File size: 32,217 Bytes

cac1c29

import re
from contextlib import contextmanager
import functools
import operator
import warnings
import numbers
from collections import namedtuple
import inspect
import math
from typing import (
    Optional,
    Union,
    TYPE_CHECKING,
    TypeVar,
)

import numpy as np
from scipy._lib._array_api import array_namespace


AxisError: type[Exception]
ComplexWarning: type[Warning]
VisibleDeprecationWarning: type[Warning]

if np.lib.NumpyVersion(np.__version__) >= '1.25.0':
    from numpy.exceptions import (
        AxisError, ComplexWarning, VisibleDeprecationWarning,
        DTypePromotionError
    )
else:
    from numpy import (
        AxisError, ComplexWarning, VisibleDeprecationWarning  # noqa: F401
    )
    DTypePromotionError = TypeError  # type: ignore

np_long: type
np_ulong: type

if np.lib.NumpyVersion(np.__version__) >= "2.0.0.dev0":
    try:
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore",
                r".*In the future `np\.long` will be defined as.*",
                FutureWarning,
            )
            np_long = np.long  # type: ignore[attr-defined]
            np_ulong = np.ulong  # type: ignore[attr-defined]
    except AttributeError:
            np_long = np.int_
            np_ulong = np.uint
else:
    np_long = np.int_
    np_ulong = np.uint

IntNumber = Union[int, np.integer]
DecimalNumber = Union[float, np.floating, np.integer]

copy_if_needed: Optional[bool]

if np.lib.NumpyVersion(np.__version__) >= "2.0.0":
    copy_if_needed = None
elif np.lib.NumpyVersion(np.__version__) < "1.28.0":
    copy_if_needed = False
else:
    # 2.0.0 dev versions, handle cases where copy may or may not exist
    try:
        np.array([1]).__array__(copy=None)  # type: ignore[call-overload]
        copy_if_needed = None
    except TypeError:
        copy_if_needed = False

# Since Generator was introduced in numpy 1.17, the following condition is needed for
# backward compatibility
if TYPE_CHECKING:
    SeedType = Optional[Union[IntNumber, np.random.Generator,
                              np.random.RandomState]]
    GeneratorType = TypeVar("GeneratorType", bound=Union[np.random.Generator,
                                                         np.random.RandomState])

try:
    from numpy.random import Generator as Generator
except ImportError:
    class Generator:  # type: ignore[no-redef]
        pass


def _lazywhere(cond, arrays, f, fillvalue=None, f2=None):
    """Return elements chosen from two possibilities depending on a condition

    Equivalent to ``f(*arrays) if cond else fillvalue`` performed elementwise.

    Parameters
    ----------
    cond : array
        The condition (expressed as a boolean array).
    arrays : tuple of array
        Arguments to `f` (and `f2`). Must be broadcastable with `cond`.
    f : callable
        Where `cond` is True, output will be ``f(arr1[cond], arr2[cond], ...)``
    fillvalue : object
        If provided, value with which to fill output array where `cond` is
        not True.
    f2 : callable
        If provided, output will be ``f2(arr1[cond], arr2[cond], ...)`` where
        `cond` is not True.

    Returns
    -------
    out : array
        An array with elements from the output of `f` where `cond` is True
        and `fillvalue` (or elements from the output of `f2`) elsewhere. The
        returned array has data type determined by Type Promotion Rules
        with the output of `f` and `fillvalue` (or the output of `f2`).

    Notes
    -----
    ``xp.where(cond, x, fillvalue)`` requires explicitly forming `x` even where
    `cond` is False. This function evaluates ``f(arr1[cond], arr2[cond], ...)``
    onle where `cond` ``is True.

    Examples
    --------
    >>> import numpy as np
    >>> a, b = np.array([1, 2, 3, 4]), np.array([5, 6, 7, 8])
    >>> def f(a, b):
    ...     return a*b
    >>> _lazywhere(a > 2, (a, b), f, np.nan)
    array([ nan,  nan,  21.,  32.])

