k: np.format_float_scientific(np.float64(x), **k) + + preckwd = lambda prec: {'unique': False, 'precision': prec} + + assert_equal(fpos32('1.0'), "1.") + assert_equal(fsci32('1.0'), "1.e+00") + assert_equal(fpos32('10.234'), "10.234") + assert_equal(fpos32('-10.234'), "-10.234") + assert_equal(fsci32('10.234'), "1.0234e+01") + assert_equal(fsci32('-10.234'), "-1.0234e+01") + assert_equal(fpos32('1000.0'), "1000.") + assert_equal(fpos32('1.0', precision=0), "1.") + assert_equal(fsci32('1.0', precision=0), "1.e+00") + assert_equal(fpos32('10.234', precision=0), "10.") + assert_equal(fpos32('-10.234', precision=0), "-10.") + assert_equal(fsci32('10.234', precision=0), "1.e+01") + assert_equal(fsci32('-10.234', precision=0), "-1.e+01") + assert_equal(fpos32('10.234', precision=2), "10.23") + assert_equal(fsci32('-10.234', precision=2), "-1.02e+01") + assert_equal(fsci64('9.9999999999999995e-08', **preckwd(16)), + '9.9999999999999995e-08') + assert_equal(fsci64('9.8813129168249309e-324', **preckwd(16)), + '9.8813129168249309e-324') + assert_equal(fsci64('9.9999999999999694e-311', **preckwd(16)), + '9.9999999999999694e-311') + + + # test rounding + # 3.1415927410 is closest float32 to np.pi + assert_equal(fpos32('3.14159265358979323846', **preckwd(10)), + "3.1415927410") + assert_equal(fsci32('3.14159265358979323846', **preckwd(10)), + "3.1415927410e+00") + assert_equal(fpos64('3.14159265358979323846', **preckwd(10)), + "3.1415926536") + assert_equal(fsci64('3.14159265358979323846', **preckwd(10)), + "3.1415926536e+00") + # 299792448 is closest float32 to 299792458 + assert_equal(fpos32('299792458.0', **preckwd(5)), "299792448.00000") + assert_equal(fsci32('299792458.0', **preckwd(5)), "2.99792e+08") + assert_equal(fpos64('299792458.0', **preckwd(5)), "299792458.00000") + assert_equal(fsci64('299792458.0', **preckwd(5)), "2.99792e+08") + + assert_equal(fpos32('3.14159265358979323846', **preckwd(25)), + "3.1415927410125732421875000") + assert_equal(fpos64('3.14159265358979323846', **preckwd(50)), + "3.14159265358979311599796346854418516159057617187500") + assert_equal(fpos64('3.14159265358979323846'), "3.141592653589793") + + + # smallest numbers + assert_equal(fpos32(0.5**(126 + 23), unique=False, precision=149), + "0.00000000000000000000000000000000000000000000140129846432" + "4817070923729583289916131280261941876515771757068283889791" + "08268586060148663818836212158203125") + + assert_equal(fpos64(5e-324, unique=False, precision=1074), + "0.00000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000049406564584124654417656" + "8792868221372365059802614324764425585682500675507270208751" + "8652998363616359923797965646954457177309266567103559397963" + "9877479601078187812630071319031140452784581716784898210368" + "8718636056998730723050006387409153564984387312473397273169" + "6151400317153853980741262385655911710266585566867681870395" + "6031062493194527159149245532930545654440112748012970999954" + "1931989409080416563324524757147869014726780159355238611550" + "1348035264934720193790268107107491703332226844753335720832" + "4319360923828934583680601060115061698097530783422773183292" + "4790498252473077637592724787465608477820373446969953364701" + "7972677717585125660551199131504891101451037862738167250955" + "8373897335989936648099411642057026370902792427675445652290" + "87538682506419718265533447265625") + + # largest numbers + f32x = np.finfo(np.float32).max + assert_equal(fpos32(f32x, **preckwd(0)), + "340282346638528859811704183484516925440.") + assert_equal(fpos64(np.finfo(np.float64).max, **preckwd(0)), + "1797693134862315708145274237317043567980705675258449965989" + "1747680315726078002853876058955863276687817154045895351438" + "2464234321326889464182768467546703537516986049910576551282" + "0762454900903893289440758685084551339423045832369032229481" + "6580855933212334827479782620414472316873817718091929988125" + "0404026184124858368.") + # Warning: In unique mode only the integer digits necessary for + # uniqueness are computed, the rest are 0. + assert_equal(fpos32(f32x), + "340282350000000000000000000000000000000.") + + # Further tests of zero-padding vs rounding in different combinations + # of unique, fractional, precision, min_digits + # precision can only reduce digits, not add them. + # min_digits can only extend digits, not reduce them. + assert_equal(fpos32(f32x, unique=True, fractional=True, precision=0), + "340282350000000000000000000000000000000.") + assert_equal(fpos32(f32x, unique=True, fractional=True, precision=4), + "340282350000000000000000000000000000000.") + assert_equal(fpos32(f32x, unique=True, fractional=True, min_digits=0), + "340282346638528859811704183484516925440.") + assert_equal(fpos32(f32x, unique=True, fractional=True, min_digits=4), + "340282346638528859811704183484516925440.0000") + assert_equal(fpos32(f32x, unique=True, fractional=True, + min_digits=4, precision=4), + "340282346638528859811704183484516925440.0000") + assert_raises(ValueError, fpos32, f32x, unique=True, fractional=False, + precision=0) + assert_equal(fpos32(f32x, unique=True, fractional=False, precision=4), + "340300000000000000000000000000000000000.") + assert_equal(fpos32(f32x, unique=True, fractional=False, precision=20), + "340282350000000000000000000000000000000.") + assert_equal(fpos32(f32x, unique=True, fractional=False, min_digits=4), + "340282350000000000000000000000000000000.") + assert_equal(fpos32(f32x, unique=True, fractional=False, + min_digits=20), + "340282346638528859810000000000000000000.") + assert_equal(fpos32(f32x, unique=True, fractional=False, + min_digits=15), + "340282346638529000000000000000000000000.") + assert_equal(fpos32(f32x, unique=False, fractional=False, precision=4), + "340300000000000000000000000000000000000.") + # test that unique rounding is preserved when precision is supplied + # but no extra digits need to be printed (gh-18609) + a = np.float64.fromhex('-1p-97') + assert_equal(fsci64(a, unique=True), '-6.310887241768095e-30') + assert_equal(fsci64(a, unique=False, precision=15), + '-6.310887241768094e-30') + assert_equal(fsci64(a, unique=True, precision=15), + '-6.310887241768095e-30') + assert_equal(fsci64(a, unique=True, min_digits=15), + '-6.310887241768095e-30') + assert_equal(fsci64(a, unique=True, precision=15, min_digits=15), + '-6.310887241768095e-30') + # adds/remove digits in unique mode with unbiased rnding + assert_equal(fsci64(a, unique=True, precision=14), + '-6.31088724176809e-30') + assert_equal(fsci64(a, unique=True, min_digits=16), + '-6.3108872417680944e-30') + assert_equal(fsci64(a, unique=True, precision=16), + '-6.310887241768095e-30') + assert_equal(fsci64(a, unique=True, min_digits=14), + '-6.310887241768095e-30') + # test min_digits in unique mode with different rounding cases + assert_equal(fsci64('1e120', min_digits=3), '1.000e+120') + assert_equal(fsci64('1e100', min_digits=3), '1.000e+100') + + # test trailing zeros + assert_equal(fpos32('1.0', unique=False, precision=3), "1.000") + assert_equal(fpos64('1.0', unique=False, precision=3), "1.000") + assert_equal(fsci32('1.0', unique=False, precision=3), "1.000e+00") + assert_equal(fsci64('1.0', unique=False, precision=3), "1.000e+00") + assert_equal(fpos32('1.5', unique=False, precision=3), "1.500") + assert_equal(fpos64('1.5', unique=False, precision=3), "1.500") + assert_equal(fsci32('1.5', unique=False, precision=3), "1.500e+00") + assert_equal(fsci64('1.5', unique=False, precision=3), "1.500e+00") + # gh-10713 + assert_equal(fpos64('324', unique=False, precision=5, + fractional=False), "324.00") + + def test_dragon4_interface(self): + tps = [np.float16, np.float32, np.float64] + # test is flaky for musllinux on np.float128 + if hasattr(np, 'float128') and not IS_MUSL: + tps.append(np.float128) + + fpos = np.format_float_positional + fsci = np.format_float_scientific + + for tp in tps: + # test padding + assert_equal(fpos(tp('1.0'), pad_left=4, pad_right=4), " 1. ") + assert_equal(fpos(tp('-1.0'), pad_left=4, pad_right=4), " -1. ") + assert_equal(fpos(tp('-10.2'), + pad_left=4, pad_right=4), " -10.2 ") + + # test exp_digits + assert_equal(fsci(tp('1.23e1'), exp_digits=5), "1.23e+00001") + + # test fixed (non-unique) mode + assert_equal(fpos(tp('1.0'), unique=False, precision=4), "1.0000") + assert_equal(fsci(tp('1.0'), unique=False, precision=4), + "1.0000e+00") + + # test trimming + # trim of 'k' or '.' only affects non-unique mode, since unique + # mode will not output trailing 0s. + assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='k'), + "1.0000") + + assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='.'), + "1.") + assert_equal(fpos(tp('1.2'), unique=False, precision=4, trim='.'), + "1.2" if tp != np.float16 else "1.2002") + + assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='0'), + "1.0") + assert_equal(fpos(tp('1.2'), unique=False, precision=4, trim='0'), + "1.2" if tp != np.float16 else "1.2002") + assert_equal(fpos(tp('1.'), trim='0'), "1.0") + + assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='-'), + "1") + assert_equal(fpos(tp('1.2'), unique=False, precision=4, trim='-'), + "1.2" if tp != np.float16 else "1.2002") + assert_equal(fpos(tp('1.'), trim='-'), "1") + assert_equal(fpos(tp('1.001'), precision=1, trim='-'), "1") + + @pytest.mark.skipif(not platform.machine().startswith("ppc64"), + reason="only applies to ppc float128 values") + def test_ppc64_ibm_double_double128(self): + # check that the precision decreases once we get into the subnormal + # range. Unlike float64, this starts around 1e-292 instead of 1e-308, + # which happens when the first double is normal and the second is + # subnormal. + x = np.float128('2.123123123123123123123123123123123e-286') + got = [str(x/np.float128('2e' + str(i))) for i in range(0,40)] + expected = [ + "1.06156156156156156156156156156157e-286", + "1.06156156156156156156156156156158e-287", + "1.06156156156156156156156156156159e-288", + "1.0615615615615615615615615615616e-289", + "1.06156156156156156156156156156157e-290", + "1.06156156156156156156156156156156e-291", + "1.0615615615615615615615615615616e-292", + "1.0615615615615615615615615615615e-293", + "1.061561561561561561561561561562e-294", + "1.06156156156156156156156156155e-295", + "1.0615615615615615615615615616e-296", + "1.06156156156156156156156156e-297", + "1.06156156156156156156156157e-298", + "1.0615615615615615615615616e-299", + "1.06156156156156156156156e-300", + "1.06156156156156156156155e-301", + "1.0615615615615615615616e-302", + "1.061561561561561561562e-303", + "1.06156156156156156156e-304", + "1.0615615615615615618e-305", + "1.06156156156156156e-306", + "1.06156156156156157e-307", + "1.0615615615615616e-308", + "1.06156156156156e-309", + "1.06156156156157e-310", + "1.0615615615616e-311", + "1.06156156156e-312", + "1.06156156154e-313", + "1.0615615616e-314", + "1.06156156e-315", + "1.06156155e-316", + "1.061562e-317", + "1.06156e-318", + "1.06155e-319", + "1.0617e-320", + "1.06e-321", + "1.04e-322", + "1e-323", + "0.0", + "0.0"] + assert_equal(got, expected) + + # Note: we follow glibc behavior, but it (or gcc) might not be right. + # In particular we can get two values that print the same but are not + # equal: + a = np.float128('2')/np.float128('3') + b = np.float128(str(a)) + assert_equal(str(a), str(b)) + assert_(a != b) + + def float32_roundtrip(self): + # gh-9360 + x = np.float32(1024 - 2**-14) + y = np.float32(1024 - 2**-13) + assert_(repr(x) != repr(y)) + assert_equal(np.float32(repr(x)), x) + assert_equal(np.float32(repr(y)), y) + + def float64_vs_python(self): + # gh-2643, gh-6136, gh-6908 + assert_equal(repr(np.float64(0.1)), repr(0.1)) + assert_(repr(np.float64(0.20000000000000004)) != repr(0.2)) diff --git a/venv/lib/python3.10/site-packages/numpy/core/tests/test_umath_accuracy.py b/venv/lib/python3.10/site-packages/numpy/core/tests/test_umath_accuracy.py new file mode 100644 index 0000000000000000000000000000000000000000..6ee4d2fee080d1b04e9fb5af21fe3ef8a9f39596 --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/tests/test_umath_accuracy.py @@ -0,0 +1,75 @@ +import numpy as np +import os +from os import path +import sys +import pytest +from ctypes import c_longlong, c_double, c_float, c_int, cast, pointer, POINTER +from numpy.testing import assert_array_max_ulp +from numpy.testing._private.utils import _glibc_older_than +from numpy.core._multiarray_umath import __cpu_features__ + +UNARY_UFUNCS = [obj for obj in np.core.umath.__dict__.values() if + isinstance(obj, np.ufunc)] +UNARY_OBJECT_UFUNCS = [uf for uf in UNARY_UFUNCS if "O->O" in uf.types] +UNARY_OBJECT_UFUNCS.remove(getattr(np, 'invert')) + +IS_AVX = __cpu_features__.get('AVX512F', False) or \ + (__cpu_features__.get('FMA3', False) and __cpu_features__.get('AVX2', False)) +# only run on linux with AVX, also avoid old glibc (numpy/numpy#20448). +runtest = (sys.platform.startswith('linux') + and IS_AVX and not _glibc_older_than("2.17")) +platform_skip = pytest.mark.skipif(not runtest, + reason="avoid testing inconsistent platform " + "library implementations") + +# convert string to hex function taken from: +# https://stackoverflow.com/questions/1592158/convert-hex-to-float # +def convert(s, datatype="np.float32"): + i = int(s, 16) # convert from hex to a Python int + if (datatype == "np.float64"): + cp = pointer(c_longlong(i)) # make this into a c long long integer + fp = cast(cp, POINTER(c_double)) # cast the int pointer to a double pointer + else: + cp = pointer(c_int(i)) # make this into a c integer + fp = cast(cp, POINTER(c_float)) # cast the int pointer to a float pointer + + return fp.contents.value # dereference the pointer, get the float + +str_to_float = np.vectorize(convert) + +class TestAccuracy: + @platform_skip + def test_validate_transcendentals(self): + with np.errstate(all='ignore'): + data_dir = path.join(path.dirname(__file__), 'data') + files = os.listdir(data_dir) + files = list(filter(lambda f: f.endswith('.csv'), files)) + for filename in files: + filepath = path.join(data_dir, filename) + with open(filepath) as fid: + file_without_comments = (r for r in fid if not r[0] in ('$', '#')) + data = np.genfromtxt(file_without_comments, + dtype=('|S39','|S39','|S39',int), + names=('type','input','output','ulperr'), + delimiter=',', + skip_header=1) + npname = path.splitext(filename)[0].split('-')[3] + npfunc = getattr(np, npname) + for datatype in np.unique(data['type']): + data_subset = data[data['type'] == datatype] + inval = np.array(str_to_float(data_subset['input'].astype(str), data_subset['type'].astype(str)), dtype=eval(datatype)) + outval = np.array(str_to_float(data_subset['output'].astype(str), data_subset['type'].astype(str)), dtype=eval(datatype)) + perm = np.random.permutation(len(inval)) + inval = inval[perm] + outval = outval[perm] + maxulperr = data_subset['ulperr'].max() + assert_array_max_ulp(npfunc(inval), outval, maxulperr) + + @pytest.mark.parametrize("ufunc", UNARY_OBJECT_UFUNCS) + def test_validate_fp16_transcendentals(self, ufunc): + with np.errstate(all='ignore'): + arr = np.arange(65536, dtype=np.int16) + datafp16 = np.frombuffer(arr.tobytes(), dtype=np.float16) + datafp32 = datafp16.astype(np.float32) + assert_array_max_ulp(ufunc(datafp16), ufunc(datafp32), + maxulp=1, dtype=np.float16) diff --git a/venv/lib/python3.10/site-packages/numpy/core/umath.py b/venv/lib/python3.10/site-packages/numpy/core/umath.py new file mode 100644 index 0000000000000000000000000000000000000000..6a5474ffed1433978428021f8cec1be0ab0222fb --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/umath.py @@ -0,0 +1,36 @@ +""" +Create the numpy.core.umath namespace for backward compatibility. In v1.16 +the multiarray and umath c-extension modules were merged into a single +_multiarray_umath extension module. So we replicate the old namespace +by importing from the extension module. + +""" + +from . import _multiarray_umath +from ._multiarray_umath import * # noqa: F403 +# These imports are needed for backward compatibility, +# do not change them. issue gh-11862 +# _ones_like is semi-public, on purpose not added to __all__ +from ._multiarray_umath import _UFUNC_API, _add_newdoc_ufunc, _ones_like + +__all__ = [ + '_UFUNC_API', 'ERR_CALL', 'ERR_DEFAULT', 'ERR_IGNORE', 'ERR_LOG', + 'ERR_PRINT', 'ERR_RAISE', 'ERR_WARN', 'FLOATING_POINT_SUPPORT', + 'FPE_DIVIDEBYZERO', 'FPE_INVALID', 'FPE_OVERFLOW', 'FPE_UNDERFLOW', 'NAN', + 'NINF', 'NZERO', 'PINF', 'PZERO', 'SHIFT_DIVIDEBYZERO', 'SHIFT_INVALID', + 'SHIFT_OVERFLOW', 'SHIFT_UNDERFLOW', 'UFUNC_BUFSIZE_DEFAULT', + 'UFUNC_PYVALS_NAME', '_add_newdoc_ufunc', 'absolute', 'add', + 'arccos', 'arccosh', 'arcsin', 'arcsinh', 'arctan', 'arctan2', 'arctanh', + 'bitwise_and', 'bitwise_or', 'bitwise_xor', 'cbrt', 'ceil', 'conj', + 'conjugate', 'copysign', 'cos', 'cosh', 'deg2rad', 'degrees', 'divide', + 'divmod', 'e', 'equal', 'euler_gamma', 'exp', 'exp2', 'expm1', 'fabs', + 'floor', 'floor_divide', 'float_power', 'fmax', 'fmin', 'fmod', 'frexp', + 'frompyfunc', 'gcd', 'geterrobj', 'greater', 'greater_equal', 'heaviside', + 'hypot', 'invert', 'isfinite', 'isinf', 'isnan', 'isnat', 'lcm', 'ldexp', + 'left_shift', 'less', 'less_equal', 'log', 'log10', 'log1p', 'log2', + 'logaddexp', 'logaddexp2', 'logical_and', 'logical_not', 'logical_or', + 'logical_xor', 'maximum', 'minimum', 'mod', 'modf', 'multiply', 'negative', + 'nextafter', 'not_equal', 'pi', 'positive', 'power', 'rad2deg', 'radians', + 'reciprocal', 'remainder', 'right_shift', 'rint', 'seterrobj', 'sign', + 'signbit', 'sin', 'sinh', 'spacing', 'sqrt', 'square', 'subtract', 'tan', + 'tanh', 'true_divide', 'trunc'] diff --git a/venv/lib/python3.10/site-packages/numpy/core/umath_tests.py b/venv/lib/python3.10/site-packages/numpy/core/umath_tests.py new file mode 100644 index 0000000000000000000000000000000000000000..90ab17e6744a751c4d60e9b86e150cdbc3f6ff2e --- /dev/null +++ b/venv/lib/python3.10/site-packages/numpy/core/umath_tests.py @@ -0,0 +1,13 @@ +""" +Shim for _umath_tests to allow a deprecation period for the new name. + +""" +import warnings + +# 2018-04-04, numpy 1.15.0 +warnings.warn(("numpy.core.umath_tests is an internal NumPy " + "module and should not be imported. It will " + "be removed in a future NumPy release."), + category=DeprecationWarning, stacklevel=2) + +from ._umath_tests import *