diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/conftest.py b/env-llmeval/lib/python3.10/site-packages/scipy/conftest.py new file mode 100644 index 0000000000000000000000000000000000000000..577987a4ac744dc598f05cfea68ce357917a8874 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/conftest.py @@ -0,0 +1,238 @@ +# Pytest customization +import json +import os +import warnings +import tempfile + +import numpy as np +import numpy.testing as npt +import pytest +import hypothesis + +from scipy._lib._fpumode import get_fpu_mode +from scipy._lib._testutils import FPUModeChangeWarning +from scipy._lib import _pep440 +from scipy._lib._array_api import SCIPY_ARRAY_API, SCIPY_DEVICE + + +def pytest_configure(config): + config.addinivalue_line("markers", + "slow: Tests that are very slow.") + config.addinivalue_line("markers", + "xslow: mark test as extremely slow (not run unless explicitly requested)") + config.addinivalue_line("markers", + "xfail_on_32bit: mark test as failing on 32-bit platforms") + try: + import pytest_timeout # noqa:F401 + except Exception: + config.addinivalue_line( + "markers", 'timeout: mark a test for a non-default timeout') + config.addinivalue_line("markers", + "skip_if_array_api(*backends, reasons=None, np_only=False, cpu_only=False): " + "mark the desired skip configuration for the `skip_if_array_api` fixture.") + + +def _get_mark(item, name): + if _pep440.parse(pytest.__version__) >= _pep440.Version("3.6.0"): + mark = item.get_closest_marker(name) + else: + mark = item.get_marker(name) + return mark + + +def pytest_runtest_setup(item): + mark = _get_mark(item, "xslow") + if mark is not None: + try: + v = int(os.environ.get('SCIPY_XSLOW', '0')) + except ValueError: + v = False + if not v: + pytest.skip("very slow test; " + "set environment variable SCIPY_XSLOW=1 to run it") + mark = _get_mark(item, 'xfail_on_32bit') + if mark is not None and np.intp(0).itemsize < 8: + pytest.xfail(f'Fails on our 32-bit test platform(s): {mark.args[0]}') + + # Older versions of threadpoolctl have an issue that may lead to this + # warning being emitted, see gh-14441 + with npt.suppress_warnings() as sup: + sup.filter(pytest.PytestUnraisableExceptionWarning) + + try: + from threadpoolctl import threadpool_limits + + HAS_THREADPOOLCTL = True + except Exception: # observed in gh-14441: (ImportError, AttributeError) + # Optional dependency only. All exceptions are caught, for robustness + HAS_THREADPOOLCTL = False + + if HAS_THREADPOOLCTL: + # Set the number of openmp threads based on the number of workers + # xdist is using to prevent oversubscription. Simplified version of what + # sklearn does (it can rely on threadpoolctl and its builtin OpenMP helper + # functions) + try: + xdist_worker_count = int(os.environ['PYTEST_XDIST_WORKER_COUNT']) + except KeyError: + # raises when pytest-xdist is not installed + return + + if not os.getenv('OMP_NUM_THREADS'): + max_openmp_threads = os.cpu_count() // 2 # use nr of physical cores + threads_per_worker = max(max_openmp_threads // xdist_worker_count, 1) + try: + threadpool_limits(threads_per_worker, user_api='blas') + except Exception: + # May raise AttributeError for older versions of OpenBLAS. + # Catch any error for robustness. + return + + +@pytest.fixture(scope="function", autouse=True) +def check_fpu_mode(request): + """ + Check FPU mode was not changed during the test. + """ + old_mode = get_fpu_mode() + yield + new_mode = get_fpu_mode() + + if old_mode != new_mode: + warnings.warn(f"FPU mode changed from {old_mode:#x} to {new_mode:#x} during " + "the test", + category=FPUModeChangeWarning, stacklevel=0) + + +# Array API backend handling +xp_available_backends = {'numpy': np} + +if SCIPY_ARRAY_API and isinstance(SCIPY_ARRAY_API, str): + # fill the dict of backends with available libraries + try: + import array_api_strict + xp_available_backends.update({'array_api_strict': array_api_strict}) + except ImportError: + pass + + try: + import torch # type: ignore[import] + xp_available_backends.update({'pytorch': torch}) + # can use `mps` or `cpu` + torch.set_default_device(SCIPY_DEVICE) + except ImportError: + pass + + try: + import cupy # type: ignore[import] + xp_available_backends.update({'cupy': cupy}) + except ImportError: + pass + + # by default, use all available backends + if SCIPY_ARRAY_API.lower() not in ("1", "true"): + SCIPY_ARRAY_API_ = json.loads(SCIPY_ARRAY_API) + + if 'all' in SCIPY_ARRAY_API_: + pass # same as True + else: + # only select a subset of backend by filtering out the dict + try: + xp_available_backends = { + backend: xp_available_backends[backend] + for backend in SCIPY_ARRAY_API_ + } + except KeyError: + msg = f"'--array-api-backend' must be in {xp_available_backends.keys()}" + raise ValueError(msg) + +if 'cupy' in xp_available_backends: + SCIPY_DEVICE = 'cuda' + +array_api_compatible = pytest.mark.parametrize("xp", xp_available_backends.values()) + + +@pytest.fixture +def skip_if_array_api(xp, request): + """ + Skip based on the ``skip_if_array_api`` marker. + + Parameters + ---------- + *backends : tuple + Backends to skip, e.g. ``("array_api_strict", "torch")``. + These are overriden when ``np_only`` is ``True``, and are not + necessary to provide for non-CPU backends when ``cpu_only`` is ``True``. + reasons : list, optional + A list of reasons for each skip. When ``np_only`` is ``True``, + this should be a singleton list. Otherwise, this should be a list + of reasons, one for each corresponding backend in ``backends``. + If unprovided, default reasons are used. Note that it is not possible + to specify a custom reason with ``cpu_only``. Default: ``None``. + np_only : bool, optional + When ``True``, the test is skipped for all backends other + than the default NumPy backend. There is no need to provide + any ``backends`` in this case. To specify a reason, pass a + singleton list to ``reasons``. Default: ``False``. + cpu_only : bool, optional + When ``True``, the test is skipped on non-CPU devices. + There is no need to provide any ``backends`` in this case, + but any ``backends`` will also be skipped on the CPU. + Default: ``False``. + """ + if "skip_if_array_api" not in request.keywords: + return + backends = request.keywords["skip_if_array_api"].args + kwargs = request.keywords["skip_if_array_api"].kwargs + np_only = kwargs.get("np_only", False) + cpu_only = kwargs.get("cpu_only", False) + if np_only: + reasons = kwargs.get("reasons", ["do not run with non-NumPy backends."]) + reason = reasons[0] + if xp.__name__ != 'numpy': + pytest.skip(reason=reason) + return + if cpu_only: + reason = "do not run with `SCIPY_ARRAY_API` set and not on CPU" + if SCIPY_ARRAY_API and SCIPY_DEVICE != 'cpu': + if xp.__name__ == 'cupy': + pytest.skip(reason=reason) + elif xp.__name__ == 'torch': + if 'cpu' not in torch.empty(0).device.type: + pytest.skip(reason=reason) + if backends is not None: + reasons = kwargs.get("reasons", False) + for i, backend in enumerate(backends): + if xp.__name__ == backend: + if not reasons: + reason = f"do not run with array API backend: {backend}" + else: + reason = reasons[i] + pytest.skip(reason=reason) + + +# Following the approach of NumPy's conftest.py... +# Use a known and persistent tmpdir for hypothesis' caches, which +# can be automatically cleared by the OS or user. +hypothesis.configuration.set_hypothesis_home_dir( + os.path.join(tempfile.gettempdir(), ".hypothesis") +) + +# We register two custom profiles for SciPy - for details see +# https://hypothesis.readthedocs.io/en/latest/settings.html +# The first is designed for our own CI runs; the latter also +# forces determinism and is designed for use via scipy.test() +hypothesis.settings.register_profile( + name="nondeterministic", deadline=None, print_blob=True, +) +hypothesis.settings.register_profile( + name="deterministic", + deadline=None, print_blob=True, database=None, derandomize=True, + suppress_health_check=list(hypothesis.HealthCheck), +) + +# Profile is currently set by environment variable `SCIPY_HYPOTHESIS_PROFILE` +# In the future, it would be good to work the choice into dev.py. +SCIPY_HYPOTHESIS_PROFILE = os.environ.get("SCIPY_HYPOTHESIS_PROFILE", + "deterministic") +hypothesis.settings.load_profile(SCIPY_HYPOTHESIS_PROFILE) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__init__.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..9ea5ba9d88b91c252e7533249aba47998a24610d --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__init__.py @@ -0,0 +1,201 @@ +""" +======================================== +Interpolation (:mod:`scipy.interpolate`) +======================================== + +.. currentmodule:: scipy.interpolate + +Sub-package for objects used in interpolation. + +As listed below, this sub-package contains spline functions and classes, +1-D and multidimensional (univariate and multivariate) +interpolation classes, Lagrange and Taylor polynomial interpolators, and +wrappers for `FITPACK `__ +and DFITPACK functions. + +Univariate interpolation +======================== + +.. autosummary:: + :toctree: generated/ + + interp1d + BarycentricInterpolator + KroghInterpolator + barycentric_interpolate + krogh_interpolate + pchip_interpolate + CubicHermiteSpline + PchipInterpolator + Akima1DInterpolator + CubicSpline + PPoly + BPoly + + +Multivariate interpolation +========================== + +Unstructured data: + +.. autosummary:: + :toctree: generated/ + + griddata + LinearNDInterpolator + NearestNDInterpolator + CloughTocher2DInterpolator + RBFInterpolator + Rbf + interp2d + +For data on a grid: + +.. autosummary:: + :toctree: generated/ + + interpn + RegularGridInterpolator + RectBivariateSpline + +.. seealso:: + + `scipy.ndimage.map_coordinates` + +Tensor product polynomials: + +.. autosummary:: + :toctree: generated/ + + NdPPoly + NdBSpline + +1-D Splines +=========== + +.. autosummary:: + :toctree: generated/ + + BSpline + make_interp_spline + make_lsq_spline + make_smoothing_spline + +Functional interface to FITPACK routines: + +.. autosummary:: + :toctree: generated/ + + splrep + splprep + splev + splint + sproot + spalde + splder + splantider + insert + +Object-oriented FITPACK interface: + +.. autosummary:: + :toctree: generated/ + + UnivariateSpline + InterpolatedUnivariateSpline + LSQUnivariateSpline + + + +2-D Splines +=========== + +For data on a grid: + +.. autosummary:: + :toctree: generated/ + + RectBivariateSpline + RectSphereBivariateSpline + +For unstructured data: + +.. autosummary:: + :toctree: generated/ + + BivariateSpline + SmoothBivariateSpline + SmoothSphereBivariateSpline + LSQBivariateSpline + LSQSphereBivariateSpline + +Low-level interface to FITPACK functions: + +.. autosummary:: + :toctree: generated/ + + bisplrep + bisplev + +Additional tools +================ + +.. autosummary:: + :toctree: generated/ + + lagrange + approximate_taylor_polynomial + pade + +.. seealso:: + + `scipy.ndimage.map_coordinates`, + `scipy.ndimage.spline_filter`, + `scipy.signal.resample`, + `scipy.signal.bspline`, + `scipy.signal.gauss_spline`, + `scipy.signal.qspline1d`, + `scipy.signal.cspline1d`, + `scipy.signal.qspline1d_eval`, + `scipy.signal.cspline1d_eval`, + `scipy.signal.qspline2d`, + `scipy.signal.cspline2d`. + +``pchip`` is an alias of `PchipInterpolator` for backward compatibility +(should not be used in new code). +""" +from ._interpolate import * +from ._fitpack_py import * + +# New interface to fitpack library: +from ._fitpack2 import * + +from ._rbf import Rbf + +from ._rbfinterp import * + +from ._polyint import * + +from ._cubic import * + +from ._ndgriddata import * + +from ._bsplines import * + +from ._pade import * + +from ._rgi import * + +from ._ndbspline import NdBSpline + +# Deprecated namespaces, to be removed in v2.0.0 +from . import fitpack, fitpack2, interpolate, ndgriddata, polyint, rbf + +__all__ = [s for s in dir() if not s.startswith('_')] + +from scipy._lib._testutils import PytestTester +test = PytestTester(__name__) +del PytestTester + +# Backward compatibility +pchip = PchipInterpolator diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__pycache__/__init__.cpython-310.pyc b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..71873336cb98548f3896b0066f19a0fd04062e50 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__pycache__/__init__.cpython-310.pyc differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__pycache__/_bsplines.cpython-310.pyc b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/__pycache__/_bsplines.cpython-310.pyc new file mode 100644 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@@ -0,0 +1,970 @@ +"""Interpolation algorithms using piecewise cubic polynomials.""" + +from __future__ import annotations + +from typing import TYPE_CHECKING + +import warnings + +import numpy as np + +from scipy.linalg import solve, solve_banded + +from . import PPoly +from ._polyint import _isscalar + +if TYPE_CHECKING: + from typing import Literal + +__all__ = ["CubicHermiteSpline", "PchipInterpolator", "pchip_interpolate", + "Akima1DInterpolator", "CubicSpline"] + + +def prepare_input(x, y, axis, dydx=None): + """Prepare input for cubic spline interpolators. + + All data are converted to numpy arrays and checked for correctness. + Axes equal to `axis` of arrays `y` and `dydx` are moved to be the 0th + axis. The value of `axis` is converted to lie in + [0, number of dimensions of `y`). + """ + + x, y = map(np.asarray, (x, y)) + if np.issubdtype(x.dtype, np.complexfloating): + raise ValueError("`x` must contain real values.") + x = x.astype(float) + + if np.issubdtype(y.dtype, np.complexfloating): + dtype = complex + else: + dtype = float + + if dydx is not None: + dydx = np.asarray(dydx) + if y.shape != dydx.shape: + raise ValueError("The shapes of `y` and `dydx` must be identical.") + if np.issubdtype(dydx.dtype, np.complexfloating): + dtype = complex + dydx = dydx.astype(dtype, copy=False) + + y = y.astype(dtype, copy=False) + axis = axis % y.ndim + if x.ndim != 1: + raise ValueError("`x` must be 1-dimensional.") + if x.shape[0] < 2: + raise ValueError("`x` must contain at least 2 elements.") + if x.shape[0] != y.shape[axis]: + raise ValueError(f"The length of `y` along `axis`={axis} doesn't " + "match the length of `x`") + + if not np.all(np.isfinite(x)): + raise ValueError("`x` must contain only finite values.") + if not np.all(np.isfinite(y)): + raise ValueError("`y` must contain only finite values.") + + if dydx is not None and not np.all(np.isfinite(dydx)): + raise ValueError("`dydx` must contain only finite values.") + + dx = np.diff(x) + if np.any(dx <= 0): + raise ValueError("`x` must be strictly increasing sequence.") + + y = np.moveaxis(y, axis, 0) + if dydx is not None: + dydx = np.moveaxis(dydx, axis, 0) + + return x, dx, y, axis, dydx + + +class CubicHermiteSpline(PPoly): + """Piecewise-cubic interpolator matching values and first derivatives. + + The result is represented as a `PPoly` instance. + + Parameters + ---------- + x : array_like, shape (n,) + 1-D array containing values of the independent variable. + Values must be real, finite and in strictly increasing order. + y : array_like + Array containing values of the dependent variable. It can have + arbitrary number of dimensions, but the length along ``axis`` + (see below) must match the length of ``x``. Values must be finite. + dydx : array_like + Array containing derivatives of the dependent variable. It can have + arbitrary number of dimensions, but the length along ``axis`` + (see below) must match the length of ``x``. Values must be finite. + axis : int, optional + Axis along which `y` is assumed to be varying. Meaning that for + ``x[i]`` the corresponding values are ``np.take(y, i, axis=axis)``. + Default is 0. + extrapolate : {bool, 'periodic', None}, optional + If bool, determines whether to extrapolate to out-of-bounds points + based on first and last intervals, or to return NaNs. If 'periodic', + periodic extrapolation is used. If None (default), it is set to True. + + Attributes + ---------- + x : ndarray, shape (n,) + Breakpoints. The same ``x`` which was passed to the constructor. + c : ndarray, shape (4, n-1, ...) + Coefficients of the polynomials on each segment. The trailing + dimensions match the dimensions of `y`, excluding ``axis``. + For example, if `y` is 1-D, then ``c[k, i]`` is a coefficient for + ``(x-x[i])**(3-k)`` on the segment between ``x[i]`` and ``x[i+1]``. + axis : int + Interpolation axis. The same axis which was passed to the + constructor. + + Methods + ------- + __call__ + derivative + antiderivative + integrate + roots + + See Also + -------- + Akima1DInterpolator : Akima 1D interpolator. + PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. + CubicSpline : Cubic spline data interpolator. + PPoly : Piecewise polynomial in terms of coefficients and breakpoints + + Notes + ----- + If you want to create a higher-order spline matching higher-order + derivatives, use `BPoly.from_derivatives`. + + References + ---------- + .. [1] `Cubic Hermite spline + `_ + on Wikipedia. + """ + + def __init__(self, x, y, dydx, axis=0, extrapolate=None): + if extrapolate is None: + extrapolate = True + + x, dx, y, axis, dydx = prepare_input(x, y, axis, dydx) + + dxr = dx.reshape([dx.shape[0]] + [1] * (y.ndim - 1)) + slope = np.diff(y, axis=0) / dxr + t = (dydx[:-1] + dydx[1:] - 2 * slope) / dxr + + c = np.empty((4, len(x) - 1) + y.shape[1:], dtype=t.dtype) + c[0] = t / dxr + c[1] = (slope - dydx[:-1]) / dxr - t + c[2] = dydx[:-1] + c[3] = y[:-1] + + super().__init__(c, x, extrapolate=extrapolate) + self.axis = axis + + +class PchipInterpolator(CubicHermiteSpline): + r"""PCHIP 1-D monotonic cubic interpolation. + + ``x`` and ``y`` are arrays of values used to approximate some function f, + with ``y = f(x)``. The interpolant uses monotonic cubic splines + to find the value of new points. (PCHIP stands for Piecewise Cubic + Hermite Interpolating Polynomial). + + Parameters + ---------- + x : ndarray, shape (npoints, ) + A 1-D array of monotonically increasing real values. ``x`` cannot + include duplicate values (otherwise f is overspecified) + y : ndarray, shape (..., npoints, ...) + A N-D array of real values. ``y``'s length along the interpolation + axis must be equal to the length of ``x``. Use the ``axis`` + parameter to select the interpolation axis. + + .. deprecated:: 1.13.0 + Complex data is deprecated and will raise an error in SciPy 1.15.0. + If you are trying to use the real components of the passed array, + use ``np.real`` on ``y``. + + axis : int, optional + Axis in the ``y`` array corresponding to the x-coordinate values. Defaults + to ``axis=0``. + extrapolate : bool, optional + Whether to extrapolate to out-of-bounds points based on first + and last intervals, or to return NaNs. + + Methods + ------- + __call__ + derivative + antiderivative + roots + + See Also + -------- + CubicHermiteSpline : Piecewise-cubic interpolator. + Akima1DInterpolator : Akima 1D interpolator. + CubicSpline : Cubic spline data interpolator. + PPoly : Piecewise polynomial in terms of coefficients and breakpoints. + + Notes + ----- + The interpolator preserves monotonicity in the interpolation data and does + not overshoot if the data is not smooth. + + The first derivatives are guaranteed to be continuous, but the second + derivatives may jump at :math:`x_k`. + + Determines the derivatives at the points :math:`x_k`, :math:`f'_k`, + by using PCHIP algorithm [1]_. + + Let :math:`h_k = x_{k+1} - x_k`, and :math:`d_k = (y_{k+1} - y_k) / h_k` + are the slopes at internal points :math:`x_k`. + If the signs of :math:`d_k` and :math:`d_{k-1}` are different or either of + them equals zero, then :math:`f'_k = 0`. Otherwise, it is given by the + weighted harmonic mean + + .. math:: + + \frac{w_1 + w_2}{f'_k} = \frac{w_1}{d_{k-1}} + \frac{w_2}{d_k} + + where :math:`w_1 = 2 h_k + h_{k-1}` and :math:`w_2 = h_k + 2 h_{k-1}`. + + The end slopes are set using a one-sided scheme [2]_. + + + References + ---------- + .. [1] F. N. Fritsch and J. Butland, + A method for constructing local + monotone piecewise cubic interpolants, + SIAM J. Sci. Comput., 5(2), 300-304 (1984). + :doi:`10.1137/0905021`. + .. [2] see, e.g., C. Moler, Numerical Computing with Matlab, 2004. + :doi:`10.1137/1.9780898717952` + + """ + + def __init__(self, x, y, axis=0, extrapolate=None): + x, _, y, axis, _ = prepare_input(x, y, axis) + if np.iscomplexobj(y): + msg = ("`PchipInterpolator` only works with real values for `y`. " + "Passing an array with a complex dtype for `y` is deprecated " + "and will raise an error in SciPy 1.15.0. If you are trying to " + "use the real components of the passed array, use `np.real` on " + "the array before passing to `PchipInterpolator`.") + warnings.warn(msg, DeprecationWarning, stacklevel=2) + xp = x.reshape((x.shape[0],) + (1,)*(y.ndim-1)) + dk = self._find_derivatives(xp, y) + super().__init__(x, y, dk, axis=0, extrapolate=extrapolate) + self.axis = axis + + @staticmethod + def _edge_case(h0, h1, m0, m1): + # one-sided three-point estimate for the derivative + d = ((2*h0 + h1)*m0 - h0*m1) / (h0 + h1) + + # try to preserve shape + mask = np.sign(d) != np.sign(m0) + mask2 = (np.sign(m0) != np.sign(m1)) & (np.abs(d) > 3.*np.abs(m0)) + mmm = (~mask) & mask2 + + d[mask] = 0. + d[mmm] = 3.*m0[mmm] + + return d + + @staticmethod + def _find_derivatives(x, y): + # Determine the derivatives at the points y_k, d_k, by using + # PCHIP algorithm is: + # We choose the derivatives at the point x_k by + # Let m_k be the slope of the kth segment (between k and k+1) + # If m_k=0 or m_{k-1}=0 or sgn(m_k) != sgn(m_{k-1}) then d_k == 0 + # else use weighted harmonic mean: + # w_1 = 2h_k + h_{k-1}, w_2 = h_k + 2h_{k-1} + # 1/d_k = 1/(w_1 + w_2)*(w_1 / m_k + w_2 / m_{k-1}) + # where h_k is the spacing between x_k and x_{k+1} + y_shape = y.shape + if y.ndim == 1: + # So that _edge_case doesn't end up assigning to scalars + x = x[:, None] + y = y[:, None] + + hk = x[1:] - x[:-1] + mk = (y[1:] - y[:-1]) / hk + + if y.shape[0] == 2: + # edge case: only have two points, use linear interpolation + dk = np.zeros_like(y) + dk[0] = mk + dk[1] = mk + return dk.reshape(y_shape) + + smk = np.sign(mk) + condition = (smk[1:] != smk[:-1]) | (mk[1:] == 0) | (mk[:-1] == 0) + + w1 = 2*hk[1:] + hk[:-1] + w2 = hk[1:] + 2*hk[:-1] + + # values where division by zero occurs will be excluded + # by 'condition' afterwards + with np.errstate(divide='ignore', invalid='ignore'): + whmean = (w1/mk[:-1] + w2/mk[1:]) / (w1 + w2) + + dk = np.zeros_like(y) + dk[1:-1][condition] = 0.0 + dk[1:-1][~condition] = 1.0 / whmean[~condition] + + # special case endpoints, as suggested in + # Cleve Moler, Numerical Computing with MATLAB, Chap 3.6 (pchiptx.m) + dk[0] = PchipInterpolator._edge_case(hk[0], hk[1], mk[0], mk[1]) + dk[-1] = PchipInterpolator._edge_case(hk[-1], hk[-2], mk[-1], mk[-2]) + + return dk.reshape(y_shape) + + +def pchip_interpolate(xi, yi, x, der=0, axis=0): + """ + Convenience function for pchip interpolation. + + xi and yi are arrays of values used to approximate some function f, + with ``yi = f(xi)``. The interpolant uses monotonic cubic splines + to find the value of new points x and the derivatives there. + + See `scipy.interpolate.PchipInterpolator` for details. + + Parameters + ---------- + xi : array_like + A sorted list of x-coordinates, of length N. + yi : array_like + A 1-D array of real values. `yi`'s length along the interpolation + axis must be equal to the length of `xi`. If N-D array, use axis + parameter to select correct axis. + + .. deprecated:: 1.13.0 + Complex data is deprecated and will raise an error in + SciPy 1.15.0. If you are trying to use the real components of + the passed array, use ``np.real`` on `yi`. + + x : scalar or array_like + Of length M. + der : int or list, optional + Derivatives to extract. The 0th derivative can be included to + return the function value. + axis : int, optional + Axis in the yi array corresponding to the x-coordinate values. + + Returns + ------- + y : scalar or array_like + The result, of length R or length M or M by R. + + See Also + -------- + PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. + + Examples + -------- + We can interpolate 2D observed data using pchip interpolation: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.interpolate import pchip_interpolate + >>> x_observed = np.linspace(0.0, 10.0, 11) + >>> y_observed = np.sin(x_observed) + >>> x = np.linspace(min(x_observed), max(x_observed), num=100) + >>> y = pchip_interpolate(x_observed, y_observed, x) + >>> plt.plot(x_observed, y_observed, "o", label="observation") + >>> plt.plot(x, y, label="pchip interpolation") + >>> plt.legend() + >>> plt.show() + + """ + P = PchipInterpolator(xi, yi, axis=axis) + + if der == 0: + return P(x) + elif _isscalar(der): + return P.derivative(der)(x) + else: + return [P.derivative(nu)(x) for nu in der] + + +class Akima1DInterpolator(CubicHermiteSpline): + r""" + Akima interpolator + + Fit piecewise cubic polynomials, given vectors x and y. The interpolation + method by Akima uses a continuously differentiable sub-spline built from + piecewise cubic polynomials. The resultant curve passes through the given + data points and will appear smooth and natural. + + Parameters + ---------- + x : ndarray, shape (npoints, ) + 1-D array of monotonically increasing real values. + y : ndarray, shape (..., npoints, ...) + N-D array of real values. The length of ``y`` along the interpolation axis + must be equal to the length of ``x``. Use the ``axis`` parameter to + select the interpolation axis. + + .. deprecated:: 1.13.0 + Complex data is deprecated and will raise an error in SciPy 1.15.0. + If you are trying to use the real components of the passed array, + use ``np.real`` on ``y``. + + axis : int, optional + Axis in the ``y`` array corresponding to the x-coordinate values. Defaults + to ``axis=0``. + method : {'akima', 'makima'}, optional + If ``"makima"``, use the modified Akima interpolation [2]_. + Defaults to ``"akima"``, use the Akima interpolation [1]_. + + .. versionadded:: 1.13.0 + + Methods + ------- + __call__ + derivative + antiderivative + roots + + See Also + -------- + PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. + CubicSpline : Cubic spline data interpolator. + PPoly : Piecewise polynomial in terms of coefficients and breakpoints + + Notes + ----- + .. versionadded:: 0.14 + + Use only for precise data, as the fitted curve passes through the given + points exactly. This routine is useful for plotting a pleasingly smooth + curve through a few given points for purposes of plotting. + + Let :math:`\delta_i = (y_{i+1} - y_i) / (x_{i+1} - x_i)` be the slopes of + the interval :math:`\left[x_i, x_{i+1}\right)`. Akima's derivative at + :math:`x_i` is defined as: + + .. math:: + + d_i = \frac{w_1}{w_1 + w_2}\delta_{i-1} + \frac{w_2}{w_1 + w_2}\delta_i + + In the Akima interpolation [1]_ (``method="akima"``), the weights are: + + .. math:: + + \begin{aligned} + w_1 &= |\delta_{i+1} - \delta_i| \\ + w_2 &= |\delta_{i-1} - \delta_{i-2}| + \end{aligned} + + In the modified Akima interpolation [2]_ (``method="makima"``), + to eliminate overshoot and avoid edge cases of both numerator and + denominator being equal to 0, the weights are modified as follows: + + .. math:: + + \begin{align*} + w_1 &= |\delta_{i+1} - \delta_i| + |\delta_{i+1} + \delta_i| / 2 \\ + w_2 &= |\delta_{i-1} - \delta_{i-2}| + |\delta_{i-1} + \delta_{i-2}| / 2 + \end{align*} + + Examples + -------- + Comparison of ``method="akima"`` and ``method="makima"``: + + >>> import numpy as np + >>> from scipy.interpolate import Akima1DInterpolator + >>> import matplotlib.pyplot as plt + >>> x = np.linspace(1, 7, 7) + >>> y = np.array([-1, -1, -1, 0, 1, 1, 1]) + >>> xs = np.linspace(min(x), max(x), num=100) + >>> y_akima = Akima1DInterpolator(x, y, method="akima")(xs) + >>> y_makima = Akima1DInterpolator(x, y, method="makima")(xs) + + >>> fig, ax = plt.subplots() + >>> ax.plot(x, y, "o", label="data") + >>> ax.plot(xs, y_akima, label="akima") + >>> ax.plot(xs, y_makima, label="makima") + >>> ax.legend() + >>> fig.show() + + The overshoot that occured in ``"akima"`` has been avoided in ``"makima"``. + + References + ---------- + .. [1] A new method of interpolation and smooth curve fitting based + on local procedures. Hiroshi Akima, J. ACM, October 1970, 17(4), + 589-602. :doi:`10.1145/321607.321609` + .. [2] Makima Piecewise Cubic Interpolation. Cleve Moler and Cosmin Ionita, 2019. + https://blogs.mathworks.com/cleve/2019/04/29/makima-piecewise-cubic-interpolation/ + + """ + + def __init__(self, x, y, axis=0, *, method: Literal["akima", "makima"]="akima"): + if method not in {"akima", "makima"}: + raise NotImplementedError(f"`method`={method} is unsupported.") + # Original implementation in MATLAB by N. Shamsundar (BSD licensed), see + # https://www.mathworks.com/matlabcentral/fileexchange/1814-akima-interpolation + x, dx, y, axis, _ = prepare_input(x, y, axis) + + if np.iscomplexobj(y): + msg = ("`Akima1DInterpolator` only works with real values for `y`. " + "Passing an array with a complex dtype for `y` is deprecated " + "and will raise an error in SciPy 1.15.0. If you are trying to " + "use the real components of the passed array, use `np.real` on " + "the array before passing to `Akima1DInterpolator`.") + warnings.warn(msg, DeprecationWarning, stacklevel=2) + + # determine slopes between breakpoints + m = np.empty((x.size + 3, ) + y.shape[1:]) + dx = dx[(slice(None), ) + (None, ) * (y.ndim - 1)] + m[2:-2] = np.diff(y, axis=0) / dx + + # add two additional points on the left ... + m[1] = 2. * m[2] - m[3] + m[0] = 2. * m[1] - m[2] + # ... and on the right + m[-2] = 2. * m[-3] - m[-4] + m[-1] = 2. * m[-2] - m[-3] + + # if m1 == m2 != m3 == m4, the slope at the breakpoint is not + # defined. This is the fill value: + t = .5 * (m[3:] + m[:-3]) + # get the denominator of the slope t + dm = np.abs(np.diff(m, axis=0)) + if method == "makima": + pm = np.abs(m[1:] + m[:-1]) + f1 = dm[2:] + 0.5 * pm[2:] + f2 = dm[:-2] + 0.5 * pm[:-2] + else: + f1 = dm[2:] + f2 = dm[:-2] + f12 = f1 + f2 + # These are the mask of where the slope at breakpoint is defined: + ind = np.nonzero(f12 > 1e-9 * np.max(f12, initial=-np.inf)) + x_ind, y_ind = ind[0], ind[1:] + # Set the slope at breakpoint + t[ind] = (f1[ind] * m[(x_ind + 1,) + y_ind] + + f2[ind] * m[(x_ind + 2,) + y_ind]) / f12[ind] + + super().__init__(x, y, t, axis=0, extrapolate=False) + self.axis = axis + + def extend(self, c, x, right=True): + raise NotImplementedError("Extending a 1-D Akima interpolator is not " + "yet implemented") + + # These are inherited from PPoly, but they do not produce an Akima + # interpolator. Hence stub them out. + @classmethod + def from_spline(cls, tck, extrapolate=None): + raise NotImplementedError("This method does not make sense for " + "an Akima interpolator.") + + @classmethod + def from_bernstein_basis(cls, bp, extrapolate=None): + raise NotImplementedError("This method does not make sense for " + "an Akima interpolator.") + + +class CubicSpline(CubicHermiteSpline): + """Cubic spline data interpolator. + + Interpolate data with a piecewise cubic polynomial which is twice + continuously differentiable [1]_. The result is represented as a `PPoly` + instance with breakpoints matching the given data. + + Parameters + ---------- + x : array_like, shape (n,) + 1-D array containing values of the independent variable. + Values must be real, finite and in strictly increasing order. + y : array_like + Array containing values of the dependent variable. It can have + arbitrary number of dimensions, but the length along ``axis`` + (see below) must match the length of ``x``. Values must be finite. + axis : int, optional + Axis along which `y` is assumed to be varying. Meaning that for + ``x[i]`` the corresponding values are ``np.take(y, i, axis=axis)``. + Default is 0. + bc_type : string or 2-tuple, optional + Boundary condition type. Two additional equations, given by the + boundary conditions, are required to determine all coefficients of + polynomials on each segment [2]_. + + If `bc_type` is a string, then the specified condition will be applied + at both ends of a spline. Available conditions are: + + * 'not-a-knot' (default): The first and second segment at a curve end + are the same polynomial. It is a good default when there is no + information on boundary conditions. + * 'periodic': The interpolated functions is assumed to be periodic + of period ``x[-1] - x[0]``. The first and last value of `y` must be + identical: ``y[0] == y[-1]``. This boundary condition will result in + ``y'[0] == y'[-1]`` and ``y''[0] == y''[-1]``. + * 'clamped': The first derivative at curves ends are zero. Assuming + a 1D `y`, ``bc_type=((1, 0.0), (1, 0.0))`` is the same condition. + * 'natural': The second derivative at curve ends are zero. Assuming + a 1D `y`, ``bc_type=((2, 0.0), (2, 0.0))`` is the same condition. + + If `bc_type` is a 2-tuple, the first and the second value will be + applied at the curve start and end respectively. The tuple values can + be one of the previously mentioned strings (except 'periodic') or a + tuple `(order, deriv_values)` allowing to specify arbitrary + derivatives at curve ends: + + * `order`: the derivative order, 1 or 2. + * `deriv_value`: array_like containing derivative values, shape must + be the same as `y`, excluding ``axis`` dimension. For example, if + `y` is 1-D, then `deriv_value` must be a scalar. If `y` is 3-D with + the shape (n0, n1, n2) and axis=2, then `deriv_value` must be 2-D + and have the shape (n0, n1). + extrapolate : {bool, 'periodic', None}, optional + If bool, determines whether to extrapolate to out-of-bounds points + based on first and last intervals, or to return NaNs. If 'periodic', + periodic extrapolation is used. If None (default), ``extrapolate`` is + set to 'periodic' for ``bc_type='periodic'`` and to True otherwise. + + Attributes + ---------- + x : ndarray, shape (n,) + Breakpoints. The same ``x`` which was passed to the constructor. + c : ndarray, shape (4, n-1, ...) + Coefficients of the polynomials on each segment. The trailing + dimensions match the dimensions of `y`, excluding ``axis``. + For example, if `y` is 1-d, then ``c[k, i]`` is a coefficient for + ``(x-x[i])**(3-k)`` on the segment between ``x[i]`` and ``x[i+1]``. + axis : int + Interpolation axis. The same axis which was passed to the + constructor. + + Methods + ------- + __call__ + derivative + antiderivative + integrate + roots + + See Also + -------- + Akima1DInterpolator : Akima 1D interpolator. + PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. + PPoly : Piecewise polynomial in terms of coefficients and breakpoints. + + Notes + ----- + Parameters `bc_type` and ``extrapolate`` work independently, i.e. the + former controls only construction of a spline, and the latter only + evaluation. + + When a boundary condition is 'not-a-knot' and n = 2, it is replaced by + a condition that the first derivative is equal to the linear interpolant + slope. When both boundary conditions are 'not-a-knot' and n = 3, the + solution is sought as a parabola passing through given points. + + When 'not-a-knot' boundary conditions is applied to both ends, the + resulting spline will be the same as returned by `splrep` (with ``s=0``) + and `InterpolatedUnivariateSpline`, but these two methods use a + representation in B-spline basis. + + .. versionadded:: 0.18.0 + + Examples + -------- + In this example the cubic spline is used to interpolate a sampled sinusoid. + You can see that the spline continuity property holds for the first and + second derivatives and violates only for the third derivative. + + >>> import numpy as np + >>> from scipy.interpolate import CubicSpline + >>> import matplotlib.pyplot as plt + >>> x = np.arange(10) + >>> y = np.sin(x) + >>> cs = CubicSpline(x, y) + >>> xs = np.arange(-0.5, 9.6, 0.1) + >>> fig, ax = plt.subplots(figsize=(6.5, 4)) + >>> ax.plot(x, y, 'o', label='data') + >>> ax.plot(xs, np.sin(xs), label='true') + >>> ax.plot(xs, cs(xs), label="S") + >>> ax.plot(xs, cs(xs, 1), label="S'") + >>> ax.plot(xs, cs(xs, 2), label="S''") + >>> ax.plot(xs, cs(xs, 3), label="S'''") + >>> ax.set_xlim(-0.5, 9.5) + >>> ax.legend(loc='lower left', ncol=2) + >>> plt.show() + + In the second example, the unit circle is interpolated with a spline. A + periodic boundary condition is used. You can see that the first derivative + values, ds/dx=0, ds/dy=1 at the periodic point (1, 0) are correctly + computed. Note that a circle cannot be exactly represented by a cubic + spline. To increase precision, more breakpoints would be required. + + >>> theta = 2 * np.pi * np.linspace(0, 1, 5) + >>> y = np.c_[np.cos(theta), np.sin(theta)] + >>> cs = CubicSpline(theta, y, bc_type='periodic') + >>> print("ds/dx={:.1f} ds/dy={:.1f}".format(cs(0, 1)[0], cs(0, 1)[1])) + ds/dx=0.0 ds/dy=1.0 + >>> xs = 2 * np.pi * np.linspace(0, 1, 100) + >>> fig, ax = plt.subplots(figsize=(6.5, 4)) + >>> ax.plot(y[:, 0], y[:, 1], 'o', label='data') + >>> ax.plot(np.cos(xs), np.sin(xs), label='true') + >>> ax.plot(cs(xs)[:, 0], cs(xs)[:, 1], label='spline') + >>> ax.axes.set_aspect('equal') + >>> ax.legend(loc='center') + >>> plt.show() + + The third example is the interpolation of a polynomial y = x**3 on the + interval 0 <= x<= 1. A cubic spline can represent this function exactly. + To achieve that we need to specify values and first derivatives at + endpoints of the interval. Note that y' = 3 * x**2 and thus y'(0) = 0 and + y'(1) = 3. + + >>> cs = CubicSpline([0, 1], [0, 1], bc_type=((1, 0), (1, 3))) + >>> x = np.linspace(0, 1) + >>> np.allclose(x**3, cs(x)) + True + + References + ---------- + .. [1] `Cubic Spline Interpolation + `_ + on Wikiversity. + .. [2] Carl de Boor, "A Practical Guide to Splines", Springer-Verlag, 1978. + """ + + def __init__(self, x, y, axis=0, bc_type='not-a-knot', extrapolate=None): + x, dx, y, axis, _ = prepare_input(x, y, axis) + n = len(x) + + bc, y = self._validate_bc(bc_type, y, y.shape[1:], axis) + + if extrapolate is None: + if bc[0] == 'periodic': + extrapolate = 'periodic' + else: + extrapolate = True + + if y.size == 0: + # bail out early for zero-sized arrays + s = np.zeros_like(y) + else: + dxr = dx.reshape([dx.shape[0]] + [1] * (y.ndim - 1)) + slope = np.diff(y, axis=0) / dxr + + # If bc is 'not-a-knot' this change is just a convention. + # If bc is 'periodic' then we already checked that y[0] == y[-1], + # and the spline is just a constant, we handle this case in the + # same way by setting the first derivatives to slope, which is 0. + if n == 2: + if bc[0] in ['not-a-knot', 'periodic']: + bc[0] = (1, slope[0]) + if bc[1] in ['not-a-knot', 'periodic']: + bc[1] = (1, slope[0]) + + # This is a special case, when both conditions are 'not-a-knot' + # and n == 3. In this case 'not-a-knot' can't be handled regularly + # as the both conditions are identical. We handle this case by + # constructing a parabola passing through given points. + if n == 3 and bc[0] == 'not-a-knot' and bc[1] == 'not-a-knot': + A = np.zeros((3, 3)) # This is a standard matrix. + b = np.empty((3,) + y.shape[1:], dtype=y.dtype) + + A[0, 0] = 1 + A[0, 1] = 1 + A[1, 0] = dx[1] + A[1, 1] = 2 * (dx[0] + dx[1]) + A[1, 2] = dx[0] + A[2, 1] = 1 + A[2, 2] = 1 + + b[0] = 2 * slope[0] + b[1] = 3 * (dxr[0] * slope[1] + dxr[1] * slope[0]) + b[2] = 2 * slope[1] + + s = solve(A, b, overwrite_a=True, overwrite_b=True, + check_finite=False) + elif n == 3 and bc[0] == 'periodic': + # In case when number of points is 3 we compute the derivatives + # manually + t = (slope / dxr).sum(0) / (1. / dxr).sum(0) + s = np.broadcast_to(t, (n,) + y.shape[1:]) + else: + # Find derivative values at each x[i] by solving a tridiagonal + # system. + A = np.zeros((3, n)) # This is a banded matrix representation. + b = np.empty((n,) + y.shape[1:], dtype=y.dtype) + + # Filling the system for i=1..n-2 + # (x[i-1] - x[i]) * s[i-1] +\ + # 2 * ((x[i] - x[i-1]) + (x[i+1] - x[i])) * s[i] +\ + # (x[i] - x[i-1]) * s[i+1] =\ + # 3 * ((x[i+1] - x[i])*(y[i] - y[i-1])/(x[i] - x[i-1]) +\ + # (x[i] - x[i-1])*(y[i+1] - y[i])/(x[i+1] - x[i])) + + A[1, 1:-1] = 2 * (dx[:-1] + dx[1:]) # The diagonal + A[0, 2:] = dx[:-1] # The upper diagonal + A[-1, :-2] = dx[1:] # The lower diagonal + + b[1:-1] = 3 * (dxr[1:] * slope[:-1] + dxr[:-1] * slope[1:]) + + bc_start, bc_end = bc + + if bc_start == 'periodic': + # Due to the periodicity, and because y[-1] = y[0], the + # linear system has (n-1) unknowns/equations instead of n: + A = A[:, 0:-1] + A[1, 0] = 2 * (dx[-1] + dx[0]) + A[0, 1] = dx[-1] + + b = b[:-1] + + # Also, due to the periodicity, the system is not tri-diagonal. + # We need to compute a "condensed" matrix of shape (n-2, n-2). + # See https://web.archive.org/web/20151220180652/http://www.cfm.brown.edu/people/gk/chap6/node14.html + # for more explanations. + # The condensed matrix is obtained by removing the last column + # and last row of the (n-1, n-1) system matrix. The removed + # values are saved in scalar variables with the (n-1, n-1) + # system matrix indices forming their names: + a_m1_0 = dx[-2] # lower left corner value: A[-1, 0] + a_m1_m2 = dx[-1] + a_m1_m1 = 2 * (dx[-1] + dx[-2]) + a_m2_m1 = dx[-3] + a_0_m1 = dx[0] + + b[0] = 3 * (dxr[0] * slope[-1] + dxr[-1] * slope[0]) + b[-1] = 3 * (dxr[-1] * slope[-2] + dxr[-2] * slope[-1]) + + Ac = A[:, :-1] + b1 = b[:-1] + b2 = np.zeros_like(b1) + b2[0] = -a_0_m1 + b2[-1] = -a_m2_m1 + + # s1 and s2 are the solutions of (n-2, n-2) system + s1 = solve_banded((1, 1), Ac, b1, overwrite_ab=False, + overwrite_b=False, check_finite=False) + + s2 = solve_banded((1, 1), Ac, b2, overwrite_ab=False, + overwrite_b=False, check_finite=False) + + # computing the s[n-2] solution: + s_m1 = ((b[-1] - a_m1_0 * s1[0] - a_m1_m2 * s1[-1]) / + (a_m1_m1 + a_m1_0 * s2[0] + a_m1_m2 * s2[-1])) + + # s is the solution of the (n, n) system: + s = np.empty((n,) + y.shape[1:], dtype=y.dtype) + s[:-2] = s1 + s_m1 * s2 + s[-2] = s_m1 + s[-1] = s[0] + else: + if bc_start == 'not-a-knot': + A[1, 0] = dx[1] + A[0, 1] = x[2] - x[0] + d = x[2] - x[0] + b[0] = ((dxr[0] + 2*d) * dxr[1] * slope[0] + + dxr[0]**2 * slope[1]) / d + elif bc_start[0] == 1: + A[1, 0] = 1 + A[0, 1] = 0 + b[0] = bc_start[1] + elif bc_start[0] == 2: + A[1, 0] = 2 * dx[0] + A[0, 1] = dx[0] + b[0] = -0.5 * bc_start[1] * dx[0]**2 + 3 * (y[1] - y[0]) + + if bc_end == 'not-a-knot': + A[1, -1] = dx[-2] + A[-1, -2] = x[-1] - x[-3] + d = x[-1] - x[-3] + b[-1] = ((dxr[-1]**2*slope[-2] + + (2*d + dxr[-1])*dxr[-2]*slope[-1]) / d) + elif bc_end[0] == 1: + A[1, -1] = 1 + A[-1, -2] = 0 + b[-1] = bc_end[1] + elif bc_end[0] == 2: + A[1, -1] = 2 * dx[-1] + A[-1, -2] = dx[-1] + b[-1] = 0.5 * bc_end[1] * dx[-1]**2 + 3 * (y[-1] - y[-2]) + + s = solve_banded((1, 1), A, b, overwrite_ab=True, + overwrite_b=True, check_finite=False) + + super().__init__(x, y, s, axis=0, extrapolate=extrapolate) + self.axis = axis + + @staticmethod + def _validate_bc(bc_type, y, expected_deriv_shape, axis): + """Validate and prepare boundary conditions. + + Returns + ------- + validated_bc : 2-tuple + Boundary conditions for a curve start and end. + y : ndarray + y casted to complex dtype if one of the boundary conditions has + complex dtype. + """ + if isinstance(bc_type, str): + if bc_type == 'periodic': + if not np.allclose(y[0], y[-1], rtol=1e-15, atol=1e-15): + raise ValueError( + f"The first and last `y` point along axis {axis} must " + "be identical (within machine precision) when " + "bc_type='periodic'.") + + bc_type = (bc_type, bc_type) + + else: + if len(bc_type) != 2: + raise ValueError("`bc_type` must contain 2 elements to " + "specify start and end conditions.") + + if 'periodic' in bc_type: + raise ValueError("'periodic' `bc_type` is defined for both " + "curve ends and cannot be used with other " + "boundary conditions.") + + validated_bc = [] + for bc in bc_type: + if isinstance(bc, str): + if bc == 'clamped': + validated_bc.append((1, np.zeros(expected_deriv_shape))) + elif bc == 'natural': + validated_bc.append((2, np.zeros(expected_deriv_shape))) + elif bc in ['not-a-knot', 'periodic']: + validated_bc.append(bc) + else: + raise ValueError(f"bc_type={bc} is not allowed.") + else: + try: + deriv_order, deriv_value = bc + except Exception as e: + raise ValueError( + "A specified derivative value must be " + "given in the form (order, value)." + ) from e + + if deriv_order not in [1, 2]: + raise ValueError("The specified derivative order must " + "be 1 or 2.") + + deriv_value = np.asarray(deriv_value) + if deriv_value.shape != expected_deriv_shape: + raise ValueError( + "`deriv_value` shape {} is not the expected one {}." + .format(deriv_value.shape, expected_deriv_shape)) + + if np.issubdtype(deriv_value.dtype, np.complexfloating): + y = y.astype(complex, copy=False) + + validated_bc.append((deriv_order, deriv_value)) + + return validated_bc, y diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack.cpython-310-x86_64-linux-gnu.so b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..cc527980099835534aad06ab0dbcb4dc4f8c7364 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack.cpython-310-x86_64-linux-gnu.so differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack_impl.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack_impl.py new file mode 100644 index 0000000000000000000000000000000000000000..99c660e2b183dca3f3f1d594bbbe6936a5eb9d7a --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack_impl.py @@ -0,0 +1,805 @@ +""" +fitpack (dierckx in netlib) --- A Python-C wrapper to FITPACK (by P. Dierckx). + FITPACK is a collection of FORTRAN programs for curve and surface + fitting with splines and tensor product splines. + +See + https://web.archive.org/web/20010524124604/http://www.cs.kuleuven.ac.be:80/cwis/research/nalag/research/topics/fitpack.html +or + http://www.netlib.org/dierckx/ + +Copyright 2002 Pearu Peterson all rights reserved, +Pearu Peterson +Permission to use, modify, and distribute this software is given under the +terms of the SciPy (BSD style) license. See LICENSE.txt that came with +this distribution for specifics. + +NO WARRANTY IS EXPRESSED OR IMPLIED. USE AT YOUR OWN RISK. + +TODO: Make interfaces to the following fitpack functions: + For univariate splines: cocosp, concon, fourco, insert + For bivariate splines: profil, regrid, parsur, surev +""" + +__all__ = ['splrep', 'splprep', 'splev', 'splint', 'sproot', 'spalde', + 'bisplrep', 'bisplev', 'insert', 'splder', 'splantider'] + +import warnings +import numpy as np +from . import _fitpack +from numpy import (atleast_1d, array, ones, zeros, sqrt, ravel, transpose, + empty, iinfo, asarray) + +# Try to replace _fitpack interface with +# f2py-generated version +from . import dfitpack + + +dfitpack_int = dfitpack.types.intvar.dtype + + +def _int_overflow(x, exception, msg=None): + """Cast the value to an dfitpack_int and raise an OverflowError if the value + cannot fit. + """ + if x > iinfo(dfitpack_int).max: + if msg is None: + msg = f'{x!r} cannot fit into an {dfitpack_int!r}' + raise exception(msg) + return dfitpack_int.type(x) + + +_iermess = { + 0: ["The spline has a residual sum of squares fp such that " + "abs(fp-s)/s<=0.001", None], + -1: ["The spline is an interpolating spline (fp=0)", None], + -2: ["The spline is weighted least-squares polynomial of degree k.\n" + "fp gives the upper bound fp0 for the smoothing factor s", None], + 1: ["The required storage space exceeds the available storage space.\n" + "Probable causes: data (x,y) size is too small or smoothing parameter" + "\ns is too small (fp>s).", ValueError], + 2: ["A theoretically impossible result when finding a smoothing spline\n" + "with fp = s. Probable cause: s too small. (abs(fp-s)/s>0.001)", + ValueError], + 3: ["The maximal number of iterations (20) allowed for finding smoothing\n" + "spline with fp=s has been reached. Probable cause: s too small.\n" + "(abs(fp-s)/s>0.001)", ValueError], + 10: ["Error on input data", ValueError], + 'unknown': ["An error occurred", TypeError] +} + +_iermess2 = { + 0: ["The spline has a residual sum of squares fp such that " + "abs(fp-s)/s<=0.001", None], + -1: ["The spline is an interpolating spline (fp=0)", None], + -2: ["The spline is weighted least-squares polynomial of degree kx and ky." + "\nfp gives the upper bound fp0 for the smoothing factor s", None], + -3: ["Warning. The coefficients of the spline have been computed as the\n" + "minimal norm least-squares solution of a rank deficient system.", + None], + 1: ["The required storage space exceeds the available storage space.\n" + "Probable causes: nxest or nyest too small or s is too small. (fp>s)", + ValueError], + 2: ["A theoretically impossible result when finding a smoothing spline\n" + "with fp = s. Probable causes: s too small or badly chosen eps.\n" + "(abs(fp-s)/s>0.001)", ValueError], + 3: ["The maximal number of iterations (20) allowed for finding smoothing\n" + "spline with fp=s has been reached. Probable cause: s too small.\n" + "(abs(fp-s)/s>0.001)", ValueError], + 4: ["No more knots can be added because the number of B-spline\n" + "coefficients already exceeds the number of data points m.\n" + "Probable causes: either s or m too small. (fp>s)", ValueError], + 5: ["No more knots can be added because the additional knot would\n" + "coincide with an old one. Probable cause: s too small or too large\n" + "a weight to an inaccurate data point. (fp>s)", ValueError], + 10: ["Error on input data", ValueError], + 11: ["rwrk2 too small, i.e., there is not enough workspace for computing\n" + "the minimal least-squares solution of a rank deficient system of\n" + "linear equations.", ValueError], + 'unknown': ["An error occurred", TypeError] +} + +_parcur_cache = {'t': array([], float), 'wrk': array([], float), + 'iwrk': array([], dfitpack_int), 'u': array([], float), + 'ub': 0, 'ue': 1} + + +def splprep(x, w=None, u=None, ub=None, ue=None, k=3, task=0, s=None, t=None, + full_output=0, nest=None, per=0, quiet=1): + # see the docstring of `_fitpack_py/splprep` + if task <= 0: + _parcur_cache = {'t': array([], float), 'wrk': array([], float), + 'iwrk': array([], dfitpack_int), 'u': array([], float), + 'ub': 0, 'ue': 1} + x = atleast_1d(x) + idim, m = x.shape + if per: + for i in range(idim): + if x[i][0] != x[i][-1]: + if not quiet: + warnings.warn(RuntimeWarning('Setting x[%d][%d]=x[%d][0]' % + (i, m, i)), + stacklevel=2) + x[i][-1] = x[i][0] + if not 0 < idim < 11: + raise TypeError('0 < idim < 11 must hold') + if w is None: + w = ones(m, float) + else: + w = atleast_1d(w) + ipar = (u is not None) + if ipar: + _parcur_cache['u'] = u + if ub is None: + _parcur_cache['ub'] = u[0] + else: + _parcur_cache['ub'] = ub + if ue is None: + _parcur_cache['ue'] = u[-1] + else: + _parcur_cache['ue'] = ue + else: + _parcur_cache['u'] = zeros(m, float) + if not (1 <= k <= 5): + raise TypeError('1 <= k= %d <=5 must hold' % k) + if not (-1 <= task <= 1): + raise TypeError('task must be -1, 0 or 1') + if (not len(w) == m) or (ipar == 1 and (not len(u) == m)): + raise TypeError('Mismatch of input dimensions') + if s is None: + s = m - sqrt(2*m) + if t is None and task == -1: + raise TypeError('Knots must be given for task=-1') + if t is not None: + _parcur_cache['t'] = atleast_1d(t) + n = len(_parcur_cache['t']) + if task == -1 and n < 2*k + 2: + raise TypeError('There must be at least 2*k+2 knots for task=-1') + if m <= k: + raise TypeError('m > k must hold') + if nest is None: + nest = m + 2*k + + if (task >= 0 and s == 0) or (nest < 0): + if per: + nest = m + 2*k + else: + nest = m + k + 1 + nest = max(nest, 2*k + 3) + u = _parcur_cache['u'] + ub = _parcur_cache['ub'] + ue = _parcur_cache['ue'] + t = _parcur_cache['t'] + wrk = _parcur_cache['wrk'] + iwrk = _parcur_cache['iwrk'] + t, c, o = _fitpack._parcur(ravel(transpose(x)), w, u, ub, ue, k, + task, ipar, s, t, nest, wrk, iwrk, per) + _parcur_cache['u'] = o['u'] + _parcur_cache['ub'] = o['ub'] + _parcur_cache['ue'] = o['ue'] + _parcur_cache['t'] = t + _parcur_cache['wrk'] = o['wrk'] + _parcur_cache['iwrk'] = o['iwrk'] + ier = o['ier'] + fp = o['fp'] + n = len(t) + u = o['u'] + c.shape = idim, n - k - 1 + tcku = [t, list(c), k], u + if ier <= 0 and not quiet: + warnings.warn(RuntimeWarning(_iermess[ier][0] + + "\tk=%d n=%d m=%d fp=%f s=%f" % + (k, len(t), m, fp, s)), + stacklevel=2) + if ier > 0 and not full_output: + if ier in [1, 2, 3]: + warnings.warn(RuntimeWarning(_iermess[ier][0]), stacklevel=2) + else: + try: + raise _iermess[ier][1](_iermess[ier][0]) + except KeyError as e: + raise _iermess['unknown'][1](_iermess['unknown'][0]) from e + if full_output: + try: + return tcku, fp, ier, _iermess[ier][0] + except KeyError: + return tcku, fp, ier, _iermess['unknown'][0] + else: + return tcku + + +_curfit_cache = {'t': array([], float), 'wrk': array([], float), + 'iwrk': array([], dfitpack_int)} + + +def splrep(x, y, w=None, xb=None, xe=None, k=3, task=0, s=None, t=None, + full_output=0, per=0, quiet=1): + # see the docstring of `_fitpack_py/splrep` + if task <= 0: + _curfit_cache = {} + x, y = map(atleast_1d, [x, y]) + m = len(x) + if w is None: + w = ones(m, float) + if s is None: + s = 0.0 + else: + w = atleast_1d(w) + if s is None: + s = m - sqrt(2*m) + if not len(w) == m: + raise TypeError('len(w)=%d is not equal to m=%d' % (len(w), m)) + if (m != len(y)) or (m != len(w)): + raise TypeError('Lengths of the first three arguments (x,y,w) must ' + 'be equal') + if not (1 <= k <= 5): + raise TypeError('Given degree of the spline (k=%d) is not supported. ' + '(1<=k<=5)' % k) + if m <= k: + raise TypeError('m > k must hold') + if xb is None: + xb = x[0] + if xe is None: + xe = x[-1] + if not (-1 <= task <= 1): + raise TypeError('task must be -1, 0 or 1') + if t is not None: + task = -1 + if task == -1: + if t is None: + raise TypeError('Knots must be given for task=-1') + numknots = len(t) + _curfit_cache['t'] = empty((numknots + 2*k + 2,), float) + _curfit_cache['t'][k+1:-k-1] = t + nest = len(_curfit_cache['t']) + elif task == 0: + if per: + nest = max(m + 2*k, 2*k + 3) + else: + nest = max(m + k + 1, 2*k + 3) + t = empty((nest,), float) + _curfit_cache['t'] = t + if task <= 0: + if per: + _curfit_cache['wrk'] = empty((m*(k + 1) + nest*(8 + 5*k),), float) + else: + _curfit_cache['wrk'] = empty((m*(k + 1) + nest*(7 + 3*k),), float) + _curfit_cache['iwrk'] = empty((nest,), dfitpack_int) + try: + t = _curfit_cache['t'] + wrk = _curfit_cache['wrk'] + iwrk = _curfit_cache['iwrk'] + except KeyError as e: + raise TypeError("must call with task=1 only after" + " call with task=0,-1") from e + if not per: + n, c, fp, ier = dfitpack.curfit(task, x, y, w, t, wrk, iwrk, + xb, xe, k, s) + else: + n, c, fp, ier = dfitpack.percur(task, x, y, w, t, wrk, iwrk, k, s) + tck = (t[:n], c[:n], k) + if ier <= 0 and not quiet: + _mess = (_iermess[ier][0] + "\tk=%d n=%d m=%d fp=%f s=%f" % + (k, len(t), m, fp, s)) + warnings.warn(RuntimeWarning(_mess), stacklevel=2) + if ier > 0 and not full_output: + if ier in [1, 2, 3]: + warnings.warn(RuntimeWarning(_iermess[ier][0]), stacklevel=2) + else: + try: + raise _iermess[ier][1](_iermess[ier][0]) + except KeyError as e: + raise _iermess['unknown'][1](_iermess['unknown'][0]) from e + if full_output: + try: + return tck, fp, ier, _iermess[ier][0] + except KeyError: + return tck, fp, ier, _iermess['unknown'][0] + else: + return tck + + +def splev(x, tck, der=0, ext=0): + # see the docstring of `_fitpack_py/splev` + t, c, k = tck + try: + c[0][0] + parametric = True + except Exception: + parametric = False + if parametric: + return list(map(lambda c, x=x, t=t, k=k, der=der: + splev(x, [t, c, k], der, ext), c)) + else: + if not (0 <= der <= k): + raise ValueError("0<=der=%d<=k=%d must hold" % (der, k)) + if ext not in (0, 1, 2, 3): + raise ValueError("ext = %s not in (0, 1, 2, 3) " % ext) + + x = asarray(x) + shape = x.shape + x = atleast_1d(x).ravel() + if der == 0: + y, ier = dfitpack.splev(t, c, k, x, ext) + else: + y, ier = dfitpack.splder(t, c, k, x, der, ext) + + if ier == 10: + raise ValueError("Invalid input data") + if ier == 1: + raise ValueError("Found x value not in the domain") + if ier: + raise TypeError("An error occurred") + + return y.reshape(shape) + + +def splint(a, b, tck, full_output=0): + # see the docstring of `_fitpack_py/splint` + t, c, k = tck + try: + c[0][0] + parametric = True + except Exception: + parametric = False + if parametric: + return list(map(lambda c, a=a, b=b, t=t, k=k: + splint(a, b, [t, c, k]), c)) + else: + aint, wrk = dfitpack.splint(t, c, k, a, b) + if full_output: + return aint, wrk + else: + return aint + + +def sproot(tck, mest=10): + # see the docstring of `_fitpack_py/sproot` + t, c, k = tck + if k != 3: + raise ValueError("sproot works only for cubic (k=3) splines") + try: + c[0][0] + parametric = True + except Exception: + parametric = False + if parametric: + return list(map(lambda c, t=t, k=k, mest=mest: + sproot([t, c, k], mest), c)) + else: + if len(t) < 8: + raise TypeError("The number of knots %d>=8" % len(t)) + z, m, ier = dfitpack.sproot(t, c, mest) + if ier == 10: + raise TypeError("Invalid input data. " + "t1<=..<=t4 1: + return list(map(lambda x, tck=tck: spalde(x, tck), x)) + d, ier = dfitpack.spalde(t, c, k+1, x[0]) + if ier == 0: + return d + if ier == 10: + raise TypeError("Invalid input data. t(k)<=x<=t(n-k+1) must hold.") + raise TypeError("Unknown error") + +# def _curfit(x,y,w=None,xb=None,xe=None,k=3,task=0,s=None,t=None, +# full_output=0,nest=None,per=0,quiet=1): + + +_surfit_cache = {'tx': array([], float), 'ty': array([], float), + 'wrk': array([], float), 'iwrk': array([], dfitpack_int)} + + +def bisplrep(x, y, z, w=None, xb=None, xe=None, yb=None, ye=None, + kx=3, ky=3, task=0, s=None, eps=1e-16, tx=None, ty=None, + full_output=0, nxest=None, nyest=None, quiet=1): + """ + Find a bivariate B-spline representation of a surface. + + Given a set of data points (x[i], y[i], z[i]) representing a surface + z=f(x,y), compute a B-spline representation of the surface. Based on + the routine SURFIT from FITPACK. + + Parameters + ---------- + x, y, z : ndarray + Rank-1 arrays of data points. + w : ndarray, optional + Rank-1 array of weights. By default ``w=np.ones(len(x))``. + xb, xe : float, optional + End points of approximation interval in `x`. + By default ``xb = x.min(), xe=x.max()``. + yb, ye : float, optional + End points of approximation interval in `y`. + By default ``yb=y.min(), ye = y.max()``. + kx, ky : int, optional + The degrees of the spline (1 <= kx, ky <= 5). + Third order (kx=ky=3) is recommended. + task : int, optional + If task=0, find knots in x and y and coefficients for a given + smoothing factor, s. + If task=1, find knots and coefficients for another value of the + smoothing factor, s. bisplrep must have been previously called + with task=0 or task=1. + If task=-1, find coefficients for a given set of knots tx, ty. + s : float, optional + A non-negative smoothing factor. If weights correspond + to the inverse of the standard-deviation of the errors in z, + then a good s-value should be found in the range + ``(m-sqrt(2*m),m+sqrt(2*m))`` where m=len(x). + eps : float, optional + A threshold for determining the effective rank of an + over-determined linear system of equations (0 < eps < 1). + `eps` is not likely to need changing. + tx, ty : ndarray, optional + Rank-1 arrays of the knots of the spline for task=-1 + full_output : int, optional + Non-zero to return optional outputs. + nxest, nyest : int, optional + Over-estimates of the total number of knots. If None then + ``nxest = max(kx+sqrt(m/2),2*kx+3)``, + ``nyest = max(ky+sqrt(m/2),2*ky+3)``. + quiet : int, optional + Non-zero to suppress printing of messages. + + Returns + ------- + tck : array_like + A list [tx, ty, c, kx, ky] containing the knots (tx, ty) and + coefficients (c) of the bivariate B-spline representation of the + surface along with the degree of the spline. + fp : ndarray + The weighted sum of squared residuals of the spline approximation. + ier : int + An integer flag about splrep success. Success is indicated if + ier<=0. If ier in [1,2,3] an error occurred but was not raised. + Otherwise an error is raised. + msg : str + A message corresponding to the integer flag, ier. + + See Also + -------- + splprep, splrep, splint, sproot, splev + UnivariateSpline, BivariateSpline + + Notes + ----- + See `bisplev` to evaluate the value of the B-spline given its tck + representation. + + If the input data is such that input dimensions have incommensurate + units and differ by many orders of magnitude, the interpolant may have + numerical artifacts. Consider rescaling the data before interpolation. + + References + ---------- + .. [1] Dierckx P.:An algorithm for surface fitting with spline functions + Ima J. Numer. Anal. 1 (1981) 267-283. + .. [2] Dierckx P.:An algorithm for surface fitting with spline functions + report tw50, Dept. Computer Science,K.U.Leuven, 1980. + .. [3] Dierckx P.:Curve and surface fitting with splines, Monographs on + Numerical Analysis, Oxford University Press, 1993. + + Examples + -------- + Examples are given :ref:`in the tutorial `. + + """ + x, y, z = map(ravel, [x, y, z]) # ensure 1-d arrays. + m = len(x) + if not (m == len(y) == len(z)): + raise TypeError('len(x)==len(y)==len(z) must hold.') + if w is None: + w = ones(m, float) + else: + w = atleast_1d(w) + if not len(w) == m: + raise TypeError('len(w)=%d is not equal to m=%d' % (len(w), m)) + if xb is None: + xb = x.min() + if xe is None: + xe = x.max() + if yb is None: + yb = y.min() + if ye is None: + ye = y.max() + if not (-1 <= task <= 1): + raise TypeError('task must be -1, 0 or 1') + if s is None: + s = m - sqrt(2*m) + if tx is None and task == -1: + raise TypeError('Knots_x must be given for task=-1') + if tx is not None: + _surfit_cache['tx'] = atleast_1d(tx) + nx = len(_surfit_cache['tx']) + if ty is None and task == -1: + raise TypeError('Knots_y must be given for task=-1') + if ty is not None: + _surfit_cache['ty'] = atleast_1d(ty) + ny = len(_surfit_cache['ty']) + if task == -1 and nx < 2*kx+2: + raise TypeError('There must be at least 2*kx+2 knots_x for task=-1') + if task == -1 and ny < 2*ky+2: + raise TypeError('There must be at least 2*ky+2 knots_x for task=-1') + if not ((1 <= kx <= 5) and (1 <= ky <= 5)): + raise TypeError('Given degree of the spline (kx,ky=%d,%d) is not ' + 'supported. (1<=k<=5)' % (kx, ky)) + if m < (kx + 1)*(ky + 1): + raise TypeError('m >= (kx+1)(ky+1) must hold') + if nxest is None: + nxest = int(kx + sqrt(m/2)) + if nyest is None: + nyest = int(ky + sqrt(m/2)) + nxest, nyest = max(nxest, 2*kx + 3), max(nyest, 2*ky + 3) + if task >= 0 and s == 0: + nxest = int(kx + sqrt(3*m)) + nyest = int(ky + sqrt(3*m)) + if task == -1: + _surfit_cache['tx'] = atleast_1d(tx) + _surfit_cache['ty'] = atleast_1d(ty) + tx, ty = _surfit_cache['tx'], _surfit_cache['ty'] + wrk = _surfit_cache['wrk'] + u = nxest - kx - 1 + v = nyest - ky - 1 + km = max(kx, ky) + 1 + ne = max(nxest, nyest) + bx, by = kx*v + ky + 1, ky*u + kx + 1 + b1, b2 = bx, bx + v - ky + if bx > by: + b1, b2 = by, by + u - kx + msg = "Too many data points to interpolate" + lwrk1 = _int_overflow(u*v*(2 + b1 + b2) + + 2*(u + v + km*(m + ne) + ne - kx - ky) + b2 + 1, + OverflowError, + msg=msg) + lwrk2 = _int_overflow(u*v*(b2 + 1) + b2, OverflowError, msg=msg) + tx, ty, c, o = _fitpack._surfit(x, y, z, w, xb, xe, yb, ye, kx, ky, + task, s, eps, tx, ty, nxest, nyest, + wrk, lwrk1, lwrk2) + _curfit_cache['tx'] = tx + _curfit_cache['ty'] = ty + _curfit_cache['wrk'] = o['wrk'] + ier, fp = o['ier'], o['fp'] + tck = [tx, ty, c, kx, ky] + + ierm = min(11, max(-3, ier)) + if ierm <= 0 and not quiet: + _mess = (_iermess2[ierm][0] + + "\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f" % + (kx, ky, len(tx), len(ty), m, fp, s)) + warnings.warn(RuntimeWarning(_mess), stacklevel=2) + if ierm > 0 and not full_output: + if ier in [1, 2, 3, 4, 5]: + _mess = ("\n\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f" % + (kx, ky, len(tx), len(ty), m, fp, s)) + warnings.warn(RuntimeWarning(_iermess2[ierm][0] + _mess), stacklevel=2) + else: + try: + raise _iermess2[ierm][1](_iermess2[ierm][0]) + except KeyError as e: + raise _iermess2['unknown'][1](_iermess2['unknown'][0]) from e + if full_output: + try: + return tck, fp, ier, _iermess2[ierm][0] + except KeyError: + return tck, fp, ier, _iermess2['unknown'][0] + else: + return tck + + +def bisplev(x, y, tck, dx=0, dy=0): + """ + Evaluate a bivariate B-spline and its derivatives. + + Return a rank-2 array of spline function values (or spline derivative + values) at points given by the cross-product of the rank-1 arrays `x` and + `y`. In special cases, return an array or just a float if either `x` or + `y` or both are floats. Based on BISPEV and PARDER from FITPACK. + + Parameters + ---------- + x, y : ndarray + Rank-1 arrays specifying the domain over which to evaluate the + spline or its derivative. + tck : tuple + A sequence of length 5 returned by `bisplrep` containing the knot + locations, the coefficients, and the degree of the spline: + [tx, ty, c, kx, ky]. + dx, dy : int, optional + The orders of the partial derivatives in `x` and `y` respectively. + + Returns + ------- + vals : ndarray + The B-spline or its derivative evaluated over the set formed by + the cross-product of `x` and `y`. + + See Also + -------- + splprep, splrep, splint, sproot, splev + UnivariateSpline, BivariateSpline + + Notes + ----- + See `bisplrep` to generate the `tck` representation. + + References + ---------- + .. [1] Dierckx P. : An algorithm for surface fitting + with spline functions + Ima J. Numer. Anal. 1 (1981) 267-283. + .. [2] Dierckx P. : An algorithm for surface fitting + with spline functions + report tw50, Dept. Computer Science,K.U.Leuven, 1980. + .. [3] Dierckx P. : Curve and surface fitting with splines, + Monographs on Numerical Analysis, Oxford University Press, 1993. + + Examples + -------- + Examples are given :ref:`in the tutorial `. + + """ + tx, ty, c, kx, ky = tck + if not (0 <= dx < kx): + raise ValueError("0 <= dx = %d < kx = %d must hold" % (dx, kx)) + if not (0 <= dy < ky): + raise ValueError("0 <= dy = %d < ky = %d must hold" % (dy, ky)) + x, y = map(atleast_1d, [x, y]) + if (len(x.shape) != 1) or (len(y.shape) != 1): + raise ValueError("First two entries should be rank-1 arrays.") + + msg = "Too many data points to interpolate." + + _int_overflow(x.size * y.size, MemoryError, msg=msg) + + if dx != 0 or dy != 0: + _int_overflow((tx.size - kx - 1)*(ty.size - ky - 1), + MemoryError, msg=msg) + z, ier = dfitpack.parder(tx, ty, c, kx, ky, dx, dy, x, y) + else: + z, ier = dfitpack.bispev(tx, ty, c, kx, ky, x, y) + + if ier == 10: + raise ValueError("Invalid input data") + if ier: + raise TypeError("An error occurred") + z.shape = len(x), len(y) + if len(z) > 1: + return z + if len(z[0]) > 1: + return z[0] + return z[0][0] + + +def dblint(xa, xb, ya, yb, tck): + """Evaluate the integral of a spline over area [xa,xb] x [ya,yb]. + + Parameters + ---------- + xa, xb : float + The end-points of the x integration interval. + ya, yb : float + The end-points of the y integration interval. + tck : list [tx, ty, c, kx, ky] + A sequence of length 5 returned by bisplrep containing the knot + locations tx, ty, the coefficients c, and the degrees kx, ky + of the spline. + + Returns + ------- + integ : float + The value of the resulting integral. + """ + tx, ty, c, kx, ky = tck + return dfitpack.dblint(tx, ty, c, kx, ky, xa, xb, ya, yb) + + +def insert(x, tck, m=1, per=0): + # see the docstring of `_fitpack_py/insert` + t, c, k = tck + try: + c[0][0] + parametric = True + except Exception: + parametric = False + if parametric: + cc = [] + for c_vals in c: + tt, cc_val, kk = insert(x, [t, c_vals, k], m) + cc.append(cc_val) + return (tt, cc, kk) + else: + tt, cc, ier = _fitpack._insert(per, t, c, k, x, m) + if ier == 10: + raise ValueError("Invalid input data") + if ier: + raise TypeError("An error occurred") + return (tt, cc, k) + + +def splder(tck, n=1): + # see the docstring of `_fitpack_py/splder` + if n < 0: + return splantider(tck, -n) + + t, c, k = tck + + if n > k: + raise ValueError(f"Order of derivative (n = {n!r}) must be <= " + f"order of spline (k = {tck[2]!r})") + + # Extra axes for the trailing dims of the `c` array: + sh = (slice(None),) + ((None,)*len(c.shape[1:])) + + with np.errstate(invalid='raise', divide='raise'): + try: + for j in range(n): + # See e.g. Schumaker, Spline Functions: Basic Theory, Chapter 5 + + # Compute the denominator in the differentiation formula. + # (and append trailing dims, if necessary) + dt = t[k+1:-1] - t[1:-k-1] + dt = dt[sh] + # Compute the new coefficients + c = (c[1:-1-k] - c[:-2-k]) * k / dt + # Pad coefficient array to same size as knots (FITPACK + # convention) + c = np.r_[c, np.zeros((k,) + c.shape[1:])] + # Adjust knots + t = t[1:-1] + k -= 1 + except FloatingPointError as e: + raise ValueError(("The spline has internal repeated knots " + "and is not differentiable %d times") % n) from e + + return t, c, k + + +def splantider(tck, n=1): + # see the docstring of `_fitpack_py/splantider` + if n < 0: + return splder(tck, -n) + + t, c, k = tck + + # Extra axes for the trailing dims of the `c` array: + sh = (slice(None),) + (None,)*len(c.shape[1:]) + + for j in range(n): + # This is the inverse set of operations to splder. + + # Compute the multiplier in the antiderivative formula. + dt = t[k+1:] - t[:-k-1] + dt = dt[sh] + # Compute the new coefficients + c = np.cumsum(c[:-k-1] * dt, axis=0) / (k + 1) + c = np.r_[np.zeros((1,) + c.shape[1:]), + c, + [c[-1]] * (k+2)] + # New knots + t = np.r_[t[0], t, t[-1]] + k += 1 + + return t, c, k diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack_py.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack_py.py new file mode 100644 index 0000000000000000000000000000000000000000..91ee711fead98bacd3f15b4175520a4d387390df --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_fitpack_py.py @@ -0,0 +1,796 @@ +__all__ = ['splrep', 'splprep', 'splev', 'splint', 'sproot', 'spalde', + 'bisplrep', 'bisplev', 'insert', 'splder', 'splantider'] + + +import numpy as np + +# These are in the API for fitpack even if not used in fitpack.py itself. +from ._fitpack_impl import bisplrep, bisplev, dblint # noqa: F401 +from . import _fitpack_impl as _impl +from ._bsplines import BSpline + + +def splprep(x, w=None, u=None, ub=None, ue=None, k=3, task=0, s=None, t=None, + full_output=0, nest=None, per=0, quiet=1): + """ + Find the B-spline representation of an N-D curve. + + Given a list of N rank-1 arrays, `x`, which represent a curve in + N-dimensional space parametrized by `u`, find a smooth approximating + spline curve g(`u`). Uses the FORTRAN routine parcur from FITPACK. + + Parameters + ---------- + x : array_like + A list of sample vector arrays representing the curve. + w : array_like, optional + Strictly positive rank-1 array of weights the same length as `x[0]`. + The weights are used in computing the weighted least-squares spline + fit. If the errors in the `x` values have standard-deviation given by + the vector d, then `w` should be 1/d. Default is ``ones(len(x[0]))``. + u : array_like, optional + An array of parameter values. If not given, these values are + calculated automatically as ``M = len(x[0])``, where + + v[0] = 0 + + v[i] = v[i-1] + distance(`x[i]`, `x[i-1]`) + + u[i] = v[i] / v[M-1] + + ub, ue : int, optional + The end-points of the parameters interval. Defaults to + u[0] and u[-1]. + k : int, optional + Degree of the spline. Cubic splines are recommended. + Even values of `k` should be avoided especially with a small s-value. + ``1 <= k <= 5``, default is 3. + task : int, optional + If task==0 (default), find t and c for a given smoothing factor, s. + If task==1, find t and c for another value of the smoothing factor, s. + There must have been a previous call with task=0 or task=1 + for the same set of data. + If task=-1 find the weighted least square spline for a given set of + knots, t. + s : float, optional + A smoothing condition. The amount of smoothness is determined by + satisfying the conditions: ``sum((w * (y - g))**2,axis=0) <= s``, + where g(x) is the smoothed interpolation of (x,y). The user can + use `s` to control the trade-off between closeness and smoothness + of fit. Larger `s` means more smoothing while smaller values of `s` + indicate less smoothing. Recommended values of `s` depend on the + weights, w. If the weights represent the inverse of the + standard-deviation of y, then a good `s` value should be found in + the range ``(m-sqrt(2*m),m+sqrt(2*m))``, where m is the number of + data points in x, y, and w. + t : array, optional + The knots needed for ``task=-1``. + There must be at least ``2*k+2`` knots. + full_output : int, optional + If non-zero, then return optional outputs. + nest : int, optional + An over-estimate of the total number of knots of the spline to + help in determining the storage space. By default nest=m/2. + Always large enough is nest=m+k+1. + per : int, optional + If non-zero, data points are considered periodic with period + ``x[m-1] - x[0]`` and a smooth periodic spline approximation is + returned. Values of ``y[m-1]`` and ``w[m-1]`` are not used. + quiet : int, optional + Non-zero to suppress messages. + + Returns + ------- + tck : tuple + A tuple, ``(t,c,k)`` containing the vector of knots, the B-spline + coefficients, and the degree of the spline. + u : array + An array of the values of the parameter. + fp : float + The weighted sum of squared residuals of the spline approximation. + ier : int + An integer flag about splrep success. Success is indicated + if ier<=0. If ier in [1,2,3] an error occurred but was not raised. + Otherwise an error is raised. + msg : str + A message corresponding to the integer flag, ier. + + See Also + -------- + splrep, splev, sproot, spalde, splint, + bisplrep, bisplev + UnivariateSpline, BivariateSpline + BSpline + make_interp_spline + + Notes + ----- + See `splev` for evaluation of the spline and its derivatives. + The number of dimensions N must be smaller than 11. + + The number of coefficients in the `c` array is ``k+1`` less than the number + of knots, ``len(t)``. This is in contrast with `splrep`, which zero-pads + the array of coefficients to have the same length as the array of knots. + These additional coefficients are ignored by evaluation routines, `splev` + and `BSpline`. + + References + ---------- + .. [1] P. Dierckx, "Algorithms for smoothing data with periodic and + parametric splines, Computer Graphics and Image Processing", + 20 (1982) 171-184. + .. [2] P. Dierckx, "Algorithms for smoothing data with periodic and + parametric splines", report tw55, Dept. Computer Science, + K.U.Leuven, 1981. + .. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs on + Numerical Analysis, Oxford University Press, 1993. + + Examples + -------- + Generate a discretization of a limacon curve in the polar coordinates: + + >>> import numpy as np + >>> phi = np.linspace(0, 2.