    """
    xp = array_namespace(cond, *arrays)

    if (f2 is fillvalue is None) or (f2 is not None and fillvalue is not None):
        raise ValueError("Exactly one of `fillvalue` or `f2` must be given.")

    args = xp.broadcast_arrays(cond, *arrays)
    bool_dtype = xp.asarray([True]).dtype  # numpy 1.xx doesn't have `bool`
    cond, arrays = xp.astype(args[0], bool_dtype, copy=False), args[1:]

    temp1 = xp.asarray(f(*(arr[cond] for arr in arrays)))

    if f2 is None:
        fillvalue = xp.asarray(fillvalue)
        dtype = xp.result_type(temp1.dtype, fillvalue.dtype)
        out = xp.full(cond.shape, fill_value=fillvalue, dtype=dtype)
    else:
        ncond = ~cond
        temp2 = xp.asarray(f2(*(arr[ncond] for arr in arrays)))
        dtype = xp.result_type(temp1, temp2)
        out = xp.empty(cond.shape, dtype=dtype)
        out[ncond] = temp2

    out[cond] = temp1

    return out


def _lazyselect(condlist, choicelist, arrays, default=0):
    """
    Mimic `np.select(condlist, choicelist)`.

    Notice, it assumes that all `arrays` are of the same shape or can be
    broadcasted together.

    All functions in `choicelist` must accept array arguments in the order
    given in `arrays` and must return an array of the same shape as broadcasted
    `arrays`.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(6)
    >>> np.select([x <3, x > 3], [x**2, x**3], default=0)
    array([  0,   1,   4,   0,  64, 125])

    >>> _lazyselect([x < 3, x > 3], [lambda x: x**2, lambda x: x**3], (x,))
    array([   0.,    1.,    4.,   0.,   64.,  125.])

    >>> a = -np.ones_like(x)
    >>> _lazyselect([x < 3, x > 3],
    ...             [lambda x, a: x**2, lambda x, a: a * x**3],
    ...             (x, a), default=np.nan)
    array([   0.,    1.,    4.,   nan,  -64., -125.])

    """
    arrays = np.broadcast_arrays(*arrays)
    tcode = np.mintypecode([a.dtype.char for a in arrays])
    out = np.full(np.shape(arrays[0]), fill_value=default, dtype=tcode)
    for func, cond in zip(choicelist, condlist):
        if np.all(cond is False):
            continue
        cond, _ = np.broadcast_arrays(cond, arrays[0])
        temp = tuple(np.extract(cond, arr) for arr in arrays)
        np.place(out, cond, func(*temp))
    return out


def _aligned_zeros(shape, dtype=float, order="C", align=None):
    """Allocate a new ndarray with aligned memory.

    Primary use case for this currently is working around a f2py issue
    in NumPy 1.9.1, where dtype.alignment is such that np.zeros() does
    not necessarily create arrays aligned up to it.

    """
    dtype = np.dtype(dtype)
    if align is None:
        align = dtype.alignment
    if not hasattr(shape, '__len__'):
        shape = (shape,)
    size = functools.reduce(operator.mul, shape) * dtype.itemsize
    buf = np.empty(size + align + 1, np.uint8)
    offset = buf.__array_interface__['data'][0] % align
    if offset != 0:
        offset = align - offset
    # Note: slices producing 0-size arrays do not necessarily change
    # data pointer --- so we use and allocate size+1
    buf = buf[offset:offset+size+1][:-1]
    data = np.ndarray(shape, dtype, buf, order=order)
    data.fill(0)
    return data


def _prune_array(array):
    """Return an array equivalent to the input array. If the input
    array is a view of a much larger array, copy its contents to a
    newly allocated array. Otherwise, return the input unchanged.
    """
    if array.base is not None and array.size < array.base.size // 2:
        return array.copy()
    return array


def float_factorial(n: int) -> float:
    """Compute the factorial and return as a float

    Returns infinity when result is too large for a double
    """
    return float(math.factorial(n)) if n < 171 else np.inf


# copy-pasted from scikit-learn utils/validation.py
# change this to scipy.stats._qmc.check_random_state once numpy 1.16 is dropped
def check_random_state(seed):
    """Turn `seed` into a `np.random.RandomState` instance.

    Parameters
    ----------
    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
        singleton is used.
        If `seed` is an int, a new ``RandomState`` instance is used,
        seeded with `seed`.
        If `seed` is already a ``Generator`` or ``RandomState`` instance then
        that instance is used.

    Returns
    -------
    seed : {`numpy.random.Generator`, `numpy.random.RandomState`}
        Random number generator.