*np.pi, 40) + >>> r = 0.5 + np.cos(phi) # polar coords + >>> x, y = r * np.cos(phi), r * np.sin(phi) # convert to cartesian + + And interpolate: + + >>> from scipy.interpolate import splprep, splev + >>> tck, u = splprep([x, y], s=0) + >>> new_points = splev(u, tck) + + Notice that (i) we force interpolation by using `s=0`, + (ii) the parameterization, ``u``, is generated automatically. + Now plot the result: + + >>> import matplotlib.pyplot as plt + >>> fig, ax = plt.subplots() + >>> ax.plot(x, y, 'ro') + >>> ax.plot(new_points[0], new_points[1], 'r-') + >>> plt.show() + + """ + + res = _impl.splprep(x, w, u, ub, ue, k, task, s, t, full_output, nest, per, + quiet) + return res + + +def splrep(x, y, w=None, xb=None, xe=None, k=3, task=0, s=None, t=None, + full_output=0, per=0, quiet=1): + """ + Find the B-spline representation of a 1-D curve. + + Given the set of data points ``(x[i], y[i])`` determine a smooth spline + approximation of degree k on the interval ``xb <= x <= xe``. + + Parameters + ---------- + x, y : array_like + The data points defining a curve ``y = f(x)``. + w : array_like, optional + Strictly positive rank-1 array of weights the same length as `x` and `y`. + The weights are used in computing the weighted least-squares spline + fit. If the errors in the `y` values have standard-deviation given by the + vector ``d``, then `w` should be ``1/d``. Default is ``ones(len(x))``. + xb, xe : float, optional + The interval to fit. If None, these default to ``x[0]`` and ``x[-1]`` + respectively. + k : int, optional + The degree of the spline fit. It is recommended to use cubic splines. + Even values of `k` should be avoided especially with small `s` values. + ``1 <= k <= 5``. + task : {1, 0, -1}, optional + If ``task==0``, find ``t`` and ``c`` for a given smoothing factor, `s`. + + If ``task==1`` find ``t`` and ``c`` for another value of the smoothing factor, + `s`. There must have been a previous call with ``task=0`` or ``task=1`` for + the same set of data (``t`` will be stored an used internally) + + If ``task=-1`` find the weighted least square spline for a given set of + knots, ``t``. These should be interior knots as knots on the ends will be + added automatically. + s : float, optional + A smoothing condition. The amount of smoothness is determined by + satisfying the conditions: ``sum((w * (y - g))**2,axis=0) <= s`` where ``g(x)`` + is the smoothed interpolation of ``(x,y)``. The user can use `s` to control + the tradeoff between closeness and smoothness of fit. Larger `s` means + more smoothing while smaller values of `s` indicate less smoothing. + Recommended values of `s` depend on the weights, `w`. If the weights + represent the inverse of the standard-deviation of `y`, then a good `s` + value should be found in the range ``(m-sqrt(2*m),m+sqrt(2*m))`` where ``m`` is + the number of datapoints in `x`, `y`, and `w`. default : ``s=m-sqrt(2*m)`` if + weights are supplied. ``s = 0.0`` (interpolating) if no weights are + supplied. + t : array_like, optional + The knots needed for ``task=-1``. If given then task is automatically set + to ``-1``. + full_output : bool, optional + If non-zero, then return optional outputs. + per : bool, optional + If non-zero, data points are considered periodic with period ``x[m-1]`` - + ``x[0]`` and a smooth periodic spline approximation is returned. Values of + ``y[m-1]`` and ``w[m-1]`` are not used. + The default is zero, corresponding to boundary condition 'not-a-knot'. + quiet : bool, optional + Non-zero to suppress messages. + + Returns + ------- + tck : tuple + A tuple ``(t,c,k)`` containing the vector of knots, the B-spline + coefficients, and the degree of the spline. + fp : array, optional + The weighted sum of squared residuals of the spline approximation. + ier : int, optional + An integer flag about splrep success. Success is indicated if ``ier<=0``. + If ``ier in [1,2,3]``, an error occurred but was not raised. Otherwise an + error is raised. + msg : str, optional + A message corresponding to the integer flag, `ier`. + + See Also + -------- + UnivariateSpline, BivariateSpline + splprep, splev, sproot, spalde, splint + bisplrep, bisplev + BSpline + make_interp_spline + + Notes + ----- + See `splev` for evaluation of the spline and its derivatives. Uses the + FORTRAN routine ``curfit`` from FITPACK. + + The user is responsible for assuring that the values of `x` are unique. + Otherwise, `splrep` will not return sensible results. + + If provided, knots `t` must satisfy the Schoenberg-Whitney conditions, + i.e., there must be a subset of data points ``x[j]`` such that + ``t[j] < x[j] < t[j+k+1]``, for ``j=0, 1,...,n-k-2``. + + This routine zero-pads the coefficients array ``c`` to have the same length + as the array of knots ``t`` (the trailing ``k + 1`` coefficients are ignored + by the evaluation routines, `splev` and `BSpline`.) This is in contrast with + `splprep`, which does not zero-pad the coefficients. + + The default boundary condition is 'not-a-knot', i.e. the first and second + segment at a curve end are the same polynomial. More boundary conditions are + available in `CubicSpline`. + + References + ---------- + Based on algorithms described in [1]_, [2]_, [3]_, and [4]_: + + .. [1] P. Dierckx, "An algorithm for smoothing, differentiation and + integration of experimental data using spline functions", + J.Comp.Appl.Maths 1 (1975) 165-184. + .. [2] P. Dierckx, "A fast algorithm for smoothing data on a rectangular + grid while using spline functions", SIAM J.Numer.Anal. 19 (1982) + 1286-1304. + .. [3] P. Dierckx, "An improved algorithm for curve fitting with spline + functions", report tw54, Dept. Computer Science,K.U. Leuven, 1981. + .. [4] P. Dierckx, "Curve and surface fitting with splines", Monographs on + Numerical Analysis, Oxford University Press, 1993. + + Examples + -------- + You can interpolate 1-D points with a B-spline curve. + Further examples are given in + :ref:`in the tutorial `. + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.interpolate import splev, splrep + >>> x = np.linspace(0, 10, 10) + >>> y = np.sin(x) + >>> spl = splrep(x, y) + >>> x2 = np.linspace(0, 10, 200) + >>> y2 = splev(x2, spl) + >>> plt.plot(x, y, 'o', x2, y2) + >>> plt.show() + + """ + res = _impl.splrep(x, y, w, xb, xe, k, task, s, t, full_output, per, quiet) + return res + + +def splev(x, tck, der=0, ext=0): + """ + Evaluate a B-spline or its derivatives. + + Given the knots and coefficients of a B-spline representation, evaluate + the value of the smoothing polynomial and its derivatives. This is a + wrapper around the FORTRAN routines splev and splder of FITPACK. + + Parameters + ---------- + x : array_like + An array of points at which to return the value of the smoothed + spline or its derivatives. If `tck` was returned from `splprep`, + then the parameter values, u should be given. + tck : 3-tuple or a BSpline object + If a tuple, then it should be a sequence of length 3 returned by + `splrep` or `splprep` containing the knots, coefficients, and degree + of the spline. (Also see Notes.) + der : int, optional + The order of derivative of the spline to compute (must be less than + or equal to k, the degree of the spline). + ext : int, optional + Controls the value returned for elements of ``x`` not in the + interval defined by the knot sequence. + + * if ext=0, return the extrapolated value. + * if ext=1, return 0 + * if ext=2, raise a ValueError + * if ext=3, return the boundary value. + + The default value is 0. + + Returns + ------- + y : ndarray or list of ndarrays + An array of values representing the spline function evaluated at + the points in `x`. If `tck` was returned from `splprep`, then this + is a list of arrays representing the curve in an N-D space. + + See Also + -------- + splprep, splrep, sproot, spalde, splint + bisplrep, bisplev + BSpline + + Notes + ----- + Manipulating the tck-tuples directly is not recommended. In new code, + prefer using `BSpline` objects. + + References + ---------- + .. [1] C. de Boor, "On calculating with b-splines", J. Approximation + Theory, 6, p.50-62, 1972. + .. [2] M. G. Cox, "The numerical evaluation of b-splines", J. Inst. Maths + Applics, 10, p.134-149, 1972. + .. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs + on Numerical Analysis, Oxford University Press, 1993. + + Examples + -------- + Examples are given :ref:`in the tutorial `. + + """ + if isinstance(tck, BSpline): + if tck.c.ndim > 1: + mesg = ("Calling splev() with BSpline objects with c.ndim > 1 is " + "not allowed. Use BSpline.__call__(x) instead.") + raise ValueError(mesg) + + # remap the out-of-bounds behavior + try: + extrapolate = {0: True, }[ext] + except KeyError as e: + raise ValueError("Extrapolation mode %s is not supported " + "by BSpline." % ext) from e + + return tck(x, der, extrapolate=extrapolate) + else: + return _impl.splev(x, tck, der, ext) + + +def splint(a, b, tck, full_output=0): + """ + Evaluate the definite integral of a B-spline between two given points. + + Parameters + ---------- + a, b : float + The end-points of the integration interval. + tck : tuple or a BSpline instance + If a tuple, then it should be a sequence of length 3, containing the + vector of knots, the B-spline coefficients, and the degree of the + spline (see `splev`). + full_output : int, optional + Non-zero to return optional output. + + Returns + ------- + integral : float + The resulting integral. + wrk : ndarray + An array containing the integrals of the normalized B-splines + defined on the set of knots. + (Only returned if `full_output` is non-zero) + + See Also + -------- + splprep, splrep, sproot, spalde, splev + bisplrep, bisplev + BSpline + + Notes + ----- + `splint` silently assumes that the spline function is zero outside the data + interval (`a`, `b`). + + Manipulating the tck-tuples directly is not recommended. In new code, + prefer using the `BSpline` objects. + + References + ---------- + .. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines", + J. Inst. Maths Applics, 17, p.37-41, 1976. + .. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs + on Numerical Analysis, Oxford University Press, 1993. + + Examples + -------- + Examples are given :ref:`in the tutorial `. + + """ + if isinstance(tck, BSpline): + if tck.c.ndim > 1: + mesg = ("Calling splint() with BSpline objects with c.ndim > 1 is " + "not allowed. Use BSpline.integrate() instead.") + raise ValueError(mesg) + + if full_output != 0: + mesg = ("full_output = %s is not supported. Proceeding as if " + "full_output = 0" % full_output) + + return tck.integrate(a, b, extrapolate=False) + else: + return _impl.splint(a, b, tck, full_output) + + +def sproot(tck, mest=10): + """ + Find the roots of a cubic B-spline. + + Given the knots (>=8) and coefficients of a cubic B-spline return the + roots of the spline. + + Parameters + ---------- + tck : tuple or a BSpline object + If a tuple, then it should be a sequence of length 3, containing the + vector of knots, the B-spline coefficients, and the degree of the + spline. + The number of knots must be >= 8, and the degree must be 3. + The knots must be a montonically increasing sequence. + mest : int, optional + An estimate of the number of zeros (Default is 10). + + Returns + ------- + zeros : ndarray + An array giving the roots of the spline. + + See Also + -------- + splprep, splrep, splint, spalde, splev + bisplrep, bisplev + BSpline + + Notes + ----- + Manipulating the tck-tuples directly is not recommended. In new code, + prefer using the `BSpline` objects. + + References + ---------- + .. [1] C. de Boor, "On calculating with b-splines", J. Approximation + Theory, 6, p.50-62, 1972. + .. [2] M. G. Cox, "The numerical evaluation of b-splines", J. Inst. Maths + Applics, 10, p.134-149, 1972. + .. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs + on Numerical Analysis, Oxford University Press, 1993. + + Examples + -------- + + For some data, this method may miss a root. This happens when one of + the spline knots (which FITPACK places automatically) happens to + coincide with the true root. A workaround is to convert to `PPoly`, + which uses a different root-finding algorithm. + + For example, + + >>> x = [1.96, 1.97, 1.98, 1.99, 2.00, 2.01, 2.02, 2.03, 2.04, 2.05] + >>> y = [-6.365470e-03, -4.790580e-03, -3.204320e-03, -1.607270e-03, + ... 4.440892e-16, 1.616930e-03, 3.243000e-03, 4.877670e-03, + ... 6.520430e-03, 8.170770e-03] + >>> from scipy.interpolate import splrep, sproot, PPoly + >>> tck = splrep(x, y, s=0) + >>> sproot(tck) + array([], dtype=float64) + + Converting to a PPoly object does find the roots at `x=2`: + + >>> ppoly = PPoly.from_spline(tck) + >>> ppoly.roots(extrapolate=False) + array([2.]) + + + Further examples are given :ref:`in the tutorial + `. + + """ + if isinstance(tck, BSpline): + if tck.c.ndim > 1: + mesg = ("Calling sproot() with BSpline objects with c.ndim > 1 is " + "not allowed.") + raise ValueError(mesg) + + t, c, k = tck.tck + + # _impl.sproot expects the interpolation axis to be last, so roll it. + # NB: This transpose is a no-op if c is 1D. + sh = tuple(range(c.ndim)) + c = c.transpose(sh[1:] + (0,)) + return _impl.sproot((t, c, k), mest) + else: + return _impl.sproot(tck, mest) + + +def spalde(x, tck): + """ + Evaluate all derivatives of a B-spline. + + Given the knots and coefficients of a cubic B-spline compute all + derivatives up to order k at a point (or set of points). + + Parameters + ---------- + x : array_like + A point or a set of points at which to evaluate the derivatives. + Note that ``t(k) <= x <= t(n-k+1)`` must hold for each `x`. + tck : tuple + A tuple (t,c,k) containing the vector of knots, + the B-spline coefficients, and the degree of the spline. + + Returns + ------- + results : {ndarray, list of ndarrays} + An array (or a list of arrays) containing all derivatives + up to order k inclusive for each point `x`. + + See Also + -------- + splprep, splrep, splint, sproot, splev, bisplrep, bisplev, + UnivariateSpline, BivariateSpline + + References + ---------- + .. [1] de Boor C : On calculating with b-splines, J. Approximation Theory + 6 (1972) 50-62. + .. [2] Cox M.G. : The numerical evaluation of b-splines, J. Inst. Maths + applics 10 (1972) 134-149. + .. [3] Dierckx P. : Curve and surface fitting with splines, Monographs on + Numerical Analysis, Oxford University Press, 1993. + + """ + if isinstance(tck, BSpline): + raise TypeError("spalde does not accept BSpline instances.") + else: + return _impl.spalde(x, tck) + + +def insert(x, tck, m=1, per=0): + """ + Insert knots into a B-spline. + + Given the knots and coefficients of a B-spline representation, create a + new B-spline with a knot inserted `m` times at point `x`. + This is a wrapper around the FORTRAN routine insert of FITPACK. + + Parameters + ---------- + x (u) : float + A knot value at which to insert a new knot. If `tck` was returned + from ``splprep``, then the parameter values, u should be given. + tck : a `BSpline` instance or a tuple + If tuple, then it is expected to be a tuple (t,c,k) containing + the vector of knots, the B-spline coefficients, and the degree of + the spline. + m : int, optional + The number of times to insert the given knot (its multiplicity). + Default is 1. + per : int, optional + If non-zero, the input spline is considered periodic. + + Returns + ------- + BSpline instance or a tuple + A new B-spline with knots t, coefficients c, and degree k. + ``t(k+1) <= x <= t(n-k)``, where k is the degree of the spline. + In case of a periodic spline (``per != 0``) there must be + either at least k interior knots t(j) satisfying ``t(k+1)>> from scipy.interpolate import splrep, insert + >>> import numpy as np + >>> x = np.linspace(0, 10, 5) + >>> y = np.sin(x) + >>> tck = splrep(x, y) + >>> tck[0] + array([ 0., 0., 0., 0., 5., 10., 10., 10., 10.]) + + A knot is inserted: + + >>> tck_inserted = insert(3, tck) + >>> tck_inserted[0] + array([ 0., 0., 0., 0., 3., 5., 10., 10., 10., 10.]) + + Some knots are inserted: + + >>> tck_inserted2 = insert(8, tck, m=3) + >>> tck_inserted2[0] + array([ 0., 0., 0., 0., 5., 8., 8., 8., 10., 10., 10., 10.]) + + """ + if isinstance(tck, BSpline): + + t, c, k = tck.tck + + # FITPACK expects the interpolation axis to be last, so roll it over + # NB: if c array is 1D, transposes are no-ops + sh = tuple(range(c.ndim)) + c = c.transpose(sh[1:] + (0,)) + t_, c_, k_ = _impl.insert(x, (t, c, k), m, per) + + # and roll the last axis back + c_ = np.asarray(c_) + c_ = c_.transpose((sh[-1],) + sh[:-1]) + return BSpline(t_, c_, k_) + else: + return _impl.insert(x, tck, m, per) + + +def splder(tck, n=1): + """ + Compute the spline representation of the derivative of a given spline + + Parameters + ---------- + tck : BSpline instance or a tuple of (t, c, k) + Spline whose derivative to compute + n : int, optional + Order of derivative to evaluate. Default: 1 + + Returns + ------- + `BSpline` instance or tuple + Spline of order k2=k-n representing the derivative + of the input spline. + A tuple is returned iff the input argument `tck` is a tuple, otherwise + a BSpline object is constructed and returned. + + See Also + -------- + splantider, splev, spalde + BSpline + + Notes + ----- + + .. versionadded:: 0.13.0 + + Examples + -------- + This can be used for finding maxima of a curve: + + >>> from scipy.interpolate import splrep, splder, sproot + >>> import numpy as np + >>> x = np.linspace(0, 10, 70) + >>> y = np.sin(x) + >>> spl = splrep(x, y, k=4) + + Now, differentiate the spline and find the zeros of the + derivative. (NB: `sproot` only works for order 3 splines, so we + fit an order 4 spline): + + >>> dspl = splder(spl) + >>> sproot(dspl) / np.pi + array([ 0.50000001, 1.5 , 2.49999998]) + + This agrees well with roots :math:`\\pi/2 + n\\pi` of + :math:`\\cos(x) = \\sin'(x)`. + + """ + if isinstance(tck, BSpline): + return tck.derivative(n) + else: + return _impl.splder(tck, n) + + +def splantider(tck, n=1): + """ + Compute the spline for the antiderivative (integral) of a given spline. + + Parameters + ---------- + tck : BSpline instance or a tuple of (t, c, k) + Spline whose antiderivative to compute + n : int, optional + Order of antiderivative to evaluate. Default: 1 + + Returns + ------- + BSpline instance or a tuple of (t2, c2, k2) + Spline of order k2=k+n representing the antiderivative of the input + spline. + A tuple is returned iff the input argument `tck` is a tuple, otherwise + a BSpline object is constructed and returned. + + See Also + -------- + splder, splev, spalde + BSpline + + Notes + ----- + The `splder` function is the inverse operation of this function. + Namely, ``splder(splantider(tck))`` is identical to `tck`, modulo + rounding error. + + .. versionadded:: 0.13.0 + + Examples + -------- + >>> from scipy.interpolate import splrep, splder, splantider, splev + >>> import numpy as np + >>> x = np.linspace(0, np.pi/2, 70) + >>> y = 1 / np.sqrt(1 - 0.8*np.sin(x)**2) + >>> spl = splrep(x, y) + + The derivative is the inverse operation of the antiderivative, + although some floating point error accumulates: + + >>> splev(1.7, spl), splev(1.7, splder(splantider(spl))) + (array(2.1565429877197317), array(2.1565429877201865)) + + Antiderivative can be used to evaluate definite integrals: + + >>> ispl = splantider(spl) + >>> splev(np.pi/2, ispl) - splev(0, ispl) + 2.2572053588768486 + + This is indeed an approximation to the complete elliptic integral + :math:`K(m) = \\int_0^{\\pi/2} [1 - m\\sin^2 x]^{-1/2} dx`: + + >>> from scipy.special import ellipk + >>> ellipk(0.8) + 2.2572053268208538 + + """ + if isinstance(tck, BSpline): + return tck.antiderivative(n) + else: + return _impl.splantider(tck, n) + diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_ndbspline.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_ndbspline.py new file mode 100644 index 0000000000000000000000000000000000000000..826dddb311d78bf8d5381b18e46ca1ba86c04b6d --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_ndbspline.py @@ -0,0 +1,358 @@ +import itertools +import functools +import operator +import numpy as np + +from math import prod + +from . import _bspl # type: ignore + +import scipy.sparse.linalg as ssl +from scipy.sparse import csr_array + +from ._bsplines import _not_a_knot + +__all__ = ["NdBSpline"] + + +def _get_dtype(dtype): + """Return np.complex128 for complex dtypes, np.float64 otherwise.""" + if np.issubdtype(dtype, np.complexfloating): + return np.complex128 + else: + return np.float64 + + +class NdBSpline: + """Tensor product spline object. + + The value at point ``xp = (x1, x2, ..., xN)`` is evaluated as a linear + combination of products of one-dimensional b-splines in each of the ``N`` + dimensions:: + + c[i1, i2, ..., iN] * B(x1; i1, t1) * B(x2; i2, t2) * ... * B(xN; iN, tN) + + + Here ``B(x; i, t)`` is the ``i``-th b-spline defined by the knot vector + ``t`` evaluated at ``x``. + + Parameters + ---------- + t : tuple of 1D ndarrays + knot vectors in directions 1, 2, ... N, + ``len(t[i]) == n[i] + k + 1`` + c : ndarray, shape (n1, n2, ..., nN, ...) + b-spline coefficients + k : int or length-d tuple of integers + spline degrees. + A single integer is interpreted as having this degree for + all dimensions. + extrapolate : bool, optional + Whether to extrapolate out-of-bounds inputs, or return `nan`. + Default is to extrapolate. + + Attributes + ---------- + t : tuple of ndarrays + Knots vectors. + c : ndarray + Coefficients of the tensor-produce spline. + k : tuple of integers + Degrees for each dimension. + extrapolate : bool, optional + Whether to extrapolate or return nans for out-of-bounds inputs. + Defaults to true. + + Methods + ------- + __call__ + design_matrix + + See Also + -------- + BSpline : a one-dimensional B-spline object + NdPPoly : an N-dimensional piecewise tensor product polynomial + + """ + def __init__(self, t, c, k, *, extrapolate=None): + ndim = len(t) + + try: + len(k) + except TypeError: + # make k a tuple + k = (k,)*ndim + + if len(k) != ndim: + raise ValueError(f"{len(t) = } != {len(k) = }.") + + self.k = tuple(operator.index(ki) for ki in k) + self.t = tuple(np.ascontiguousarray(ti, dtype=float) for ti in t) + self.c = np.asarray(c) + + if extrapolate is None: + extrapolate = True + self.extrapolate = bool(extrapolate) + + self.c = np.asarray(c) + + for d in range(ndim): + td = self.t[d] + kd = self.k[d] + n = td.shape[0] - kd - 1 + if kd < 0: + raise ValueError(f"Spline degree in dimension {d} cannot be" + f" negative.") + if td.ndim != 1: + raise ValueError(f"Knot vector in dimension {d} must be" + f" one-dimensional.") + if n < kd + 1: + raise ValueError(f"Need at least {2*kd + 2} knots for degree" + f" {kd} in dimension {d}.") + if (np.diff(td) < 0).any(): + raise ValueError(f"Knots in dimension {d} must be in a" + f" non-decreasing order.") + if len(np.unique(td[kd:n + 1])) < 2: + raise ValueError(f"Need at least two internal knots in" + f" dimension {d}.") + if not np.isfinite(td).all(): + raise ValueError(f"Knots in dimension {d} should not have" + f" nans or infs.") + if self.c.ndim < ndim: + raise ValueError(f"Coefficients must be at least" + f" {d}-dimensional.") + if self.c.shape[d] != n: + raise ValueError(f"Knots, coefficients and degree in dimension" + f" {d} are inconsistent:" + f" got {self.c.shape[d]} coefficients for" + f" {len(td)} knots, need at least {n} for" + f" k={k}.") + + dt = _get_dtype(self.c.dtype) + self.c = np.ascontiguousarray(self.c, dtype=dt) + + def __call__(self, xi, *, nu=None, extrapolate=None): + """Evaluate the tensor product b-spline at ``xi``. + + Parameters + ---------- + xi : array_like, shape(..., ndim) + The coordinates to evaluate the interpolator at. + This can be a list or tuple of ndim-dimensional points + or an array with the shape (num_points, ndim). + nu : array_like, optional, shape (ndim,) + Orders of derivatives to evaluate. Each must be non-negative. + Defaults to the zeroth derivivative. + extrapolate : bool, optional + Whether to exrapolate based on first and last intervals in each + dimension, or return `nan`. Default is to ``self.extrapolate``. + + Returns + ------- + values : ndarray, shape ``xi.shape[:-1] + self.c.shape[ndim:]`` + Interpolated values at ``xi`` + """ + ndim = len(self.t) + + if extrapolate is None: + extrapolate = self.extrapolate + extrapolate = bool(extrapolate) + + if nu is None: + nu = np.zeros((ndim,), dtype=np.intc) + else: + nu = np.asarray(nu, dtype=np.intc) + if nu.ndim != 1 or nu.shape[0] != ndim: + raise ValueError( + f"invalid number of derivative orders {nu = } for " + f"ndim = {len(self.t)}.") + if any(nu < 0): + raise ValueError(f"derivatives must be positive, got {nu = }") + + # prepare xi : shape (..., m1, ..., md) -> (1, m1, ..., md) + xi = np.asarray(xi, dtype=float) + xi_shape = xi.shape + xi = xi.reshape(-1, xi_shape[-1]) + xi = np.ascontiguousarray(xi) + + if xi_shape[-1] != ndim: + raise ValueError(f"Shapes: xi.shape={xi_shape} and ndim={ndim}") + + # prepare k & t + _k = np.asarray(self.k, dtype=np.dtype("long")) + + # pack the knots into a single array + len_t = [len(ti) for ti in self.t] + _t = np.empty((ndim, max(len_t)), dtype=float) + _t.fill(np.nan) + for d in range(ndim): + _t[d, :len(self.t[d])] = self.t[d] + len_t = np.asarray(len_t, dtype=np.dtype("long")) + + # tabulate the flat indices for iterating over the (k+1)**ndim subarray + shape = tuple(kd + 1 for kd in self.k) + indices = np.unravel_index(np.arange(prod(shape)), shape) + _indices_k1d = np.asarray(indices, dtype=np.intp).T + + # prepare the coefficients: flatten the trailing dimensions + c1 = self.c.reshape(self.c.shape[:ndim] + (-1,)) + c1r = c1.ravel() + + # replacement for np.ravel_multi_index for indexing of `c1`: + _strides_c1 = np.asarray([s // c1.dtype.itemsize + for s in c1.strides], dtype=np.intp) + + num_c_tr = c1.shape[-1] # # of trailing coefficients + out = np.empty(xi.shape[:-1] + (num_c_tr,), dtype=c1.dtype) + + _bspl.evaluate_ndbspline(xi, + _t, + len_t, + _k, + nu, + extrapolate, + c1r, + num_c_tr, + _strides_c1, + _indices_k1d, + out,) + + return out.reshape(xi_shape[:-1] + self.c.shape[ndim:]) + + @classmethod + def design_matrix(cls, xvals, t, k, extrapolate=True): + """Construct the design matrix as a CSR format sparse array. + + Parameters + ---------- + xvals : ndarray, shape(npts, ndim) + Data points. ``xvals[j, :]`` gives the ``j``-th data point as an + ``ndim``-dimensional array. + t : tuple of 1D ndarrays, length-ndim + Knot vectors in directions 1, 2, ... ndim, + k : int + B-spline degree. + extrapolate : bool, optional + Whether to extrapolate out-of-bounds values of raise a `ValueError` + + Returns + ------- + design_matrix : a CSR array + Each row of the design matrix corresponds to a value in `xvals` and + contains values of b-spline basis elements which are non-zero + at this value. + + """ + xvals = np.asarray(xvals, dtype=float) + ndim = xvals.shape[-1] + if len(t) != ndim: + raise ValueError( + f"Data and knots are inconsistent: len(t) = {len(t)} for " + f" {ndim = }." + ) + try: + len(k) + except TypeError: + # make k a tuple + k = (k,)*ndim + + kk = np.asarray(k, dtype=np.int32) + data, indices, indptr = _bspl._colloc_nd(xvals, t, kk) + return csr_array((data, indices, indptr)) + + +def _iter_solve(a, b, solver=ssl.gcrotmk, **solver_args): + # work around iterative solvers not accepting multiple r.h.s. + + # also work around a.dtype == float64 and b.dtype == complex128 + # cf https://github.com/scipy/scipy/issues/19644 + if np.issubdtype(b.dtype, np.complexfloating): + real = _iter_solve(a, b.real, solver, **solver_args) + imag = _iter_solve(a, b.imag, solver, **solver_args) + return real + 1j*imag + + if b.ndim == 2 and b.shape[1] !=1: + res = np.empty_like(b) + for j in range(b.shape[1]): + res[:, j], info = solver(a, b[:, j], **solver_args) + if info != 0: + raise ValueError(f"{solver = } returns {info =} for column {j}.") + return res + else: + res, info = solver(a, b, **solver_args) + if info != 0: + raise ValueError(f"{solver = } returns {info = }.") + return res + + +def make_ndbspl(points, values, k=3, *, solver=ssl.gcrotmk, **solver_args): + """Construct an interpolating NdBspline. + + Parameters + ---------- + points : tuple of ndarrays of float, with shapes (m1,), ... (mN,) + The points defining the regular grid in N dimensions. The points in + each dimension (i.e. every element of the `points` tuple) must be + strictly ascending or descending. + values : ndarray of float, shape (m1, ..., mN, ...) + The data on the regular grid in n dimensions. + k : int, optional + The spline degree. Must be odd. Default is cubic, k=3 + solver : a `scipy.sparse.linalg` solver (iterative or direct), optional. + An iterative solver from `scipy.sparse.linalg` or a direct one, + `sparse.sparse.linalg.spsolve`. + Used to solve the sparse linear system + ``design_matrix @ coefficients = rhs`` for the coefficients. + Default is `scipy.sparse.linalg.gcrotmk` + solver_args : dict, optional + Additional arguments for the solver. The call signature is + ``solver(csr_array, rhs_vector, **solver_args)`` + + Returns + ------- + spl : NdBSpline object + + Notes + ----- + Boundary conditions are not-a-knot in all dimensions. + """ + ndim = len(points) + xi_shape = tuple(len(x) for x in points) + + try: + len(k) + except TypeError: + # make k a tuple + k = (k,)*ndim + + for d, point in enumerate(points): + numpts = len(np.atleast_1d(point)) + if numpts <= k[d]: + raise ValueError(f"There are {numpts} points in dimension {d}," + f" but order {k[d]} requires at least " + f" {k[d]+1} points per dimension.") + + t = tuple(_not_a_knot(np.asarray(points[d], dtype=float), k[d]) + for d in range(ndim)) + xvals = np.asarray([xv for xv in itertools.product(*points)], dtype=float) + + # construct the colocation matrix + matr = NdBSpline.design_matrix(xvals, t, k) + + # Solve for the coefficients given `values`. + # Trailing dimensions: first ndim dimensions are data, the rest are batch + # dimensions, so stack `values` into a 2D array for `spsolve` to undestand. + v_shape = values.shape + vals_shape = (prod(v_shape[:ndim]), prod(v_shape[ndim:])) + vals = values.reshape(vals_shape) + + if solver != ssl.spsolve: + solver = functools.partial(_iter_solve, solver=solver) + if "atol" not in solver_args: + # avoid a DeprecationWarning, grumble grumble + solver_args["atol"] = 1e-6 + + coef = solver(matr, vals, **solver_args) + coef = coef.reshape(xi_shape + v_shape[ndim:]) + return NdBSpline(t, coef, k) + diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_ndgriddata.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_ndgriddata.py new file mode 100644 index 0000000000000000000000000000000000000000..2724d78f61416256357c4b2789c860a604845548 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_ndgriddata.py @@ -0,0 +1,332 @@ +""" +Convenience interface to N-D interpolation + +.. versionadded:: 0.9 + +""" +import numpy as np +from .interpnd import LinearNDInterpolator, NDInterpolatorBase, \ + CloughTocher2DInterpolator, _ndim_coords_from_arrays +from scipy.spatial import cKDTree + +__all__ = ['griddata', 'NearestNDInterpolator', 'LinearNDInterpolator', + 'CloughTocher2DInterpolator'] + +#------------------------------------------------------------------------------ +# Nearest-neighbor interpolation +#------------------------------------------------------------------------------ + + +class NearestNDInterpolator(NDInterpolatorBase): + """NearestNDInterpolator(x, y). + + Nearest-neighbor interpolator in N > 1 dimensions. + + .. versionadded:: 0.9 + + Methods + ------- + __call__ + + Parameters + ---------- + x : (npoints, ndims) 2-D ndarray of floats + Data point coordinates. + y : (npoints, ) 1-D ndarray of float or complex + Data values. + rescale : boolean, optional + Rescale points to unit cube before performing interpolation. + This is useful if some of the input dimensions have + incommensurable units and differ by many orders of magnitude. + + .. versionadded:: 0.14.0 + tree_options : dict, optional + Options passed to the underlying ``cKDTree``. + + .. versionadded:: 0.17.0 + + See Also + -------- + griddata : + Interpolate unstructured D-D data. + LinearNDInterpolator : + Piecewise linear interpolator in N dimensions. + CloughTocher2DInterpolator : + Piecewise cubic, C1 smooth, curvature-minimizing interpolator in 2D. + interpn : Interpolation on a regular grid or rectilinear grid. + RegularGridInterpolator : Interpolator on a regular or rectilinear grid + in arbitrary dimensions (`interpn` wraps this + class). + + Notes + ----- + Uses ``scipy.spatial.cKDTree`` + + .. note:: For data on a regular grid use `interpn` instead. + + Examples + -------- + We can interpolate values on a 2D plane: + + >>> from scipy.interpolate import NearestNDInterpolator + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + >>> x = rng.random(10) - 0.5 + >>> y = rng.random(10) - 0.5 + >>> z = np.hypot(x, y) + >>> X = np.linspace(min(x), max(x)) + >>> Y = np.linspace(min(y), max(y)) + >>> X, Y = np.meshgrid(X, Y) # 2D grid for interpolation + >>> interp = NearestNDInterpolator(list(zip(x, y)), z) + >>> Z = interp(X, Y) + >>> plt.pcolormesh(X, Y, Z, shading='auto') + >>> plt.plot(x, y, "ok", label="input point") + >>> plt.legend() + >>> plt.colorbar() + >>> plt.axis("equal") + >>> plt.show() + + """ + + def __init__(self, x, y, rescale=False, tree_options=None): + NDInterpolatorBase.__init__(self, x, y, rescale=rescale, + need_contiguous=False, + need_values=False) + if tree_options is None: + tree_options = dict() + self.tree = cKDTree(self.points, **tree_options) + self.values = np.asarray(y) + + def __call__(self, *args, **query_options): + """ + Evaluate interpolator at given points. + + Parameters + ---------- + x1, x2, ... xn : array-like of float + Points where to interpolate data at. + x1, x2, ... xn can be array-like of float with broadcastable shape. + or x1 can be array-like of float with shape ``(..., ndim)`` + **query_options + This allows ``eps``, ``p``, ``distance_upper_bound``, and ``workers`` + being passed to the cKDTree's query function to be explicitly set. + See `scipy.spatial.cKDTree.query` for an overview of the different options. + + .. versionadded:: 1.12.0 + + """ + # For the sake of enabling subclassing, NDInterpolatorBase._set_xi performs + # some operations which are not required by NearestNDInterpolator.__call__, + # hence here we operate on xi directly, without calling a parent class function. + xi = _ndim_coords_from_arrays(args, ndim=self.points.shape[1]) + xi = self._check_call_shape(xi) + xi = self._scale_x(xi) + + # We need to handle two important cases: + # (1) the case where xi has trailing dimensions (..., ndim), and + # (2) the case where y has trailing dimensions + # We will first flatten xi to deal with case (1), + # do the computation in flattened array while retaining y's dimensionality, + # and then reshape the interpolated values back to match xi's shape. + + # Flatten xi for the query + xi_flat = xi.reshape(-1, xi.shape[-1]) + original_shape = xi.shape + flattened_shape = xi_flat.shape + + # if distance_upper_bound is set to not be infinite, + # then we need to consider the case where cKDtree + # does not find any points within distance_upper_bound to return. + # It marks those points as having infinte distance, which is what will be used + # below to mask the array and return only the points that were deemed + # to have a close enough neighbor to return something useful. + dist, i = self.tree.query(xi_flat, **query_options) + valid_mask = np.isfinite(dist) + + # create a holder interp_values array and fill with nans. + if self.values.ndim > 1: + interp_shape = flattened_shape[:-1] + self.values.shape[1:] + else: + interp_shape = flattened_shape[:-1] + + if np.issubdtype(self.values.dtype, np.complexfloating): + interp_values = np.full(interp_shape, np.nan, dtype=self.values.dtype) + else: + interp_values = np.full(interp_shape, np.nan) + + interp_values[valid_mask] = self.values[i[valid_mask], ...] + + if self.values.ndim > 1: + new_shape = original_shape[:-1] + self.values.shape[1:] + else: + new_shape = original_shape[:-1] + interp_values = interp_values.reshape(new_shape) + + return interp_values + + +#------------------------------------------------------------------------------ +# Convenience interface function +#------------------------------------------------------------------------------ + + +def griddata(points, values, xi, method='linear', fill_value=np.nan, + rescale=False): + """ + Interpolate unstructured D-D data. + + Parameters + ---------- + points : 2-D ndarray of floats with shape (n, D), or length D tuple of 1-D ndarrays with shape (n,). + Data point coordinates. + values : ndarray of float or complex, shape (n,) + Data values. + xi : 2-D ndarray of floats with shape (m, D), or length D tuple of ndarrays broadcastable to the same shape. + Points at which to interpolate data. + method : {'linear', 'nearest', 'cubic'}, optional + Method of interpolation. One of + + ``nearest`` + return the value at the data point closest to + the point of interpolation. See `NearestNDInterpolator` for + more details. + + ``linear`` + tessellate the input point set to N-D + simplices, and interpolate linearly on each simplex. See + `LinearNDInterpolator` for more details. + + ``cubic`` (1-D) + return the value determined from a cubic + spline. + + ``cubic`` (2-D) + return the value determined from a + piecewise cubic, continuously differentiable (C1), and + approximately curvature-minimizing polynomial surface. See + `CloughTocher2DInterpolator` for more details. + fill_value : float, optional + Value used to fill in for requested points outside of the + convex hull of the input points. If not provided, then the + default is ``nan``. This option has no effect for the + 'nearest' method. + rescale : bool, optional + Rescale points to unit cube before performing interpolation. + This is useful if some of the input dimensions have + incommensurable units and differ by many orders of magnitude. + + .. versionadded:: 0.14.0 + + Returns + ------- + ndarray + Array of interpolated values. + + See Also + -------- + LinearNDInterpolator : + Piecewise linear interpolator in N dimensions. + NearestNDInterpolator : + Nearest-neighbor interpolator in N dimensions. + CloughTocher2DInterpolator : + Piecewise cubic, C1 smooth, curvature-minimizing interpolator in 2D. + interpn : Interpolation on a regular grid or rectilinear grid. + RegularGridInterpolator : Interpolator on a regular or rectilinear grid + in arbitrary dimensions (`interpn` wraps this + class). + + Notes + ----- + + .. versionadded:: 0.9 + + .. note:: For data on a regular grid use `interpn` instead. + + Examples + -------- + + Suppose we want to interpolate the 2-D function + + >>> import numpy as np + >>> def func(x, y): + ... return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2 + + on a grid in [0, 1]x[0, 1] + + >>> grid_x, grid_y = np.mgrid[0:1:100j, 0:1:200j] + + but we only know its values at 1000 data points: + + >>> rng = np.random.default_rng() + >>> points = rng.random((1000, 2)) + >>> values = func(points[:,0], points[:,1]) + + This can be done with `griddata` -- below we try out all of the + interpolation methods: + + >>> from scipy.interpolate import griddata + >>> grid_z0 = griddata(points, values, (grid_x, grid_y), method='nearest') + >>> grid_z1 = griddata(points, values, (grid_x, grid_y), method='linear') + >>> grid_z2 = griddata(points, values, (grid_x, grid_y), method='cubic') + + One can see that the exact result is reproduced by all of the + methods to some degree, but for this smooth function the piecewise + cubic interpolant gives the best results: + + >>> import matplotlib.pyplot as plt + >>> plt.subplot(221) + >>> plt.imshow(func(grid_x, grid_y).T, extent=(0,1,0,1), origin='lower') + >>> plt.plot(points[:,0], points[:,1], 'k.', ms=1) + >>> plt.title('Original') + >>> plt.subplot(222) + >>> plt.imshow(grid_z0.T, extent=(0,1,0,1), origin='lower') + >>> plt.title('Nearest') + >>> plt.subplot(223) + >>> plt.imshow(grid_z1.T, extent=(0,1,0,1), origin='lower') + >>> plt.title('Linear') + >>> plt.subplot(224) + >>> plt.imshow(grid_z2.T, extent=(0,1,0,1), origin='lower') + >>> plt.title('Cubic') + >>> plt.gcf().set_size_inches(6, 6) + >>> plt.show() + + """ # numpy/numpydoc#87 # noqa: E501 + + points = _ndim_coords_from_arrays(points) + + if points.ndim < 2: + ndim = points.ndim + else: + ndim = points.shape[-1] + + if ndim == 1 and method in ('nearest', 'linear', 'cubic'): + from ._interpolate import interp1d + points = points.ravel() + if isinstance(xi, tuple): + if len(xi) != 1: + raise ValueError("invalid number of dimensions in xi") + xi, = xi + # Sort points/values together, necessary as input for interp1d + idx = np.argsort(points) + points = points[idx] + values = values[idx] + if method == 'nearest': + fill_value = 'extrapolate' + ip = interp1d(points, values, kind=method, axis=0, bounds_error=False, + fill_value=fill_value) + return ip(xi) + elif method == 'nearest': + ip = NearestNDInterpolator(points, values, rescale=rescale) + return ip(xi) + elif method == 'linear': + ip = LinearNDInterpolator(points, values, fill_value=fill_value, + rescale=rescale) + return ip(xi) + elif method == 'cubic' and ndim == 2: + ip = CloughTocher2DInterpolator(points, values, fill_value=fill_value, + rescale=rescale) + return ip(xi) + else: + raise ValueError("Unknown interpolation method %r for " + "%d dimensional data" % (method, ndim)) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_polyint.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_polyint.py new file mode 100644 index 0000000000000000000000000000000000000000..6ed06d8abdba9597397295a0ca3c4a2bc3b25659 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_polyint.py @@ -0,0 +1,938 @@ +import warnings + +import numpy as np +from scipy.special import factorial +from scipy._lib._util import _asarray_validated, float_factorial, check_random_state + + +__all__ = ["KroghInterpolator", "krogh_interpolate", + "BarycentricInterpolator", "barycentric_interpolate", + "approximate_taylor_polynomial"] + + +def _isscalar(x): + """Check whether x is if a scalar type, or 0-dim""" + return np.isscalar(x) or hasattr(x, 'shape') and x.shape == () + + +class _Interpolator1D: + """ + Common features in univariate interpolation + + Deal with input data type and interpolation axis rolling. The + actual interpolator can assume the y-data is of shape (n, r) where + `n` is the number of x-points, and `r` the number of variables, + and use self.dtype as the y-data type. + + Attributes + ---------- + _y_axis + Axis along which the interpolation goes in the original array + _y_extra_shape + Additional trailing shape of the input arrays, excluding + the interpolation axis. + dtype + Dtype of the y-data arrays. Can be set via _set_dtype, which + forces it to be float or complex. + + Methods + ------- + __call__ + _prepare_x + _finish_y + _reshape_yi + _set_yi + _set_dtype + _evaluate + + """ + + __slots__ = ('_y_axis', '_y_extra_shape', 'dtype') + + def __init__(self, xi=None, yi=None, axis=None): + self._y_axis = axis + self._y_extra_shape = None + self.dtype = None + if yi is not None: + self._set_yi(yi, xi=xi, axis=axis) + + def __call__(self, x): + """ + Evaluate the interpolant + + Parameters + ---------- + x : array_like + Point or points at which to evaluate the interpolant. + + Returns + ------- + y : array_like + Interpolated values. Shape is determined by replacing + the interpolation axis in the original array with the shape of `x`. + + Notes + ----- + Input values `x` must be convertible to `float` values like `int` + or `float`. + + """ + x, x_shape = self._prepare_x(x) + y = self._evaluate(x) + return self._finish_y(y, x_shape) + + def _evaluate(self, x): + """ + Actually evaluate the value of the interpolator. + """ + raise NotImplementedError() + + def _prepare_x(self, x): + """Reshape input x array to 1-D""" + x = _asarray_validated(x, check_finite=False, as_inexact=True) + x_shape = x.shape + return x.ravel(), x_shape + + def _finish_y(self, y, x_shape): + """Reshape interpolated y back to an N-D array similar to initial y""" + y = y.reshape(x_shape + self._y_extra_shape) + if self._y_axis != 0 and x_shape != (): + nx = len(x_shape) + ny = len(self._y_extra_shape) + s = (list(range(nx, nx + self._y_axis)) + + list(range(nx)) + list(range(nx+self._y_axis, nx+ny))) + y = y.transpose(s) + return y + + def _reshape_yi(self, yi, check=False): + yi = np.moveaxis(np.asarray(yi), self._y_axis, 0) + if check and yi.shape[1:] != self._y_extra_shape: + ok_shape = "{!r} + (N,) + {!r}".format(self._y_extra_shape[-self._y_axis:], + self._y_extra_shape[:-self._y_axis]) + raise ValueError("Data must be of shape %s" % ok_shape) + return yi.reshape((yi.shape[0], -1)) + + def _set_yi(self, yi, xi=None, axis=None): + if axis is None: + axis = self._y_axis + if axis is None: + raise ValueError("no interpolation axis specified") + + yi = np.asarray(yi) + + shape = yi.shape + if shape == (): + shape = (1,) + if xi is not None and shape[axis] != len(xi): + raise ValueError("x and y arrays must be equal in length along " + "interpolation axis.") + + self._y_axis = (axis % yi.ndim) + self._y_extra_shape = yi.shape[:self._y_axis] + yi.shape[self._y_axis+1:] + self.dtype = None + self._set_dtype(yi.dtype) + + def _set_dtype(self, dtype, union=False): + if np.issubdtype(dtype, np.complexfloating) \ + or np.issubdtype(self.dtype, np.complexfloating): + self.dtype = np.complex128 + else: + if not union or self.dtype != np.complex128: + self.dtype = np.float64 + + +class _Interpolator1DWithDerivatives(_Interpolator1D): + def derivatives(self, x, der=None): + """ + Evaluate several derivatives of the polynomial at the point `x` + + Produce an array of derivatives evaluated at the point `x`. + + Parameters + ---------- + x : array_like + Point or points at which to evaluate the derivatives + der : int or list or None, optional + How many derivatives to evaluate, or None for all potentially + nonzero derivatives (that is, a number equal to the number + of points), or a list of derivatives to evaluate. This number + includes the function value as the '0th' derivative. + + Returns + ------- + d : ndarray + Array with derivatives; ``d[j]`` contains the jth derivative. + Shape of ``d[j]`` is determined by replacing the interpolation + axis in the original array with the shape of `x`. + + Examples + -------- + >>> from scipy.interpolate import KroghInterpolator + >>> KroghInterpolator([0,0,0],[1,2,3]).derivatives(0) + array([1.0,2.0,3.0]) + >>> KroghInterpolator([0,0,0],[1,2,3]).derivatives([0,0]) + array([[1.0,1.0], + [2.0,2.0], + [3.0,3.0]]) + + """ + x, x_shape = self._prepare_x(x) + y = self._evaluate_derivatives(x, der) + + y = y.reshape((y.shape[0],) + x_shape + self._y_extra_shape) + if self._y_axis != 0 and x_shape != (): + nx = len(x_shape) + ny = len(self._y_extra_shape) + s = ([0] + list(range(nx+1, nx + self._y_axis+1)) + + list(range(1, nx+1)) + + list(range(nx+1+self._y_axis, nx+ny+1))) + y = y.transpose(s) + return y + + def derivative(self, x, der=1): + """ + Evaluate a single derivative of the polynomial at the point `x`. + + Parameters + ---------- + x : array_like + Point or points at which to evaluate the derivatives + + der : integer, optional + Which derivative to evaluate (default: first derivative). + This number includes the function value as 0th derivative. + + Returns + ------- + d : ndarray + Derivative interpolated at the x-points. Shape of `d` is + determined by replacing the interpolation axis in the + original array with the shape of `x`. + + Notes + ----- + This may be computed by evaluating all derivatives up to the desired + one (using self.derivatives()) and then discarding the rest. + + """ + x, x_shape = self._prepare_x(x) + y = self._evaluate_derivatives(x, der+1) + return self._finish_y(y[der], x_shape) + + def _evaluate_derivatives(self, x, der=None): + """ + Actually evaluate the derivatives. + + Parameters + ---------- + x : array_like + 1D array of points at which to evaluate the derivatives + der : integer, optional + The number of derivatives to evaluate, from 'order 0' (der=1) + to order der-1. If omitted, return all possibly-non-zero + derivatives, ie 0 to order n-1. + + Returns + ------- + d : ndarray + Array of shape ``(der, x.size, self.yi.shape[1])`` containing + the derivatives from 0 to der-1 + """ + raise NotImplementedError() + + +class KroghInterpolator(_Interpolator1DWithDerivatives): + """ + Interpolating polynomial for a set of points. + + The polynomial passes through all the pairs ``(xi, yi)``. One may + additionally specify a number of derivatives at each point `xi`; + this is done by repeating the value `xi` and specifying the + derivatives as successive `yi` values. + + Allows evaluation of the polynomial and all its derivatives. + For reasons of numerical stability, this function does not compute + the coefficients of the polynomial, although they can be obtained + by evaluating all the derivatives. + + Parameters + ---------- + xi : array_like, shape (npoints, ) + Known x-coordinates. Must be sorted in increasing order. + yi : array_like, shape (..., npoints, ...) + Known y-coordinates. When an xi occurs two or more times in + a row, the corresponding yi's represent derivative values. The length of `yi` + along the interpolation axis must be equal to the length of `xi`. Use the + `axis` parameter to select the correct axis. + axis : int, optional + Axis in the `yi` array corresponding to the x-coordinate values. Defaults to + ``axis=0``. + + Notes + ----- + Be aware that the algorithms implemented here are not necessarily + the most numerically stable known. Moreover, even in a world of + exact computation, unless the x coordinates are chosen very + carefully - Chebyshev zeros (e.g., cos(i*pi/n)) are a good choice - + polynomial interpolation itself is a very ill-conditioned process + due to the Runge phenomenon. In general, even with well-chosen + x values, degrees higher than about thirty cause problems with + numerical instability in this code. + + Based on [1]_. + + References + ---------- + .. [1] Krogh, "Efficient Algorithms for Polynomial Interpolation + and Numerical Differentiation", 1970. + + Examples + -------- + To produce a polynomial that is zero at 0 and 1 and has + derivative 2 at 0, call + + >>> from scipy.interpolate import KroghInterpolator + >>> KroghInterpolator([0,0,1],[0,2,0]) + + This constructs the quadratic :math:`2x^2-2x`. The derivative condition + is indicated by the repeated zero in the `xi` array; the corresponding + yi values are 0, the function value, and 2, the derivative value. + + For another example, given `xi`, `yi`, and a derivative `ypi` for each + point, appropriate arrays can be constructed as: + + >>> import numpy as np + >>> rng = np.random.default_rng() + >>> xi = np.linspace(0, 1, 5) + >>> yi, ypi = rng.random((2, 5)) + >>> xi_k, yi_k = np.repeat(xi, 2), np.ravel(np.dstack((yi,ypi))) + >>> KroghInterpolator(xi_k, yi_k) + + To produce a vector-valued polynomial, supply a higher-dimensional + array for `yi`: + + >>> KroghInterpolator([0,1],[[2,3],[4,5]]) + + This constructs a linear polynomial giving (2,3) at 0 and (4,5) at 1. + + """ + + def __init__(self, xi, yi, axis=0): + super().__init__(xi, yi, axis) + + self.xi = np.asarray(xi) + self.yi = self._reshape_yi(yi) + self.n, self.r = self.yi.shape + + if (deg := self.xi.size) > 30: + warnings.warn(f"{deg} degrees provided, degrees higher than about" + " thirty cause problems with numerical instability " + "with 'KroghInterpolator'", stacklevel=2) + + c = np.zeros((self.n+1, self.r), dtype=self.dtype) + c[0] = self.yi[0] + Vk = np.zeros((self.n, self.r), dtype=self.dtype) + for k in range(1, self.n): + s = 0 + while s <= k and xi[k-s] == xi[k]: + s += 1 + s -= 1 + Vk[0] = self.yi[k]/float_factorial(s) + for i in range(k-s): + if xi[i] == xi[k]: + raise ValueError("Elements of `xi` can't be equal.") + if s == 0: + Vk[i+1] = (c[i]-Vk[i])/(xi[i]-xi[k]) + else: + Vk[i+1] = (Vk[i+1]-Vk[i])/(xi[i]-xi[k]) + c[k] = Vk[k-s] + self.c = c + + def _evaluate(self, x): + pi = 1 + p = np.zeros((len(x), self.r), dtype=self.dtype) + p += self.c[0,np.newaxis,:] + for k in range(1, self.n): + w = x - self.xi[k-1] + pi = w*pi + p += pi[:,np.newaxis] * self.c[k] + return p + + def _evaluate_derivatives(self, x, der=None): + n = self.n + r = self.r + + if der is None: + der = self.n + + pi = np.zeros((n, len(x))) + w = np.zeros((n, len(x))) + pi[0] = 1 + p = np.zeros((len(x), self.r), dtype=self.dtype) + p += self.c[0, np.newaxis, :] + + for k in range(1, n): + w[k-1] = x - self.xi[k-1] + pi[k] = w[k-1] * pi[k-1] + p += pi[k, :, np.newaxis] * self.c[k] + + cn = np.zeros((max(der, n+1), len(x), r), dtype=self.dtype) + cn[:n+1, :, :] += self.c[:n+1, np.newaxis, :] + cn[0] = p + for k in range(1, n): + for i in range(1, n-k+1): + pi[i] = w[k+i-1]*pi[i-1] + pi[i] + cn[k] = cn[k] + pi[i, :, np.newaxis]*cn[k+i] + cn[k] *= float_factorial(k) + + cn[n, :, :] = 0 + return cn[:der] + + +def krogh_interpolate(xi, yi, x, der=0, axis=0): + """ + Convenience function for polynomial interpolation. + + See `KroghInterpolator` for more details. + + Parameters + ---------- + xi : array_like + Interpolation points (known x-coordinates). + yi : array_like + Known y-coordinates, of shape ``(xi.size, R)``. Interpreted as + vectors of length R, or scalars if R=1. + x : array_like + Point or points at which to evaluate the derivatives. + der : int or list or None, optional + How many derivatives to evaluate, or None for all potentially + nonzero derivatives (that is, a number equal to the number + of points), or a list of derivatives to evaluate. This number + includes the function value as the '0th' derivative. + axis : int, optional + Axis in the `yi` array corresponding to the x-coordinate values. + + Returns + ------- + d : ndarray + If the interpolator's values are R-D then the + returned array will be the number of derivatives by N by R. + If `x` is a scalar, the middle dimension will be dropped; if + the `yi` are scalars then the last dimension will be dropped. + + See Also + -------- + KroghInterpolator : Krogh interpolator + + Notes + ----- + Construction of the interpolating polynomial is a relatively expensive + process. If you want to evaluate it repeatedly consider using the class + KroghInterpolator (which is what this function uses). + + Examples + -------- + We can interpolate 2D observed data using Krogh interpolation: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.interpolate import krogh_interpolate + >>> x_observed = np.linspace(0.0, 10.0, 11) + >>> y_observed = np.sin(x_observed) + >>> x = np.linspace(min(x_observed), max(x_observed), num=100) + >>> y = krogh_interpolate(x_observed, y_observed, x) + >>> plt.plot(x_observed, y_observed, "o", label="observation") + >>> plt.plot(x, y, label="krogh interpolation") + >>> plt.legend() + >>> plt.show() + """ + + P = KroghInterpolator(xi, yi, axis=axis) + if der == 0: + return P(x) + elif _isscalar(der): + return P.derivative(x, der=der) + else: + return P.derivatives(x, der=np.amax(der)+1)[der] + + +def approximate_taylor_polynomial(f,x,degree,scale,order=None): + """ + Estimate the Taylor polynomial of f at x by polynomial fitting. + + Parameters + ---------- + f : callable + The function whose Taylor polynomial is sought. Should accept + a vector of `x` values. + x : scalar + The point at which the polynomial is to be evaluated. + degree : int + The degree of the Taylor polynomial + scale : scalar + The width of the interval to use to evaluate the Taylor polynomial. + Function values spread over a range this wide are used to fit the + polynomial. Must be chosen carefully. + order : int or None, optional + The order of the polynomial to be used in the fitting; `f` will be + evaluated ``order+1`` times. If None, use `degree`. + + Returns + ------- + p : poly1d instance + The Taylor polynomial (translated to the origin, so that + for example p(0)=f(x)). + + Notes + ----- + The appropriate choice of "scale" is a trade-off; too large and the + function differs from its Taylor polynomial too much to get a good + answer, too small and round-off errors overwhelm the higher-order terms. + The algorithm used becomes numerically unstable around order 30 even + under ideal circumstances. + + Choosing order somewhat larger than degree may improve the higher-order + terms. + + Examples + -------- + We can calculate Taylor approximation polynomials of sin function with + various degrees: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.interpolate import approximate_taylor_polynomial + >>> x = np.linspace(-10.0, 10.0, num=100) + >>> plt.plot(x, np.sin(x), label="sin curve") + >>> for degree in np.arange(1, 15, step=2): + ... sin_taylor = approximate_taylor_polynomial(np.sin, 0, degree, 1, + ... order=degree + 2) + ... plt.plot(x, sin_taylor(x), label=f"degree={degree}") + >>> plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', + ... borderaxespad=0.0, shadow=True) + >>> plt.tight_layout() + >>> plt.axis([-10, 10, -10, 10]) + >>> plt.show() + + """ + if order is None: + order = degree + + n = order+1 + # Choose n points that cluster near the endpoints of the interval in + # a way that avoids the Runge phenomenon. Ensure, by including the + # endpoint or not as appropriate, that one point always falls at x + # exactly. + xs = scale*np.cos(np.linspace(0,np.pi,n,endpoint=n % 1)) + x + + P = KroghInterpolator(xs, f(xs)) + d = P.derivatives(x,der=degree+1) + + return np.poly1d((d/factorial(np.arange(degree+1)))[::-1]) + + +class BarycentricInterpolator(_Interpolator1DWithDerivatives): + r"""Interpolating polynomial for a set of points. + + Constructs a polynomial that passes through a given set of points. + Allows evaluation of the polynomial and all its derivatives, + efficient changing of the y-values to be interpolated, + and updating by adding more x- and y-values. + + For reasons of numerical stability, this function does not compute + the coefficients of the polynomial. + + The values `yi` need to be provided before the function is + evaluated, but none of the preprocessing depends on them, so rapid + updates are possible. + + Parameters + ---------- + xi : array_like, shape (npoints, ) + 1-D array of x coordinates of the points the polynomial + should pass through + yi : array_like, shape (..., npoints, ...), optional + N-D array of y coordinates of the points the polynomial should pass through. + If None, the y values will be supplied later via the `set_y` method. + The length of `yi` along the interpolation axis must be equal to the length + of `xi`. Use the ``axis`` parameter to select correct axis. + axis : int, optional + Axis in the yi array corresponding to the x-coordinate values. Defaults + to ``axis=0``. + wi : array_like, optional + The barycentric weights for the chosen interpolation points `xi`. + If absent or None, the weights will be computed from `xi` (default). + This allows for the reuse of the weights `wi` if several interpolants + are being calculated using the same nodes `xi`, without re-computation. + random_state : {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. + + Notes + ----- + This class uses a "barycentric interpolation" method that treats + the problem as a special case of rational function interpolation. + This algorithm is quite stable, numerically, but even in a world of + exact computation, unless the x coordinates are chosen very + carefully - Chebyshev zeros (e.g., cos(i*pi/n)) are a good choice - + polynomial interpolation itself is a very ill-conditioned process + due to the Runge phenomenon. + + Based on Berrut and Trefethen 2004, "Barycentric Lagrange Interpolation". + + Examples + -------- + To produce a quintic barycentric interpolant approximating the function + :math:`\sin x`, and its first four derivatives, using six randomly-spaced + nodes in :math:`(0, \frac{\pi}{2})`: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.interpolate import BarycentricInterpolator + >>> rng = np.random.default_rng() + >>> xi = rng.random(6) * np.pi/2 + >>> f, f_d1, f_d2, f_d3, f_d4 = np.sin, np.cos, lambda x: -np.sin(x), lambda x: -np.cos(x), np.sin + >>> P = BarycentricInterpolator(xi, f(xi), random_state=rng) + >>> fig, axs = plt.subplots(5, 1, sharex=True, layout='constrained', figsize=(7,10)) + >>> x = np.linspace(0, np.pi, 100) + >>> axs[0].plot(x, P(x), 'r:', x, f(x), 'k--', xi, f(xi), 'xk') + >>> axs[1].plot(x, P.derivative(x), 'r:', x, f_d1(x), 'k--', xi, f_d1(xi), 'xk') + >>> axs[2].plot(x, P.derivative(x, 2), 'r:', x, f_d2(x), 'k--', xi, f_d2(xi), 'xk') + >>> axs[3].plot(x, P.derivative(x, 3), 'r:', x, f_d3(x), 'k--', xi, f_d3(xi), 'xk') + >>> axs[4].plot(x, P.derivative(x, 4), 'r:', x, f_d4(x), 'k--', xi, f_d4(xi), 'xk') + >>> axs[0].set_xlim(0, np.pi) + >>> axs[4].set_xlabel(r"$x$") + >>> axs[4].set_xticks([i * np.pi / 4 for i in range(5)], + ... ["0", r"$\frac{\pi}{4}$", r"$\frac{\pi}{2}$", r"$\frac{3\pi}{4}$", r"$\pi$"]) + >>> axs[0].set_ylabel("$f(x)$") + >>> axs[1].set_ylabel("$f'(x)$") + >>> axs[2].set_ylabel("$f''(x)$") + >>> axs[3].set_ylabel("$f^{(3)}(x)$") + >>> axs[4].set_ylabel("$f^{(4)}(x)$") + >>> labels = ['Interpolation nodes', 'True function $f$', 'Barycentric interpolation'] + >>> axs[0].legend(axs[0].get_lines()[::-1], labels, bbox_to_anchor=(0., 1.02, 1., .102), + ... loc='lower left', ncols=3, mode="expand", borderaxespad=0., frameon=False) + >>> plt.show() + """ # numpy/numpydoc#87 # noqa: E501 + + def __init__(self, xi, yi=None, axis=0, *, wi=None, random_state=None): + super().__init__(xi, yi, axis) + + random_state = check_random_state(random_state) + + self.xi = np.asarray(xi, dtype=np.float64) + self.set_yi(yi) + self.n = len(self.xi) + + # cache derivative object to avoid re-computing the weights with every call. + self._diff_cij = None + + if wi is not None: + self.wi = wi + else: + # See page 510 of Berrut and Trefethen 2004 for an explanation of the + # capacity scaling and the suggestion of using a random permutation of + # the input factors. + # At the moment, the permutation is not performed for xi that are + # appended later through the add_xi interface. It's not clear to me how + # to implement that and it seems that most situations that require + # these numerical stability improvements will be able to provide all + # the points to the constructor. + self._inv_capacity = 4.0 / (np.max(self.xi) - np.min(self.xi)) + permute = random_state.permutation(self.n, ) + inv_permute = np.zeros(self.n, dtype=np.int32) + inv_permute[permute] = np.arange(self.n) + self.wi = np.zeros(self.n) + + for i in range(self.n): + dist = self._inv_capacity * (self.xi[i] - self.xi[permute]) + dist[inv_permute[i]] = 1.0 + prod = np.prod(dist) + if prod == 0.0: + raise ValueError("Interpolation points xi must be" + " distinct.") + self.wi[i] = 1.0 / prod + + def set_yi(self, yi, axis=None): + """ + Update the y values to be interpolated + + The barycentric interpolation algorithm requires the calculation + of weights, but these depend only on the `xi`. The `yi` can be changed + at any time. + + Parameters + ---------- + yi : array_like + The y-coordinates of the points the polynomial will pass through. + If None, the y values must be supplied later. + axis : int, optional + Axis in the `yi` array corresponding to the x-coordinate values. + + """ + if yi is None: + self.yi = None + return + self._set_yi(yi, xi=self.xi, axis=axis) + self.yi = self._reshape_yi(yi) + self.n, self.r = self.yi.shape + self._diff_baryint = None + + def add_xi(self, xi, yi=None): + """ + Add more x values to the set to be interpolated + + The barycentric interpolation algorithm allows easy updating by + adding more points for the polynomial to pass through. + + Parameters + ---------- + xi : array_like + The x coordinates of the points that the polynomial should pass + through. + yi : array_like, optional + The y coordinates of the points the polynomial should pass through. + Should have shape ``(xi.size, R)``; if R > 1 then the polynomial is + vector-valued. + If `yi` is not given, the y values will be supplied later. `yi` + should be given if and only if the interpolator has y values + specified. + + Notes + ----- + The new points added by `add_xi` are not randomly permuted + so there is potential for numerical instability, + especially for a large number of points. If this + happens, please reconstruct interpolation from scratch instead. + """ + if yi is not None: + if self.yi is None: + raise ValueError("No previous yi value to update!") + yi = self._reshape_yi(yi, check=True) + self.yi = np.vstack((self.yi,yi)) + else: + if self.yi is not None: + raise ValueError("No update to yi provided!") + old_n = self.n + self.xi = np.concatenate((self.xi,xi)) + self.n = len(self.xi) + self.wi **= -1 + old_wi = self.wi + self.wi = np.zeros(self.n) + self.wi[:old_n] = old_wi + for j in range(old_n, self.n): + self.wi[:j] *= self._inv_capacity * (self.xi[j]-self.xi[:j]) + self.wi[j] = np.multiply.reduce( + self._inv_capacity * (self.xi[:j]-self.xi[j]) + ) + self.wi **= -1 + self._diff_cij = None + self._diff_baryint = None + + def __call__(self, x): + """Evaluate the interpolating polynomial at the points x + + Parameters + ---------- + x : array_like + Point or points at which to evaluate the interpolant. + + Returns + ------- + y : array_like + Interpolated values. Shape is determined by replacing + the interpolation axis in the original array with the shape of `x`. + + Notes + ----- + Currently the code computes an outer product between `x` and the + weights, that is, it constructs an intermediate array of size + ``(N, len(x))``, where N is the degree of the polynomial. + """ + return _Interpolator1D.__call__(self, x) + + def _evaluate(self, x): + if x.size == 0: + p = np.zeros((0, self.r), dtype=self.dtype) + else: + c = x[..., np.newaxis] - self.xi + z = c == 0 + c[z] = 1 + c = self.wi / c + with np.errstate(divide='ignore'): + p = np.dot(c, self.yi) / np.sum(c, axis=-1)[..., np.newaxis] + # Now fix where x==some xi + r = np.nonzero(z) + if len(r) == 1: # evaluation at a scalar + if len(r[0]) > 0: # equals one of the points + p = self.yi[r[0][0]] + else: + p[r[:-1]] = self.yi[r[-1]] + return p + + def derivative(self, x, der=1): + """ + Evaluate a single derivative of the polynomial at the point x. + + Parameters + ---------- + x : array_like + Point or points at which to evaluate the derivatives + der : integer, optional + Which derivative to evaluate (default: first derivative). + This number includes the function value as 0th derivative. + + Returns + ------- + d : ndarray + Derivative interpolated at the x-points. Shape of `d` is + determined by replacing the interpolation axis in the + original array with the shape of `x`. + """ + x, x_shape = self._prepare_x(x) + y = self._evaluate_derivatives(x, der+1, all_lower=False) + return self._finish_y(y, x_shape) + + def _evaluate_derivatives(self, x, der=None, all_lower=True): + # NB: der here is not the order of the highest derivative; + # instead, it is the size of the derivatives matrix that + # would be returned with all_lower=True, including the + # '0th' derivative (the undifferentiated function). + # E.g. to evaluate the 5th derivative alone, call + # _evaluate_derivatives(x, der=6, all_lower=False). + + if (not all_lower) and (x.size == 0 or self.r == 0): + return np.zeros((0, self.r), dtype=self.dtype) + + if (not all_lower) and der == 1: + return self._evaluate(x) + + if (not all_lower) and (der > self.n): + return np.zeros((len(x), self.r), dtype=self.dtype) + + if der is None: + der = self.n + + if all_lower and (x.size == 0 or self.r == 0): + return np.zeros((der, len(x), self.r), dtype=self.dtype) + + if self._diff_cij is None: + # c[i,j] = xi[i] - xi[j] + c = self.xi[:, np.newaxis] - self.xi + + # avoid division by 0 (diagonal entries are so far zero by construction) + np.fill_diagonal(c, 1) + + # c[i,j] = (w[j] / w[i]) / (xi[i] - xi[j]) (equation 9.4) + c = self.wi/ (c * self.wi[..., np.newaxis]) + + # fill in correct diagonal entries: each column sums to 0 + np.fill_diagonal(c, 0) + + # calculate diagonal + # c[j,j] = -sum_{i != j} c[i,j] (equation 9.5) + d = -c.sum(axis=1) + # c[i,j] = l_j(x_i) + np.fill_diagonal(c, d) + + self._diff_cij = c + + if self._diff_baryint is None: + # initialise and cache derivative interpolator and cijs; + # reuse weights wi (which depend only on interpolation points xi), + # to avoid unnecessary re-computation + self._diff_baryint = BarycentricInterpolator(xi=self.xi, + yi=self._diff_cij @ self.yi, + wi=self.wi) + self._diff_baryint._diff_cij = self._diff_cij + + if all_lower: + # assemble matrix of derivatives from order 0 to order der-1, + # in the format required by _Interpolator1DWithDerivatives. + cn = np.zeros((der, len(x), self.r), dtype=self.dtype) + for d in range(der): + cn[d, :, :] = self._evaluate_derivatives(x, d+1, all_lower=False) + return cn + + # recursively evaluate only the derivative requested + return self._diff_baryint._evaluate_derivatives(x, der-1, all_lower=False) + + +def barycentric_interpolate(xi, yi, x, axis=0, *, der=0): + """ + Convenience function for polynomial interpolation. + + Constructs a polynomial that passes through a given set of points, + then evaluates the polynomial. For reasons of numerical stability, + this function does not compute the coefficients of the polynomial. + + This function uses a "barycentric interpolation" method that treats + the problem as a special case of rational function interpolation. + This algorithm is quite stable, numerically, but even in a world of + exact computation, unless the `x` coordinates are chosen very + carefully - Chebyshev zeros (e.g., cos(i*pi/n)) are a good choice - + polynomial interpolation itself is a very ill-conditioned process + due to the Runge phenomenon. + + Parameters + ---------- + xi : array_like + 1-D array of x coordinates of the points the polynomial should + pass through + yi : array_like + The y coordinates of the points the polynomial should pass through. + x : scalar or array_like + Point or points at which to evaluate the interpolant. + der : int or list or None, optional + How many derivatives to evaluate, or None for all potentially + nonzero derivatives (that is, a number equal to the number + of points), or a list of derivatives to evaluate. This number + includes the function value as the '0th' derivative. + axis : int, optional + Axis in the `yi` array corresponding to the x-coordinate values. + + Returns + ------- + y : scalar or array_like + Interpolated values. Shape is determined by replacing + the interpolation axis in the original array with the shape of `x`. + + See Also + -------- + BarycentricInterpolator : Barycentric interpolator + + Notes + ----- + Construction of the interpolation weights is a relatively slow process. + If you want to call this many times with the same xi (but possibly + varying yi or x) you should use the class `BarycentricInterpolator`. + This is what this function uses internally. + + Examples + -------- + We can interpolate 2D observed data using barycentric interpolation: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.interpolate import barycentric_interpolate + >>> x_observed = np.linspace(0.0, 10.0, 11) + >>> y_observed = np.sin(x_observed) + >>> x = np.linspace(min(x_observed), max(x_observed), num=100) + >>> y = barycentric_interpolate(x_observed, y_observed, x) + >>> plt.plot(x_observed, y_observed, "o", label="observation") + >>> plt.plot(x, y, label="barycentric interpolation") + >>> plt.legend() + >>> plt.show() + + """ + P = BarycentricInterpolator(xi, yi, axis=axis) + if der == 0: + return P(x) + elif _isscalar(der): + return P.derivative(x, der=der) + else: + return P.derivatives(x, der=np.amax(der)+1)[der] diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rbf.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rbf.py new file mode 100644 index 0000000000000000000000000000000000000000..ed52230dd1cce678e56ca4427e10bafd07e501c0 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rbf.py @@ -0,0 +1,290 @@ +"""rbf - Radial basis functions for interpolation/smoothing scattered N-D data. + +Written by John Travers , February 2007 +Based closely on Matlab code by Alex Chirokov +Additional, large, improvements by Robert Hetland +Some additional alterations by Travis Oliphant +Interpolation with multi-dimensional target domain by Josua Sassen + +Permission to use, modify, and distribute this software is given under the +terms of the SciPy (BSD style) license. See LICENSE.txt that came with +this distribution for specifics. + +NO WARRANTY IS EXPRESSED OR IMPLIED. USE AT YOUR OWN RISK. + +Copyright (c) 2006-2007, Robert Hetland +Copyright (c) 2007, John Travers + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + + * Redistributions in binary form must reproduce the above + copyright notice, this list of conditions and the following + disclaimer in the documentation and/or other materials provided + with the distribution. + + * Neither the name of Robert Hetland nor the names of any + contributors may be used to endorse or promote products derived + from this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +""" +import numpy as np + +from scipy import linalg +from scipy.special import xlogy +from scipy.spatial.distance import cdist, pdist, squareform + +__all__ = ['Rbf'] + + +class Rbf: + """ + Rbf(*args, **kwargs) + + A class for radial basis function interpolation of functions from + N-D scattered data to an M-D domain. + + .. legacy:: class + + `Rbf` is legacy code, for new usage please use `RBFInterpolator` + instead. + + Parameters + ---------- + *args : arrays + x, y, z, ..., d, where x, y, z, ... are the coordinates of the nodes + and d is the array of values at the nodes + function : str or callable, optional + The radial basis function, based on the radius, r, given by the norm + (default is Euclidean distance); the default is 'multiquadric':: + + 'multiquadric': sqrt((r/self.epsilon)**2 + 1) + 'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1) + 'gaussian': exp(-(r/self.epsilon)**2) + 'linear': r + 'cubic': r**3 + 'quintic': r**5 + 'thin_plate': r**2 * log(r) + + If callable, then it must take 2 arguments (self, r). The epsilon + parameter will be available as self.epsilon. Other keyword + arguments passed in will be available as well. + + epsilon : float, optional + Adjustable constant for gaussian or multiquadrics functions + - defaults to approximate average distance between nodes (which is + a good start). + smooth : float, optional + Values greater than zero increase the smoothness of the + approximation. 0 is for interpolation (default), the function will + always go through the nodal points in this case. + norm : str, callable, optional + A function that returns the 'distance' between two points, with + inputs as arrays of positions (x, y, z, ...), and an output as an + array of distance. E.g., the default: 'euclidean', such that the result + is a matrix of the distances from each point in ``x1`` to each point in + ``x2``. For more options, see documentation of + `scipy.spatial.distances.cdist`. + mode : str, optional + Mode of the interpolation, can be '1-D' (default) or 'N-D'. When it is + '1-D' the data `d` will be considered as 1-D and flattened + internally. When it is 'N-D' the data `d` is assumed to be an array of + shape (n_samples, m), where m is the dimension of the target domain. + + + Attributes + ---------- + N : int + The number of data points (as determined by the input arrays). + di : ndarray + The 1-D array of data values at each of the data coordinates `xi`. + xi : ndarray + The 2-D array of data coordinates. + function : str or callable + The radial basis function. See description under Parameters. + epsilon : float + Parameter used by gaussian or multiquadrics functions. See Parameters. + smooth : float + Smoothing parameter. See description under Parameters. + norm : str or callable + The distance function. See description under Parameters. + mode : str + Mode of the interpolation. See description under Parameters. + nodes : ndarray + A 1-D array of node values for the interpolation. + A : internal property, do not use + + See Also + -------- + RBFInterpolator + + Examples + -------- + >>> import numpy as np + >>> from scipy.interpolate import Rbf + >>> rng = np.random.default_rng() + >>> x, y, z, d = rng.random((4, 50)) + >>> rbfi = Rbf(x, y, z, d) # radial basis function interpolator instance + >>> xi = yi = zi = np.linspace(0, 1, 20) + >>> di = rbfi(xi, yi, zi) # interpolated values + >>> di.shape + (20,) + + """ + # Available radial basis functions that can be selected as strings; + # they all start with _h_ (self._init_function relies on that) + def _h_multiquadric(self, r): + return np.sqrt((1.0/self.epsilon*r)**2 + 1) + + def _h_inverse_multiquadric(self, r): + return 1.0/np.sqrt((1.0/self.epsilon*r)**2 + 1) + + def _h_gaussian(self, r): + return np.exp(-(1.0/self.epsilon*r)**2) + + def _h_linear(self, r): + return r + + def _h_cubic(self, r): + return r**3 + + def _h_quintic(self, r): + return r**5 + + def _h_thin_plate(self, r): + return xlogy(r**2, r) + + # Setup self._function and do smoke test on initial r + def _init_function(self, r): + if isinstance(self.function, str): + self.function = self.function.lower() + _mapped = {'inverse': 'inverse_multiquadric', + 'inverse multiquadric': 'inverse_multiquadric', + 'thin-plate': 'thin_plate'} + if self.function in _mapped: + self.function = _mapped[self.function] + + func_name = "_h_" + self.function + if hasattr(self, func_name): + self._function = getattr(self, func_name) + else: + functionlist = [x[3:] for x in dir(self) + if x.startswith('_h_')] + raise ValueError("function must be a callable or one of " + + ", ".join(functionlist)) + self._function = getattr(self, "_h_"+self.function) + elif callable(self.function): + allow_one = False + if hasattr(self.function, 'func_code') or \ + hasattr(self.function, '__code__'): + val = self.function + allow_one = True + elif hasattr(self.function, "__call__"): + val = self.function.__call__.__func__ + else: + raise ValueError("Cannot determine number of arguments to " + "function") + + argcount = val.__code__.co_argcount + if allow_one and argcount == 1: + self._function = self.function + elif argcount == 2: + self._function = self.function.__get__(self, Rbf) + else: + raise ValueError("Function argument must take 1 or 2 " + "arguments.") + + a0 = self._function(r) + if a0.shape != r.shape: + raise ValueError("Callable must take array and return array of " + "the same shape") + return a0 + + def __init__(self, *args, **kwargs): + # `args` can be a variable number of arrays; we flatten them and store + # them as a single 2-D array `xi` of shape (n_args-1, array_size), + # plus a 1-D array `di` for the values. + # All arrays must have the same number of elements + self.xi = np.asarray([np.asarray(a, dtype=np.float64).flatten() + for a in args[:-1]]) + self.N = self.xi.shape[-1] + + self.mode = kwargs.pop('mode', '1-D') + + if self.mode == '1-D': + self.di = np.asarray(args[-1]).flatten() + self._target_dim = 1 + elif self.mode == 'N-D': + self.di = np.asarray(args[-1]) + self._target_dim = self.di.shape[-1] + else: + raise ValueError("Mode has to be 1-D or N-D.") + + if not all([x.size == self.di.shape[0] for x in self.xi]): + raise ValueError("All arrays must be equal length.") + + self.norm = kwargs.pop('norm', 'euclidean') + self.epsilon = kwargs.pop('epsilon', None) + if self.epsilon is None: + # default epsilon is the "the average distance between nodes" based + # on a bounding hypercube + ximax = np.amax(self.xi, axis=1) + ximin = np.amin(self.xi, axis=1) + edges = ximax - ximin + edges = edges[np.nonzero(edges)] + self.epsilon = np.power(np.prod(edges)/self.N, 1.0/edges.size) + + self.smooth = kwargs.pop('smooth', 0.0) + self.function = kwargs.pop('function', 'multiquadric') + + # attach anything left in kwargs to self for use by any user-callable + # function or to save on the object returned. + for item, value in kwargs.items(): + setattr(self, item, value) + + # Compute weights + if self._target_dim > 1: # If we have more than one target dimension, + # we first factorize the matrix + self.nodes = np.zeros((self.N, self._target_dim), dtype=self.di.dtype) + lu, piv = linalg.lu_factor(self.A) + for i in range(self._target_dim): + self.nodes[:, i] = linalg.lu_solve((lu, piv), self.di[:, i]) + else: + self.nodes = linalg.solve(self.A, self.di) + + @property + def A(self): + # this only exists for backwards compatibility: self.A was available + # and, at least technically, public. + r = squareform(pdist(self.xi.T, self.norm)) # Pairwise norm + return self._init_function(r) - np.eye(self.N)*self.smooth + + def _call_norm(self, x1, x2): + return cdist(x1.T, x2.T, self.norm) + + def __call__(self, *args): + args = [np.asarray(x) for x in args] + if not all([x.shape == y.shape for x in args for y in args]): + raise ValueError("Array lengths must be equal") + if self._target_dim > 1: + shp = args[0].shape + (self._target_dim,) + else: + shp = args[0].shape + xa = np.asarray([a.flatten() for a in args], dtype=np.float64) + r = self._call_norm(xa, self.xi) + return np.dot(self._function(r), self.nodes).reshape(shp) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rbfinterp.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rbfinterp.py new file mode 100644 index 0000000000000000000000000000000000000000..6690e6ccf7d5499db10efffb0ef1c0139a90d2ba --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rbfinterp.py @@ -0,0 +1,550 @@ +"""Module for RBF interpolation.""" +import warnings +from itertools import combinations_with_replacement + +import numpy as np +from numpy.linalg import LinAlgError +from scipy.spatial import KDTree +from scipy.special import comb +from scipy.linalg.lapack import dgesv # type: ignore[attr-defined] + +from ._rbfinterp_pythran import (_build_system, + _build_evaluation_coefficients, + _polynomial_matrix) + + +__all__ = ["RBFInterpolator"] + + +# These RBFs are implemented. +_AVAILABLE = { + "linear", + "thin_plate_spline", + "cubic", + "quintic", + "multiquadric", + "inverse_multiquadric", + "inverse_quadratic", + "gaussian" + } + + +# The shape parameter does not need to be specified when using these RBFs. +_SCALE_INVARIANT = {"linear", "thin_plate_spline", "cubic", "quintic"} + + +# For RBFs that are conditionally positive definite of order m, the interpolant +# should include polynomial terms with degree >= m - 1. Define the minimum +# degrees here. These values are from Chapter 8 of Fasshauer's "Meshfree +# Approximation Methods with MATLAB". The RBFs that are not in this dictionary +# are positive definite and do not need polynomial terms. +_NAME_TO_MIN_DEGREE = { + "multiquadric": 0, + "linear": 0, + "thin_plate_spline": 1, + "cubic": 1, + "quintic": 2 + } + + +def _monomial_powers(ndim, degree): + """Return the powers for each monomial in a polynomial. + + Parameters + ---------- + ndim : int + Number of variables in the polynomial. + degree : int + Degree of the polynomial. + + Returns + ------- + (nmonos, ndim) int ndarray + Array where each row contains the powers for each variable in a + monomial. + + """ + nmonos = comb(degree + ndim, ndim, exact=True) + out = np.zeros((nmonos, ndim), dtype=np.dtype("long")) + count = 0 + for deg in range(degree + 1): + for mono in combinations_with_replacement(range(ndim), deg): + # `mono` is a tuple of variables in the current monomial with + # multiplicity indicating power (e.g., (0, 1, 1) represents x*y**2) + for var in mono: + out[count, var] += 1 + + count += 1 + + return out + + +def _build_and_solve_system(y, d, smoothing, kernel, epsilon, powers): + """Build and solve the RBF interpolation system of equations. + + Parameters + ---------- + y : (P, N) float ndarray + Data point coordinates. + d : (P, S) float ndarray + Data values at `y`. + smoothing : (P,) float ndarray + Smoothing parameter for each data point. + kernel : str + Name of the RBF. + epsilon : float + Shape parameter. + powers : (R, N) int ndarray + The exponents for each monomial in the polynomial. + + Returns + ------- + coeffs : (P + R, S) float ndarray + Coefficients for each RBF and monomial. + shift : (N,) float ndarray + Domain shift used to create the polynomial matrix. + scale : (N,) float ndarray + Domain scaling used to create the polynomial matrix. + + """ + lhs, rhs, shift, scale = _build_system( + y, d, smoothing, kernel, epsilon, powers + ) + _, _, coeffs, info = dgesv(lhs, rhs, overwrite_a=True, overwrite_b=True) + if info < 0: + raise ValueError(f"The {-info}-th argument had an illegal value.") + elif info > 0: + msg = "Singular matrix." + nmonos = powers.shape[0] + if nmonos > 0: + pmat = _polynomial_matrix((y - shift)/scale, powers) + rank = np.linalg.matrix_rank(pmat) + if rank < nmonos: + msg = ( + "Singular matrix. The matrix of monomials evaluated at " + "the data point coordinates does not have full column " + f"rank ({rank}/{nmonos})." + ) + + raise LinAlgError(msg) + + return shift, scale, coeffs + + +class RBFInterpolator: + """Radial basis function (RBF) interpolation in N dimensions. + + Parameters + ---------- + y : (npoints, ndims) array_like + 2-D array of data point coordinates. + d : (npoints, ...) array_like + N-D array of data values at `y`. The length of `d` along the first + axis must be equal to the length of `y`. Unlike some interpolators, the + interpolation axis cannot be changed. + neighbors : int, optional + If specified, the value of the interpolant at each evaluation point + will be computed using only this many nearest data points. All the data + points are used by default. + smoothing : float or (npoints, ) array_like, optional + Smoothing parameter. The interpolant perfectly fits the data when this + is set to 0. For large values, the interpolant approaches a least + squares fit of a polynomial with the specified degree. Default is 0. + kernel : str, optional + Type of RBF. This should be one of + + - 'linear' : ``-r`` + - 'thin_plate_spline' : ``r**2 * log(r)`` + - 'cubic' : ``r**3`` + - 'quintic' : ``-r**5`` + - 'multiquadric' : ``-sqrt(1 + r**2)`` + - 'inverse_multiquadric' : ``1/sqrt(1 + r**2)`` + - 'inverse_quadratic' : ``1/(1 + r**2)`` + - 'gaussian' : ``exp(-r**2)`` + + Default is 'thin_plate_spline'. + epsilon : float, optional + Shape parameter that scales the input to the RBF. If `kernel` is + 'linear', 'thin_plate_spline', 'cubic', or 'quintic', this defaults to + 1 and can be ignored because it has the same effect as scaling the + smoothing parameter. Otherwise, this must be specified. + degree : int, optional + Degree of the added polynomial. For some RBFs the interpolant may not + be well-posed if the polynomial degree is too small. Those RBFs and + their corresponding minimum degrees are + + - 'multiquadric' : 0 + - 'linear' : 0 + - 'thin_plate_spline' : 1 + - 'cubic' : 1 + - 'quintic' : 2 + + The default value is the minimum degree for `kernel` or 0 if there is + no minimum degree. Set this to -1 for no added polynomial. + + Notes + ----- + An RBF is a scalar valued function in N-dimensional space whose value at + :math:`x` can be expressed in terms of :math:`r=||x - c||`, where :math:`c` + is the center of the RBF. + + An RBF interpolant for the vector of data values :math:`d`, which are from + locations :math:`y`, is a linear combination of RBFs centered at :math:`y` + plus a polynomial with a specified degree. The RBF interpolant is written + as + + .. math:: + f(x) = K(x, y) a + P(x) b, + + where :math:`K(x, y)` is a matrix of RBFs with centers at :math:`y` + evaluated at the points :math:`x`, and :math:`P(x)` is a matrix of + monomials, which span polynomials with the specified degree, evaluated at + :math:`x`. The coefficients :math:`a` and :math:`b` are the solution to the + linear equations + + .. math:: + (K(y, y) + \\lambda I) a + P(y) b = d + + and + + .. math:: + P(y)^T a = 0, + + where :math:`\\lambda` is a non-negative smoothing parameter that controls + how well we want to fit the data. The data are fit exactly when the + smoothing parameter is 0. + + The above system is uniquely solvable if the following requirements are + met: + + - :math:`P(y)` must have full column rank. :math:`P(y)` always has full + column rank when `degree` is -1 or 0. When `degree` is 1, + :math:`P(y)` has full column rank if the data point locations are not + all collinear (N=2), coplanar (N=3), etc. + - If `kernel` is 'multiquadric', 'linear', 'thin_plate_spline', + 'cubic', or 'quintic', then `degree` must not be lower than the + minimum value listed above. + - If `smoothing` is 0, then each data point location must be distinct. + + When using an RBF that is not scale invariant ('multiquadric', + 'inverse_multiquadric', 'inverse_quadratic', or 'gaussian'), an appropriate + shape parameter must be chosen (e.g., through cross validation). Smaller + values for the shape parameter correspond to wider RBFs. The problem can + become ill-conditioned or singular when the shape parameter is too small. + + The memory required to solve for the RBF interpolation coefficients + increases quadratically with the number of data points, which can become + impractical when interpolating more than about a thousand data points. + To overcome memory limitations for large interpolation problems, the + `neighbors` argument can be specified to compute an RBF interpolant for + each evaluation point using only the nearest data points. + + .. versionadded:: 1.7.0 + + See Also + -------- + NearestNDInterpolator + LinearNDInterpolator + CloughTocher2DInterpolator + + References + ---------- + .. [1] Fasshauer, G., 2007. Meshfree Approximation Methods with Matlab. + World Scientific Publishing Co. + + .. [2] http://amadeus.math.iit.edu/~fass/603_ch3.pdf + + .. [3] Wahba, G., 1990. Spline Models for Observational Data. SIAM. + + .. [4] http://pages.stat.wisc.edu/~wahba/stat860public/lect/lect8/lect8.pdf + + Examples + -------- + Demonstrate interpolating scattered data to a grid in 2-D. + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.interpolate import RBFInterpolator + >>> from scipy.stats.qmc import Halton + + >>> rng = np.random.default_rng() + >>> xobs = 2*Halton(2, seed=rng).random(100) - 1 + >>> yobs = np.sum(xobs, axis=1)*np.exp(-6*np.sum(xobs**2, axis=1)) + + >>> xgrid = np.mgrid[-1:1:50j, -1:1:50j] + >>> xflat = xgrid.reshape(2, -1).T + >>> yflat = RBFInterpolator(xobs, yobs)(xflat) + >>> ygrid = yflat.reshape(50, 50) + + >>> fig, ax = plt.subplots() + >>> ax.pcolormesh(*xgrid, ygrid, vmin=-0.25, vmax=0.25, shading='gouraud') + >>> p = ax.scatter(*xobs.T, c=yobs, s=50, ec='k', vmin=-0.25, vmax=0.25) + >>> fig.colorbar(p) + >>> plt.show() + + """ + + def __init__(self, y, d, + neighbors=None, + smoothing=0.0, + kernel="thin_plate_spline", + epsilon=None, + degree=None): + y = np.asarray(y, dtype=float, order="C") + if y.ndim != 2: + raise ValueError("`y` must be a 2-dimensional array.") + + ny, ndim = y.shape + + d_dtype = complex if np.iscomplexobj(d) else float + d = np.asarray(d, dtype=d_dtype, order="C") + if d.shape[0] != ny: + raise ValueError( + f"Expected the first axis of `d` to have length {ny}." + ) + + d_shape = d.shape[1:] + d = d.reshape((ny, -1)) + # If `d` is complex, convert it to a float array with twice as many + # columns. Otherwise, the LHS matrix would need to be converted to + # complex and take up 2x more memory than necessary. + d = d.view(float) + + if np.isscalar(smoothing): + smoothing = np.full(ny, smoothing, dtype=float) + else: + smoothing = np.asarray(smoothing, dtype=float, order="C") + if smoothing.shape != (ny,): + raise ValueError( + "Expected `smoothing` to be a scalar or have shape " + f"({ny},)." + ) + + kernel = kernel.lower() + if kernel not in _AVAILABLE: + raise ValueError(f"`kernel` must be one of {_AVAILABLE}.") + + if epsilon is None: + if kernel in _SCALE_INVARIANT: + epsilon = 1.0 + else: + raise ValueError( + "`epsilon` must be specified if `kernel` is not one of " + f"{_SCALE_INVARIANT}." + ) + else: + epsilon = float(epsilon) + + min_degree = _NAME_TO_MIN_DEGREE.get(kernel, -1) + if degree is None: + degree = max(min_degree, 0) + else: + degree = int(degree) + if degree < -1: + raise ValueError("`degree` must be at least -1.") + elif -1 < degree < min_degree: + warnings.warn( + f"`degree` should not be below {min_degree} except -1 " + f"when `kernel` is '{kernel}'." + f"The interpolant may not be uniquely " + f"solvable, and the smoothing parameter may have an " + f"unintuitive effect.", + UserWarning, stacklevel=2 + ) + + if neighbors is None: + nobs = ny + else: + # Make sure the number of nearest neighbors used for interpolation + # does not exceed the number of observations. + neighbors = int(min(neighbors, ny)) + nobs = neighbors + + powers = _monomial_powers(ndim, degree) + # The polynomial matrix must have full column rank in order for the + # interpolant to be well-posed, which is not possible if there are + # fewer observations than monomials. + if powers.shape[0] > nobs: + raise ValueError( + f"At least {powers.shape[0]} data points are required when " + f"`degree` is {degree} and the number of dimensions is {ndim}." + ) + + if neighbors is None: + shift, scale, coeffs = _build_and_solve_system( + y, d, smoothing, kernel, epsilon, powers + ) + + # Make these attributes private since they do not always exist. + self._shift = shift + self._scale = scale + self._coeffs = coeffs + + else: + self._tree = KDTree(y) + + self.y = y + self.d = d + self.d_shape = d_shape + self.d_dtype = d_dtype + self.neighbors = neighbors + self.smoothing = smoothing + self.kernel = kernel + self.epsilon = epsilon + self.powers = powers + + def _chunk_evaluator( + self, + x, + y, + shift, + scale, + coeffs, + memory_budget=1000000 + ): + """ + Evaluate the interpolation while controlling memory consumption. + We chunk the input if we need more memory than specified. + + Parameters + ---------- + x : (Q, N) float ndarray + array of points on which to evaluate + y: (P, N) float ndarray + array of points on which we know function values + shift: (N, ) ndarray + Domain shift used to create the polynomial matrix. + scale : (N,) float ndarray + Domain scaling used to create the polynomial matrix. + coeffs: (P+R, S) float ndarray + Coefficients in front of basis functions + memory_budget: int + Total amount of memory (in units of sizeof(float)) we wish + to devote for storing the array of coefficients for + interpolated points. If we need more memory than that, we + chunk the input. + + Returns + ------- + (Q, S) float ndarray + Interpolated array + """ + nx, ndim = x.shape + if self.neighbors is None: + nnei = len(y) + else: + nnei = self.neighbors + # in each chunk we consume the same space we already occupy + chunksize = memory_budget // (self.powers.shape[0] + nnei) + 1 + if chunksize <= nx: + out = np.empty((nx, self.d.shape[1]), dtype=float) + for i in range(0, nx, chunksize): + vec = _build_evaluation_coefficients( + x[i:i + chunksize, :], + y, + self.kernel, + self.epsilon, + self.powers, + shift, + scale) + out[i:i + chunksize, :] = np.dot(vec, coeffs) + else: + vec = _build_evaluation_coefficients( + x, + y, + self.kernel, + self.epsilon, + self.powers, + shift, + scale) + out = np.dot(vec, coeffs) + return out + + def __call__(self, x): + """Evaluate the interpolant at `x`. + + Parameters + ---------- + x : (Q, N) array_like + Evaluation point coordinates. + + Returns + ------- + (Q, ...) ndarray + Values of the interpolant at `x`. + + """ + x = np.asarray(x, dtype=float, order="C") + if x.ndim != 2: + raise ValueError("`x` must be a 2-dimensional array.") + + nx, ndim = x.shape + if ndim != self.y.shape[1]: + raise ValueError("Expected the second axis of `x` to have length " + f"{self.y.shape[1]}.") + + # Our memory budget for storing RBF coefficients is + # based on how many floats in memory we already occupy + # If this number is below 1e6 we just use 1e6 + # This memory budget is used to decide how we chunk + # the inputs + memory_budget = max(x.size + self.y.size + self.d.size, 1000000) + + if self.neighbors is None: + out = self._chunk_evaluator( + x, + self.y, + self._shift, + self._scale, + self._coeffs, + memory_budget=memory_budget) + else: + # Get the indices of the k nearest observation points to each + # evaluation point. + _, yindices = self._tree.query(x, self.neighbors) + if self.neighbors == 1: + # `KDTree` squeezes the output when neighbors=1. + yindices = yindices[:, None] + + # Multiple evaluation points may have the same neighborhood of + # observation points. Make the neighborhoods unique so that we only + # compute the interpolation coefficients once for each + # neighborhood. + yindices = np.sort(yindices, axis=1) + yindices, inv = np.unique(yindices, return_inverse=True, axis=0) + inv = np.reshape(inv, (-1,)) # flatten, we need 1-D indices + # `inv` tells us which neighborhood will be used by each evaluation + # point. Now we find which evaluation points will be using each + # neighborhood. + xindices = [[] for _ in range(len(yindices))] + for i, j in enumerate(inv): + xindices[j].append(i) + + out = np.empty((nx, self.d.shape[1]), dtype=float) + for xidx, yidx in zip(xindices, yindices): + # `yidx` are the indices of the observations in this + # neighborhood. `xidx` are the indices of the evaluation points + # that are using this neighborhood. + xnbr = x[xidx] + ynbr = self.y[yidx] + dnbr = self.d[yidx] + snbr = self.smoothing[yidx] + shift, scale, coeffs = _build_and_solve_system( + ynbr, + dnbr, + snbr, + self.kernel, + self.epsilon, + self.powers, + ) + out[xidx] = self._chunk_evaluator( + xnbr, + ynbr, + shift, + scale, + coeffs, + memory_budget=memory_budget) + + out = out.view(self.d_dtype) + out = out.reshape((nx, ) + self.d_shape) + return out diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rgi.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rgi.py new file mode 100644 index 0000000000000000000000000000000000000000..eb17bf9c8b57e8716be4fcfc6296c1ee21ebb985 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rgi.py @@ -0,0 +1,766 @@ +__all__ = ['RegularGridInterpolator', 'interpn'] + +import itertools +import warnings + +import numpy as np + +import scipy.sparse.linalg as ssl + +from .interpnd import _ndim_coords_from_arrays +from ._cubic import PchipInterpolator +from ._rgi_cython import evaluate_linear_2d, find_indices +from ._bsplines import make_interp_spline +from ._fitpack2 import RectBivariateSpline +from ._ndbspline import make_ndbspl + + +def _check_points(points): + descending_dimensions = [] + grid = [] + for i, p in enumerate(points): + # early make points float + # see https://github.com/scipy/scipy/pull/17230 + p = np.asarray(p, dtype=float) + if not np.all(p[1:] > p[:-1]): + if np.all(p[1:] < p[:-1]): + # input is descending, so make it ascending + descending_dimensions.append(i) + p = np.flip(p) + else: + raise ValueError( + "The points in dimension %d must be strictly " + "ascending or descending" % i) + # see https://github.com/scipy/scipy/issues/17716 + p = np.ascontiguousarray(p) + grid.append(p) + return tuple(grid), tuple(descending_dimensions) + + +def _check_dimensionality(points, values): + if len(points) > values.ndim: + raise ValueError("There are %d point arrays, but values has %d " + "dimensions" % (len(points), values.ndim)) + for i, p in enumerate(points): + if not np.asarray(p).ndim == 1: + raise ValueError("The points in dimension %d must be " + "1-dimensional" % i) + if not values.shape[i] == len(p): + raise ValueError("There are %d points and %d values in " + "dimension %d" % (len(p), values.shape[i], i)) + + +class RegularGridInterpolator: + """ + Interpolator on a regular or rectilinear grid in arbitrary dimensions. + + The data must be defined on a rectilinear grid; that is, a rectangular + grid with even or uneven spacing. Linear, nearest-neighbor, spline + interpolations are supported. After setting up the interpolator object, + the interpolation method may be chosen at each evaluation. + + Parameters + ---------- + points : tuple of ndarray of float, with shapes (m1, ), ..., (mn, ) + The points defining the regular grid in n dimensions. The points in + each dimension (i.e. every elements of the points tuple) must be + strictly ascending or descending. + + values : array_like, shape (m1, ..., mn, ...) + The data on the regular grid in n dimensions. Complex data is + accepted. + + .. deprecated:: 1.13.0 + Complex data is deprecated with ``method="pchip"`` and will raise an + error in SciPy 1.15.0. This is because ``PchipInterpolator`` only + works with real values. If you are trying to use the real components of + the passed array, use ``np.real`` on ``values``. + + method : str, optional + The method of interpolation to perform. Supported are "linear", + "nearest", "slinear", "cubic", "quintic" and "pchip". This + parameter will become the default for the object's ``__call__`` + method. Default is "linear". + + bounds_error : bool, optional + If True, when interpolated values are requested outside of the + domain of the input data, a ValueError is raised. + If False, then `fill_value` is used. + Default is True. + + fill_value : float or None, optional + The value to use for points outside of the interpolation domain. + If None, values outside the domain are extrapolated. + Default is ``np.nan``. + + solver : callable, optional + Only used for methods "slinear", "cubic" and "quintic". + Sparse linear algebra solver for construction of the NdBSpline instance. + Default is the iterative solver `scipy.sparse.linalg.gcrotmk`. + + .. versionadded:: 1.13 + + solver_args: dict, optional + Additional arguments to pass to `solver`, if any. + + .. versionadded:: 1.13 + + Methods + ------- + __call__ + + Attributes + ---------- + grid : tuple of ndarrays + The points defining the regular grid in n dimensions. + This tuple defines the full grid via + ``np.meshgrid(*grid, indexing='ij')`` + values : ndarray + Data values at the grid. + method : str + Interpolation method. + fill_value : float or ``None`` + Use this value for out-of-bounds arguments to `__call__`. + bounds_error : bool + If ``True``, out-of-bounds argument raise a ``ValueError``. + + Notes + ----- + Contrary to `LinearNDInterpolator` and `NearestNDInterpolator`, this class + avoids expensive triangulation of the input data by taking advantage of the + regular grid structure. + + In other words, this class assumes that the data is defined on a + *rectilinear* grid. + + .. versionadded:: 0.14 + + The 'slinear'(k=1), 'cubic'(k=3), and 'quintic'(k=5) methods are + tensor-product spline interpolators, where `k` is the spline degree, + If any dimension has fewer points than `k` + 1, an error will be raised. + + .. versionadded:: 1.9 + + If the input data is such that dimensions have incommensurate + units and differ by many orders of magnitude, the interpolant may have + numerical artifacts. Consider rescaling the data before interpolating. + + **Choosing a solver for spline methods** + + Spline methods, "slinear", "cubic" and "quintic" involve solving a + large sparse linear system at instantiation time. Depending on data, + the default solver may or may not be adequate. When it is not, you may + need to experiment with an optional `solver` argument, where you may + choose between the direct solver (`scipy.sparse.linalg.spsolve`) or + iterative solvers from `scipy.sparse.linalg`. You may need to supply + additional parameters via the optional `solver_args` parameter (for instance, + you may supply the starting value or target tolerance). See the + `scipy.sparse.linalg` documentation for the full list of available options. + + Alternatively, you may instead use the legacy methods, "slinear_legacy", + "cubic_legacy" and "quintic_legacy". These methods allow faster construction + but evaluations will be much slower. + + Examples + -------- + **Evaluate a function on the points of a 3-D grid** + + As a first example, we evaluate a simple example function on the points of + a 3-D grid: + + >>> from scipy.interpolate import RegularGridInterpolator + >>> import numpy as np + >>> def f(x, y, z): + ... return 2 * x**3 + 3 * y**2 - z + >>> x = np.linspace(1, 4, 11) + >>> y = np.linspace(4, 7, 22) + >>> z = np.linspace(7, 9, 33) + >>> xg, yg ,zg = np.meshgrid(x, y, z, indexing='ij', sparse=True) + >>> data = f(xg, yg, zg) + + ``data`` is now a 3-D array with ``data[i, j, k] = f(x[i], y[j], z[k])``. + Next, define an interpolating function from this data: + + >>> interp = RegularGridInterpolator((x, y, z), data) + + Evaluate the interpolating function at the two points + ``(x,y,z) = (2.1, 6.2, 8.3)`` and ``(3.3, 5.2, 7.1)``: + + >>> pts = np.array([[2.1, 6.2, 8.3], + ... [3.3, 5.2, 7.1]]) + >>> interp(pts) + array([ 125.80469388, 146.30069388]) + + which is indeed a close approximation to + + >>> f(2.1, 6.2, 8.3), f(3.3, 5.2, 7.1) + (125.54200000000002, 145.894) + + **Interpolate and extrapolate a 2D dataset** + + As a second example, we interpolate and extrapolate a 2D data set: + + >>> x, y = np.array([-2, 0, 4]), np.array([-2, 0, 2, 5]) + >>> def ff(x, y): + ... return x**2 + y**2 + + >>> xg, yg = np.meshgrid(x, y, indexing='ij') + >>> data = ff(xg, yg) + >>> interp = RegularGridInterpolator((x, y), data, + ... bounds_error=False, fill_value=None) + + >>> import matplotlib.pyplot as plt + >>> fig = plt.figure() + >>> ax = fig.add_subplot(projection='3d') + >>> ax.scatter(xg.ravel(), yg.ravel(), data.ravel(), + ... s=60, c='k', label='data') + + Evaluate and plot the interpolator on a finer grid + + >>> xx = np.linspace(-4, 9, 31) + >>> yy = np.linspace(-4, 9, 31) + >>> X, Y = np.meshgrid(xx, yy, indexing='ij') + + >>> # interpolator + >>> ax.plot_wireframe(X, Y, interp((X, Y)), rstride=3, cstride=3, + ... alpha=0.4, color='m', label='linear interp') + + >>> # ground truth + >>> ax.plot_wireframe(X, Y, ff(X, Y), rstride=3, cstride=3, + ... alpha=0.4, label='ground truth') + >>> plt.legend() + >>> plt.show() + + Other examples are given + :ref:`in the tutorial `. + + See Also + -------- + NearestNDInterpolator : Nearest neighbor interpolator on *unstructured* + data in N dimensions + + LinearNDInterpolator : Piecewise linear interpolator on *unstructured* data + in N dimensions + + interpn : a convenience function which wraps `RegularGridInterpolator` + + scipy.ndimage.map_coordinates : interpolation on grids with equal spacing + (suitable for e.g., N-D image resampling) + + References + ---------- + .. [1] Python package *regulargrid* by Johannes Buchner, see + https://pypi.python.org/pypi/regulargrid/ + .. [2] Wikipedia, "Trilinear interpolation", + https://en.wikipedia.org/wiki/Trilinear_interpolation + .. [3] Weiser, Alan, and Sergio E. Zarantonello. "A note on piecewise linear + and multilinear table interpolation in many dimensions." MATH. + COMPUT. 50.181 (1988): 189-196. + https://www.ams.org/journals/mcom/1988-50-181/S0025-5718-1988-0917826-0/S0025-5718-1988-0917826-0.pdf + :doi:`10.1090/S0025-5718-1988-0917826-0` + + """ + # this class is based on code originally programmed by Johannes Buchner, + # see https://github.com/JohannesBuchner/regulargrid + + _SPLINE_DEGREE_MAP = {"slinear": 1, "cubic": 3, "quintic": 5, 'pchip': 3, + "slinear_legacy": 1, "cubic_legacy": 3, "quintic_legacy": 5,} + _SPLINE_METHODS_recursive = {"slinear_legacy", "cubic_legacy", + "quintic_legacy", "pchip"} + _SPLINE_METHODS_ndbspl = {"slinear", "cubic", "quintic"} + _SPLINE_METHODS = list(_SPLINE_DEGREE_MAP.keys()) + _ALL_METHODS = ["linear", "nearest"] + _SPLINE_METHODS + + def __init__(self, points, values, method="linear", bounds_error=True, + fill_value=np.nan, *, solver=None, solver_args=None): + if method not in self._ALL_METHODS: + raise ValueError("Method '%s' is not defined" % method) + elif method in self._SPLINE_METHODS: + self._validate_grid_dimensions(points, method) + self.method = method + self.bounds_error = bounds_error + self.grid, self._descending_dimensions = _check_points(points) + self.values = self._check_values(values) + self._check_dimensionality(self.grid, self.values) + self.fill_value = self._check_fill_value(self.values, fill_value) + if self._descending_dimensions: + self.values = np.flip(values, axis=self._descending_dimensions) + if self.method == "pchip" and np.iscomplexobj(self.values): + msg = ("`PchipInterpolator` only works with real values. Passing " + "complex-dtyped `values` with `method='pchip'` is deprecated " + "and will raise an error in SciPy 1.15.0. If you are trying to " + "use the real components of the passed array, use `np.real` on " + "the array before passing to `RegularGridInterpolator`.") + warnings.warn(msg, DeprecationWarning, stacklevel=2) + if method in self._SPLINE_METHODS_ndbspl: + if solver_args is None: + solver_args = {} + self._spline = self._construct_spline(method, solver, **solver_args) + else: + if solver is not None or solver_args: + raise ValueError( + f"{method =} does not accept the 'solver' argument. Got " + f" {solver = } and with arguments {solver_args}." + ) + + def _construct_spline(self, method, solver=None, **solver_args): + if solver is None: + solver = ssl.gcrotmk + spl = make_ndbspl( + self.grid, self.values, self._SPLINE_DEGREE_MAP[method], + solver=solver, **solver_args + ) + return spl + + def _check_dimensionality(self, grid, values): + _check_dimensionality(grid, values) + + def _check_points(self, points): + return _check_points(points) + + def _check_values(self, values): + if not hasattr(values, 'ndim'): + # allow reasonable duck-typed values + values = np.asarray(values) + + if hasattr(values, 'dtype') and hasattr(values, 'astype'): + if not np.issubdtype(values.dtype, np.inexact): + values = values.astype(float) + + return values + + def _check_fill_value(self, values, fill_value): + if fill_value is not None: + fill_value_dtype = np.asarray(fill_value).dtype + if (hasattr(values, 'dtype') and not + np.can_cast(fill_value_dtype, values.dtype, + casting='same_kind')): + raise ValueError("fill_value must be either 'None' or " + "of a type compatible with values") + return fill_value + + def __call__(self, xi, method=None, *, nu=None): + """ + Interpolation at coordinates. + + Parameters + ---------- + xi : ndarray of shape (..., ndim) + The coordinates to evaluate the interpolator at. + + method : str, optional + The method of interpolation to perform. Supported are "linear", + "nearest", "slinear", "cubic", "quintic" and "pchip". Default is + the method chosen when the interpolator was created. + + nu : sequence of ints, length ndim, optional + If not None, the orders of the derivatives to evaluate. + Each entry must be non-negative. + Only allowed for methods "slinear", "cubic" and "quintic". + + .. versionadded:: 1.13 + + Returns + ------- + values_x : ndarray, shape xi.shape[:-1] + values.shape[ndim:] + Interpolated values at `xi`. See notes for behaviour when + ``xi.ndim == 1``. + + Notes + ----- + In the case that ``xi.ndim == 1`` a new axis is inserted into + the 0 position of the returned array, values_x, so its shape is + instead ``(1,) + values.shape[ndim:]``. + + Examples + -------- + Here we define a nearest-neighbor interpolator of a simple function + + >>> import numpy as np + >>> x, y = np.array([0, 1, 2]), np.array([1, 3, 7]) + >>> def f(x, y): + ... return x**2 + y**2 + >>> data = f(*np.meshgrid(x, y, indexing='ij', sparse=True)) + >>> from scipy.interpolate import RegularGridInterpolator + >>> interp = RegularGridInterpolator((x, y), data, method='nearest') + + By construction, the interpolator uses the nearest-neighbor + interpolation + + >>> interp([[1.5, 1.3], [0.3, 4.5]]) + array([2., 9.]) + + We can however evaluate the linear interpolant by overriding the + `method` parameter + + >>> interp([[1.5, 1.3], [0.3, 4.5]], method='linear') + array([ 4.7, 24.3]) + """ + method = self.method if method is None else method + is_method_changed = self.method != method + if method not in self._ALL_METHODS: + raise ValueError("Method '%s' is not defined" % method) + if is_method_changed and method in self._SPLINE_METHODS_ndbspl: + self._spline = self._construct_spline(method) + + if nu is not None and method not in self._SPLINE_METHODS_ndbspl: + raise ValueError( + f"Can only compute derivatives for methods " + f"{self._SPLINE_METHODS_ndbspl}, got {method =}." + ) + + xi, xi_shape, ndim, nans, out_of_bounds = self._prepare_xi(xi) + + if method == "linear": + indices, norm_distances = self._find_indices(xi.T) + if (ndim == 2 and hasattr(self.values, 'dtype') and + self.values.ndim == 2 and self.values.flags.writeable and + self.values.dtype in (np.float64, np.complex128) and + self.values.dtype.byteorder == '='): + # until cython supports const fused types, the fast path + # cannot support non-writeable values + # a fast path + out = np.empty(indices.shape[1], dtype=self.values.dtype) + result = evaluate_linear_2d(self.values, + indices, + norm_distances, + self.grid, + out) + else: + result = self._evaluate_linear(indices, norm_distances) + elif method == "nearest": + indices, norm_distances = self._find_indices(xi.T) + result = self._evaluate_nearest(indices, norm_distances) + elif method in self._SPLINE_METHODS: + if is_method_changed: + self._validate_grid_dimensions(self.grid, method) + if method in self._SPLINE_METHODS_recursive: + result = self._evaluate_spline(xi, method) + else: + result = self._spline(xi, nu=nu) + + if not self.bounds_error and self.fill_value is not None: + result[out_of_bounds] = self.fill_value + + # f(nan) = nan, if any + if np.any(nans): + result[nans] = np.nan + return result.reshape(xi_shape[:-1] + self.values.shape[ndim:]) + + def _prepare_xi(self, xi): + ndim = len(self.grid) + xi = _ndim_coords_from_arrays(xi, ndim=ndim) + if xi.shape[-1] != len(self.grid): + raise ValueError("The requested sample points xi have dimension " + f"{xi.shape[-1]} but this " + f"RegularGridInterpolator has dimension {ndim}") + + xi_shape = xi.shape + xi = xi.reshape(-1, xi_shape[-1]) + xi = np.asarray(xi, dtype=float) + + # find nans in input + nans = np.any(np.isnan(xi), axis=-1) + + if self.bounds_error: + for i, p in enumerate(xi.T): + if not np.logical_and(np.all(self.grid[i][0] <= p), + np.all(p <= self.grid[i][-1])): + raise ValueError("One of the requested xi is out of bounds " + "in dimension %d" % i) + out_of_bounds = None + else: + out_of_bounds = self._find_out_of_bounds(xi.T) + + return xi, xi_shape, ndim, nans, out_of_bounds + + def _evaluate_linear(self, indices, norm_distances): + # slice for broadcasting over trailing dimensions in self.values + vslice = (slice(None),) + (None,)*(self.values.ndim - len(indices)) + + # Compute shifting up front before zipping everything together + shift_norm_distances = [1 - yi for yi in norm_distances] + shift_indices = [i + 1 for i in indices] + + # The formula for linear interpolation in 2d takes the form: + # values = self.values[(i0, i1)] * (1 - y0) * (1 - y1) + \ + # self.values[(i0, i1 + 1)] * (1 - y0) * y1 + \ + # self.values[(i0 + 1, i1)] * y0 * (1 - y1) + \ + # self.values[(i0 + 1, i1 + 1)] * y0 * y1 + # We pair i with 1 - yi (zipped1) and i + 1 with yi (zipped2) + zipped1 = zip(indices, shift_norm_distances) + zipped2 = zip(shift_indices, norm_distances) + + # Take all products of zipped1 and zipped2 and iterate over them + # to get the terms in the above formula. This corresponds to iterating + # over the vertices of a hypercube. + hypercube = itertools.product(*zip(zipped1, zipped2)) + value = np.array([0.]) + for h in hypercube: + edge_indices, weights = zip(*h) + weight = np.array([1.]) + for w in weights: + weight = weight * w + term = np.asarray(self.values[edge_indices]) * weight[vslice] + value = value + term # cannot use += because broadcasting + return value + + def _evaluate_nearest(self, indices, norm_distances): + idx_res = [np.where(yi <= .5, i, i + 1) + for i, yi in zip(indices, norm_distances)] + return self.values[tuple(idx_res)] + + def _validate_grid_dimensions(self, points, method): + k = self._SPLINE_DEGREE_MAP[method] + for i, point in enumerate(points): + ndim = len(np.atleast_1d(point)) + if ndim <= k: + raise ValueError(f"There are {ndim} points in dimension {i}," + f" but method {method} requires at least " + f" {k+1} points per dimension.") + + def _evaluate_spline(self, xi, method): + # ensure xi is 2D list of points to evaluate (`m` is the number of + # points and `n` is the number of interpolation dimensions, + # ``n == len(self.grid)``.) + if xi.ndim == 1: + xi = xi.reshape((1, xi.size)) + m, n = xi.shape + + # Reorder the axes: n-dimensional process iterates over the + # interpolation axes from the last axis downwards: E.g. for a 4D grid + # the order of axes is 3, 2, 1, 0. Each 1D interpolation works along + # the 0th axis of its argument array (for 1D routine it's its ``y`` + # array). Thus permute the interpolation axes of `values` *and keep + # trailing dimensions trailing*. + axes = tuple(range(self.values.ndim)) + axx = axes[:n][::-1] + axes[n:] + values = self.values.transpose(axx) + + if method == 'pchip': + _eval_func = self._do_pchip + else: + _eval_func = self._do_spline_fit + k = self._SPLINE_DEGREE_MAP[method] + + # Non-stationary procedure: difficult to vectorize this part entirely + # into numpy-level operations. Unfortunately this requires explicit + # looping over each point in xi. + + # can at least vectorize the first pass across all points in the + # last variable of xi. + last_dim = n - 1 + first_values = _eval_func(self.grid[last_dim], + values, + xi[:, last_dim], + k) + + # the rest of the dimensions have to be on a per point-in-xi basis + shape = (m, *self.values.shape[n:]) + result = np.empty(shape, dtype=self.values.dtype) + for j in range(m): + # Main process: Apply 1D interpolate in each dimension + # sequentially, starting with the last dimension. + # These are then "folded" into the next dimension in-place. + folded_values = first_values[j, ...] + for i in range(last_dim-1, -1, -1): + # Interpolate for each 1D from the last dimensions. + # This collapses each 1D sequence into a scalar. + folded_values = _eval_func(self.grid[i], + folded_values, + xi[j, i], + k) + result[j, ...] = folded_values + + return result + + @staticmethod + def _do_spline_fit(x, y, pt, k): + local_interp = make_interp_spline(x, y, k=k, axis=0) + values = local_interp(pt) + return values + + @staticmethod + def _do_pchip(x, y, pt, k): + local_interp = PchipInterpolator(x, y, axis=0) + values = local_interp(pt) + return values + + def _find_indices(self, xi): + return find_indices(self.grid, xi) + + def _find_out_of_bounds(self, xi): + # check for out of bounds xi + out_of_bounds = np.zeros((xi.shape[1]), dtype=bool) + # iterate through dimensions + for x, grid in zip(xi, self.grid): + out_of_bounds += x < grid[0] + out_of_bounds += x > grid[-1] + return out_of_bounds + + +def interpn(points, values, xi, method="linear", bounds_error=True, + fill_value=np.nan): + """ + Multidimensional interpolation on regular or rectilinear grids. + + Strictly speaking, not all regular grids are supported - this function + works on *rectilinear* grids, that is, a rectangular grid with even or + uneven spacing. + + Parameters + ---------- + points : tuple of ndarray of float, with shapes (m1, ), ..., (mn, ) + The points defining the regular grid in n dimensions. The points in + each dimension (i.e. every elements of the points tuple) must be + strictly ascending or descending. + + values : array_like, shape (m1, ..., mn, ...) + The data on the regular grid in n dimensions. Complex data is + accepted. + + .. deprecated:: 1.13.0 + Complex data is deprecated with ``method="pchip"`` and will raise an + error in SciPy 1.15.0. This is because ``PchipInterpolator`` only + works with real values. If you are trying to use the real components of + the passed array, use ``np.real`` on ``values``. + + xi : ndarray of shape (..., ndim) + The coordinates to sample the gridded data at + + method : str, optional + The method of interpolation to perform. Supported are "linear", + "nearest", "slinear", "cubic", "quintic", "pchip", and "splinef2d". + "splinef2d" is only supported for 2-dimensional data. + + bounds_error : bool, optional + If True, when interpolated values are requested outside of the + domain of the input data, a ValueError is raised. + If False, then `fill_value` is used. + + fill_value : number, optional + If provided, the value to use for points outside of the + interpolation domain. If None, values outside + the domain are extrapolated. Extrapolation is not supported by method + "splinef2d". + + Returns + ------- + values_x : ndarray, shape xi.shape[:-1] + values.shape[ndim:] + Interpolated values at `xi`. See notes for behaviour when + ``xi.ndim == 1``. + + See Also + -------- + NearestNDInterpolator : Nearest neighbor interpolation on unstructured + data in N dimensions + LinearNDInterpolator : Piecewise linear interpolant on unstructured data + in N dimensions + RegularGridInterpolator : interpolation on a regular or rectilinear grid + in arbitrary dimensions (`interpn` wraps this + class). + RectBivariateSpline : Bivariate spline approximation over a rectangular mesh + scipy.ndimage.map_coordinates : interpolation on grids with equal spacing + (suitable for e.g., N-D image resampling) + + Notes + ----- + + .. versionadded:: 0.14 + + In the case that ``xi.ndim == 1`` a new axis is inserted into + the 0 position of the returned array, values_x, so its shape is + instead ``(1,) + values.shape[ndim:]``. + + If the input data is such that input dimensions have incommensurate + units and differ by many orders of magnitude, the interpolant may have + numerical artifacts. Consider rescaling the data before interpolation. + + Examples + -------- + Evaluate a simple example function on the points of a regular 3-D grid: + + >>> import numpy as np + >>> from scipy.interpolate import interpn + >>> def value_func_3d(x, y, z): + ... return 2 * x + 3 * y - z + >>> x = np.linspace(0, 4, 5) + >>> y = np.linspace(0, 5, 6) + >>> z = np.linspace(0, 6, 7) + >>> points = (x, y, z) + >>> values = value_func_3d(*np.meshgrid(*points, indexing='ij')) + + Evaluate the interpolating function at a point + + >>> point = np.array([2.21, 3.12, 1.15]) + >>> print(interpn(points, values, point)) + [12.63] + + """ + # sanity check 'method' kwarg + if method not in ["linear", "nearest", "cubic", "quintic", "pchip", + "splinef2d", "slinear", + "slinear_legacy", "cubic_legacy", "quintic_legacy"]: + raise ValueError("interpn only understands the methods 'linear', " + "'nearest', 'slinear', 'cubic', 'quintic', 'pchip', " + f"and 'splinef2d'. You provided {method}.") + + if not hasattr(values, 'ndim'): + values = np.asarray(values) + + ndim = values.ndim + if ndim > 2 and method == "splinef2d": + raise ValueError("The method splinef2d can only be used for " + "2-dimensional input data") + if not bounds_error and fill_value is None and method == "splinef2d": + raise ValueError("The method splinef2d does not support extrapolation.") + + # sanity check consistency of input dimensions + if len(points) > ndim: + raise ValueError("There are %d point arrays, but values has %d " + "dimensions" % (len(points), ndim)) + if len(points) != ndim and method == 'splinef2d': + raise ValueError("The method splinef2d can only be used for " + "scalar data with one point per coordinate") + + grid, descending_dimensions = _check_points(points) + _check_dimensionality(grid, values) + + # sanity check requested xi + xi = _ndim_coords_from_arrays(xi, ndim=len(grid)) + if xi.shape[-1] != len(grid): + raise ValueError("The requested sample points xi have dimension " + "%d, but this RegularGridInterpolator has " + "dimension %d" % (xi.shape[-1], len(grid))) + + if bounds_error: + for i, p in enumerate(xi.T): + if not np.logical_and(np.all(grid[i][0] <= p), + np.all(p <= grid[i][-1])): + raise ValueError("One of the requested xi is out of bounds " + "in dimension %d" % i) + + # perform interpolation + if method in RegularGridInterpolator._ALL_METHODS: + interp = RegularGridInterpolator(points, values, method=method, + bounds_error=bounds_error, + fill_value=fill_value) + return interp(xi) + elif method == "splinef2d": + xi_shape = xi.shape + xi = xi.reshape(-1, xi.shape[-1]) + + # RectBivariateSpline doesn't support fill_value; we need to wrap here + idx_valid = np.all((grid[0][0] <= xi[:, 0], xi[:, 0] <= grid[0][-1], + grid[1][0] <= xi[:, 1], xi[:, 1] <= grid[1][-1]), + axis=0) + result = np.empty_like(xi[:, 0]) + + # make a copy of values for RectBivariateSpline + interp = RectBivariateSpline(points[0], points[1], values[:]) + result[idx_valid] = interp.ev(xi[idx_valid, 0], xi[idx_valid, 1]) + result[np.logical_not(idx_valid)] = fill_value + + return result.reshape(xi_shape[:-1]) + else: + raise ValueError(f"unknown {method = }") diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rgi_cython.cpython-310-x86_64-linux-gnu.so b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rgi_cython.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..0afeb4d77b43683326c00eeaf689e7f65f4a870d Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/_rgi_cython.cpython-310-x86_64-linux-gnu.so differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/dfitpack.cpython-310-x86_64-linux-gnu.so b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/dfitpack.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..df9e100e29dad7228ffb5e5c1414d1797a9eb367 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/dfitpack.cpython-310-x86_64-linux-gnu.so differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/fitpack.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/fitpack.py new file mode 100644 index 0000000000000000000000000000000000000000..68a6a240961018cac8e59419245ee6791cba7a67 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/fitpack.py @@ -0,0 +1,32 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.interpolate` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'BSpline', + 'bisplev', + 'bisplrep', + 'dblint', + 'insert', + 'spalde', + 'splantider', + 'splder', + 'splev', + 'splint', + 'splprep', + 'splrep', + 'sproot', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="interpolate", module="fitpack", + private_modules=["_fitpack_py"], all=__all__, + attribute=name) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/ndgriddata.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/ndgriddata.py new file mode 100644 index 0000000000000000000000000000000000000000..bb2b1694d244d00b6aea9784fc0ad384a793d57d --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/ndgriddata.py @@ -0,0 +1,25 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.interpolate` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'CloughTocher2DInterpolator', + 'LinearNDInterpolator', + 'NDInterpolatorBase', + 'NearestNDInterpolator', + 'cKDTree', + 'griddata', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="interpolate", module="ndgriddata", + private_modules=["_ndgriddata"], all=__all__, + attribute=name) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/rbf.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/rbf.py new file mode 100644 index 0000000000000000000000000000000000000000..7ae1facd687108fcba124e43f71eda01f45a48e3 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/rbf.py @@ -0,0 +1,25 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.interpolate` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'Rbf', + 'cdist', + 'linalg', + 'pdist', + 'squareform', + 'xlogy', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return 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b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_bsplines.py new file mode 100644 index 0000000000000000000000000000000000000000..3a75f4d30743aee33676ee11b7ff9da0628fe340 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_bsplines.py @@ -0,0 +1,2621 @@ +import os +import operator +import itertools + +import numpy as np +from numpy.testing import assert_equal, assert_allclose, assert_ +from pytest import raises as assert_raises +import pytest + +from scipy.interpolate import ( + BSpline, BPoly, PPoly, make_interp_spline, make_lsq_spline, _bspl, + splev, splrep, splprep, splder, splantider, sproot, splint, insert, + CubicSpline, NdBSpline, make_smoothing_spline, RegularGridInterpolator, +) +import scipy.linalg as sl +import scipy.sparse.linalg as ssl + +from scipy.interpolate._bsplines import (_not_a_knot, _augknt, + _woodbury_algorithm, _periodic_knots, + _make_interp_per_full_matr) +import scipy.interpolate._fitpack_impl as _impl +from scipy._lib._util import AxisError + +# XXX: move to the interpolate namespace +from scipy.interpolate._ndbspline import make_ndbspl + +from scipy.interpolate import dfitpack +from scipy.interpolate import _bsplines as _b + + +class TestBSpline: + + def test_ctor(self): + # knots should be an ordered 1-D array of finite real numbers + assert_raises((TypeError, ValueError), BSpline, + **dict(t=[1, 1.j], c=[1.], k=0)) + with np.errstate(invalid='ignore'): + assert_raises(ValueError, BSpline, **dict(t=[1, np.nan], c=[1.], k=0)) + assert_raises(ValueError, BSpline, **dict(t=[1, np.inf], c=[1.], k=0)) + assert_raises(ValueError, BSpline, **dict(t=[1, -1], c=[1.], k=0)) + assert_raises(ValueError, BSpline, **dict(t=[[1], [1]], c=[1.], k=0)) + + # for n+k+1 knots and degree k need at least n coefficients + assert_raises(ValueError, BSpline, **dict(t=[0, 1, 2], c=[1], k=0)) + assert_raises(ValueError, BSpline, + **dict(t=[0, 1, 2, 3, 4], c=[1., 1.], k=2)) + + # non-integer orders + assert_raises(TypeError, BSpline, + **dict(t=[0., 0., 1., 2., 3., 4.], c=[1., 1., 1.], k="cubic")) + assert_raises(TypeError, BSpline, + **dict(t=[0., 0., 1., 2., 3., 4.], c=[1., 1., 1.], k=2.5)) + + # basic interval cannot have measure zero (here: [1..1]) + assert_raises(ValueError, BSpline, + **dict(t=[0., 0, 1, 1, 2, 3], c=[1., 1, 1], k=2)) + + # tck vs self.tck + n, k = 11, 3 + t = np.arange(n+k+1) + c = np.random.random(n) + b = BSpline(t, c, k) + + assert_allclose(t, b.t) + assert_allclose(c, b.c) + assert_equal(k, b.k) + + def test_tck(self): + b = _make_random_spline() + tck = b.tck + + assert_allclose(b.t, tck[0], atol=1e-15, rtol=1e-15) + assert_allclose(b.c, tck[1], atol=1e-15, rtol=1e-15) + assert_equal(b.k, tck[2]) + + # b.tck is read-only + with pytest.raises(AttributeError): + b.tck = 'foo' + + def test_degree_0(self): + xx = np.linspace(0, 1, 10) + + b = BSpline(t=[0, 1], c=[3.], k=0) + assert_allclose(b(xx), 3) + + b = BSpline(t=[0, 0.35, 1], c=[3, 4], k=0) + assert_allclose(b(xx), np.where(xx < 0.35, 3, 4)) + + def test_degree_1(self): + t = [0, 1, 2, 3, 4] + c = [1, 2, 3] + k = 1 + b = BSpline(t, c, k) + + x = np.linspace(1, 3, 50) + assert_allclose(c[0]*B_012(x) + c[1]*B_012(x-1) + c[2]*B_012(x-2), + b(x), atol=1e-14) + assert_allclose(splev(x, (t, c, k)), b(x), atol=1e-14) + + def test_bernstein(self): + # a special knot vector: Bernstein polynomials + k = 3 + t = np.asarray([0]*(k+1) + [1]*(k+1)) + c = np.asarray([1., 2., 3., 4.]) + bp = BPoly(c.reshape(-1, 1), [0, 1]) + bspl = BSpline(t, c, k) + + xx = np.linspace(-1., 2., 10) + assert_allclose(bp(xx, extrapolate=True), + bspl(xx, extrapolate=True), atol=1e-14) + assert_allclose(splev(xx, (t, c, k)), + bspl(xx), atol=1e-14) + + def test_rndm_naive_eval(self): + # test random coefficient spline *on the base interval*, + # t[k] <= x < t[-k-1] + b = _make_random_spline() + t, c, k = b.tck + xx = np.linspace(t[k], t[-k-1], 50) + y_b = b(xx) + + y_n = [_naive_eval(x, t, c, k) for x in xx] + assert_allclose(y_b, y_n, atol=1e-14) + + y_n2 = [_naive_eval_2(x, t, c, k) for x in xx] + assert_allclose(y_b, y_n2, atol=1e-14) + + def test_rndm_splev(self): + b = _make_random_spline() + t, c, k = b.tck + xx = np.linspace(t[k], t[-k-1], 50) + assert_allclose(b(xx), splev(xx, (t, c, k)), atol=1e-14) + + def test_rndm_splrep(self): + np.random.seed(1234) + x = np.sort(np.random.random(20)) + y = np.random.random(20) + + tck = splrep(x, y) + b = BSpline(*tck) + + t, k = b.t, b.k + xx = np.linspace(t[k], t[-k-1], 80) + assert_allclose(b(xx), splev(xx, tck), atol=1e-14) + + def test_rndm_unity(self): + b = _make_random_spline() + b.c = np.ones_like(b.c) + xx = np.linspace(b.t[b.k], b.t[-b.k-1], 100) + assert_allclose(b(xx), 1.) + + def test_vectorization(self): + n, k = 22, 3 + t = np.sort(np.random.random(n)) + c = np.random.random(size=(n, 6, 7)) + b = BSpline(t, c, k) + tm, tp = t[k], t[-k-1] + xx = tm + (tp - tm) * np.random.random((3, 4, 5)) + assert_equal(b(xx).shape, (3, 4, 5, 6, 7)) + + def test_len_c(self): + # for n+k+1 knots, only first n coefs are used. + # and BTW this is consistent with FITPACK + n, k = 33, 3 + t = np.sort(np.random.random(n+k+1)) + c = np.random.random(n) + + # pad coefficients with random garbage + c_pad = np.r_[c, np.random.random(k+1)] + + b, b_pad = BSpline(t, c, k), BSpline(t, c_pad, k) + + dt = t[-1] - t[0] + xx = np.linspace(t[0] - dt, t[-1] + dt, 50) + assert_allclose(b(xx), b_pad(xx), atol=1e-14) + assert_allclose(b(xx), splev(xx, (t, c, k)), atol=1e-14) + assert_allclose(b(xx), splev(xx, (t, c_pad, k)), atol=1e-14) + + def test_endpoints(self): + # base interval is closed + b = _make_random_spline() + t, _, k = b.tck + tm, tp = t[k], t[-k-1] + for extrap in (True, False): + assert_allclose(b([tm, tp], extrap), + b([tm + 1e-10, tp - 1e-10], extrap), atol=1e-9) + + def test_continuity(self): + # assert continuity at internal knots + b = _make_random_spline() + t, _, k = b.tck + assert_allclose(b(t[k+1:-k-1] - 1e-10), b(t[k+1:-k-1] + 1e-10), + atol=1e-9) + + def test_extrap(self): + b = _make_random_spline() + t, c, k = b.tck + dt = t[-1] - t[0] + xx = np.linspace(t[k] - dt, t[-k-1] + dt, 50) + mask = (t[k] < xx) & (xx < t[-k-1]) + + # extrap has no effect within the base interval + assert_allclose(b(xx[mask], extrapolate=True), + b(xx[mask], extrapolate=False)) + + # extrapolated values agree with FITPACK + assert_allclose(b(xx, extrapolate=True), + splev(xx, (t, c, k), ext=0)) + + def test_default_extrap(self): + # BSpline defaults to extrapolate=True + b = _make_random_spline() + t, _, k = b.tck + xx = [t[0] - 1, t[-1] + 1] + yy = b(xx) + assert_(not np.all(np.isnan(yy))) + + def test_periodic_extrap(self): + np.random.seed(1234) + t = np.sort(np.random.random(8)) + c = np.random.random(4) + k = 3 + b = BSpline(t, c, k, extrapolate='periodic') + n = t.size - (k + 1) + + dt = t[-1] - t[0] + xx = np.linspace(t[k] - dt, t[n] + dt, 50) + xy = t[k] + (xx - t[k]) % (t[n] - t[k]) + assert_allclose(b(xx), splev(xy, (t, c, k))) + + # Direct check + xx = [-1, 0, 0.5, 1] + xy = t[k] + (xx - t[k]) % (t[n] - t[k]) + assert_equal(b(xx, extrapolate='periodic'), b(xy, extrapolate=True)) + + def test_ppoly(self): + b = _make_random_spline() + t, c, k = b.tck + pp = PPoly.from_spline((t, c, k)) + + xx = np.linspace(t[k], t[-k], 100) + assert_allclose(b(xx), pp(xx), atol=1e-14, rtol=1e-14) + + def test_derivative_rndm(self): + b = _make_random_spline() + t, c, k = b.tck + xx = np.linspace(t[0], t[-1], 50) + xx = np.r_[xx, t] + + for der in range(1, k+1): + yd = splev(xx, (t, c, k), der=der) + assert_allclose(yd, b(xx, nu=der), atol=1e-14) + + # higher derivatives all vanish + assert_allclose(b(xx, nu=k+1), 0, atol=1e-14) + + def test_derivative_jumps(self): + # example from de Boor, Chap IX, example (24) + # NB: knots augmented & corresp coefs are zeroed out + # in agreement with the convention (29) + k = 2 + t = [-1, -1, 0, 1, 1, 3, 4, 6, 6, 6, 7, 7] + np.random.seed(1234) + c = np.r_[0, 0, np.random.random(5), 0, 0] + b = BSpline(t, c, k) + + # b is continuous at x != 6 (triple knot) + x = np.asarray([1, 3, 4, 6]) + assert_allclose(b(x[x != 6] - 1e-10), + b(x[x != 6] + 1e-10)) + assert_(not np.allclose(b(6.-1e-10), b(6+1e-10))) + + # 1st derivative jumps at double knots, 1 & 6: + x0 = np.asarray([3, 4]) + assert_allclose(b(x0 - 1e-10, nu=1), + b(x0 + 1e-10, nu=1)) + x1 = np.asarray([1, 6]) + assert_(not np.all(np.allclose(b(x1 - 1e-10, nu=1), + b(x1 + 1e-10, nu=1)))) + + # 2nd derivative is not guaranteed to be continuous either + assert_(not np.all(np.allclose(b(x - 1e-10, nu=2), + b(x + 1e-10, nu=2)))) + + def test_basis_element_quadratic(self): + xx = np.linspace(-1, 4, 20) + b = BSpline.basis_element(t=[0, 1, 2, 3]) + assert_allclose(b(xx), + splev(xx, (b.t, b.c, b.k)), atol=1e-14) + assert_allclose(b(xx), + B_0123(xx), atol=1e-14) + + b = BSpline.basis_element(t=[0, 1, 1, 2]) + xx = np.linspace(0, 2, 10) + assert_allclose(b(xx), + np.where(xx < 1, xx*xx, (2.-xx)**2), atol=1e-14) + + def test_basis_element_rndm(self): + b = _make_random_spline() + t, c, k = b.tck + xx = np.linspace(t[k], t[-k-1], 20) + assert_allclose(b(xx), _sum_basis_elements(xx, t, c, k), atol=1e-14) + + def test_cmplx(self): + b = _make_random_spline() + t, c, k = b.tck + cc = c * (1. + 3.j) + + b = BSpline(t, cc, k) + b_re = BSpline(t, b.c.real, k) + b_im = BSpline(t, b.c.imag, k) + + xx = np.linspace(t[k], t[-k-1], 20) + assert_allclose(b(xx).real, b_re(xx), atol=1e-14) + assert_allclose(b(xx).imag, b_im(xx), atol=1e-14) + + def test_nan(self): + # nan in, nan out. + b = BSpline.basis_element([0, 1, 1, 2]) + assert_(np.isnan(b(np.nan))) + + def test_derivative_method(self): + b = _make_random_spline(k=5) + t, c, k = b.tck + b0 = BSpline(t, c, k) + xx = np.linspace(t[k], t[-k-1], 20) + for j in range(1, k): + b = b.derivative() + assert_allclose(b0(xx, j), b(xx), atol=1e-12, rtol=1e-12) + + def test_antiderivative_method(self): + b = _make_random_spline() + t, c, k = b.tck + xx = np.linspace(t[k], t[-k-1], 20) + assert_allclose(b.antiderivative().derivative()(xx), + b(xx), atol=1e-14, rtol=1e-14) + + # repeat with N-D array for c + c = np.c_[c, c, c] + c = np.dstack((c, c)) + b = BSpline(t, c, k) + assert_allclose(b.antiderivative().derivative()(xx), + b(xx), atol=1e-14, rtol=1e-14) + + def test_integral(self): + b = BSpline.basis_element([0, 1, 2]) # x for x < 1 else 2 - x + assert_allclose(b.integrate(0, 1), 0.5) + assert_allclose(b.integrate(1, 0), -1 * 0.5) + assert_allclose(b.integrate(1, 0), -0.5) + + # extrapolate or zeros outside of [0, 2]; default is yes + assert_allclose(b.integrate(-1, 1), 0) + assert_allclose(b.integrate(-1, 1, extrapolate=True), 0) + assert_allclose(b.integrate(-1, 1, extrapolate=False), 0.5) + assert_allclose(b.integrate(1, -1, extrapolate=False), -1 * 0.5) + + # Test ``_fitpack._splint()`` + assert_allclose(b.integrate(1, -1, extrapolate=False), + _impl.splint(1, -1, b.tck)) + + # Test ``extrapolate='periodic'``. + b.extrapolate = 'periodic' + i = b.antiderivative() + period_int = i(2) - i(0) + + assert_allclose(b.integrate(0, 2), period_int) + assert_allclose(b.integrate(2, 0), -1 * period_int) + assert_allclose(b.integrate(-9, -7), period_int) + assert_allclose(b.integrate(-8, -4), 2 * period_int) + + assert_allclose(b.integrate(0.5, 1.5), i(1.5) - i(0.5)) + assert_allclose(b.integrate(1.5, 3), i(1) - i(0) + i(2) - i(1.5)) + assert_allclose(b.integrate(1.5 + 12, 3 + 12), + i(1) - i(0) + i(2) - i(1.5)) + assert_allclose(b.integrate(1.5, 3 + 12), + i(1) - i(0) + i(2) - i(1.5) + 6 * period_int) + + assert_allclose(b.integrate(0, -1), i(0) - i(1)) + assert_allclose(b.integrate(-9, -10), i(0) - i(1)) + assert_allclose(b.integrate(0, -9), i(1) - i(2) - 4 * period_int) + + def test_integrate_ppoly(self): + # test .integrate method to be consistent with PPoly.integrate + x = [0, 1, 2, 3, 4] + b = make_interp_spline(x, x) + b.extrapolate = 'periodic' + p = PPoly.from_spline(b) + + for x0, x1 in [(-5, 0.5), (0.5, 5), (-4, 13)]: + assert_allclose(b.integrate(x0, x1), + p.integrate(x0, x1)) + + def test_subclassing(self): + # classmethods should not decay to the base class + class B(BSpline): + pass + + b = B.basis_element([0, 1, 2, 2]) + assert_equal(b.__class__, B) + assert_equal(b.derivative().__class__, B) + assert_equal(b.antiderivative().__class__, B) + + @pytest.mark.parametrize('axis', range(-4, 4)) + def test_axis(self, axis): + n, k = 22, 3 + t = np.linspace(0, 1, n + k + 1) + sh = [6, 7, 8] + # We need the positive axis for some of the indexing and slices used + # in this test. + pos_axis = axis % 4 + sh.insert(pos_axis, n) # [22, 6, 7, 8] etc + c = np.random.random(size=sh) + b = BSpline(t, c, k, axis=axis) + assert_equal(b.c.shape, + [sh[pos_axis],] + sh[:pos_axis] + sh[pos_axis+1:]) + + xp = np.random.random((3, 4, 5)) + assert_equal(b(xp).shape, + sh[:pos_axis] + list(xp.shape) + sh[pos_axis+1:]) + + # -c.ndim <= axis < c.ndim + for ax in [-c.ndim - 1, c.ndim]: + assert_raises(AxisError, BSpline, + **dict(t=t, c=c, k=k, axis=ax)) + + # derivative, antiderivative keeps the axis + for b1 in [BSpline(t, c, k, axis=axis).derivative(), + BSpline(t, c, k, axis=axis).derivative(2), + BSpline(t, c, k, axis=axis).antiderivative(), + BSpline(t, c, k, axis=axis).antiderivative(2)]: + assert_equal(b1.axis, b.axis) + + def test_neg_axis(self): + k = 2 + t = [0, 1, 2, 3, 4, 5, 6] + c = np.array([[-1, 2, 0, -1], [2, 0, -3, 1]]) + + spl = BSpline(t, c, k, axis=-1) + spl0 = BSpline(t, c[0], k) + spl1 = BSpline(t, c[1], k) + assert_equal(spl(2.5), [spl0(2.5), spl1(2.5)]) + + def test_design_matrix_bc_types(self): + ''' + Splines with different boundary conditions are built on different + types of vectors of knots. As far as design matrix depends only on + vector of knots, `k` and `x` it is useful to make tests for different + boundary conditions (and as following different vectors of knots). + ''' + def run_design_matrix_tests(n, k, bc_type): + ''' + To avoid repetition of code the following function is provided. + ''' + np.random.seed(1234) + x = np.sort(np.random.random_sample(n) * 40 - 20) + y = np.random.random_sample(n) * 40 - 20 + if bc_type == "periodic": + y[0] = y[-1] + + bspl = make_interp_spline(x, y, k=k, bc_type=bc_type) + + c = np.eye(len(bspl.t) - k - 1) + des_matr_def = BSpline(bspl.t, c, k)(x) + des_matr_csr = BSpline.design_matrix(x, + bspl.t, + k).toarray() + assert_allclose(des_matr_csr @ bspl.c, y, atol=1e-14) + assert_allclose(des_matr_def, des_matr_csr, atol=1e-14) + + # "clamped" and "natural" work only with `k = 3` + n = 11 + k = 3 + for bc in ["clamped", "natural"]: + run_design_matrix_tests(n, k, bc) + + # "not-a-knot" works with odd `k` + for k in range(3, 8, 2): + run_design_matrix_tests(n, k, "not-a-knot") + + # "periodic" works with any `k` (even more than `n`) + n = 5 # smaller `n` to test `k > n` case + for k in range(2, 7): + run_design_matrix_tests(n, k, "periodic") + + @pytest.mark.parametrize('extrapolate', [False, True, 'periodic']) + @pytest.mark.parametrize('degree', range(5)) + def test_design_matrix_same_as_BSpline_call(self, extrapolate, degree): + """Test that design_matrix(x) is equivalent to BSpline(..)(x).""" + np.random.seed(1234) + x = np.random.random_sample(10 * (degree + 1)) + xmin, xmax = np.amin(x), np.amax(x) + k = degree + t = np.r_[np.linspace(xmin - 2, xmin - 1, degree), + np.linspace(xmin, xmax, 2 * (degree + 1)), + np.linspace(xmax + 1, xmax + 2, degree)] + c = np.eye(len(t) - k - 1) + bspline = BSpline(t, c, k, extrapolate) + assert_allclose( + bspline(x), BSpline.design_matrix(x, t, k, extrapolate).toarray() + ) + + # extrapolation regime + x = np.array([xmin - 10, xmin - 1, xmax + 1.5, xmax + 10]) + if not extrapolate: + with pytest.raises(ValueError): + BSpline.design_matrix(x, t, k, extrapolate) + else: + assert_allclose( + bspline(x), + BSpline.design_matrix(x, t, k, extrapolate).toarray() + ) + + def test_design_matrix_x_shapes(self): + # test for different `x` shapes + np.random.seed(1234) + n = 10 + k = 3 + x = np.sort(np.random.random_sample(n) * 40 - 20) + y = np.random.random_sample(n) * 40 - 20 + + bspl = make_interp_spline(x, y, k=k) + for i in range(1, 4): + xc = x[:i] + yc = y[:i] + des_matr_csr = BSpline.design_matrix(xc, + bspl.t, + k).toarray() + assert_allclose(des_matr_csr @ bspl.c, yc, atol=1e-14) + + def test_design_matrix_t_shapes(self): + # test for minimal possible `t` shape + t = [1., 1., 1., 2., 3., 4., 4., 4.] + des_matr = BSpline.design_matrix(2., t, 3).toarray() + assert_allclose(des_matr, + [[0.25, 0.58333333, 0.16666667, 0.]], + atol=1e-14) + + def test_design_matrix_asserts(self): + np.random.seed(1234) + n = 10 + k = 3 + x = np.sort(np.random.random_sample(n) * 40 - 20) + y = np.random.random_sample(n) * 40 - 20 + bspl = make_interp_spline(x, y, k=k) + # invalid vector of knots (should be a 1D non-descending array) + # here the actual vector of knots is reversed, so it is invalid + with assert_raises(ValueError): + BSpline.design_matrix(x, bspl.t[::-1], k) + k = 2 + t = [0., 1., 2., 3., 4., 5.] + x = [1., 2., 3., 4.] + # out of bounds + with assert_raises(ValueError): + BSpline.design_matrix(x, t, k) + + @pytest.mark.parametrize('bc_type', ['natural', 'clamped', + 'periodic', 'not-a-knot']) + def test_from_power_basis(self, bc_type): + np.random.seed(1234) + x = np.sort(np.random.random(20)) + y = np.random.random(20) + if bc_type == 'periodic': + y[-1] = y[0] + cb = CubicSpline(x, y, bc_type=bc_type) + bspl = BSpline.from_power_basis(cb, bc_type=bc_type) + xx = np.linspace(0, 1, 20) + assert_allclose(cb(xx), bspl(xx), atol=1e-15) + bspl_new = make_interp_spline(x, y, bc_type=bc_type) + assert_allclose(bspl.c, bspl_new.c, atol=1e-15) + + @pytest.mark.parametrize('bc_type', ['natural', 'clamped', + 'periodic', 'not-a-knot']) + def test_from_power_basis_complex(self, bc_type): + np.random.seed(1234) + x = np.sort(np.random.random(20)) + y = np.random.random(20) + np.random.random(20) * 1j + if bc_type == 'periodic': + y[-1] = y[0] + cb = CubicSpline(x, y, bc_type=bc_type) + bspl = BSpline.from_power_basis(cb, bc_type=bc_type) + bspl_new_real = make_interp_spline(x, y.real, bc_type=bc_type) + bspl_new_imag = make_interp_spline(x, y.imag, bc_type=bc_type) + assert_equal(bspl.c.dtype, (bspl_new_real.c + + 1j * bspl_new_imag.c).dtype) + assert_allclose(bspl.c, bspl_new_real.c + + 1j * bspl_new_imag.c, atol=1e-15) + + def test_from_power_basis_exmp(self): + ''' + For x = [0, 1, 2, 3, 4] and y = [1, 1, 1, 1, 1] + the coefficients of Cubic Spline in the power basis: + + $[[0, 0, 0, 0, 0],\\$ + $[0, 0, 0, 0, 0],\\$ + $[0, 0, 0, 0, 0],\\$ + $[1, 1, 1, 1, 1]]$ + + It could be shown explicitly that coefficients of the interpolating + function in B-spline basis are c = [1, 1, 1, 1, 1, 1, 1] + ''' + x = np.array([0, 1, 2, 3, 4]) + y = np.array([1, 1, 1, 1, 1]) + bspl = BSpline.from_power_basis(CubicSpline(x, y, bc_type='natural'), + bc_type='natural') + assert_allclose(bspl.c, [1, 1, 1, 1, 1, 1, 1], atol=1e-15) + + def test_read_only(self): + # BSpline must work on read-only knots and coefficients. + t = np.array([0, 1]) + c = np.array([3.0]) + t.setflags(write=False) + c.setflags(write=False) + + xx = np.linspace(0, 1, 10) + xx.setflags(write=False) + + b = BSpline(t=t, c=c, k=0) + assert_allclose(b(xx), 3) + + +class TestInsert: + + @pytest.mark.parametrize('xval', [0.0, 1.0, 2.5, 4, 6.5, 7.0]) + def test_insert(self, xval): + # insert a knot, incl edges (0.0, 7.0) and exactly at an existing knot (4.0) + x = np.arange(8) + y = np.sin(x)**3 + spl = make_interp_spline(x, y, k=3) + + spl_1f = insert(xval, spl) # FITPACK + spl_1 = spl.insert_knot(xval) + + assert_allclose(spl_1.t, spl_1f.t, atol=1e-15) + assert_allclose(spl_1.c, spl_1f.c[:-spl.k-1], atol=1e-15) + + # knot insertion preserves values, unless multiplicity >= k+1 + xx = x if xval != x[-1] else x[:-1] + xx = np.r_[xx, 0.5*(x[1:] + x[:-1])] + assert_allclose(spl(xx), spl_1(xx), atol=1e-15) + + # ... repeat with ndim > 1 + y1 = np.cos(x)**3 + spl_y1 = make_interp_spline(x, y1, k=3) + spl_yy = make_interp_spline(x, np.c_[y, y1], k=3) + spl_yy1 = spl_yy.insert_knot(xval) + + assert_allclose(spl_yy1.t, spl_1.t, atol=1e-15) + assert_allclose(spl_yy1.c, np.c_[spl.insert_knot(xval).c, + spl_y1.insert_knot(xval).c], atol=1e-15) + + xx = x if xval != x[-1] else x[:-1] + xx = np.r_[xx, 0.5*(x[1:] + x[:-1])] + assert_allclose(spl_yy(xx), spl_yy1(xx), atol=1e-15) + + + @pytest.mark.parametrize( + 'xval, m', [(0.0, 2), (1.0, 3), (1.5, 5), (4, 2), (7.0, 2)] + ) + def test_insert_multi(self, xval, m): + x = np.arange(8) + y = np.sin(x)**3 + spl = make_interp_spline(x, y, k=3) + + spl_1f = insert(xval, spl, m=m) + spl_1 = spl.insert_knot(xval, m) + + assert_allclose(spl_1.t, spl_1f.t, atol=1e-15) + assert_allclose(spl_1.c, spl_1f.c[:-spl.k-1], atol=1e-15) + + xx = x if xval != x[-1] else x[:-1] + xx = np.r_[xx, 0.5*(x[1:] + x[:-1])] + assert_allclose(spl(xx), spl_1(xx), atol=1e-15) + + def test_insert_random(self): + rng = np.random.default_rng(12345) + n, k = 11, 3 + + t = np.sort(rng.uniform(size=n+k+1)) + c = rng.uniform(size=(n, 3, 2)) + spl = BSpline(t, c, k) + + xv = rng.uniform(low=t[k+1], high=t[-k-1]) + spl_1 = spl.insert_knot(xv) + + xx = rng.uniform(low=t[k+1], high=t[-k-1], size=33) + assert_allclose(spl(xx), spl_1(xx), atol=1e-15) + + @pytest.mark.parametrize('xv', [0, 0.1, 2.0, 4.0, 4.5, # l.h. edge + 5.5, 6.0, 6.1, 7.0] # r.h. edge + ) + def test_insert_periodic(self, xv): + x = np.arange(8) + y = np.sin(x)**3 + tck = splrep(x, y, k=3) + spl = BSpline(*tck, extrapolate="periodic") + + spl_1 = spl.insert_knot(xv) + tf, cf, k = insert(xv, spl.tck, per=True) + + assert_allclose(spl_1.t, tf, atol=1e-15) + assert_allclose(spl_1.c[:-k-1], cf[:-k-1], atol=1e-15) + + xx = np.random.default_rng(1234).uniform(low=0, high=7, size=41) + assert_allclose(spl_1(xx), splev(xx, (tf, cf, k)), atol=1e-15) + + def test_insert_periodic_too_few_internal_knots(self): + # both FITPACK and spl.insert_knot raise when there's not enough + # internal knots to make a periodic extension. + # Below the internal knots are 2, 3, , 4, 5 + # ^ + # 2, 3, 3.5, 4, 5 + # so two knots from each side from the new one, while need at least + # from either left or right. + xv = 3.5 + k = 3 + t = np.array([0]*(k+1) + [2, 3, 4, 5] + [7]*(k+1)) + c = np.ones(len(t) - k - 1) + spl = BSpline(t, c, k, extrapolate="periodic") + + with assert_raises(ValueError): + insert(xv, (t, c, k), per=True) + + with assert_raises(ValueError): + spl.insert_knot(xv) + + def test_insert_no_extrap(self): + k = 3 + t = np.array([0]*(k+1) + [2, 3, 4, 5] + [7]*(k+1)) + c = np.ones(len(t) - k - 1) + spl = BSpline(t, c, k) + + with assert_raises(ValueError): + spl.insert_knot(-1) + + with assert_raises(ValueError): + spl.insert_knot(8) + + with assert_raises(ValueError): + spl.insert_knot(3, m=0) + + +def test_knots_multiplicity(): + # Take a spline w/ random coefficients, throw in knots of varying + # multiplicity. + + def check_splev(b, j, der=0, atol=1e-14, rtol=1e-14): + # check evaluations against FITPACK, incl extrapolations + t, c, k = b.tck + x = np.unique(t) + x = np.r_[t[0]-0.1, 0.5*(x[1:] + x[:1]), t[-1]+0.1] + assert_allclose(splev(x, (t, c, k), der), b(x, der), + atol=atol, rtol=rtol, err_msg=f'der = {der} k = {b.k}') + + # test loop itself + # [the index `j` is for interpreting the traceback in case of a failure] + for k in [1, 2, 3, 4, 5]: + b = _make_random_spline(k=k) + for j, b1 in enumerate(_make_multiples(b)): + check_splev(b1, j) + for der in range(1, k+1): + check_splev(b1, j, der, 1e-12, 1e-12) + + +### stolen from @pv, verbatim +def _naive_B(x, k, i, t): + """ + Naive way to compute B-spline basis functions. Useful only for testing! + computes B(x; t[i],..., t[i+k+1]) + """ + if k == 0: + return 1.0 if t[i] <= x < t[i+1] else 0.0 + if t[i+k] == t[i]: + c1 = 0.0 + else: + c1 = (x - t[i])/(t[i+k] - t[i]) * _naive_B(x, k-1, i, t) + if t[i+k+1] == t[i+1]: + c2 = 0.0 + else: + c2 = (t[i+k+1] - x)/(t[i+k+1] - t[i+1]) * _naive_B(x, k-1, i+1, t) + return (c1 + c2) + + +### stolen from @pv, verbatim +def _naive_eval(x, t, c, k): + """ + Naive B-spline evaluation. Useful only for testing! + """ + if x == t[k]: + i = k + else: + i = np.searchsorted(t, x) - 1 + assert t[i] <= x <= t[i+1] + assert i >= k and i < len(t) - k + return sum(c[i-j] * _naive_B(x, k, i-j, t) for j in range(0, k+1)) + + +def _naive_eval_2(x, t, c, k): + """Naive B-spline evaluation, another way.""" + n = len(t) - (k+1) + assert n >= k+1 + assert len(c) >= n + assert t[k] <= x <= t[n] + return sum(c[i] * _naive_B(x, k, i, t) for i in range(n)) + + +def _sum_basis_elements(x, t, c, k): + n = len(t) - (k+1) + assert n >= k+1 + assert len(c) >= n + s = 0. + for i in range(n): + b = BSpline.basis_element(t[i:i+k+2], extrapolate=False)(x) + s += c[i] * np.nan_to_num(b) # zero out out-of-bounds elements + return s + + +def B_012(x): + """ A linear B-spline function B(x | 0, 1, 2).""" + x = np.atleast_1d(x) + return np.piecewise(x, [(x < 0) | (x > 2), + (x >= 0) & (x < 1), + (x >= 1) & (x <= 2)], + [lambda x: 0., lambda x: x, lambda x: 2.-x]) + + +def B_0123(x, der=0): + """A quadratic B-spline function B(x | 0, 1, 2, 3).""" + x = np.atleast_1d(x) + conds = [x < 1, (x > 1) & (x < 2), x > 2] + if der == 0: + funcs = [lambda x: x*x/2., + lambda x: 3./4 - (x-3./2)**2, + lambda x: (3.-x)**2 / 2] + elif der == 2: + funcs = [lambda x: 1., + lambda x: -2., + lambda x: 1.] + else: + raise ValueError('never be here: der=%s' % der) + pieces = np.piecewise(x, conds, funcs) + return pieces + + +def _make_random_spline(n=35, k=3): + np.random.seed(123) + t = np.sort(np.random.random(n+k+1)) + c = np.random.random(n) + return BSpline.construct_fast(t, c, k) + + +def _make_multiples(b): + """Increase knot multiplicity.""" + c, k = b.c, b.k + + t1 = b.t.copy() + t1[17:19] = t1[17] + t1[22] = t1[21] + yield BSpline(t1, c, k) + + t1 = b.t.copy() + t1[:k+1] = t1[0] + yield BSpline(t1, c, k) + + t1 = b.t.copy() + t1[-k-1:] = t1[-1] + yield BSpline(t1, c, k) + + +class TestInterop: + # + # Test that FITPACK-based spl* functions can deal with BSpline objects + # + def setup_method(self): + xx = np.linspace(0, 4.