    """
    if seed is None or seed is np.random:
        return np.random.mtrand._rand
    if isinstance(seed, (numbers.Integral, np.integer)):
        return np.random.RandomState(seed)
    if isinstance(seed, (np.random.RandomState, np.random.Generator)):
        return seed

    raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
                     ' instance' % seed)


def _asarray_validated(a, check_finite=True,
                       sparse_ok=False, objects_ok=False, mask_ok=False,
                       as_inexact=False):
    """
    Helper function for SciPy argument validation.

    Many SciPy linear algebra functions do support arbitrary array-like
    input arguments. Examples of commonly unsupported inputs include
    matrices containing inf/nan, sparse matrix representations, and
    matrices with complicated elements.

    Parameters
    ----------
    a : array_like
        The array-like input.
    check_finite : bool, optional
        Whether to check that the input matrices contain only finite numbers.
        Disabling may give a performance gain, but may result in problems
        (crashes, non-termination) if the inputs do contain infinities or NaNs.
        Default: True
    sparse_ok : bool, optional
        True if scipy sparse matrices are allowed.
    objects_ok : bool, optional
        True if arrays with dype('O') are allowed.
    mask_ok : bool, optional
        True if masked arrays are allowed.
    as_inexact : bool, optional
        True to convert the input array to a np.inexact dtype.

    Returns
    -------
    ret : ndarray
        The converted validated array.

    """
    if not sparse_ok:
        import scipy.sparse
        if scipy.sparse.issparse(a):
            msg = ('Sparse matrices are not supported by this function. '
                   'Perhaps one of the scipy.sparse.linalg functions '
                   'would work instead.')
            raise ValueError(msg)
    if not mask_ok:
        if np.ma.isMaskedArray(a):
            raise ValueError('masked arrays are not supported')
    toarray = np.asarray_chkfinite if check_finite else np.asarray
    a = toarray(a)
    if not objects_ok:
        if a.dtype is np.dtype('O'):
            raise ValueError('object arrays are not supported')
    if as_inexact:
        if not np.issubdtype(a.dtype, np.inexact):
            a = toarray(a, dtype=np.float64)
    return a


def _validate_int(k, name, minimum=None):
    """
    Validate a scalar integer.

    This function can be used to validate an argument to a function
    that expects the value to be an integer.  It uses `operator.index`
    to validate the value (so, for example, k=2.0 results in a
    TypeError).

    Parameters
    ----------
    k : int
        The value to be validated.
    name : str
        The name of the parameter.
    minimum : int, optional
        An optional lower bound.
    """
    try:
        k = operator.index(k)
    except TypeError:
        raise TypeError(f'{name} must be an integer.') from None
    if minimum is not None and k < minimum:
        raise ValueError(f'{name} must be an integer not less '
                         f'than {minimum}') from None
    return k


# Add a replacement for inspect.getfullargspec()/
# The version below is borrowed from Django,
# https://github.com/django/django/pull/4846.

# Note an inconsistency between inspect.getfullargspec(func) and
# inspect.signature(func). If `func` is a bound method, the latter does *not*
# list `self` as a first argument, while the former *does*.
# Hence, cook up a common ground replacement: `getfullargspec_no_self` which
# mimics `inspect.getfullargspec` but does not list `self`.
#
# This way, the caller code does not need to know whether it uses a legacy
# .getfullargspec or a bright and shiny .signature.

FullArgSpec = namedtuple('FullArgSpec',
                         ['args', 'varargs', 'varkw', 'defaults',
                          'kwonlyargs', 'kwonlydefaults', 'annotations'])


def getfullargspec_no_self(func):
    """inspect.getfullargspec replacement using inspect.signature.

    If func is a bound method, do not list the 'self' parameter.

    Parameters
    ----------
    func : callable
        A callable to inspect

    Returns
    -------
    fullargspec : FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
                              kwonlydefaults, annotations)

        NOTE: if the first argument of `func` is self, it is *not*, I repeat
        *not*, included in fullargspec.args.
        This is done for consistency between inspect.getargspec() under
        Python 2.x, and inspect.signature() under Python 3.x.