*np.pi, 41) + yy = np.cos(xx) + b = make_interp_spline(xx, yy) + self.tck = (b.t, b.c, b.k) + self.xx, self.yy, self.b = xx, yy, b + + self.xnew = np.linspace(0, 4.*np.pi, 21) + + c2 = np.c_[b.c, b.c, b.c] + self.c2 = np.dstack((c2, c2)) + self.b2 = BSpline(b.t, self.c2, b.k) + + def test_splev(self): + xnew, b, b2 = self.xnew, self.b, self.b2 + + # check that splev works with 1-D array of coefficients + # for array and scalar `x` + assert_allclose(splev(xnew, b), + b(xnew), atol=1e-15, rtol=1e-15) + assert_allclose(splev(xnew, b.tck), + b(xnew), atol=1e-15, rtol=1e-15) + assert_allclose([splev(x, b) for x in xnew], + b(xnew), atol=1e-15, rtol=1e-15) + + # With N-D coefficients, there's a quirck: + # splev(x, BSpline) is equivalent to BSpline(x) + with assert_raises(ValueError, match="Calling splev.. with BSpline"): + splev(xnew, b2) + + # However, splev(x, BSpline.tck) needs some transposes. This is because + # BSpline interpolates along the first axis, while the legacy FITPACK + # wrapper does list(map(...)) which effectively interpolates along the + # last axis. Like so: + sh = tuple(range(1, b2.c.ndim)) + (0,) # sh = (1, 2, 0) + cc = b2.c.transpose(sh) + tck = (b2.t, cc, b2.k) + assert_allclose(splev(xnew, tck), + b2(xnew).transpose(sh), atol=1e-15, rtol=1e-15) + + def test_splrep(self): + x, y = self.xx, self.yy + # test that "new" splrep is equivalent to _impl.splrep + tck = splrep(x, y) + t, c, k = _impl.splrep(x, y) + assert_allclose(tck[0], t, atol=1e-15) + assert_allclose(tck[1], c, atol=1e-15) + assert_equal(tck[2], k) + + # also cover the `full_output=True` branch + tck_f, _, _, _ = splrep(x, y, full_output=True) + assert_allclose(tck_f[0], t, atol=1e-15) + assert_allclose(tck_f[1], c, atol=1e-15) + assert_equal(tck_f[2], k) + + # test that the result of splrep roundtrips with splev: + # evaluate the spline on the original `x` points + yy = splev(x, tck) + assert_allclose(y, yy, atol=1e-15) + + # ... and also it roundtrips if wrapped in a BSpline + b = BSpline(*tck) + assert_allclose(y, b(x), atol=1e-15) + + def test_splrep_errors(self): + # test that both "old" and "new" splrep raise for an N-D ``y`` array + # with n > 1 + x, y = self.xx, self.yy + y2 = np.c_[y, y] + with assert_raises(ValueError): + splrep(x, y2) + with assert_raises(ValueError): + _impl.splrep(x, y2) + + # input below minimum size + with assert_raises(TypeError, match="m > k must hold"): + splrep(x[:3], y[:3]) + with assert_raises(TypeError, match="m > k must hold"): + _impl.splrep(x[:3], y[:3]) + + def test_splprep(self): + x = np.arange(15).reshape((3, 5)) + b, u = splprep(x) + tck, u1 = _impl.splprep(x) + + # test the roundtrip with splev for both "old" and "new" output + assert_allclose(u, u1, atol=1e-15) + assert_allclose(splev(u, b), x, atol=1e-15) + assert_allclose(splev(u, tck), x, atol=1e-15) + + # cover the ``full_output=True`` branch + (b_f, u_f), _, _, _ = splprep(x, s=0, full_output=True) + assert_allclose(u, u_f, atol=1e-15) + assert_allclose(splev(u_f, b_f), x, atol=1e-15) + + def test_splprep_errors(self): + # test that both "old" and "new" code paths raise for x.ndim > 2 + x = np.arange(3*4*5).reshape((3, 4, 5)) + with assert_raises(ValueError, match="too many values to unpack"): + splprep(x) + with assert_raises(ValueError, match="too many values to unpack"): + _impl.splprep(x) + + # input below minimum size + x = np.linspace(0, 40, num=3) + with assert_raises(TypeError, match="m > k must hold"): + splprep([x]) + with assert_raises(TypeError, match="m > k must hold"): + _impl.splprep([x]) + + # automatically calculated parameters are non-increasing + # see gh-7589 + x = [-50.49072266, -50.49072266, -54.49072266, -54.49072266] + with assert_raises(ValueError, match="Invalid inputs"): + splprep([x]) + with assert_raises(ValueError, match="Invalid inputs"): + _impl.splprep([x]) + + # given non-increasing parameter values u + x = [1, 3, 2, 4] + u = [0, 0.3, 0.2, 1] + with assert_raises(ValueError, match="Invalid inputs"): + splprep(*[[x], None, u]) + + def test_sproot(self): + b, b2 = self.b, self.b2 + roots = np.array([0.5, 1.5, 2.5, 3.5])*np.pi + # sproot accepts a BSpline obj w/ 1-D coef array + assert_allclose(sproot(b), roots, atol=1e-7, rtol=1e-7) + assert_allclose(sproot((b.t, b.c, b.k)), roots, atol=1e-7, rtol=1e-7) + + # ... and deals with trailing dimensions if coef array is N-D + with assert_raises(ValueError, match="Calling sproot.. with BSpline"): + sproot(b2, mest=50) + + # and legacy behavior is preserved for a tck tuple w/ N-D coef + c2r = b2.c.transpose(1, 2, 0) + rr = np.asarray(sproot((b2.t, c2r, b2.k), mest=50)) + assert_equal(rr.shape, (3, 2, 4)) + assert_allclose(rr - roots, 0, atol=1e-12) + + def test_splint(self): + # test that splint accepts BSpline objects + b, b2 = self.b, self.b2 + assert_allclose(splint(0, 1, b), + splint(0, 1, b.tck), atol=1e-14) + assert_allclose(splint(0, 1, b), + b.integrate(0, 1), atol=1e-14) + + # ... and deals with N-D arrays of coefficients + with assert_raises(ValueError, match="Calling splint.. with BSpline"): + splint(0, 1, b2) + + # and the legacy behavior is preserved for a tck tuple w/ N-D coef + c2r = b2.c.transpose(1, 2, 0) + integr = np.asarray(splint(0, 1, (b2.t, c2r, b2.k))) + assert_equal(integr.shape, (3, 2)) + assert_allclose(integr, + splint(0, 1, b), atol=1e-14) + + def test_splder(self): + for b in [self.b, self.b2]: + # pad the c array (FITPACK convention) + ct = len(b.t) - len(b.c) + if ct > 0: + b.c = np.r_[b.c, np.zeros((ct,) + b.c.shape[1:])] + + for n in [1, 2, 3]: + bd = splder(b) + tck_d = _impl.splder((b.t, b.c, b.k)) + assert_allclose(bd.t, tck_d[0], atol=1e-15) + assert_allclose(bd.c, tck_d[1], atol=1e-15) + assert_equal(bd.k, tck_d[2]) + assert_(isinstance(bd, BSpline)) + assert_(isinstance(tck_d, tuple)) # back-compat: tck in and out + + def test_splantider(self): + for b in [self.b, self.b2]: + # pad the c array (FITPACK convention) + ct = len(b.t) - len(b.c) + if ct > 0: + b.c = np.r_[b.c, np.zeros((ct,) + b.c.shape[1:])] + + for n in [1, 2, 3]: + bd = splantider(b) + tck_d = _impl.splantider((b.t, b.c, b.k)) + assert_allclose(bd.t, tck_d[0], atol=1e-15) + assert_allclose(bd.c, tck_d[1], atol=1e-15) + assert_equal(bd.k, tck_d[2]) + assert_(isinstance(bd, BSpline)) + assert_(isinstance(tck_d, tuple)) # back-compat: tck in and out + + def test_insert(self): + b, b2, xx = self.b, self.b2, self.xx + + j = b.t.size // 2 + tn = 0.5*(b.t[j] + b.t[j+1]) + + bn, tck_n = insert(tn, b), insert(tn, (b.t, b.c, b.k)) + assert_allclose(splev(xx, bn), + splev(xx, tck_n), atol=1e-15) + assert_(isinstance(bn, BSpline)) + assert_(isinstance(tck_n, tuple)) # back-compat: tck in, tck out + + # for N-D array of coefficients, BSpline.c needs to be transposed + # after that, the results are equivalent. + sh = tuple(range(b2.c.ndim)) + c_ = b2.c.transpose(sh[1:] + (0,)) + tck_n2 = insert(tn, (b2.t, c_, b2.k)) + + bn2 = insert(tn, b2) + + # need a transpose for comparing the results, cf test_splev + assert_allclose(np.asarray(splev(xx, tck_n2)).transpose(2, 0, 1), + bn2(xx), atol=1e-15) + assert_(isinstance(bn2, BSpline)) + assert_(isinstance(tck_n2, tuple)) # back-compat: tck in, tck out + + +class TestInterp: + # + # Test basic ways of constructing interpolating splines. + # + xx = np.linspace(0., 2.*np.pi) + yy = np.sin(xx) + + def test_non_int_order(self): + with assert_raises(TypeError): + make_interp_spline(self.xx, self.yy, k=2.5) + + def test_order_0(self): + b = make_interp_spline(self.xx, self.yy, k=0) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + b = make_interp_spline(self.xx, self.yy, k=0, axis=-1) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + + def test_linear(self): + b = make_interp_spline(self.xx, self.yy, k=1) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + b = make_interp_spline(self.xx, self.yy, k=1, axis=-1) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + + @pytest.mark.parametrize('k', [0, 1, 2, 3]) + def test_incompatible_x_y(self, k): + x = [0, 1, 2, 3, 4, 5] + y = [0, 1, 2, 3, 4, 5, 6, 7] + with assert_raises(ValueError, match="Shapes of x"): + make_interp_spline(x, y, k=k) + + @pytest.mark.parametrize('k', [0, 1, 2, 3]) + def test_broken_x(self, k): + x = [0, 1, 1, 2, 3, 4] # duplicates + y = [0, 1, 2, 3, 4, 5] + with assert_raises(ValueError, match="x to not have duplicates"): + make_interp_spline(x, y, k=k) + + x = [0, 2, 1, 3, 4, 5] # unsorted + with assert_raises(ValueError, match="Expect x to be a 1D strictly"): + make_interp_spline(x, y, k=k) + + x = [0, 1, 2, 3, 4, 5] + x = np.asarray(x).reshape((1, -1)) # 1D + with assert_raises(ValueError, match="Expect x to be a 1D strictly"): + make_interp_spline(x, y, k=k) + + def test_not_a_knot(self): + for k in [3, 5]: + b = make_interp_spline(self.xx, self.yy, k) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + + def test_periodic(self): + # k = 5 here for more derivatives + b = make_interp_spline(self.xx, self.yy, k=5, bc_type='periodic') + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + # in periodic case it is expected equality of k-1 first + # derivatives at the boundaries + for i in range(1, 5): + assert_allclose(b(self.xx[0], nu=i), b(self.xx[-1], nu=i), atol=1e-11) + # tests for axis=-1 + b = make_interp_spline(self.xx, self.yy, k=5, bc_type='periodic', axis=-1) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + for i in range(1, 5): + assert_allclose(b(self.xx[0], nu=i), b(self.xx[-1], nu=i), atol=1e-11) + + @pytest.mark.parametrize('k', [2, 3, 4, 5, 6, 7]) + def test_periodic_random(self, k): + # tests for both cases (k > n and k <= n) + n = 5 + np.random.seed(1234) + x = np.sort(np.random.random_sample(n) * 10) + y = np.random.random_sample(n) * 100 + y[0] = y[-1] + b = make_interp_spline(x, y, k=k, bc_type='periodic') + assert_allclose(b(x), y, atol=1e-14) + + def test_periodic_axis(self): + n = self.xx.shape[0] + np.random.seed(1234) + x = np.random.random_sample(n) * 2 * np.pi + x = np.sort(x) + x[0] = 0. + x[-1] = 2 * np.pi + y = np.zeros((2, n)) + y[0] = np.sin(x) + y[1] = np.cos(x) + b = make_interp_spline(x, y, k=5, bc_type='periodic', axis=1) + for i in range(n): + assert_allclose(b(x[i]), y[:, i], atol=1e-14) + assert_allclose(b(x[0]), b(x[-1]), atol=1e-14) + + def test_periodic_points_exception(self): + # first and last points should match when periodic case expected + np.random.seed(1234) + k = 5 + n = 8 + x = np.sort(np.random.random_sample(n)) + y = np.random.random_sample(n) + y[0] = y[-1] - 1 # to be sure that they are not equal + with assert_raises(ValueError): + make_interp_spline(x, y, k=k, bc_type='periodic') + + def test_periodic_knots_exception(self): + # `periodic` case does not work with passed vector of knots + np.random.seed(1234) + k = 3 + n = 7 + x = np.sort(np.random.random_sample(n)) + y = np.random.random_sample(n) + t = np.zeros(n + 2 * k) + with assert_raises(ValueError): + make_interp_spline(x, y, k, t, 'periodic') + + @pytest.mark.parametrize('k', [2, 3, 4, 5]) + def test_periodic_splev(self, k): + # comparison values of periodic b-spline with splev + b = make_interp_spline(self.xx, self.yy, k=k, bc_type='periodic') + tck = splrep(self.xx, self.yy, per=True, k=k) + spl = splev(self.xx, tck) + assert_allclose(spl, b(self.xx), atol=1e-14) + + # comparison derivatives of periodic b-spline with splev + for i in range(1, k): + spl = splev(self.xx, tck, der=i) + assert_allclose(spl, b(self.xx, nu=i), atol=1e-10) + + def test_periodic_cubic(self): + # comparison values of cubic periodic b-spline with CubicSpline + b = make_interp_spline(self.xx, self.yy, k=3, bc_type='periodic') + cub = CubicSpline(self.xx, self.yy, bc_type='periodic') + assert_allclose(b(self.xx), cub(self.xx), atol=1e-14) + + # edge case: Cubic interpolation on 3 points + n = 3 + x = np.sort(np.random.random_sample(n) * 10) + y = np.random.random_sample(n) * 100 + y[0] = y[-1] + b = make_interp_spline(x, y, k=3, bc_type='periodic') + cub = CubicSpline(x, y, bc_type='periodic') + assert_allclose(b(x), cub(x), atol=1e-14) + + def test_periodic_full_matrix(self): + # comparison values of cubic periodic b-spline with + # solution of the system with full matrix + k = 3 + b = make_interp_spline(self.xx, self.yy, k=k, bc_type='periodic') + t = _periodic_knots(self.xx, k) + c = _make_interp_per_full_matr(self.xx, self.yy, t, k) + b1 = np.vectorize(lambda x: _naive_eval(x, t, c, k)) + assert_allclose(b(self.xx), b1(self.xx), atol=1e-14) + + def test_quadratic_deriv(self): + der = [(1, 8.)] # order, value: f'(x) = 8. + + # derivative at right-hand edge + b = make_interp_spline(self.xx, self.yy, k=2, bc_type=(None, der)) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + assert_allclose(b(self.xx[-1], 1), der[0][1], atol=1e-14, rtol=1e-14) + + # derivative at left-hand edge + b = make_interp_spline(self.xx, self.yy, k=2, bc_type=(der, None)) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + assert_allclose(b(self.xx[0], 1), der[0][1], atol=1e-14, rtol=1e-14) + + def test_cubic_deriv(self): + k = 3 + + # first derivatives at left & right edges: + der_l, der_r = [(1, 3.)], [(1, 4.)] + b = make_interp_spline(self.xx, self.yy, k, bc_type=(der_l, der_r)) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + assert_allclose([b(self.xx[0], 1), b(self.xx[-1], 1)], + [der_l[0][1], der_r[0][1]], atol=1e-14, rtol=1e-14) + + # 'natural' cubic spline, zero out 2nd derivatives at the boundaries + der_l, der_r = [(2, 0)], [(2, 0)] + b = make_interp_spline(self.xx, self.yy, k, bc_type=(der_l, der_r)) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + + def test_quintic_derivs(self): + k, n = 5, 7 + x = np.arange(n).astype(np.float64) + y = np.sin(x) + der_l = [(1, -12.), (2, 1)] + der_r = [(1, 8.), (2, 3.)] + b = make_interp_spline(x, y, k=k, bc_type=(der_l, der_r)) + assert_allclose(b(x), y, atol=1e-14, rtol=1e-14) + assert_allclose([b(x[0], 1), b(x[0], 2)], + [val for (nu, val) in der_l]) + assert_allclose([b(x[-1], 1), b(x[-1], 2)], + [val for (nu, val) in der_r]) + + @pytest.mark.xfail(reason='unstable') + def test_cubic_deriv_unstable(self): + # 1st and 2nd derivative at x[0], no derivative information at x[-1] + # The problem is not that it fails [who would use this anyway], + # the problem is that it fails *silently*, and I've no idea + # how to detect this sort of instability. + # In this particular case: it's OK for len(t) < 20, goes haywire + # at larger `len(t)`. + k = 3 + t = _augknt(self.xx, k) + + der_l = [(1, 3.), (2, 4.)] + b = make_interp_spline(self.xx, self.yy, k, t, bc_type=(der_l, None)) + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + + def test_knots_not_data_sites(self): + # Knots need not coincide with the data sites. + # use a quadratic spline, knots are at data averages, + # two additional constraints are zero 2nd derivatives at edges + k = 2 + t = np.r_[(self.xx[0],)*(k+1), + (self.xx[1:] + self.xx[:-1]) / 2., + (self.xx[-1],)*(k+1)] + b = make_interp_spline(self.xx, self.yy, k, t, + bc_type=([(2, 0)], [(2, 0)])) + + assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14) + assert_allclose([b(self.xx[0], 2), b(self.xx[-1], 2)], [0., 0.], + atol=1e-14) + + def test_minimum_points_and_deriv(self): + # interpolation of f(x) = x**3 between 0 and 1. f'(x) = 3 * xx**2 and + # f'(0) = 0, f'(1) = 3. + k = 3 + x = [0., 1.] + y = [0., 1.] + b = make_interp_spline(x, y, k, bc_type=([(1, 0.)], [(1, 3.)])) + + xx = np.linspace(0., 1.) + yy = xx**3 + assert_allclose(b(xx), yy, atol=1e-14, rtol=1e-14) + + def test_deriv_spec(self): + # If one of the derivatives is omitted, the spline definition is + # incomplete. + x = y = [1.0, 2, 3, 4, 5, 6] + + with assert_raises(ValueError): + make_interp_spline(x, y, bc_type=([(1, 0.)], None)) + + with assert_raises(ValueError): + make_interp_spline(x, y, bc_type=(1, 0.)) + + with assert_raises(ValueError): + make_interp_spline(x, y, bc_type=[(1, 0.)]) + + with assert_raises(ValueError): + make_interp_spline(x, y, bc_type=42) + + # CubicSpline expects`bc_type=(left_pair, right_pair)`, while + # here we expect `bc_type=(iterable, iterable)`. + l, r = (1, 0.0), (1, 0.0) + with assert_raises(ValueError): + make_interp_spline(x, y, bc_type=(l, r)) + + def test_complex(self): + k = 3 + xx = self.xx + yy = self.yy + 1.j*self.yy + + # first derivatives at left & right edges: + der_l, der_r = [(1, 3.j)], [(1, 4.+2.j)] + b = make_interp_spline(xx, yy, k, bc_type=(der_l, der_r)) + assert_allclose(b(xx), yy, atol=1e-14, rtol=1e-14) + assert_allclose([b(xx[0], 1), b(xx[-1], 1)], + [der_l[0][1], der_r[0][1]], atol=1e-14, rtol=1e-14) + + # also test zero and first order + for k in (0, 1): + b = make_interp_spline(xx, yy, k=k) + assert_allclose(b(xx), yy, atol=1e-14, rtol=1e-14) + + def test_int_xy(self): + x = np.arange(10).astype(int) + y = np.arange(10).astype(int) + + # Cython chokes on "buffer type mismatch" (construction) or + # "no matching signature found" (evaluation) + for k in (0, 1, 2, 3): + b = make_interp_spline(x, y, k=k) + b(x) + + def test_sliced_input(self): + # Cython code chokes on non C contiguous arrays + xx = np.linspace(-1, 1, 100) + + x = xx[::5] + y = xx[::5] + + for k in (0, 1, 2, 3): + make_interp_spline(x, y, k=k) + + def test_check_finite(self): + # check_finite defaults to True; nans and such trigger a ValueError + x = np.arange(10).astype(float) + y = x**2 + + for z in [np.nan, np.inf, -np.inf]: + y[-1] = z + assert_raises(ValueError, make_interp_spline, x, y) + + @pytest.mark.parametrize('k', [1, 2, 3, 5]) + def test_list_input(self, k): + # regression test for gh-8714: TypeError for x, y being lists and k=2 + x = list(range(10)) + y = [a**2 for a in x] + make_interp_spline(x, y, k=k) + + def test_multiple_rhs(self): + yy = np.c_[np.sin(self.xx), np.cos(self.xx)] + der_l = [(1, [1., 2.])] + der_r = [(1, [3., 4.])] + + b = make_interp_spline(self.xx, yy, k=3, bc_type=(der_l, der_r)) + assert_allclose(b(self.xx), yy, atol=1e-14, rtol=1e-14) + assert_allclose(b(self.xx[0], 1), der_l[0][1], atol=1e-14, rtol=1e-14) + assert_allclose(b(self.xx[-1], 1), der_r[0][1], atol=1e-14, rtol=1e-14) + + def test_shapes(self): + np.random.seed(1234) + k, n = 3, 22 + x = np.sort(np.random.random(size=n)) + y = np.random.random(size=(n, 5, 6, 7)) + + b = make_interp_spline(x, y, k) + assert_equal(b.c.shape, (n, 5, 6, 7)) + + # now throw in some derivatives + d_l = [(1, np.random.random((5, 6, 7)))] + d_r = [(1, np.random.random((5, 6, 7)))] + b = make_interp_spline(x, y, k, bc_type=(d_l, d_r)) + assert_equal(b.c.shape, (n + k - 1, 5, 6, 7)) + + def test_string_aliases(self): + yy = np.sin(self.xx) + + # a single string is duplicated + b1 = make_interp_spline(self.xx, yy, k=3, bc_type='natural') + b2 = make_interp_spline(self.xx, yy, k=3, bc_type=([(2, 0)], [(2, 0)])) + assert_allclose(b1.c, b2.c, atol=1e-15) + + # two strings are handled + b1 = make_interp_spline(self.xx, yy, k=3, + bc_type=('natural', 'clamped')) + b2 = make_interp_spline(self.xx, yy, k=3, + bc_type=([(2, 0)], [(1, 0)])) + assert_allclose(b1.c, b2.c, atol=1e-15) + + # one-sided BCs are OK + b1 = make_interp_spline(self.xx, yy, k=2, bc_type=(None, 'clamped')) + b2 = make_interp_spline(self.xx, yy, k=2, bc_type=(None, [(1, 0.0)])) + assert_allclose(b1.c, b2.c, atol=1e-15) + + # 'not-a-knot' is equivalent to None + b1 = make_interp_spline(self.xx, yy, k=3, bc_type='not-a-knot') + b2 = make_interp_spline(self.xx, yy, k=3, bc_type=None) + assert_allclose(b1.c, b2.c, atol=1e-15) + + # unknown strings do not pass + with assert_raises(ValueError): + make_interp_spline(self.xx, yy, k=3, bc_type='typo') + + # string aliases are handled for 2D values + yy = np.c_[np.sin(self.xx), np.cos(self.xx)] + der_l = [(1, [0., 0.])] + der_r = [(2, [0., 0.])] + b2 = make_interp_spline(self.xx, yy, k=3, bc_type=(der_l, der_r)) + b1 = make_interp_spline(self.xx, yy, k=3, + bc_type=('clamped', 'natural')) + assert_allclose(b1.c, b2.c, atol=1e-15) + + # ... and for N-D values: + np.random.seed(1234) + k, n = 3, 22 + x = np.sort(np.random.random(size=n)) + y = np.random.random(size=(n, 5, 6, 7)) + + # now throw in some derivatives + d_l = [(1, np.zeros((5, 6, 7)))] + d_r = [(1, np.zeros((5, 6, 7)))] + b1 = make_interp_spline(x, y, k, bc_type=(d_l, d_r)) + b2 = make_interp_spline(x, y, k, bc_type='clamped') + assert_allclose(b1.c, b2.c, atol=1e-15) + + def test_full_matrix(self): + np.random.seed(1234) + k, n = 3, 7 + x = np.sort(np.random.random(size=n)) + y = np.random.random(size=n) + t = _not_a_knot(x, k) + + b = make_interp_spline(x, y, k, t) + cf = make_interp_full_matr(x, y, t, k) + assert_allclose(b.c, cf, atol=1e-14, rtol=1e-14) + + def test_woodbury(self): + ''' + Random elements in diagonal matrix with blocks in the + left lower and right upper corners checking the + implementation of Woodbury algorithm. + ''' + np.random.seed(1234) + n = 201 + for k in range(3, 32, 2): + offset = int((k - 1) / 2) + a = np.diagflat(np.random.random((1, n))) + for i in range(1, offset + 1): + a[:-i, i:] += np.diagflat(np.random.random((1, n - i))) + a[i:, :-i] += np.diagflat(np.random.random((1, n - i))) + ur = np.random.random((offset, offset)) + a[:offset, -offset:] = ur + ll = np.random.random((offset, offset)) + a[-offset:, :offset] = ll + d = np.zeros((k, n)) + for i, j in enumerate(range(offset, -offset - 1, -1)): + if j < 0: + d[i, :j] = np.diagonal(a, offset=j) + else: + d[i, j:] = np.diagonal(a, offset=j) + b = np.random.random(n) + assert_allclose(_woodbury_algorithm(d, ur, ll, b, k), + np.linalg.solve(a, b), atol=1e-14) + + +def make_interp_full_matr(x, y, t, k): + """Assemble an spline order k with knots t to interpolate + y(x) using full matrices. + Not-a-knot BC only. + + This routine is here for testing only (even though it's functional). + """ + assert x.size == y.size + assert t.size == x.size + k + 1 + n = x.size + + A = np.zeros((n, n), dtype=np.float64) + + for j in range(n): + xval = x[j] + if xval == t[k]: + left = k + else: + left = np.searchsorted(t, xval) - 1 + + # fill a row + bb = _bspl.evaluate_all_bspl(t, k, xval, left) + A[j, left-k:left+1] = bb + + c = sl.solve(A, y) + return c + + +def make_lsq_full_matrix(x, y, t, k=3): + """Make the least-square spline, full matrices.""" + x, y, t = map(np.asarray, (x, y, t)) + m = x.size + n = t.size - k - 1 + + A = np.zeros((m, n), dtype=np.float64) + + for j in range(m): + xval = x[j] + # find interval + if xval == t[k]: + left = k + else: + left = np.searchsorted(t, xval) - 1 + + # fill a row + bb = _bspl.evaluate_all_bspl(t, k, xval, left) + A[j, left-k:left+1] = bb + + # have observation matrix, can solve the LSQ problem + B = np.dot(A.T, A) + Y = np.dot(A.T, y) + c = sl.solve(B, Y) + + return c, (A, Y) + + +class TestLSQ: + # + # Test make_lsq_spline + # + np.random.seed(1234) + n, k = 13, 3 + x = np.sort(np.random.random(n)) + y = np.random.random(n) + t = _augknt(np.linspace(x[0], x[-1], 7), k) + + def test_lstsq(self): + # check LSQ construction vs a full matrix version + x, y, t, k = self.x, self.y, self.t, self.k + + c0, AY = make_lsq_full_matrix(x, y, t, k) + b = make_lsq_spline(x, y, t, k) + + assert_allclose(b.c, c0) + assert_equal(b.c.shape, (t.size - k - 1,)) + + # also check against numpy.lstsq + aa, yy = AY + c1, _, _, _ = np.linalg.lstsq(aa, y, rcond=-1) + assert_allclose(b.c, c1) + + def test_weights(self): + # weights = 1 is same as None + x, y, t, k = self.x, self.y, self.t, self.k + w = np.ones_like(x) + + b = make_lsq_spline(x, y, t, k) + b_w = make_lsq_spline(x, y, t, k, w=w) + + assert_allclose(b.t, b_w.t, atol=1e-14) + assert_allclose(b.c, b_w.c, atol=1e-14) + assert_equal(b.k, b_w.k) + + def test_multiple_rhs(self): + x, t, k, n = self.x, self.t, self.k, self.n + y = np.random.random(size=(n, 5, 6, 7)) + + b = make_lsq_spline(x, y, t, k) + assert_equal(b.c.shape, (t.size-k-1, 5, 6, 7)) + + def test_complex(self): + # cmplx-valued `y` + x, t, k = self.x, self.t, self.k + yc = self.y * (1. + 2.j) + + b = make_lsq_spline(x, yc, t, k) + b_re = make_lsq_spline(x, yc.real, t, k) + b_im = make_lsq_spline(x, yc.imag, t, k) + + assert_allclose(b(x), b_re(x) + 1.j*b_im(x), atol=1e-15, rtol=1e-15) + + def test_int_xy(self): + x = np.arange(10).astype(int) + y = np.arange(10).astype(int) + t = _augknt(x, k=1) + # Cython chokes on "buffer type mismatch" + make_lsq_spline(x, y, t, k=1) + + def test_sliced_input(self): + # Cython code chokes on non C contiguous arrays + xx = np.linspace(-1, 1, 100) + + x = xx[::3] + y = xx[::3] + t = _augknt(x, 1) + make_lsq_spline(x, y, t, k=1) + + def test_checkfinite(self): + # check_finite defaults to True; nans and such trigger a ValueError + x = np.arange(12).astype(float) + y = x**2 + t = _augknt(x, 3) + + for z in [np.nan, np.inf, -np.inf]: + y[-1] = z + assert_raises(ValueError, make_lsq_spline, x, y, t) + + def test_read_only(self): + # Check that make_lsq_spline works with read only arrays + x, y, t = self.x, self.y, self.t + x.setflags(write=False) + y.setflags(write=False) + t.setflags(write=False) + make_lsq_spline(x=x, y=y, t=t) + + +def data_file(basename): + return os.path.join(os.path.abspath(os.path.dirname(__file__)), + 'data', basename) + + +class TestSmoothingSpline: + # + # test make_smoothing_spline + # + def test_invalid_input(self): + np.random.seed(1234) + n = 100 + x = np.sort(np.random.random_sample(n) * 4 - 2) + y = x**2 * np.sin(4 * x) + x**3 + np.random.normal(0., 1.5, n) + + # ``x`` and ``y`` should have same shapes (1-D array) + with assert_raises(ValueError): + make_smoothing_spline(x, y[1:]) + with assert_raises(ValueError): + make_smoothing_spline(x[1:], y) + with assert_raises(ValueError): + make_smoothing_spline(x.reshape(1, n), y) + + # ``x`` should be an ascending array + with assert_raises(ValueError): + make_smoothing_spline(x[::-1], y) + + x_dupl = np.copy(x) + x_dupl[0] = x_dupl[1] + + with assert_raises(ValueError): + make_smoothing_spline(x_dupl, y) + + # x and y length must be >= 5 + x = np.arange(4) + y = np.ones(4) + exception_message = "``x`` and ``y`` length must be at least 5" + with pytest.raises(ValueError, match=exception_message): + make_smoothing_spline(x, y) + + def test_compare_with_GCVSPL(self): + """ + Data is generated in the following way: + >>> np.random.seed(1234) + >>> n = 100 + >>> x = np.sort(np.random.random_sample(n) * 4 - 2) + >>> y = np.sin(x) + np.random.normal(scale=.5, size=n) + >>> np.savetxt('x.csv', x) + >>> np.savetxt('y.csv', y) + + We obtain the result of performing the GCV smoothing splines + package (by Woltring, gcvspl) on the sample data points + using its version for Octave (https://github.com/srkuberski/gcvspl). + In order to use this implementation, one should clone the repository + and open the folder in Octave. + In Octave, we load up ``x`` and ``y`` (generated from Python code + above): + + >>> x = csvread('x.csv'); + >>> y = csvread('y.csv'); + + Then, in order to access the implementation, we compile gcvspl files in + Octave: + + >>> mex gcvsplmex.c gcvspl.c + >>> mex spldermex.c gcvspl.c + + The first function computes the vector of unknowns from the dataset + (x, y) while the second one evaluates the spline in certain points + with known vector of coefficients. + + >>> c = gcvsplmex( x, y, 2 ); + >>> y0 = spldermex( x, c, 2, x, 0 ); + + If we want to compare the results of the gcvspl code, we can save + ``y0`` in csv file: + + >>> csvwrite('y0.csv', y0); + + """ + # load the data sample + with np.load(data_file('gcvspl.npz')) as data: + # data points + x = data['x'] + y = data['y'] + + y_GCVSPL = data['y_GCVSPL'] + y_compr = make_smoothing_spline(x, y)(x) + + # such tolerance is explained by the fact that the spline is built + # using an iterative algorithm for minimizing the GCV criteria. These + # algorithms may vary, so the tolerance should be rather low. + assert_allclose(y_compr, y_GCVSPL, atol=1e-4, rtol=1e-4) + + def test_non_regularized_case(self): + """ + In case the regularization parameter is 0, the resulting spline + is an interpolation spline with natural boundary conditions. + """ + # create data sample + np.random.seed(1234) + n = 100 + x = np.sort(np.random.random_sample(n) * 4 - 2) + y = x**2 * np.sin(4 * x) + x**3 + np.random.normal(0., 1.5, n) + + spline_GCV = make_smoothing_spline(x, y, lam=0.) + spline_interp = make_interp_spline(x, y, 3, bc_type='natural') + + grid = np.linspace(x[0], x[-1], 2 * n) + assert_allclose(spline_GCV(grid), + spline_interp(grid), + atol=1e-15) + + def test_weighted_smoothing_spline(self): + # create data sample + np.random.seed(1234) + n = 100 + x = np.sort(np.random.random_sample(n) * 4 - 2) + y = x**2 * np.sin(4 * x) + x**3 + np.random.normal(0., 1.5, n) + + spl = make_smoothing_spline(x, y) + + # in order not to iterate over all of the indices, we select 10 of + # them randomly + for ind in np.random.choice(range(100), size=10): + w = np.ones(n) + w[ind] = 30. + spl_w = make_smoothing_spline(x, y, w) + # check that spline with weight in a certain point is closer to the + # original point than the one without weights + orig = abs(spl(x[ind]) - y[ind]) + weighted = abs(spl_w(x[ind]) - y[ind]) + + if orig < weighted: + raise ValueError(f'Spline with weights should be closer to the' + f' points than the original one: {orig:.4} < ' + f'{weighted:.4}') + + +################################ +# NdBSpline tests +def bspline2(xy, t, c, k): + """A naive 2D tensort product spline evaluation.""" + x, y = xy + tx, ty = t + nx = len(tx) - k - 1 + assert (nx >= k+1) + ny = len(ty) - k - 1 + assert (ny >= k+1) + return sum(c[ix, iy] * B(x, k, ix, tx) * B(y, k, iy, ty) + for ix in range(nx) for iy in range(ny)) + + +def B(x, k, i, t): + if k == 0: + return 1.0 if t[i] <= x < t[i+1] else 0.0 + if t[i+k] == t[i]: + c1 = 0.0 + else: + c1 = (x - t[i])/(t[i+k] - t[i]) * B(x, k-1, i, t) + if t[i+k+1] == t[i+1]: + c2 = 0.0 + else: + c2 = (t[i+k+1] - x)/(t[i+k+1] - t[i+1]) * B(x, k-1, i+1, t) + return c1 + c2 + + +def bspline(x, t, c, k): + n = len(t) - k - 1 + assert (n >= k+1) and (len(c) >= n) + return sum(c[i] * B(x, k, i, t) for i in range(n)) + + +class NdBSpline0: + def __init__(self, t, c, k=3): + """Tensor product spline object. + + c[i1, i2, ..., id] * B(x1, i1) * B(x2, i2) * ... * B(xd, id) + + Parameters + ---------- + c : ndarray, shape (n1, n2, ..., nd, ...) + b-spline coefficients + t : tuple of 1D ndarrays + knot vectors in directions 1, 2, ... d + ``len(t[i]) == n[i] + k + 1`` + k : int or length-d tuple of integers + spline degrees. + """ + ndim = len(t) + assert ndim <= len(c.shape) + + try: + len(k) + except TypeError: + # make k a tuple + k = (k,)*ndim + + self.k = tuple(operator.index(ki) for ki in k) + self.t = tuple(np.asarray(ti, dtype=float) for ti in t) + self.c = c + + def __call__(self, x): + ndim = len(self.t) + # a single evaluation point: `x` is a 1D array_like, shape (ndim,) + assert len(x) == ndim + + # get the indices in an ndim-dimensional vector + i = ['none', ]*ndim + for d in range(ndim): + td, xd = self.t[d], x[d] + k = self.k[d] + + # find the index for x[d] + if xd == td[k]: + i[d] = k + else: + i[d] = np.searchsorted(td, xd) - 1 + assert td[i[d]] <= xd <= td[i[d]+1] + assert i[d] >= k and i[d] < len(td) - k + i = tuple(i) + + # iterate over the dimensions, form linear combinations of + # products B(x_1) * B(x_2) * ... B(x_N) of (k+1)**N b-splines + # which are non-zero at `i = (i_1, i_2, ..., i_N)`. + result = 0 + iters = [range(i[d] - self.k[d], i[d] + 1) for d in range(ndim)] + for idx in itertools.product(*iters): + term = self.c[idx] * np.prod([B(x[d], self.k[d], idx[d], self.t[d]) + for d in range(ndim)]) + result += term + return result + + +class TestNdBSpline: + + def test_1D(self): + # test ndim=1 agrees with BSpline + rng = np.random.default_rng(12345) + n, k = 11, 3 + n_tr = 7 + t = np.sort(rng.uniform(size=n + k + 1)) + c = rng.uniform(size=(n, n_tr)) + + b = BSpline(t, c, k) + nb = NdBSpline((t,), c, k) + + xi = rng.uniform(size=21) + # NdBSpline expects xi.shape=(npts, ndim) + assert_allclose(nb(xi[:, None]), + b(xi), atol=1e-14) + assert nb(xi[:, None]).shape == (xi.shape[0], c.shape[1]) + + def make_2d_case(self): + # make a 2D separable spline + x = np.arange(6) + y = x**3 + spl = make_interp_spline(x, y, k=3) + + y_1 = x**3 + 2*x + spl_1 = make_interp_spline(x, y_1, k=3) + + t2 = (spl.t, spl_1.t) + c2 = spl.c[:, None] * spl_1.c[None, :] + + return t2, c2, 3 + + def make_2d_mixed(self): + # make a 2D separable spline w/ kx=3, ky=2 + x = np.arange(6) + y = x**3 + spl = make_interp_spline(x, y, k=3) + + x = np.arange(5) + 1.5 + y_1 = x**2 + 2*x + spl_1 = make_interp_spline(x, y_1, k=2) + + t2 = (spl.t, spl_1.t) + c2 = spl.c[:, None] * spl_1.c[None, :] + + return t2, c2, spl.k, spl_1.k + + def test_2D_separable(self): + xi = [(1.5, 2.5), (2.5, 1), (0.5, 1.5)] + t2, c2, k = self.make_2d_case() + target = [x**3 * (y**3 + 2*y) for (x, y) in xi] + + # sanity check: bspline2 gives the product as constructed + assert_allclose([bspline2(xy, t2, c2, k) for xy in xi], + target, + atol=1e-14) + + # check evaluation on a 2D array: the 1D array of 2D points + bspl2 = NdBSpline(t2, c2, k=3) + assert bspl2(xi).shape == (len(xi), ) + assert_allclose(bspl2(xi), + target, atol=1e-14) + + # now check on a multidim xi + rng = np.random.default_rng(12345) + xi = rng.uniform(size=(4, 3, 2)) * 5 + result = bspl2(xi) + assert result.shape == (4, 3) + + # also check the values + x, y = xi.reshape((-1, 2)).T + assert_allclose(result.ravel(), + x**3 * (y**3 + 2*y), atol=1e-14) + + def test_2D_separable_2(self): + # test `c` with trailing dimensions, i.e. c.ndim > ndim + ndim = 2 + xi = [(1.5, 2.5), (2.5, 1), (0.5, 1.5)] + target = [x**3 * (y**3 + 2*y) for (x, y) in xi] + + t2, c2, k = self.make_2d_case() + c2_4 = np.dstack((c2, c2, c2, c2)) # c22.shape = (6, 6, 4) + + xy = (1.5, 2.5) + bspl2_4 = NdBSpline(t2, c2_4, k=3) + result = bspl2_4(xy) + val_single = NdBSpline(t2, c2, k)(xy) + assert result.shape == (4,) + assert_allclose(result, + [val_single, ]*4, atol=1e-14) + + # now try the array xi : the output.shape is (3, 4) where 3 + # is the number of points in xi and 4 is the trailing dimension of c + assert bspl2_4(xi).shape == np.shape(xi)[:-1] + bspl2_4.c.shape[ndim:] + assert_allclose(bspl2_4(xi) - np.asarray(target)[:, None], + 0, atol=5e-14) + + # two trailing dimensions + c2_22 = c2_4.reshape((6, 6, 2, 2)) + bspl2_22 = NdBSpline(t2, c2_22, k=3) + + result = bspl2_22(xy) + assert result.shape == (2, 2) + assert_allclose(result, + [[val_single, val_single], + [val_single, val_single]], atol=1e-14) + + # now try the array xi : the output shape is (3, 2, 2) + # for 3 points in xi and c trailing dimensions being (2, 2) + assert (bspl2_22(xi).shape == + np.shape(xi)[:-1] + bspl2_22.c.shape[ndim:]) + assert_allclose(bspl2_22(xi) - np.asarray(target)[:, None, None], + 0, atol=5e-14) + + def test_2D_random(self): + rng = np.random.default_rng(12345) + k = 3 + tx = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=7)) * 3, 3, 3, 3, 3] + ty = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=8)) * 4, 4, 4, 4, 4] + c = rng.uniform(size=(tx.size-k-1, ty.size-k-1)) + + spl = NdBSpline((tx, ty), c, k=k) + + xi = (1., 1.) + assert_allclose(spl(xi), + bspline2(xi, (tx, ty), c, k), atol=1e-14) + + xi = np.c_[[1, 1.5, 2], + [1.1, 1.6, 2.1]] + assert_allclose(spl(xi), + [bspline2(xy, (tx, ty), c, k) for xy in xi], + atol=1e-14) + + def test_2D_mixed(self): + t2, c2, kx, ky = self.make_2d_mixed() + xi = [(1.4, 4.5), (2.5, 2.4), (4.5, 3.5)] + target = [x**3 * (y**2 + 2*y) for (x, y) in xi] + bspl2 = NdBSpline(t2, c2, k=(kx, ky)) + assert bspl2(xi).shape == (len(xi), ) + assert_allclose(bspl2(xi), + target, atol=1e-14) + + def test_2D_derivative(self): + t2, c2, kx, ky = self.make_2d_mixed() + xi = [(1.4, 4.5), (2.5, 2.4), (4.5, 3.5)] + bspl2 = NdBSpline(t2, c2, k=(kx, ky)) + + der = bspl2(xi, nu=(1, 0)) + assert_allclose(der, + [3*x**2 * (y**2 + 2*y) for x, y in xi], atol=1e-14) + + der = bspl2(xi, nu=(1, 1)) + assert_allclose(der, + [3*x**2 * (2*y + 2) for x, y in xi], atol=1e-14) + + der = bspl2(xi, nu=(0, 0)) + assert_allclose(der, + [x**3 * (y**2 + 2*y) for x, y in xi], atol=1e-14) + + with assert_raises(ValueError): + # all(nu >= 0) + der = bspl2(xi, nu=(-1, 0)) + + with assert_raises(ValueError): + # len(nu) == ndim + der = bspl2(xi, nu=(-1, 0, 1)) + + def test_2D_mixed_random(self): + rng = np.random.default_rng(12345) + kx, ky = 2, 3 + tx = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=7)) * 3, 3, 3, 3, 3] + ty = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=8)) * 4, 4, 4, 4, 4] + c = rng.uniform(size=(tx.size - kx - 1, ty.size - ky - 1)) + + xi = np.c_[[1, 1.5, 2], + [1.1, 1.6, 2.1]] + + bspl2 = NdBSpline((tx, ty), c, k=(kx, ky)) + bspl2_0 = NdBSpline0((tx, ty), c, k=(kx, ky)) + + assert_allclose(bspl2(xi), + [bspl2_0(xp) for xp in xi], atol=1e-14) + + def test_tx_neq_ty(self): + # 2D separable spline w/ len(tx) != len(ty) + x = np.arange(6) + y = np.arange(7) + 1.5 + + spl_x = make_interp_spline(x, x**3, k=3) + spl_y = make_interp_spline(y, y**2 + 2*y, k=3) + cc = spl_x.c[:, None] * spl_y.c[None, :] + bspl = NdBSpline((spl_x.t, spl_y.t), cc, (spl_x.k, spl_y.k)) + + values = (x**3)[:, None] * (y**2 + 2*y)[None, :] + rgi = RegularGridInterpolator((x, y), values) + + xi = [(a, b) for a, b in itertools.product(x, y)] + bxi = bspl(xi) + + assert not np.isnan(bxi).any() + assert_allclose(bxi, rgi(xi), atol=1e-14) + assert_allclose(bxi.reshape(values.shape), values, atol=1e-14) + + def make_3d_case(self): + # make a 3D separable spline + x = np.arange(6) + y = x**3 + spl = make_interp_spline(x, y, k=3) + + y_1 = x**3 + 2*x + spl_1 = make_interp_spline(x, y_1, k=3) + + y_2 = x**3 + 3*x + 1 + spl_2 = make_interp_spline(x, y_2, k=3) + + t2 = (spl.t, spl_1.t, spl_2.t) + c2 = (spl.c[:, None, None] * + spl_1.c[None, :, None] * + spl_2.c[None, None, :]) + + return t2, c2, 3 + + def test_3D_separable(self): + rng = np.random.default_rng(12345) + x, y, z = rng.uniform(size=(3, 11)) * 5 + target = x**3 * (y**3 + 2*y) * (z**3 + 3*z + 1) + + t3, c3, k = self.make_3d_case() + bspl3 = NdBSpline(t3, c3, k=3) + + xi = [_ for _ in zip(x, y, z)] + result = bspl3(xi) + assert result.shape == (11,) + assert_allclose(result, target, atol=1e-14) + + def test_3D_derivative(self): + t3, c3, k = self.make_3d_case() + bspl3 = NdBSpline(t3, c3, k=3) + rng = np.random.default_rng(12345) + x, y, z = rng.uniform(size=(3, 11)) * 5 + xi = [_ for _ in zip(x, y, z)] + + assert_allclose(bspl3(xi, nu=(1, 0, 0)), + 3*x**2 * (y**3 + 2*y) * (z**3 + 3*z + 1), atol=1e-14) + + assert_allclose(bspl3(xi, nu=(2, 0, 0)), + 6*x * (y**3 + 2*y) * (z**3 + 3*z + 1), atol=1e-14) + + assert_allclose(bspl3(xi, nu=(2, 1, 0)), + 6*x * (3*y**2 + 2) * (z**3 + 3*z + 1), atol=1e-14) + + assert_allclose(bspl3(xi, nu=(2, 1, 3)), + 6*x * (3*y**2 + 2) * (6), atol=1e-14) + + assert_allclose(bspl3(xi, nu=(2, 1, 4)), + np.zeros(len(xi)), atol=1e-14) + + def test_3D_random(self): + rng = np.random.default_rng(12345) + k = 3 + tx = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=7)) * 3, 3, 3, 3, 3] + ty = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=8)) * 4, 4, 4, 4, 4] + tz = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=8)) * 4, 4, 4, 4, 4] + c = rng.uniform(size=(tx.size-k-1, ty.size-k-1, tz.size-k-1)) + + spl = NdBSpline((tx, ty, tz), c, k=k) + spl_0 = NdBSpline0((tx, ty, tz), c, k=k) + + xi = (1., 1., 1) + assert_allclose(spl(xi), spl_0(xi), atol=1e-14) + + xi = np.c_[[1, 1.5, 2], + [1.1, 1.6, 2.1], + [0.9, 1.4, 1.9]] + assert_allclose(spl(xi), [spl_0(xp) for xp in xi], atol=1e-14) + + def test_3D_random_complex(self): + rng = np.random.default_rng(12345) + k = 3 + tx = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=7)) * 3, 3, 3, 3, 3] + ty = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=8)) * 4, 4, 4, 4, 4] + tz = np.r_[0, 0, 0, 0, np.sort(rng.uniform(size=8)) * 4, 4, 4, 4, 4] + c = (rng.uniform(size=(tx.size-k-1, ty.size-k-1, tz.size-k-1)) + + rng.uniform(size=(tx.size-k-1, ty.size-k-1, tz.size-k-1))*1j) + + spl = NdBSpline((tx, ty, tz), c, k=k) + spl_re = NdBSpline((tx, ty, tz), c.real, k=k) + spl_im = NdBSpline((tx, ty, tz), c.imag, k=k) + + xi = np.c_[[1, 1.5, 2], + [1.1, 1.6, 2.1], + [0.9, 1.4, 1.9]] + assert_allclose(spl(xi), + spl_re(xi) + 1j*spl_im(xi), atol=1e-14) + + @pytest.mark.parametrize('cls_extrap', [None, True]) + @pytest.mark.parametrize('call_extrap', [None, True]) + def test_extrapolate_3D_separable(self, cls_extrap, call_extrap): + # test that extrapolate=True does extrapolate + t3, c3, k = self.make_3d_case() + bspl3 = NdBSpline(t3, c3, k=3, extrapolate=cls_extrap) + + # evaluate out of bounds + x, y, z = [-2, -1, 7], [-3, -0.5, 6.5], [-1, -1.5, 7.5] + x, y, z = map(np.asarray, (x, y, z)) + xi = [_ for _ in zip(x, y, z)] + target = x**3 * (y**3 + 2*y) * (z**3 + 3*z + 1) + + result = bspl3(xi, extrapolate=call_extrap) + assert_allclose(result, target, atol=1e-14) + + @pytest.mark.parametrize('extrap', [(False, True), (True, None)]) + def test_extrapolate_3D_separable_2(self, extrap): + # test that call(..., extrapolate=None) defers to self.extrapolate, + # otherwise supersedes self.extrapolate + t3, c3, k = self.make_3d_case() + cls_extrap, call_extrap = extrap + bspl3 = NdBSpline(t3, c3, k=3, extrapolate=cls_extrap) + + # evaluate out of bounds + x, y, z = [-2, -1, 7], [-3, -0.5, 6.5], [-1, -1.5, 7.5] + x, y, z = map(np.asarray, (x, y, z)) + xi = [_ for _ in zip(x, y, z)] + target = x**3 * (y**3 + 2*y) * (z**3 + 3*z + 1) + + result = bspl3(xi, extrapolate=call_extrap) + assert_allclose(result, target, atol=1e-14) + + def test_extrapolate_false_3D_separable(self): + # test that extrapolate=False produces nans for out-of-bounds values + t3, c3, k = self.make_3d_case() + bspl3 = NdBSpline(t3, c3, k=3) + + # evaluate out of bounds and inside + x, y, z = [-2, 1, 7], [-3, 0.5, 6.5], [-1, 1.5, 7.5] + x, y, z = map(np.asarray, (x, y, z)) + xi = [_ for _ in zip(x, y, z)] + target = x**3 * (y**3 + 2*y) * (z**3 + 3*z + 1) + + result = bspl3(xi, extrapolate=False) + assert np.isnan(result[0]) + assert np.isnan(result[-1]) + assert_allclose(result[1:-1], target[1:-1], atol=1e-14) + + def test_x_nan_3D(self): + # test that spline(nan) is nan + t3, c3, k = self.make_3d_case() + bspl3 = NdBSpline(t3, c3, k=3) + + # evaluate out of bounds and inside + x = np.asarray([-2, 3, np.nan, 1, 2, 7, np.nan]) + y = np.asarray([-3, 3.5, 1, np.nan, 3, 6.5, 6.5]) + z = np.asarray([-1, 3.5, 2, 3, np.nan, 7.5, 7.5]) + xi = [_ for _ in zip(x, y, z)] + target = x**3 * (y**3 + 2*y) * (z**3 + 3*z + 1) + mask = np.isnan(x) | np.isnan(y) | np.isnan(z) + target[mask] = np.nan + + result = bspl3(xi) + assert np.isnan(result[mask]).all() + assert_allclose(result, target, atol=1e-14) + + def test_non_c_contiguous(self): + # check that non C-contiguous inputs are OK + rng = np.random.default_rng(12345) + kx, ky = 3, 3 + tx = np.sort(rng.uniform(low=0, high=4, size=16)) + tx = np.r_[(tx[0],)*kx, tx, (tx[-1],)*kx] + ty = np.sort(rng.uniform(low=0, high=4, size=16)) + ty = np.r_[(ty[0],)*ky, ty, (ty[-1],)*ky] + + assert not tx[::2].flags.c_contiguous + assert not ty[::2].flags.c_contiguous + + c = rng.uniform(size=(tx.size//2 - kx - 1, ty.size//2 - ky - 1)) + c = c.T + assert not c.flags.c_contiguous + + xi = np.c_[[1, 1.5, 2], + [1.1, 1.6, 2.1]] + + bspl2 = NdBSpline((tx[::2], ty[::2]), c, k=(kx, ky)) + bspl2_0 = NdBSpline0((tx[::2], ty[::2]), c, k=(kx, ky)) + + assert_allclose(bspl2(xi), + [bspl2_0(xp) for xp in xi], atol=1e-14) + + def test_readonly(self): + t3, c3, k = self.make_3d_case() + bspl3 = NdBSpline(t3, c3, k=3) + + for i in range(3): + t3[i].flags.writeable = False + c3.flags.writeable = False + + bspl3_ = NdBSpline(t3, c3, k=3) + + assert bspl3((1, 2, 3)) == bspl3_((1, 2, 3)) + + def test_design_matrix(self): + t3, c3, k = self.make_3d_case() + + xi = np.asarray([[1, 2, 3], [4, 5, 6]]) + dm = NdBSpline(t3, c3, k).design_matrix(xi, t3, k) + dm1 = NdBSpline.design_matrix(xi, t3, [k, k, k]) + assert dm.shape[0] == xi.shape[0] + assert_allclose(dm.todense(), dm1.todense(), atol=1e-16) + + with assert_raises(ValueError): + NdBSpline.design_matrix([1, 2, 3], t3, [k]*3) + + with assert_raises(ValueError, match="Data and knots*"): + NdBSpline.design_matrix([[1, 2]], t3, [k]*3) + + +class TestMakeND: + def test_2D_separable_simple(self): + x = np.arange(6) + y = np.arange(6) + 0.5 + values = x[:, None]**3 * (y**3 + 2*y)[None, :] + xi = [(a, b) for a, b in itertools.product(x, y)] + + bspl = make_ndbspl((x, y), values, k=1) + assert_allclose(bspl(xi), values.ravel(), atol=1e-15) + + # test the coefficients vs outer product of 1D coefficients + spl_x = make_interp_spline(x, x**3, k=1) + spl_y = make_interp_spline(y, y**3 + 2*y, k=1) + cc = spl_x.c[:, None] * spl_y.c[None, :] + assert_allclose(cc, bspl.c, atol=1e-11, rtol=0) + + # test against RGI + from scipy.interpolate import RegularGridInterpolator as RGI + rgi = RGI((x, y), values, method='linear') + assert_allclose(rgi(xi), bspl(xi), atol=1e-14) + + def test_2D_separable_trailing_dims(self): + # test `c` with trailing dimensions, i.e. c.ndim > ndim + x = np.arange(6) + y = np.arange(6) + xi = [(a, b) for a, b in itertools.product(x, y)] + + # make values4.shape = (6, 6, 4) + values = x[:, None]**3 * (y**3 + 2*y)[None, :] + values4 = np.dstack((values, values, values, values)) + bspl = make_ndbspl((x, y), values4, k=3, solver=ssl.spsolve) + + result = bspl(xi) + target = np.dstack((values, values, values, values)) + assert result.shape == (36, 4) + assert_allclose(result.reshape(6, 6, 4), + target, atol=1e-14) + + # now two trailing dimensions + values22 = values4.reshape((6, 6, 2, 2)) + bspl = make_ndbspl((x, y), values22, k=3, solver=ssl.spsolve) + + result = bspl(xi) + assert result.shape == (36, 2, 2) + assert_allclose(result.reshape(6, 6, 2, 2), + target.reshape((6, 6, 2, 2)), atol=1e-14) + + @pytest.mark.parametrize('k', [(3, 3), (1, 1), (3, 1), (1, 3), (3, 5)]) + def test_2D_mixed(self, k): + # make a 2D separable spline w/ len(tx) != len(ty) + x = np.arange(6) + y = np.arange(7) + 1.5 + xi = [(a, b) for a, b in itertools.product(x, y)] + + values = (x**3)[:, None] * (y**2 + 2*y)[None, :] + bspl = make_ndbspl((x, y), values, k=k, solver=ssl.spsolve) + assert_allclose(bspl(xi), values.ravel(), atol=1e-15) + + def _get_sample_2d_data(self): + # from test_rgi.py::TestIntepN + x = np.array([.5, 2., 3., 4., 5.5, 6.]) + y = np.array([.5, 2., 3., 4., 5.5, 6.]) + z = np.array( + [ + [1, 2, 1, 2, 1, 1], + [1, 2, 1, 2, 1, 1], + [1, 2, 3, 2, 1, 1], + [1, 2, 2, 2, 1, 1], + [1, 2, 1, 2, 1, 1], + [1, 2, 2, 2, 1, 1], + ] + ) + return x, y, z + + def test_2D_vs_RGI_linear(self): + x, y, z = self._get_sample_2d_data() + bspl = make_ndbspl((x, y), z, k=1) + rgi = RegularGridInterpolator((x, y), z, method='linear') + + xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + + assert_allclose(bspl(xi), rgi(xi), atol=1e-14) + + def test_2D_vs_RGI_cubic(self): + x, y, z = self._get_sample_2d_data() + bspl = make_ndbspl((x, y), z, k=3, solver=ssl.spsolve) + rgi = RegularGridInterpolator((x, y), z, method='cubic_legacy') + + xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + + assert_allclose(bspl(xi), rgi(xi), atol=1e-14) + + @pytest.mark.parametrize('solver', [ssl.gmres, ssl.gcrotmk]) + def test_2D_vs_RGI_cubic_iterative(self, solver): + # same as `test_2D_vs_RGI_cubic`, only with an iterative solver. + # Note the need to add an explicit `rtol` solver_arg to achieve the + # target accuracy of 1e-14. (the relation between solver atol/rtol + # and the accuracy of the final result is not direct and needs experimenting) + x, y, z = self._get_sample_2d_data() + bspl = make_ndbspl((x, y), z, k=3, solver=solver, rtol=1e-6) + rgi = RegularGridInterpolator((x, y), z, method='cubic_legacy') + + xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + + assert_allclose(bspl(xi), rgi(xi), atol=1e-14) + + def test_2D_vs_RGI_quintic(self): + x, y, z = self._get_sample_2d_data() + bspl = make_ndbspl((x, y), z, k=5, solver=ssl.spsolve) + rgi = RegularGridInterpolator((x, y), z, method='quintic_legacy') + + xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + + assert_allclose(bspl(xi), rgi(xi), atol=1e-14) + + @pytest.mark.parametrize( + 'k, meth', [(1, 'linear'), (3, 'cubic_legacy'), (5, 'quintic_legacy')] + ) + def test_3D_random_vs_RGI(self, k, meth): + rndm = np.random.default_rng(123456) + x = np.cumsum(rndm.uniform(size=6)) + y = np.cumsum(rndm.uniform(size=7)) + z = np.cumsum(rndm.uniform(size=8)) + values = rndm.uniform(size=(6, 7, 8)) + + bspl = make_ndbspl((x, y, z), values, k=k, solver=ssl.spsolve) + rgi = RegularGridInterpolator((x, y, z), values, method=meth) + + xi = np.random.uniform(low=0.7, high=2.1, size=(11, 3)) + assert_allclose(bspl(xi), rgi(xi), atol=1e-14) + + def test_solver_err_not_converged(self): + x, y, z = self._get_sample_2d_data() + solver_args = {'maxiter': 1} + with assert_raises(ValueError, match='solver'): + make_ndbspl((x, y), z, k=3, **solver_args) + + with assert_raises(ValueError, match='solver'): + make_ndbspl((x, y), np.dstack((z, z)), k=3, **solver_args) + + +class TestFpchec: + # https://github.com/scipy/scipy/blob/main/scipy/interpolate/fitpack/fpchec.f + + def test_1D_x_t(self): + k = 1 + t = np.arange(12).reshape(2, 6) + x = np.arange(12) + + with pytest.raises(ValueError, match="1D sequence"): + _b.fpcheck(x, t, k) + + with pytest.raises(ValueError, match="1D sequence"): + _b.fpcheck(t, x, k) + + def test_condition_1(self): + # c 1) k+1 <= n-k-1 <= m + k = 3 + n = 2*(k + 1) - 1 # not OK + m = n + 11 # OK + t = np.arange(n) + x = np.arange(m) + + assert dfitpack.fpchec(x, t, k) == 10 + with pytest.raises(ValueError, match="Need k+1*"): + _b.fpcheck(x, t, k) + + n = 2*(k+1) + 1 # OK + m = n - k - 2 # not OK + t = np.arange(n) + x = np.arange(m) + + assert dfitpack.fpchec(x, t, k) == 10 + with pytest.raises(ValueError, match="Need k+1*"): + _b.fpcheck(x, t, k) + + def test_condition_2(self): + # c 2) t(1) <= t(2) <= ... <= t(k+1) + # c t(n-k) <= t(n-k+1) <= ... <= t(n) + k = 3 + t = [0]*(k+1) + [2] + [5]*(k+1) # this is OK + x = [1, 2, 3, 4, 4.5] + + assert dfitpack.fpchec(x, t, k) == 0 + assert _b.fpcheck(x, t, k) is None # does not raise + + tt = t.copy() + tt[-1] = tt[0] # not OK + assert dfitpack.fpchec(x, tt, k) == 20 + with pytest.raises(ValueError, match="Last k knots*"): + _b.fpcheck(x, tt, k) + + tt = t.copy() + tt[0] = tt[-1] # not OK + assert dfitpack.fpchec(x, tt, k) == 20 + with pytest.raises(ValueError, match="First k knots*"): + _b.fpcheck(x, tt, k) + + def test_condition_3(self): + # c 3) t(k+1) < t(k+2) < ... < t(n-k) + k = 3 + t = [0]*(k+1) + [2, 3] + [5]*(k+1) # this is OK + x = [1, 2, 3, 3.5, 4, 4.5] + assert dfitpack.fpchec(x, t, k) == 0 + assert _b.fpcheck(x, t, k) is None + + t = [0]*(k+1) + [2, 2] + [5]*(k+1) # this is not OK + assert dfitpack.fpchec(x, t, k) == 30 + with pytest.raises(ValueError, match="Internal knots*"): + _b.fpcheck(x, t, k) + + def test_condition_4(self): + # c 4) t(k+1) <= x(i) <= t(n-k) + # NB: FITPACK's fpchec only checks x[0] & x[-1], so we follow. + k = 3 + t = [0]*(k+1) + [5]*(k+1) + x = [1, 2, 3, 3.5, 4, 4.5] # this is OK + assert dfitpack.fpchec(x, t, k) == 0 + assert _b.fpcheck(x, t, k) is None + + xx = x.copy() + xx[0] = t[0] # still OK + assert dfitpack.fpchec(xx, t, k) == 0 + assert _b.fpcheck(x, t, k) is None + + xx = x.copy() + xx[0] = t[0] - 1 # not OK + assert dfitpack.fpchec(xx, t, k) == 40 + with pytest.raises(ValueError, match="Out of bounds*"): + _b.fpcheck(xx, t, k) + + xx = x.copy() + xx[-1] = t[-1] + 1 # not OK + assert dfitpack.fpchec(xx, t, k) == 40 + with pytest.raises(ValueError, match="Out of bounds*"): + _b.fpcheck(xx, t, k) + + # ### Test the S-W condition (no 5) + # c 5) the conditions specified by schoenberg and whitney must hold + # c for at least one subset of data points, i.e. there must be a + # c subset of data points y(j) such that + # c t(j) < y(j) < t(j+k+1), j=1,2,...,n-k-1 + def test_condition_5_x1xm(self): + # x(1).ge.t(k2) .or. x(m).le.t(nk1) + k = 1 + t = [0, 0, 1, 2, 2] + x = [1.1, 1.1, 1.1] + assert dfitpack.fpchec(x, t, k) == 50 + with pytest.raises(ValueError, match="Schoenberg-Whitney*"): + _b.fpcheck(x, t, k) + + x = [0.5, 0.5, 0.5] + assert dfitpack.fpchec(x, t, k) == 50 + with pytest.raises(ValueError, match="Schoenberg-Whitney*"): + _b.fpcheck(x, t, k) + + def test_condition_5_k1(self): + # special case nk3 (== n - k - 2) < 2 + k = 1 + t = [0, 0, 1, 1] + x = [0.5, 0.6] + assert dfitpack.fpchec(x, t, k) == 0 + assert _b.fpcheck(x, t, k) is None + + def test_condition_5_1(self): + # basically, there can't be an interval of t[j]..t[j+k+1] with no x + k = 3 + t = [0]*(k+1) + [2] + [5]*(k+1) + x = [3]*5 + assert dfitpack.fpchec(x, t, k) == 50 + with pytest.raises(ValueError, match="Schoenberg-Whitney*"): + _b.fpcheck(x, t, k) + + t = [0]*(k+1) + [2] + [5]*(k+1) + x = [1]*5 + assert dfitpack.fpchec(x, t, k) == 50 + with pytest.raises(ValueError, match="Schoenberg-Whitney*"): + _b.fpcheck(x, t, k) + + def test_condition_5_2(self): + # same as _5_1, only the empty interval is in the middle + k = 3 + t = [0]*(k+1) + [2, 3] + [5]*(k+1) + x = [1.1]*5 + [4] + + assert dfitpack.fpchec(x, t, k) == 50 + with pytest.raises(ValueError, match="Schoenberg-Whitney*"): + _b.fpcheck(x, t, k) + + # and this one is OK + x = [1.1]*4 + [4, 4] + assert dfitpack.fpchec(x, t, k) == 0 + assert _b.fpcheck(x, t, k) is None + + def test_condition_5_3(self): + # similar to _5_2, covers a different failure branch + k = 1 + t = [0, 0, 2, 3, 4, 5, 6, 7, 7] + x = [1, 1, 1, 5.2, 5.2, 5.2, 6.5] + + assert dfitpack.fpchec(x, t, k) == 50 + with pytest.raises(ValueError, match="Schoenberg-Whitney*"): + _b.fpcheck(x, t, k) + diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_fitpack.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_fitpack.py new file mode 100644 index 0000000000000000000000000000000000000000..c76178681de063e21fda5afedd4759248e8e19bb --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_fitpack.py @@ -0,0 +1,503 @@ +import itertools +import os + +import numpy as np +from numpy.testing import (assert_equal, assert_allclose, assert_, + assert_almost_equal, assert_array_almost_equal) +from pytest import raises as assert_raises +import pytest +from scipy._lib._testutils import check_free_memory + +from scipy.interpolate import RectBivariateSpline + +from scipy.interpolate._fitpack_py import (splrep, splev, bisplrep, bisplev, + sproot, splprep, splint, spalde, splder, splantider, insert, dblint) +from scipy.interpolate.dfitpack import regrid_smth +from scipy.interpolate._fitpack2 import dfitpack_int + + +def data_file(basename): + return os.path.join(os.path.abspath(os.path.dirname(__file__)), + 'data', basename) + + +def norm2(x): + return np.sqrt(np.dot(x.T, x)) + + +def f1(x, d=0): + """Derivatives of sin->cos->-sin->-cos.""" + if d % 4 == 0: + return np.sin(x) + if d % 4 == 1: + return np.cos(x) + if d % 4 == 2: + return -np.sin(x) + if d % 4 == 3: + return -np.cos(x) + + +def makepairs(x, y): + """Helper function to create an array of pairs of x and y.""" + xy = np.array(list(itertools.product(np.asarray(x), np.asarray(y)))) + return xy.T + + +class TestSmokeTests: + """ + Smoke tests (with a few asserts) for fitpack routines -- mostly + check that they are runnable + """ + def check_1(self, per=0, s=0, a=0, b=2*np.pi, at_nodes=False, + xb=None, xe=None): + if xb is None: + xb = a + if xe is None: + xe = b + + N = 20 + # nodes and middle points of the nodes + x = np.linspace(a, b, N + 1) + x1 = a + (b - a) * np.arange(1, N, dtype=float) / float(N - 1) + v = f1(x) + + def err_est(k, d): + # Assume f has all derivatives < 1 + h = 1.0 / N + tol = 5 * h**(.75*(k-d)) + if s > 0: + tol += 1e5*s + return tol + + for k in range(1, 6): + tck = splrep(x, v, s=s, per=per, k=k, xe=xe) + tt = tck[0][k:-k] if at_nodes else x1 + + for d in range(k+1): + tol = err_est(k, d) + err = norm2(f1(tt, d) - splev(tt, tck, d)) / norm2(f1(tt, d)) + assert err < tol + + def check_2(self, per=0, N=20, ia=0, ib=2*np.pi): + a, b, dx = 0, 2*np.pi, 0.2*np.pi + x = np.linspace(a, b, N+1) # nodes + v = np.sin(x) + + def err_est(k, d): + # Assume f has all derivatives < 1 + h = 1.0 / N + tol = 5 * h**(.75*(k-d)) + return tol + + nk = [] + for k in range(1, 6): + tck = splrep(x, v, s=0, per=per, k=k, xe=b) + nk.append([splint(ia, ib, tck), spalde(dx, tck)]) + + k = 1 + for r in nk: + d = 0 + for dr in r[1]: + tol = err_est(k, d) + assert_allclose(dr, f1(dx, d), atol=0, rtol=tol) + d = d+1 + k = k+1 + + def test_smoke_splrep_splev(self): + self.check_1(s=1e-6) + self.check_1(b=1.5*np.pi) + self.check_1(b=1.5*np.pi, xe=2*np.pi, per=1, s=1e-1) + + @pytest.mark.parametrize('per', [0, 1]) + @pytest.mark.parametrize('at_nodes', [True, False]) + def test_smoke_splrep_splev_2(self, per, at_nodes): + self.check_1(per=per, at_nodes=at_nodes) + + @pytest.mark.parametrize('N', [20, 50]) + @pytest.mark.parametrize('per', [0, 1]) + def test_smoke_splint_spalde(self, N, per): + self.check_2(per=per, N=N) + + @pytest.mark.parametrize('N', [20, 50]) + @pytest.mark.parametrize('per', [0, 1]) + def test_smoke_splint_spalde_iaib(self, N, per): + self.check_2(ia=0.2*np.pi, ib=np.pi, N=N, per=per) + + def test_smoke_sproot(self): + # sproot is only implemented for k=3 + a, b = 0.1, 15 + x = np.linspace(a, b, 20) + v = np.sin(x) + + for k in [1, 2, 4, 5]: + tck = splrep(x, v, s=0, per=0, k=k, xe=b) + with assert_raises(ValueError): + sproot(tck) + + k = 3 + tck = splrep(x, v, s=0, k=3) + roots = sproot(tck) + assert_allclose(splev(roots, tck), 0, atol=1e-10, rtol=1e-10) + assert_allclose(roots, np.pi * np.array([1, 2, 3, 4]), rtol=1e-3) + + @pytest.mark.parametrize('N', [20, 50]) + @pytest.mark.parametrize('k', [1, 2, 3, 4, 5]) + def test_smoke_splprep_splrep_splev(self, N, k): + a, b, dx = 0, 2.*np.pi, 0.2*np.pi + x = np.linspace(a, b, N+1) # nodes + v = np.sin(x) + + tckp, u = splprep([x, v], s=0, per=0, k=k, nest=-1) + uv = splev(dx, tckp) + err1 = abs(uv[1] - np.sin(uv[0])) + assert err1 < 1e-2 + + tck = splrep(x, v, s=0, per=0, k=k) + err2 = abs(splev(uv[0], tck) - np.sin(uv[0])) + assert err2 < 1e-2 + + # Derivatives of parametric cubic spline at u (first function) + if k == 3: + tckp, u = splprep([x, v], s=0, per=0, k=k, nest=-1) + for d in range(1, k+1): + uv = splev(dx, tckp, d) + + def test_smoke_bisplrep_bisplev(self): + xb, xe = 0, 2.*np.pi + yb, ye = 0, 2.*np.pi + kx, ky = 3, 3 + Nx, Ny = 20, 20 + + def f2(x, y): + return np.sin(x+y) + + x = np.linspace(xb, xe, Nx + 1) + y = np.linspace(yb, ye, Ny + 1) + xy = makepairs(x, y) + tck = bisplrep(xy[0], xy[1], f2(xy[0], xy[1]), s=0, kx=kx, ky=ky) + + tt = [tck[0][kx:-kx], tck[1][ky:-ky]] + t2 = makepairs(tt[0], tt[1]) + v1 = bisplev(tt[0], tt[1], tck) + v2 = f2(t2[0], t2[1]) + v2.shape = len(tt[0]), len(tt[1]) + + assert norm2(np.ravel(v1 - v2)) < 1e-2 + + +class TestSplev: + def test_1d_shape(self): + x = [1,2,3,4,5] + y = [4,5,6,7,8] + tck = splrep(x, y) + z = splev([1], tck) + assert_equal(z.shape, (1,)) + z = splev(1, tck) + assert_equal(z.shape, ()) + + def test_2d_shape(self): + x = [1, 2, 3, 4, 5] + y = [4, 5, 6, 7, 8] + tck = splrep(x, y) + t = np.array([[1.0, 1.5, 2.0, 2.5], + [3.0, 3.5, 4.0, 4.5]]) + z = splev(t, tck) + z0 = splev(t[0], tck) + z1 = splev(t[1], tck) + assert_equal(z, np.vstack((z0, z1))) + + def test_extrapolation_modes(self): + # test extrapolation modes + # * if ext=0, return the extrapolated value. + # * if ext=1, return 0 + # * if ext=2, raise a ValueError + # * if ext=3, return the boundary value. + x = [1,2,3] + y = [0,2,4] + tck = splrep(x, y, k=1) + + rstl = [[-2, 6], [0, 0], None, [0, 4]] + for ext in (0, 1, 3): + assert_array_almost_equal(splev([0, 4], tck, ext=ext), rstl[ext]) + + assert_raises(ValueError, splev, [0, 4], tck, ext=2) + + +class TestSplder: + def setup_method(self): + # non-uniform grid, just to make it sure + x = np.linspace(0, 1, 100)**3 + y = np.sin(20 * x) + self.spl = splrep(x, y) + + # double check that knots are non-uniform + assert_(np.ptp(np.diff(self.spl[0])) > 0) + + def test_inverse(self): + # Check that antiderivative + derivative is identity. + for n in range(5): + spl2 = splantider(self.spl, n) + spl3 = splder(spl2, n) + assert_allclose(self.spl[0], spl3[0]) + assert_allclose(self.spl[1], spl3[1]) + assert_equal(self.spl[2], spl3[2]) + + def test_splder_vs_splev(self): + # Check derivative vs. FITPACK + + for n in range(3+1): + # Also extrapolation! + xx = np.linspace(-1, 2, 2000) + if n == 3: + # ... except that FITPACK extrapolates strangely for + # order 0, so let's not check that. + xx = xx[(xx >= 0) & (xx <= 1)] + + dy = splev(xx, self.spl, n) + spl2 = splder(self.spl, n) + dy2 = splev(xx, spl2) + if n == 1: + assert_allclose(dy, dy2, rtol=2e-6) + else: + assert_allclose(dy, dy2) + + def test_splantider_vs_splint(self): + # Check antiderivative vs. FITPACK + spl2 = splantider(self.spl) + + # no extrapolation, splint assumes function is zero outside + # range + xx = np.linspace(0, 1, 20) + + for x1 in xx: + for x2 in xx: + y1 = splint(x1, x2, self.spl) + y2 = splev(x2, spl2) - splev(x1, spl2) + assert_allclose(y1, y2) + + def test_order0_diff(self): + assert_raises(ValueError, splder, self.spl, 4) + + def test_kink(self): + # Should refuse to differentiate splines with kinks + + spl2 = insert(0.5, self.spl, m=2) + splder(spl2, 2) # Should work + assert_raises(ValueError, splder, spl2, 3) + + spl2 = insert(0.5, self.spl, m=3) + splder(spl2, 1) # Should work + assert_raises(ValueError, splder, spl2, 2) + + spl2 = insert(0.5, self.spl, m=4) + assert_raises(ValueError, splder, spl2, 1) + + def test_multidim(self): + # c can have trailing dims + for n in range(3): + t, c, k = self.spl + c2 = np.c_[c, c, c] + c2 = np.dstack((c2, c2)) + + spl2 = splantider((t, c2, k), n) + spl3 = splder(spl2, n) + + assert_allclose(t, spl3[0]) + assert_allclose(c2, spl3[1]) + assert_equal(k, spl3[2]) + + +class TestSplint: + def test_len_c(self): + n, k = 7, 3 + x = np.arange(n) + y = x**3 + t, c, k = splrep(x, y, s=0) + + # note that len(c) == len(t) == 11 (== len(x) + 2*(k-1)) + assert len(t) == len(c) == n + 2*(k-1) + + # integrate directly: $\int_0^6 x^3 dx = 6^4 / 4$ + res = splint(0, 6, (t, c, k)) + assert_allclose(res, 6**4 / 4, atol=1e-15) + + # check that the coefficients past len(t) - k - 1 are ignored + c0 = c.copy() + c0[len(t)-k-1:] = np.nan + res0 = splint(0, 6, (t, c0, k)) + assert_allclose(res0, 6**4 / 4, atol=1e-15) + + # however, all other coefficients *are* used + c0[6] = np.nan + assert np.isnan(splint(0, 6, (t, c0, k))) + + # check that the coefficient array can have length `len(t) - k - 1` + c1 = c[:len(t) - k - 1] + res1 = splint(0, 6, (t, c1, k)) + assert_allclose(res1, 6**4 / 4, atol=1e-15) + + # however shorter c arrays raise. The error from f2py is a + # `dftipack.error`, which is an Exception but not ValueError etc. + with assert_raises(Exception, match=r">=n-k-1"): + splint(0, 1, (np.ones(10), np.ones(5), 3)) + + +class TestBisplrep: + def test_overflow(self): + from numpy.lib.stride_tricks import as_strided + if dfitpack_int.itemsize == 8: + size = 1500000**2 + else: + size = 400**2 + # Don't allocate a real array, as it's very big, but rely + # on that it's not referenced + x = as_strided(np.zeros(()), shape=(size,)) + assert_raises(OverflowError, bisplrep, x, x, x, w=x, + xb=0, xe=1, yb=0, ye=1, s=0) + + def test_regression_1310(self): + # Regression test for gh-1310 + with np.load(data_file('bug-1310.npz')) as loaded_data: + data = loaded_data['data'] + + # Shouldn't crash -- the input data triggers work array sizes + # that caused previously some data to not be aligned on + # sizeof(double) boundaries in memory, which made the Fortran + # code to crash when compiled with -O3 + bisplrep(data[:,0], data[:,1], data[:,2], kx=3, ky=3, s=0, + full_output=True) + + @pytest.mark.skipif(dfitpack_int != np.int64, reason="needs ilp64 fitpack") + def test_ilp64_bisplrep(self): + check_free_memory(28000) # VM size, doesn't actually use the pages + x = np.linspace(0, 1, 400) + y = np.linspace(0, 1, 400) + x, y = np.meshgrid(x, y) + z = np.zeros_like(x) + tck = bisplrep(x, y, z, kx=3, ky=3, s=0) + assert_allclose(bisplev(0.5, 0.5, tck), 0.0) + + +def test_dblint(): + # Basic test to see it runs and gives the correct result on a trivial + # problem. Note that `dblint` is not exposed in the interpolate namespace. + x = np.linspace(0, 1) + y = np.linspace(0, 1) + xx, yy = np.meshgrid(x, y) + rect = RectBivariateSpline(x, y, 4 * xx * yy) + tck = list(rect.tck) + tck.extend(rect.degrees) + + assert_almost_equal(dblint(0, 1, 0, 1, tck), 1) + assert_almost_equal(dblint(0, 0.5, 0, 1, tck), 0.25) + assert_almost_equal(dblint(0.5, 1, 0, 1, tck), 0.75) + assert_almost_equal(dblint(-100, 100, -100, 100, tck), 1) + + +def test_splev_der_k(): + # regression test for gh-2188: splev(x, tck, der=k) gives garbage or crashes + # for x outside of knot range + + # test case from gh-2188 + tck = (np.array([0., 0., 2.5, 2.5]), + np.array([-1.56679978, 2.43995873, 0., 0.]), + 1) + t, c, k = tck + x = np.array([-3, 0, 2.5, 3]) + + # an explicit form of the linear spline + assert_allclose(splev(x, tck), c[0] + (c[1] - c[0]) * x/t[2]) + assert_allclose(splev(x, tck, 1), (c[1]-c[0]) / t[2]) + + # now check a random spline vs splder + np.random.seed(1234) + x = np.sort(np.random.random(30)) + y = np.random.random(30) + t, c, k = splrep(x, y) + + x = [t[0] - 1., t[-1] + 1.] + tck2 = splder((t, c, k), k) + assert_allclose(splev(x, (t, c, k), k), splev(x, tck2)) + + +def test_splprep_segfault(): + # regression test for gh-3847: splprep segfaults if knots are specified + # for task=-1 + t = np.arange(0, 1.1, 0.1) + x = np.sin(2*np.pi*t) + y = np.cos(2*np.pi*t) + tck, u = splprep([x, y], s=0) + np.arange(0, 1.01, 0.01) + + uknots = tck[0] # using the knots from the previous fitting + tck, u = splprep([x, y], task=-1, t=uknots) # here is the crash + + +def test_bisplev_integer_overflow(): + np.random.seed(1) + + x = np.linspace(0, 1, 11) + y = x + z = np.random.randn(11, 11).ravel() + kx = 1 + ky = 1 + + nx, tx, ny, ty, c, fp, ier = regrid_smth( + x, y, z, None, None, None, None, kx=kx, ky=ky, s=0.0) + tck = (tx[:nx], ty[:ny], c[:(nx - kx - 1) * (ny - ky - 1)], kx, ky) + + xp = np.zeros([2621440]) + yp = np.zeros([2621440]) + + assert_raises((RuntimeError, MemoryError), bisplev, xp, yp, tck) + + +@pytest.mark.xslow +def test_gh_1766(): + # this should fail gracefully instead of segfaulting (int overflow) + size = 22 + kx, ky = 3, 3 + def f2(x, y): + return np.sin(x+y) + + x = np.linspace(0, 10, size) + y = np.linspace(50, 700, size) + xy = makepairs(x, y) + tck = bisplrep(xy[0], xy[1], f2(xy[0], xy[1]), s=0, kx=kx, ky=ky) + # the size value here can either segfault + # or produce a MemoryError on main + tx_ty_size = 500000 + tck[0] = np.arange(tx_ty_size) + tck[1] = np.arange(tx_ty_size) * 4 + tt_0 = np.arange(50) + tt_1 = np.arange(50) * 3 + with pytest.raises(MemoryError): + bisplev(tt_0, tt_1, tck, 1, 1) + + +def test_spalde_scalar_input(): + # Ticket #629 + x = np.linspace(0, 10) + y = x**3 + tck = splrep(x, y, k=3, t=[5]) + res = spalde(np.float64(1), tck) + des = np.array([1., 3., 6., 6.]) + assert_almost_equal(res, des) + + +def test_spalde_nc(): + # regression test for https://github.com/scipy/scipy/issues/19002 + # here len(t) = 29 and len(c) = 25 (== len(t) - k - 1) + x = np.asarray([-10., -9., -8., -7., -6., -5., -4., -3., -2.5, -2., -1.5, + -1., -0.5, 0., 0.5, 1., 1.5, 2., 2.5, 3., 4., 5., 6.], + dtype="float") + t = [-10.0, -10.0, -10.0, -10.0, -9.0, -8.0, -7.0, -6.0, -5.0, -4.0, -3.0, + -2.5, -2.0, -1.5, -1.0, -0.5, 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, + 5.0, 6.0, 6.0, 6.0, 6.0] + c = np.asarray([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.]) + k = 3 + + res = spalde(x, (t, c, k)) + res_splev = np.asarray([splev(x, (t, c, k), nu) for nu in range(4)]) + assert_allclose(res, res_splev.T, atol=1e-15) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_fitpack2.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_fitpack2.py new file mode 100644 index 0000000000000000000000000000000000000000..f1ebf0d26e8795c5230b4336a02126a8e1e53096 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_fitpack2.py @@ -0,0 +1,1355 @@ +# Created by Pearu Peterson, June 2003 +import itertools +import numpy as np +from numpy.testing import (assert_equal, assert_almost_equal, assert_array_equal, + assert_array_almost_equal, assert_allclose, suppress_warnings) +from pytest import raises as assert_raises + +from numpy import array, diff, linspace, meshgrid, ones, pi, shape +from scipy.interpolate._fitpack_py import bisplrep, bisplev, splrep, spalde +from scipy.interpolate._fitpack2 import (UnivariateSpline, + LSQUnivariateSpline, InterpolatedUnivariateSpline, + LSQBivariateSpline, SmoothBivariateSpline, RectBivariateSpline, + LSQSphereBivariateSpline, SmoothSphereBivariateSpline, + RectSphereBivariateSpline) + + +class TestUnivariateSpline: + def test_linear_constant(self): + x = [1,2,3] + y = [3,3,3] + lut = UnivariateSpline(x,y,k=1) + assert_array_almost_equal(lut.get_knots(),[1,3]) + assert_array_almost_equal(lut.get_coeffs(),[3,3]) + assert_almost_equal(lut.get_residual(),0.0) + assert_array_almost_equal(lut([1,1.5,2]),[3,3,3]) + + def test_preserve_shape(self): + x = [1, 2, 3] + y = [0, 2, 4] + lut = UnivariateSpline(x, y, k=1) + arg = 2 + assert_equal(shape(arg), shape(lut(arg))) + assert_equal(shape(arg), shape(lut(arg, nu=1))) + arg = [1.5, 2, 2.5] + assert_equal(shape(arg), shape(lut(arg))) + assert_equal(shape(arg), shape(lut(arg, nu=1))) + + def test_linear_1d(self): + x = [1,2,3] + y = [0,2,4] + lut = UnivariateSpline(x,y,k=1) + assert_array_almost_equal(lut.get_knots(),[1,3]) + assert_array_almost_equal(lut.get_coeffs(),[0,4]) + assert_almost_equal(lut.get_residual(),0.0) + assert_array_almost_equal(lut([1,1.5,2]),[0,1,2]) + + def test_subclassing(self): + # See #731 + + class ZeroSpline(UnivariateSpline): + def __call__(self, x): + return 0*array(x) + + sp = ZeroSpline([1,2,3,4,5], [3,2,3,2,3], k=2) + assert_array_equal(sp([1.5, 2.5]), [0., 0.]) + + def test_empty_input(self): + # Test whether empty input returns an empty output. Ticket 1014 + x = [1,3,5,7,9] + y = [0,4,9,12,21] + spl = UnivariateSpline(x, y, k=3) + assert_array_equal(spl([]), array([])) + + def test_roots(self): + x = [1, 3, 5, 7, 9] + y = [0, 4, 9, 12, 21] + spl = UnivariateSpline(x, y, k=3) + assert_almost_equal(spl.roots()[0], 1.050290639101332) + + def test_roots_length(self): # for gh18335 + x = np.linspace(0, 50 * np.pi, 1000) + y = np.cos(x) + spl = UnivariateSpline(x, y, s=0) + assert_equal(len(spl.roots()), 50) + + def test_derivatives(self): + x = [1, 3, 5, 7, 9] + y = [0, 4, 9, 12, 21] + spl = UnivariateSpline(x, y, k=3) + assert_almost_equal(spl.derivatives(3.5), + [5.5152902, 1.7146577, -0.1830357, 0.3125]) + + def test_derivatives_2(self): + x = np.arange(8) + y = x**3 + 2.