    """
    sig = inspect.signature(func)
    args = [
        p.name for p in sig.parameters.values()
        if p.kind in [inspect.Parameter.POSITIONAL_OR_KEYWORD,
                      inspect.Parameter.POSITIONAL_ONLY]
    ]
    varargs = [
        p.name for p in sig.parameters.values()
        if p.kind == inspect.Parameter.VAR_POSITIONAL
    ]
    varargs = varargs[0] if varargs else None
    varkw = [
        p.name for p in sig.parameters.values()
        if p.kind == inspect.Parameter.VAR_KEYWORD
    ]
    varkw = varkw[0] if varkw else None
    defaults = tuple(
        p.default for p in sig.parameters.values()
        if (p.kind == inspect.Parameter.POSITIONAL_OR_KEYWORD and
            p.default is not p.empty)
    ) or None
    kwonlyargs = [
        p.name for p in sig.parameters.values()
        if p.kind == inspect.Parameter.KEYWORD_ONLY
    ]
    kwdefaults = {p.name: p.default for p in sig.parameters.values()
                  if p.kind == inspect.Parameter.KEYWORD_ONLY and
                  p.default is not p.empty}
    annotations = {p.name: p.annotation for p in sig.parameters.values()
                   if p.annotation is not p.empty}
    return FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
                       kwdefaults or None, annotations)


class _FunctionWrapper:
    """
    Object to wrap user's function, allowing picklability
    """
    def __init__(self, f, args):
        self.f = f
        self.args = [] if args is None else args

    def __call__(self, x):
        return self.f(x, *self.args)


class MapWrapper:
    """
    Parallelisation wrapper for working with map-like callables, such as
    `multiprocessing.Pool.map`.

    Parameters
    ----------
    pool : int or map-like callable
        If `pool` is an integer, then it specifies the number of threads to
        use for parallelization. If ``int(pool) == 1``, then no parallel
        processing is used and the map builtin is used.
        If ``pool == -1``, then the pool will utilize all available CPUs.
        If `pool` is a map-like callable that follows the same
        calling sequence as the built-in map function, then this callable is
        used for parallelization.
    """
    def __init__(self, pool=1):
        self.pool = None
        self._mapfunc = map
        self._own_pool = False

        if callable(pool):
            self.pool = pool
            self._mapfunc = self.pool
        else:
            from multiprocessing import Pool
            # user supplies a number
            if int(pool) == -1:
                # use as many processors as possible
                self.pool = Pool()
                self._mapfunc = self.pool.map
                self._own_pool = True
            elif int(pool) == 1:
                pass
            elif int(pool) > 1:
                # use the number of processors requested
                self.pool = Pool(processes=int(pool))
                self._mapfunc = self.pool.map
                self._own_pool = True
            else:
                raise RuntimeError("Number of workers specified must be -1,"
                                   " an int >= 1, or an object with a 'map' "
                                   "method")

    def __enter__(self):
        return self

    def terminate(self):
        if self._own_pool:
            self.pool.terminate()

    def join(self):
        if self._own_pool:
            self.pool.join()

    def close(self):
        if self._own_pool:
            self.pool.close()

    def __exit__(self, exc_type, exc_value, traceback):
        if self._own_pool:
            self.pool.close()
            self.pool.terminate()

    def __call__(self, func, iterable):
        # only accept one iterable because that's all Pool.map accepts
        try:
            return self._mapfunc(func, iterable)
        except TypeError as e:
            # wrong number of arguments
            raise TypeError("The map-like callable must be of the"
                            " form f(func, iterable)") from e


def rng_integers(gen, low, high=None, size=None, dtype='int64',
                 endpoint=False):
    """
    Return random integers from low (inclusive) to high (exclusive), or if
    endpoint=True, low (inclusive) to high (inclusive). Replaces
    `RandomState.randint` (with endpoint=False) and
    `RandomState.random_integers` (with endpoint=True).

    Return random integers from the "discrete uniform" distribution of the
    specified dtype. If high is None (the default), then results are from
    0 to low.