*x**2 + + tck = splrep(x, y, s=0) + ders = spalde(3, tck) + assert_allclose(ders, [45., # 3**3 + 2*(3)**2 + 39., # 3*(3)**2 + 4*(3) + 22., # 6*(3) + 4 + 6.], # 6*3**0 + atol=1e-15) + spl = UnivariateSpline(x, y, s=0, k=3) + assert_allclose(spl.derivatives(3), + ders, + atol=1e-15) + + def test_resize_regression(self): + """Regression test for #1375.""" + x = [-1., -0.65016502, -0.58856235, -0.26903553, -0.17370892, + -0.10011001, 0., 0.10011001, 0.17370892, 0.26903553, 0.58856235, + 0.65016502, 1.] + y = [1.,0.62928599, 0.5797223, 0.39965815, 0.36322694, 0.3508061, + 0.35214793, 0.3508061, 0.36322694, 0.39965815, 0.5797223, + 0.62928599, 1.] + w = [1.00000000e+12, 6.88875973e+02, 4.89314737e+02, 4.26864807e+02, + 6.07746770e+02, 4.51341444e+02, 3.17480210e+02, 4.51341444e+02, + 6.07746770e+02, 4.26864807e+02, 4.89314737e+02, 6.88875973e+02, + 1.00000000e+12] + spl = UnivariateSpline(x=x, y=y, w=w, s=None) + desired = array([0.35100374, 0.51715855, 0.87789547, 0.98719344]) + assert_allclose(spl([0.1, 0.5, 0.9, 0.99]), desired, atol=5e-4) + + def test_out_of_range_regression(self): + # Test different extrapolation modes. See ticket 3557 + x = np.arange(5, dtype=float) + y = x**3 + + xp = linspace(-8, 13, 100) + xp_zeros = xp.copy() + xp_zeros[np.logical_or(xp_zeros < 0., xp_zeros > 4.)] = 0 + xp_clip = xp.copy() + xp_clip[xp_clip < x[0]] = x[0] + xp_clip[xp_clip > x[-1]] = x[-1] + + for cls in [UnivariateSpline, InterpolatedUnivariateSpline]: + spl = cls(x=x, y=y) + for ext in [0, 'extrapolate']: + assert_allclose(spl(xp, ext=ext), xp**3, atol=1e-16) + assert_allclose(cls(x, y, ext=ext)(xp), xp**3, atol=1e-16) + for ext in [1, 'zeros']: + assert_allclose(spl(xp, ext=ext), xp_zeros**3, atol=1e-16) + assert_allclose(cls(x, y, ext=ext)(xp), xp_zeros**3, atol=1e-16) + for ext in [2, 'raise']: + assert_raises(ValueError, spl, xp, **dict(ext=ext)) + for ext in [3, 'const']: + assert_allclose(spl(xp, ext=ext), xp_clip**3, atol=1e-16) + assert_allclose(cls(x, y, ext=ext)(xp), xp_clip**3, atol=1e-16) + + # also test LSQUnivariateSpline [which needs explicit knots] + t = spl.get_knots()[3:4] # interior knots w/ default k=3 + spl = LSQUnivariateSpline(x, y, t) + assert_allclose(spl(xp, ext=0), xp**3, atol=1e-16) + assert_allclose(spl(xp, ext=1), xp_zeros**3, atol=1e-16) + assert_raises(ValueError, spl, xp, **dict(ext=2)) + assert_allclose(spl(xp, ext=3), xp_clip**3, atol=1e-16) + + # also make sure that unknown values for `ext` are caught early + for ext in [-1, 'unknown']: + spl = UnivariateSpline(x, y) + assert_raises(ValueError, spl, xp, **dict(ext=ext)) + assert_raises(ValueError, UnivariateSpline, + **dict(x=x, y=y, ext=ext)) + + def test_lsq_fpchec(self): + xs = np.arange(100) * 1. + ys = np.arange(100) * 1. + knots = np.linspace(0, 99, 10) + bbox = (-1, 101) + assert_raises(ValueError, LSQUnivariateSpline, xs, ys, knots, + bbox=bbox) + + def test_derivative_and_antiderivative(self): + # Thin wrappers to splder/splantider, so light smoke test only. + x = np.linspace(0, 1, 70)**3 + y = np.cos(x) + + spl = UnivariateSpline(x, y, s=0) + spl2 = spl.antiderivative(2).derivative(2) + assert_allclose(spl(0.3), spl2(0.3)) + + spl2 = spl.antiderivative(1) + assert_allclose(spl2(0.6) - spl2(0.2), + spl.integral(0.2, 0.6)) + + def test_derivative_extrapolation(self): + # Regression test for gh-10195: for a const-extrapolation spline + # its derivative evaluates to zero for extrapolation + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5, 5] + f = UnivariateSpline(x_values, y_values, ext='const', k=3) + + x = [-1, 0, -0.5, 9, 9.5, 10] + assert_allclose(f.derivative()(x), 0, atol=1e-15) + + def test_integral_out_of_bounds(self): + # Regression test for gh-7906: .integral(a, b) is wrong if both + # a and b are out-of-bounds + x = np.linspace(0., 1., 7) + for ext in range(4): + f = UnivariateSpline(x, x, s=0, ext=ext) + for (a, b) in [(1, 1), (1, 5), (2, 5), + (0, 0), (-2, 0), (-2, -1)]: + assert_allclose(f.integral(a, b), 0, atol=1e-15) + + def test_nan(self): + # bail out early if the input data contains nans + x = np.arange(10, dtype=float) + y = x**3 + w = np.ones_like(x) + # also test LSQUnivariateSpline [which needs explicit knots] + spl = UnivariateSpline(x, y, check_finite=True) + t = spl.get_knots()[3:4] # interior knots w/ default k=3 + y_end = y[-1] + for z in [np.nan, np.inf, -np.inf]: + y[-1] = z + assert_raises(ValueError, UnivariateSpline, + **dict(x=x, y=y, check_finite=True)) + assert_raises(ValueError, InterpolatedUnivariateSpline, + **dict(x=x, y=y, check_finite=True)) + assert_raises(ValueError, LSQUnivariateSpline, + **dict(x=x, y=y, t=t, check_finite=True)) + y[-1] = y_end # check valid y but invalid w + w[-1] = z + assert_raises(ValueError, UnivariateSpline, + **dict(x=x, y=y, w=w, check_finite=True)) + assert_raises(ValueError, InterpolatedUnivariateSpline, + **dict(x=x, y=y, w=w, check_finite=True)) + assert_raises(ValueError, LSQUnivariateSpline, + **dict(x=x, y=y, t=t, w=w, check_finite=True)) + + def test_strictly_increasing_x(self): + # Test the x is required to be strictly increasing for + # UnivariateSpline if s=0 and for InterpolatedUnivariateSpline, + # but merely increasing for UnivariateSpline if s>0 + # and for LSQUnivariateSpline; see gh-8535 + xx = np.arange(10, dtype=float) + yy = xx**3 + x = np.arange(10, dtype=float) + x[1] = x[0] + y = x**3 + w = np.ones_like(x) + # also test LSQUnivariateSpline [which needs explicit knots] + spl = UnivariateSpline(xx, yy, check_finite=True) + t = spl.get_knots()[3:4] # interior knots w/ default k=3 + UnivariateSpline(x=x, y=y, w=w, s=1, check_finite=True) + LSQUnivariateSpline(x=x, y=y, t=t, w=w, check_finite=True) + assert_raises(ValueError, UnivariateSpline, + **dict(x=x, y=y, s=0, check_finite=True)) + assert_raises(ValueError, InterpolatedUnivariateSpline, + **dict(x=x, y=y, check_finite=True)) + + def test_increasing_x(self): + # Test that x is required to be increasing, see gh-8535 + xx = np.arange(10, dtype=float) + yy = xx**3 + x = np.arange(10, dtype=float) + x[1] = x[0] - 1.0 + y = x**3 + w = np.ones_like(x) + # also test LSQUnivariateSpline [which needs explicit knots] + spl = UnivariateSpline(xx, yy, check_finite=True) + t = spl.get_knots()[3:4] # interior knots w/ default k=3 + assert_raises(ValueError, UnivariateSpline, + **dict(x=x, y=y, check_finite=True)) + assert_raises(ValueError, InterpolatedUnivariateSpline, + **dict(x=x, y=y, check_finite=True)) + assert_raises(ValueError, LSQUnivariateSpline, + **dict(x=x, y=y, t=t, w=w, check_finite=True)) + + def test_invalid_input_for_univariate_spline(self): + + with assert_raises(ValueError) as info: + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5] + UnivariateSpline(x_values, y_values) + assert "x and y should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5, 2.8] + w_values = [-1.0, 1.0, 1.0, 1.0] + UnivariateSpline(x_values, y_values, w=w_values) + assert "x, y, and w should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + bbox = (-1) + UnivariateSpline(x_values, y_values, bbox=bbox) + assert "bbox shape should be (2,)" in str(info.value) + + with assert_raises(ValueError) as info: + UnivariateSpline(x_values, y_values, k=6) + assert "k should be 1 <= k <= 5" in str(info.value) + + with assert_raises(ValueError) as info: + UnivariateSpline(x_values, y_values, s=-1.0) + assert "s should be s >= 0.0" in str(info.value) + + def test_invalid_input_for_interpolated_univariate_spline(self): + + with assert_raises(ValueError) as info: + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5] + InterpolatedUnivariateSpline(x_values, y_values) + assert "x and y should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5, 2.8] + w_values = [-1.0, 1.0, 1.0, 1.0] + InterpolatedUnivariateSpline(x_values, y_values, w=w_values) + assert "x, y, and w should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + bbox = (-1) + InterpolatedUnivariateSpline(x_values, y_values, bbox=bbox) + assert "bbox shape should be (2,)" in str(info.value) + + with assert_raises(ValueError) as info: + InterpolatedUnivariateSpline(x_values, y_values, k=6) + assert "k should be 1 <= k <= 5" in str(info.value) + + def test_invalid_input_for_lsq_univariate_spline(self): + + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5, 2.8] + spl = UnivariateSpline(x_values, y_values, check_finite=True) + t_values = spl.get_knots()[3:4] # interior knots w/ default k=3 + + with assert_raises(ValueError) as info: + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5] + LSQUnivariateSpline(x_values, y_values, t_values) + assert "x and y should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + x_values = [1, 2, 4, 6, 8.5] + y_values = [0.5, 0.8, 1.3, 2.5, 2.8] + w_values = [1.0, 1.0, 1.0, 1.0] + LSQUnivariateSpline(x_values, y_values, t_values, w=w_values) + assert "x, y, and w should have a same length" in str(info.value) + + message = "Interior knots t must satisfy Schoenberg-Whitney conditions" + with assert_raises(ValueError, match=message) as info: + bbox = (100, -100) + LSQUnivariateSpline(x_values, y_values, t_values, bbox=bbox) + + with assert_raises(ValueError) as info: + bbox = (-1) + LSQUnivariateSpline(x_values, y_values, t_values, bbox=bbox) + assert "bbox shape should be (2,)" in str(info.value) + + with assert_raises(ValueError) as info: + LSQUnivariateSpline(x_values, y_values, t_values, k=6) + assert "k should be 1 <= k <= 5" in str(info.value) + + def test_array_like_input(self): + x_values = np.array([1, 2, 4, 6, 8.5]) + y_values = np.array([0.5, 0.8, 1.3, 2.5, 2.8]) + w_values = np.array([1.0, 1.0, 1.0, 1.0, 1.0]) + bbox = np.array([-100, 100]) + # np.array input + spl1 = UnivariateSpline(x=x_values, y=y_values, w=w_values, + bbox=bbox) + # list input + spl2 = UnivariateSpline(x=x_values.tolist(), y=y_values.tolist(), + w=w_values.tolist(), bbox=bbox.tolist()) + + assert_allclose(spl1([0.1, 0.5, 0.9, 0.99]), + spl2([0.1, 0.5, 0.9, 0.99])) + + def test_fpknot_oob_crash(self): + # https://github.com/scipy/scipy/issues/3691 + x = range(109) + y = [0., 0., 0., 0., 0., 10.9, 0., 11., 0., + 0., 0., 10.9, 0., 0., 0., 0., 0., 0., + 10.9, 0., 0., 0., 11., 0., 0., 0., 10.9, + 0., 0., 0., 10.5, 0., 0., 0., 10.7, 0., + 0., 0., 11., 0., 0., 0., 0., 0., 0., + 10.9, 0., 0., 10.7, 0., 0., 0., 10.6, 0., + 0., 0., 10.5, 0., 0., 10.7, 0., 0., 10.5, + 0., 0., 11.5, 0., 0., 0., 10.7, 0., 0., + 10.7, 0., 0., 10.9, 0., 0., 10.8, 0., 0., + 0., 10.7, 0., 0., 10.6, 0., 0., 0., 10.4, + 0., 0., 10.6, 0., 0., 10.5, 0., 0., 0., + 10.7, 0., 0., 0., 10.4, 0., 0., 0., 10.8, 0.] + with suppress_warnings() as sup: + r = sup.record( + UserWarning, + r""" +The maximal number of iterations maxit \(set to 20 by the program\) +allowed for finding a smoothing spline with fp=s has been reached: s +too small. +There is an approximation returned but the corresponding weighted sum +of squared residuals does not satisfy the condition abs\(fp-s\)/s < tol.""") + UnivariateSpline(x, y, k=1) + assert_equal(len(r), 1) + + +class TestLSQBivariateSpline: + # NOTE: The systems in this test class are rank-deficient + def test_linear_constant(self): + x = [1,1,1,2,2,2,3,3,3] + y = [1,2,3,1,2,3,1,2,3] + z = [3,3,3,3,3,3,3,3,3] + s = 0.1 + tx = [1+s,3-s] + ty = [1+s,3-s] + with suppress_warnings() as sup: + r = sup.record(UserWarning, "\nThe coefficients of the spline") + lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1) + assert_equal(len(r), 1) + + assert_almost_equal(lut(2,2), 3.) + + def test_bilinearity(self): + x = [1,1,1,2,2,2,3,3,3] + y = [1,2,3,1,2,3,1,2,3] + z = [0,7,8,3,4,7,1,3,4] + s = 0.1 + tx = [1+s,3-s] + ty = [1+s,3-s] + with suppress_warnings() as sup: + # This seems to fail (ier=1, see ticket 1642). + sup.filter(UserWarning, "\nThe coefficients of the spline") + lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1) + + tx, ty = lut.get_knots() + for xa, xb in zip(tx[:-1], tx[1:]): + for ya, yb in zip(ty[:-1], ty[1:]): + for t in [0.1, 0.5, 0.9]: + for s in [0.3, 0.4, 0.7]: + xp = xa*(1-t) + xb*t + yp = ya*(1-s) + yb*s + zp = (+ lut(xa, ya)*(1-t)*(1-s) + + lut(xb, ya)*t*(1-s) + + lut(xa, yb)*(1-t)*s + + lut(xb, yb)*t*s) + assert_almost_equal(lut(xp,yp), zp) + + def test_integral(self): + x = [1,1,1,2,2,2,8,8,8] + y = [1,2,3,1,2,3,1,2,3] + z = array([0,7,8,3,4,7,1,3,4]) + + s = 0.1 + tx = [1+s,3-s] + ty = [1+s,3-s] + with suppress_warnings() as sup: + r = sup.record(UserWarning, "\nThe coefficients of the spline") + lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1) + assert_equal(len(r), 1) + tx, ty = lut.get_knots() + tz = lut(tx, ty) + trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:] + * (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum() + + assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), + trpz) + + def test_empty_input(self): + # Test whether empty inputs returns an empty output. Ticket 1014 + x = [1,1,1,2,2,2,3,3,3] + y = [1,2,3,1,2,3,1,2,3] + z = [3,3,3,3,3,3,3,3,3] + s = 0.1 + tx = [1+s,3-s] + ty = [1+s,3-s] + with suppress_warnings() as sup: + r = sup.record(UserWarning, "\nThe coefficients of the spline") + lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1) + assert_equal(len(r), 1) + + assert_array_equal(lut([], []), np.zeros((0,0))) + assert_array_equal(lut([], [], grid=False), np.zeros((0,))) + + def test_invalid_input(self): + s = 0.1 + tx = [1 + s, 3 - s] + ty = [1 + s, 3 - s] + + with assert_raises(ValueError) as info: + x = np.linspace(1.0, 10.0) + y = np.linspace(1.0, 10.0) + z = np.linspace(1.0, 10.0, num=10) + LSQBivariateSpline(x, y, z, tx, ty) + assert "x, y, and z should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + x = np.linspace(1.0, 10.0) + y = np.linspace(1.0, 10.0) + z = np.linspace(1.0, 10.0) + w = np.linspace(1.0, 10.0, num=20) + LSQBivariateSpline(x, y, z, tx, ty, w=w) + assert "x, y, z, and w should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + w = np.linspace(-1.0, 10.0) + LSQBivariateSpline(x, y, z, tx, ty, w=w) + assert "w should be positive" in str(info.value) + + with assert_raises(ValueError) as info: + bbox = (-100, 100, -100) + LSQBivariateSpline(x, y, z, tx, ty, bbox=bbox) + assert "bbox shape should be (4,)" in str(info.value) + + with assert_raises(ValueError) as info: + LSQBivariateSpline(x, y, z, tx, ty, kx=10, ky=10) + assert "The length of x, y and z should be at least (kx+1) * (ky+1)" in \ + str(info.value) + + with assert_raises(ValueError) as exc_info: + LSQBivariateSpline(x, y, z, tx, ty, eps=0.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + LSQBivariateSpline(x, y, z, tx, ty, eps=1.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + def test_array_like_input(self): + s = 0.1 + tx = np.array([1 + s, 3 - s]) + ty = np.array([1 + s, 3 - s]) + x = np.linspace(1.0, 10.0) + y = np.linspace(1.0, 10.0) + z = np.linspace(1.0, 10.0) + w = np.linspace(1.0, 10.0) + bbox = np.array([1.0, 10.0, 1.0, 10.0]) + + with suppress_warnings() as sup: + r = sup.record(UserWarning, "\nThe coefficients of the spline") + # np.array input + spl1 = LSQBivariateSpline(x, y, z, tx, ty, w=w, bbox=bbox) + # list input + spl2 = LSQBivariateSpline(x.tolist(), y.tolist(), z.tolist(), + tx.tolist(), ty.tolist(), w=w.tolist(), + bbox=bbox) + assert_allclose(spl1(2.0, 2.0), spl2(2.0, 2.0)) + assert_equal(len(r), 2) + + def test_unequal_length_of_knots(self): + """Test for the case when the input knot-location arrays in x and y are + of different lengths. + """ + x, y = np.mgrid[0:100, 0:100] + x = x.ravel() + y = y.ravel() + z = 3.0 * np.ones_like(x) + tx = np.linspace(0.1, 98.0, 29) + ty = np.linspace(0.1, 98.0, 33) + with suppress_warnings() as sup: + r = sup.record(UserWarning, "\nThe coefficients of the spline") + lut = LSQBivariateSpline(x,y,z,tx,ty) + assert_equal(len(r), 1) + + assert_almost_equal(lut(x, y, grid=False), z) + + +class TestSmoothBivariateSpline: + def test_linear_constant(self): + x = [1,1,1,2,2,2,3,3,3] + y = [1,2,3,1,2,3,1,2,3] + z = [3,3,3,3,3,3,3,3,3] + lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1) + assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3])) + assert_array_almost_equal(lut.get_coeffs(),[3,3,3,3]) + assert_almost_equal(lut.get_residual(),0.0) + assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[3,3],[3,3],[3,3]]) + + def test_linear_1d(self): + x = [1,1,1,2,2,2,3,3,3] + y = [1,2,3,1,2,3,1,2,3] + z = [0,0,0,2,2,2,4,4,4] + lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1) + assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3])) + assert_array_almost_equal(lut.get_coeffs(),[0,0,4,4]) + assert_almost_equal(lut.get_residual(),0.0) + assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[0,0],[1,1],[2,2]]) + + def test_integral(self): + x = [1,1,1,2,2,2,4,4,4] + y = [1,2,3,1,2,3,1,2,3] + z = array([0,7,8,3,4,7,1,3,4]) + + with suppress_warnings() as sup: + # This seems to fail (ier=1, see ticket 1642). + sup.filter(UserWarning, "\nThe required storage space") + lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0) + + tx = [1,2,4] + ty = [1,2,3] + + tz = lut(tx, ty) + trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:] + * (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum() + assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz) + + lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0) + assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz, + decimal=0) # the quadratures give 23.75 and 23.85 + + tz = lut(tx[:-1], ty[:-1]) + trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:] + * (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum() + assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz) + + def test_rerun_lwrk2_too_small(self): + # in this setting, lwrk2 is too small in the default run. Here we + # check for equality with the bisplrep/bisplev output because there, + # an automatic re-run of the spline representation is done if ier>10. + x = np.linspace(-2, 2, 80) + y = np.linspace(-2, 2, 80) + z = x + y + xi = np.linspace(-1, 1, 100) + yi = np.linspace(-2, 2, 100) + tck = bisplrep(x, y, z) + res1 = bisplev(xi, yi, tck) + interp_ = SmoothBivariateSpline(x, y, z) + res2 = interp_(xi, yi) + assert_almost_equal(res1, res2) + + def test_invalid_input(self): + + with assert_raises(ValueError) as info: + x = np.linspace(1.0, 10.0) + y = np.linspace(1.0, 10.0) + z = np.linspace(1.0, 10.0, num=10) + SmoothBivariateSpline(x, y, z) + assert "x, y, and z should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + x = np.linspace(1.0, 10.0) + y = np.linspace(1.0, 10.0) + z = np.linspace(1.0, 10.0) + w = np.linspace(1.0, 10.0, num=20) + SmoothBivariateSpline(x, y, z, w=w) + assert "x, y, z, and w should have a same length" in str(info.value) + + with assert_raises(ValueError) as info: + w = np.linspace(-1.0, 10.0) + SmoothBivariateSpline(x, y, z, w=w) + assert "w should be positive" in str(info.value) + + with assert_raises(ValueError) as info: + bbox = (-100, 100, -100) + SmoothBivariateSpline(x, y, z, bbox=bbox) + assert "bbox shape should be (4,)" in str(info.value) + + with assert_raises(ValueError) as info: + SmoothBivariateSpline(x, y, z, kx=10, ky=10) + assert "The length of x, y and z should be at least (kx+1) * (ky+1)" in\ + str(info.value) + + with assert_raises(ValueError) as info: + SmoothBivariateSpline(x, y, z, s=-1.0) + assert "s should be s >= 0.0" in str(info.value) + + with assert_raises(ValueError) as exc_info: + SmoothBivariateSpline(x, y, z, eps=0.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + SmoothBivariateSpline(x, y, z, eps=1.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + def test_array_like_input(self): + x = np.array([1, 1, 1, 2, 2, 2, 3, 3, 3]) + y = np.array([1, 2, 3, 1, 2, 3, 1, 2, 3]) + z = np.array([3, 3, 3, 3, 3, 3, 3, 3, 3]) + w = np.array([1, 1, 1, 1, 1, 1, 1, 1, 1]) + bbox = np.array([1.0, 3.0, 1.0, 3.0]) + # np.array input + spl1 = SmoothBivariateSpline(x, y, z, w=w, bbox=bbox, kx=1, ky=1) + # list input + spl2 = SmoothBivariateSpline(x.tolist(), y.tolist(), z.tolist(), + bbox=bbox.tolist(), w=w.tolist(), + kx=1, ky=1) + assert_allclose(spl1(0.1, 0.5), spl2(0.1, 0.5)) + + +class TestLSQSphereBivariateSpline: + def setup_method(self): + # define the input data and coordinates + ntheta, nphi = 70, 90 + theta = linspace(0.5/(ntheta - 1), 1 - 0.5/(ntheta - 1), ntheta) * pi + phi = linspace(0.5/(nphi - 1), 1 - 0.5/(nphi - 1), nphi) * 2. * pi + data = ones((theta.shape[0], phi.shape[0])) + # define knots and extract data values at the knots + knotst = theta[::5] + knotsp = phi[::5] + knotdata = data[::5, ::5] + # calculate spline coefficients + lats, lons = meshgrid(theta, phi) + lut_lsq = LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), + data.T.ravel(), knotst, knotsp) + self.lut_lsq = lut_lsq + self.data = knotdata + self.new_lons, self.new_lats = knotsp, knotst + + def test_linear_constant(self): + assert_almost_equal(self.lut_lsq.get_residual(), 0.0) + assert_array_almost_equal(self.lut_lsq(self.new_lats, self.new_lons), + self.data) + + def test_empty_input(self): + assert_array_almost_equal(self.lut_lsq([], []), np.zeros((0,0))) + assert_array_almost_equal(self.lut_lsq([], [], grid=False), np.zeros((0,))) + + def test_invalid_input(self): + ntheta, nphi = 70, 90 + theta = linspace(0.5 / (ntheta - 1), 1 - 0.5 / (ntheta - 1), + ntheta) * pi + phi = linspace(0.5 / (nphi - 1), 1 - 0.5 / (nphi - 1), nphi) * 2. * pi + data = ones((theta.shape[0], phi.shape[0])) + # define knots and extract data values at the knots + knotst = theta[::5] + knotsp = phi[::5] + + with assert_raises(ValueError) as exc_info: + invalid_theta = linspace(-0.1, 1.0, num=ntheta) * pi + invalid_lats, lons = meshgrid(invalid_theta, phi) + LSQSphereBivariateSpline(invalid_lats.ravel(), lons.ravel(), + data.T.ravel(), knotst, knotsp) + assert "theta should be between [0, pi]" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_theta = linspace(0.1, 1.1, num=ntheta) * pi + invalid_lats, lons = meshgrid(invalid_theta, phi) + LSQSphereBivariateSpline(invalid_lats.ravel(), lons.ravel(), + data.T.ravel(), knotst, knotsp) + assert "theta should be between [0, pi]" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_phi = linspace(-0.1, 1.0, num=ntheta) * 2.0 * pi + lats, invalid_lons = meshgrid(theta, invalid_phi) + LSQSphereBivariateSpline(lats.ravel(), invalid_lons.ravel(), + data.T.ravel(), knotst, knotsp) + assert "phi should be between [0, 2pi]" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_phi = linspace(0.0, 1.1, num=ntheta) * 2.0 * pi + lats, invalid_lons = meshgrid(theta, invalid_phi) + LSQSphereBivariateSpline(lats.ravel(), invalid_lons.ravel(), + data.T.ravel(), knotst, knotsp) + assert "phi should be between [0, 2pi]" in str(exc_info.value) + + lats, lons = meshgrid(theta, phi) + + with assert_raises(ValueError) as exc_info: + invalid_knotst = np.copy(knotst) + invalid_knotst[0] = -0.1 + LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), + data.T.ravel(), invalid_knotst, knotsp) + assert "tt should be between (0, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_knotst = np.copy(knotst) + invalid_knotst[0] = pi + LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), + data.T.ravel(), invalid_knotst, knotsp) + assert "tt should be between (0, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_knotsp = np.copy(knotsp) + invalid_knotsp[0] = -0.1 + LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), + data.T.ravel(), knotst, invalid_knotsp) + assert "tp should be between (0, 2pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_knotsp = np.copy(knotsp) + invalid_knotsp[0] = 2 * pi + LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), + data.T.ravel(), knotst, invalid_knotsp) + assert "tp should be between (0, 2pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_w = array([-1.0, 1.0, 1.5, 0.5, 1.0, 1.5, 0.5, 1.0, 1.0]) + LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), data.T.ravel(), + knotst, knotsp, w=invalid_w) + assert "w should be positive" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), data.T.ravel(), + knotst, knotsp, eps=0.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), data.T.ravel(), + knotst, knotsp, eps=1.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + def test_array_like_input(self): + ntheta, nphi = 70, 90 + theta = linspace(0.5 / (ntheta - 1), 1 - 0.5 / (ntheta - 1), + ntheta) * pi + phi = linspace(0.5 / (nphi - 1), 1 - 0.5 / (nphi - 1), + nphi) * 2. * pi + lats, lons = meshgrid(theta, phi) + data = ones((theta.shape[0], phi.shape[0])) + # define knots and extract data values at the knots + knotst = theta[::5] + knotsp = phi[::5] + w = ones(lats.ravel().shape[0]) + + # np.array input + spl1 = LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), + data.T.ravel(), knotst, knotsp, w=w) + # list input + spl2 = LSQSphereBivariateSpline(lats.ravel().tolist(), + lons.ravel().tolist(), + data.T.ravel().tolist(), + knotst.tolist(), + knotsp.tolist(), w=w.tolist()) + assert_array_almost_equal(spl1(1.0, 1.0), spl2(1.0, 1.0)) + + +class TestSmoothSphereBivariateSpline: + def setup_method(self): + theta = array([.25*pi, .25*pi, .25*pi, .5*pi, .5*pi, .5*pi, .75*pi, + .75*pi, .75*pi]) + phi = array([.5 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, .5 * pi, pi, + 1.5 * pi]) + r = array([3, 3, 3, 3, 3, 3, 3, 3, 3]) + self.lut = SmoothSphereBivariateSpline(theta, phi, r, s=1E10) + + def test_linear_constant(self): + assert_almost_equal(self.lut.get_residual(), 0.) + assert_array_almost_equal(self.lut([1, 1.5, 2],[1, 1.5]), + [[3, 3], [3, 3], [3, 3]]) + + def test_empty_input(self): + assert_array_almost_equal(self.lut([], []), np.zeros((0,0))) + assert_array_almost_equal(self.lut([], [], grid=False), np.zeros((0,))) + + def test_invalid_input(self): + theta = array([.25 * pi, .25 * pi, .25 * pi, .5 * pi, .5 * pi, .5 * pi, + .75 * pi, .75 * pi, .75 * pi]) + phi = array([.5 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, .5 * pi, pi, + 1.5 * pi]) + r = array([3, 3, 3, 3, 3, 3, 3, 3, 3]) + + with assert_raises(ValueError) as exc_info: + invalid_theta = array([-0.1 * pi, .25 * pi, .25 * pi, .5 * pi, + .5 * pi, .5 * pi, .75 * pi, .75 * pi, + .75 * pi]) + SmoothSphereBivariateSpline(invalid_theta, phi, r, s=1E10) + assert "theta should be between [0, pi]" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_theta = array([.25 * pi, .25 * pi, .25 * pi, .5 * pi, + .5 * pi, .5 * pi, .75 * pi, .75 * pi, + 1.1 * pi]) + SmoothSphereBivariateSpline(invalid_theta, phi, r, s=1E10) + assert "theta should be between [0, pi]" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_phi = array([-.1 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, + .5 * pi, pi, 1.5 * pi]) + SmoothSphereBivariateSpline(theta, invalid_phi, r, s=1E10) + assert "phi should be between [0, 2pi]" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_phi = array([1.0 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, + .5 * pi, pi, 2.1 * pi]) + SmoothSphereBivariateSpline(theta, invalid_phi, r, s=1E10) + assert "phi should be between [0, 2pi]" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + invalid_w = array([-1.0, 1.0, 1.5, 0.5, 1.0, 1.5, 0.5, 1.0, 1.0]) + SmoothSphereBivariateSpline(theta, phi, r, w=invalid_w, s=1E10) + assert "w should be positive" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + SmoothSphereBivariateSpline(theta, phi, r, s=-1.0) + assert "s should be positive" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + SmoothSphereBivariateSpline(theta, phi, r, eps=-1.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + SmoothSphereBivariateSpline(theta, phi, r, eps=1.0) + assert "eps should be between (0, 1)" in str(exc_info.value) + + def test_array_like_input(self): + theta = np.array([.25 * pi, .25 * pi, .25 * pi, .5 * pi, .5 * pi, + .5 * pi, .75 * pi, .75 * pi, .75 * pi]) + phi = np.array([.5 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, .5 * pi, + pi, 1.5 * pi]) + r = np.array([3, 3, 3, 3, 3, 3, 3, 3, 3]) + w = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]) + + # np.array input + spl1 = SmoothSphereBivariateSpline(theta, phi, r, w=w, s=1E10) + + # list input + spl2 = SmoothSphereBivariateSpline(theta.tolist(), phi.tolist(), + r.tolist(), w=w.tolist(), s=1E10) + assert_array_almost_equal(spl1(1.0, 1.0), spl2(1.0, 1.0)) + + +class TestRectBivariateSpline: + def test_defaults(self): + x = array([1,2,3,4,5]) + y = array([1,2,3,4,5]) + z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]]) + lut = RectBivariateSpline(x,y,z) + assert_array_almost_equal(lut(x,y),z) + + def test_evaluate(self): + x = array([1,2,3,4,5]) + y = array([1,2,3,4,5]) + z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]]) + lut = RectBivariateSpline(x,y,z) + + xi = [1, 2.3, 5.3, 0.5, 3.3, 1.2, 3] + yi = [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3] + zi = lut.ev(xi, yi) + zi2 = array([lut(xp, yp)[0,0] for xp, yp in zip(xi, yi)]) + + assert_almost_equal(zi, zi2) + + def test_derivatives_grid(self): + x = array([1,2,3,4,5]) + y = array([1,2,3,4,5]) + z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]]) + dx = array([[0,0,-20,0,0],[0,0,13,0,0],[0,0,4,0,0], + [0,0,-11,0,0],[0,0,4,0,0]])/6. + dy = array([[4,-1,0,1,-4],[4,-1,0,1,-4],[0,1.5,0,-1.5,0], + [2,.25,0,-.25,-2],[4,-1,0,1,-4]]) + dxdy = array([[40,-25,0,25,-40],[-26,16.25,0,-16.25,26], + [-8,5,0,-5,8],[22,-13.75,0,13.75,-22],[-8,5,0,-5,8]])/6. + lut = RectBivariateSpline(x,y,z) + assert_array_almost_equal(lut(x,y,dx=1),dx) + assert_array_almost_equal(lut(x,y,dy=1),dy) + assert_array_almost_equal(lut(x,y,dx=1,dy=1),dxdy) + + def test_derivatives(self): + x = array([1,2,3,4,5]) + y = array([1,2,3,4,5]) + z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]]) + dx = array([0,0,2./3,0,0]) + dy = array([4,-1,0,-.25,-4]) + dxdy = array([160,65,0,55,32])/24. + lut = RectBivariateSpline(x,y,z) + assert_array_almost_equal(lut(x,y,dx=1,grid=False),dx) + assert_array_almost_equal(lut(x,y,dy=1,grid=False),dy) + assert_array_almost_equal(lut(x,y,dx=1,dy=1,grid=False),dxdy) + + def test_partial_derivative_method_grid(self): + x = array([1, 2, 3, 4, 5]) + y = array([1, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2, 1], + [1, 2, 1, 2, 1], + [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], + [1, 2, 1, 2, 1]]) + dx = array([[0, 0, -20, 0, 0], + [0, 0, 13, 0, 0], + [0, 0, 4, 0, 0], + [0, 0, -11, 0, 0], + [0, 0, 4, 0, 0]]) / 6. + dy = array([[4, -1, 0, 1, -4], + [4, -1, 0, 1, -4], + [0, 1.5, 0, -1.5, 0], + [2, .25, 0, -.25, -2], + [4, -1, 0, 1, -4]]) + dxdy = array([[40, -25, 0, 25, -40], + [-26, 16.25, 0, -16.25, 26], + [-8, 5, 0, -5, 8], + [22, -13.75, 0, 13.75, -22], + [-8, 5, 0, -5, 8]]) / 6. + lut = RectBivariateSpline(x, y, z) + assert_array_almost_equal(lut.partial_derivative(1, 0)(x, y), dx) + assert_array_almost_equal(lut.partial_derivative(0, 1)(x, y), dy) + assert_array_almost_equal(lut.partial_derivative(1, 1)(x, y), dxdy) + + def test_partial_derivative_method(self): + x = array([1, 2, 3, 4, 5]) + y = array([1, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2, 1], + [1, 2, 1, 2, 1], + [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], + [1, 2, 1, 2, 1]]) + dx = array([0, 0, 2./3, 0, 0]) + dy = array([4, -1, 0, -.25, -4]) + dxdy = array([160, 65, 0, 55, 32]) / 24. + lut = RectBivariateSpline(x, y, z) + assert_array_almost_equal(lut.partial_derivative(1, 0)(x, y, + grid=False), + dx) + assert_array_almost_equal(lut.partial_derivative(0, 1)(x, y, + grid=False), + dy) + assert_array_almost_equal(lut.partial_derivative(1, 1)(x, y, + grid=False), + dxdy) + + def test_partial_derivative_order_too_large(self): + x = array([0, 1, 2, 3, 4], dtype=float) + y = x.copy() + z = ones((x.size, y.size)) + lut = RectBivariateSpline(x, y, z) + with assert_raises(ValueError): + lut.partial_derivative(4, 1) + + def test_broadcast(self): + x = array([1,2,3,4,5]) + y = array([1,2,3,4,5]) + z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]]) + lut = RectBivariateSpline(x,y,z) + assert_allclose(lut(x, y), lut(x[:,None], y[None,:], grid=False)) + + def test_invalid_input(self): + + with assert_raises(ValueError) as info: + x = array([6, 2, 3, 4, 5]) + y = array([1, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], [1, 2, 1, 2, 1]]) + RectBivariateSpline(x, y, z) + assert "x must be strictly increasing" in str(info.value) + + with assert_raises(ValueError) as info: + x = array([1, 2, 3, 4, 5]) + y = array([2, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], [1, 2, 1, 2, 1]]) + RectBivariateSpline(x, y, z) + assert "y must be strictly increasing" in str(info.value) + + with assert_raises(ValueError) as info: + x = array([1, 2, 3, 4, 5]) + y = array([1, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1]]) + RectBivariateSpline(x, y, z) + assert "x dimension of z must have same number of elements as x"\ + in str(info.value) + + with assert_raises(ValueError) as info: + x = array([1, 2, 3, 4, 5]) + y = array([1, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2], [1, 2, 1, 2], [1, 2, 3, 2], + [1, 2, 2, 2], [1, 2, 1, 2]]) + RectBivariateSpline(x, y, z) + assert "y dimension of z must have same number of elements as y"\ + in str(info.value) + + with assert_raises(ValueError) as info: + x = array([1, 2, 3, 4, 5]) + y = array([1, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], [1, 2, 1, 2, 1]]) + bbox = (-100, 100, -100) + RectBivariateSpline(x, y, z, bbox=bbox) + assert "bbox shape should be (4,)" in str(info.value) + + with assert_raises(ValueError) as info: + RectBivariateSpline(x, y, z, s=-1.0) + assert "s should be s >= 0.0" in str(info.value) + + def test_array_like_input(self): + x = array([1, 2, 3, 4, 5]) + y = array([1, 2, 3, 4, 5]) + z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], [1, 2, 1, 2, 1]]) + bbox = array([1, 5, 1, 5]) + + spl1 = RectBivariateSpline(x, y, z, bbox=bbox) + spl2 = RectBivariateSpline(x.tolist(), y.tolist(), z.tolist(), + bbox=bbox.tolist()) + assert_array_almost_equal(spl1(1.0, 1.0), spl2(1.0, 1.0)) + + def test_not_increasing_input(self): + # gh-8565 + NSamp = 20 + Theta = np.random.uniform(0, np.pi, NSamp) + Phi = np.random.uniform(0, 2 * np.pi, NSamp) + Data = np.ones(NSamp) + + Interpolator = SmoothSphereBivariateSpline(Theta, Phi, Data, s=3.5) + + NLon = 6 + NLat = 3 + GridPosLats = np.arange(NLat) / NLat * np.pi + GridPosLons = np.arange(NLon) / NLon * 2 * np.pi + + # No error + Interpolator(GridPosLats, GridPosLons) + + nonGridPosLats = GridPosLats.copy() + nonGridPosLats[2] = 0.001 + with assert_raises(ValueError) as exc_info: + Interpolator(nonGridPosLats, GridPosLons) + assert "x must be strictly increasing" in str(exc_info.value) + + nonGridPosLons = GridPosLons.copy() + nonGridPosLons[2] = 0.001 + with assert_raises(ValueError) as exc_info: + Interpolator(GridPosLats, nonGridPosLons) + assert "y must be strictly increasing" in str(exc_info.value) + + +class TestRectSphereBivariateSpline: + def test_defaults(self): + y = linspace(0.01, 2*pi-0.01, 7) + x = linspace(0.01, pi-0.01, 7) + z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1], + [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1], + [1,2,1,2,1,2,1]]) + lut = RectSphereBivariateSpline(x,y,z) + assert_array_almost_equal(lut(x,y),z) + + def test_evaluate(self): + y = linspace(0.01, 2*pi-0.01, 7) + x = linspace(0.01, pi-0.01, 7) + z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1], + [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1], + [1,2,1,2,1,2,1]]) + lut = RectSphereBivariateSpline(x,y,z) + yi = [0.2, 1, 2.3, 2.35, 3.0, 3.99, 5.25] + xi = [1.5, 0.4, 1.1, 0.45, 0.2345, 1., 0.0001] + zi = lut.ev(xi, yi) + zi2 = array([lut(xp, yp)[0,0] for xp, yp in zip(xi, yi)]) + assert_almost_equal(zi, zi2) + + def test_invalid_input(self): + data = np.dot(np.atleast_2d(90. - np.linspace(-80., 80., 18)).T, + np.atleast_2d(180. - np.abs(np.linspace(0., 350., 9)))).T + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(-1, 170, 9) * np.pi / 180. + lons = np.linspace(0, 350, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "u should be between (0, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 181, 9) * np.pi / 180. + lons = np.linspace(0, 350, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "u should be between (0, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 170, 9) * np.pi / 180. + lons = np.linspace(-181, 10, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "v[0] should be between [-pi, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 170, 9) * np.pi / 180. + lons = np.linspace(-10, 360, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "v[-1] should be v[0] + 2pi or less" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 170, 9) * np.pi / 180. + lons = np.linspace(10, 350, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data, s=-1) + assert "s should be positive" in str(exc_info.value) + + def test_derivatives_grid(self): + y = linspace(0.01, 2*pi-0.01, 7) + x = linspace(0.01, pi-0.01, 7) + z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1], + [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1], + [1,2,1,2,1,2,1]]) + + lut = RectSphereBivariateSpline(x,y,z) + + y = linspace(0.02, 2*pi-0.02, 7) + x = linspace(0.02, pi-0.02, 7) + + assert_allclose(lut(x, y, dtheta=1), _numdiff_2d(lut, x, y, dx=1), + rtol=1e-4, atol=1e-4) + assert_allclose(lut(x, y, dphi=1), _numdiff_2d(lut, x, y, dy=1), + rtol=1e-4, atol=1e-4) + assert_allclose(lut(x, y, dtheta=1, dphi=1), + _numdiff_2d(lut, x, y, dx=1, dy=1, eps=1e-6), + rtol=1e-3, atol=1e-3) + + assert_array_equal(lut(x, y, dtheta=1), + lut.partial_derivative(1, 0)(x, y)) + assert_array_equal(lut(x, y, dphi=1), + lut.partial_derivative(0, 1)(x, y)) + assert_array_equal(lut(x, y, dtheta=1, dphi=1), + lut.partial_derivative(1, 1)(x, y)) + + assert_array_equal(lut(x, y, dtheta=1, grid=False), + lut.partial_derivative(1, 0)(x, y, grid=False)) + assert_array_equal(lut(x, y, dphi=1, grid=False), + lut.partial_derivative(0, 1)(x, y, grid=False)) + assert_array_equal(lut(x, y, dtheta=1, dphi=1, grid=False), + lut.partial_derivative(1, 1)(x, y, grid=False)) + + def test_derivatives(self): + y = linspace(0.01, 2*pi-0.01, 7) + x = linspace(0.01, pi-0.01, 7) + z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1], + [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1], + [1,2,1,2,1,2,1]]) + + lut = RectSphereBivariateSpline(x,y,z) + + y = linspace(0.02, 2*pi-0.02, 7) + x = linspace(0.02, pi-0.02, 7) + + assert_equal(lut(x, y, dtheta=1, grid=False).shape, x.shape) + assert_allclose(lut(x, y, dtheta=1, grid=False), + _numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dx=1), + rtol=1e-4, atol=1e-4) + assert_allclose(lut(x, y, dphi=1, grid=False), + _numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dy=1), + rtol=1e-4, atol=1e-4) + assert_allclose(lut(x, y, dtheta=1, dphi=1, grid=False), + _numdiff_2d(lambda x,y: lut(x,y,grid=False), + x, y, dx=1, dy=1, eps=1e-6), + rtol=1e-3, atol=1e-3) + + def test_invalid_input_2(self): + data = np.dot(np.atleast_2d(90. - np.linspace(-80., 80., 18)).T, + np.atleast_2d(180. - np.abs(np.linspace(0., 350., 9)))).T + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(0, 170, 9) * np.pi / 180. + lons = np.linspace(0, 350, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "u should be between (0, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 180, 9) * np.pi / 180. + lons = np.linspace(0, 350, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "u should be between (0, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 170, 9) * np.pi / 180. + lons = np.linspace(-181, 10, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "v[0] should be between [-pi, pi)" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 170, 9) * np.pi / 180. + lons = np.linspace(-10, 360, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data) + assert "v[-1] should be v[0] + 2pi or less" in str(exc_info.value) + + with assert_raises(ValueError) as exc_info: + lats = np.linspace(10, 170, 9) * np.pi / 180. + lons = np.linspace(10, 350, 18) * np.pi / 180. + RectSphereBivariateSpline(lats, lons, data, s=-1) + assert "s should be positive" in str(exc_info.value) + + def test_array_like_input(self): + y = linspace(0.01, 2 * pi - 0.01, 7) + x = linspace(0.01, pi - 0.01, 7) + z = array([[1, 2, 1, 2, 1, 2, 1], [1, 2, 1, 2, 1, 2, 1], + [1, 2, 3, 2, 1, 2, 1], + [1, 2, 2, 2, 1, 2, 1], [1, 2, 1, 2, 1, 2, 1], + [1, 2, 2, 2, 1, 2, 1], + [1, 2, 1, 2, 1, 2, 1]]) + # np.array input + spl1 = RectSphereBivariateSpline(x, y, z) + # list input + spl2 = RectSphereBivariateSpline(x.tolist(), y.tolist(), z.tolist()) + assert_array_almost_equal(spl1(x, y), spl2(x, y)) + + def test_negative_evaluation(self): + lats = np.array([25, 30, 35, 40, 45]) + lons = np.array([-90, -85, -80, -75, 70]) + mesh = np.meshgrid(lats, lons) + data = mesh[0] + mesh[1] # lon + lat value + lat_r = np.radians(lats) + lon_r = np.radians(lons) + interpolator = RectSphereBivariateSpline(lat_r, lon_r, data) + query_lat = np.radians(np.array([35, 37.5])) + query_lon = np.radians(np.array([-80, -77.5])) + data_interp = interpolator(query_lat, query_lon) + ans = np.array([[-45.0, -42.480862], + [-49.0625, -46.54315]]) + assert_array_almost_equal(data_interp, ans) + + def test_pole_continuity_gh_14591(self): + # regression test for https://github.com/scipy/scipy/issues/14591 + # with pole_continuty=(True, True), the internal work array size + # was too small, leading to a FITPACK data validation error. + + # The reproducer in gh-14591 was using a NetCDF4 file with + # 361x507 arrays, so here we trivialize array sizes to a minimum + # which still demonstrates the issue. + u = np.arange(1, 10) * np.pi / 10 + v = np.arange(1, 10) * np.pi / 10 + r = np.zeros((9, 9)) + for p in [(True, True), (True, False), (False, False)]: + RectSphereBivariateSpline(u, v, r, s=0, pole_continuity=p) + + +def _numdiff_2d(func, x, y, dx=0, dy=0, eps=1e-8): + if dx == 0 and dy == 0: + return func(x, y) + elif dx == 1 and dy == 0: + return (func(x + eps, y) - func(x - eps, y)) / (2*eps) + elif dx == 0 and dy == 1: + return (func(x, y + eps) - func(x, y - eps)) / (2*eps) + elif dx == 1 and dy == 1: + return (func(x + eps, y + eps) - func(x - eps, y + eps) + - func(x + eps, y - eps) + func(x - eps, y - eps)) / (2*eps)**2 + else: + raise ValueError("invalid derivative order") + + +class Test_DerivedBivariateSpline: + """Test the creation, usage, and attribute access of the (private) + _DerivedBivariateSpline class. + """ + def setup_method(self): + x = np.concatenate(list(zip(range(10), range(10)))) + y = np.concatenate(list(zip(range(10), range(1, 11)))) + z = np.concatenate((np.linspace(3, 1, 10), np.linspace(1, 3, 10))) + with suppress_warnings() as sup: + sup.record(UserWarning, "\nThe coefficients of the spline") + self.lut_lsq = LSQBivariateSpline(x, y, z, + linspace(0.5, 19.5, 4), + linspace(1.5, 20.5, 4), + eps=1e-2) + self.lut_smooth = SmoothBivariateSpline(x, y, z) + xx = linspace(0, 1, 20) + yy = xx + 1.0 + zz = array([np.roll(z, i) for i in range(z.size)]) + self.lut_rect = RectBivariateSpline(xx, yy, zz) + self.orders = list(itertools.product(range(3), range(3))) + + def test_creation_from_LSQ(self): + for nux, nuy in self.orders: + lut_der = self.lut_lsq.partial_derivative(nux, nuy) + a = lut_der(3.5, 3.5, grid=False) + b = self.lut_lsq(3.5, 3.5, dx=nux, dy=nuy, grid=False) + assert_equal(a, b) + + def test_creation_from_Smooth(self): + for nux, nuy in self.orders: + lut_der = self.lut_smooth.partial_derivative(nux, nuy) + a = lut_der(5.5, 5.5, grid=False) + b = self.lut_smooth(5.5, 5.5, dx=nux, dy=nuy, grid=False) + assert_equal(a, b) + + def test_creation_from_Rect(self): + for nux, nuy in self.orders: + lut_der = self.lut_rect.partial_derivative(nux, nuy) + a = lut_der(0.5, 1.5, grid=False) + b = self.lut_rect(0.5, 1.5, dx=nux, dy=nuy, grid=False) + assert_equal(a, b) + + def test_invalid_attribute_fp(self): + der = self.lut_rect.partial_derivative(1, 1) + with assert_raises(AttributeError): + der.fp + + def test_invalid_attribute_get_residual(self): + der = self.lut_smooth.partial_derivative(1, 1) + with assert_raises(AttributeError): + der.get_residual() diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_gil.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_gil.py new file mode 100644 index 0000000000000000000000000000000000000000..0902308fb6af6802ba216e3aeec499d0ddfb1407 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_gil.py @@ -0,0 +1,65 @@ +import itertools +import threading +import time + +import numpy as np +from numpy.testing import assert_equal +import pytest +import scipy.interpolate + + +class TestGIL: + """Check if the GIL is properly released by scipy.interpolate functions.""" + + def setup_method(self): + self.messages = [] + + def log(self, message): + self.messages.append(message) + + def make_worker_thread(self, target, args): + log = self.log + + class WorkerThread(threading.Thread): + def run(self): + log('interpolation started') + target(*args) + log('interpolation complete') + + return WorkerThread() + + @pytest.mark.slow + @pytest.mark.xfail(reason='race conditions, may depend on system load') + def test_rectbivariatespline(self): + def generate_params(n_points): + x = y = np.linspace(0, 1000, n_points) + x_grid, y_grid = np.meshgrid(x, y) + z = x_grid * y_grid + return x, y, z + + def calibrate_delay(requested_time): + for n_points in itertools.count(5000, 1000): + args = generate_params(n_points) + time_started = time.time() + interpolate(*args) + if time.time() - time_started > requested_time: + return args + + def interpolate(x, y, z): + scipy.interpolate.RectBivariateSpline(x, y, z) + + args = calibrate_delay(requested_time=3) + worker_thread = self.make_worker_thread(interpolate, args) + worker_thread.start() + for i in range(3): + time.sleep(0.5) + self.log('working') + worker_thread.join() + assert_equal(self.messages, [ + 'interpolation started', + 'working', + 'working', + 'working', + 'interpolation complete', + ]) + diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_interpnd.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_interpnd.py new file mode 100644 index 0000000000000000000000000000000000000000..2c7d52b422fb79971ddf86247196e92ea606a22d --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_interpnd.py @@ -0,0 +1,387 @@ +import os + +import numpy as np +from numpy.testing import (assert_equal, assert_allclose, assert_almost_equal, + suppress_warnings) +from pytest import raises as assert_raises +import pytest + +import scipy.interpolate.interpnd as interpnd +import scipy.spatial._qhull as qhull + +import pickle + + +def data_file(basename): + return os.path.join(os.path.abspath(os.path.dirname(__file__)), + 'data', basename) + + +class TestLinearNDInterpolation: + def test_smoketest(self): + # Test at single points + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + + yi = interpnd.LinearNDInterpolator(x, y)(x) + assert_almost_equal(y, yi) + + def test_smoketest_alternate(self): + # Test at single points, alternate calling convention + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + + yi = interpnd.LinearNDInterpolator((x[:,0], x[:,1]), y)(x[:,0], x[:,1]) + assert_almost_equal(y, yi) + + def test_complex_smoketest(self): + # Test at single points + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 3j*y + + yi = interpnd.LinearNDInterpolator(x, y)(x) + assert_almost_equal(y, yi) + + def test_tri_input(self): + # Test at single points + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 3j*y + + tri = qhull.Delaunay(x) + yi = interpnd.LinearNDInterpolator(tri, y)(x) + assert_almost_equal(y, yi) + + def test_square(self): + # Test barycentric interpolation on a square against a manual + # implementation + + points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64) + values = np.array([1., 2., -3., 5.], dtype=np.float64) + + # NB: assume triangles (0, 1, 3) and (1, 2, 3) + # + # 1----2 + # | \ | + # | \ | + # 0----3 + + def ip(x, y): + t1 = (x + y <= 1) + t2 = ~t1 + + x1 = x[t1] + y1 = y[t1] + + x2 = x[t2] + y2 = y[t2] + + z = 0*x + + z[t1] = (values[0]*(1 - x1 - y1) + + values[1]*y1 + + values[3]*x1) + + z[t2] = (values[2]*(x2 + y2 - 1) + + values[1]*(1 - x2) + + values[3]*(1 - y2)) + return z + + xx, yy = np.broadcast_arrays(np.linspace(0, 1, 14)[:,None], + np.linspace(0, 1, 14)[None,:]) + xx = xx.ravel() + yy = yy.ravel() + + xi = np.array([xx, yy]).T.copy() + zi = interpnd.LinearNDInterpolator(points, values)(xi) + + assert_almost_equal(zi, ip(xx, yy)) + + def test_smoketest_rescale(self): + # Test at single points + x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + + yi = interpnd.LinearNDInterpolator(x, y, rescale=True)(x) + assert_almost_equal(y, yi) + + def test_square_rescale(self): + # Test barycentric interpolation on a rectangle with rescaling + # agaings the same implementation without rescaling + + points = np.array([(0,0), (0,100), (10,100), (10,0)], dtype=np.float64) + values = np.array([1., 2., -3., 5.], dtype=np.float64) + + xx, yy = np.broadcast_arrays(np.linspace(0, 10, 14)[:,None], + np.linspace(0, 100, 14)[None,:]) + xx = xx.ravel() + yy = yy.ravel() + xi = np.array([xx, yy]).T.copy() + zi = interpnd.LinearNDInterpolator(points, values)(xi) + zi_rescaled = interpnd.LinearNDInterpolator(points, values, + rescale=True)(xi) + + assert_almost_equal(zi, zi_rescaled) + + def test_tripoints_input_rescale(self): + # Test at single points + x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 3j*y + + tri = qhull.Delaunay(x) + yi = interpnd.LinearNDInterpolator(tri.points, y)(x) + yi_rescale = interpnd.LinearNDInterpolator(tri.points, y, + rescale=True)(x) + assert_almost_equal(yi, yi_rescale) + + def test_tri_input_rescale(self): + # Test at single points + x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 3j*y + + tri = qhull.Delaunay(x) + match = ("Rescaling is not supported when passing a " + "Delaunay triangulation as ``points``.") + with pytest.raises(ValueError, match=match): + interpnd.LinearNDInterpolator(tri, y, rescale=True)(x) + + def test_pickle(self): + # Test at single points + np.random.seed(1234) + x = np.random.rand(30, 2) + y = np.random.rand(30) + 1j*np.random.rand(30) + + ip = interpnd.LinearNDInterpolator(x, y) + ip2 = pickle.loads(pickle.dumps(ip)) + + assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5)) + + +class TestEstimateGradients2DGlobal: + def test_smoketest(self): + x = np.array([(0, 0), (0, 2), + (1, 0), (1, 2), (0.25, 0.75), (0.6, 0.8)], dtype=float) + tri = qhull.Delaunay(x) + + # Should be exact for linear functions, independent of triangulation + + funcs = [ + (lambda x, y: 0*x + 1, (0, 0)), + (lambda x, y: 0 + x, (1, 0)), + (lambda x, y: -2 + y, (0, 1)), + (lambda x, y: 3 + 3*x + 14.15*y, (3, 14.15)) + ] + + for j, (func, grad) in enumerate(funcs): + z = func(x[:,0], x[:,1]) + dz = interpnd.estimate_gradients_2d_global(tri, z, tol=1e-6) + + assert_equal(dz.shape, (6, 2)) + assert_allclose(dz, np.array(grad)[None,:] + 0*dz, + rtol=1e-5, atol=1e-5, err_msg="item %d" % j) + + def test_regression_2359(self): + # Check regression --- for certain point sets, gradient + # estimation could end up in an infinite loop + points = np.load(data_file('estimate_gradients_hang.npy')) + values = np.random.rand(points.shape[0]) + tri = qhull.Delaunay(points) + + # This should not hang + with suppress_warnings() as sup: + sup.filter(interpnd.GradientEstimationWarning, + "Gradient estimation did not converge") + interpnd.estimate_gradients_2d_global(tri, values, maxiter=1) + + +class TestCloughTocher2DInterpolator: + + def _check_accuracy(self, func, x=None, tol=1e-6, alternate=False, + rescale=False, **kw): + np.random.seed(1234) + if x is None: + x = np.array([(0, 0), (0, 1), + (1, 0), (1, 1), (0.25, 0.75), (0.6, 0.8), + (0.5, 0.2)], + dtype=float) + + if not alternate: + ip = interpnd.CloughTocher2DInterpolator(x, func(x[:,0], x[:,1]), + tol=1e-6, rescale=rescale) + else: + ip = interpnd.CloughTocher2DInterpolator((x[:,0], x[:,1]), + func(x[:,0], x[:,1]), + tol=1e-6, rescale=rescale) + + p = np.random.rand(50, 2) + + if not alternate: + a = ip(p) + else: + a = ip(p[:,0], p[:,1]) + b = func(p[:,0], p[:,1]) + + try: + assert_allclose(a, b, **kw) + except AssertionError: + print("_check_accuracy: abs(a-b):", abs(a - b)) + print("ip.grad:", ip.grad) + raise + + def test_linear_smoketest(self): + # Should be exact for linear functions, independent of triangulation + funcs = [ + lambda x, y: 0*x + 1, + lambda x, y: 0 + x, + lambda x, y: -2 + y, + lambda x, y: 3 + 3*x + 14.15*y, + ] + + for j, func in enumerate(funcs): + self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7, + err_msg="Function %d" % j) + self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7, + alternate=True, + err_msg="Function (alternate) %d" % j) + # check rescaling + self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7, + err_msg="Function (rescaled) %d" % j, rescale=True) + self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7, + alternate=True, rescale=True, + err_msg="Function (alternate, rescaled) %d" % j) + + def test_quadratic_smoketest(self): + # Should be reasonably accurate for quadratic functions + funcs = [ + lambda x, y: x**2, + lambda x, y: y**2, + lambda x, y: x**2 - y**2, + lambda x, y: x*y, + ] + + for j, func in enumerate(funcs): + self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0, + err_msg="Function %d" % j) + self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0, + err_msg="Function %d" % j, rescale=True) + + def test_tri_input(self): + # Test at single points + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 3j*y + + tri = qhull.Delaunay(x) + yi = interpnd.CloughTocher2DInterpolator(tri, y)(x) + assert_almost_equal(y, yi) + + def test_tri_input_rescale(self): + # Test at single points + x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 3j*y + + tri = qhull.Delaunay(x) + match = ("Rescaling is not supported when passing a " + "Delaunay triangulation as ``points``.") + with pytest.raises(ValueError, match=match): + interpnd.CloughTocher2DInterpolator(tri, y, rescale=True)(x) + + def test_tripoints_input_rescale(self): + # Test at single points + x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 3j*y + + tri = qhull.Delaunay(x) + yi = interpnd.CloughTocher2DInterpolator(tri.points, y)(x) + yi_rescale = interpnd.CloughTocher2DInterpolator(tri.points, y, rescale=True)(x) + assert_almost_equal(yi, yi_rescale) + + def test_dense(self): + # Should be more accurate for dense meshes + funcs = [ + lambda x, y: x**2, + lambda x, y: y**2, + lambda x, y: x**2 - y**2, + lambda x, y: x*y, + lambda x, y: np.cos(2*np.pi*x)*np.sin(2*np.pi*y) + ] + + np.random.seed(4321) # use a different seed than the check! + grid = np.r_[np.array([(0,0), (0,1), (1,0), (1,1)], dtype=float), + np.random.rand(30*30, 2)] + + for j, func in enumerate(funcs): + self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2, + err_msg="Function %d" % j) + self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2, + err_msg="Function %d" % j, rescale=True) + + def test_wrong_ndim(self): + x = np.random.randn(30, 3) + y = np.random.randn(30) + assert_raises(ValueError, interpnd.CloughTocher2DInterpolator, x, y) + + def test_pickle(self): + # Test at single points + np.random.seed(1234) + x = np.random.rand(30, 2) + y = np.random.rand(30) + 1j*np.random.rand(30) + + ip = interpnd.CloughTocher2DInterpolator(x, y) + ip2 = pickle.loads(pickle.dumps(ip)) + + assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5)) + + def test_boundary_tri_symmetry(self): + # Interpolation at neighbourless triangles should retain + # symmetry with mirroring the triangle. + + # Equilateral triangle + points = np.array([(0, 0), (1, 0), (0.5, np.sqrt(3)/2)]) + values = np.array([1, 0, 0]) + + ip = interpnd.CloughTocher2DInterpolator(points, values) + + # Set gradient to zero at vertices + ip.grad[...] = 0 + + # Interpolation should be symmetric vs. bisector + alpha = 0.3 + p1 = np.array([0.5 * np.cos(alpha), 0.5 * np.sin(alpha)]) + p2 = np.array([0.5 * np.cos(np.pi/3 - alpha), 0.5 * np.sin(np.pi/3 - alpha)]) + + v1 = ip(p1) + v2 = ip(p2) + assert_allclose(v1, v2) + + # ... and affine invariant + np.random.seed(1) + A = np.random.randn(2, 2) + b = np.random.randn(2) + + points = A.dot(points.T).T + b[None,:] + p1 = A.dot(p1) + b + p2 = A.dot(p2) + b + + ip = interpnd.CloughTocher2DInterpolator(points, values) + ip.grad[...] = 0 + + w1 = ip(p1) + w2 = ip(p2) + assert_allclose(w1, v1) + assert_allclose(w2, v2) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_interpolate.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_interpolate.py new file mode 100644 index 0000000000000000000000000000000000000000..e5a1dd600c16cbe1886a31d979b561438df7c13a --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_interpolate.py @@ -0,0 +1,2584 @@ +from numpy.testing import (assert_, assert_equal, assert_almost_equal, + assert_array_almost_equal, assert_array_equal, + assert_allclose, suppress_warnings) +from pytest import raises as assert_raises +import pytest + +from numpy import mgrid, pi, sin, ogrid, poly1d, linspace +import numpy as np + +from scipy.interpolate import (interp1d, interp2d, lagrange, PPoly, BPoly, + splrep, splev, splantider, splint, sproot, Akima1DInterpolator, + NdPPoly, BSpline) + +from scipy.special import poch, gamma + +from scipy.interpolate import _ppoly + +from scipy._lib._gcutils import assert_deallocated, IS_PYPY + +from scipy.integrate import nquad + +from scipy.special import binom + + +class TestInterp2D: + def test_interp2d(self): + y, x = mgrid[0:2:20j, 0:pi:21j] + z = sin(x+0.5*y) + with suppress_warnings() as sup: + sup.filter(DeprecationWarning) + II = interp2d(x, y, z) + assert_almost_equal(II(1.0, 2.0), sin(2.0), decimal=2) + + v, u = ogrid[0:2:24j, 0:pi:25j] + assert_almost_equal(II(u.ravel(), v.ravel()), + sin(u+0.5*v), decimal=2) + + def test_interp2d_meshgrid_input(self): + # Ticket #703 + x = linspace(0, 2, 16) + y = linspace(0, pi, 21) + z = sin(x[None, :] + y[:, None]/2.) + with suppress_warnings() as sup: + sup.filter(DeprecationWarning) + II = interp2d(x, y, z) + assert_almost_equal(II(1.0, 2.0), sin(2.0), decimal=2) + + def test_interp2d_meshgrid_input_unsorted(self): + np.random.seed(1234) + x = linspace(0, 2, 16) + y = linspace(0, pi, 21) + + z = sin(x[None, :] + y[:, None] / 2.) + with suppress_warnings() as sup: + sup.filter(DeprecationWarning) + ip1 = interp2d(x.copy(), y.copy(), z, kind='cubic') + + np.random.shuffle(x) + z = sin(x[None, :] + y[:, None]/2.) + ip2 = interp2d(x.copy(), y.copy(), z, kind='cubic') + + np.random.shuffle(x) + np.random.shuffle(y) + z = sin(x[None, :] + y[:, None] / 2.) + ip3 = interp2d(x, y, z, kind='cubic') + + x = linspace(0, 2, 31) + y = linspace(0, pi, 30) + + assert_equal(ip1(x, y), ip2(x, y)) + assert_equal(ip1(x, y), ip3(x, y)) + + def test_interp2d_eval_unsorted(self): + y, x = mgrid[0:2:20j, 0:pi:21j] + z = sin(x + 0.5*y) + with suppress_warnings() as sup: + sup.filter(DeprecationWarning) + func = interp2d(x, y, z) + + xe = np.array([3, 4, 5]) + ye = np.array([5.3, 7.1]) + assert_allclose(func(xe, ye), func(xe, ye[::-1])) + + assert_raises(ValueError, func, xe, ye[::-1], 0, 0, True) + + def test_interp2d_linear(self): + # Ticket #898 + a = np.zeros([5, 5]) + a[2, 2] = 1.0 + x = y = np.arange(5) + with suppress_warnings() as sup: + sup.filter(DeprecationWarning) + b = interp2d(x, y, a, 'linear') + assert_almost_equal(b(2.0, 1.5), np.array([0.5]), decimal=2) + assert_almost_equal(b(2.0, 2.5), np.array([0.5]), decimal=2) + + def test_interp2d_bounds(self): + x = np.linspace(0, 1, 5) + y = np.linspace(0, 2, 7) + z = x[None, :]**2 + y[:, None] + + ix = np.linspace(-1, 3, 31) + iy = np.linspace(-1, 3, 33) + + with suppress_warnings() as sup: + sup.filter(DeprecationWarning) + + b = interp2d(x, y, z, bounds_error=True) + assert_raises(ValueError, b, ix, iy) + + b = interp2d(x, y, z, fill_value=np.nan) + iz = b(ix, iy) + mx = (ix < 0) | (ix > 1) + my = (iy < 0) | (iy > 2) + assert_(np.isnan(iz[my, :]).all()) + assert_(np.isnan(iz[:, mx]).all()) + assert_(np.isfinite(iz[~my, :][:, ~mx]).all()) + + +class TestInterp1D: + + def setup_method(self): + self.x5 = np.arange(5.) + self.x10 = np.arange(10.) + self.y10 = np.arange(10.) + self.x25 = self.x10.reshape((2,5)) + self.x2 = np.arange(2.) + self.y2 = np.arange(2.) + self.x1 = np.array([0.]) + self.y1 = np.array([0.]) + + self.y210 = np.arange(20.).reshape((2, 10)) + self.y102 = np.arange(20.).reshape((10, 2)) + self.y225 = np.arange(20.).reshape((2, 2, 5)) + self.y25 = np.arange(10.).reshape((2, 5)) + self.y235 = np.arange(30.).reshape((2, 3, 5)) + self.y325 = np.arange(30.).reshape((3, 2, 5)) + + # Edge updated test matrix 1 + # array([[ 30, 1, 2, 3, 4, 5, 6, 7, 8, -30], + # [ 30, 11, 12, 13, 14, 15, 16, 17, 18, -30]]) + self.y210_edge_updated = np.arange(20.).reshape((2, 10)) + self.y210_edge_updated[:, 0] = 30 + self.y210_edge_updated[:, -1] = -30 + + # Edge updated test matrix 2 + # array([[ 30, 30], + # [ 2, 3], + # [ 4, 5], + # [ 6, 7], + # [ 8, 9], + # [ 10, 11], + # [ 12, 13], + # [ 14, 15], + # [ 16, 17], + # [-30, -30]]) + self.y102_edge_updated = np.arange(20.).reshape((10, 2)) + self.y102_edge_updated[0, :] = 30 + self.y102_edge_updated[-1, :] = -30 + + self.fill_value = -100.0 + + def test_validation(self): + # Make sure that appropriate exceptions are raised when invalid values + # are given to the constructor. + + # These should all work. + for kind in ('nearest', 'nearest-up', 'zero', 'linear', 'slinear', + 'quadratic', 'cubic', 'previous', 'next'): + interp1d(self.x10, self.y10, kind=kind) + interp1d(self.x10, self.y10, kind=kind, fill_value="extrapolate") + interp1d(self.x10, self.y10, kind='linear', fill_value=(-1, 1)) + interp1d(self.x10, self.y10, kind='linear', + fill_value=np.array([-1])) + interp1d(self.x10, self.y10, kind='linear', + fill_value=(-1,)) + interp1d(self.x10, self.y10, kind='linear', + fill_value=-1) + interp1d(self.x10, self.y10, kind='linear', + fill_value=(-1, -1)) + interp1d(self.x10, self.y10, kind=0) + interp1d(self.x10, self.y10, kind=1) + interp1d(self.x10, self.y10, kind=2) + interp1d(self.x10, self.y10, kind=3) + interp1d(self.x10, self.y210, kind='linear', axis=-1, + fill_value=(-1, -1)) + interp1d(self.x2, self.y210, kind='linear', axis=0, + fill_value=np.ones(10)) + interp1d(self.x2, self.y210, kind='linear', axis=0, + fill_value=(np.ones(10), np.ones(10))) + interp1d(self.x2, self.y210, kind='linear', axis=0, + fill_value=(np.ones(10), -1)) + + # x array must be 1D. + assert_raises(ValueError, interp1d, self.x25, self.y10) + + # y array cannot be a scalar. + assert_raises(ValueError, interp1d, self.x10, np.array(0)) + + # Check for x and y arrays having the same length. + assert_raises(ValueError, interp1d, self.x10, self.y2) + assert_raises(ValueError, interp1d, self.x2, self.y10) + assert_raises(ValueError, interp1d, self.x10, self.y102) + interp1d(self.x10, self.y210) + interp1d(self.x10, self.y102, axis=0) + + # Check for x and y having at least 1 element. + assert_raises(ValueError, interp1d, self.x1, self.y10) + assert_raises(ValueError, interp1d, self.x10, self.y1) + + # Bad fill values + assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear', + fill_value=(-1, -1, -1)) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear', + fill_value=[-1, -1, -1]) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear', + fill_value=np.array((-1, -1, -1))) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear', + fill_value=[[-1]]) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear', + fill_value=[-1, -1]) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear', + fill_value=np.array([])) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear', + fill_value=()) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x2, self.y210, kind='linear', + axis=0, fill_value=[-1, -1]) # doesn't broadcast + assert_raises(ValueError, interp1d, self.x2, self.y210, kind='linear', + axis=0, fill_value=(0., [-1, -1])) # above doesn't bc + + def test_init(self): + # Check that the attributes are initialized appropriately by the + # constructor. + assert_(interp1d(self.x10, self.y10).copy) + assert_(not interp1d(self.x10, self.y10, copy=False).copy) + assert_(interp1d(self.x10, self.y10).bounds_error) + assert_(not interp1d(self.x10, self.y10, bounds_error=False).bounds_error) + assert_(np.isnan(interp1d(self.x10, self.y10).fill_value)) + assert_equal(interp1d(self.x10, self.y10, fill_value=3.0).fill_value, + 3.0) + assert_equal(interp1d(self.x10, self.y10, fill_value=(1.0, 2.0)).fill_value, + (1.0, 2.0)) + assert_equal(interp1d(self.x10, self.y10).axis, 0) + assert_equal(interp1d(self.x10, self.y210).axis, 1) + assert_equal(interp1d(self.x10, self.y102, axis=0).axis, 0) + assert_array_equal(interp1d(self.x10, self.y10).x, self.x10) + assert_array_equal(interp1d(self.x10, self.y10).y, self.y10) + assert_array_equal(interp1d(self.x10, self.y210).y, self.y210) + + def test_assume_sorted(self): + # Check for unsorted arrays + interp10 = interp1d(self.x10, self.y10) + interp10_unsorted = interp1d(self.x10[::-1], self.y10[::-1]) + + assert_array_almost_equal(interp10_unsorted(self.x10), self.y10) + assert_array_almost_equal(interp10_unsorted(1.2), np.array([1.2])) + assert_array_almost_equal(interp10_unsorted([2.4, 5.6, 6.0]), + interp10([2.4, 5.6, 6.0])) + + # Check assume_sorted keyword (defaults to False) + interp10_assume_kw = interp1d(self.x10[::-1], self.y10[::-1], + assume_sorted=False) + assert_array_almost_equal(interp10_assume_kw(self.x10), self.y10) + + interp10_assume_kw2 = interp1d(self.x10[::-1], self.y10[::-1], + assume_sorted=True) + # Should raise an error for unsorted input if assume_sorted=True + assert_raises(ValueError, interp10_assume_kw2, self.x10) + + # Check that if y is a 2-D array, things are still consistent + interp10_y_2d = interp1d(self.x10, self.y210) + interp10_y_2d_unsorted = interp1d(self.x10[::-1], self.y210[:, ::-1]) + assert_array_almost_equal(interp10_y_2d(self.x10), + interp10_y_2d_unsorted(self.x10)) + + def test_linear(self): + for kind in ['linear', 'slinear']: + self._check_linear(kind) + + def _check_linear(self, kind): + # Check the actual implementation of linear interpolation. + interp10 = interp1d(self.x10, self.y10, kind=kind) + assert_array_almost_equal(interp10(self.x10), self.y10) + assert_array_almost_equal(interp10(1.2), np.array([1.2])) + assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), + np.array([2.4, 5.6, 6.0])) + + # test fill_value="extrapolate" + extrapolator = interp1d(self.x10, self.y10, kind=kind, + fill_value='extrapolate') + assert_allclose(extrapolator([-1., 0, 9, 11]), + [-1, 0, 9, 11], rtol=1e-14) + + opts = dict(kind=kind, + fill_value='extrapolate', + bounds_error=True) + assert_raises(ValueError, interp1d, self.x10, self.y10, **opts) + + def test_linear_dtypes(self): + # regression test for gh-5898, where 1D linear interpolation has been + # delegated to numpy.interp for all float dtypes, and the latter was + # not handling e.g. np.float128. + for dtyp in [np.float16, + np.float32, + np.float64, + np.longdouble]: + x = np.arange(8, dtype=dtyp) + y = x + yp = interp1d(x, y, kind='linear')(x) + assert_equal(yp.dtype, dtyp) + assert_allclose(yp, y, atol=1e-15) + + # regression test for gh-14531, where 1D linear interpolation has been + # has been extended to delegate to numpy.interp for integer dtypes + x = [0, 1, 2] + y = [np.nan, 0, 1] + yp = interp1d(x, y)(x) + assert_allclose(yp, y, atol=1e-15) + + def test_slinear_dtypes(self): + # regression test for gh-7273: 1D slinear interpolation fails with + # float32 inputs + dt_r = [np.float16, np.float32, np.float64] + dt_rc = dt_r + [np.complex64, np.complex128] + spline_kinds = ['slinear', 'zero', 'quadratic', 'cubic'] + for dtx in dt_r: + x = np.arange(0, 10, dtype=dtx) + for dty in dt_rc: + y = np.exp(-x/3.0).astype(dty) + for dtn in dt_r: + xnew = x.astype(dtn) + for kind in spline_kinds: + f = interp1d(x, y, kind=kind, bounds_error=False) + assert_allclose(f(xnew), y, atol=1e-7, + err_msg=f"{dtx}, {dty} {dtn}") + + def test_cubic(self): + # Check the actual implementation of spline interpolation. + interp10 = interp1d(self.x10, self.y10, kind='cubic') + assert_array_almost_equal(interp10(self.x10), self.y10) + assert_array_almost_equal(interp10(1.2), np.array([1.2])) + assert_array_almost_equal(interp10(1.5), np.array([1.5])) + assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), + np.array([2.4, 5.6, 6.0]),) + + def test_nearest(self): + # Check the actual implementation of nearest-neighbour interpolation. + # Nearest asserts that half-integer case (1.5) rounds down to 1 + interp10 = interp1d(self.x10, self.y10, kind='nearest') + assert_array_almost_equal(interp10(self.x10), self.y10) + assert_array_almost_equal(interp10(1.2), np.array(1.)) + assert_array_almost_equal(interp10(1.5), np.array(1.)) + assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), + np.array([2., 6., 6.]),) + + # test fill_value="extrapolate" + extrapolator = interp1d(self.x10, self.y10, kind='nearest', + fill_value='extrapolate') + assert_allclose(extrapolator([-1., 0, 9, 11]), + [0, 0, 9, 9], rtol=1e-14) + + opts = dict(kind='nearest', + fill_value='extrapolate', + bounds_error=True) + assert_raises(ValueError, interp1d, self.x10, self.y10, **opts) + + def test_nearest_up(self): + # Check the actual implementation of nearest-neighbour interpolation. + # Nearest-up asserts that half-integer case (1.5) rounds up to 2 + interp10 = interp1d(self.x10, self.y10, kind='nearest-up') + assert_array_almost_equal(interp10(self.x10), self.y10) + assert_array_almost_equal(interp10(1.2), np.array(1.)) + assert_array_almost_equal(interp10(1.5), np.array(2.)) + assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), + np.array([2., 6., 6.]),) + + # test fill_value="extrapolate" + extrapolator = interp1d(self.x10, self.y10, kind='nearest-up', + fill_value='extrapolate') + assert_allclose(extrapolator([-1., 0, 9, 11]), + [0, 0, 9, 9], rtol=1e-14) + + opts = dict(kind='nearest-up', + fill_value='extrapolate', + bounds_error=True) + assert_raises(ValueError, interp1d, self.x10, self.y10, **opts) + + def test_previous(self): + # Check the actual implementation of previous interpolation. + interp10 = interp1d(self.x10, self.y10, kind='previous') + assert_array_almost_equal(interp10(self.x10), self.y10) + assert_array_almost_equal(interp10(1.2), np.array(1.)) + assert_array_almost_equal(interp10(1.5), np.array(1.)) + assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), + np.array([2., 5., 6.]),) + + # test fill_value="extrapolate" + extrapolator = interp1d(self.x10, self.y10, kind='previous', + fill_value='extrapolate') + assert_allclose(extrapolator([-1., 0, 9, 11]), + [np.nan, 0, 9, 9], rtol=1e-14) + + # Tests for gh-9591 + interpolator1D = interp1d(self.x10, self.y10, kind="previous", + fill_value='extrapolate') + assert_allclose(interpolator1D([-1, -2, 5, 8, 12, 25]), + [np.nan, np.nan, 5, 8, 9, 9]) + + interpolator2D = interp1d(self.x10, self.y210, kind="previous", + fill_value='extrapolate') + assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]), + [[np.nan, np.nan, 5, 8, 9, 9], + [np.nan, np.nan, 15, 18, 19, 19]]) + + interpolator2DAxis0 = interp1d(self.x10, self.y102, kind="previous", + axis=0, fill_value='extrapolate') + assert_allclose(interpolator2DAxis0([-2, 5, 12]), + [[np.nan, np.nan], + [10, 11], + [18, 19]]) + + opts = dict(kind='previous', + fill_value='extrapolate', + bounds_error=True) + assert_raises(ValueError, interp1d, self.x10, self.y10, **opts) + + # Tests for gh-16813 + interpolator1D = interp1d([0, 1, 2], + [0, 1, -1], kind="previous", + fill_value='extrapolate', + assume_sorted=True) + assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]), + [np.nan, np.nan, 0, 1, -1, -1, -1]) + + interpolator1D = interp1d([2, 0, 1], # x is not ascending + [-1, 0, 1], kind="previous", + fill_value='extrapolate', + assume_sorted=False) + assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]), + [np.nan, np.nan, 0, 1, -1, -1, -1]) + + interpolator2D = interp1d(self.x10, self.y210_edge_updated, + kind="previous", + fill_value='extrapolate') + assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]), + [[np.nan, np.nan, 5, 8, -30, -30], + [np.nan, np.nan, 15, 18, -30, -30]]) + + interpolator2DAxis0 = interp1d(self.x10, self.y102_edge_updated, + kind="previous", + axis=0, fill_value='extrapolate') + assert_allclose(interpolator2DAxis0([-2, 5, 12]), + [[np.nan, np.nan], + [10, 11], + [-30, -30]]) + + def test_next(self): + # Check the actual implementation of next interpolation. + interp10 = interp1d(self.x10, self.y10, kind='next') + assert_array_almost_equal(interp10(self.x10), self.y10) + assert_array_almost_equal(interp10(1.2), np.array(2.)) + assert_array_almost_equal(interp10(1.5), np.array(2.)) + assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), + np.array([3., 6., 6.]),) + + # test fill_value="extrapolate" + extrapolator = interp1d(self.x10, self.y10, kind='next', + fill_value='extrapolate') + assert_allclose(extrapolator([-1., 0, 9, 11]), + [0, 0, 9, np.nan], rtol=1e-14) + + # Tests for gh-9591 + interpolator1D = interp1d(self.x10, self.y10, kind="next", + fill_value='extrapolate') + assert_allclose(interpolator1D([-1, -2, 5, 8, 12, 25]), + [0, 0, 5, 8, np.nan, np.nan]) + + interpolator2D = interp1d(self.x10, self.y210, kind="next", + fill_value='extrapolate') + assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]), + [[0, 0, 5, 8, np.nan, np.nan], + [10, 10, 15, 18, np.nan, np.nan]]) + + interpolator2DAxis0 = interp1d(self.x10, self.y102, kind="next", + axis=0, fill_value='extrapolate') + assert_allclose(interpolator2DAxis0([-2, 5, 12]), + [[0, 1], + [10, 11], + [np.nan, np.nan]]) + + opts = dict(kind='next', + fill_value='extrapolate', + bounds_error=True) + assert_raises(ValueError, interp1d, self.x10, self.y10, **opts) + + # Tests for gh-16813 + interpolator1D = interp1d([0, 1, 2], + [0, 1, -1], kind="next", + fill_value='extrapolate', + assume_sorted=True) + assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]), + [0, 0, 0, 1, -1, np.nan, np.nan]) + + interpolator1D = interp1d([2, 0, 1], # x is not ascending + [-1, 0, 1], kind="next", + fill_value='extrapolate', + assume_sorted=False) + assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]), + [0, 0, 0, 1, -1, np.nan, np.nan]) + + interpolator2D = interp1d(self.x10, self.y210_edge_updated, + kind="next", + fill_value='extrapolate') + assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]), + [[30, 30, 5, 8, np.nan, np.nan], + [30, 30, 15, 18, np.nan, np.nan]]) + + interpolator2DAxis0 = interp1d(self.x10, self.y102_edge_updated, + kind="next", + axis=0, fill_value='extrapolate') + assert_allclose(interpolator2DAxis0([-2, 5, 12]), + [[30, 30], + [10, 11], + [np.nan, np.nan]]) + + def test_zero(self): + # Check the actual implementation of zero-order spline interpolation. + interp10 = interp1d(self.x10, self.y10, kind='zero') + assert_array_almost_equal(interp10(self.x10), self.y10) + assert_array_almost_equal(interp10(1.2), np.array(1.)) + assert_array_almost_equal(interp10(1.5), np.array(1.)) + assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), + np.array([2., 5., 6.])) + + def bounds_check_helper(self, interpolant, test_array, fail_value): + # Asserts that a ValueError is raised and that the error message + # contains the value causing this exception. + assert_raises(ValueError, interpolant, test_array) + try: + interpolant(test_array) + except ValueError as err: + assert (f"{fail_value}" in str(err)) + + def _bounds_check(self, kind='linear'): + # Test that our handling of out-of-bounds input is correct. + extrap10 = interp1d(self.x10, self.y10, fill_value=self.fill_value, + bounds_error=False, kind=kind) + + assert_array_equal(extrap10(11.2), np.array(self.fill_value)) + assert_array_equal(extrap10(-3.4), np.array(self.fill_value)) + assert_array_equal(extrap10([[[11.2], [-3.4], [12.6], [19.3]]]), + np.array(self.fill_value),) + assert_array_equal(extrap10._check_bounds( + np.array([-1.0, 0.0, 5.0, 9.0, 11.0])), + np.array([[True, False, False, False, False], + [False, False, False, False, True]])) + + raises_bounds_error = interp1d(self.x10, self.y10, bounds_error=True, + kind=kind) + + self.bounds_check_helper(raises_bounds_error, -1.0, -1.0) + self.bounds_check_helper(raises_bounds_error, 11.0, 11.0) + self.bounds_check_helper(raises_bounds_error, [0.0, -1.0, 0.0], -1.0) + self.bounds_check_helper(raises_bounds_error, [0.0, 1.0, 21.0], 21.0) + + raises_bounds_error([0.0, 5.0, 9.0]) + + def _bounds_check_int_nan_fill(self, kind='linear'): + x = np.arange(10).astype(int) + y = np.arange(10).astype(int) + c = interp1d(x, y, kind=kind, fill_value=np.nan, bounds_error=False) + yi = c(x - 1) + assert_(np.isnan(yi[0])) + assert_array_almost_equal(yi, np.r_[np.nan, y[:-1]]) + + def test_bounds(self): + for kind in ('linear', 'cubic', 'nearest', 'previous', 'next', + 'slinear', 'zero', 'quadratic'): + self._bounds_check(kind) + self._bounds_check_int_nan_fill(kind) + + def _check_fill_value(self, kind): + interp = interp1d(self.x10, self.y10, kind=kind, + fill_value=(-100, 100), bounds_error=False) + assert_array_almost_equal(interp(10), 100) + assert_array_almost_equal(interp(-10), -100) + assert_array_almost_equal(interp([-10, 10]), [-100, 100]) + + # Proper broadcasting: + # interp along axis of length 5 + # other dim=(2, 3), (3, 2), (2, 2), or (2,) + + # one singleton fill_value (works for all) + for y in (self.y235, self.y325, self.y225, self.y25): + interp = interp1d(self.x5, y, kind=kind, axis=-1, + fill_value=100, bounds_error=False) + assert_array_almost_equal(interp(10), 100) + assert_array_almost_equal(interp(-10), 100) + assert_array_almost_equal(interp([-10, 10]), 100) + + # singleton lower, singleton upper + interp = interp1d(self.x5, y, kind=kind, axis=-1, + fill_value=(-100, 100), bounds_error=False) + assert_array_almost_equal(interp(10), 100) + assert_array_almost_equal(interp(-10), -100) + if y.ndim == 3: + result = [[[-100, 100]] * y.shape[1]] * y.shape[0] + else: + result = [[-100, 100]] * y.shape[0] + assert_array_almost_equal(interp([-10, 10]), result) + + # one broadcastable (3,) fill_value + fill_value = [100, 200, 300] + for y in (self.y325, self.y225): + assert_raises(ValueError, interp1d, self.x5, y, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + interp = interp1d(self.x5, self.y235, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + assert_array_almost_equal(interp(10), [[100, 200, 300]] * 2) + assert_array_almost_equal(interp(-10), [[100, 200, 300]] * 2) + assert_array_almost_equal(interp([-10, 10]), [[[100, 100], + [200, 200], + [300, 300]]] * 2) + + # one broadcastable (2,) fill_value + fill_value = [100, 200] + assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + for y in (self.y225, self.y325, self.y25): + interp = interp1d(self.x5, y, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + result = [100, 200] + if y.ndim == 3: + result = [result] * y.shape[0] + assert_array_almost_equal(interp(10), result) + assert_array_almost_equal(interp(-10), result) + result = [[100, 100], [200, 200]] + if y.ndim == 3: + result = [result] * y.shape[0] + assert_array_almost_equal(interp([-10, 10]), result) + + # broadcastable (3,) lower, singleton upper + fill_value = (np.array([-100, -200, -300]), 100) + for y in (self.y325, self.y225): + assert_raises(ValueError, interp1d, self.x5, y, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + interp = interp1d(self.x5, self.y235, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + assert_array_almost_equal(interp(10), 100) + assert_array_almost_equal(interp(-10), [[-100, -200, -300]] * 2) + assert_array_almost_equal(interp([-10, 10]), [[[-100, 100], + [-200, 100], + [-300, 100]]] * 2) + + # broadcastable (2,) lower, singleton upper + fill_value = (np.array([-100, -200]), 100) + assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + for y in (self.y225, self.y325, self.y25): + interp = interp1d(self.x5, y, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + assert_array_almost_equal(interp(10), 100) + result = [-100, -200] + if y.ndim == 3: + result = [result] * y.shape[0] + assert_array_almost_equal(interp(-10), result) + result = [[-100, 100], [-200, 100]] + if y.ndim == 3: + result = [result] * y.shape[0] + assert_array_almost_equal(interp([-10, 10]), result) + + # broadcastable (3,) lower, broadcastable (3,) upper + fill_value = ([-100, -200, -300], [100, 200, 300]) + for y in (self.y325, self.y225): + assert_raises(ValueError, interp1d, self.x5, y, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + for ii in range(2): # check ndarray as well as list here + if ii == 1: + fill_value = tuple(np.array(f) for f in fill_value) + interp = interp1d(self.x5, self.y235, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + assert_array_almost_equal(interp(10), [[100, 200, 300]] * 2) + assert_array_almost_equal(interp(-10), [[-100, -200, -300]] * 2) + assert_array_almost_equal(interp([-10, 10]), [[[-100, 100], + [-200, 200], + [-300, 300]]] * 2) + # broadcastable (2,) lower, broadcastable (2,) upper + fill_value = ([-100, -200], [100, 200]) + assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + for y in (self.y325, self.y225, self.y25): + interp = interp1d(self.x5, y, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + result = [100, 200] + if y.ndim == 3: + result = [result] * y.shape[0] + assert_array_almost_equal(interp(10), result) + result = [-100, -200] + if y.ndim == 3: + result = [result] * y.shape[0] + assert_array_almost_equal(interp(-10), result) + result = [[-100, 100], [-200, 200]] + if y.ndim == 3: + result = [result] * y.shape[0] + assert_array_almost_equal(interp([-10, 10]), result) + + # one broadcastable (2, 2) array-like + fill_value = [[100, 200], [1000, 2000]] + for y in (self.y235, self.y325, self.y25): + assert_raises(ValueError, interp1d, self.x5, y, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + for ii in range(2): + if ii == 1: + fill_value = np.array(fill_value) + interp = interp1d(self.x5, self.y225, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + assert_array_almost_equal(interp(10), [[100, 200], [1000, 2000]]) + assert_array_almost_equal(interp(-10), [[100, 200], [1000, 2000]]) + assert_array_almost_equal(interp([-10, 10]), [[[100, 100], + [200, 200]], + [[1000, 1000], + [2000, 2000]]]) + + # broadcastable (2, 2) lower, broadcastable (2, 2) upper + fill_value = ([[-100, -200], [-1000, -2000]], + [[100, 200], [1000, 2000]]) + for y in (self.y235, self.y325, self.y25): + assert_raises(ValueError, interp1d, self.x5, y, kind=kind, + axis=-1, fill_value=fill_value, bounds_error=False) + for ii in range(2): + if ii == 1: + fill_value = (np.array(fill_value[0]), np.array(fill_value[1])) + interp = interp1d(self.x5, self.y225, kind=kind, axis=-1, + fill_value=fill_value, bounds_error=False) + assert_array_almost_equal(interp(10), [[100, 200], [1000, 2000]]) + assert_array_almost_equal(interp(-10), [[-100, -200], + [-1000, -2000]]) + assert_array_almost_equal(interp([-10, 10]), [[[-100, 100], + [-200, 200]], + [[-1000, 1000], + [-2000, 2000]]]) + + def test_fill_value(self): + # test that two-element fill value works + for kind in ('linear', 'nearest', 'cubic', 'slinear', 'quadratic', + 'zero', 'previous', 'next'): + self._check_fill_value(kind) + + def test_fill_value_writeable(self): + # backwards compat: fill_value is a public writeable attribute + interp = interp1d(self.x10, self.y10, fill_value=123.0) + assert_equal(interp.fill_value, 123.0) + interp.fill_value = 321.0 + assert_equal(interp.fill_value, 321.0) + + def _nd_check_interp(self, kind='linear'): + # Check the behavior when the inputs and outputs are multidimensional. + + # Multidimensional input. + interp10 = interp1d(self.x10, self.y10, kind=kind) + assert_array_almost_equal(interp10(np.array([[3., 5.], [2., 7.]])), + np.array([[3., 5.], [2., 7.]])) + + # Scalar input -> 0-dim scalar array output + assert_(isinstance(interp10(1.2), np.ndarray)) + assert_equal(interp10(1.2).shape, ()) + + # Multidimensional outputs. + interp210 = interp1d(self.x10, self.y210, kind=kind) + assert_array_almost_equal(interp210(1.), np.array([1., 11.])) + assert_array_almost_equal(interp210(np.array([1., 2.])), + np.array([[1., 2.], [11., 12.]])) + + interp102 = interp1d(self.x10, self.y102, axis=0, kind=kind) + assert_array_almost_equal(interp102(1.), np.array([2.0, 3.0])) + assert_array_almost_equal(interp102(np.array([1., 3.])), + np.array([[2., 3.], [6., 7.]])) + + # Both at the same time! + x_new = np.array([[3., 5.], [2., 7.]]) + assert_array_almost_equal(interp210(x_new), + np.array([[[3., 5.], [2., 7.]], + [[13., 15.], [12., 17.]]])) + assert_array_almost_equal(interp102(x_new), + np.array([[[6., 7.], [10., 11.]], + [[4., 5.], [14., 15.]]])) + + def _nd_check_shape(self, kind='linear'): + # Check large N-D output shape + a = [4, 5, 6, 7] + y = np.arange(np.prod(a)).reshape(*a) + for n, s in enumerate(a): + x = np.arange(s) + z = interp1d(x, y, axis=n, kind=kind) + assert_array_almost_equal(z(x), y, err_msg=kind) + + x2 = np.arange(2*3*1).reshape((2,3,1)) / 12. + b = list(a) + b[n:n+1] = [2,3,1] + assert_array_almost_equal(z(x2).shape, b, err_msg=kind) + + def test_nd(self): + for kind in ('linear', 'cubic', 'slinear', 'quadratic', 'nearest', + 'zero', 'previous', 'next'): + self._nd_check_interp(kind) + self._nd_check_shape(kind) + + def _check_complex(self, dtype=np.complex128, kind='linear'): + x = np.array([1, 2.5, 3, 3.1, 4, 6.4, 7.9, 8.0, 9.5, 10]) + y = x * x ** (1 + 2j) + y = y.astype(dtype) + + # simple test + c = interp1d(x, y, kind=kind) + assert_array_almost_equal(y[:-1], c(x)[:-1]) + + # check against interpolating real+imag separately + xi = np.linspace(1, 10, 31) + cr = interp1d(x, y.real, kind=kind) + ci = interp1d(x, y.imag, kind=kind) + assert_array_almost_equal(c(xi).real, cr(xi)) + assert_array_almost_equal(c(xi).imag, ci(xi)) + + def test_complex(self): + for kind in ('linear', 'nearest', 'cubic', 'slinear', 'quadratic', + 'zero', 'previous', 'next'): + self._check_complex(np.complex64, kind) + self._check_complex(np.complex128, kind) + + @pytest.mark.skipif(IS_PYPY, reason="Test not meaningful on PyPy") + def test_circular_refs(self): + # Test interp1d can be automatically garbage collected + x = np.linspace(0, 1) + y = np.linspace(0, 1) + # Confirm interp can be released from memory after use + with assert_deallocated(interp1d, x, y) as interp: + interp([0.1, 0.2]) + del interp + + def test_overflow_nearest(self): + # Test that the x range doesn't overflow when given integers as input + for kind in ('nearest', 'previous', 'next'): + x = np.array([0, 50, 127], dtype=np.int8) + ii = interp1d(x, x, kind=kind) + assert_array_almost_equal(ii(x), x) + + def test_local_nans(self): + # check that for local interpolation kinds (slinear, zero) a single nan + # only affects its local neighborhood + x = np.arange(10).astype(float) + y = x.copy() + y[6] = np.nan + for kind in ('zero', 'slinear'): + ir = interp1d(x, y, kind=kind) + vals = ir([4.9, 7.0]) + assert_(np.isfinite(vals).all()) + + def test_spline_nans(self): + # Backwards compat: a single nan makes the whole spline interpolation + # return nans in an array of the correct shape. And it doesn't raise, + # just quiet nans because of backcompat. + x = np.arange(8).astype(float) + y = x.copy() + yn = y.copy() + yn[3] = np.nan + + for kind in ['quadratic', 'cubic']: + ir = interp1d(x, y, kind=kind) + irn = interp1d(x, yn, kind=kind) + for xnew in (6, [1, 6], [[1, 6], [3, 5]]): + xnew = np.asarray(xnew) + out, outn = ir(x), irn(x) + assert_(np.isnan(outn).all()) + assert_equal(out.shape, outn.shape) + + def test_all_nans(self): + # regression test for gh-11637: interp1d core dumps with all-nan `x` + x = np.ones(10) * np.nan + y = np.arange(10) + with assert_raises(ValueError): + interp1d(x, y, kind='cubic') + + def test_read_only(self): + x = np.arange(0, 10) + y = np.exp(-x / 3.0) + xnew = np.arange(0, 9, 0.1) + # Check both read-only and not read-only: + for xnew_writeable in (True, False): + xnew.flags.writeable = xnew_writeable + x.flags.writeable = False + for kind in ('linear', 'nearest', 'zero', 'slinear', 'quadratic', + 'cubic'): + f = interp1d(x, y, kind=kind) + vals = f(xnew) + assert_(np.isfinite(vals).all()) + + @pytest.mark.parametrize( + "kind", ("linear", "nearest", "nearest-up", "previous", "next") + ) + def test_single_value(self, kind): + # https://github.com/scipy/scipy/issues/4043 + f = interp1d([1.5], [6], kind=kind, bounds_error=False, + fill_value=(2, 10)) + assert_array_equal(f([1, 1.5, 2]), [2, 6, 10]) + # check still error if bounds_error=True + f = interp1d([1.5], [6], kind=kind, bounds_error=True) + with assert_raises(ValueError, match="x_new is above"): + f(2.0) + + +class TestLagrange: + + def test_lagrange(self): + p = poly1d([5,2,1,4,3]) + xs = np.arange(len(p.coeffs)) + ys = p(xs) + pl = lagrange(xs,ys) + assert_array_almost_equal(p.coeffs,pl.coeffs) + + +class TestAkima1DInterpolator: + def test_eval(self): + x = np.arange(0., 11.) + y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) + ak = Akima1DInterpolator(x, y) + xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2, + 8.6, 9.9, 10.]) + yi = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375, + 4.1363636363636366866103344, 5.9803623910336236590978842, + 5.5067291516462386624652936, 5.2031367459745245795943447, + 4.1796554159017080820603951, 3.4110386597938129327189927, + 3.]) + assert_allclose(ak(xi), yi) + + def test_eval_mod(self): + # Reference values generated with the following MATLAB code: + # format longG + # x = 0:10; y = [0. 2. 1. 3. 2. 6. 5.5 5.5 2.7 5.1 3.]; + # xi = [0. 0.5 1. 1.5 2.5 3.5 4.5 5.1 6.5 7.2 8.6 9.9 10.]; + # makima(x, y, xi) + x = np.arange(0., 11.) + y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) + ak = Akima1DInterpolator(x, y, method="makima") + xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2, + 8.6, 9.9, 10.]) + yi = np.array([ + 0.0, 1.34471153846154, 2.0, 1.44375, 1.94375, 2.51939102564103, + 4.10366931918656, 5.98501550899192, 5.51756330960439, 5.1757231914014, + 4.12326636931311, 3.32931513157895, 3.0]) + assert_allclose(ak(xi), yi) + + def test_eval_2d(self): + x = np.arange(0., 11.) + y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) + y = np.column_stack((y, 2. * y)) + ak = Akima1DInterpolator(x, y) + xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2, + 8.6, 9.9, 10.]) + yi = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375, + 4.1363636363636366866103344, + 5.9803623910336236590978842, + 5.5067291516462386624652936, + 5.2031367459745245795943447, + 4.1796554159017080820603951, + 3.4110386597938129327189927, 3.]) + yi = np.column_stack((yi, 2. * yi)) + assert_allclose(ak(xi), yi) + + def test_eval_3d(self): + x = np.arange(0., 11.) + y_ = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) + y = np.empty((11, 2, 2)) + y[:, 0, 0] = y_ + y[:, 1, 0] = 2. * y_ + y[:, 0, 1] = 3. * y_ + y[:, 1, 1] = 4. * y_ + ak = Akima1DInterpolator(x, y) + xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2, + 8.6, 9.9, 10.]) + yi = np.empty((13, 2, 2)) + yi_ = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375, + 4.1363636363636366866103344, + 5.9803623910336236590978842, + 5.5067291516462386624652936, + 5.2031367459745245795943447, + 4.1796554159017080820603951, + 3.4110386597938129327189927, 3.]) + yi[:, 0, 0] = yi_ + yi[:, 1, 0] = 2. * yi_ + yi[:, 0, 1] = 3. * yi_ + yi[:, 1, 1] = 4. * yi_ + assert_allclose(ak(xi), yi) + + def test_degenerate_case_multidimensional(self): + # This test is for issue #5683. + x = np.array([0, 1, 2]) + y = np.vstack((x, x**2)).T + ak = Akima1DInterpolator(x, y) + x_eval = np.array([0.5, 1.5]) + y_eval = ak(x_eval) + assert_allclose(y_eval, np.vstack((x_eval, x_eval**2)).T) + + def test_extend(self): + x = np.arange(0., 11.) + y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) + ak = Akima1DInterpolator(x, y) + match = "Extending a 1-D Akima interpolator is not yet implemented" + with pytest.raises(NotImplementedError, match=match): + ak.extend(None, None) + + def test_mod_invalid_method(self): + x = np.arange(0., 11.) + y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) + match = "`method`=invalid is unsupported." + with pytest.raises(NotImplementedError, match=match): + Akima1DInterpolator(x, y, method="invalid") # type: ignore + + def test_complex(self): + # Complex-valued data deprecated + x = np.arange(0., 11.) + y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) + y = y - 2j*y + # actually raises ComplexWarning, which subclasses RuntimeWarning, see + # https://github.com/numpy/numpy/blob/main/numpy/exceptions.py + msg = "Passing an array with a complex.*|Casting complex values to real.*" + with pytest.warns((RuntimeWarning, DeprecationWarning), match=msg): + Akima1DInterpolator(x, y) + + +class TestPPolyCommon: + # test basic functionality for PPoly and BPoly + def test_sort_check(self): + c = np.array([[1, 4], [2, 5], [3, 6]]) + x = np.array([0, 1, 0.5]) + assert_raises(ValueError, PPoly, c, x) + assert_raises(ValueError, BPoly, c, x) + + def test_ctor_c(self): + # wrong shape: `c` must be at least 2D + with assert_raises(ValueError): + PPoly([1, 2], [0, 1]) + + def test_extend(self): + # Test adding new points to the piecewise polynomial + np.random.seed(1234) + + order = 3 + x = np.unique(np.r_[0, 10 * np.random.rand(30), 10]) + c = 2*np.random.rand(order+1, len(x)-1, 2, 3) - 1 + + for cls in (PPoly, BPoly): + pp = cls(c[:,:9], x[:10]) + pp.extend(c[:,9:], x[10:]) + + pp2 = cls(c[:, 10:], x[10:]) + pp2.extend(c[:, :10], x[:10]) + + pp3 = cls(c, x) + + assert_array_equal(pp.c, pp3.c) + assert_array_equal(pp.x, pp3.x) + assert_array_equal(pp2.c, pp3.c) + assert_array_equal(pp2.x, pp3.x) + + def test_extend_diff_orders(self): + # Test extending polynomial with different order one + np.random.seed(1234) + + x = np.linspace(0, 1, 6) + c = np.random.rand(2, 5) + + x2 = np.linspace(1, 2, 6) + c2 = np.random.rand(4, 5) + + for cls in (PPoly, BPoly): + pp1 = cls(c, x) + pp2 = cls(c2, x2) + + pp_comb = cls(c, x) + pp_comb.extend(c2, x2[1:]) + + # NB. doesn't match to pp1 at the endpoint, because pp1 is not + # continuous with pp2 as we took random coefs. + xi1 = np.linspace(0, 1, 300, endpoint=False) + xi2 = np.linspace(1, 2, 300) + + assert_allclose(pp1(xi1), pp_comb(xi1)) + assert_allclose(pp2(xi2), pp_comb(xi2)) + + def test_extend_descending(self): + np.random.seed(0) + + order = 3 + x = np.sort(np.random.uniform(0, 10, 20)) + c = np.random.rand(order + 1, x.shape[0] - 1, 2, 3) + + for cls in (PPoly, BPoly): + p = cls(c, x) + + p1 = cls(c[:, :9], x[:10]) + p1.extend(c[:, 9:], x[10:]) + + p2 = cls(c[:, 10:], x[10:]) + p2.extend(c[:, :10], x[:10]) + + assert_array_equal(p1.c, p.c) + assert_array_equal(p1.x, p.x) + assert_array_equal(p2.c, p.c) + assert_array_equal(p2.x, p.x) + + def test_shape(self): + np.random.seed(1234) + c = np.random.rand(8, 12, 5, 6, 7) + x = np.sort(np.random.rand(13)) + xp = np.random.rand(3, 4) + for cls in (PPoly, BPoly): + p = cls(c, x) + assert_equal(p(xp).shape, (3, 4, 5, 6, 7)) + + # 'scalars' + for cls in (PPoly, BPoly): + p = cls(c[..., 0, 0, 0], x) + + assert_equal(np.shape(p(0.5)), ()) + assert_equal(np.shape(p(np.array(0.5))), ()) + + assert_raises(ValueError, p, np.array([[0.1, 0.2], [0.4]], dtype=object)) + + def test_complex_coef(self): + np.random.seed(12345) + x = np.sort(np.random.random(13)) + c = np.random.random((8, 12)) * (1. + 0.3j) + c_re, c_im = c.real, c.imag + xp = np.random.random(5) + for cls in (PPoly, BPoly): + p, p_re, p_im = cls(c, x), cls(c_re, x), cls(c_im, x) + for nu in [0, 1, 2]: + assert_allclose(p(xp, nu).real, p_re(xp, nu)) + assert_allclose(p(xp, nu).imag, p_im(xp, nu)) + + def test_axis(self): + np.random.seed(12345) + c = np.random.rand(3, 4, 5, 6, 7, 8) + c_s = c.shape + xp = np.random.random((1, 2)) + for axis in (0, 1, 2, 3): + m = c.shape[axis+1] + x = np.sort(np.random.rand(m+1)) + for cls in (PPoly, BPoly): + p = cls(c, x, axis=axis) + assert_equal(p.c.shape, + c_s[axis:axis+2] + c_s[:axis] + c_s[axis+2:]) + res = p(xp) + targ_shape = c_s[:axis] + xp.shape + c_s[2+axis:] + assert_equal(res.shape, targ_shape) + + # deriv/antideriv does not drop the axis + for p1 in [cls(c, x, axis=axis).derivative(), + cls(c, x, axis=axis).derivative(2), + cls(c, x, axis=axis).antiderivative(), + cls(c, x, axis=axis).antiderivative(2)]: + assert_equal(p1.axis, p.axis) + + # c array needs two axes for the coefficients and intervals, so + # 0 <= axis < c.ndim-1; raise otherwise + for axis in (-1, 4, 5, 6): + for cls in (BPoly, PPoly): + assert_raises(ValueError, cls, **dict(c=c, x=x, axis=axis)) + + +class TestPolySubclassing: + class P(PPoly): + pass + + class B(BPoly): + pass + + def _make_polynomials(self): + np.random.seed(1234) + x = np.sort(np.random.random(3)) + c = np.random.random((4, 2)) + return self.P(c, x), self.B(c, x) + + def test_derivative(self): + pp, bp = self._make_polynomials() + for p in (pp, bp): + pd = p.derivative() + assert_equal(p.__class__, pd.__class__) + + ppa = pp.antiderivative() + assert_equal(pp.__class__, ppa.__class__) + + def test_from_spline(self): + np.random.seed(1234) + x = np.sort(np.r_[0, np.random.rand(11), 1]) + y = np.random.rand(len(x)) + + spl = splrep(x, y, s=0) + pp = self.P.from_spline(spl) + assert_equal(pp.__class__, self.P) + + def test_conversions(self): + pp, bp = self._make_polynomials() + + pp1 = self.P.from_bernstein_basis(bp) + assert_equal(pp1.__class__, self.P) + + bp1 = self.B.from_power_basis(pp) + assert_equal(bp1.__class__, self.B) + + def test_from_derivatives(self): + x = [0, 1, 2] + y = [[1], [2], [3]] + bp = self.B.from_derivatives(x, y) + assert_equal(bp.__class__, self.B) + + +class TestPPoly: + def test_simple(self): + c = np.array([[1, 4], [2, 5], [3, 6]]) + x = np.array([0, 0.5, 1]) + p = PPoly(c, x) + assert_allclose(p(0.3), 1*0.3**2 + 2*0.3 + 3) + assert_allclose(p(0.7), 4*(0.7-0.5)**2 + 5*(0.7-0.5) + 6) + + def test_periodic(self): + c = np.array([[1, 4], [2, 5], [3, 6]]) + x = np.array([0, 0.5, 1]) + p = PPoly(c, x, extrapolate='periodic') + + assert_allclose(p(1.3), 1 * 0.3 ** 2 + 2 * 0.3 + 3) + assert_allclose(p(-0.3), 4 * (0.7 - 0.5) ** 2 + 5 * (0.7 - 0.5) + 6) + + assert_allclose(p(1.3, 1), 2 * 0.3 + 2) + assert_allclose(p(-0.3, 1), 8 * (0.7 - 0.5) + 5) + + def test_read_only(self): + c = np.array([[1, 4], [2, 5], [3, 6]]) + x = np.array([0, 0.5, 1]) + xnew = np.array([0, 0.1, 0.2]) + PPoly(c, x, extrapolate='periodic') + + for writeable in (True, False): + x.flags.writeable = writeable + c.flags.writeable = writeable + f = PPoly(c, x) + vals = f(xnew) + assert_(np.isfinite(vals).all()) + + def test_descending(self): + def binom_matrix(power): + n = np.arange(power + 1).reshape(-1, 1) + k = np.arange(power + 1) + B = binom(n, k) + return B[::-1, ::-1] + + np.random.seed(0) + + power = 3 + for m in [10, 20, 30]: + x = np.sort(np.random.uniform(0, 10, m + 1)) + ca = np.random.uniform(-2, 2, size=(power + 1, m)) + + h = np.diff(x) + h_powers = h[None, :] ** np.arange(power + 1)[::-1, None] + B = binom_matrix(power) + cap = ca * h_powers + cdp = np.dot(B.T, cap) + cd = cdp / h_powers + + pa = PPoly(ca, x, extrapolate=True) + pd = PPoly(cd[:, ::-1], x[::-1], extrapolate=True) + + x_test = np.random.uniform(-10, 20, 100) + assert_allclose(pa(x_test), pd(x_test), rtol=1e-13) + assert_allclose(pa(x_test, 1), pd(x_test, 1), rtol=1e-13) + + pa_d = pa.derivative() + pd_d = pd.derivative() + + assert_allclose(pa_d(x_test), pd_d(x_test), rtol=1e-13) + + # Antiderivatives won't be equal because fixing continuity is + # done in the reverse order, but surely the differences should be + # equal. + pa_i = pa.antiderivative() + pd_i = pd.antiderivative() + for a, b in np.random.uniform(-10, 20, (5, 2)): + int_a = pa.integrate(a, b) + int_d = pd.integrate(a, b) + assert_allclose(int_a, int_d, rtol=1e-13) + assert_allclose(pa_i(b) - pa_i(a), pd_i(b) - pd_i(a), + rtol=1e-13) + + roots_d = pd.roots() + roots_a = pa.roots() + assert_allclose(roots_a, np.sort(roots_d), rtol=1e-12) + + def test_multi_shape(self): + c = np.random.rand(6, 2, 1, 2, 3) + x = np.array([0, 0.5, 1]) + p = PPoly(c, x) + assert_equal(p.x.shape, x.shape) + assert_equal(p.c.shape, c.shape) + assert_equal(p(0.3).shape, c.shape[2:]) + + assert_equal(p(np.random.rand(5, 6)).shape, (5, 6) + c.shape[2:]) + + dp = p.derivative() + assert_equal(dp.c.shape, (5, 2, 1, 2, 3)) + ip = p.antiderivative() + assert_equal(ip.c.shape, (7, 2, 1, 2, 3)) + + def test_construct_fast(self): + np.random.seed(1234) + c = np.array([[1, 4], [2, 5], [3, 6]], dtype=float) + x = np.array([0, 0.5, 1]) + p = PPoly.construct_fast(c, x) + assert_allclose(p(0.3), 1*0.3**2 + 2*0.3 + 3) + assert_allclose(p(0.7), 4*(0.7-0.5)**2 + 5*(0.7-0.5) + 6) + + def test_vs_alternative_implementations(self): + np.random.seed(1234) + c = np.random.rand(3, 12, 22) + x = np.sort(np.r_[0, np.random.rand(11), 1]) + + p = PPoly(c, x) + + xp = np.r_[0.3, 0.5, 0.33, 0.6] + expected = _ppoly_eval_1(c, x, xp) + assert_allclose(p(xp), expected) + + expected = _ppoly_eval_2(c[:,:,0], x, xp) + assert_allclose(p(xp)[:,0], expected) + + def test_from_spline(self): + np.random.seed(1234) + x = np.sort(np.r_[0, np.random.rand(11), 1]) + y = np.random.rand(len(x)) + + spl = splrep(x, y, s=0) + pp = PPoly.from_spline(spl) + + xi = np.linspace(0, 1, 200) + assert_allclose(pp(xi), splev(xi, spl)) + + # make sure .from_spline accepts BSpline objects + b = BSpline(*spl) + ppp = PPoly.from_spline(b) + assert_allclose(ppp(xi), b(xi)) + + # BSpline's extrapolate attribute propagates unless overridden + t, c, k = spl + for extrap in (None, True, False): + b = BSpline(t, c, k, extrapolate=extrap) + p = PPoly.from_spline(b) + assert_equal(p.extrapolate, b.extrapolate) + + def test_derivative_simple(self): + np.random.seed(1234) + c = np.array([[4, 3, 2, 1]]).T + dc = np.array([[3*4, 2*3, 2]]).T + ddc = np.array([[2*3*4, 1*2*3]]).T + x = np.array([0, 1]) + + pp = PPoly(c, x) + dpp = PPoly(dc, x) + ddpp = PPoly(ddc, x) + + assert_allclose(pp.derivative().c, dpp.c) + assert_allclose(pp.derivative(2).c, ddpp.c) + + def test_derivative_eval(self): + np.random.seed(1234) + x = np.sort(np.r_[0, np.random.rand(11), 1]) + y = np.random.rand(len(x)) + + spl = splrep(x, y, s=0) + pp = PPoly.from_spline(spl) + + xi = np.linspace(0, 1, 200) + for dx in range(0, 3): + assert_allclose(pp(xi, dx), splev(xi, spl, dx)) + + def test_derivative(self): + np.random.seed(1234) + x = np.sort(np.r_[0, np.random.rand(11), 1]) + y = np.random.rand(len(x)) + + spl = splrep(x, y, s=0, k=5) + pp = PPoly.from_spline(spl) + + xi = np.linspace(0, 1, 200) + for dx in range(0, 10): + assert_allclose(pp(xi, dx), pp.derivative(dx)(xi), + err_msg="dx=%d" % (dx,)) + + def test_antiderivative_of_constant(self): + # https://github.com/scipy/scipy/issues/4216 + p = PPoly([[1.]], [0, 1]) + assert_equal(p.antiderivative().c, PPoly([[1], [0]], [0, 1]).c) + assert_equal(p.antiderivative().x, PPoly([[1], [0]], [0, 1]).x) + + def test_antiderivative_regression_4355(self): + # https://github.com/scipy/scipy/issues/4355 + p = PPoly([[1., 0.5]], [0, 1, 2]) + q = p.antiderivative() + assert_equal(q.c, [[1, 0.5], [0, 1]]) + assert_equal(q.x, [0, 1, 2]) + assert_allclose(p.integrate(0, 2), 1.5) + assert_allclose(q(2) - q(0), 1.5) + + def test_antiderivative_simple(self): + np.random.seed(1234) + # [ p1(x) = 3*x**2 + 2*x + 1, + # p2(x) = 1.6875] + c = np.array([[3, 2, 1], [0, 0, 1.6875]]).T + # [ pp1(x) = x**3 + x**2 + x, + # pp2(x) = 1.6875*(x - 0.25) + pp1(0.25)] + ic = np.array([[1, 1, 1, 0], [0, 0, 1.6875, 0.328125]]).T + # [ ppp1(x) = (1/4)*x**4 + (1/3)*x**3 + (1/2)*x**2, + # ppp2(x) = (1.6875/2)*(x - 0.25)**2 + pp1(0.25)*x + ppp1(0.25)] + iic = np.array([[1/4, 1/3, 1/2, 0, 0], + [0, 0, 1.6875/2, 0.328125, 0.037434895833333336]]).T + x = np.array([0, 0.25, 1]) + + pp = PPoly(c, x) + ipp = pp.antiderivative() + iipp = pp.antiderivative(2) + iipp2 = ipp.antiderivative() + + assert_allclose(ipp.x, x) + assert_allclose(ipp.c.T, ic.T) + assert_allclose(iipp.c.T, iic.T) + assert_allclose(iipp2.c.T, iic.T) + + def test_antiderivative_vs_derivative(self): + np.random.seed(1234) + x = np.linspace(0, 1, 30)**2 + y = np.random.rand(len(x)) + spl = splrep(x, y, s=0, k=5) + pp = PPoly.from_spline(spl) + + for dx in range(0, 10): + ipp = pp.antiderivative(dx) + + # check that derivative is inverse op + pp2 = ipp.derivative(dx) + assert_allclose(pp.c, pp2.c) + + # check continuity + for k in range(dx): + pp2 = ipp.derivative(k) + + r = 1e-13 + endpoint = r*pp2.x[:-1] + (1 - r)*pp2.x[1:] + + assert_allclose(pp2(pp2.x[1:]), pp2(endpoint), + rtol=1e-7, err_msg="dx=%d k=%d" % (dx, k)) + + def test_antiderivative_vs_spline(self): + np.random.seed(1234) + x = np.sort(np.r_[0, np.random.rand(11), 1]) + y = np.random.rand(len(x)) + + spl = splrep(x, y, s=0, k=5) + pp = PPoly.from_spline(spl) + + for dx in range(0, 10): + pp2 = pp.antiderivative(dx) + spl2 = splantider(spl, dx) + + xi = np.linspace(0, 1, 200) + assert_allclose(pp2(xi), splev(xi, spl2), + rtol=1e-7) + + def test_antiderivative_continuity(self): + c = np.array([[2, 1, 2, 2], [2, 1, 3, 3]]).T + x = np.array([0, 0.5, 1]) + + p = PPoly(c, x) + ip = p.antiderivative() + + # check continuity + assert_allclose(ip(0.5 - 1e-9), ip(0.5 + 1e-9), rtol=1e-8) + + # check that only lowest order coefficients were changed + p2 = ip.derivative() + assert_allclose(p2.c, p.c) + + def test_integrate(self): + np.random.seed(1234) + x = np.sort(np.r_[0, np.random.rand(11), 1]) + y = np.random.rand(len(x)) + + spl = splrep(x, y, s=0, k=5) + pp = PPoly.from_spline(spl) + + a, b = 0.3, 0.9 + ig = pp.integrate(a, b) + + ipp = pp.antiderivative() + assert_allclose(ig, ipp(b) - ipp(a)) + assert_allclose(ig, splint(a, b, spl)) + + a, b = -0.3, 0.9 + ig = pp.integrate(a, b, extrapolate=True) + assert_allclose(ig, ipp(b) - ipp(a)) + + assert_(np.isnan(pp.integrate(a, b, extrapolate=False)).all()) + + def test_integrate_readonly(self): + x = np.array([1, 2, 4]) + c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]]) + + for writeable in (True, False): + x.flags.writeable = writeable + + P = PPoly(c, x) + vals = P.integrate(1, 4) + + assert_(np.isfinite(vals).all()) + + def test_integrate_periodic(self): + x = np.array([1, 2, 4]) + c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]]) + + P = PPoly(c, x, extrapolate='periodic') + I = P.antiderivative() + + period_int = I(4) - I(1) + + assert_allclose(P.integrate(1, 4), period_int) + assert_allclose(P.integrate(-10, -7), period_int) + assert_allclose(P.integrate(-10, -4), 2 * period_int) + + assert_allclose(P.integrate(1.5, 2.5), I(2.5) - I(1.5)) + assert_allclose(P.integrate(3.5, 5), I(2) - I(1) + I(4) - I(3.5)) + assert_allclose(P.integrate(3.5 + 12, 5 + 12), + I(2) - I(1) + I(4) - I(3.5)) + assert_allclose(P.integrate(3.5, 5 + 12), + I(2) - I(1) + I(4) - I(3.5) + 4 * period_int) + + assert_allclose(P.integrate(0, -1), I(2) - I(3)) + assert_allclose(P.integrate(-9, -10), I(2) - I(3)) + assert_allclose(P.integrate(0, -10), I(2) - I(3) - 3 * period_int) + + def test_roots(self): + x = np.linspace(0, 1, 31)**2 + y = np.sin(30*x) + + spl = splrep(x, y, s=0, k=3) + pp = PPoly.from_spline(spl) + + r = pp.roots() + r = r[(r >= 0 - 1e-15) & (r <= 1 + 1e-15)] + assert_allclose(r, sproot(spl), atol=1e-15) + + def test_roots_idzero(self): + # Roots for piecewise polynomials with identically zero + # sections. + c = np.array([[-1, 0.25], [0, 0], [-1, 0.25]]).T + x = np.array([0, 0.4, 0.6, 1.0]) + + pp = PPoly(c, x) + assert_array_equal(pp.roots(), + [0.25, 0.4, np.nan, 0.6 + 0.25]) + + # ditto for p.solve(const) with sections identically equal const + const = 2. + c1 = c.copy() + c1[1, :] += const + pp1 = PPoly(c1, x) + + assert_array_equal(pp1.solve(const), + [0.25, 0.4, np.nan, 0.6 + 0.25]) + + def test_roots_all_zero(self): + # test the code path for the polynomial being identically zero everywhere + c = [[0], [0]] + x = [0, 1] + p = PPoly(c, x) + assert_array_equal(p.roots(), [0, np.nan]) + assert_array_equal(p.solve(0), [0, np.nan]) + assert_array_equal(p.solve(1), []) + + c = [[0, 0], [0, 0]] + x = [0, 1, 2] + p = PPoly(c, x) + assert_array_equal(p.roots(), [0, np.nan, 1, np.nan]) + assert_array_equal(p.solve(0), [0, np.nan, 1, np.nan]) + assert_array_equal(p.solve(1), []) + + def test_roots_repeated(self): + # Check roots repeated in multiple sections are reported only + # once. + + # [(x + 1)**2 - 1, -x**2] ; x == 0 is a repeated root + c = np.array([[1, 0, -1], [-1, 0, 0]]).T + x = np.array([-1, 0, 1]) + + pp = PPoly(c, x) + assert_array_equal(pp.roots(), [-2, 0]) + assert_array_equal(pp.roots(extrapolate=False), [0]) + + def test_roots_discont(self): + # Check that a discontinuity across zero is reported as root + c = np.array([[1], [-1]]).T + x = np.array([0, 0.5, 1]) + pp = PPoly(c, x) + assert_array_equal(pp.roots(), [0.5]) + assert_array_equal(pp.roots(discontinuity=False), []) + + # ditto for a discontinuity across y: + assert_array_equal(pp.solve(0.5), [0.5]) + assert_array_equal(pp.solve(0.5, discontinuity=False), []) + + assert_array_equal(pp.solve(1.5), []) + assert_array_equal(pp.solve(1.5, discontinuity=False), []) + + def test_roots_random(self): + # Check high-order polynomials with random coefficients + np.random.seed(1234) + + num = 0 + + for extrapolate in (True, False): + for order in range(0, 20): + x = np.unique(np.r_[0, 10 * np.random.rand(30), 10]) + c = 2*np.random.rand(order+1, len(x)-1, 2, 3) - 1 + + pp = PPoly(c, x) + for y in [0, np.random.random()]: + r = pp.solve(y, discontinuity=False, extrapolate=extrapolate) + + for i in range(2): + for j in range(3): + rr = r[i,j] + if rr.size > 0: + # Check that the reported roots indeed are roots + num += rr.size + val = pp(rr, extrapolate=extrapolate)[:,i,j] + cmpval = pp(rr, nu=1, + extrapolate=extrapolate)[:,i,j] + msg = f"({extrapolate!r}) r = {repr(rr)}" + assert_allclose((val-y) / cmpval, 0, atol=1e-7, + err_msg=msg) + + # Check that we checked a number of roots + assert_(num > 100, repr(num)) + + def test_roots_croots(self): + # Test the complex root finding algorithm + np.random.seed(1234) + + for k in range(1, 15): + c = np.random.rand(k, 1, 130) + + if k == 3: + # add a case with zero discriminant + c[:,0,0] = 1, 2, 1 + + for y in [0, np.random.random()]: + w = np.empty(c.shape, dtype=complex) + _ppoly._croots_poly1(c, w) + + if k == 1: + assert_(np.isnan(w).all()) + continue + + res = 0 + cres = 0 + for i in range(k): + res += c[i,None] * w**(k-1-i) + cres += abs(c[i,None] * w**(k-1-i)) + with np.errstate(invalid='ignore'): + res /= cres + res = res.ravel() + res = res[~np.isnan(res)] + assert_allclose(res, 0, atol=1e-10) + + def test_extrapolate_attr(self): + # [ 1 - x**2 ] + c = np.array([[-1, 0, 1]]).T + x = np.array([0, 1]) + + for extrapolate in [True, False, None]: + pp = PPoly(c, x, extrapolate=extrapolate) + pp_d = pp.derivative() + pp_i = pp.antiderivative() + + if extrapolate is False: + assert_(np.isnan(pp([-0.1, 1.1])).all()) + assert_(np.isnan(pp_i([-0.1, 1.1])).all()) + assert_(np.isnan(pp_d([-0.1, 1.1])).all()) + assert_equal(pp.roots(), [1]) + else: + assert_allclose(pp([-0.1, 1.1]), [1-0.1**2, 1-1.1**2]) + assert_(not np.isnan(pp_i([-0.1, 1.1])).any()) + assert_(not np.isnan(pp_d([-0.1, 1.1])).any()) + assert_allclose(pp.roots(), [1, -1]) + + +class TestBPoly: + def test_simple(self): + x = [0, 1] + c = [[3]] + bp = BPoly(c, x) + assert_allclose(bp(0.1), 3.) + + def test_simple2(self): + x = [0, 1] + c = [[3], [1]] + bp = BPoly(c, x) # 3*(1-x) + 1*x + assert_allclose(bp(0.1), 3*0.9 + 1.*0.1) + + def test_simple3(self): + x = [0, 1] + c = [[3], [1], [4]] + bp = BPoly(c, x) # 3 * (1-x)**2 + 2 * x (1-x) + 4 * x**2 + assert_allclose(bp(0.2), + 3 * 0.8*0.8 + 1 * 2*0.2*0.8 + 4 * 0.2*0.2) + + def test_simple4(self): + x = [0, 1] + c = [[1], [1], [1], [2]] + bp = BPoly(c, x) + assert_allclose(bp(0.3), 0.7**3 + + 3 * 0.7**2 * 0.3 + + 3 * 0.7 * 0.3**2 + + 2 * 0.3**3) + + def test_simple5(self): + x = [0, 1] + c = [[1], [1], [8], [2], [1]] + bp = BPoly(c, x) + assert_allclose(bp(0.3), 0.7**4 + + 4 * 0.7**3 * 0.3 + + 8 * 6 * 0.7**2 * 0.3**2 + + 2 * 4 * 0.7 * 0.3**3 + + 0.3**4) + + def test_periodic(self): + x = [0, 1, 3] + c = [[3, 0], [0, 0], [0, 2]] + # [3*(1-x)**2, 2*((x-1)/2)**2] + bp = BPoly(c, x, extrapolate='periodic') + + assert_allclose(bp(3.4), 3 * 0.6**2) + assert_allclose(bp(-1.3), 2 * (0.7/2)**2) + + assert_allclose(bp(3.4, 1), -6 * 0.6) + assert_allclose(bp(-1.3, 1), 2 * (0.7/2)) + + def test_descending(self): + np.random.seed(0) + + power = 3 + for m in [10, 20, 30]: + x = np.sort(np.random.uniform(0, 10, m + 1)) + ca = np.random.uniform(-0.1, 0.1, size=(power + 1, m)) + # We need only to flip coefficients to get it right! + cd = ca[::-1].copy() + + pa = BPoly(ca, x, extrapolate=True) + pd = BPoly(cd[:, ::-1], x[::-1], extrapolate=True) + + x_test = np.random.uniform(-10, 20, 100) + assert_allclose(pa(x_test), pd(x_test), rtol=1e-13) + assert_allclose(pa(x_test, 1), pd(x_test, 1), rtol=1e-13) + + pa_d = pa.derivative() + pd_d = pd.derivative() + + assert_allclose(pa_d(x_test), pd_d(x_test), rtol=1e-13) + + # Antiderivatives won't be equal because fixing continuity is + # done in the reverse order, but surely the differences should be + # equal. + pa_i = pa.antiderivative() + pd_i = pd.antiderivative() + for a, b in np.random.uniform(-10, 20, (5, 2)): + int_a = pa.integrate(a, b) + int_d = pd.integrate(a, b) + assert_allclose(int_a, int_d, rtol=1e-12) + assert_allclose(pa_i(b) - pa_i(a), pd_i(b) - pd_i(a), + rtol=1e-12) + + def test_multi_shape(self): + c = np.random.rand(6, 2, 1, 2, 3) + x = np.array([0, 0.5, 1]) + p = BPoly(c, x) + assert_equal(p.x.shape, x.shape) + assert_equal(p.c.shape, c.shape) + assert_equal(p(0.3).shape, c.shape[2:]) + assert_equal(p(np.random.rand(5,6)).shape, + (5,6)+c.shape[2:]) + + dp = p.derivative() + assert_equal(dp.c.shape, (5, 2, 1, 2, 3)) + + def test_interval_length(self): + x = [0, 2] + c = [[3], [1], [4]] + bp = BPoly(c, x) + xval = 0.1 + s = xval / 2 # s = (x - xa) / (xb - xa) + assert_allclose(bp(xval), 3 * (1-s)*(1-s) + 1 * 2*s*(1-s) + 4 * s*s) + + def test_two_intervals(self): + x = [0, 1, 3] + c = [[3, 0], [0, 0], [0, 2]] + bp = BPoly(c, x) # [3*(1-x)**2, 2*((x-1)/2)**2] + + assert_allclose(bp(0.4), 3 * 0.6*0.6) + assert_allclose(bp(1.7), 2 * (0.7/2)**2) + + def test_extrapolate_attr(self): + x = [0, 2] + c = [[3], [1], [4]] + bp = BPoly(c, x) + + for extrapolate in (True, False, None): + bp = BPoly(c, x, extrapolate=extrapolate) + bp_d = bp.derivative() + if extrapolate is False: + assert_(np.isnan(bp([-0.1, 2.1])).all()) + assert_(np.isnan(bp_d([-0.1, 2.1])).all()) + else: + assert_(not np.isnan(bp([-0.1, 2.1])).any()) + assert_(not np.isnan(bp_d([-0.1, 2.1])).any()) + + +class TestBPolyCalculus: + def test_derivative(self): + x = [0, 1, 3] + c = [[3, 0], [0, 0], [0, 2]] + bp = BPoly(c, x) # [3*(1-x)**2, 2*((x-1)/2)**2] + bp_der = bp.derivative() + assert_allclose(bp_der(0.4), -6*(0.6)) + assert_allclose(bp_der(1.7), 0.7) + + # derivatives in-place + assert_allclose([bp(0.4, nu=1), bp(0.4, nu=2), bp(0.4, nu=3)], + [-6*(1-0.4), 6., 0.]) + assert_allclose([bp(1.7, nu=1), bp(1.7, nu=2), bp(1.7, nu=3)], + [0.7, 1., 0]) + + def test_derivative_ppoly(self): + # make sure it's consistent w/ power basis + np.random.seed(1234) + m, k = 5, 8 # number of intervals, order + x = np.sort(np.random.random(m)) + c = np.random.random((k, m-1)) + bp = BPoly(c, x) + pp = PPoly.from_bernstein_basis(bp) + + for d in range(k): + bp = bp.derivative() + pp = pp.derivative() + xp = np.linspace(x[0], x[-1], 21) + assert_allclose(bp(xp), pp(xp)) + + def test_deriv_inplace(self): + np.random.seed(1234) + m, k = 5, 8 # number of intervals, order + x = np.sort(np.random.random(m)) + c = np.random.random((k, m-1)) + + # test both real and complex coefficients + for cc in [c.copy(), c*(1. + 2.j)]: + bp = BPoly(cc, x) + xp = np.linspace(x[0], x[-1], 21) + for i in range(k): + assert_allclose(bp(xp, i), bp.derivative(i)(xp)) + + def test_antiderivative_simple(self): + # f(x) = x for x \in [0, 1), + # (x-1)/2 for x \in [1, 3] + # + # antiderivative is then + # F(x) = x**2 / 2 for x \in [0, 1), + # 0.5*x*(x/2 - 1) + A for x \in [1, 3] + # where A = 3/4 for continuity at x = 1. + x = [0, 1, 3] + c = [[0, 0], [1, 1]] + + bp = BPoly(c, x) + bi = bp.antiderivative() + + xx = np.linspace(0, 3, 11) + assert_allclose(bi(xx), + np.where(xx < 1, xx**2 / 2., + 0.5 * xx * (xx/2. - 1) + 3./4), + atol=1e-12, rtol=1e-12) + + def test_der_antider(self): + np.random.seed(1234) + x = np.sort(np.random.random(11)) + c = np.random.random((4, 10, 2, 3)) + bp = BPoly(c, x) + + xx = np.linspace(x[0], x[-1], 100) + assert_allclose(bp.antiderivative().derivative()(xx), + bp(xx), atol=1e-12, rtol=1e-12) + + def test_antider_ppoly(self): + np.random.seed(1234) + x = np.sort(np.random.random(11)) + c = np.random.random((4, 10, 2, 3)) + bp = BPoly(c, x) + pp = PPoly.from_bernstein_basis(bp) + + xx = np.linspace(x[0], x[-1], 10) + + assert_allclose(bp.antiderivative(2)(xx), + pp.antiderivative(2)(xx), atol=1e-12, rtol=1e-12) + + def test_antider_continuous(self): + np.random.seed(1234) + x = np.sort(np.random.random(11)) + c = np.random.random((4, 10)) + bp = BPoly(c, x).antiderivative() + + xx = bp.x[1:-1] + assert_allclose(bp(xx - 1e-14), + bp(xx + 1e-14), atol=1e-12, rtol=1e-12) + + def test_integrate(self): + np.random.seed(1234) + x = np.sort(np.random.random(11)) + c = np.random.random((4, 10)) + bp = BPoly(c, x) + pp = PPoly.from_bernstein_basis(bp) + assert_allclose(bp.integrate(0, 1), + pp.integrate(0, 1), atol=1e-12, rtol=1e-12) + + def test_integrate_extrap(self): + c = [[1]] + x = [0, 1] + b = BPoly(c, x) + + # default is extrapolate=True + assert_allclose(b.integrate(0, 2), 2., atol=1e-14) + + # .integrate argument overrides self.extrapolate + b1 = BPoly(c, x, extrapolate=False) + assert_(np.isnan(b1.integrate(0, 2))) + assert_allclose(b1.integrate(0, 2, extrapolate=True), 2., atol=1e-14) + + def test_integrate_periodic(self): + x = np.array([1, 2, 4]) + c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]]) + + P = BPoly.from_power_basis(PPoly(c, x), extrapolate='periodic') + I = P.antiderivative() + + period_int = I(4) - I(1) + + assert_allclose(P.integrate(1, 4), period_int) + assert_allclose(P.integrate(-10, -7), period_int) + assert_allclose(P.integrate(-10, -4), 2 * period_int) + + assert_allclose(P.integrate(1.5, 2.5), I(2.5) - I(1.5)) + assert_allclose(P.integrate(3.5, 5), I(2) - I(1) + I(4) - I(3.5)) + assert_allclose(P.integrate(3.5 + 12, 5 + 12), + I(2) - I(1) + I(4) - I(3.5)) + assert_allclose(P.integrate(3.5, 5 + 12), + I(2) - I(1) + I(4) - I(3.5) + 4 * period_int) + + assert_allclose(P.integrate(0, -1), I(2) - I(3)) + assert_allclose(P.integrate(-9, -10), I(2) - I(3)) + assert_allclose(P.integrate(0, -10), I(2) - I(3) - 3 * period_int) + + def test_antider_neg(self): + # .derivative(-nu) ==> .andiderivative(nu) and vice versa + c = [[1]] + x = [0, 1] + b = BPoly(c, x) + + xx = np.linspace(0, 1, 21) + + assert_allclose(b.derivative(-1)(xx), b.antiderivative()(xx), + atol=1e-12, rtol=1e-12) + assert_allclose(b.derivative(1)(xx), b.antiderivative(-1)(xx), + atol=1e-12, rtol=1e-12) + + +class TestPolyConversions: + def test_bp_from_pp(self): + x = [0, 1, 3] + c = [[3, 2], [1, 8], [4, 3]] + pp = PPoly(c, x) + bp = BPoly.from_power_basis(pp) + pp1 = PPoly.from_bernstein_basis(bp) + + xp = [0.1, 1.4] + assert_allclose(pp(xp), bp(xp)) + assert_allclose(pp(xp), pp1(xp)) + + def test_bp_from_pp_random(self): + np.random.seed(1234) + m, k = 5, 8 # number of intervals, order + x = np.sort(np.random.random(m)) + c = np.random.random((k, m-1)) + pp = PPoly(c, x) + bp = BPoly.from_power_basis(pp) + pp1 = PPoly.from_bernstein_basis(bp) + + xp = np.linspace(x[0], x[-1], 21) + assert_allclose(pp(xp), bp(xp)) + assert_allclose(pp(xp), pp1(xp)) + + def test_pp_from_bp(self): + x = [0, 1, 3] + c = [[3, 3], [1, 1], [4, 2]] + bp = BPoly(c, x) + pp = PPoly.from_bernstein_basis(bp) + bp1 = BPoly.from_power_basis(pp) + + xp = [0.1, 1.4] + assert_allclose(bp(xp), pp(xp)) + assert_allclose(bp(xp), bp1(xp)) + + def test_broken_conversions(self): + # regression test for gh-10597: from_power_basis only accepts PPoly etc. + x = [0, 1, 3] + c = [[3, 3], [1, 1], [4, 2]] + pp = PPoly(c, x) + with assert_raises(TypeError): + PPoly.from_bernstein_basis(pp) + + bp = BPoly(c, x) + with assert_raises(TypeError): + BPoly.from_power_basis(bp) + + +class TestBPolyFromDerivatives: + def test_make_poly_1(self): + c1 = BPoly._construct_from_derivatives(0, 1, [2], [3]) + assert_allclose(c1, [2., 3.]) + + def test_make_poly_2(self): + c1 = BPoly._construct_from_derivatives(0, 1, [1, 0], [1]) + assert_allclose(c1, [1., 1., 1.]) + + # f'(0) = 3 + c2 = BPoly._construct_from_derivatives(0, 1, [2, 3], [1]) + assert_allclose(c2, [2., 7./2, 1.]) + + # f'(1) = 3 + c3 = BPoly._construct_from_derivatives(0, 1, [2], [1, 3]) + assert_allclose(c3, [2., -0.5, 1.]) + + def test_make_poly_3(self): + # f'(0)=2, f''(0)=3 + c1 = BPoly._construct_from_derivatives(0, 1, [1, 2, 3], [4]) + assert_allclose(c1, [1., 5./3, 17./6, 4.]) + + # f'(1)=2, f''(1)=3 + c2 = BPoly._construct_from_derivatives(0, 1, [1], [4, 2, 3]) + assert_allclose(c2, [1., 19./6, 10./3, 4.]) + + # f'(0)=2, f'(1)=3 + c3 = BPoly._construct_from_derivatives(0, 1, [1, 2], [4, 3]) + assert_allclose(c3, [1., 5./3, 3., 4.]) + + def test_make_poly_12(self): + np.random.seed(12345) + ya = np.r_[0, np.random.random(5)] + yb = np.r_[0, np.random.random(5)] + + c = BPoly._construct_from_derivatives(0, 1, ya, yb) + pp = BPoly(c[:, None], [0, 1]) + for j in range(6): + assert_allclose([pp(0.), pp(1.)], [ya[j], yb[j]]) + pp = pp.derivative() + + def test_raise_degree(self): + np.random.seed(12345) + x = [0, 1] + k, d = 8, 5 + c = np.random.random((k, 1, 2, 3, 4)) + bp = BPoly(c, x) + + c1 = BPoly._raise_degree(c, d) + bp1 = BPoly(c1, x) + + xp = np.linspace(0, 1, 11) + assert_allclose(bp(xp), bp1(xp)) + + def test_xi_yi(self): + assert_raises(ValueError, BPoly.from_derivatives, [0, 1], [0]) + + def test_coords_order(self): + xi = [0, 0, 1] + yi = [[0], [0], [0]] + assert_raises(ValueError, BPoly.from_derivatives, xi, yi) + + def test_zeros(self): + xi = [0, 1, 2, 3] + yi = [[0, 0], [0], [0, 0], [0, 0]] # NB: will have to raise the degree + pp = BPoly.from_derivatives(xi, yi) + assert_(pp.c.shape == (4, 3)) + + ppd = pp.derivative() + for xp in [0., 0.1, 1., 1.1, 1.9, 2., 2.5]: + assert_allclose([pp(xp), ppd(xp)], [0., 0.]) + + def _make_random_mk(self, m, k): + # k derivatives at each breakpoint + np.random.seed(1234) + xi = np.asarray([1. * j**2 for j in range(m+1)]) + yi = [np.random.random(k) for j in range(m+1)] + return xi, yi + + def test_random_12(self): + m, k = 5, 12 + xi, yi = self._make_random_mk(m, k) + pp = BPoly.from_derivatives(xi, yi) + + for order in range(k//2): + assert_allclose(pp(xi), [yy[order] for yy in yi]) + pp = pp.derivative() + + def test_order_zero(self): + m, k = 5, 12 + xi, yi = self._make_random_mk(m, k) + assert_raises(ValueError, BPoly.from_derivatives, + **dict(xi=xi, yi=yi, orders=0)) + + def test_orders_too_high(self): + m, k = 5, 12 + xi, yi = self._make_random_mk(m, k) + + BPoly.from_derivatives(xi, yi, orders=2*k-1) # this is still ok + assert_raises(ValueError, BPoly.from_derivatives, # but this is not + **dict(xi=xi, yi=yi, orders=2*k)) + + def test_orders_global(self): + m, k = 5, 12 + xi, yi = self._make_random_mk(m, k) + + # ok, this is confusing. Local polynomials will be of the order 5 + # which means that up to the 2nd derivatives will be used at each point + order = 5 + pp = BPoly.from_derivatives(xi, yi, orders=order) + + for j in range(order//2+1): + assert_allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12)) + pp = pp.derivative() + assert_(not np.allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12))) + + # now repeat with `order` being even: on each interval, it uses + # order//2 'derivatives' @ the right-hand endpoint and + # order//2+1 @ 'derivatives' the left-hand endpoint + order = 6 + pp = BPoly.from_derivatives(xi, yi, orders=order) + for j in range(order//2): + assert_allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12)) + pp = pp.derivative() + assert_(not np.allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12))) + + def test_orders_local(self): + m, k = 7, 12 + xi, yi = self._make_random_mk(m, k) + + orders = [o + 1 for o in range(m)] + for i, x in enumerate(xi[1:-1]): + pp = BPoly.from_derivatives(xi, yi, orders=orders) + for j in range(orders[i] // 2 + 1): + assert_allclose(pp(x - 1e-12), pp(x + 1e-12)) + pp = pp.derivative() + assert_(not np.allclose(pp(x - 1e-12), pp(x + 1e-12))) + + def test_yi_trailing_dims(self): + m, k = 7, 5 + xi = np.sort(np.random.random(m+1)) + yi = np.random.random((m+1, k, 6, 7, 8)) + pp = BPoly.from_derivatives(xi, yi) + assert_equal(pp.c.shape, (2*k, m, 6, 7, 8)) + + def test_gh_5430(self): + # At least one of these raises an error unless gh-5430 is + # fixed. In py2k an int is implemented using a C long, so + # which one fails depends on your system. In py3k there is only + # one arbitrary precision integer type, so both should fail. + orders = np.int32(1) + p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders) + assert_almost_equal(p(0), 0) + orders = np.int64(1) + p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders) + assert_almost_equal(p(0), 0) + orders = 1 + # This worked before; make sure it still works + p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders) + assert_almost_equal(p(0), 0) + orders = 1 + + +class TestNdPPoly: + def test_simple_1d(self): + np.random.seed(1234) + + c = np.random.rand(4, 5) + x = np.linspace(0, 1, 5+1) + + xi = np.random.rand(200) + + p = NdPPoly(c, (x,)) + v1 = p((xi,)) + + v2 = _ppoly_eval_1(c[:,:,None], x, xi).ravel() + assert_allclose(v1, v2) + + def test_simple_2d(self): + np.random.seed(1234) + + c = np.random.rand(4, 5, 6, 7) + x = np.linspace(0, 1, 6+1) + y = np.linspace(0, 1, 7+1)**2 + + xi = np.random.rand(200) + yi = np.random.rand(200) + + v1 = np.empty([len(xi), 1], dtype=c.dtype) + v1.fill(np.nan) + _ppoly.evaluate_nd(c.reshape(4*5, 6*7, 1), + (x, y), + np.array([4, 5], dtype=np.intc), + np.c_[xi, yi], + np.array([0, 0], dtype=np.intc), + 1, + v1) + v1 = v1.ravel() + v2 = _ppoly2d_eval(c, (x, y), xi, yi) + assert_allclose(v1, v2) + + p = NdPPoly(c, (x, y)) + for nu in (None, (0, 0), (0, 1), (1, 0), (2, 3), (9, 2)): + v1 = p(np.c_[xi, yi], nu=nu) + v2 = _ppoly2d_eval(c, (x, y), xi, yi, nu=nu) + assert_allclose(v1, v2, err_msg=repr(nu)) + + def test_simple_3d(self): + np.random.seed(1234) + + c = np.random.rand(4, 5, 6, 7, 8, 9) + x = np.linspace(0, 1, 7+1) + y = np.linspace(0, 1, 8+1)**2 + z = np.linspace(0, 1, 9+1)**3 + + xi = np.random.rand(40) + yi = np.random.rand(40) + zi = np.random.rand(40) + + p = NdPPoly(c, (x, y, z)) + + for nu in (None, (0, 0, 0), (0, 1, 0), (1, 0, 0), (2, 3, 0), + (6, 0, 2)): + v1 = p((xi, yi, zi), nu=nu) + v2 = _ppoly3d_eval(c, (x, y, z), xi, yi, zi, nu=nu) + assert_allclose(v1, v2, err_msg=repr(nu)) + + def test_simple_4d(self): + np.random.seed(1234) + + c = np.random.rand(4, 5, 6, 7, 8, 9, 10, 11) + x = np.linspace(0, 1, 8+1) + y = np.linspace(0, 1, 9+1)**2 + z = np.linspace(0, 1, 10+1)**3 + u = np.linspace(0, 1, 11+1)**4 + + xi = np.random.rand(20) + yi = np.random.rand(20) + zi = np.random.rand(20) + ui = np.random.rand(20) + + p = NdPPoly(c, (x, y, z, u)) + v1 = p((xi, yi, zi, ui)) + + v2 = _ppoly4d_eval(c, (x, y, z, u), xi, yi, zi, ui) + assert_allclose(v1, v2) + + def test_deriv_1d(self): + np.random.seed(1234) + + c = np.random.rand(4, 5) + x = np.linspace(0, 1, 5+1) + + p = NdPPoly(c, (x,)) + + # derivative + dp = p.derivative(nu=[1]) + p1 = PPoly(c, x) + dp1 = p1.derivative() + assert_allclose(dp.c, dp1.c) + + # antiderivative + dp = p.antiderivative(nu=[2]) + p1 = PPoly(c, x) + dp1 = p1.antiderivative(2) + assert_allclose(dp.c, dp1.c) + + def test_deriv_3d(self): + np.random.seed(1234) + + c = np.random.rand(4, 5, 6, 7, 8, 9) + x = np.linspace(0, 1, 7+1) + y = np.linspace(0, 1, 8+1)**2 + z = np.linspace(0, 1, 9+1)**3 + + p = NdPPoly(c, (x, y, z)) + + # differentiate vs x + p1 = PPoly(c.transpose(0, 3, 1, 2, 4, 5), x) + dp = p.derivative(nu=[2]) + dp1 = p1.derivative(2) + assert_allclose(dp.c, + dp1.c.transpose(0, 2, 3, 1, 4, 5)) + + # antidifferentiate vs y + p1 = PPoly(c.transpose(1, 4, 0, 2, 3, 5), y) + dp = p.antiderivative(nu=[0, 1, 0]) + dp1 = p1.antiderivative(1) + assert_allclose(dp.c, + dp1.c.transpose(2, 0, 3, 4, 1, 5)) + + # differentiate vs z + p1 = PPoly(c.transpose(2, 5, 0, 1, 3, 4), z) + dp = p.derivative(nu=[0, 0, 3]) + dp1 = p1.derivative(3) + assert_allclose(dp.c, + dp1.c.transpose(2, 3, 0, 4, 5, 1)) + + def test_deriv_3d_simple(self): + # Integrate to obtain function x y**2 z**4 / (2! 4!) + + c = np.ones((1, 1, 1, 3, 4, 5)) + x = np.linspace(0, 1, 3+1)**1 + y = np.linspace(0, 1, 4+1)**2 + z = np.linspace(0, 1, 5+1)**3 + + p = NdPPoly(c, (x, y, z)) + ip = p.antiderivative((1, 0, 4)) + ip = ip.antiderivative((0, 2, 0)) + + xi = np.random.rand(20) + yi = np.random.rand(20) + zi = np.random.rand(20) + + assert_allclose(ip((xi, yi, zi)), + xi * yi**2 * zi**4 / (gamma(3)*gamma(5))) + + def test_integrate_2d(self): + np.random.seed(1234) + c = np.random.rand(4, 5, 16, 17) + x = np.linspace(0, 1, 16+1)**1 + y = np.linspace(0, 1, 17+1)**2 + + # make continuously differentiable so that nquad() has an + # easier time + c = c.transpose(0, 2, 1, 3) + cx = c.reshape(c.shape[0], c.shape[1], -1).copy() + _ppoly.fix_continuity(cx, x, 2) + c = cx.reshape(c.shape) + c = c.transpose(0, 2, 1, 3) + c = c.transpose(1, 3, 0, 2) + cx = c.reshape(c.shape[0], c.shape[1], -1).copy() + _ppoly.fix_continuity(cx, y, 2) + c = cx.reshape(c.shape) + c = c.transpose(2, 0, 3, 1).copy() + + # Check integration + p = NdPPoly(c, (x, y)) + + for ranges in [[(0, 1), (0, 1)], + [(0, 0.5), (0, 1)], + [(0, 1), (0, 0.5)], + [(0.3, 0.7), (0.6, 0.2)]]: + + ig = p.integrate(ranges) + ig2, err2 = nquad(lambda x, y: p((x, y)), ranges, + opts=[dict(epsrel=1e-5, epsabs=1e-5)]*2) + assert_allclose(ig, ig2, rtol=1e-5, atol=1e-5, + err_msg=repr(ranges)) + + def test_integrate_1d(self): + np.random.seed(1234) + c = np.random.rand(4, 5, 6, 16, 17, 18) + x = np.linspace(0, 1, 16+1)**1 + y = np.linspace(0, 1, 17+1)**2 + z = np.linspace(0, 1, 18+1)**3 + + # Check 1-D integration + p = NdPPoly(c, (x, y, z)) + + u = np.random.rand(200) + v = np.random.rand(200) + a, b = 0.2, 0.7 + + px = p.integrate_1d(a, b, axis=0) + pax = p.antiderivative((1, 0, 0)) + assert_allclose(px((u, v)), pax((b, u, v)) - pax((a, u, v))) + + py = p.integrate_1d(a, b, axis=1) + pay = p.antiderivative((0, 1, 0)) + assert_allclose(py((u, v)), pay((u, b, v)) - pay((u, a, v))) + + pz = p.integrate_1d(a, b, axis=2) + paz = p.antiderivative((0, 0, 1)) + assert_allclose(pz((u, v)), paz((u, v, b)) - paz((u, v, a))) + + +def _ppoly_eval_1(c, x, xps): + """Evaluate piecewise polynomial manually""" + out = np.zeros((len(xps), c.shape[2])) + for i, xp in enumerate(xps): + if xp < 0 or xp > 1: + out[i,:] = np.nan + continue + j = np.searchsorted(x, xp) - 1 + d = xp - x[j] + assert_(x[j] <= xp < x[j+1]) + r = sum(c[k,j] * d**(c.shape[0]-k-1) + for k in range(c.shape[0])) + out[i,:] = r + return out + + +def _ppoly_eval_2(coeffs, breaks, xnew, fill=np.nan): + """Evaluate piecewise polynomial manually (another way)""" + a = breaks[0] + b = breaks[-1] + K = coeffs.shape[0] + + saveshape = np.shape(xnew) + xnew = np.ravel(xnew) + res = np.empty_like(xnew) + mask = (xnew >= a) & (xnew <= b) + res[~mask] = fill + xx = xnew.compress(mask) + indxs = np.searchsorted(breaks, xx)-1 + indxs = indxs.clip(0, len(breaks)) + pp = coeffs + diff = xx - breaks.take(indxs) + V = np.vander(diff, N=K) + values = np.array([np.dot(V[k, :], pp[:, indxs[k]]) for k in range(len(xx))]) + res[mask] = values + res.shape = saveshape + return res + + +def _dpow(x, y, n): + """ + d^n (x**y) / dx^n + """ + if n < 0: + raise ValueError("invalid derivative order") + elif n > y: + return 0 + else: + return poch(y - n + 1, n) * x**(y - n) + + +def _ppoly2d_eval(c, xs, xnew, ynew, nu=None): + """ + Straightforward evaluation of 2-D piecewise polynomial + """ + if nu is None: + nu = (0, 0) + + out = np.empty((len(xnew),), dtype=c.dtype) + + nx, ny = c.shape[:2] + + for jout, (x, y) in enumerate(zip(xnew, ynew)): + if not ((xs[0][0] <= x <= xs[0][-1]) and + (xs[1][0] <= y <= xs[1][-1])): + out[jout] = np.nan + continue + + j1 = np.searchsorted(xs[0], x) - 1 + j2 = np.searchsorted(xs[1], y) - 1 + + s1 = x - xs[0][j1] + s2 = y - xs[1][j2] + + val = 0 + + for k1 in range(c.shape[0]): + for k2 in range(c.shape[1]): + val += (c[nx-k1-1,ny-k2-1,j1,j2] + * _dpow(s1, k1, nu[0]) + * _dpow(s2, k2, nu[1])) + + out[jout] = val + + return out + + +def _ppoly3d_eval(c, xs, xnew, ynew, znew, nu=None): + """ + Straightforward evaluation of 3-D piecewise polynomial + """ + if nu is None: + nu = (0, 0, 0) + + out = np.empty((len(xnew),), dtype=c.dtype) + + nx, ny, nz = c.shape[:3] + + for jout, (x, y, z) in enumerate(zip(xnew, ynew, znew)): + if not ((xs[0][0] <= x <= xs[0][-1]) and + (xs[1][0] <= y <= xs[1][-1]) and + (xs[2][0] <= z <= xs[2][-1])): + out[jout] = np.nan + continue + + j1 = np.searchsorted(xs[0], x) - 1 + j2 = np.searchsorted(xs[1], y) - 1 + j3 = np.searchsorted(xs[2], z) - 1 + + s1 = x - xs[0][j1] + s2 = y - xs[1][j2] + s3 = z - xs[2][j3] + + val = 0 + for k1 in range(c.shape[0]): + for k2 in range(c.shape[1]): + for k3 in range(c.shape[2]): + val += (c[nx-k1-1,ny-k2-1,nz-k3-1,j1,j2,j3] + * _dpow(s1, k1, nu[0]) + * _dpow(s2, k2, nu[1]) + * _dpow(s3, k3, nu[2])) + + out[jout] = val + + return out + + +def _ppoly4d_eval(c, xs, xnew, ynew, znew, unew, nu=None): + """ + Straightforward evaluation of 4-D piecewise polynomial + """ + if nu is None: + nu = (0, 0, 0, 0) + + out = np.empty((len(xnew),), dtype=c.dtype) + + mx, my, mz, mu = c.shape[:4] + + for jout, (x, y, z, u) in enumerate(zip(xnew, ynew, znew, unew)): + if not ((xs[0][0] <= x <= xs[0][-1]) and + (xs[1][0] <= y <= xs[1][-1]) and + (xs[2][0] <= z <= xs[2][-1]) and + (xs[3][0] <= u <= xs[3][-1])): + out[jout] = np.nan + continue + + j1 = np.searchsorted(xs[0], x) - 1 + j2 = np.searchsorted(xs[1], y) - 1 + j3 = np.searchsorted(xs[2], z) - 1 + j4 = np.searchsorted(xs[3], u) - 1 + + s1 = x - xs[0][j1] + s2 = y - xs[1][j2] + s3 = z - xs[2][j3] + s4 = u - xs[3][j4] + + val = 0 + for k1 in range(c.shape[0]): + for k2 in range(c.shape[1]): + for k3 in range(c.shape[2]): + for k4 in range(c.shape[3]): + val += (c[mx-k1-1,my-k2-1,mz-k3-1,mu-k4-1,j1,j2,j3,j4] + * _dpow(s1, k1, nu[0]) + * _dpow(s2, k2, nu[1]) + * _dpow(s3, k3, nu[2]) + * _dpow(s4, k4, nu[3])) + + out[jout] = val + + return out diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_ndgriddata.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_ndgriddata.py new file mode 100644 index 0000000000000000000000000000000000000000..e3e1ed8968ae5fd55e2f55d8a24c0ee2fa4ade45 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_ndgriddata.py @@ -0,0 +1,284 @@ +import numpy as np +from numpy.testing import assert_equal, assert_array_equal, assert_allclose +import pytest +from pytest import raises as assert_raises + +from scipy.interpolate import (griddata, NearestNDInterpolator, + LinearNDInterpolator, + CloughTocher2DInterpolator) + + +parametrize_interpolators = pytest.mark.parametrize( + "interpolator", [NearestNDInterpolator, LinearNDInterpolator, + CloughTocher2DInterpolator] +) + +class TestGriddata: + def test_fill_value(self): + x = [(0,0), (0,1), (1,0)] + y = [1, 2, 3] + + yi = griddata(x, y, [(1,1), (1,2), (0,0)], fill_value=-1) + assert_array_equal(yi, [-1., -1, 1]) + + yi = griddata(x, y, [(1,1), (1,2), (0,0)]) + assert_array_equal(yi, [np.nan, np.nan, 1]) + + def test_alternative_call(self): + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = (np.arange(x.shape[0], dtype=np.float64)[:,None] + + np.array([0,1])[None,:]) + + for method in ('nearest', 'linear', 'cubic'): + for rescale in (True, False): + msg = repr((method, rescale)) + yi = griddata((x[:,0], x[:,1]), y, (x[:,0], x[:,1]), method=method, + rescale=rescale) + assert_allclose(y, yi, atol=1e-14, err_msg=msg) + + def test_multivalue_2d(self): + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = (np.arange(x.shape[0], dtype=np.float64)[:,None] + + np.array([0,1])[None,:]) + + for method in ('nearest', 'linear', 'cubic'): + for rescale in (True, False): + msg = repr((method, rescale)) + yi = griddata(x, y, x, method=method, rescale=rescale) + assert_allclose(y, yi, atol=1e-14, err_msg=msg) + + def test_multipoint_2d(self): + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + + xi = x[:,None,:] + np.array([0,0,0])[None,:,None] + + for method in ('nearest', 'linear', 'cubic'): + for rescale in (True, False): + msg = repr((method, rescale)) + yi = griddata(x, y, xi, method=method, rescale=rescale) + + assert_equal(yi.shape, (5, 3), err_msg=msg) + assert_allclose(yi, np.tile(y[:,None], (1, 3)), + atol=1e-14, err_msg=msg) + + def test_complex_2d(self): + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 2j*y[::-1] + + xi = x[:,None,:] + np.array([0,0,0])[None,:,None] + + for method in ('nearest', 'linear', 'cubic'): + for rescale in (True, False): + msg = repr((method, rescale)) + yi = griddata(x, y, xi, method=method, rescale=rescale) + + assert_equal(yi.shape, (5, 3), err_msg=msg) + assert_allclose(yi, np.tile(y[:,None], (1, 3)), + atol=1e-14, err_msg=msg) + + def test_1d(self): + x = np.array([1, 2.5, 3, 4.5, 5, 6]) + y = np.array([1, 2, 0, 3.9, 2, 1]) + + for method in ('nearest', 'linear', 'cubic'): + assert_allclose(griddata(x, y, x, method=method), y, + err_msg=method, atol=1e-14) + assert_allclose(griddata(x.reshape(6, 1), y, x, method=method), y, + err_msg=method, atol=1e-14) + assert_allclose(griddata((x,), y, (x,), method=method), y, + err_msg=method, atol=1e-14) + + def test_1d_borders(self): + # Test for nearest neighbor case with xi outside + # the range of the values. + x = np.array([1, 2.5, 3, 4.5, 5, 6]) + y = np.array([1, 2, 0, 3.9, 2, 1]) + xi = np.array([0.9, 6.5]) + yi_should = np.array([1.0, 1.0]) + + method = 'nearest' + assert_allclose(griddata(x, y, xi, + method=method), yi_should, + err_msg=method, + atol=1e-14) + assert_allclose(griddata(x.reshape(6, 1), y, xi, + method=method), yi_should, + err_msg=method, + atol=1e-14) + assert_allclose(griddata((x, ), y, (xi, ), + method=method), yi_should, + err_msg=method, + atol=1e-14) + + def test_1d_unsorted(self): + x = np.array([2.5, 1, 4.5, 5, 6, 3]) + y = np.array([1, 2, 0, 3.9, 2, 1]) + + for method in ('nearest', 'linear', 'cubic'): + assert_allclose(griddata(x, y, x, method=method), y, + err_msg=method, atol=1e-10) + assert_allclose(griddata(x.reshape(6, 1), y, x, method=method), y, + err_msg=method, atol=1e-10) + assert_allclose(griddata((x,), y, (x,), method=method), y, + err_msg=method, atol=1e-10) + + def test_square_rescale_manual(self): + points = np.array([(0,0), (0,100), (10,100), (10,0), (1, 5)], dtype=np.float64) + points_rescaled = np.array([(0,0), (0,1), (1,1), (1,0), (0.1, 0.05)], + dtype=np.float64) + values = np.array([1., 2., -3., 5., 9.], dtype=np.float64) + + xx, yy = np.broadcast_arrays(np.linspace(0, 10, 14)[:,None], + np.linspace(0, 100, 14)[None,:]) + xx = xx.ravel() + yy = yy.ravel() + xi = np.array([xx, yy]).T.copy() + + for method in ('nearest', 'linear', 'cubic'): + msg = method + zi = griddata(points_rescaled, values, xi/np.array([10, 100.]), + method=method) + zi_rescaled = griddata(points, values, xi, method=method, + rescale=True) + assert_allclose(zi, zi_rescaled, err_msg=msg, + atol=1e-12) + + def test_xi_1d(self): + # Check that 1-D xi is interpreted as a coordinate + x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)], + dtype=np.float64) + y = np.arange(x.shape[0], dtype=np.float64) + y = y - 2j*y[::-1] + + xi = np.array([0.5, 0.5]) + + for method in ('nearest', 'linear', 'cubic'): + p1 = griddata(x, y, xi, method=method) + p2 = griddata(x, y, xi[None,:], method=method) + assert_allclose(p1, p2, err_msg=method) + + xi1 = np.array([0.5]) + xi3 = np.array([0.5, 0.5, 0.5]) + assert_raises(ValueError, griddata, x, y, xi1, + method=method) + assert_raises(ValueError, griddata, x, y, xi3, + method=method) + + +class TestNearestNDInterpolator: + def test_nearest_options(self): + # smoke test that NearestNDInterpolator accept cKDTree options + npts, nd = 4, 3 + x = np.arange(npts*nd).reshape((npts, nd)) + y = np.arange(npts) + nndi = NearestNDInterpolator(x, y) + + opts = {'balanced_tree': False, 'compact_nodes': False} + nndi_o = NearestNDInterpolator(x, y, tree_options=opts) + assert_allclose(nndi(x), nndi_o(x), atol=1e-14) + + def test_nearest_list_argument(self): + nd = np.array([[0, 0, 0, 0, 1, 0, 1], + [0, 0, 0, 0, 0, 1, 1], + [0, 0, 0, 0, 1, 1, 2]]) + d = nd[:, 3:] + + # z is np.array + NI = NearestNDInterpolator((d[0], d[1]), d[2]) + assert_array_equal(NI([0.1, 0.9], [0.1, 0.9]), [0, 2]) + + # z is list + NI = NearestNDInterpolator((d[0], d[1]), list(d[2])) + assert_array_equal(NI([0.1, 0.9], [0.1, 0.9]), [0, 2]) + + def test_nearest_query_options(self): + nd = np.array([[0, 0.5, 0, 1], + [0, 0, 0.5, 1], + [0, 1, 1, 2]]) + delta = 0.1 + query_points = [0 + delta, 1 + delta], [0 + delta, 1 + delta] + + # case 1 - query max_dist is smaller than + # the query points' nearest distance to nd. + NI = NearestNDInterpolator((nd[0], nd[1]), nd[2]) + distance_upper_bound = np.sqrt(delta ** 2 + delta ** 2) - 1e-7 + assert_array_equal(NI(query_points, distance_upper_bound=distance_upper_bound), + [np.nan, np.nan]) + + # case 2 - query p is inf, will return [0, 2] + distance_upper_bound = np.sqrt(delta ** 2 + delta ** 2) - 1e-7 + p = np.inf + assert_array_equal( + NI(query_points, distance_upper_bound=distance_upper_bound, p=p), + [0, 2] + ) + + # case 3 - query max_dist is larger, so should return non np.nan + distance_upper_bound = np.sqrt(delta ** 2 + delta ** 2) + 1e-7 + assert_array_equal( + NI(query_points, distance_upper_bound=distance_upper_bound), + [0, 2] + ) + + def test_nearest_query_valid_inputs(self): + nd = np.array([[0, 1, 0, 1], + [0, 0, 1, 1], + [0, 1, 1, 2]]) + NI = NearestNDInterpolator((nd[0], nd[1]), nd[2]) + with assert_raises(TypeError): + NI([0.5, 0.5], query_options="not a dictionary") + + +class TestNDInterpolators: + @parametrize_interpolators + def test_broadcastable_input(self, interpolator): + # input data + np.random.seed(0) + x = np.random.random(10) + y = np.random.random(10) + z = np.hypot(x, y) + + # x-y grid for interpolation + X = np.linspace(min(x), max(x)) + Y = np.linspace(min(y), max(y)) + X, Y = np.meshgrid(X, Y) + XY = np.vstack((X.ravel(), Y.ravel())).T + interp = interpolator(list(zip(x, y)), z) + # single array input + interp_points0 = interp(XY) + # tuple input + interp_points1 = interp((X, Y)) + interp_points2 = interp((X, 0.0)) + # broadcastable input + interp_points3 = interp(X, Y) + interp_points4 = interp(X, 0.0) + + assert_equal(interp_points0.size == + interp_points1.size == + interp_points2.size == + interp_points3.size == + interp_points4.size, True) + + @parametrize_interpolators + def test_read_only(self, interpolator): + # input data + np.random.seed(0) + xy = np.random.random((10, 2)) + x, y = xy[:, 0], xy[:, 1] + z = np.hypot(x, y) + + # interpolation points + XY = np.random.random((50, 2)) + + xy.setflags(write=False) + z.setflags(write=False) + XY.setflags(write=False) + + interp = interpolator(xy, z) + interp(XY) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_pade.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_pade.py new file mode 100644 index 0000000000000000000000000000000000000000..f58e01e5e730d2e5c4630f41933a0b77a17efc77 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_pade.py @@ -0,0 +1,104 @@ +from numpy.testing import (assert_array_equal, assert_array_almost_equal) +from scipy.interpolate import pade + +def test_pade_trivial(): + nump, denomp = pade([1.0], 0) + assert_array_equal(nump.c, [1.0]) + assert_array_equal(denomp.c, [1.0]) + + nump, denomp = pade([1.0], 0, 0) + assert_array_equal(nump.c, [1.0]) + assert_array_equal(denomp.c, [1.0]) + + +def test_pade_4term_exp(): + # First four Taylor coefficients of exp(x). + # Unlike poly1d, the first array element is the zero-order term. + an = [1.0, 1.0, 0.5, 1.0/6] + + nump, denomp = pade(an, 0) + assert_array_almost_equal(nump.c, [1.0/6, 0.5, 1.0, 1.0]) + assert_array_almost_equal(denomp.c, [1.0]) + + nump, denomp = pade(an, 1) + assert_array_almost_equal(nump.c, [1.0/6, 2.0/3, 1.0]) + assert_array_almost_equal(denomp.c, [-1.0/3, 1.0]) + + nump, denomp = pade(an, 2) + assert_array_almost_equal(nump.c, [1.0/3, 1.0]) + assert_array_almost_equal(denomp.c, [1.0/6, -2.0/3, 1.0]) + + nump, denomp = pade(an, 3) + assert_array_almost_equal(nump.c, [1.0]) + assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0]) + + # Testing inclusion of optional parameter + nump, denomp = pade(an, 0, 3) + assert_array_almost_equal(nump.c, [1.0/6, 0.5, 1.0, 1.0]) + assert_array_almost_equal(denomp.c, [1.0]) + + nump, denomp = pade(an, 1, 2) + assert_array_almost_equal(nump.c, [1.0/6, 2.0/3, 1.0]) + assert_array_almost_equal(denomp.c, [-1.0/3, 1.0]) + + nump, denomp = pade(an, 2, 1) + assert_array_almost_equal(nump.c, [1.0/3, 1.0]) + assert_array_almost_equal(denomp.c, [1.0/6, -2.0/3, 1.0]) + + nump, denomp = pade(an, 3, 0) + assert_array_almost_equal(nump.c, [1.0]) + assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0]) + + # Testing reducing array. + nump, denomp = pade(an, 0, 2) + assert_array_almost_equal(nump.c, [0.5, 1.0, 1.0]) + assert_array_almost_equal(denomp.c, [1.0]) + + nump, denomp = pade(an, 1, 1) + assert_array_almost_equal(nump.c, [1.0/2, 1.0]) + assert_array_almost_equal(denomp.c, [-1.0/2, 1.0]) + + nump, denomp = pade(an, 2, 0) + assert_array_almost_equal(nump.c, [1.0]) + assert_array_almost_equal(denomp.c, [1.0/2, -1.0, 1.0]) + + +def test_pade_ints(): + # Simple test sequences (one of ints, one of floats). + an_int = [1, 2, 3, 4] + an_flt = [1.0, 2.0, 3.0, 4.0] + + # Make sure integer arrays give the same result as float arrays with same values. + for i in range(0, len(an_int)): + for j in range(0, len(an_int) - i): + + # Create float and int pade approximation for given order. + nump_int, denomp_int = pade(an_int, i, j) + nump_flt, denomp_flt = pade(an_flt, i, j) + + # Check that they are the same. + assert_array_equal(nump_int.c, nump_flt.c) + assert_array_equal(denomp_int.c, denomp_flt.c) + + +def test_pade_complex(): + # Test sequence with known solutions - see page 6 of 10.1109/PESGM.2012.6344759. + # Variable x is parameter - these tests will work with any complex number. + x = 0.2 + 0.6j + an = [1.0, x, -x*x.conjugate(), x.conjugate()*(x**2) + x*(x.conjugate()**2), + -(x**3)*x.conjugate() - 3*(x*x.conjugate())**2 - x*(x.conjugate()**3)] + + nump, denomp = pade(an, 1, 1) + assert_array_almost_equal(nump.c, [x + x.conjugate(), 1.0]) + assert_array_almost_equal(denomp.c, [x.conjugate(), 1.0]) + + nump, denomp = pade(an, 1, 2) + assert_array_almost_equal(nump.c, [x**2, 2*x + x.conjugate(), 1.0]) + assert_array_almost_equal(denomp.c, [x + x.conjugate(), 1.0]) + + nump, denomp = pade(an, 2, 2) + assert_array_almost_equal( + nump.c, + [x**2 + x*x.conjugate() + x.conjugate()**2, 2*(x + x.conjugate()), 1.0] + ) + assert_array_almost_equal(denomp.c, [x.conjugate()**2, x + 2*x.conjugate(), 1.0]) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_polyint.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_polyint.py new file mode 100644 index 0000000000000000000000000000000000000000..31215b1e986a9fc57a3b0f18823bcc6ffd9e81f9 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_polyint.py @@ -0,0 +1,941 @@ +import warnings +import io +import numpy as np + +from numpy.testing import ( + assert_almost_equal, assert_array_equal, assert_array_almost_equal, + assert_allclose, assert_equal, assert_) +from pytest import raises as assert_raises +import pytest + +from scipy.interpolate import ( + KroghInterpolator, krogh_interpolate, + BarycentricInterpolator, barycentric_interpolate, + approximate_taylor_polynomial, CubicHermiteSpline, pchip, + PchipInterpolator, pchip_interpolate, Akima1DInterpolator, CubicSpline, + make_interp_spline) + + +def check_shape(interpolator_cls, x_shape, y_shape, deriv_shape=None, axis=0, + extra_args={}): + np.random.seed(1234) + + x = [-1, 0, 1, 2, 3, 4] + s = list(range(1, len(y_shape)+1)) + s.insert(axis % (len(y_shape)+1), 0) + y = np.random.rand(*((6,) + y_shape)).transpose(s) + + xi = np.zeros(x_shape) + if interpolator_cls is CubicHermiteSpline: + dydx = np.random.rand(*((6,) + y_shape)).transpose(s) + yi = interpolator_cls(x, y, dydx, axis=axis, **extra_args)(xi) + else: + yi = interpolator_cls(x, y, axis=axis, **extra_args)(xi) + + target_shape = ((deriv_shape or ()) + y.shape[:axis] + + x_shape + y.shape[axis:][1:]) + assert_equal(yi.shape, target_shape) + + # check it works also with lists + if x_shape and y.size > 0: + if interpolator_cls is CubicHermiteSpline: + interpolator_cls(list(x), list(y), list(dydx), axis=axis, + **extra_args)(list(xi)) + else: + interpolator_cls(list(x), list(y), axis=axis, + **extra_args)(list(xi)) + + # check also values + if xi.size > 0 and deriv_shape is None: + bs_shape = y.shape[:axis] + (1,)*len(x_shape) + y.shape[axis:][1:] + yv = y[((slice(None,),)*(axis % y.ndim)) + (1,)] + yv = yv.reshape(bs_shape) + + yi, y = np.broadcast_arrays(yi, yv) + assert_allclose(yi, y) + + +SHAPES = [(), (0,), (1,), (6, 2, 5)] + + +def test_shapes(): + + def spl_interp(x, y, axis): + return make_interp_spline(x, y, axis=axis) + + for ip in [KroghInterpolator, BarycentricInterpolator, CubicHermiteSpline, + pchip, Akima1DInterpolator, CubicSpline, spl_interp]: + for s1 in SHAPES: + for s2 in SHAPES: + for axis in range(-len(s2), len(s2)): + if ip != CubicSpline: + check_shape(ip, s1, s2, None, axis) + else: + for bc in ['natural', 'clamped']: + extra = {'bc_type': bc} + check_shape(ip, s1, s2, None, axis, extra) + +def test_derivs_shapes(): + for ip in [KroghInterpolator, BarycentricInterpolator]: + def interpolator_derivs(x, y, axis=0): + return ip(x, y, axis).derivatives + + for s1 in SHAPES: + for s2 in SHAPES: + for axis in range(-len(s2), len(s2)): + check_shape(interpolator_derivs, s1, s2, (6,), axis) + + +def test_deriv_shapes(): + def krogh_deriv(x, y, axis=0): + return KroghInterpolator(x, y, axis).derivative + + def bary_deriv(x, y, axis=0): + return BarycentricInterpolator(x, y, axis).derivative + + def pchip_deriv(x, y, axis=0): + return pchip(x, y, axis).derivative() + + def pchip_deriv2(x, y, axis=0): + return pchip(x, y, axis).derivative(2) + + def pchip_antideriv(x, y, axis=0): + return pchip(x, y, axis).antiderivative() + + def pchip_antideriv2(x, y, axis=0): + return pchip(x, y, axis).antiderivative(2) + + def pchip_deriv_inplace(x, y, axis=0): + class P(PchipInterpolator): + def __call__(self, x): + return PchipInterpolator.