    Parameters
    ----------
    gen : {None, np.random.RandomState, np.random.Generator}
        Random number generator. If None, then the np.random.RandomState
        singleton is used.
    low : int or array-like of ints
        Lowest (signed) integers to be drawn from the distribution (unless
        high=None, in which case this parameter is 0 and this value is used
        for high).
    high : int or array-like of ints
        If provided, one above the largest (signed) integer to be drawn from
        the distribution (see above for behavior if high=None). If array-like,
        must contain integer values.
    size : array-like of ints, optional
        Output shape. If the given shape is, e.g., (m, n, k), then m * n * k
        samples are drawn. Default is None, in which case a single value is
        returned.
    dtype : {str, dtype}, optional
        Desired dtype of the result. All dtypes are determined by their name,
        i.e., 'int64', 'int', etc, so byteorder is not available and a specific
        precision may have different C types depending on the platform.
        The default value is 'int64'.
    endpoint : bool, optional
        If True, sample from the interval [low, high] instead of the default
        [low, high) Defaults to False.

    Returns
    -------
    out: int or ndarray of ints
        size-shaped array of random integers from the appropriate distribution,
        or a single such random int if size not provided.
    """
    if isinstance(gen, Generator):
        return gen.integers(low, high=high, size=size, dtype=dtype,
                            endpoint=endpoint)
    else:
        if gen is None:
            # default is RandomState singleton used by np.random.
            gen = np.random.mtrand._rand
        if endpoint:
            # inclusive of endpoint
            # remember that low and high can be arrays, so don't modify in
            # place
            if high is None:
                return gen.randint(low + 1, size=size, dtype=dtype)
            if high is not None:
                return gen.randint(low, high=high + 1, size=size, dtype=dtype)

        # exclusive
        return gen.randint(low, high=high, size=size, dtype=dtype)


@contextmanager
def _fixed_default_rng(seed=1638083107694713882823079058616272161):
    """Context with a fixed np.random.default_rng seed."""
    orig_fun = np.random.default_rng
    np.random.default_rng = lambda seed=seed: orig_fun(seed)
    try:
        yield
    finally:
        np.random.default_rng = orig_fun


def _rng_html_rewrite(func):
    """Rewrite the HTML rendering of ``np.random.default_rng``.

    This is intended to decorate
    ``numpydoc.docscrape_sphinx.SphinxDocString._str_examples``.

    Examples are only run by Sphinx when there are plot involved. Even so,
    it does not change the result values getting printed.
    """
    # hexadecimal or number seed, case-insensitive
    pattern = re.compile(r'np.random.default_rng\((0x[0-9A-F]+|\d+)\)', re.I)

    def _wrapped(*args, **kwargs):
        res = func(*args, **kwargs)
        lines = [
            re.sub(pattern, 'np.random.default_rng()', line)
            for line in res
        ]
        return lines

    return _wrapped


def _argmin(a, keepdims=False, axis=None):
    """
    argmin with a `keepdims` parameter.

    See https://github.com/numpy/numpy/issues/8710

    If axis is not None, a.shape[axis] must be greater than 0.
    """
    res = np.argmin(a, axis=axis)
    if keepdims and axis is not None:
        res = np.expand_dims(res, axis=axis)
    return res


def _first_nonnan(a, axis):
    """
    Return the first non-nan value along the given axis.

    If a slice is all nan, nan is returned for that slice.

    The shape of the return value corresponds to ``keepdims=True``.

    Examples
    --------
    >>> import numpy as np
    >>> nan = np.nan
    >>> a = np.array([[ 3.,  3., nan,  3.],
                      [ 1., nan,  2.,  4.],
                      [nan, nan,  9., -1.],
                      [nan,  5.,  4.,  3.],
                      [ 2.,  2.,  2.,  2.],
                      [nan, nan, nan, nan]])
    >>> _first_nonnan(a, axis=0)
    array([[3., 3., 2., 3.]])
    >>> _first_nonnan(a, axis=1)
    array([[ 3.],
           [ 1.],
           [ 9.],
           [ 5.],
           [ 2.],
           [nan]])
    """
    k = _argmin(np.isnan(a), axis=axis, keepdims=True)
    return np.take_along_axis(a, k, axis=axis)


def _nan_allsame(a, axis, keepdims=False):
    """
    Determine if the values along an axis are all the same.

    nan values are ignored.

    `a` must be a numpy array.

    `axis` is assumed to be normalized; that is, 0 <= axis < a.ndim.

    For an axis of length 0, the result is True.  That is, we adopt the
    convention that ``allsame([])`` is True. (There are no values in the
    input that are different.)

    `True` is returned for slices that are all nan--not because all the
    values are the same, but because this is equivalent to ``allsame([])``.