__call__(self, x, 1) + pass + return P(x, y, axis) + + def akima_deriv(x, y, axis=0): + return Akima1DInterpolator(x, y, axis).derivative() + + def akima_antideriv(x, y, axis=0): + return Akima1DInterpolator(x, y, axis).antiderivative() + + def cspline_deriv(x, y, axis=0): + return CubicSpline(x, y, axis).derivative() + + def cspline_antideriv(x, y, axis=0): + return CubicSpline(x, y, axis).antiderivative() + + def bspl_deriv(x, y, axis=0): + return make_interp_spline(x, y, axis=axis).derivative() + + def bspl_antideriv(x, y, axis=0): + return make_interp_spline(x, y, axis=axis).antiderivative() + + for ip in [krogh_deriv, bary_deriv, pchip_deriv, pchip_deriv2, pchip_deriv_inplace, + pchip_antideriv, pchip_antideriv2, akima_deriv, akima_antideriv, + cspline_deriv, cspline_antideriv, bspl_deriv, bspl_antideriv]: + for s1 in SHAPES: + for s2 in SHAPES: + for axis in range(-len(s2), len(s2)): + check_shape(ip, s1, s2, (), axis) + + +def test_complex(): + x = [1, 2, 3, 4] + y = [1, 2, 1j, 3] + + for ip in [KroghInterpolator, BarycentricInterpolator, CubicSpline]: + p = ip(x, y) + assert_allclose(y, p(x)) + + dydx = [0, -1j, 2, 3j] + p = CubicHermiteSpline(x, y, dydx) + assert_allclose(y, p(x)) + assert_allclose(dydx, p(x, 1)) + + +class TestKrogh: + def setup_method(self): + self.true_poly = np.polynomial.Polynomial([-4, 5, 1, 3, -2]) + self.test_xs = np.linspace(-1,1,100) + self.xs = np.linspace(-1,1,5) + self.ys = self.true_poly(self.xs) + + def test_lagrange(self): + P = KroghInterpolator(self.xs,self.ys) + assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs)) + + def test_scalar(self): + P = KroghInterpolator(self.xs,self.ys) + assert_almost_equal(self.true_poly(7),P(7)) + assert_almost_equal(self.true_poly(np.array(7)), P(np.array(7))) + + def test_derivatives(self): + P = KroghInterpolator(self.xs,self.ys) + D = P.derivatives(self.test_xs) + for i in range(D.shape[0]): + assert_almost_equal(self.true_poly.deriv(i)(self.test_xs), + D[i]) + + def test_low_derivatives(self): + P = KroghInterpolator(self.xs,self.ys) + D = P.derivatives(self.test_xs,len(self.xs)+2) + for i in range(D.shape[0]): + assert_almost_equal(self.true_poly.deriv(i)(self.test_xs), + D[i]) + + def test_derivative(self): + P = KroghInterpolator(self.xs,self.ys) + m = 10 + r = P.derivatives(self.test_xs,m) + for i in range(m): + assert_almost_equal(P.derivative(self.test_xs,i),r[i]) + + def test_high_derivative(self): + P = KroghInterpolator(self.xs,self.ys) + for i in range(len(self.xs), 2*len(self.xs)): + assert_almost_equal(P.derivative(self.test_xs,i), + np.zeros(len(self.test_xs))) + + def test_ndim_derivatives(self): + poly1 = self.true_poly + poly2 = np.polynomial.Polynomial([-2, 5, 3, -1]) + poly3 = np.polynomial.Polynomial([12, -3, 4, -5, 6]) + ys = np.stack((poly1(self.xs), poly2(self.xs), poly3(self.xs)), axis=-1) + + P = KroghInterpolator(self.xs, ys, axis=0) + D = P.derivatives(self.test_xs) + for i in range(D.shape[0]): + assert_allclose(D[i], + np.stack((poly1.deriv(i)(self.test_xs), + poly2.deriv(i)(self.test_xs), + poly3.deriv(i)(self.test_xs)), + axis=-1)) + + def test_ndim_derivative(self): + poly1 = self.true_poly + poly2 = np.polynomial.Polynomial([-2, 5, 3, -1]) + poly3 = np.polynomial.Polynomial([12, -3, 4, -5, 6]) + ys = np.stack((poly1(self.xs), poly2(self.xs), poly3(self.xs)), axis=-1) + + P = KroghInterpolator(self.xs, ys, axis=0) + for i in range(P.n): + assert_allclose(P.derivative(self.test_xs, i), + np.stack((poly1.deriv(i)(self.test_xs), + poly2.deriv(i)(self.test_xs), + poly3.deriv(i)(self.test_xs)), + axis=-1)) + + def test_hermite(self): + P = KroghInterpolator(self.xs,self.ys) + assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs)) + + def test_vector(self): + xs = [0, 1, 2] + ys = np.array([[0,1],[1,0],[2,1]]) + P = KroghInterpolator(xs,ys) + Pi = [KroghInterpolator(xs,ys[:,i]) for i in range(ys.shape[1])] + test_xs = np.linspace(-1,3,100) + assert_almost_equal(P(test_xs), + np.asarray([p(test_xs) for p in Pi]).T) + assert_almost_equal(P.derivatives(test_xs), + np.transpose(np.asarray([p.derivatives(test_xs) for p in Pi]), + (1,2,0))) + + def test_empty(self): + P = KroghInterpolator(self.xs,self.ys) + assert_array_equal(P([]), []) + + def test_shapes_scalarvalue(self): + P = KroghInterpolator(self.xs,self.ys) + assert_array_equal(np.shape(P(0)), ()) + assert_array_equal(np.shape(P(np.array(0))), ()) + assert_array_equal(np.shape(P([0])), (1,)) + assert_array_equal(np.shape(P([0,1])), (2,)) + + def test_shapes_scalarvalue_derivative(self): + P = KroghInterpolator(self.xs,self.ys) + n = P.n + assert_array_equal(np.shape(P.derivatives(0)), (n,)) + assert_array_equal(np.shape(P.derivatives(np.array(0))), (n,)) + assert_array_equal(np.shape(P.derivatives([0])), (n,1)) + assert_array_equal(np.shape(P.derivatives([0,1])), (n,2)) + + def test_shapes_vectorvalue(self): + P = KroghInterpolator(self.xs,np.outer(self.ys,np.arange(3))) + assert_array_equal(np.shape(P(0)), (3,)) + assert_array_equal(np.shape(P([0])), (1,3)) + assert_array_equal(np.shape(P([0,1])), (2,3)) + + def test_shapes_1d_vectorvalue(self): + P = KroghInterpolator(self.xs,np.outer(self.ys,[1])) + assert_array_equal(np.shape(P(0)), (1,)) + assert_array_equal(np.shape(P([0])), (1,1)) + assert_array_equal(np.shape(P([0,1])), (2,1)) + + def test_shapes_vectorvalue_derivative(self): + P = KroghInterpolator(self.xs,np.outer(self.ys,np.arange(3))) + n = P.n + assert_array_equal(np.shape(P.derivatives(0)), (n,3)) + assert_array_equal(np.shape(P.derivatives([0])), (n,1,3)) + assert_array_equal(np.shape(P.derivatives([0,1])), (n,2,3)) + + def test_wrapper(self): + P = KroghInterpolator(self.xs, self.ys) + ki = krogh_interpolate + assert_almost_equal(P(self.test_xs), ki(self.xs, self.ys, self.test_xs)) + assert_almost_equal(P.derivative(self.test_xs, 2), + ki(self.xs, self.ys, self.test_xs, der=2)) + assert_almost_equal(P.derivatives(self.test_xs, 2), + ki(self.xs, self.ys, self.test_xs, der=[0, 1])) + + def test_int_inputs(self): + # Check input args are cast correctly to floats, gh-3669 + x = [0, 234, 468, 702, 936, 1170, 1404, 2340, 3744, 6084, 8424, + 13104, 60000] + offset_cdf = np.array([-0.95, -0.86114777, -0.8147762, -0.64072425, + -0.48002351, -0.34925329, -0.26503107, + -0.13148093, -0.12988833, -0.12979296, + -0.12973574, -0.08582937, 0.05]) + f = KroghInterpolator(x, offset_cdf) + + assert_allclose(abs((f(x) - offset_cdf) / f.derivative(x, 1)), + 0, atol=1e-10) + + def test_derivatives_complex(self): + # regression test for gh-7381: krogh.derivatives(0) fails complex y + x, y = np.array([-1, -1, 0, 1, 1]), np.array([1, 1.0j, 0, -1, 1.0j]) + func = KroghInterpolator(x, y) + cmplx = func.derivatives(0) + + cmplx2 = (KroghInterpolator(x, y.real).derivatives(0) + + 1j*KroghInterpolator(x, y.imag).derivatives(0)) + assert_allclose(cmplx, cmplx2, atol=1e-15) + + def test_high_degree_warning(self): + with pytest.warns(UserWarning, match="40 degrees provided,"): + KroghInterpolator(np.arange(40), np.ones(40)) + + +class TestTaylor: + def test_exponential(self): + degree = 5 + p = approximate_taylor_polynomial(np.exp, 0, degree, 1, 15) + for i in range(degree+1): + assert_almost_equal(p(0),1) + p = p.deriv() + assert_almost_equal(p(0),0) + + +class TestBarycentric: + def setup_method(self): + self.true_poly = np.polynomial.Polynomial([-4, 5, 1, 3, -2]) + self.test_xs = np.linspace(-1, 1, 100) + self.xs = np.linspace(-1, 1, 5) + self.ys = self.true_poly(self.xs) + + def test_lagrange(self): + P = BarycentricInterpolator(self.xs, self.ys) + assert_allclose(P(self.test_xs), self.true_poly(self.test_xs)) + + def test_scalar(self): + P = BarycentricInterpolator(self.xs, self.ys) + assert_allclose(P(7), self.true_poly(7)) + assert_allclose(P(np.array(7)), self.true_poly(np.array(7))) + + def test_derivatives(self): + P = BarycentricInterpolator(self.xs, self.ys) + D = P.derivatives(self.test_xs) + for i in range(D.shape[0]): + assert_allclose(self.true_poly.deriv(i)(self.test_xs), D[i]) + + def test_low_derivatives(self): + P = BarycentricInterpolator(self.xs, self.ys) + D = P.derivatives(self.test_xs, len(self.xs)+2) + for i in range(D.shape[0]): + assert_allclose(self.true_poly.deriv(i)(self.test_xs), + D[i], + atol=1e-12) + + def test_derivative(self): + P = BarycentricInterpolator(self.xs, self.ys) + m = 10 + r = P.derivatives(self.test_xs, m) + for i in range(m): + assert_allclose(P.derivative(self.test_xs, i), r[i]) + + def test_high_derivative(self): + P = BarycentricInterpolator(self.xs, self.ys) + for i in range(len(self.xs), 5*len(self.xs)): + assert_allclose(P.derivative(self.test_xs, i), + np.zeros(len(self.test_xs))) + + def test_ndim_derivatives(self): + poly1 = self.true_poly + poly2 = np.polynomial.Polynomial([-2, 5, 3, -1]) + poly3 = np.polynomial.Polynomial([12, -3, 4, -5, 6]) + ys = np.stack((poly1(self.xs), poly2(self.xs), poly3(self.xs)), axis=-1) + + P = BarycentricInterpolator(self.xs, ys, axis=0) + D = P.derivatives(self.test_xs) + for i in range(D.shape[0]): + assert_allclose(D[i], + np.stack((poly1.deriv(i)(self.test_xs), + poly2.deriv(i)(self.test_xs), + poly3.deriv(i)(self.test_xs)), + axis=-1), + atol=1e-12) + + def test_ndim_derivative(self): + poly1 = self.true_poly + poly2 = np.polynomial.Polynomial([-2, 5, 3, -1]) + poly3 = np.polynomial.Polynomial([12, -3, 4, -5, 6]) + ys = np.stack((poly1(self.xs), poly2(self.xs), poly3(self.xs)), axis=-1) + + P = BarycentricInterpolator(self.xs, ys, axis=0) + for i in range(P.n): + assert_allclose(P.derivative(self.test_xs, i), + np.stack((poly1.deriv(i)(self.test_xs), + poly2.deriv(i)(self.test_xs), + poly3.deriv(i)(self.test_xs)), + axis=-1), + atol=1e-12) + + def test_delayed(self): + P = BarycentricInterpolator(self.xs) + P.set_yi(self.ys) + assert_almost_equal(self.true_poly(self.test_xs), P(self.test_xs)) + + def test_append(self): + P = BarycentricInterpolator(self.xs[:3], self.ys[:3]) + P.add_xi(self.xs[3:], self.ys[3:]) + assert_almost_equal(self.true_poly(self.test_xs), P(self.test_xs)) + + def test_vector(self): + xs = [0, 1, 2] + ys = np.array([[0, 1], [1, 0], [2, 1]]) + BI = BarycentricInterpolator + P = BI(xs, ys) + Pi = [BI(xs, ys[:, i]) for i in range(ys.shape[1])] + test_xs = np.linspace(-1, 3, 100) + assert_almost_equal(P(test_xs), + np.asarray([p(test_xs) for p in Pi]).T) + + def test_shapes_scalarvalue(self): + P = BarycentricInterpolator(self.xs, self.ys) + assert_array_equal(np.shape(P(0)), ()) + assert_array_equal(np.shape(P(np.array(0))), ()) + assert_array_equal(np.shape(P([0])), (1,)) + assert_array_equal(np.shape(P([0, 1])), (2,)) + + def test_shapes_scalarvalue_derivative(self): + P = BarycentricInterpolator(self.xs,self.ys) + n = P.n + assert_array_equal(np.shape(P.derivatives(0)), (n,)) + assert_array_equal(np.shape(P.derivatives(np.array(0))), (n,)) + assert_array_equal(np.shape(P.derivatives([0])), (n,1)) + assert_array_equal(np.shape(P.derivatives([0,1])), (n,2)) + + def test_shapes_vectorvalue(self): + P = BarycentricInterpolator(self.xs, np.outer(self.ys, np.arange(3))) + assert_array_equal(np.shape(P(0)), (3,)) + assert_array_equal(np.shape(P([0])), (1, 3)) + assert_array_equal(np.shape(P([0, 1])), (2, 3)) + + def test_shapes_1d_vectorvalue(self): + P = BarycentricInterpolator(self.xs, np.outer(self.ys, [1])) + assert_array_equal(np.shape(P(0)), (1,)) + assert_array_equal(np.shape(P([0])), (1, 1)) + assert_array_equal(np.shape(P([0,1])), (2, 1)) + + def test_shapes_vectorvalue_derivative(self): + P = BarycentricInterpolator(self.xs,np.outer(self.ys,np.arange(3))) + n = P.n + assert_array_equal(np.shape(P.derivatives(0)), (n,3)) + assert_array_equal(np.shape(P.derivatives([0])), (n,1,3)) + assert_array_equal(np.shape(P.derivatives([0,1])), (n,2,3)) + + def test_wrapper(self): + P = BarycentricInterpolator(self.xs, self.ys) + bi = barycentric_interpolate + assert_allclose(P(self.test_xs), bi(self.xs, self.ys, self.test_xs)) + assert_allclose(P.derivative(self.test_xs, 2), + bi(self.xs, self.ys, self.test_xs, der=2)) + assert_allclose(P.derivatives(self.test_xs, 2), + bi(self.xs, self.ys, self.test_xs, der=[0, 1])) + + def test_int_input(self): + x = 1000 * np.arange(1, 11) # np.prod(x[-1] - x[:-1]) overflows + y = np.arange(1, 11) + value = barycentric_interpolate(x, y, 1000 * 9.5) + assert_almost_equal(value, 9.5) + + def test_large_chebyshev(self): + # The weights for Chebyshev points of the second kind have analytically + # solvable weights. Naive calculation of barycentric weights will fail + # for large N because of numerical underflow and overflow. We test + # correctness for large N against analytical Chebyshev weights. + + # Without capacity scaling or permutation, n=800 fails, + # With just capacity scaling, n=1097 fails + # With both capacity scaling and random permutation, n=30000 succeeds + n = 1100 + j = np.arange(n + 1).astype(np.float64) + x = np.cos(j * np.pi / n) + + # See page 506 of Berrut and Trefethen 2004 for this formula + w = (-1) ** j + w[0] *= 0.5 + w[-1] *= 0.5 + + P = BarycentricInterpolator(x) + + # It's okay to have a constant scaling factor in the weights because it + # cancels out in the evaluation of the polynomial. + factor = P.wi[0] + assert_almost_equal(P.wi / (2 * factor), w) + + def test_warning(self): + # Test if the divide-by-zero warning is properly ignored when computing + # interpolated values equals to interpolation points + P = BarycentricInterpolator([0, 1], [1, 2]) + with np.errstate(divide='raise'): + yi = P(P.xi) + + # Check if the interpolated values match the input values + # at the nodes + assert_almost_equal(yi, P.yi.ravel()) + + def test_repeated_node(self): + # check that a repeated node raises a ValueError + # (computing the weights requires division by xi[i] - xi[j]) + xis = np.array([0.1, 0.5, 0.9, 0.5]) + ys = np.array([1, 2, 3, 4]) + with pytest.raises(ValueError, + match="Interpolation points xi must be distinct."): + BarycentricInterpolator(xis, ys) + + +class TestPCHIP: + def _make_random(self, npts=20): + np.random.seed(1234) + xi = np.sort(np.random.random(npts)) + yi = np.random.random(npts) + return pchip(xi, yi), xi, yi + + def test_overshoot(self): + # PCHIP should not overshoot + p, xi, yi = self._make_random() + for i in range(len(xi)-1): + x1, x2 = xi[i], xi[i+1] + y1, y2 = yi[i], yi[i+1] + if y1 > y2: + y1, y2 = y2, y1 + xp = np.linspace(x1, x2, 10) + yp = p(xp) + assert_(((y1 <= yp + 1e-15) & (yp <= y2 + 1e-15)).all()) + + def test_monotone(self): + # PCHIP should preserve monotonicty + p, xi, yi = self._make_random() + for i in range(len(xi)-1): + x1, x2 = xi[i], xi[i+1] + y1, y2 = yi[i], yi[i+1] + xp = np.linspace(x1, x2, 10) + yp = p(xp) + assert_(((y2-y1) * (yp[1:] - yp[:1]) > 0).all()) + + def test_cast(self): + # regression test for integer input data, see gh-3453 + data = np.array([[0, 4, 12, 27, 47, 60, 79, 87, 99, 100], + [-33, -33, -19, -2, 12, 26, 38, 45, 53, 55]]) + xx = np.arange(100) + curve = pchip(data[0], data[1])(xx) + + data1 = data * 1.0 + curve1 = pchip(data1[0], data1[1])(xx) + + assert_allclose(curve, curve1, atol=1e-14, rtol=1e-14) + + def test_nag(self): + # Example from NAG C implementation, + # http://nag.com/numeric/cl/nagdoc_cl25/html/e01/e01bec.html + # suggested in gh-5326 as a smoke test for the way the derivatives + # are computed (see also gh-3453) + dataStr = ''' + 7.99 0.00000E+0 + 8.09 0.27643E-4 + 8.19 0.43750E-1 + 8.70 0.16918E+0 + 9.20 0.46943E+0 + 10.00 0.94374E+0 + 12.00 0.99864E+0 + 15.00 0.99992E+0 + 20.00 0.99999E+0 + ''' + data = np.loadtxt(io.StringIO(dataStr)) + pch = pchip(data[:,0], data[:,1]) + + resultStr = ''' + 7.9900 0.0000 + 9.1910 0.4640 + 10.3920 0.9645 + 11.5930 0.9965 + 12.7940 0.9992 + 13.9950 0.9998 + 15.1960 0.9999 + 16.3970 1.0000 + 17.5980 1.0000 + 18.7990 1.0000 + 20.0000 1.0000 + ''' + result = np.loadtxt(io.StringIO(resultStr)) + assert_allclose(result[:,1], pch(result[:,0]), rtol=0., atol=5e-5) + + def test_endslopes(self): + # this is a smoke test for gh-3453: PCHIP interpolator should not + # set edge slopes to zero if the data do not suggest zero edge derivatives + x = np.array([0.0, 0.1, 0.25, 0.35]) + y1 = np.array([279.35, 0.5e3, 1.0e3, 2.5e3]) + y2 = np.array([279.35, 2.5e3, 1.50e3, 1.0e3]) + for pp in (pchip(x, y1), pchip(x, y2)): + for t in (x[0], x[-1]): + assert_(pp(t, 1) != 0) + + def test_all_zeros(self): + x = np.arange(10) + y = np.zeros_like(x) + + # this should work and not generate any warnings + with warnings.catch_warnings(): + warnings.filterwarnings('error') + pch = pchip(x, y) + + xx = np.linspace(0, 9, 101) + assert_equal(pch(xx), 0.) + + def test_two_points(self): + # regression test for gh-6222: pchip([0, 1], [0, 1]) fails because + # it tries to use a three-point scheme to estimate edge derivatives, + # while there are only two points available. + # Instead, it should construct a linear interpolator. + x = np.linspace(0, 1, 11) + p = pchip([0, 1], [0, 2]) + assert_allclose(p(x), 2*x, atol=1e-15) + + def test_pchip_interpolate(self): + assert_array_almost_equal( + pchip_interpolate([1,2,3], [4,5,6], [0.5], der=1), + [1.]) + + assert_array_almost_equal( + pchip_interpolate([1,2,3], [4,5,6], [0.5], der=0), + [3.5]) + + assert_array_almost_equal( + pchip_interpolate([1,2,3], [4,5,6], [0.5], der=[0, 1]), + [[3.5], [1]]) + + def test_roots(self): + # regression test for gh-6357: .roots method should work + p = pchip([0, 1], [-1, 1]) + r = p.roots() + assert_allclose(r, 0.5) + + +class TestCubicSpline: + @staticmethod + def check_correctness(S, bc_start='not-a-knot', bc_end='not-a-knot', + tol=1e-14): + """Check that spline coefficients satisfy the continuity and boundary + conditions.""" + x = S.x + c = S.c + dx = np.diff(x) + dx = dx.reshape([dx.shape[0]] + [1] * (c.ndim - 2)) + dxi = dx[:-1] + + # Check C2 continuity. + assert_allclose(c[3, 1:], c[0, :-1] * dxi**3 + c[1, :-1] * dxi**2 + + c[2, :-1] * dxi + c[3, :-1], rtol=tol, atol=tol) + assert_allclose(c[2, 1:], 3 * c[0, :-1] * dxi**2 + + 2 * c[1, :-1] * dxi + c[2, :-1], rtol=tol, atol=tol) + assert_allclose(c[1, 1:], 3 * c[0, :-1] * dxi + c[1, :-1], + rtol=tol, atol=tol) + + # Check that we found a parabola, the third derivative is 0. + if x.size == 3 and bc_start == 'not-a-knot' and bc_end == 'not-a-knot': + assert_allclose(c[0], 0, rtol=tol, atol=tol) + return + + # Check periodic boundary conditions. + if bc_start == 'periodic': + assert_allclose(S(x[0], 0), S(x[-1], 0), rtol=tol, atol=tol) + assert_allclose(S(x[0], 1), S(x[-1], 1), rtol=tol, atol=tol) + assert_allclose(S(x[0], 2), S(x[-1], 2), rtol=tol, atol=tol) + return + + # Check other boundary conditions. + if bc_start == 'not-a-knot': + if x.size == 2: + slope = (S(x[1]) - S(x[0])) / dx[0] + assert_allclose(S(x[0], 1), slope, rtol=tol, atol=tol) + else: + assert_allclose(c[0, 0], c[0, 1], rtol=tol, atol=tol) + elif bc_start == 'clamped': + assert_allclose(S(x[0], 1), 0, rtol=tol, atol=tol) + elif bc_start == 'natural': + assert_allclose(S(x[0], 2), 0, rtol=tol, atol=tol) + else: + order, value = bc_start + assert_allclose(S(x[0], order), value, rtol=tol, atol=tol) + + if bc_end == 'not-a-knot': + if x.size == 2: + slope = (S(x[1]) - S(x[0])) / dx[0] + assert_allclose(S(x[1], 1), slope, rtol=tol, atol=tol) + else: + assert_allclose(c[0, -1], c[0, -2], rtol=tol, atol=tol) + elif bc_end == 'clamped': + assert_allclose(S(x[-1], 1), 0, rtol=tol, atol=tol) + elif bc_end == 'natural': + assert_allclose(S(x[-1], 2), 0, rtol=2*tol, atol=2*tol) + else: + order, value = bc_end + assert_allclose(S(x[-1], order), value, rtol=tol, atol=tol) + + def check_all_bc(self, x, y, axis): + deriv_shape = list(y.shape) + del deriv_shape[axis] + first_deriv = np.empty(deriv_shape) + first_deriv.fill(2) + second_deriv = np.empty(deriv_shape) + second_deriv.fill(-1) + bc_all = [ + 'not-a-knot', + 'natural', + 'clamped', + (1, first_deriv), + (2, second_deriv) + ] + for bc in bc_all[:3]: + S = CubicSpline(x, y, axis=axis, bc_type=bc) + self.check_correctness(S, bc, bc) + + for bc_start in bc_all: + for bc_end in bc_all: + S = CubicSpline(x, y, axis=axis, bc_type=(bc_start, bc_end)) + self.check_correctness(S, bc_start, bc_end, tol=2e-14) + + def test_general(self): + x = np.array([-1, 0, 0.5, 2, 4, 4.5, 5.5, 9]) + y = np.array([0, -0.5, 2, 3, 2.5, 1, 1, 0.5]) + for n in [2, 3, x.size]: + self.check_all_bc(x[:n], y[:n], 0) + + Y = np.empty((2, n, 2)) + Y[0, :, 0] = y[:n] + Y[0, :, 1] = y[:n] - 1 + Y[1, :, 0] = y[:n] + 2 + Y[1, :, 1] = y[:n] + 3 + self.check_all_bc(x[:n], Y, 1) + + def test_periodic(self): + for n in [2, 3, 5]: + x = np.linspace(0, 2 * np.pi, n) + y = np.cos(x) + S = CubicSpline(x, y, bc_type='periodic') + self.check_correctness(S, 'periodic', 'periodic') + + Y = np.empty((2, n, 2)) + Y[0, :, 0] = y + Y[0, :, 1] = y + 2 + Y[1, :, 0] = y - 1 + Y[1, :, 1] = y + 5 + S = CubicSpline(x, Y, axis=1, bc_type='periodic') + self.check_correctness(S, 'periodic', 'periodic') + + def test_periodic_eval(self): + x = np.linspace(0, 2 * np.pi, 10) + y = np.cos(x) + S = CubicSpline(x, y, bc_type='periodic') + assert_almost_equal(S(1), S(1 + 2 * np.pi), decimal=15) + + def test_second_derivative_continuity_gh_11758(self): + # gh-11758: C2 continuity fail + x = np.array([0.9, 1.3, 1.9, 2.1, 2.6, 3.0, 3.9, 4.4, 4.7, 5.0, 6.0, + 7.0, 8.0, 9.2, 10.5, 11.3, 11.6, 12.0, 12.6, 13.0, 13.3]) + y = np.array([1.3, 1.5, 1.85, 2.1, 2.6, 2.7, 2.4, 2.15, 2.05, 2.1, + 2.25, 2.3, 2.25, 1.95, 1.4, 0.9, 0.7, 0.6, 0.5, 0.4, 1.3]) + S = CubicSpline(x, y, bc_type='periodic', extrapolate='periodic') + self.check_correctness(S, 'periodic', 'periodic') + + def test_three_points(self): + # gh-11758: Fails computing a_m2_m1 + # In this case, s (first derivatives) could be found manually by solving + # system of 2 linear equations. Due to solution of this system, + # s[i] = (h1m2 + h2m1) / (h1 + h2), where h1 = x[1] - x[0], h2 = x[2] - x[1], + # m1 = (y[1] - y[0]) / h1, m2 = (y[2] - y[1]) / h2 + x = np.array([1.0, 2.75, 3.0]) + y = np.array([1.0, 15.0, 1.0]) + S = CubicSpline(x, y, bc_type='periodic') + self.check_correctness(S, 'periodic', 'periodic') + assert_allclose(S.derivative(1)(x), np.array([-48.0, -48.0, -48.0])) + + def test_periodic_three_points_multidim(self): + # make sure one multidimensional interpolator does the same as multiple + # one-dimensional interpolators + x = np.array([0.0, 1.0, 3.0]) + y = np.array([[0.0, 1.0], [1.0, 0.0], [0.0, 1.0]]) + S = CubicSpline(x, y, bc_type="periodic") + self.check_correctness(S, 'periodic', 'periodic') + S0 = CubicSpline(x, y[:, 0], bc_type="periodic") + S1 = CubicSpline(x, y[:, 1], bc_type="periodic") + q = np.linspace(0, 2, 5) + assert_allclose(S(q)[:, 0], S0(q)) + assert_allclose(S(q)[:, 1], S1(q)) + + def test_dtypes(self): + x = np.array([0, 1, 2, 3], dtype=int) + y = np.array([-5, 2, 3, 1], dtype=int) + S = CubicSpline(x, y) + self.check_correctness(S) + + y = np.array([-1+1j, 0.0, 1-1j, 0.5-1.5j]) + S = CubicSpline(x, y) + self.check_correctness(S) + + S = CubicSpline(x, x ** 3, bc_type=("natural", (1, 2j))) + self.check_correctness(S, "natural", (1, 2j)) + + y = np.array([-5, 2, 3, 1]) + S = CubicSpline(x, y, bc_type=[(1, 2 + 0.5j), (2, 0.5 - 1j)]) + self.check_correctness(S, (1, 2 + 0.5j), (2, 0.5 - 1j)) + + def test_small_dx(self): + rng = np.random.RandomState(0) + x = np.sort(rng.uniform(size=100)) + y = 1e4 + rng.uniform(size=100) + S = CubicSpline(x, y) + self.check_correctness(S, tol=1e-13) + + def test_incorrect_inputs(self): + x = np.array([1, 2, 3, 4]) + y = np.array([1, 2, 3, 4]) + xc = np.array([1 + 1j, 2, 3, 4]) + xn = np.array([np.nan, 2, 3, 4]) + xo = np.array([2, 1, 3, 4]) + yn = np.array([np.nan, 2, 3, 4]) + y3 = [1, 2, 3] + x1 = [1] + y1 = [1] + + assert_raises(ValueError, CubicSpline, xc, y) + assert_raises(ValueError, CubicSpline, xn, y) + assert_raises(ValueError, CubicSpline, x, yn) + assert_raises(ValueError, CubicSpline, xo, y) + assert_raises(ValueError, CubicSpline, x, y3) + assert_raises(ValueError, CubicSpline, x[:, np.newaxis], y) + assert_raises(ValueError, CubicSpline, x1, y1) + + wrong_bc = [('periodic', 'clamped'), + ((2, 0), (3, 10)), + ((1, 0), ), + (0., 0.), + 'not-a-typo'] + + for bc_type in wrong_bc: + assert_raises(ValueError, CubicSpline, x, y, 0, bc_type, True) + + # Shapes mismatch when giving arbitrary derivative values: + Y = np.c_[y, y] + bc1 = ('clamped', (1, 0)) + bc2 = ('clamped', (1, [0, 0, 0])) + bc3 = ('clamped', (1, [[0, 0]])) + assert_raises(ValueError, CubicSpline, x, Y, 0, bc1, True) + assert_raises(ValueError, CubicSpline, x, Y, 0, bc2, True) + assert_raises(ValueError, CubicSpline, x, Y, 0, bc3, True) + + # periodic condition, y[-1] must be equal to y[0]: + assert_raises(ValueError, CubicSpline, x, y, 0, 'periodic', True) + + +def test_CubicHermiteSpline_correctness(): + x = [0, 2, 7] + y = [-1, 2, 3] + dydx = [0, 3, 7] + s = CubicHermiteSpline(x, y, dydx) + assert_allclose(s(x), y, rtol=1e-15) + assert_allclose(s(x, 1), dydx, rtol=1e-15) + + +def test_CubicHermiteSpline_error_handling(): + x = [1, 2, 3] + y = [0, 3, 5] + dydx = [1, -1, 2, 3] + assert_raises(ValueError, CubicHermiteSpline, x, y, dydx) + + dydx_with_nan = [1, 0, np.nan] + assert_raises(ValueError, CubicHermiteSpline, x, y, dydx_with_nan) + + +def test_roots_extrapolate_gh_11185(): + x = np.array([0.001, 0.002]) + y = np.array([1.66066935e-06, 1.10410807e-06]) + dy = np.array([-1.60061854, -1.600619]) + p = CubicHermiteSpline(x, y, dy) + + # roots(extrapolate=True) for a polynomial with a single interval + # should return all three real roots + r = p.roots(extrapolate=True) + assert_equal(p.c.shape[1], 1) + assert_equal(r.size, 3) + + +class TestZeroSizeArrays: + # regression tests for gh-17241 : CubicSpline et al must not segfault + # when y.size == 0 + # The two methods below are _almost_ the same, but not quite: + # one is for objects which have the `bc_type` argument (CubicSpline) + # and the other one is for those which do not (Pchip, Akima1D) + + @pytest.mark.parametrize('y', [np.zeros((10, 0, 5)), + np.zeros((10, 5, 0))]) + @pytest.mark.parametrize('bc_type', + ['not-a-knot', 'periodic', 'natural', 'clamped']) + @pytest.mark.parametrize('axis', [0, 1, 2]) + @pytest.mark.parametrize('cls', [make_interp_spline, CubicSpline]) + def test_zero_size(self, cls, y, bc_type, axis): + x = np.arange(10) + xval = np.arange(3) + + obj = cls(x, y, bc_type=bc_type) + assert obj(xval).size == 0 + assert obj(xval).shape == xval.shape + y.shape[1:] + + # Also check with an explicit non-default axis + yt = np.moveaxis(y, 0, axis) # (10, 0, 5) --> (0, 10, 5) if axis=1 etc + + obj = cls(x, yt, bc_type=bc_type, axis=axis) + sh = yt.shape[:axis] + (xval.size, ) + yt.shape[axis+1:] + assert obj(xval).size == 0 + assert obj(xval).shape == sh + + @pytest.mark.parametrize('y', [np.zeros((10, 0, 5)), + np.zeros((10, 5, 0))]) + @pytest.mark.parametrize('axis', [0, 1, 2]) + @pytest.mark.parametrize('cls', [PchipInterpolator, Akima1DInterpolator]) + def test_zero_size_2(self, cls, y, axis): + x = np.arange(10) + xval = np.arange(3) + + obj = cls(x, y) + assert obj(xval).size == 0 + assert obj(xval).shape == xval.shape + y.shape[1:] + + # Also check with an explicit non-default axis + yt = np.moveaxis(y, 0, axis) # (10, 0, 5) --> (0, 10, 5) if axis=1 etc + + obj = cls(x, yt, axis=axis) + sh = yt.shape[:axis] + (xval.size, ) + yt.shape[axis+1:] + assert obj(xval).size == 0 + assert obj(xval).shape == sh diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rbf.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rbf.py new file mode 100644 index 0000000000000000000000000000000000000000..418042c65a906430ddecc5dabd98af2777747184 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rbf.py @@ -0,0 +1,222 @@ +# Created by John Travers, Robert Hetland, 2007 +""" Test functions for rbf module """ + +import numpy as np +from numpy.testing import (assert_, assert_array_almost_equal, + assert_almost_equal) +from numpy import linspace, sin, cos, random, exp, allclose +from scipy.interpolate._rbf import Rbf + +FUNCTIONS = ('multiquadric', 'inverse multiquadric', 'gaussian', + 'cubic', 'quintic', 'thin-plate', 'linear') + + +def check_rbf1d_interpolation(function): + # Check that the Rbf function interpolates through the nodes (1D) + x = linspace(0,10,9) + y = sin(x) + rbf = Rbf(x, y, function=function) + yi = rbf(x) + assert_array_almost_equal(y, yi) + assert_almost_equal(rbf(float(x[0])), y[0]) + + +def check_rbf2d_interpolation(function): + # Check that the Rbf function interpolates through the nodes (2D). + x = random.rand(50,1)*4-2 + y = random.rand(50,1)*4-2 + z = x*exp(-x**2-1j*y**2) + rbf = Rbf(x, y, z, epsilon=2, function=function) + zi = rbf(x, y) + zi.shape = x.shape + assert_array_almost_equal(z, zi) + + +def check_rbf3d_interpolation(function): + # Check that the Rbf function interpolates through the nodes (3D). + x = random.rand(50, 1)*4 - 2 + y = random.rand(50, 1)*4 - 2 + z = random.rand(50, 1)*4 - 2 + d = x*exp(-x**2 - y**2) + rbf = Rbf(x, y, z, d, epsilon=2, function=function) + di = rbf(x, y, z) + di.shape = x.shape + assert_array_almost_equal(di, d) + + +def test_rbf_interpolation(): + for function in FUNCTIONS: + check_rbf1d_interpolation(function) + check_rbf2d_interpolation(function) + check_rbf3d_interpolation(function) + + +def check_2drbf1d_interpolation(function): + # Check that the 2-D Rbf function interpolates through the nodes (1D) + x = linspace(0, 10, 9) + y0 = sin(x) + y1 = cos(x) + y = np.vstack([y0, y1]).T + rbf = Rbf(x, y, function=function, mode='N-D') + yi = rbf(x) + assert_array_almost_equal(y, yi) + assert_almost_equal(rbf(float(x[0])), y[0]) + + +def check_2drbf2d_interpolation(function): + # Check that the 2-D Rbf function interpolates through the nodes (2D). + x = random.rand(50, ) * 4 - 2 + y = random.rand(50, ) * 4 - 2 + z0 = x * exp(-x ** 2 - 1j * y ** 2) + z1 = y * exp(-y ** 2 - 1j * x ** 2) + z = np.vstack([z0, z1]).T + rbf = Rbf(x, y, z, epsilon=2, function=function, mode='N-D') + zi = rbf(x, y) + zi.shape = z.shape + assert_array_almost_equal(z, zi) + + +def check_2drbf3d_interpolation(function): + # Check that the 2-D Rbf function interpolates through the nodes (3D). + x = random.rand(50, ) * 4 - 2 + y = random.rand(50, ) * 4 - 2 + z = random.rand(50, ) * 4 - 2 + d0 = x * exp(-x ** 2 - y ** 2) + d1 = y * exp(-y ** 2 - x ** 2) + d = np.vstack([d0, d1]).T + rbf = Rbf(x, y, z, d, epsilon=2, function=function, mode='N-D') + di = rbf(x, y, z) + di.shape = d.shape + assert_array_almost_equal(di, d) + + +def test_2drbf_interpolation(): + for function in FUNCTIONS: + check_2drbf1d_interpolation(function) + check_2drbf2d_interpolation(function) + check_2drbf3d_interpolation(function) + + +def check_rbf1d_regularity(function, atol): + # Check that the Rbf function approximates a smooth function well away + # from the nodes. + x = linspace(0, 10, 9) + y = sin(x) + rbf = Rbf(x, y, function=function) + xi = linspace(0, 10, 100) + yi = rbf(xi) + msg = "abs-diff: %f" % abs(yi - sin(xi)).max() + assert_(allclose(yi, sin(xi), atol=atol), msg) + + +def test_rbf_regularity(): + tolerances = { + 'multiquadric': 0.1, + 'inverse multiquadric': 0.15, + 'gaussian': 0.15, + 'cubic': 0.15, + 'quintic': 0.1, + 'thin-plate': 0.1, + 'linear': 0.2 + } + for function in FUNCTIONS: + check_rbf1d_regularity(function, tolerances.get(function, 1e-2)) + + +def check_2drbf1d_regularity(function, atol): + # Check that the 2-D Rbf function approximates a smooth function well away + # from the nodes. + x = linspace(0, 10, 9) + y0 = sin(x) + y1 = cos(x) + y = np.vstack([y0, y1]).T + rbf = Rbf(x, y, function=function, mode='N-D') + xi = linspace(0, 10, 100) + yi = rbf(xi) + msg = "abs-diff: %f" % abs(yi - np.vstack([sin(xi), cos(xi)]).T).max() + assert_(allclose(yi, np.vstack([sin(xi), cos(xi)]).T, atol=atol), msg) + + +def test_2drbf_regularity(): + tolerances = { + 'multiquadric': 0.1, + 'inverse multiquadric': 0.15, + 'gaussian': 0.15, + 'cubic': 0.15, + 'quintic': 0.1, + 'thin-plate': 0.15, + 'linear': 0.2 + } + for function in FUNCTIONS: + check_2drbf1d_regularity(function, tolerances.get(function, 1e-2)) + + +def check_rbf1d_stability(function): + # Check that the Rbf function with default epsilon is not subject + # to overshoot. Regression for issue #4523. + # + # Generate some data (fixed random seed hence deterministic) + np.random.seed(1234) + x = np.linspace(0, 10, 50) + z = x + 4.0 * np.random.randn(len(x)) + + rbf = Rbf(x, z, function=function) + xi = np.linspace(0, 10, 1000) + yi = rbf(xi) + + # subtract the linear trend and make sure there no spikes + assert_(np.abs(yi-xi).max() / np.abs(z-x).max() < 1.1) + +def test_rbf_stability(): + for function in FUNCTIONS: + check_rbf1d_stability(function) + + +def test_default_construction(): + # Check that the Rbf class can be constructed with the default + # multiquadric basis function. Regression test for ticket #1228. + x = linspace(0,10,9) + y = sin(x) + rbf = Rbf(x, y) + yi = rbf(x) + assert_array_almost_equal(y, yi) + + +def test_function_is_callable(): + # Check that the Rbf class can be constructed with function=callable. + x = linspace(0,10,9) + y = sin(x) + def linfunc(x): + return x + rbf = Rbf(x, y, function=linfunc) + yi = rbf(x) + assert_array_almost_equal(y, yi) + + +def test_two_arg_function_is_callable(): + # Check that the Rbf class can be constructed with a two argument + # function=callable. + def _func(self, r): + return self.epsilon + r + + x = linspace(0,10,9) + y = sin(x) + rbf = Rbf(x, y, function=_func) + yi = rbf(x) + assert_array_almost_equal(y, yi) + + +def test_rbf_epsilon_none(): + x = linspace(0, 10, 9) + y = sin(x) + Rbf(x, y, epsilon=None) + + +def test_rbf_epsilon_none_collinear(): + # Check that collinear points in one dimension doesn't cause an error + # due to epsilon = 0 + x = [1, 2, 3] + y = [4, 4, 4] + z = [5, 6, 7] + rbf = Rbf(x, y, z, epsilon=None) + assert_(rbf.epsilon > 0) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rbfinterp.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rbfinterp.py new file mode 100644 index 0000000000000000000000000000000000000000..188d5e1d8ad9b6e0d93ba0d02736dc11042dacaf --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rbfinterp.py @@ -0,0 +1,516 @@ +import pickle +import pytest +import numpy as np +from numpy.linalg import LinAlgError +from numpy.testing import assert_allclose, assert_array_equal +from scipy.stats.qmc import Halton +from scipy.spatial import cKDTree +from scipy.interpolate._rbfinterp import ( + _AVAILABLE, _SCALE_INVARIANT, _NAME_TO_MIN_DEGREE, _monomial_powers, + RBFInterpolator + ) +from scipy.interpolate import _rbfinterp_pythran + + +def _vandermonde(x, degree): + # Returns a matrix of monomials that span polynomials with the specified + # degree evaluated at x. + powers = _monomial_powers(x.shape[1], degree) + return _rbfinterp_pythran._polynomial_matrix(x, powers) + + +def _1d_test_function(x): + # Test function used in Wahba's "Spline Models for Observational Data". + # domain ~= (0, 3), range ~= (-1.0, 0.2) + x = x[:, 0] + y = 4.26*(np.exp(-x) - 4*np.exp(-2*x) + 3*np.exp(-3*x)) + return y + + +def _2d_test_function(x): + # Franke's test function. + # domain ~= (0, 1) X (0, 1), range ~= (0.0, 1.2) + x1, x2 = x[:, 0], x[:, 1] + term1 = 0.75 * np.exp(-(9*x1-2)**2/4 - (9*x2-2)**2/4) + term2 = 0.75 * np.exp(-(9*x1+1)**2/49 - (9*x2+1)/10) + term3 = 0.5 * np.exp(-(9*x1-7)**2/4 - (9*x2-3)**2/4) + term4 = -0.2 * np.exp(-(9*x1-4)**2 - (9*x2-7)**2) + y = term1 + term2 + term3 + term4 + return y + + +def _is_conditionally_positive_definite(kernel, m): + # Tests whether the kernel is conditionally positive definite of order m. + # See chapter 7 of Fasshauer's "Meshfree Approximation Methods with + # MATLAB". + nx = 10 + ntests = 100 + for ndim in [1, 2, 3, 4, 5]: + # Generate sample points with a Halton sequence to avoid samples that + # are too close to each other, which can make the matrix singular. + seq = Halton(ndim, scramble=False, seed=np.random.RandomState()) + for _ in range(ntests): + x = 2*seq.random(nx) - 1 + A = _rbfinterp_pythran._kernel_matrix(x, kernel) + P = _vandermonde(x, m - 1) + Q, R = np.linalg.qr(P, mode='complete') + # Q2 forms a basis spanning the space where P.T.dot(x) = 0. Project + # A onto this space, and then see if it is positive definite using + # the Cholesky decomposition. If not, then the kernel is not c.p.d. + # of order m. + Q2 = Q[:, P.shape[1]:] + B = Q2.T.dot(A).dot(Q2) + try: + np.linalg.cholesky(B) + except np.linalg.LinAlgError: + return False + + return True + + +# Sorting the parametrize arguments is necessary to avoid a parallelization +# issue described here: https://github.com/pytest-dev/pytest-xdist/issues/432. +@pytest.mark.parametrize('kernel', sorted(_AVAILABLE)) +def test_conditionally_positive_definite(kernel): + # Test if each kernel in _AVAILABLE is conditionally positive definite of + # order m, where m comes from _NAME_TO_MIN_DEGREE. This is a necessary + # condition for the smoothed RBF interpolant to be well-posed in general. + m = _NAME_TO_MIN_DEGREE.get(kernel, -1) + 1 + assert _is_conditionally_positive_definite(kernel, m) + + +class _TestRBFInterpolator: + @pytest.mark.parametrize('kernel', sorted(_SCALE_INVARIANT)) + def test_scale_invariance_1d(self, kernel): + # Verify that the functions in _SCALE_INVARIANT are insensitive to the + # shape parameter (when smoothing == 0) in 1d. + seq = Halton(1, scramble=False, seed=np.random.RandomState()) + x = 3*seq.random(50) + y = _1d_test_function(x) + xitp = 3*seq.random(50) + yitp1 = self.build(x, y, epsilon=1.0, kernel=kernel)(xitp) + yitp2 = self.build(x, y, epsilon=2.0, kernel=kernel)(xitp) + assert_allclose(yitp1, yitp2, atol=1e-8) + + @pytest.mark.parametrize('kernel', sorted(_SCALE_INVARIANT)) + def test_scale_invariance_2d(self, kernel): + # Verify that the functions in _SCALE_INVARIANT are insensitive to the + # shape parameter (when smoothing == 0) in 2d. + seq = Halton(2, scramble=False, seed=np.random.RandomState()) + x = seq.random(100) + y = _2d_test_function(x) + xitp = seq.random(100) + yitp1 = self.build(x, y, epsilon=1.0, kernel=kernel)(xitp) + yitp2 = self.build(x, y, epsilon=2.0, kernel=kernel)(xitp) + assert_allclose(yitp1, yitp2, atol=1e-8) + + @pytest.mark.parametrize('kernel', sorted(_AVAILABLE)) + def test_extreme_domains(self, kernel): + # Make sure the interpolant remains numerically stable for very + # large/small domains. + seq = Halton(2, scramble=False, seed=np.random.RandomState()) + scale = 1e50 + shift = 1e55 + + x = seq.random(100) + y = _2d_test_function(x) + xitp = seq.random(100) + + if kernel in _SCALE_INVARIANT: + yitp1 = self.build(x, y, kernel=kernel)(xitp) + yitp2 = self.build( + x*scale + shift, y, + kernel=kernel + )(xitp*scale + shift) + else: + yitp1 = self.build(x, y, epsilon=5.0, kernel=kernel)(xitp) + yitp2 = self.build( + x*scale + shift, y, + epsilon=5.0/scale, + kernel=kernel + )(xitp*scale + shift) + + assert_allclose(yitp1, yitp2, atol=1e-8) + + def test_polynomial_reproduction(self): + # If the observed data comes from a polynomial, then the interpolant + # should be able to reproduce the polynomial exactly, provided that + # `degree` is sufficiently high. + rng = np.random.RandomState(0) + seq = Halton(2, scramble=False, seed=rng) + degree = 3 + + x = seq.random(50) + xitp = seq.random(50) + + P = _vandermonde(x, degree) + Pitp = _vandermonde(xitp, degree) + + poly_coeffs = rng.normal(0.0, 1.0, P.shape[1]) + + y = P.dot(poly_coeffs) + yitp1 = Pitp.dot(poly_coeffs) + yitp2 = self.build(x, y, degree=degree)(xitp) + + assert_allclose(yitp1, yitp2, atol=1e-8) + + @pytest.mark.slow + def test_chunking(self, monkeypatch): + # If the observed data comes from a polynomial, then the interpolant + # should be able to reproduce the polynomial exactly, provided that + # `degree` is sufficiently high. + rng = np.random.RandomState(0) + seq = Halton(2, scramble=False, seed=rng) + degree = 3 + + largeN = 1000 + 33 + # this is large to check that chunking of the RBFInterpolator is tested + x = seq.random(50) + xitp = seq.random(largeN) + + P = _vandermonde(x, degree) + Pitp = _vandermonde(xitp, degree) + + poly_coeffs = rng.normal(0.0, 1.0, P.shape[1]) + + y = P.dot(poly_coeffs) + yitp1 = Pitp.dot(poly_coeffs) + interp = self.build(x, y, degree=degree) + ce_real = interp._chunk_evaluator + + def _chunk_evaluator(*args, **kwargs): + kwargs.update(memory_budget=100) + return ce_real(*args, **kwargs) + + monkeypatch.setattr(interp, '_chunk_evaluator', _chunk_evaluator) + yitp2 = interp(xitp) + assert_allclose(yitp1, yitp2, atol=1e-8) + + def test_vector_data(self): + # Make sure interpolating a vector field is the same as interpolating + # each component separately. + seq = Halton(2, scramble=False, seed=np.random.RandomState()) + + x = seq.random(100) + xitp = seq.random(100) + + y = np.array([_2d_test_function(x), + _2d_test_function(x[:, ::-1])]).T + + yitp1 = self.build(x, y)(xitp) + yitp2 = self.build(x, y[:, 0])(xitp) + yitp3 = self.build(x, y[:, 1])(xitp) + + assert_allclose(yitp1[:, 0], yitp2) + assert_allclose(yitp1[:, 1], yitp3) + + def test_complex_data(self): + # Interpolating complex input should be the same as interpolating the + # real and complex components. + seq = Halton(2, scramble=False, seed=np.random.RandomState()) + + x = seq.random(100) + xitp = seq.random(100) + + y = _2d_test_function(x) + 1j*_2d_test_function(x[:, ::-1]) + + yitp1 = self.build(x, y)(xitp) + yitp2 = self.build(x, y.real)(xitp) + yitp3 = self.build(x, y.imag)(xitp) + + assert_allclose(yitp1.real, yitp2) + assert_allclose(yitp1.imag, yitp3) + + @pytest.mark.parametrize('kernel', sorted(_AVAILABLE)) + def test_interpolation_misfit_1d(self, kernel): + # Make sure that each kernel, with its default `degree` and an + # appropriate `epsilon`, does a good job at interpolation in 1d. + seq = Halton(1, scramble=False, seed=np.random.RandomState()) + + x = 3*seq.random(50) + xitp = 3*seq.random(50) + + y = _1d_test_function(x) + ytrue = _1d_test_function(xitp) + yitp = self.build(x, y, epsilon=5.0, kernel=kernel)(xitp) + + mse = np.mean((yitp - ytrue)**2) + assert mse < 1.0e-4 + + @pytest.mark.parametrize('kernel', sorted(_AVAILABLE)) + def test_interpolation_misfit_2d(self, kernel): + # Make sure that each kernel, with its default `degree` and an + # appropriate `epsilon`, does a good job at interpolation in 2d. + seq = Halton(2, scramble=False, seed=np.random.RandomState()) + + x = seq.random(100) + xitp = seq.random(100) + + y = _2d_test_function(x) + ytrue = _2d_test_function(xitp) + yitp = self.build(x, y, epsilon=5.0, kernel=kernel)(xitp) + + mse = np.mean((yitp - ytrue)**2) + assert mse < 2.0e-4 + + @pytest.mark.parametrize('kernel', sorted(_AVAILABLE)) + def test_smoothing_misfit(self, kernel): + # Make sure we can find a smoothing parameter for each kernel that + # removes a sufficient amount of noise. + rng = np.random.RandomState(0) + seq = Halton(1, scramble=False, seed=rng) + + noise = 0.2 + rmse_tol = 0.1 + smoothing_range = 10**np.linspace(-4, 1, 20) + + x = 3*seq.random(100) + y = _1d_test_function(x) + rng.normal(0.0, noise, (100,)) + ytrue = _1d_test_function(x) + rmse_within_tol = False + for smoothing in smoothing_range: + ysmooth = self.build( + x, y, + epsilon=1.0, + smoothing=smoothing, + kernel=kernel)(x) + rmse = np.sqrt(np.mean((ysmooth - ytrue)**2)) + if rmse < rmse_tol: + rmse_within_tol = True + break + + assert rmse_within_tol + + def test_array_smoothing(self): + # Test using an array for `smoothing` to give less weight to a known + # outlier. + rng = np.random.RandomState(0) + seq = Halton(1, scramble=False, seed=rng) + degree = 2 + + x = seq.random(50) + P = _vandermonde(x, degree) + poly_coeffs = rng.normal(0.0, 1.0, P.shape[1]) + y = P.dot(poly_coeffs) + y_with_outlier = np.copy(y) + y_with_outlier[10] += 1.0 + smoothing = np.zeros((50,)) + smoothing[10] = 1000.0 + yitp = self.build(x, y_with_outlier, smoothing=smoothing)(x) + # Should be able to reproduce the uncorrupted data almost exactly. + assert_allclose(yitp, y, atol=1e-4) + + def test_inconsistent_x_dimensions_error(self): + # ValueError should be raised if the observation points and evaluation + # points have a different number of dimensions. + y = Halton(2, scramble=False, seed=np.random.RandomState()).random(10) + d = _2d_test_function(y) + x = Halton(1, scramble=False, seed=np.random.RandomState()).random(10) + match = 'Expected the second axis of `x`' + with pytest.raises(ValueError, match=match): + self.build(y, d)(x) + + def test_inconsistent_d_length_error(self): + y = np.linspace(0, 1, 5)[:, None] + d = np.zeros(1) + match = 'Expected the first axis of `d`' + with pytest.raises(ValueError, match=match): + self.build(y, d) + + def test_y_not_2d_error(self): + y = np.linspace(0, 1, 5) + d = np.zeros(5) + match = '`y` must be a 2-dimensional array.' + with pytest.raises(ValueError, match=match): + self.build(y, d) + + def test_inconsistent_smoothing_length_error(self): + y = np.linspace(0, 1, 5)[:, None] + d = np.zeros(5) + smoothing = np.ones(1) + match = 'Expected `smoothing` to be' + with pytest.raises(ValueError, match=match): + self.build(y, d, smoothing=smoothing) + + def test_invalid_kernel_name_error(self): + y = np.linspace(0, 1, 5)[:, None] + d = np.zeros(5) + match = '`kernel` must be one of' + with pytest.raises(ValueError, match=match): + self.build(y, d, kernel='test') + + def test_epsilon_not_specified_error(self): + y = np.linspace(0, 1, 5)[:, None] + d = np.zeros(5) + for kernel in _AVAILABLE: + if kernel in _SCALE_INVARIANT: + continue + + match = '`epsilon` must be specified' + with pytest.raises(ValueError, match=match): + self.build(y, d, kernel=kernel) + + def test_x_not_2d_error(self): + y = np.linspace(0, 1, 5)[:, None] + x = np.linspace(0, 1, 5) + d = np.zeros(5) + match = '`x` must be a 2-dimensional array.' + with pytest.raises(ValueError, match=match): + self.build(y, d)(x) + + def test_not_enough_observations_error(self): + y = np.linspace(0, 1, 1)[:, None] + d = np.zeros(1) + match = 'At least 2 data points are required' + with pytest.raises(ValueError, match=match): + self.build(y, d, kernel='thin_plate_spline') + + def test_degree_warning(self): + y = np.linspace(0, 1, 5)[:, None] + d = np.zeros(5) + for kernel, deg in _NAME_TO_MIN_DEGREE.items(): + # Only test for kernels that its minimum degree is not 0. + if deg >= 1: + match = f'`degree` should not be below {deg}' + with pytest.warns(Warning, match=match): + self.build(y, d, epsilon=1.0, kernel=kernel, degree=deg-1) + + def test_minus_one_degree(self): + # Make sure a degree of -1 is accepted without any warning. + y = np.linspace(0, 1, 5)[:, None] + d = np.zeros(5) + for kernel, _ in _NAME_TO_MIN_DEGREE.items(): + self.build(y, d, epsilon=1.0, kernel=kernel, degree=-1) + + def test_rank_error(self): + # An error should be raised when `kernel` is "thin_plate_spline" and + # observations are 2-D and collinear. + y = np.array([[2.0, 0.0], [1.0, 0.0], [0.0, 0.0]]) + d = np.array([0.0, 0.0, 0.0]) + match = 'does not have full column rank' + with pytest.raises(LinAlgError, match=match): + self.build(y, d, kernel='thin_plate_spline')(y) + + def test_single_point(self): + # Make sure interpolation still works with only one point (in 1, 2, and + # 3 dimensions). + for dim in [1, 2, 3]: + y = np.zeros((1, dim)) + d = np.ones((1,)) + f = self.build(y, d, kernel='linear')(y) + assert_allclose(d, f) + + def test_pickleable(self): + # Make sure we can pickle and unpickle the interpolant without any + # changes in the behavior. + seq = Halton(1, scramble=False, seed=np.random.RandomState(2305982309)) + + x = 3*seq.random(50) + xitp = 3*seq.random(50) + + y = _1d_test_function(x) + + interp = self.build(x, y) + + yitp1 = interp(xitp) + yitp2 = pickle.loads(pickle.dumps(interp))(xitp) + + assert_array_equal(yitp1, yitp2) + + +class TestRBFInterpolatorNeighborsNone(_TestRBFInterpolator): + def build(self, *args, **kwargs): + return RBFInterpolator(*args, **kwargs) + + def test_smoothing_limit_1d(self): + # For large smoothing parameters, the interpolant should approach a + # least squares fit of a polynomial with the specified degree. + seq = Halton(1, scramble=False, seed=np.random.RandomState()) + + degree = 3 + smoothing = 1e8 + + x = 3*seq.random(50) + xitp = 3*seq.random(50) + + y = _1d_test_function(x) + + yitp1 = self.build( + x, y, + degree=degree, + smoothing=smoothing + )(xitp) + + P = _vandermonde(x, degree) + Pitp = _vandermonde(xitp, degree) + yitp2 = Pitp.dot(np.linalg.lstsq(P, y, rcond=None)[0]) + + assert_allclose(yitp1, yitp2, atol=1e-8) + + def test_smoothing_limit_2d(self): + # For large smoothing parameters, the interpolant should approach a + # least squares fit of a polynomial with the specified degree. + seq = Halton(2, scramble=False, seed=np.random.RandomState()) + + degree = 3 + smoothing = 1e8 + + x = seq.random(100) + xitp = seq.random(100) + + y = _2d_test_function(x) + + yitp1 = self.build( + x, y, + degree=degree, + smoothing=smoothing + )(xitp) + + P = _vandermonde(x, degree) + Pitp = _vandermonde(xitp, degree) + yitp2 = Pitp.dot(np.linalg.lstsq(P, y, rcond=None)[0]) + + assert_allclose(yitp1, yitp2, atol=1e-8) + + +class TestRBFInterpolatorNeighbors20(_TestRBFInterpolator): + # RBFInterpolator using 20 nearest neighbors. + def build(self, *args, **kwargs): + return RBFInterpolator(*args, **kwargs, neighbors=20) + + def test_equivalent_to_rbf_interpolator(self): + seq = Halton(2, scramble=False, seed=np.random.RandomState()) + + x = seq.random(100) + xitp = seq.random(100) + + y = _2d_test_function(x) + + yitp1 = self.build(x, y)(xitp) + + yitp2 = [] + tree = cKDTree(x) + for xi in xitp: + _, nbr = tree.query(xi, 20) + yitp2.append(RBFInterpolator(x[nbr], y[nbr])(xi[None])[0]) + + assert_allclose(yitp1, yitp2, atol=1e-8) + + +class TestRBFInterpolatorNeighborsInf(TestRBFInterpolatorNeighborsNone): + # RBFInterpolator using neighbors=np.inf. This should give exactly the same + # results as neighbors=None, but it will be slower. + def build(self, *args, **kwargs): + return RBFInterpolator(*args, **kwargs, neighbors=np.inf) + + def test_equivalent_to_rbf_interpolator(self): + seq = Halton(1, scramble=False, seed=np.random.RandomState()) + + x = 3*seq.random(50) + xitp = 3*seq.random(50) + + y = _1d_test_function(x) + yitp1 = self.build(x, y)(xitp) + yitp2 = RBFInterpolator(x, y)(xitp) + + assert_allclose(yitp1, yitp2, atol=1e-8) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rgi.py b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rgi.py new file mode 100644 index 0000000000000000000000000000000000000000..5503b39dc67eb3c1d50e338ac26708095aff55d6 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/interpolate/tests/test_rgi.py @@ -0,0 +1,1111 @@ +import itertools + +import pytest +import numpy as np + +from numpy.testing import (assert_allclose, assert_equal, assert_warns, + assert_array_almost_equal, assert_array_equal) +from pytest import raises as assert_raises + +from scipy.interpolate import (RegularGridInterpolator, interpn, + RectBivariateSpline, + NearestNDInterpolator, LinearNDInterpolator) + +from scipy.sparse._sputils import matrix +from scipy._lib._util import ComplexWarning + + +parametrize_rgi_interp_methods = pytest.mark.parametrize( + "method", RegularGridInterpolator._ALL_METHODS +) + +class TestRegularGridInterpolator: + def _get_sample_4d(self): + # create a 4-D grid of 3 points in each dimension + points = [(0., .5, 1.)] * 4 + values = np.asarray([0., .5, 1.]) + values0 = values[:, np.newaxis, np.newaxis, np.newaxis] + values1 = values[np.newaxis, :, np.newaxis, np.newaxis] + values2 = values[np.newaxis, np.newaxis, :, np.newaxis] + values3 = values[np.newaxis, np.newaxis, np.newaxis, :] + values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) + return points, values + + def _get_sample_4d_2(self): + # create another 4-D grid of 3 points in each dimension + points = [(0., .5, 1.)] * 2 + [(0., 5., 10.)] * 2 + values = np.asarray([0., .5, 1.]) + values0 = values[:, np.newaxis, np.newaxis, np.newaxis] + values1 = values[np.newaxis, :, np.newaxis, np.newaxis] + values2 = values[np.newaxis, np.newaxis, :, np.newaxis] + values3 = values[np.newaxis, np.newaxis, np.newaxis, :] + values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) + return points, values + + def _get_sample_4d_3(self): + # create another 4-D grid of 7 points in each dimension + points = [(0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0)] * 4 + values = np.asarray([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0]) + values0 = values[:, np.newaxis, np.newaxis, np.newaxis] + values1 = values[np.newaxis, :, np.newaxis, np.newaxis] + values2 = values[np.newaxis, np.newaxis, :, np.newaxis] + values3 = values[np.newaxis, np.newaxis, np.newaxis, :] + values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) + return points, values + + def _get_sample_4d_4(self): + # create another 4-D grid of 2 points in each dimension + points = [(0.0, 1.0)] * 4 + values = np.asarray([0.0, 1.0]) + values0 = values[:, np.newaxis, np.newaxis, np.newaxis] + values1 = values[np.newaxis, :, np.newaxis, np.newaxis] + values2 = values[np.newaxis, np.newaxis, :, np.newaxis] + values3 = values[np.newaxis, np.newaxis, np.newaxis, :] + values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) + return points, values + + @parametrize_rgi_interp_methods + def test_list_input(self, method): + points, values = self._get_sample_4d_3() + + sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], + [0.5, 0.5, .5, .5]]) + + interp = RegularGridInterpolator(points, + values.tolist(), + method=method) + v1 = interp(sample.tolist()) + interp = RegularGridInterpolator(points, + values, + method=method) + v2 = interp(sample) + assert_allclose(v1, v2) + + @pytest.mark.parametrize('method', ['cubic', 'quintic', 'pchip']) + def test_spline_dim_error(self, method): + points, values = self._get_sample_4d_4() + match = "points in dimension" + + # Check error raise when creating interpolator + with pytest.raises(ValueError, match=match): + RegularGridInterpolator(points, values, method=method) + + # Check error raise when creating interpolator + interp = RegularGridInterpolator(points, values) + sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], + [0.5, 0.5, .5, .5]]) + with pytest.raises(ValueError, match=match): + interp(sample, method=method) + + @pytest.mark.parametrize( + "points_values, sample", + [ + ( + _get_sample_4d, + np.asarray( + [[0.1, 0.1, 1.0, 0.9], + [0.2, 0.1, 0.45, 0.8], + [0.5, 0.5, 0.5, 0.5]] + ), + ), + (_get_sample_4d_2, np.asarray([0.1, 0.1, 10.0, 9.0])), + ], + ) + def test_linear_and_slinear_close(self, points_values, sample): + points, values = points_values(self) + interp = RegularGridInterpolator(points, values, method="linear") + v1 = interp(sample) + interp = RegularGridInterpolator(points, values, method="slinear") + v2 = interp(sample) + assert_allclose(v1, v2) + + def test_derivatives(self): + points, values = self._get_sample_4d() + sample = np.array([[0.1 , 0.1 , 1. , 0.9 ], + [0.2 , 0.1 , 0.45, 0.8 ], + [0.5 , 0.5 , 0.5 , 0.5 ]]) + interp = RegularGridInterpolator(points, values, method="slinear") + + with assert_raises(ValueError): + # wrong number of derivatives (need 4) + interp(sample, nu=1) + + assert_allclose(interp(sample, nu=(1, 0, 0, 0)), + [1, 1, 1], atol=1e-15) + assert_allclose(interp(sample, nu=(0, 1, 0, 0)), + [10, 10, 10], atol=1e-15) + + # 2nd derivatives of a linear function are zero + assert_allclose(interp(sample, nu=(0, 1, 1, 0)), + [0, 0, 0], atol=1e-12) + + @parametrize_rgi_interp_methods + def test_complex(self, method): + if method == "pchip": + pytest.skip("pchip does not make sense for complex data") + points, values = self._get_sample_4d_3() + values = values - 2j*values + sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], + [0.5, 0.5, .5, .5]]) + + interp = RegularGridInterpolator(points, values, method=method) + rinterp = RegularGridInterpolator(points, values.real, method=method) + iinterp = RegularGridInterpolator(points, values.imag, method=method) + + v1 = interp(sample) + v2 = rinterp(sample) + 1j*iinterp(sample) + assert_allclose(v1, v2) + + def test_cubic_vs_pchip(self): + x, y = [1, 2, 3, 4], [1, 2, 3, 4] + xg, yg = np.meshgrid(x, y, indexing='ij') + + values = (lambda x, y: x**4 * y**4)(xg, yg) + cubic = RegularGridInterpolator((x, y), values, method='cubic') + pchip = RegularGridInterpolator((x, y), values, method='pchip') + + vals_cubic = cubic([1.5, 2]) + vals_pchip = pchip([1.5, 2]) + assert not np.allclose(vals_cubic, vals_pchip, atol=1e-14, rtol=0) + + def test_linear_xi1d(self): + points, values = self._get_sample_4d_2() + interp = RegularGridInterpolator(points, values) + sample = np.asarray([0.1, 0.1, 10., 9.]) + wanted = 1001.1 + assert_array_almost_equal(interp(sample), wanted) + + def test_linear_xi3d(self): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values) + sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], + [0.5, 0.5, .5, .5]]) + wanted = np.asarray([1001.1, 846.2, 555.5]) + assert_array_almost_equal(interp(sample), wanted) + + @pytest.mark.parametrize( + "sample, wanted", + [ + (np.asarray([0.1, 0.1, 0.9, 0.9]), 1100.0), + (np.asarray([0.1, 0.1, 0.1, 0.1]), 0.0), + (np.asarray([0.0, 0.0, 0.0, 0.0]), 0.0), + (np.asarray([1.0, 1.0, 1.0, 1.0]), 1111.0), + (np.asarray([0.1, 0.4, 0.6, 0.9]), 1055.0), + ], + ) + def test_nearest(self, sample, wanted): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values, method="nearest") + assert_array_almost_equal(interp(sample), wanted) + + def test_linear_edges(self): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values) + sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.]]) + wanted = np.asarray([0., 1111.]) + assert_array_almost_equal(interp(sample), wanted) + + def test_valid_create(self): + # create a 2-D grid of 3 points in each dimension + points = [(0., .5, 1.), (0., 1., .5)] + values = np.asarray([0., .5, 1.]) + values0 = values[:, np.newaxis] + values1 = values[np.newaxis, :] + values = (values0 + values1 * 10) + assert_raises(ValueError, RegularGridInterpolator, points, values) + points = [((0., .5, 1.), ), (0., .5, 1.)] + assert_raises(ValueError, RegularGridInterpolator, points, values) + points = [(0., .5, .75, 1.), (0., .5, 1.)] + assert_raises(ValueError, RegularGridInterpolator, points, values) + points = [(0., .5, 1.), (0., .5, 1.), (0., .5, 1.)] + assert_raises(ValueError, RegularGridInterpolator, points, values) + points = [(0., .5, 1.), (0., .5, 1.)] + assert_raises(ValueError, RegularGridInterpolator, points, values, + method="undefmethod") + + def test_valid_call(self): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values) + sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.]]) + assert_raises(ValueError, interp, sample, "undefmethod") + sample = np.asarray([[0., 0., 0.], [1., 1., 1.]]) + assert_raises(ValueError, interp, sample) + sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.1]]) + assert_raises(ValueError, interp, sample) + + def test_out_of_bounds_extrap(self): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values, bounds_error=False, + fill_value=None) + sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1], + [21, 2.1, -1.1, -11], [2.1, 2.1, -1.1, -1.1]]) + wanted = np.asarray([0., 1111., 11., 11.]) + assert_array_almost_equal(interp(sample, method="nearest"), wanted) + wanted = np.asarray([-111.1, 1222.1, -11068., -1186.9]) + assert_array_almost_equal(interp(sample, method="linear"), wanted) + + def test_out_of_bounds_extrap2(self): + points, values = self._get_sample_4d_2() + interp = RegularGridInterpolator(points, values, bounds_error=False, + fill_value=None) + sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1], + [21, 2.1, -1.1, -11], [2.1, 2.1, -1.1, -1.1]]) + wanted = np.asarray([0., 11., 11., 11.]) + assert_array_almost_equal(interp(sample, method="nearest"), wanted) + wanted = np.asarray([-12.1, 133.1, -1069., -97.9]) + assert_array_almost_equal(interp(sample, method="linear"), wanted) + + def test_out_of_bounds_fill(self): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values, bounds_error=False, + fill_value=np.nan) + sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1], + [2.1, 2.1, -1.1, -1.1]]) + wanted = np.asarray([np.nan, np.nan, np.nan]) + assert_array_almost_equal(interp(sample, method="nearest"), wanted) + assert_array_almost_equal(interp(sample, method="linear"), wanted) + sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], + [0.5, 0.5, .5, .5]]) + wanted = np.asarray([1001.1, 846.2, 555.5]) + assert_array_almost_equal(interp(sample), wanted) + + def test_nearest_compare_qhull(self): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values, method="nearest") + points_qhull = itertools.product(*points) + points_qhull = [p for p in points_qhull] + points_qhull = np.asarray(points_qhull) + values_qhull = values.reshape(-1) + interp_qhull = NearestNDInterpolator(points_qhull, values_qhull) + sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], + [0.5, 0.5, .5, .5]]) + assert_array_almost_equal(interp(sample), interp_qhull(sample)) + + def test_linear_compare_qhull(self): + points, values = self._get_sample_4d() + interp = RegularGridInterpolator(points, values) + points_qhull = itertools.product(*points) + points_qhull = [p for p in points_qhull] + points_qhull = np.asarray(points_qhull) + values_qhull = values.reshape(-1) + interp_qhull = LinearNDInterpolator(points_qhull, values_qhull) + sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], + [0.5, 0.5, .5, .5]]) + assert_array_almost_equal(interp(sample), interp_qhull(sample)) + + @pytest.mark.parametrize("method", ["nearest", "linear"]) + def test_duck_typed_values(self, method): + x = np.linspace(0, 2, 5) + y = np.linspace(0, 1, 7) + + values = MyValue((5, 7)) + + interp = RegularGridInterpolator((x, y), values, method=method) + v1 = interp([0.4, 0.7]) + + interp = RegularGridInterpolator((x, y), values._v, method=method) + v2 = interp([0.4, 0.7]) + assert_allclose(v1, v2) + + def test_invalid_fill_value(self): + np.random.seed(1234) + x = np.linspace(0, 2, 5) + y = np.linspace(0, 1, 7) + values = np.random.rand(5, 7) + + # integers can be cast to floats + RegularGridInterpolator((x, y), values, fill_value=1) + + # complex values cannot + assert_raises(ValueError, RegularGridInterpolator, + (x, y), values, fill_value=1+2j) + + def test_fillvalue_type(self): + # from #3703; test that interpolator object construction succeeds + values = np.ones((10, 20, 30), dtype='>f4') + points = [np.arange(n) for n in values.shape] + # xi = [(1, 1, 1)] + RegularGridInterpolator(points, values) + RegularGridInterpolator(points, values, fill_value=0.) + + def test_length_one_axis(self): + # gh-5890, gh-9524 : length-1 axis is legal for method='linear'. + # Along the axis it's linear interpolation; away from the length-1 + # axis, it's an extrapolation, so fill_value should be used. + def f(x, y): + return x + y + x = np.linspace(1, 1, 1) + y = np.linspace(1, 10, 10) + data = f(*np.meshgrid(x, y, indexing="ij", sparse=True)) + + interp = RegularGridInterpolator((x, y), data, method="linear", + bounds_error=False, fill_value=101) + + # check values at the grid + assert_allclose(interp(np.array([[1, 1], [1, 5], [1, 10]])), + [2, 6, 11], + atol=1e-14) + + # check off-grid interpolation is indeed linear + assert_allclose(interp(np.array([[1, 1.4], [1, 5.3], [1, 10]])), + [2.4, 6.3, 11], + atol=1e-14) + + # check exrapolation w/ fill_value + assert_allclose(interp(np.array([1.1, 2.4])), + interp.fill_value, + atol=1e-14) + + # check extrapolation: linear along the `y` axis, const along `x` + interp.fill_value = None + assert_allclose(interp([[1, 0.3], [1, 11.5]]), + [1.3, 12.5], atol=1e-15) + + assert_allclose(interp([[1.5, 0.3], [1.9, 11.5]]), + [1.3, 12.5], atol=1e-15) + + # extrapolation with method='nearest' + interp = RegularGridInterpolator((x, y), data, method="nearest", + bounds_error=False, fill_value=None) + assert_allclose(interp([[1.5, 1.8], [-4, 5.1]]), + [3, 6], + atol=1e-15) + + @pytest.mark.parametrize("fill_value", [None, np.nan, np.pi]) + @pytest.mark.parametrize("method", ['linear', 'nearest']) + def test_length_one_axis2(self, fill_value, method): + options = {"fill_value": fill_value, "bounds_error": False, + "method": method} + + x = np.linspace(0, 2*np.pi, 20) + z = np.sin(x) + + fa = RegularGridInterpolator((x,), z[:], **options) + fb = RegularGridInterpolator((x, [0]), z[:, None], **options) + + x1a = np.linspace(-1, 2*np.pi+1, 100) + za = fa(x1a) + + # evaluated at provided y-value, fb should behave exactly as fa + y1b = np.zeros(100) + zb = fb(np.vstack([x1a, y1b]).T) + assert_allclose(zb, za) + + # evaluated at a different y-value, fb should return fill value + y1b = np.ones(100) + zb = fb(np.vstack([x1a, y1b]).T) + if fill_value is None: + assert_allclose(zb, za) + else: + assert_allclose(zb, fill_value) + + @pytest.mark.parametrize("method", ['nearest', 'linear']) + def test_nan_x_1d(self, method): + # gh-6624 : if x is nan, result should be nan + f = RegularGridInterpolator(([1, 2, 3],), [10, 20, 30], fill_value=1, + bounds_error=False, method=method) + assert np.isnan(f([np.nan])) + + # test arbitrary nan pattern + rng = np.random.default_rng(8143215468) + x = rng.random(size=100)*4 + i = rng.random(size=100) > 0.5 + x[i] = np.nan + with np.errstate(invalid='ignore'): + # out-of-bounds comparisons, `out_of_bounds += x < grid[0]`, + # generate numpy warnings if `x` contains nans. + # These warnings should propagate to user (since `x` is user + # input) and we simply filter them out. + res = f(x) + + assert_equal(res[i], np.nan) + assert_equal(res[~i], f(x[~i])) + + # also test the length-one axis f(nan) + x = [1, 2, 3] + y = [1, ] + data = np.ones((3, 1)) + f = RegularGridInterpolator((x, y), data, fill_value=1, + bounds_error=False, method=method) + assert np.isnan(f([np.nan, 1])) + assert np.isnan(f([1, np.nan])) + + @pytest.mark.parametrize("method", ['nearest', 'linear']) + def test_nan_x_2d(self, method): + x, y = np.array([0, 1, 2]), np.array([1, 3, 7]) + + def f(x, y): + return x**2 + y**2 + + xg, yg = np.meshgrid(x, y, indexing='ij', sparse=True) + data = f(xg, yg) + interp = RegularGridInterpolator((x, y), data, + method=method, bounds_error=False) + + with np.errstate(invalid='ignore'): + res = interp([[1.5, np.nan], [1, 1]]) + assert_allclose(res[1], 2, atol=1e-14) + assert np.isnan(res[0]) + + # test arbitrary nan pattern + rng = np.random.default_rng(8143215468) + x = rng.random(size=100)*4-1 + y = rng.random(size=100)*8 + i1 = rng.random(size=100) > 0.5 + i2 = rng.random(size=100) > 0.5 + i = i1 | i2 + x[i1] = np.nan + y[i2] = np.nan + z = np.array([x, y]).T + with np.errstate(invalid='ignore'): + # out-of-bounds comparisons, `out_of_bounds += x < grid[0]`, + # generate numpy warnings if `x` contains nans. + # These warnings should propagate to user (since `x` is user + # input) and we simply filter them out. + res = interp(z) + + assert_equal(res[i], np.nan) + assert_equal(res[~i], interp(z[~i])) + + @parametrize_rgi_interp_methods + @pytest.mark.parametrize(("ndims", "func"), [ + (2, lambda x, y: 2 * x ** 3 + 3 * y ** 2), + (3, lambda x, y, z: 2 * x ** 3 + 3 * y ** 2 - z), + (4, lambda x, y, z, a: 2 * x ** 3 + 3 * y ** 2 - z + a), + (5, lambda x, y, z, a, b: 2 * x ** 3 + 3 * y ** 2 - z + a * b), + ]) + def test_descending_points_nd(self, method, ndims, func): + + if ndims == 5 and method in {"cubic", "quintic"}: + pytest.skip("too slow; OOM (quintic); or nearly so (cubic)") + + rng = np.random.default_rng(42) + sample_low = 1 + sample_high = 5 + test_points = rng.uniform(sample_low, sample_high, size=(2, ndims)) + + ascending_points = [np.linspace(sample_low, sample_high, 12) + for _ in range(ndims)] + + ascending_values = func(*np.meshgrid(*ascending_points, + indexing="ij", + sparse=True)) + + ascending_interp = RegularGridInterpolator(ascending_points, + ascending_values, + method=method) + ascending_result = ascending_interp(test_points) + + descending_points = [xi[::-1] for xi in ascending_points] + descending_values = func(*np.meshgrid(*descending_points, + indexing="ij", + sparse=True)) + descending_interp = RegularGridInterpolator(descending_points, + descending_values, + method=method) + descending_result = descending_interp(test_points) + + assert_array_equal(ascending_result, descending_result) + + def test_invalid_points_order(self): + def val_func_2d(x, y): + return 2 * x ** 3 + 3 * y ** 2 + + x = np.array([.5, 2., 0., 4., 5.5]) # not ascending or descending + y = np.array([.5, 2., 3., 4., 5.5]) + points = (x, y) + values = val_func_2d(*np.meshgrid(*points, indexing='ij', + sparse=True)) + match = "must be strictly ascending or descending" + with pytest.raises(ValueError, match=match): + RegularGridInterpolator(points, values) + + @parametrize_rgi_interp_methods + def test_fill_value(self, method): + interp = RegularGridInterpolator([np.arange(6)], np.ones(6), + method=method, bounds_error=False) + assert np.isnan(interp([10])) + + @parametrize_rgi_interp_methods + def test_nonscalar_values(self, method): + + if method == "quintic": + pytest.skip("Way too slow.") + + # Verify that non-scalar valued values also works + points = [(0.0, 0.5, 1.0, 1.5, 2.0, 2.5)] * 2 + [ + (0.0, 5.0, 10.0, 15.0, 20, 25.0) + ] * 2 + + rng = np.random.default_rng(1234) + values = rng.random((6, 6, 6, 6, 8)) + sample = rng.random((7, 3, 4)) + + interp = RegularGridInterpolator(points, values, method=method, + bounds_error=False) + v = interp(sample) + assert_equal(v.shape, (7, 3, 8), err_msg=method) + + vs = [] + for j in range(8): + interp = RegularGridInterpolator(points, values[..., j], + method=method, + bounds_error=False) + vs.append(interp(sample)) + v2 = np.array(vs).transpose(1, 2, 0) + + assert_allclose(v, v2, atol=1e-14, err_msg=method) + + @parametrize_rgi_interp_methods + @pytest.mark.parametrize("flip_points", [False, True]) + def test_nonscalar_values_2(self, method, flip_points): + + if method in {"cubic", "quintic"}: + pytest.skip("Way too slow.") + + # Verify that non-scalar valued values also work : use different + # lengths of axes to simplify tracing the internals + points = [(0.0, 0.5, 1.0, 1.5, 2.0, 2.5), + (0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0), + (0.0, 5.0, 10.0, 15.0, 20, 25.0, 35.0, 36.0), + (0.0, 5.0, 10.0, 15.0, 20, 25.0, 35.0, 36.0, 47)] + + # verify, that strictly decreasing dimensions work + if flip_points: + points = [tuple(reversed(p)) for p in points] + + rng = np.random.default_rng(1234) + + trailing_points = (3, 2) + # NB: values has a `num_trailing_dims` trailing dimension + values = rng.random((6, 7, 8, 9, *trailing_points)) + sample = rng.random(4) # a single sample point ! + + interp = RegularGridInterpolator(points, values, method=method, + bounds_error=False) + v = interp(sample) + + # v has a single sample point *per entry in the trailing dimensions* + assert v.shape == (1, *trailing_points) + + # check the values, too : manually loop over the trailing dimensions + vs = np.empty(values.shape[-2:]) + for i in range(values.shape[-2]): + for j in range(values.shape[-1]): + interp = RegularGridInterpolator(points, values[..., i, j], + method=method, + bounds_error=False) + vs[i, j] = interp(sample).item() + v2 = np.expand_dims(vs, axis=0) + assert_allclose(v, v2, atol=1e-14, err_msg=method) + + def test_nonscalar_values_linear_2D(self): + # Verify that non-scalar values work in the 2D fast path + method = 'linear' + points = [(0.0, 0.5, 1.0, 1.5, 2.0, 2.5), + (0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0), ] + + rng = np.random.default_rng(1234) + + trailing_points = (3, 4) + # NB: values has a `num_trailing_dims` trailing dimension + values = rng.random((6, 7, *trailing_points)) + sample = rng.random(2) # a single sample point ! + + interp = RegularGridInterpolator(points, values, method=method, + bounds_error=False) + v = interp(sample) + + # v has a single sample point *per entry in the trailing dimensions* + assert v.shape == (1, *trailing_points) + + # check the values, too : manually loop over the trailing dimensions + vs = np.empty(values.shape[-2:]) + for i in range(values.shape[-2]): + for j in range(values.shape[-1]): + interp = RegularGridInterpolator(points, values[..., i, j], + method=method, + bounds_error=False) + vs[i, j] = interp(sample).item() + v2 = np.expand_dims(vs, axis=0) + assert_allclose(v, v2, atol=1e-14, err_msg=method) + + @pytest.mark.parametrize( + "dtype", + [np.float32, np.float64, np.complex64, np.complex128] + ) + @pytest.mark.parametrize("xi_dtype", [np.float32, np.float64]) + def test_float32_values(self, dtype, xi_dtype): + # regression test for gh-17718: values.dtype=float32 fails + def f(x, y): + return 2 * x**3 + 3 * y**2 + + x = np.linspace(1, 4, 11) + y = np.linspace(4, 7, 22) + + xg, yg = np.meshgrid(x, y, indexing='ij', sparse=True) + data = f(xg, yg) + + data = data.astype(dtype) + + interp = RegularGridInterpolator((x, y), data) + + pts = np.array([[2.1, 6.2], + [3.3, 5.2]], dtype=xi_dtype) + + # the values here are just what the call returns; the test checks that + # that the call succeeds at all, instead of failing with cython not + # having a float32 kernel + assert_allclose(interp(pts), [134.10469388, 153.40069388], atol=1e-7) + + def test_bad_solver(self): + x = np.linspace(0, 3, 7) + y = np.linspace(0, 3, 7) + xg, yg = np.meshgrid(x, y, indexing='ij', sparse=True) + data = xg + yg + + # default method 'linear' does not accept 'solver' + with assert_raises(ValueError): + RegularGridInterpolator((x, y), data, solver=lambda x: x) + + with assert_raises(TypeError): + # wrong solver interface + RegularGridInterpolator( + (x, y), data, method='slinear', solver=lambda x: x + ) + + with assert_raises(TypeError): + # unknown argument + RegularGridInterpolator( + (x, y), data, method='slinear', solver=lambda x: x, woof='woof' + ) + + with assert_raises(TypeError): + # unknown argument + RegularGridInterpolator( + (x, y), data, method='slinear', solver_args={'woof': 42} + ) + + +class MyValue: + """ + Minimal indexable object + """ + + def __init__(self, shape): + self.ndim = 2 + self.shape = shape + self._v = np.arange(np.prod(shape)).reshape(shape) + + def __getitem__(self, idx): + return self._v[idx] + + def __array_interface__(self): + return None + + def __array__(self, dtype=None, copy=None): + raise RuntimeError("No array representation") + + +class TestInterpN: + def _sample_2d_data(self): + x = np.array([.5, 2., 3., 4., 5.5, 6.]) + y = np.array([.5, 2., 3., 4., 5.5, 6.]) + z = np.array( + [ + [1, 2, 1, 2, 1, 1], + [1, 2, 1, 2, 1, 1], + [1, 2, 3, 2, 1, 1], + [1, 2, 2, 2, 1, 1], + [1, 2, 1, 2, 1, 1], + [1, 2, 2, 2, 1, 1], + ] + ) + return x, y, z + + def test_spline_2d(self): + x, y, z = self._sample_2d_data() + lut = RectBivariateSpline(x, y, z) + + xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + assert_array_almost_equal(interpn((x, y), z, xi, method="splinef2d"), + lut.ev(xi[:, 0], xi[:, 1])) + + @parametrize_rgi_interp_methods + def test_list_input(self, method): + x, y, z = self._sample_2d_data() + xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + v1 = interpn((x, y), z, xi, method=method) + v2 = interpn( + (x.tolist(), y.tolist()), z.tolist(), xi.tolist(), method=method + ) + assert_allclose(v1, v2, err_msg=method) + + def test_spline_2d_outofbounds(self): + x = np.array([.5, 2., 3., 4., 5.5]) + y = np.array([.5, 2., 3., 4., 5.5]) + z = np.array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], [1, 2, 1, 2, 1]]) + lut = RectBivariateSpline(x, y, z) + + xi = np.array([[1, 2.3, 6.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, -4.0, 5.0, 1.0, 3]]).T + actual = interpn((x, y), z, xi, method="splinef2d", + bounds_error=False, fill_value=999.99) + expected = lut.ev(xi[:, 0], xi[:, 1]) + expected[2:4] = 999.99 + assert_array_almost_equal(actual, expected) + + # no extrapolation for splinef2d + assert_raises(ValueError, interpn, (x, y), z, xi, method="splinef2d", + bounds_error=False, fill_value=None) + + def _sample_4d_data(self): + points = [(0., .5, 1.)] * 2 + [(0., 5., 10.)] * 2 + values = np.asarray([0., .5, 1.]) + values0 = values[:, np.newaxis, np.newaxis, np.newaxis] + values1 = values[np.newaxis, :, np.newaxis, np.newaxis] + values2 = values[np.newaxis, np.newaxis, :, np.newaxis] + values3 = values[np.newaxis, np.newaxis, np.newaxis, :] + values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) + return points, values + + def test_linear_4d(self): + # create a 4-D grid of 3 points in each dimension + points, values = self._sample_4d_data() + interp_rg = RegularGridInterpolator(points, values) + sample = np.asarray([[0.1, 0.1, 10., 9.]]) + wanted = interpn(points, values, sample, method="linear") + assert_array_almost_equal(interp_rg(sample), wanted) + + def test_4d_linear_outofbounds(self): + # create a 4-D grid of 3 points in each dimension + points, values = self._sample_4d_data() + sample = np.asarray([[0.1, -0.1, 10.1, 9.]]) + wanted = 999.99 + actual = interpn(points, values, sample, method="linear", + bounds_error=False, fill_value=999.99) + assert_array_almost_equal(actual, wanted) + + def test_nearest_4d(self): + # create a 4-D grid of 3 points in each dimension + points, values = self._sample_4d_data() + interp_rg = RegularGridInterpolator(points, values, method="nearest") + sample = np.asarray([[0.1, 0.1, 10., 9.]]) + wanted = interpn(points, values, sample, method="nearest") + assert_array_almost_equal(interp_rg(sample), wanted) + + def test_4d_nearest_outofbounds(self): + # create a 4-D grid of 3 points in each dimension + points, values = self._sample_4d_data() + sample = np.asarray([[0.1, -0.1, 10.1, 9.]]) + wanted = 999.99 + actual = interpn(points, values, sample, method="nearest", + bounds_error=False, fill_value=999.99) + assert_array_almost_equal(actual, wanted) + + def test_xi_1d(self): + # verify that 1-D xi works as expected + points, values = self._sample_4d_data() + sample = np.asarray([0.1, 0.1, 10., 9.]) + v1 = interpn(points, values, sample, bounds_error=False) + v2 = interpn(points, values, sample[None,:], bounds_error=False) + assert_allclose(v1, v2) + + def test_xi_nd(self): + # verify that higher-d xi works as expected + points, values = self._sample_4d_data() + + np.random.seed(1234) + sample = np.random.rand(2, 3, 4) + + v1 = interpn(points, values, sample, method='nearest', + bounds_error=False) + assert_equal(v1.shape, (2, 3)) + + v2 = interpn(points, values, sample.reshape(-1, 4), + method='nearest', bounds_error=False) + assert_allclose(v1, v2.reshape(v1.shape)) + + @parametrize_rgi_interp_methods + def test_xi_broadcast(self, method): + # verify that the interpolators broadcast xi + x, y, values = self._sample_2d_data() + points = (x, y) + + xi = np.linspace(0, 1, 2) + yi = np.linspace(0, 3, 3) + + sample = (xi[:, None], yi[None, :]) + v1 = interpn(points, values, sample, method=method, bounds_error=False) + assert_equal(v1.shape, (2, 3)) + + xx, yy = np.meshgrid(xi, yi) + sample = np.c_[xx.T.ravel(), yy.T.ravel()] + + v2 = interpn(points, values, sample, + method=method, bounds_error=False) + assert_allclose(v1, v2.reshape(v1.shape)) + + @parametrize_rgi_interp_methods + def test_nonscalar_values(self, method): + + if method == "quintic": + pytest.skip("Way too slow.") + + # Verify that non-scalar valued values also works + points = [(0.0, 0.5, 1.0, 1.5, 2.0, 2.5)] * 2 + [ + (0.0, 5.0, 10.0, 15.0, 20, 25.0) + ] * 2 + + rng = np.random.default_rng(1234) + values = rng.random((6, 6, 6, 6, 8)) + sample = rng.random((7, 3, 4)) + + v = interpn(points, values, sample, method=method, + bounds_error=False) + assert_equal(v.shape, (7, 3, 8), err_msg=method) + + vs = [interpn(points, values[..., j], sample, method=method, + bounds_error=False) for j in range(8)] + v2 = np.array(vs).transpose(1, 2, 0) + + assert_allclose(v, v2, atol=1e-14, err_msg=method) + + @parametrize_rgi_interp_methods + def test_nonscalar_values_2(self, method): + + if method in {"cubic", "quintic"}: + pytest.skip("Way too slow.") + + # Verify that non-scalar valued values also work : use different + # lengths of axes to simplify tracing the internals + points = [(0.0, 0.5, 1.0, 1.5, 2.0, 2.5), + (0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0), + (0.0, 5.0, 10.0, 15.0, 20, 25.0, 35.0, 36.0), + (0.0, 5.0, 10.0, 15.0, 20, 25.0, 35.0, 36.0, 47)] + + rng = np.random.default_rng(1234) + + trailing_points = (3, 2) + # NB: values has a `num_trailing_dims` trailing dimension + values = rng.random((6, 7, 8, 9, *trailing_points)) + sample = rng.random(4) # a single sample point ! + + v = interpn(points, values, sample, method=method, bounds_error=False) + + # v has a single sample point *per entry in the trailing dimensions* + assert v.shape == (1, *trailing_points) + + # check the values, too : manually loop over the trailing dimensions + vs = [[ + interpn(points, values[..., i, j], sample, method=method, + bounds_error=False) for i in range(values.shape[-2]) + ] for j in range(values.shape[-1])] + + assert_allclose(v, np.asarray(vs).T, atol=1e-14, err_msg=method) + + def test_non_scalar_values_splinef2d(self): + # Vector-valued splines supported with fitpack + points, values = self._sample_4d_data() + + np.random.seed(1234) + values = np.random.rand(3, 3, 3, 3, 6) + sample = np.random.rand(7, 11, 4) + assert_raises(ValueError, interpn, points, values, sample, + method='splinef2d') + + @parametrize_rgi_interp_methods + def test_complex(self, method): + if method == "pchip": + pytest.skip("pchip does not make sense for complex data") + + x, y, values = self._sample_2d_data() + points = (x, y) + values = values - 2j*values + + sample = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + + v1 = interpn(points, values, sample, method=method) + v2r = interpn(points, values.real, sample, method=method) + v2i = interpn(points, values.imag, sample, method=method) + v2 = v2r + 1j*v2i + + assert_allclose(v1, v2) + + def test_complex_pchip(self): + # Complex-valued data deprecated for pchip + x, y, values = self._sample_2d_data() + points = (x, y) + values = values - 2j*values + + sample = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + with pytest.deprecated_call(match='complex'): + interpn(points, values, sample, method='pchip') + + def test_complex_spline2fd(self): + # Complex-valued data not supported by spline2fd + x, y, values = self._sample_2d_data() + points = (x, y) + values = values - 2j*values + + sample = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T + with assert_warns(ComplexWarning): + interpn(points, values, sample, method='splinef2d') + + @pytest.mark.parametrize( + "method", + ["linear", "nearest"] + ) + def test_duck_typed_values(self, method): + x = np.linspace(0, 2, 5) + y = np.linspace(0, 1, 7) + + values = MyValue((5, 7)) + + v1 = interpn((x, y), values, [0.4, 0.7], method=method) + v2 = interpn((x, y), values._v, [0.4, 0.7], method=method) + assert_allclose(v1, v2) + + @parametrize_rgi_interp_methods + def test_matrix_input(self, method): + x = np.linspace(0, 2, 6) + y = np.linspace(0, 1, 7) + + values = matrix(np.random.rand(6, 7)) + + sample = np.random.rand(3, 7, 2) + + v1 = interpn((x, y), values, sample, method=method) + v2 = interpn((x, y), np.asarray(values), sample, method=method) + assert_allclose(v1, v2) + + def test_length_one_axis(self): + # gh-5890, gh-9524 : length-1 axis is legal for method='linear'. + # Along the axis it's linear interpolation; away from the length-1 + # axis, it's an extrapolation, so fill_value should be used. + + values = np.array([[0.1, 1, 10]]) + xi = np.array([[1, 2.2], [1, 3.2], [1, 3.8]]) + + res = interpn(([1], [2, 3, 4]), values, xi) + wanted = [0.9*0.2 + 0.1, # on [2, 3) it's 0.9*(x-2) + 0.1 + 9*0.2 + 1, # on [3, 4] it's 9*(x-3) + 1 + 9*0.8 + 1] + + assert_allclose(res, wanted, atol=1e-15) + + # check extrapolation + xi = np.array([[1.1, 2.2], [1.5, 3.2], [-2.3, 3.8]]) + res = interpn(([1], [2, 3, 4]), values, xi, + bounds_error=False, fill_value=None) + + assert_allclose(res, wanted, atol=1e-15) + + def test_descending_points(self): + def value_func_4d(x, y, z, a): + return 2 * x ** 3 + 3 * y ** 2 - z - a + + x1 = np.array([0, 1, 2, 3]) + x2 = np.array([0, 10, 20, 30]) + x3 = np.array([0, 10, 20, 30]) + x4 = np.array([0, .1, .2, .30]) + points = (x1, x2, x3, x4) + values = value_func_4d( + *np.meshgrid(*points, indexing='ij', sparse=True)) + pts = (0.1, 0.3, np.transpose(np.linspace(0, 30, 4)), + np.linspace(0, 0.3, 4)) + correct_result = interpn(points, values, pts) + + x1_descend = x1[::-1] + x2_descend = x2[::-1] + x3_descend = x3[::-1] + x4_descend = x4[::-1] + points_shuffled = (x1_descend, x2_descend, x3_descend, x4_descend) + values_shuffled = value_func_4d( + *np.meshgrid(*points_shuffled, indexing='ij', sparse=True)) + test_result = interpn(points_shuffled, values_shuffled, pts) + + assert_array_equal(correct_result, test_result) + + def test_invalid_points_order(self): + x = np.array([.5, 2., 0., 4., 5.5]) # not ascending or descending + y = np.array([.5, 2., 3., 4., 5.5]) + z = np.array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1], + [1, 2, 2, 2, 1], [1, 2, 1, 2, 1]]) + xi = np.array([[1, 2.3, 6.3, 0.5, 3.3, 1.2, 3], + [1, 3.3, 1.2, -4.0, 5.0, 1.0, 3]]).T + + match = "must be strictly ascending or descending" + with pytest.raises(ValueError, match=match): + interpn((x, y), z, xi) + + def test_invalid_xi_dimensions(self): + # https://github.com/scipy/scipy/issues/16519 + points = [(0, 1)] + values = [0, 1] + xi = np.ones((1, 1, 3)) + msg = ("The requested sample points xi have dimension 3, but this " + "RegularGridInterpolator has dimension 1") + with assert_raises(ValueError, match=msg): + interpn(points, values, xi) + + def test_readonly_grid(self): + # https://github.com/scipy/scipy/issues/17716 + x = np.linspace(0, 4, 5) + y = np.linspace(0, 5, 6) + z = np.linspace(0, 6, 7) + points = (x, y, z) + values = np.ones((5, 6, 7)) + point = np.array([2.21, 3.12, 1.15]) + for d in points: + d.flags.writeable = False + values.flags.writeable = False + point.flags.writeable = False + interpn(points, values, point) + RegularGridInterpolator(points, values)(point) + + def test_2d_readonly_grid(self): + # https://github.com/scipy/scipy/issues/17716 + # test special 2d case + x = np.linspace(0, 4, 5) + y = np.linspace(0, 5, 6) + points = (x, y) + values = np.ones((5, 6)) + point = np.array([2.21, 3.12]) + for d in points: + d.flags.writeable = False + values.flags.writeable = False + point.flags.writeable = False + interpn(points, values, point) + RegularGridInterpolator(points, values)(point) + + def test_non_c_contiguous_grid(self): + # https://github.com/scipy/scipy/issues/17716 + x = np.linspace(0, 4, 5) + x = np.vstack((x, np.empty_like(x))).T.copy()[:, 0] + assert not x.flags.c_contiguous + y = np.linspace(0, 5, 6) + z = np.linspace(0, 6, 7) + points = (x, y, z) + values = np.ones((5, 6, 7)) + point = np.array([2.21, 3.12, 1.15]) + interpn(points, values, point) + RegularGridInterpolator(points, values)(point) + + @pytest.mark.parametrize("dtype", ['>f8', ' int: + return len(self._shape) + + @property + def _shape_as_2d(self): + s = self._shape + return (1, s[-1]) if len(s) == 1 else s + + @property + def _bsr_container(self): + from ._bsr import bsr_array + return bsr_array + + @property + def _coo_container(self): + from ._coo import coo_array + return coo_array + + @property + def _csc_container(self): + from ._csc import csc_array + return csc_array + + @property + def _csr_container(self): + from ._csr import csr_array + return csr_array + + @property + def _dia_container(self): + from ._dia import dia_array + return dia_array + + @property + def _dok_container(self): + from ._dok import dok_array + return dok_array + + @property + def _lil_container(self): + from ._lil import lil_array + return lil_array + + def __init__(self, maxprint=MAXPRINT): + self._shape = None + if self.