    Examples
    --------
    >>> from numpy import nan, array
    >>> a = array([[ 3.,  3., nan,  3.],
    ...            [ 1., nan,  2.,  4.],
    ...            [nan, nan,  9., -1.],
    ...            [nan,  5.,  4.,  3.],
    ...            [ 2.,  2.,  2.,  2.],
    ...            [nan, nan, nan, nan]])
    >>> _nan_allsame(a, axis=1, keepdims=True)
    array([[ True],
           [False],
           [False],
           [False],
           [ True],
           [ True]])
    """
    if axis is None:
        if a.size == 0:
            return True
        a = a.ravel()
        axis = 0
    else:
        shp = a.shape
        if shp[axis] == 0:
            shp = shp[:axis] + (1,)*keepdims + shp[axis + 1:]
            return np.full(shp, fill_value=True, dtype=bool)
    a0 = _first_nonnan(a, axis=axis)
    return ((a0 == a) | np.isnan(a)).all(axis=axis, keepdims=keepdims)


def _contains_nan(a, nan_policy='propagate', use_summation=True,
                  policies=None):
    if not isinstance(a, np.ndarray):
        use_summation = False  # some array_likes ignore nans (e.g. pandas)
    if policies is None:
        policies = ['propagate', 'raise', 'omit']
    if nan_policy not in policies:
        raise ValueError("nan_policy must be one of {%s}" %
                         ', '.join("'%s'" % s for s in policies))

    if np.issubdtype(a.dtype, np.inexact):
        # The summation method avoids creating a (potentially huge) array.
        if use_summation:
            with np.errstate(invalid='ignore', over='ignore'):
                contains_nan = np.isnan(np.sum(a))
        else:
            contains_nan = np.isnan(a).any()
    elif np.issubdtype(a.dtype, object):
        contains_nan = False
        for el in a.ravel():
            # isnan doesn't work on non-numeric elements
            if np.issubdtype(type(el), np.number) and np.isnan(el):
                contains_nan = True
                break
    else:
        # Only `object` and `inexact` arrays can have NaNs
        contains_nan = False

    if contains_nan and nan_policy == 'raise':
        raise ValueError("The input contains nan values")

    return contains_nan, nan_policy


def _rename_parameter(old_name, new_name, dep_version=None):
    """
    Generate decorator for backward-compatible keyword renaming.

    Apply the decorator generated by `_rename_parameter` to functions with a
    recently renamed parameter to maintain backward-compatibility.

    After decoration, the function behaves as follows:
    If only the new parameter is passed into the function, behave as usual.
    If only the old parameter is passed into the function (as a keyword), raise
    a DeprecationWarning if `dep_version` is provided, and behave as usual
    otherwise.
    If both old and new parameters are passed into the function, raise a
    DeprecationWarning if `dep_version` is provided, and raise the appropriate
    TypeError (function got multiple values for argument).

    Parameters
    ----------
    old_name : str
        Old name of parameter
    new_name : str
        New name of parameter
    dep_version : str, optional
        Version of SciPy in which old parameter was deprecated in the format
        'X.Y.Z'. If supplied, the deprecation message will indicate that
        support for the old parameter will be removed in version 'X.Y+2.Z'

    Notes
    -----
    Untested with functions that accept *args. Probably won't work as written.

    """
    def decorator(fun):
        @functools.wraps(fun)
        def wrapper(*args, **kwargs):
            if old_name in kwargs:
                if dep_version:
                    end_version = dep_version.split('.')
                    end_version[1] = str(int(end_version[1]) + 2)
                    end_version = '.'.join(end_version)
                    message = (f"Use of keyword argument `{old_name}` is "
                               f"deprecated and replaced by `{new_name}`.  "
                               f"Support for `{old_name}` will be removed "
                               f"in SciPy {end_version}.")
                    warnings.warn(message, DeprecationWarning, stacklevel=2)
                if new_name in kwargs:
                    message = (f"{fun.__name__}() got multiple values for "
                               f"argument now known as `{new_name}`")
                    raise TypeError(message)
                kwargs[new_name] = kwargs.pop(old_name)
            return fun(*args, **kwargs)
        return wrapper
    return decorator


def _rng_spawn(rng, n_children):
    # spawns independent RNGs from a parent RNG
    bg = rng._bit_generator
    ss = bg._seed_seq
    child_rngs = [np.random.Generator(type(bg)(child_ss))
                  for child_ss in ss.spawn(n_children)]
    return child_rngs


def _get_nan(*data):
    # Get NaN of appropriate dtype for data
    data = [np.asarray(item) for item in data]
    try:
        dtype = np.result_type(*data, np.half)  # must be a float16 at least
    except DTypePromotionError:
        # fallback to float64
        return np.array(np.nan, dtype=np.float64)[()]
    return np.array(np.nan, dtype=dtype)[()]


def normalize_axis_index(axis, ndim):
    # Check if `axis` is in the correct range and normalize it
    if axis < -ndim or axis >= ndim:
        msg = f"axis {axis} is out of bounds for array of dimension {ndim}"
        raise AxisError(msg)

    if axis < 0:
        axis = axis + ndim
    return axis


def _call_callback_maybe_halt(callback, res):
    """Call wrapped callback; return True if algorithm should stop.

    Parameters
    ----------
    callback : callable or None
        A user-provided callback wrapped with `_wrap_callback`
    res : OptimizeResult
        Information about the current iterate

    Returns
    -------
    halt : bool
        True if minimization should stop

    """
    if callback is None:
        return False
    try:
        callback(res)
        return False
    except StopIteration:
        callback.stop_iteration = True
        return True


class _RichResult(dict):
    """ Container for multiple outputs with pretty-printing """
    def __getattr__(self, name):
        try:
            return self[name]
        except KeyError as e:
            raise AttributeError(name) from e

    __setattr__ = dict.__setitem__
    __delattr__ = dict.__delitem__

    def __repr__(self):
        order_keys = ['message', 'success', 'status', 'fun', 'funl', 'x', 'xl',
                      'col_ind', 'nit', 'lower', 'upper', 'eqlin', 'ineqlin',
                      'converged', 'flag', 'function_calls', 'iterations',
                      'root']
        order_keys = getattr(self, '_order_keys', order_keys)
        # 'slack', 'con' are redundant with residuals
        # 'crossover_nit' is probably not interesting to most users
        omit_keys = {'slack', 'con', 'crossover_nit', '_order_keys'}

        def key(item):
            try:
                return order_keys.index(item[0].lower())
            except ValueError:  # item not in list
                return np.inf

        def omit_redundant(items):
            for item in items:
                if item[0] in omit_keys:
                    continue
                yield item

        def item_sorter(d):
            return sorted(omit_redundant(d.items()), key=key)

        if self.keys():
            return _dict_formatter(self, sorter=item_sorter)
        else:
            return self.__class__.__name__ + "()"

    def __dir__(self):
        return list(self.keys())


def _indenter(s, n=0):
    """
    Ensures that lines after the first are indented by the specified amount
    """
    split = s.split("\n")
    indent = " "*n
    return ("\n" + indent).join(split)


def _float_formatter_10(x):
    """
    Returns a string representation of a float with exactly ten characters
    """
    if np.isposinf(x):
        return "       inf"
    elif np.isneginf(x):
        return "      -inf"
    elif np.isnan(x):
        return "       nan"
    return np.format_float_scientific(x, precision=3, pad_left=2, unique=False)


def _dict_formatter(d, n=0, mplus=1, sorter=None):
    """
    Pretty printer for dictionaries

    `n` keeps track of the starting indentation;
    lines are indented by this much after a line break.
    `mplus` is additional left padding applied to keys
    """
    if isinstance(d, dict):
        m = max(map(len, list(d.keys()))) + mplus  # width to print keys
        s = '\n'.join([k.rjust(m) + ': ' +  # right justified, width m
                       _indenter(_dict_formatter(v, m+n+2, 0, sorter), m+2)
                       for k, v in sorter(d)])  # +2 for ': '
    else:
        # By default, NumPy arrays print with linewidth=76. `n` is
        # the indent at which a line begins printing, so it is subtracted
        # from the default to avoid exceeding 76 characters total.
        # `edgeitems` is the number of elements to include before and after
        # ellipses when arrays are not shown in full.
        # `threshold` is the maximum number of elements for which an
        # array is shown in full.
        # These values tend to work well for use with OptimizeResult.
        with np.printoptions(linewidth=76-n, edgeitems=2, threshold=12,
                             formatter={'float_kind': _float_formatter_10}):
            s = str(d)
    return s