__class__.__name__ == '_spbase': + raise ValueError("This class is not intended" + " to be instantiated directly.") + self.maxprint = maxprint + + # Use this in 1.14.0 and later: + # + # @property + # def shape(self): + # return self._shape + + def reshape(self, *args, **kwargs): + """reshape(self, shape, order='C', copy=False) + + Gives a new shape to a sparse array/matrix without changing its data. + + Parameters + ---------- + shape : length-2 tuple of ints + The new shape should be compatible with the original shape. + order : {'C', 'F'}, optional + Read the elements using this index order. 'C' means to read and + write the elements using C-like index order; e.g., read entire first + row, then second row, etc. 'F' means to read and write the elements + using Fortran-like index order; e.g., read entire first column, then + second column, etc. + copy : bool, optional + Indicates whether or not attributes of self should be copied + whenever possible. The degree to which attributes are copied varies + depending on the type of sparse array being used. + + Returns + ------- + reshaped : sparse array/matrix + A sparse array/matrix with the given `shape`, not necessarily of the same + format as the current object. + + See Also + -------- + numpy.reshape : NumPy's implementation of 'reshape' for ndarrays + """ + # If the shape already matches, don't bother doing an actual reshape + # Otherwise, the default is to convert to COO and use its reshape + is_array = isinstance(self, sparray) + shape = check_shape(args, self.shape, allow_1d=is_array) + order, copy = check_reshape_kwargs(kwargs) + if shape == self.shape: + if copy: + return self.copy() + else: + return self + + return self.tocoo(copy=copy).reshape(shape, order=order, copy=False) + + def resize(self, shape): + """Resize the array/matrix in-place to dimensions given by ``shape`` + + Any elements that lie within the new shape will remain at the same + indices, while non-zero elements lying outside the new shape are + removed. + + Parameters + ---------- + shape : (int, int) + number of rows and columns in the new array/matrix + + Notes + ----- + The semantics are not identical to `numpy.ndarray.resize` or + `numpy.resize`. Here, the same data will be maintained at each index + before and after reshape, if that index is within the new bounds. In + numpy, resizing maintains contiguity of the array, moving elements + around in the logical array but not within a flattened representation. + + We give no guarantees about whether the underlying data attributes + (arrays, etc.) will be modified in place or replaced with new objects. + """ + # As an inplace operation, this requires implementation in each format. + raise NotImplementedError( + f'{type(self).__name__}.resize is not implemented') + + def astype(self, dtype, casting='unsafe', copy=True): + """Cast the array/matrix elements to a specified type. + + Parameters + ---------- + dtype : string or numpy dtype + Typecode or data-type to which to cast the data. + 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. + copy : bool, optional + If `copy` is `False`, the result might share some memory with this + array/matrix. If `copy` is `True`, it is guaranteed that the result and + this array/matrix do not share any memory. + """ + + dtype = np.dtype(dtype) + if self.dtype != dtype: + return self.tocsr().astype( + dtype, casting=casting, copy=copy).asformat(self.format) + elif copy: + return self.copy() + else: + return self + + @classmethod + def _ascontainer(cls, X, **kwargs): + if issubclass(cls, sparray): + return np.asarray(X, **kwargs) + else: + return asmatrix(X, **kwargs) + + @classmethod + def _container(cls, X, **kwargs): + if issubclass(cls, sparray): + return np.array(X, **kwargs) + else: + return matrix(X, **kwargs) + + def _asfptype(self): + """Upcast array to a floating point format (if necessary)""" + + fp_types = ['f', 'd', 'F', 'D'] + + if self.dtype.char in fp_types: + return self + else: + for fp_type in fp_types: + if self.dtype <= np.dtype(fp_type): + return self.astype(fp_type) + + raise TypeError('cannot upcast [%s] to a floating ' + 'point format' % self.dtype.name) + + def __iter__(self): + for r in range(self.shape[0]): + yield self[r] + + def _getmaxprint(self): + """Maximum number of elements to display when printed.""" + return self.maxprint + + def count_nonzero(self): + """Number of non-zero entries, equivalent to + + np.count_nonzero(a.toarray()) + + Unlike the nnz property, which return the number of stored + entries (the length of the data attribute), this method counts the + actual number of non-zero entries in data. + """ + raise NotImplementedError("count_nonzero not implemented for %s." % + self.__class__.__name__) + + def _getnnz(self, axis=None): + """Number of stored values, including explicit zeros. + + Parameters + ---------- + axis : None, 0, or 1 + Select between the number of values across the whole array, in + each column, or in each row. + + See also + -------- + count_nonzero : Number of non-zero entries + """ + raise NotImplementedError("getnnz not implemented for %s." % + self.__class__.__name__) + + @property + def nnz(self) -> int: + """Number of stored values, including explicit zeros. + + See also + -------- + count_nonzero : Number of non-zero entries + """ + return self._getnnz() + + @property + def size(self) -> int: + """Number of stored values. + + See also + -------- + count_nonzero : Number of non-zero values. + """ + return self._getnnz() + + @property + def format(self) -> str: + """Format string for matrix.""" + return self._format + + @property + def A(self) -> np.ndarray: + """DEPRECATED: Return a dense array. + + .. deprecated:: 1.11.0 + + `.A` is deprecated and will be removed in v1.14.0. + Use `.toarray()` instead. + """ + if isinstance(self, sparray): + message = ("`.A` is deprecated and will be removed in v1.14.0. " + "Use `.toarray()` instead.") + warn(VisibleDeprecationWarning(message), stacklevel=2) + return self.toarray() + + @property + def T(self): + """Transpose.""" + return self.transpose() + + @property + def H(self): + """DEPRECATED: Returns the (complex) conjugate transpose. + + .. deprecated:: 1.11.0 + + `.H` is deprecated and will be removed in v1.14.0. + Please use `.T.conjugate()` instead. + """ + if isinstance(self, sparray): + message = ("`.H` is deprecated and will be removed in v1.14.0. " + "Please use `.T.conjugate()` instead.") + warn(VisibleDeprecationWarning(message), stacklevel=2) + return self.T.conjugate() + + @property + def real(self): + return self._real() + + @property + def imag(self): + return self._imag() + + def __repr__(self): + _, format_name = _formats[self.format] + sparse_cls = 'array' if isinstance(self, sparray) else 'matrix' + shape_str = 'x'.join(str(x) for x in self.shape) + return ( + f"<{shape_str} sparse {sparse_cls} of type '{self.dtype.type}'\n" + f"\twith {self.nnz} stored elements in {format_name} format>" + ) + + def __str__(self): + maxprint = self._getmaxprint() + + A = self.tocoo() + + # helper function, outputs "(i,j) v" + def tostr(row, col, data): + triples = zip(list(zip(row, col)), data) + return '\n'.join([(' {}\t{}'.format(*t)) for t in triples]) + + if self.nnz > maxprint: + half = maxprint // 2 + out = tostr(A.row[:half], A.col[:half], A.data[:half]) + out += "\n :\t:\n" + half = maxprint - maxprint//2 + out += tostr(A.row[-half:], A.col[-half:], A.data[-half:]) + else: + out = tostr(A.row, A.col, A.data) + + return out + + def __bool__(self): # Simple -- other ideas? + if self.shape == (1, 1): + return self.nnz != 0 + else: + raise ValueError("The truth value of an array with more than one " + "element is ambiguous. Use a.any() or a.all().") + __nonzero__ = __bool__ + + # What should len(sparse) return? For consistency with dense matrices, + # perhaps it should be the number of rows? But for some uses the number of + # non-zeros is more important. For now, raise an exception! + def __len__(self): + raise TypeError("sparse array length is ambiguous; use getnnz()" + " or shape[0]") + + def asformat(self, format, copy=False): + """Return this array/matrix in the passed format. + + Parameters + ---------- + format : {str, None} + The desired sparse format ("csr", "csc", "lil", "dok", "array", ...) + or None for no conversion. + copy : bool, optional + If True, the result is guaranteed to not share data with self. + + Returns + ------- + A : This array/matrix in the passed format. + """ + if format is None or format == self.format: + if copy: + return self.copy() + else: + return self + else: + try: + convert_method = getattr(self, 'to' + format) + except AttributeError as e: + raise ValueError(f'Format {format} is unknown.') from e + + # Forward the copy kwarg, if it's accepted. + try: + return convert_method(copy=copy) + except TypeError: + return convert_method() + + ################################################################### + # NOTE: All arithmetic operations use csr_matrix by default. + # Therefore a new sparse array format just needs to define a + # .tocsr() method to provide arithmetic support. Any of these + # methods can be overridden for efficiency. + #################################################################### + + def multiply(self, other): + """Point-wise multiplication by another array/matrix.""" + return self.tocsr().multiply(other) + + def maximum(self, other): + """Element-wise maximum between this and another array/matrix.""" + return self.tocsr().maximum(other) + + def minimum(self, other): + """Element-wise minimum between this and another array/matrix.""" + return self.tocsr().minimum(other) + + def dot(self, other): + """Ordinary dot product + + Examples + -------- + >>> import numpy as np + >>> from scipy.sparse import csr_array + >>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]]) + >>> v = np.array([1, 0, -1]) + >>> A.dot(v) + array([ 1, -3, -1], dtype=int64) + + """ + if np.isscalar(other): + return self * other + else: + return self @ other + + def power(self, n, dtype=None): + """Element-wise power.""" + return self.tocsr().power(n, dtype=dtype) + + def __eq__(self, other): + return self.tocsr().__eq__(other) + + def __ne__(self, other): + return self.tocsr().__ne__(other) + + def __lt__(self, other): + return self.tocsr().__lt__(other) + + def __gt__(self, other): + return self.tocsr().__gt__(other) + + def __le__(self, other): + return self.tocsr().__le__(other) + + def __ge__(self, other): + return self.tocsr().__ge__(other) + + def __abs__(self): + return abs(self.tocsr()) + + def __round__(self, ndigits=0): + return round(self.tocsr(), ndigits=ndigits) + + def _add_sparse(self, other): + return self.tocsr()._add_sparse(other) + + def _add_dense(self, other): + return self.tocoo()._add_dense(other) + + def _sub_sparse(self, other): + return self.tocsr()._sub_sparse(other) + + def _sub_dense(self, other): + return self.todense() - other + + def _rsub_dense(self, other): + # note: this can't be replaced by other + (-self) for unsigned types + return other - self.todense() + + def __add__(self, other): # self + other + if isscalarlike(other): + if other == 0: + return self.copy() + # Now we would add this scalar to every element. + raise NotImplementedError('adding a nonzero scalar to a ' + 'sparse array is not supported') + elif issparse(other): + if other.shape != self.shape: + raise ValueError("inconsistent shapes") + return self._add_sparse(other) + elif isdense(other): + other = np.broadcast_to(other, self.shape) + return self._add_dense(other) + else: + return NotImplemented + + def __radd__(self,other): # other + self + return self.__add__(other) + + def __sub__(self, other): # self - other + if isscalarlike(other): + if other == 0: + return self.copy() + raise NotImplementedError('subtracting a nonzero scalar from a ' + 'sparse array is not supported') + elif issparse(other): + if other.shape != self.shape: + raise ValueError("inconsistent shapes") + return self._sub_sparse(other) + elif isdense(other): + other = np.broadcast_to(other, self.shape) + return self._sub_dense(other) + else: + return NotImplemented + + def __rsub__(self,other): # other - self + if isscalarlike(other): + if other == 0: + return -self.copy() + raise NotImplementedError('subtracting a sparse array from a ' + 'nonzero scalar is not supported') + elif isdense(other): + other = np.broadcast_to(other, self.shape) + return self._rsub_dense(other) + else: + return NotImplemented + + def _matmul_dispatch(self, other): + """np.array-like matmul & `np.matrix`-like mul, i.e. `dot` or `NotImplemented` + + interpret other and call one of the following + self._mul_scalar() + self._matmul_vector() + self._matmul_multivector() + self._matmul_sparse() + """ + # This method has to be different from `__matmul__` because it is also + # called by sparse matrix classes. + + # Currently matrix multiplication is only supported + # for 2D arrays. Hence we unpacked and use only the + # two last axes' lengths. + M, N = self._shape_as_2d + + if other.__class__ is np.ndarray: + # Fast path for the most common case + if other.shape == (N,): + return self._matmul_vector(other) + elif other.shape == (N, 1): + result = self._matmul_vector(other.ravel()) + if self.ndim == 1: + return result + return result.reshape(M, 1) + elif other.ndim == 2 and other.shape[0] == N: + return self._matmul_multivector(other) + + if isscalarlike(other): + # scalar value + return self._mul_scalar(other) + + if issparse(other): + if self.shape[-1] != other.shape[0]: + raise ValueError('dimension mismatch') + if other.ndim == 1: + raise ValueError('Cannot yet multiply a 1d sparse array') + return self._matmul_sparse(other) + + # If it's a list or whatever, treat it like an array + other_a = np.asanyarray(other) + + if other_a.ndim == 0 and other_a.dtype == np.object_: + # Not interpretable as an array; return NotImplemented so that + # other's __rmatmul__ can kick in if that's implemented. + return NotImplemented + + try: + other.shape + except AttributeError: + other = other_a + + if other.ndim == 1 or other.ndim == 2 and other.shape[1] == 1: + # dense row or column vector + if other.shape != (N,) and other.shape != (N, 1): + raise ValueError('dimension mismatch') + + result = self._matmul_vector(np.ravel(other)) + + if isinstance(other, np.matrix): + result = self._ascontainer(result) + + if other.ndim == 2 and other.shape[1] == 1: + # If 'other' was an (nx1) column vector, reshape the result + result = result.reshape(-1, 1) + + return result + + elif other.ndim == 2: + ## + # dense 2D array or matrix ("multivector") + + if other.shape[0] != N: + raise ValueError('dimension mismatch') + + result = self._matmul_multivector(np.asarray(other)) + + if isinstance(other, np.matrix): + result = self._ascontainer(result) + + return result + + else: + raise ValueError('could not interpret dimensions') + + def __mul__(self, *args, **kwargs): + return self.multiply(*args, **kwargs) + + def __rmul__(self, *args, **kwargs): # other * self + return self.multiply(*args, **kwargs) + + # by default, use CSR for __mul__ handlers + def _mul_scalar(self, other): + return self.tocsr()._mul_scalar(other) + + def _matmul_vector(self, other): + return self.tocsr()._matmul_vector(other) + + def _matmul_multivector(self, other): + return self.tocsr()._matmul_multivector(other) + + def _matmul_sparse(self, other): + return self.tocsr()._matmul_sparse(other) + + def _rmatmul_dispatch(self, other): + if isscalarlike(other): + return self._mul_scalar(other) + else: + # Don't use asarray unless we have to + try: + tr = other.transpose() + except AttributeError: + tr = np.asarray(other).transpose() + ret = self.transpose()._matmul_dispatch(tr) + if ret is NotImplemented: + return NotImplemented + return ret.transpose() + + ####################### + # matmul (@) operator # + ####################### + + def __matmul__(self, other): + if isscalarlike(other): + raise ValueError("Scalar operands are not allowed, " + "use '*' instead") + return self._matmul_dispatch(other) + + def __rmatmul__(self, other): + if isscalarlike(other): + raise ValueError("Scalar operands are not allowed, " + "use '*' instead") + return self._rmatmul_dispatch(other) + + #################### + # Other Arithmetic # + #################### + + def _divide(self, other, true_divide=False, rdivide=False): + if isscalarlike(other): + if rdivide: + if true_divide: + return np.true_divide(other, self.todense()) + else: + return np.divide(other, self.todense()) + + if true_divide and np.can_cast(self.dtype, np.float64): + return self.astype(np.float64)._mul_scalar(1./other) + else: + r = self._mul_scalar(1./other) + + scalar_dtype = np.asarray(other).dtype + if (np.issubdtype(self.dtype, np.integer) and + np.issubdtype(scalar_dtype, np.integer)): + return r.astype(self.dtype) + else: + return r + + elif isdense(other): + if not rdivide: + if true_divide: + recip = np.true_divide(1., other) + else: + recip = np.divide(1., other) + return self.multiply(recip) + else: + if true_divide: + return np.true_divide(other, self.todense()) + else: + return np.divide(other, self.todense()) + elif issparse(other): + if rdivide: + return other._divide(self, true_divide, rdivide=False) + + self_csr = self.tocsr() + if true_divide and np.can_cast(self.dtype, np.float64): + return self_csr.astype(np.float64)._divide_sparse(other) + else: + return self_csr._divide_sparse(other) + else: + return NotImplemented + + def __truediv__(self, other): + return self._divide(other, true_divide=True) + + def __div__(self, other): + # Always do true division + return self._divide(other, true_divide=True) + + def __rtruediv__(self, other): + # Implementing this as the inverse would be too magical -- bail out + return NotImplemented + + def __rdiv__(self, other): + # Implementing this as the inverse would be too magical -- bail out + return NotImplemented + + def __neg__(self): + return -self.tocsr() + + def __iadd__(self, other): + return NotImplemented + + def __isub__(self, other): + return NotImplemented + + def __imul__(self, other): + return NotImplemented + + def __idiv__(self, other): + return self.__itruediv__(other) + + def __itruediv__(self, other): + return NotImplemented + + def __pow__(self, *args, **kwargs): + return self.power(*args, **kwargs) + + def transpose(self, axes=None, copy=False): + """ + Reverses the dimensions of the sparse array/matrix. + + Parameters + ---------- + axes : None, optional + This argument is in the signature *solely* for NumPy + compatibility reasons. Do not pass in anything except + for the default value. + copy : bool, optional + Indicates whether or not attributes of `self` should be + copied whenever possible. The degree to which attributes + are copied varies depending on the type of sparse array/matrix + being used. + + Returns + ------- + p : `self` with the dimensions reversed. + + Notes + ----- + If `self` is a `csr_array` or a `csc_array`, then this will return a + `csc_array` or a `csr_array`, respectively. + + See Also + -------- + numpy.transpose : NumPy's implementation of 'transpose' for ndarrays + """ + return self.tocsr(copy=copy).transpose(axes=axes, copy=False) + + def conjugate(self, copy=True): + """Element-wise complex conjugation. + + If the array/matrix is of non-complex data type and `copy` is False, + this method does nothing and the data is not copied. + + Parameters + ---------- + copy : bool, optional + If True, the result is guaranteed to not share data with self. + + Returns + ------- + A : The element-wise complex conjugate. + + """ + if np.issubdtype(self.dtype, np.complexfloating): + return self.tocsr(copy=copy).conjugate(copy=False) + elif copy: + return self.copy() + else: + return self + + def conj(self, copy=True): + return self.conjugate(copy=copy) + + conj.__doc__ = conjugate.__doc__ + + def _real(self): + return self.tocsr()._real() + + def _imag(self): + return self.tocsr()._imag() + + def nonzero(self): + """Nonzero indices of the array/matrix. + + Returns a tuple of arrays (row,col) containing the indices + of the non-zero elements of the array. + + Examples + -------- + >>> from scipy.sparse import csr_array + >>> A = csr_array([[1,2,0],[0,0,3],[4,0,5]]) + >>> A.nonzero() + (array([0, 0, 1, 2, 2]), array([0, 1, 2, 0, 2])) + + """ + + # convert to COOrdinate format + A = self.tocoo() + nz_mask = A.data != 0 + return (A.row[nz_mask], A.col[nz_mask]) + + def _getcol(self, j): + """Returns a copy of column j of the array, as an (m x 1) sparse + array (column vector). + """ + if self.ndim == 1: + raise ValueError("getcol not provided for 1d arrays. Use indexing A[j]") + # Subclasses should override this method for efficiency. + # Post-multiply by a (n x 1) column vector 'a' containing all zeros + # except for a_j = 1 + N = self.shape[-1] + if j < 0: + j += N + if j < 0 or j >= N: + raise IndexError("index out of bounds") + col_selector = self._csc_container(([1], [[j], [0]]), + shape=(N, 1), dtype=self.dtype) + result = self @ col_selector + return result + + def _getrow(self, i): + """Returns a copy of row i of the array, as a (1 x n) sparse + array (row vector). + """ + if self.ndim == 1: + raise ValueError("getrow not meaningful for a 1d array") + # Subclasses should override this method for efficiency. + # Pre-multiply by a (1 x m) row vector 'a' containing all zeros + # except for a_i = 1 + M = self.shape[0] + if i < 0: + i += M + if i < 0 or i >= M: + raise IndexError("index out of bounds") + row_selector = self._csr_container(([1], [[0], [i]]), + shape=(1, M), dtype=self.dtype) + return row_selector @ self + + # The following dunder methods cannot be implemented. + # + # def __array__(self): + # # Sparse matrices rely on NumPy wrapping them in object arrays under + # # the hood to make unary ufuncs work on them. So we cannot raise + # # TypeError here - which would be handy to not give users object + # # arrays they probably don't want (they're looking for `.toarray()`). + # # + # # Conversion with `toarray()` would also break things because of the + # # behavior discussed above, plus we want to avoid densification by + # # accident because that can too easily blow up memory. + # + # def __array_ufunc__(self): + # # We cannot implement __array_ufunc__ due to mismatching semantics. + # # See gh-7707 and gh-7349 for details. + # + # def __array_function__(self): + # # We cannot implement __array_function__ due to mismatching semantics. + # # See gh-10362 for details. + + def todense(self, order=None, out=None): + """ + Return a dense representation of this sparse array/matrix. + + Parameters + ---------- + order : {'C', 'F'}, optional + Whether to store multi-dimensional data in C (row-major) + or Fortran (column-major) order in memory. The default + is 'None', which provides no ordering guarantees. + Cannot be specified in conjunction with the `out` + argument. + + out : ndarray, 2-D, optional + If specified, uses this array (or `numpy.matrix`) as the + output buffer instead of allocating a new array to + return. The provided array must have the same shape and + dtype as the sparse array/matrix on which you are calling the + method. + + Returns + ------- + arr : numpy.matrix, 2-D + A NumPy matrix object with the same shape and containing + the same data represented by the sparse array/matrix, with the + requested memory order. If `out` was passed and was an + array (rather than a `numpy.matrix`), it will be filled + with the appropriate values and returned wrapped in a + `numpy.matrix` object that shares the same memory. + """ + return self._ascontainer(self.toarray(order=order, out=out)) + + def toarray(self, order=None, out=None): + """ + Return a dense ndarray representation of this sparse array/matrix. + + Parameters + ---------- + order : {'C', 'F'}, optional + Whether to store multidimensional data in C (row-major) + or Fortran (column-major) order in memory. The default + is 'None', which provides no ordering guarantees. + Cannot be specified in conjunction with the `out` + argument. + + out : ndarray, 2-D, optional + If specified, uses this array as the output buffer + instead of allocating a new array to return. The provided + array must have the same shape and dtype as the sparse + array/matrix on which you are calling the method. For most + sparse types, `out` is required to be memory contiguous + (either C or Fortran ordered). + + Returns + ------- + arr : ndarray, 2-D + An array with the same shape and containing the same + data represented by the sparse array/matrix, with the requested + memory order. If `out` was passed, the same object is + returned after being modified in-place to contain the + appropriate values. + """ + return self.tocoo(copy=False).toarray(order=order, out=out) + + # Any sparse array format deriving from _spbase must define one of + # tocsr or tocoo. The other conversion methods may be implemented for + # efficiency, but are not required. + def tocsr(self, copy=False): + """Convert this array/matrix to Compressed Sparse Row format. + + With copy=False, the data/indices may be shared between this array/matrix and + the resultant csr_array/matrix. + """ + return self.tocoo(copy=copy).tocsr(copy=False) + + def todok(self, copy=False): + """Convert this array/matrix to Dictionary Of Keys format. + + With copy=False, the data/indices may be shared between this array/matrix and + the resultant dok_array/matrix. + """ + return self.tocoo(copy=copy).todok(copy=False) + + def tocoo(self, copy=False): + """Convert this array/matrix to COOrdinate format. + + With copy=False, the data/indices may be shared between this array/matrix and + the resultant coo_array/matrix. + """ + return self.tocsr(copy=False).tocoo(copy=copy) + + def tolil(self, copy=False): + """Convert this array/matrix to List of Lists format. + + With copy=False, the data/indices may be shared between this array/matrix and + the resultant lil_array/matrix. + """ + return self.tocsr(copy=False).tolil(copy=copy) + + def todia(self, copy=False): + """Convert this array/matrix to sparse DIAgonal format. + + With copy=False, the data/indices may be shared between this array/matrix and + the resultant dia_array/matrix. + """ + return self.tocoo(copy=copy).todia(copy=False) + + def tobsr(self, blocksize=None, copy=False): + """Convert this array/matrix to Block Sparse Row format. + + With copy=False, the data/indices may be shared between this array/matrix and + the resultant bsr_array/matrix. + + When blocksize=(R, C) is provided, it will be used for construction of + the bsr_array/matrix. + """ + return self.tocsr(copy=False).tobsr(blocksize=blocksize, copy=copy) + + def tocsc(self, copy=False): + """Convert this array/matrix to Compressed Sparse Column format. + + With copy=False, the data/indices may be shared between this array/matrix and + the resultant csc_array/matrix. + """ + return self.tocsr(copy=copy).tocsc(copy=False) + + def copy(self): + """Returns a copy of this array/matrix. + + No data/indices will be shared between the returned value and current + array/matrix. + """ + return self.__class__(self, copy=True) + + def sum(self, axis=None, dtype=None, out=None): + """ + Sum the array/matrix elements over a given axis. + + Parameters + ---------- + axis : {-2, -1, 0, 1, None} optional + Axis along which the sum is computed. The default is to + compute the sum of all the array/matrix elements, returning a scalar + (i.e., `axis` = `None`). + dtype : dtype, optional + The type of the returned array/matrix 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. + + .. versionadded:: 0.18.0 + + out : np.matrix, optional + Alternative output matrix 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. + + .. versionadded:: 0.18.0 + + Returns + ------- + sum_along_axis : np.matrix + A matrix with the same shape as `self`, with the specified + axis removed. + + See Also + -------- + numpy.matrix.sum : NumPy's implementation of 'sum' for matrices + + """ + validateaxis(axis) + + # Mimic numpy's casting. + res_dtype = get_sum_dtype(self.dtype) + + if self.ndim == 1: + if axis not in (None, -1, 0): + raise ValueError("axis must be None, -1 or 0") + ret = (self @ np.ones(self.shape, dtype=res_dtype)).astype(dtype) + + if out is not None: + if any(dim != 1 for dim in out.shape): + raise ValueError("dimensions do not match") + out[...] = ret + return ret + + # We use multiplication by a matrix of ones to achieve this. + # For some sparse array formats more efficient methods are + # possible -- these should override this function. + M, N = self.shape + + if axis is None: + # sum over rows and columns + return ( + self @ self._ascontainer(np.ones((N, 1), dtype=res_dtype)) + ).sum(dtype=dtype, out=out) + + if axis < 0: + axis += 2 + + # axis = 0 or 1 now + if axis == 0: + # sum over columns + ret = self._ascontainer( + np.ones((1, M), dtype=res_dtype) + ) @ self + else: + # sum over rows + ret = self @ self._ascontainer( + np.ones((N, 1), dtype=res_dtype) + ) + + if out is not None and out.shape != ret.shape: + raise ValueError("dimensions do not match") + + return ret.sum(axis=axis, dtype=dtype, out=out) + + def mean(self, axis=None, dtype=None, out=None): + """ + Compute the arithmetic mean along the specified axis. + + Returns the average of the array/matrix elements. The average is taken + over all elements in the array/matrix by default, otherwise over the + specified axis. `float64` intermediate and return values are used + for integer inputs. + + Parameters + ---------- + axis : {-2, -1, 0, 1, None} optional + Axis along which the mean is computed. The default is to compute + the mean of all elements in the array/matrix (i.e., `axis` = `None`). + 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. + + .. versionadded:: 0.18.0 + + out : np.matrix, optional + Alternative output matrix 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. + + .. versionadded:: 0.18.0 + + Returns + ------- + m : np.matrix + + See Also + -------- + numpy.matrix.mean : NumPy's implementation of 'mean' for matrices + + """ + validateaxis(axis) + + res_dtype = self.dtype.type + integral = (np.issubdtype(self.dtype, np.integer) or + np.issubdtype(self.dtype, np.bool_)) + + # output dtype + if dtype is None: + if integral: + res_dtype = np.float64 + else: + res_dtype = np.dtype(dtype).type + + # intermediate dtype for summation + inter_dtype = np.float64 if integral else res_dtype + inter_self = self.astype(inter_dtype) + + if self.ndim == 1: + if axis not in (None, -1, 0): + raise ValueError("axis must be None, -1 or 0") + res = inter_self / self.shape[-1] + return res.sum(dtype=res_dtype, out=out) + + if axis is None: + return (inter_self / (self.shape[0] * self.shape[1]))\ + .sum(dtype=res_dtype, out=out) + + if axis < 0: + axis += 2 + + # axis = 0 or 1 now + if axis == 0: + return (inter_self * (1.0 / self.shape[0])).sum( + axis=0, dtype=res_dtype, out=out) + else: + return (inter_self * (1.0 / self.shape[1])).sum( + axis=1, dtype=res_dtype, out=out) + + def diagonal(self, k=0): + """Returns the kth diagonal of the array/matrix. + + Parameters + ---------- + k : int, optional + Which diagonal to get, corresponding to elements a[i, i+k]. + Default: 0 (the main diagonal). + + .. versionadded:: 1.0 + + See also + -------- + numpy.diagonal : Equivalent numpy function. + + Examples + -------- + >>> from scipy.sparse import csr_array + >>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]]) + >>> A.diagonal() + array([1, 0, 5]) + >>> A.diagonal(k=1) + array([2, 3]) + """ + return self.tocsr().diagonal(k=k) + + def trace(self, offset=0): + """Returns the sum along diagonals of the sparse array/matrix. + + Parameters + ---------- + offset : int, optional + Which diagonal to get, corresponding to elements a[i, i+offset]. + Default: 0 (the main diagonal). + + """ + return self.diagonal(k=offset).sum() + + def setdiag(self, values, k=0): + """ + Set diagonal or off-diagonal elements of the array/matrix. + + Parameters + ---------- + values : array_like + New values of the diagonal elements. + + Values may have any length. If the diagonal is longer than values, + then the remaining diagonal entries will not be set. If values are + longer than the diagonal, then the remaining values are ignored. + + If a scalar value is given, all of the diagonal is set to it. + + k : int, optional + Which off-diagonal to set, corresponding to elements a[i,i+k]. + Default: 0 (the main diagonal). + + """ + M, N = self.shape + if (k > 0 and k >= N) or (k < 0 and -k >= M): + raise ValueError("k exceeds array dimensions") + self._setdiag(np.asarray(values), k) + + def _setdiag(self, values, k): + """This part of the implementation gets overridden by the + different formats. + """ + M, N = self.shape + if k < 0: + if values.ndim == 0: + # broadcast + max_index = min(M+k, N) + for i in range(max_index): + self[i - k, i] = values + else: + max_index = min(M+k, N, len(values)) + if max_index <= 0: + return + for i, v in enumerate(values[:max_index]): + self[i - k, i] = v + else: + if values.ndim == 0: + # broadcast + max_index = min(M, N-k) + for i in range(max_index): + self[i, i + k] = values + else: + max_index = min(M, N-k, len(values)) + if max_index <= 0: + return + for i, v in enumerate(values[:max_index]): + self[i, i + k] = v + + def _process_toarray_args(self, order, out): + if out is not None: + if order is not None: + raise ValueError('order cannot be specified if out ' + 'is not None') + if out.shape != self.shape or out.dtype != self.dtype: + raise ValueError('out array must be same dtype and shape as ' + 'sparse array') + out[...] = 0. + return out + else: + return np.zeros(self.shape, dtype=self.dtype, order=order) + + def _get_index_dtype(self, arrays=(), maxval=None, check_contents=False): + """ + Determine index dtype for array. + + This wraps _sputils.get_index_dtype, providing compatibility for both + array and matrix API sparse matrices. Matrix API sparse matrices would + attempt to downcast the indices - which can be computationally + expensive and undesirable for users. The array API changes this + behaviour. + + See discussion: https://github.com/scipy/scipy/issues/16774 + + The get_index_dtype import is due to implementation details of the test + suite. It allows the decorator ``with_64bit_maxval_limit`` to mock a + lower int32 max value for checks on the matrix API's downcasting + behaviour. + """ + from ._sputils import get_index_dtype + + # Don't check contents for array API + return get_index_dtype(arrays, + maxval, + (check_contents and not isinstance(self, sparray))) + + + ## All methods below are deprecated and should be removed in + ## scipy 1.14.0 + ## + ## Also uncomment the definition of shape above. + + def get_shape(self): + """Get shape of a sparse array/matrix. + + .. deprecated:: 1.11.0 + This method will be removed in SciPy 1.14.0. + Use `X.shape` instead. + """ + msg = ( + "`get_shape` is deprecated and will be removed in v1.14.0; " + "use `X.shape` instead." + ) + warn(msg, DeprecationWarning, stacklevel=2) + + return self._shape + + def set_shape(self, shape): + """See `reshape`. + + .. deprecated:: 1.11.0 + This method will be removed in SciPy 1.14.0. + Use `X.reshape` instead. + """ + msg = ( + "Shape assignment is deprecated and will be removed in v1.14.0; " + "use `reshape` instead." + ) + warn(msg, DeprecationWarning, stacklevel=2) + + # Make sure copy is False since this is in place + # Make sure format is unchanged because we are doing a __dict__ swap + new_self = self.reshape(shape, copy=False).asformat(self.format) + self.__dict__ = new_self.__dict__ + + shape = property( + fget=lambda self: self._shape, + fset=set_shape, + doc="""The shape of the array. + +Note that, starting in SciPy 1.14.0, this property will no longer be +settable. To change the array shape, use `X.reshape` instead. +""" + ) + + def asfptype(self): + """Upcast array/matrix to a floating point format (if necessary) + + .. deprecated:: 1.11.0 + This method is for internal use only, and will be removed from the + public API in SciPy 1.14.0. + """ + msg = ( + "`asfptype` is an internal function, and is deprecated " + "as part of the public API. It will be removed in v1.14.0." + ) + warn(msg, DeprecationWarning, stacklevel=2) + return self._asfptype() + + def getmaxprint(self): + """Maximum number of elements to display when printed. + + .. deprecated:: 1.11.0 + This method is for internal use only, and will be removed from the + public API in SciPy 1.14.0. + """ + msg = ( + "`getmaxprint` is an internal function, and is deprecated " + "as part of the public API. It will be removed in v1.14.0." + ) + warn(msg, DeprecationWarning, stacklevel=2) + return self._getmaxprint() + + def getformat(self): + """Sparse array/matrix storage format. + + .. deprecated:: 1.11.0 + This method will be removed in SciPy 1.14.0. + Use `X.format` instead. + """ + msg = ( + "`getformat` is deprecated and will be removed in v1.14.0; " + "use `X.format` instead." + ) + warn(msg, DeprecationWarning, stacklevel=2) + return self.format + + def getnnz(self, axis=None): + """Number of stored values, including explicit zeros. + + Parameters + ---------- + axis : None, 0, or 1 + Select between the number of values across the whole array/matrix, in + each column, or in each row. + + See also + -------- + count_nonzero : Number of non-zero entries + """ + return self._getnnz(axis=axis) + + def getH(self): + """Return the Hermitian transpose of this array/matrix. + + .. deprecated:: 1.11.0 + This method will be removed in SciPy 1.14.0. + Use `X.conj().T` instead. + """ + msg = ( + "`getH` is deprecated and will be removed in v1.14.0; " + "use `X.conj().T` instead." + ) + warn(msg, DeprecationWarning, stacklevel=2) + return self.conjugate().transpose() + + def getcol(self, j): + """Returns a copy of column j of the array/matrix, as an (m x 1) sparse + array/matrix (column vector). + + .. deprecated:: 1.11.0 + This method will be removed in SciPy 1.14.0. + Use array/matrix indexing instead. + """ + msg = ( + "`getcol` is deprecated and will be removed in v1.14.0; " + f"use `X[:, [{j}]]` instead." + ) + warn(msg, DeprecationWarning, stacklevel=2) + return self._getcol(j) + + def getrow(self, i): + """Returns a copy of row i of the array/matrix, as a (1 x n) sparse + array/matrix (row vector). + + .. deprecated:: 1.11.0 + This method will be removed in SciPy 1.14.0. + Use array/matrix indexing instead. + """ + msg = ( + "`getrow` is deprecated and will be removed in v1.14.0; " + f"use `X[[{i}]]` instead." + ) + warn(msg, DeprecationWarning, stacklevel=2) + return self._getrow(i) + + ## End 1.14.0 deprecated methods + + +class sparray: + """A namespace class to separate sparray from spmatrix""" + pass + +sparray.__doc__ = _spbase.__doc__ + + +def issparse(x): + """Is `x` of a sparse array or sparse matrix type? + + Parameters + ---------- + x + object to check for being a sparse array or sparse matrix + + Returns + ------- + bool + True if `x` is a sparse array or a sparse matrix, False otherwise + + Examples + -------- + >>> import numpy as np + >>> from scipy.sparse import csr_array, csr_matrix, issparse + >>> issparse(csr_matrix([[5]])) + True + >>> issparse(csr_array([[5]])) + True + >>> issparse(np.array([[5]])) + False + >>> issparse(5) + False + """ + return isinstance(x, _spbase) + + +def isspmatrix(x): + """Is `x` of a sparse matrix type? + + Parameters + ---------- + x + object to check for being a sparse matrix + + Returns + ------- + bool + True if `x` is a sparse matrix, False otherwise + + Examples + -------- + >>> import numpy as np + >>> from scipy.sparse import csr_array, csr_matrix, isspmatrix + >>> isspmatrix(csr_matrix([[5]])) + True + >>> isspmatrix(csr_array([[5]])) + False + >>> isspmatrix(np.array([[5]])) + False + >>> isspmatrix(5) + False + """ + return isinstance(x, spmatrix) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_coo.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_coo.py new file mode 100644 index 0000000000000000000000000000000000000000..f8c5039f94ed939cd149dbe1bc7e258153d0b32d --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_coo.py @@ -0,0 +1,858 @@ +""" A sparse matrix in COOrdinate or 'triplet' format""" + +__docformat__ = "restructuredtext en" + +__all__ = ['coo_array', 'coo_matrix', 'isspmatrix_coo'] + +import math +from warnings import warn + +import numpy as np + +from .._lib._util import copy_if_needed +from ._matrix import spmatrix +from ._sparsetools import coo_tocsr, coo_todense, coo_matvec +from ._base import issparse, SparseEfficiencyWarning, _spbase, sparray +from ._data import _data_matrix, _minmax_mixin +from ._sputils import (upcast_char, to_native, isshape, getdtype, + getdata, downcast_intp_index, get_index_dtype, + check_shape, check_reshape_kwargs) + +import operator + + +class _coo_base(_data_matrix, _minmax_mixin): + _format = 'coo' + + def __init__(self, arg1, shape=None, dtype=None, copy=False): + _data_matrix.__init__(self) + is_array = isinstance(self, sparray) + if not copy: + copy = copy_if_needed + + if isinstance(arg1, tuple): + if isshape(arg1, allow_1d=is_array): + self._shape = check_shape(arg1, allow_1d=is_array) + idx_dtype = self._get_index_dtype(maxval=max(self._shape)) + data_dtype = getdtype(dtype, default=float) + self.coords = tuple(np.array([], dtype=idx_dtype) + for _ in range(len(self._shape))) + self.data = np.array([], dtype=data_dtype) + self.has_canonical_format = True + else: + try: + obj, coords = arg1 + except (TypeError, ValueError) as e: + raise TypeError('invalid input format') from e + + if shape is None: + if any(len(idx) == 0 for idx in coords): + raise ValueError('cannot infer dimensions from zero ' + 'sized index arrays') + shape = tuple(operator.index(np.max(idx)) + 1 + for idx in coords) + self._shape = check_shape(shape, allow_1d=is_array) + + idx_dtype = self._get_index_dtype(coords, + maxval=max(self.shape), + check_contents=True) + self.coords = tuple(np.array(idx, copy=copy, dtype=idx_dtype) + for idx in coords) + self.data = getdata(obj, copy=copy, dtype=dtype) + self.has_canonical_format = False + else: + if issparse(arg1): + if arg1.format == self.format and copy: + self.coords = tuple(idx.copy() for idx in arg1.coords) + self.data = arg1.data.copy() + self._shape = check_shape(arg1.shape, allow_1d=is_array) + self.has_canonical_format = arg1.has_canonical_format + else: + coo = arg1.tocoo() + self.coords = tuple(coo.coords) + self.data = coo.data + self._shape = check_shape(coo.shape, allow_1d=is_array) + self.has_canonical_format = False + else: + # dense argument + M = np.asarray(arg1) + if not is_array: + M = np.atleast_2d(M) + if M.ndim != 2: + raise TypeError('expected dimension <= 2 array or matrix') + + self._shape = check_shape(M.shape, allow_1d=is_array) + if shape is not None: + if check_shape(shape, allow_1d=is_array) != self._shape: + message = f'inconsistent shapes: {shape} != {self._shape}' + raise ValueError(message) + index_dtype = self._get_index_dtype(maxval=max(self._shape)) + coords = M.nonzero() + self.coords = tuple(idx.astype(index_dtype, copy=False) + for idx in coords) + self.data = M[coords] + self.has_canonical_format = True + + if dtype is not None: + self.data = self.data.astype(dtype, copy=False) + + self._check() + + @property + def row(self): + if self.ndim > 1: + return self.coords[-2] + result = np.zeros_like(self.col) + result.setflags(write=False) + return result + + + @row.setter + def row(self, new_row): + if self.ndim < 2: + raise ValueError('cannot set row attribute of a 1-dimensional sparse array') + new_row = np.asarray(new_row, dtype=self.coords[-2].dtype) + self.coords = self.coords[:-2] + (new_row,) + self.coords[-1:] + + @property + def col(self): + return self.coords[-1] + + @col.setter + def col(self, new_col): + new_col = np.asarray(new_col, dtype=self.coords[-1].dtype) + self.coords = self.coords[:-1] + (new_col,) + + def reshape(self, *args, **kwargs): + is_array = isinstance(self, sparray) + shape = check_shape(args, self.shape, allow_1d=is_array) + order, copy = check_reshape_kwargs(kwargs) + + # Return early if reshape is not required + if shape == self.shape: + if copy: + return self.copy() + else: + return self + + # When reducing the number of dimensions, we need to be careful about + # index overflow. This is why we can't simply call + # `np.ravel_multi_index()` followed by `np.unravel_index()` here. + flat_coords = _ravel_coords(self.coords, self.shape, order=order) + if len(shape) == 2: + if order == 'C': + new_coords = divmod(flat_coords, shape[1]) + else: + new_coords = divmod(flat_coords, shape[0])[::-1] + else: + new_coords = np.unravel_index(flat_coords, shape, order=order) + + # Handle copy here rather than passing on to the constructor so that no + # copy will be made of `new_coords` regardless. + if copy: + new_data = self.data.copy() + else: + new_data = self.data + + return self.__class__((new_data, new_coords), shape=shape, copy=False) + + reshape.__doc__ = _spbase.reshape.__doc__ + + def _getnnz(self, axis=None): + if axis is None or (axis == 0 and self.ndim == 1): + nnz = len(self.data) + if any(len(idx) != nnz for idx in self.coords): + raise ValueError('all index and data arrays must have the ' + 'same length') + + if self.data.ndim != 1 or any(idx.ndim != 1 for idx in self.coords): + raise ValueError('row, column, and data arrays must be 1-D') + + return int(nnz) + + if axis < 0: + axis += self.ndim + if axis >= self.ndim: + raise ValueError('axis out of bounds') + if self.ndim > 2: + raise NotImplementedError('per-axis nnz for COO arrays with >2 ' + 'dimensions is not supported') + return np.bincount(downcast_intp_index(self.coords[1 - axis]), + minlength=self.shape[1 - axis]) + + _getnnz.__doc__ = _spbase._getnnz.__doc__ + + def _check(self): + """ Checks data structure for consistency """ + if self.ndim != len(self.coords): + raise ValueError('mismatching number of index arrays for shape; ' + f'got {len(self.coords)}, expected {self.ndim}') + + # index arrays should have integer data types + for i, idx in enumerate(self.coords): + if idx.dtype.kind != 'i': + warn(f'index array {i} has non-integer dtype ({idx.dtype.name})', + stacklevel=3) + + idx_dtype = self._get_index_dtype(self.coords, maxval=max(self.shape)) + self.coords = tuple(np.asarray(idx, dtype=idx_dtype) + for idx in self.coords) + self.data = to_native(self.data) + + if self.nnz > 0: + for i, idx in enumerate(self.coords): + if idx.max() >= self.shape[i]: + raise ValueError(f'axis {i} index {idx.max()} exceeds ' + f'matrix dimension {self.shape[i]}') + if idx.min() < 0: + raise ValueError(f'negative axis {i} index: {idx.min()}') + + def transpose(self, axes=None, copy=False): + if axes is None: + axes = range(self.ndim)[::-1] + elif isinstance(self, sparray): + if len(axes) != self.ndim: + raise ValueError("axes don't match matrix dimensions") + if len(set(axes)) != self.ndim: + raise ValueError("repeated axis in transpose") + elif axes != (1, 0): + raise ValueError("Sparse matrices do not support an 'axes' " + "parameter because swapping dimensions is the " + "only logical permutation.") + + permuted_shape = tuple(self._shape[i] for i in axes) + permuted_coords = tuple(self.coords[i] for i in axes) + return self.__class__((self.data, permuted_coords), + shape=permuted_shape, copy=copy) + + transpose.__doc__ = _spbase.transpose.__doc__ + + def resize(self, *shape) -> None: + is_array = isinstance(self, sparray) + shape = check_shape(shape, allow_1d=is_array) + + # Check for added dimensions. + if len(shape) > self.ndim: + flat_coords = _ravel_coords(self.coords, self.shape) + max_size = math.prod(shape) + self.coords = np.unravel_index(flat_coords[:max_size], shape) + self.data = self.data[:max_size] + self._shape = shape + return + + # Check for removed dimensions. + if len(shape) < self.ndim: + tmp_shape = ( + self._shape[:len(shape) - 1] # Original shape without last axis + + (-1,) # Last axis is used to flatten the array + + (1,) * (self.ndim - len(shape)) # Pad with ones + ) + tmp = self.reshape(tmp_shape) + self.coords = tmp.coords[:len(shape)] + self._shape = tmp.shape[:len(shape)] + + # Handle truncation of existing dimensions. + is_truncating = any(old > new for old, new in zip(self.shape, shape)) + if is_truncating: + mask = np.logical_and.reduce([ + idx < size for idx, size in zip(self.coords, shape) + ]) + if not mask.all(): + self.coords = tuple(idx[mask] for idx in self.coords) + self.data = self.data[mask] + + self._shape = shape + + resize.__doc__ = _spbase.resize.__doc__ + + def toarray(self, order=None, out=None): + B = self._process_toarray_args(order, out) + fortran = int(B.flags.f_contiguous) + if not fortran and not B.flags.c_contiguous: + raise ValueError("Output array must be C or F contiguous") + if self.ndim > 2: + raise ValueError("Cannot densify higher-rank sparse array") + # This handles both 0D and 1D cases correctly regardless of the + # original shape. + M, N = self._shape_as_2d + coo_todense(M, N, self.nnz, self.row, self.col, self.data, + B.ravel('A'), fortran) + # Note: reshape() doesn't copy here, but does return a new array (view). + return B.reshape(self.shape) + + toarray.__doc__ = _spbase.toarray.__doc__ + + def tocsc(self, copy=False): + """Convert this array/matrix to Compressed Sparse Column format + + Duplicate entries will be summed together. + + Examples + -------- + >>> from numpy import array + >>> from scipy.sparse import coo_array + >>> row = array([0, 0, 1, 3, 1, 0, 0]) + >>> col = array([0, 2, 1, 3, 1, 0, 0]) + >>> data = array([1, 1, 1, 1, 1, 1, 1]) + >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsc() + >>> A.toarray() + array([[3, 0, 1, 0], + [0, 2, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 1]]) + + """ + if self.ndim != 2: + raise ValueError("Cannot convert a 1d sparse array to csc format") + if self.nnz == 0: + return self._csc_container(self.shape, dtype=self.dtype) + else: + from ._csc import csc_array + indptr, indices, data, shape = self._coo_to_compressed(csc_array._swap) + + x = self._csc_container((data, indices, indptr), shape=shape) + if not self.has_canonical_format: + x.sum_duplicates() + return x + + def tocsr(self, copy=False): + """Convert this array/matrix to Compressed Sparse Row format + + Duplicate entries will be summed together. + + Examples + -------- + >>> from numpy import array + >>> from scipy.sparse import coo_array + >>> row = array([0, 0, 1, 3, 1, 0, 0]) + >>> col = array([0, 2, 1, 3, 1, 0, 0]) + >>> data = array([1, 1, 1, 1, 1, 1, 1]) + >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsr() + >>> A.toarray() + array([[3, 0, 1, 0], + [0, 2, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 1]]) + + """ + if self.ndim != 2: + raise ValueError("Cannot convert a 1d sparse array to csr format") + if self.nnz == 0: + return self._csr_container(self.shape, dtype=self.dtype) + else: + from ._csr import csr_array + indptr, indices, data, shape = self._coo_to_compressed(csr_array._swap) + + x = self._csr_container((data, indices, indptr), shape=self.shape) + if not self.has_canonical_format: + x.sum_duplicates() + return x + + def _coo_to_compressed(self, swap): + """convert (shape, coords, data) to (indptr, indices, data, shape)""" + M, N = swap(self.shape) + major, minor = swap(self.coords) + nnz = len(major) + # convert idx_dtype intc to int32 for pythran. + # tested in scipy/optimize/tests/test__numdiff.py::test_group_columns + idx_dtype = self._get_index_dtype(self.coords, maxval=max(self.nnz, N)) + major = major.astype(idx_dtype, copy=False) + minor = minor.astype(idx_dtype, copy=False) + + indptr = np.empty(M + 1, dtype=idx_dtype) + indices = np.empty_like(minor, dtype=idx_dtype) + data = np.empty_like(self.data, dtype=self.dtype) + + coo_tocsr(M, N, nnz, major, minor, self.data, indptr, indices, data) + return indptr, indices, data, self.shape + + def tocoo(self, copy=False): + if copy: + return self.copy() + else: + return self + + tocoo.__doc__ = _spbase.tocoo.__doc__ + + def todia(self, copy=False): + if self.ndim != 2: + raise ValueError("Cannot convert a 1d sparse array to dia format") + self.sum_duplicates() + ks = self.col - self.row # the diagonal for each nonzero + diags, diag_idx = np.unique(ks, return_inverse=True) + + if len(diags) > 100: + # probably undesired, should todia() have a maxdiags parameter? + warn("Constructing a DIA matrix with %d diagonals " + "is inefficient" % len(diags), + SparseEfficiencyWarning, stacklevel=2) + + #initialize and fill in data array + if self.data.size == 0: + data = np.zeros((0, 0), dtype=self.dtype) + else: + data = np.zeros((len(diags), self.col.max()+1), dtype=self.dtype) + data[diag_idx, self.col] = self.data + + return self._dia_container((data, diags), shape=self.shape) + + todia.__doc__ = _spbase.todia.__doc__ + + def todok(self, copy=False): + self.sum_duplicates() + dok = self._dok_container(self.shape, dtype=self.dtype) + # ensure that 1d coordinates are not tuples + if self.ndim == 1: + coords = self.coords[0] + else: + coords = zip(*self.coords) + + dok._dict = dict(zip(coords, self.data)) + return dok + + todok.__doc__ = _spbase.todok.__doc__ + + def diagonal(self, k=0): + if self.ndim != 2: + raise ValueError("diagonal requires two dimensions") + rows, cols = self.shape + if k <= -rows or k >= cols: + return np.empty(0, dtype=self.data.dtype) + diag = np.zeros(min(rows + min(k, 0), cols - max(k, 0)), + dtype=self.dtype) + diag_mask = (self.row + k) == self.col + + if self.has_canonical_format: + row = self.row[diag_mask] + data = self.data[diag_mask] + else: + inds = tuple(idx[diag_mask] for idx in self.coords) + (row, _), data = self._sum_duplicates(inds, self.data[diag_mask]) + diag[row + min(k, 0)] = data + + return diag + + diagonal.__doc__ = _data_matrix.diagonal.__doc__ + + def _setdiag(self, values, k): + if self.ndim != 2: + raise ValueError("setting a diagonal requires two dimensions") + M, N = self.shape + if values.ndim and not len(values): + return + idx_dtype = self.row.dtype + + # Determine which triples to keep and where to put the new ones. + full_keep = self.col - self.row != k + if k < 0: + max_index = min(M+k, N) + if values.ndim: + max_index = min(max_index, len(values)) + keep = np.logical_or(full_keep, self.col >= max_index) + new_row = np.arange(-k, -k + max_index, dtype=idx_dtype) + new_col = np.arange(max_index, dtype=idx_dtype) + else: + max_index = min(M, N-k) + if values.ndim: + max_index = min(max_index, len(values)) + keep = np.logical_or(full_keep, self.row >= max_index) + new_row = np.arange(max_index, dtype=idx_dtype) + new_col = np.arange(k, k + max_index, dtype=idx_dtype) + + # Define the array of data consisting of the entries to be added. + if values.ndim: + new_data = values[:max_index] + else: + new_data = np.empty(max_index, dtype=self.dtype) + new_data[:] = values + + # Update the internal structure. + self.coords = (np.concatenate((self.row[keep], new_row)), + np.concatenate((self.col[keep], new_col))) + self.data = np.concatenate((self.data[keep], new_data)) + self.has_canonical_format = False + + # needed by _data_matrix + def _with_data(self, data, copy=True): + """Returns a matrix with the same sparsity structure as self, + but with different data. By default the index arrays are copied. + """ + if copy: + coords = tuple(idx.copy() for idx in self.coords) + else: + coords = self.coords + return self.__class__((data, coords), shape=self.shape, dtype=data.dtype) + + def sum_duplicates(self) -> None: + """Eliminate duplicate entries by adding them together + + This is an *in place* operation + """ + if self.has_canonical_format: + return + summed = self._sum_duplicates(self.coords, self.data) + self.coords, self.data = summed + self.has_canonical_format = True + + def _sum_duplicates(self, coords, data): + # Assumes coords not in canonical format. + if len(data) == 0: + return coords, data + # Sort coords w.r.t. rows, then cols. This corresponds to C-order, + # which we rely on for argmin/argmax to return the first index in the + # same way that numpy does (in the case of ties). + order = np.lexsort(coords[::-1]) + coords = tuple(idx[order] for idx in coords) + data = data[order] + unique_mask = np.logical_or.reduce([ + idx[1:] != idx[:-1] for idx in coords + ]) + unique_mask = np.append(True, unique_mask) + coords = tuple(idx[unique_mask] for idx in coords) + unique_inds, = np.nonzero(unique_mask) + data = np.add.reduceat(data, unique_inds, dtype=self.dtype) + return coords, data + + def eliminate_zeros(self): + """Remove zero entries from the array/matrix + + This is an *in place* operation + """ + mask = self.data != 0 + self.data = self.data[mask] + self.coords = tuple(idx[mask] for idx in self.coords) + + ####################### + # Arithmetic handlers # + ####################### + + def _add_dense(self, other): + if other.shape != self.shape: + raise ValueError(f'Incompatible shapes ({self.shape} and {other.shape})') + dtype = upcast_char(self.dtype.char, other.dtype.char) + result = np.array(other, dtype=dtype, copy=True) + fortran = int(result.flags.f_contiguous) + M, N = self._shape_as_2d + coo_todense(M, N, self.nnz, self.row, self.col, self.data, + result.ravel('A'), fortran) + return self._container(result, copy=False) + + def _matmul_vector(self, other): + result_shape = self.shape[0] if self.ndim > 1 else 1 + result = np.zeros(result_shape, + dtype=upcast_char(self.dtype.char, other.dtype.char)) + + if self.ndim == 2: + col = self.col + row = self.row + elif self.ndim == 1: + col = self.coords[0] + row = np.zeros_like(col) + else: + raise NotImplementedError( + f"coo_matvec not implemented for ndim={self.ndim}") + + coo_matvec(self.nnz, row, col, self.data, other, result) + # Array semantics return a scalar here, not a single-element array. + if isinstance(self, sparray) and result_shape == 1: + return result[0] + return result + + def _matmul_multivector(self, other): + result_dtype = upcast_char(self.dtype.char, other.dtype.char) + if self.ndim == 2: + result_shape = (other.shape[1], self.shape[0]) + col = self.col + row = self.row + elif self.ndim == 1: + result_shape = (other.shape[1],) + col = self.coords[0] + row = np.zeros_like(col) + else: + raise NotImplementedError( + f"coo_matvec not implemented for ndim={self.ndim}") + + result = np.zeros(result_shape, dtype=result_dtype) + for i, other_col in enumerate(other.T): + coo_matvec(self.nnz, row, col, self.data, other_col, result[i:i + 1]) + return result.T.view(type=type(other)) + + +def _ravel_coords(coords, shape, order='C'): + """Like np.ravel_multi_index, but avoids some overflow issues.""" + if len(coords) == 1: + return coords[0] + # Handle overflow as in https://github.com/scipy/scipy/pull/9132 + if len(coords) == 2: + nrows, ncols = shape + row, col = coords + if order == 'C': + maxval = (ncols * max(0, nrows - 1) + max(0, ncols - 1)) + idx_dtype = get_index_dtype(maxval=maxval) + return np.multiply(ncols, row, dtype=idx_dtype) + col + elif order == 'F': + maxval = (nrows * max(0, ncols - 1) + max(0, nrows - 1)) + idx_dtype = get_index_dtype(maxval=maxval) + return np.multiply(nrows, col, dtype=idx_dtype) + row + else: + raise ValueError("'order' must be 'C' or 'F'") + return np.ravel_multi_index(coords, shape, order=order) + + +def isspmatrix_coo(x): + """Is `x` of coo_matrix type? + + Parameters + ---------- + x + object to check for being a coo matrix + + Returns + ------- + bool + True if `x` is a coo matrix, False otherwise + + Examples + -------- + >>> from scipy.sparse import coo_array, coo_matrix, csr_matrix, isspmatrix_coo + >>> isspmatrix_coo(coo_matrix([[5]])) + True + >>> isspmatrix_coo(coo_array([[5]])) + False + >>> isspmatrix_coo(csr_matrix([[5]])) + False + """ + return isinstance(x, coo_matrix) + + +# This namespace class separates array from matrix with isinstance +class coo_array(_coo_base, sparray): + """ + A sparse array in COOrdinate format. + + Also known as the 'ijv' or 'triplet' format. + + This can be instantiated in several ways: + coo_array(D) + where D is an ndarray + + coo_array(S) + with another sparse array or matrix S (equivalent to S.tocoo()) + + coo_array(shape, [dtype]) + to construct an empty sparse array with shape `shape` + dtype is optional, defaulting to dtype='d'. + + coo_array((data, coords), [shape]) + to construct from existing data and index arrays: + 1. data[:] the entries of the sparse array, in any order + 2. coords[i][:] the axis-i coordinates of the data entries + + Where ``A[coords] = data``, and coords is a tuple of index arrays. + When shape is not specified, it is inferred from the index arrays. + + Attributes + ---------- + dtype : dtype + Data type of the sparse array + shape : tuple of integers + Shape of the sparse array + ndim : int + Number of dimensions of the sparse array + nnz + size + data + COO format data array of the sparse array + coords + COO format tuple of index arrays + has_canonical_format : bool + Whether the matrix has sorted coordinates and no duplicates + format + T + + Notes + ----- + + Sparse arrays can be used in arithmetic operations: they support + addition, subtraction, multiplication, division, and matrix power. + + Advantages of the COO format + - facilitates fast conversion among sparse formats + - permits duplicate entries (see example) + - very fast conversion to and from CSR/CSC formats + + Disadvantages of the COO format + - does not directly support: + + arithmetic operations + + slicing + + Intended Usage + - COO is a fast format for constructing sparse arrays + - Once a COO array has been constructed, convert to CSR or + CSC format for fast arithmetic and matrix vector operations + - By default when converting to CSR or CSC format, duplicate (i,j) + entries will be summed together. This facilitates efficient + construction of finite element matrices and the like. (see example) + + Canonical format + - Entries and coordinates sorted by row, then column. + - There are no duplicate entries (i.e. duplicate (i,j) locations) + - Data arrays MAY have explicit zeros. + + Examples + -------- + + >>> # Constructing an empty sparse array + >>> import numpy as np + >>> from scipy.sparse import coo_array + >>> coo_array((3, 4), dtype=np.int8).toarray() + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int8) + + >>> # Constructing a sparse array using ijv format + >>> row = np.array([0, 3, 1, 0]) + >>> col = np.array([0, 3, 1, 2]) + >>> data = np.array([4, 5, 7, 9]) + >>> coo_array((data, (row, col)), shape=(4, 4)).toarray() + array([[4, 0, 9, 0], + [0, 7, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 5]]) + + >>> # Constructing a sparse array with duplicate coordinates + >>> row = np.array([0, 0, 1, 3, 1, 0, 0]) + >>> col = np.array([0, 2, 1, 3, 1, 0, 0]) + >>> data = np.array([1, 1, 1, 1, 1, 1, 1]) + >>> coo = coo_array((data, (row, col)), shape=(4, 4)) + >>> # Duplicate coordinates are maintained until implicitly or explicitly summed + >>> np.max(coo.data) + 1 + >>> coo.toarray() + array([[3, 0, 1, 0], + [0, 2, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 1]]) + + """ + + +class coo_matrix(spmatrix, _coo_base): + """ + A sparse matrix in COOrdinate format. + + Also known as the 'ijv' or 'triplet' format. + + This can be instantiated in several ways: + coo_matrix(D) + where D is a 2-D ndarray + + coo_matrix(S) + with another sparse array or matrix S (equivalent to S.tocoo()) + + coo_matrix((M, N), [dtype]) + to construct an empty matrix with shape (M, N) + dtype is optional, defaulting to dtype='d'. + + coo_matrix((data, (i, j)), [shape=(M, N)]) + to construct from three arrays: + 1. data[:] the entries of the matrix, in any order + 2. i[:] the row indices of the matrix entries + 3. j[:] the column indices of the matrix entries + + Where ``A[i[k], j[k]] = data[k]``. When shape is not + specified, it is inferred from the index arrays + + Attributes + ---------- + dtype : dtype + Data type of the matrix + shape : 2-tuple + Shape of the matrix + ndim : int + Number of dimensions (this is always 2) + nnz + size + data + COO format data array of the matrix + row + COO format row index array of the matrix + col + COO format column index array of the matrix + has_canonical_format : bool + Whether the matrix has sorted indices and no duplicates + format + T + + Notes + ----- + + Sparse matrices can be used in arithmetic operations: they support + addition, subtraction, multiplication, division, and matrix power. + + Advantages of the COO format + - facilitates fast conversion among sparse formats + - permits duplicate entries (see example) + - very fast conversion to and from CSR/CSC formats + + Disadvantages of the COO format + - does not directly support: + + arithmetic operations + + slicing + + Intended Usage + - COO is a fast format for constructing sparse matrices + - Once a COO matrix has been constructed, convert to CSR or + CSC format for fast arithmetic and matrix vector operations + - By default when converting to CSR or CSC format, duplicate (i,j) + entries will be summed together. This facilitates efficient + construction of finite element matrices and the like. (see example) + + Canonical format + - Entries and coordinates sorted by row, then column. + - There are no duplicate entries (i.e. duplicate (i,j) locations) + - Data arrays MAY have explicit zeros. + + Examples + -------- + + >>> # Constructing an empty matrix + >>> import numpy as np + >>> from scipy.sparse import coo_matrix + >>> coo_matrix((3, 4), dtype=np.int8).toarray() + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int8) + + >>> # Constructing a matrix using ijv format + >>> row = np.array([0, 3, 1, 0]) + >>> col = np.array([0, 3, 1, 2]) + >>> data = np.array([4, 5, 7, 9]) + >>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray() + array([[4, 0, 9, 0], + [0, 7, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 5]]) + + >>> # Constructing a matrix with duplicate coordinates + >>> row = np.array([0, 0, 1, 3, 1, 0, 0]) + >>> col = np.array([0, 2, 1, 3, 1, 0, 0]) + >>> data = np.array([1, 1, 1, 1, 1, 1, 1]) + >>> coo = coo_matrix((data, (row, col)), shape=(4, 4)) + >>> # Duplicate coordinates are maintained until implicitly or explicitly summed + >>> np.max(coo.data) + 1 + >>> coo.toarray() + array([[3, 0, 1, 0], + [0, 2, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 1]]) + + """ + + def __setstate__(self, state): + if 'coords' not in state: + # For retro-compatibility with the previous attributes + # storing nnz coordinates for 2D COO matrix. + state['coords'] = (state.pop('row'), state.pop('col')) + self.__dict__.update(state) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_csc.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_csc.py new file mode 100644 index 0000000000000000000000000000000000000000..3fcdeb49cc0a951b9a2df955b971d5148916f289 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_csc.py @@ -0,0 +1,364 @@ +"""Compressed Sparse Column matrix format""" +__docformat__ = "restructuredtext en" + +__all__ = ['csc_array', 'csc_matrix', 'isspmatrix_csc'] + + +import numpy as np + +from ._matrix import spmatrix +from ._base import _spbase, sparray +from ._sparsetools import csc_tocsr, expandptr +from ._sputils import upcast + +from ._compressed import _cs_matrix + + +class _csc_base(_cs_matrix): + _format = 'csc' + + def transpose(self, axes=None, copy=False): + if axes is not None and axes != (1, 0): + raise ValueError("Sparse arrays/matrices do not support " + "an 'axes' parameter because swapping " + "dimensions is the only logical permutation.") + + M, N = self.shape + + return self._csr_container((self.data, self.indices, + self.indptr), (N, M), copy=copy) + + transpose.__doc__ = _spbase.transpose.__doc__ + + def __iter__(self): + yield from self.tocsr() + + def tocsc(self, copy=False): + if copy: + return self.copy() + else: + return self + + tocsc.__doc__ = _spbase.tocsc.__doc__ + + def tocsr(self, copy=False): + M,N = self.shape + idx_dtype = self._get_index_dtype((self.indptr, self.indices), + maxval=max(self.nnz, N)) + indptr = np.empty(M + 1, dtype=idx_dtype) + indices = np.empty(self.nnz, dtype=idx_dtype) + data = np.empty(self.nnz, dtype=upcast(self.dtype)) + + csc_tocsr(M, N, + self.indptr.astype(idx_dtype), + self.indices.astype(idx_dtype), + self.data, + indptr, + indices, + data) + + A = self._csr_container( + (data, indices, indptr), + shape=self.shape, copy=False + ) + A.has_sorted_indices = True + return A + + tocsr.__doc__ = _spbase.tocsr.__doc__ + + def nonzero(self): + # CSC can't use _cs_matrix's .nonzero method because it + # returns the indices sorted for self transposed. + + # Get row and col indices, from _cs_matrix.tocoo + major_dim, minor_dim = self._swap(self.shape) + minor_indices = self.indices + major_indices = np.empty(len(minor_indices), dtype=self.indices.dtype) + expandptr(major_dim, self.indptr, major_indices) + row, col = self._swap((major_indices, minor_indices)) + + # Remove explicit zeros + nz_mask = self.data != 0 + row = row[nz_mask] + col = col[nz_mask] + + # Sort them to be in C-style order + ind = np.argsort(row, kind='mergesort') + row = row[ind] + col = col[ind] + + return row, col + + nonzero.__doc__ = _cs_matrix.nonzero.__doc__ + + def _getrow(self, i): + """Returns a copy of row i of the matrix, as a (1 x n) + CSR matrix (row vector). + """ + M, N = self.shape + i = int(i) + if i < 0: + i += M + if i < 0 or i >= M: + raise IndexError('index (%d) out of range' % i) + return self._get_submatrix(minor=i).tocsr() + + def _getcol(self, i): + """Returns a copy of column i of the matrix, as a (m x 1) + CSC matrix (column vector). + """ + M, N = self.shape + i = int(i) + if i < 0: + i += N + if i < 0 or i >= N: + raise IndexError('index (%d) out of range' % i) + return self._get_submatrix(major=i, copy=True) + + def _get_intXarray(self, row, col): + return self._major_index_fancy(col)._get_submatrix(minor=row) + + def _get_intXslice(self, row, col): + if col.step in (1, None): + return self._get_submatrix(major=col, minor=row, copy=True) + return self._major_slice(col)._get_submatrix(minor=row) + + def _get_sliceXint(self, row, col): + if row.step in (1, None): + return self._get_submatrix(major=col, minor=row, copy=True) + return self._get_submatrix(major=col)._minor_slice(row) + + def _get_sliceXarray(self, row, col): + return self._major_index_fancy(col)._minor_slice(row) + + def _get_arrayXint(self, row, col): + return self._get_submatrix(major=col)._minor_index_fancy(row) + + def _get_arrayXslice(self, row, col): + return self._major_slice(col)._minor_index_fancy(row) + + # these functions are used by the parent class (_cs_matrix) + # to remove redundancy between csc_array and csr_matrix + @staticmethod + def _swap(x): + """swap the members of x if this is a column-oriented matrix + """ + return x[1], x[0] + + +def isspmatrix_csc(x): + """Is `x` of csc_matrix type? + + Parameters + ---------- + x + object to check for being a csc matrix + + Returns + ------- + bool + True if `x` is a csc matrix, False otherwise + + Examples + -------- + >>> from scipy.sparse import csc_array, csc_matrix, coo_matrix, isspmatrix_csc + >>> isspmatrix_csc(csc_matrix([[5]])) + True + >>> isspmatrix_csc(csc_array([[5]])) + False + >>> isspmatrix_csc(coo_matrix([[5]])) + False + """ + return isinstance(x, csc_matrix) + + +# This namespace class separates array from matrix with isinstance +class csc_array(_csc_base, sparray): + """ + Compressed Sparse Column array. + + This can be instantiated in several ways: + csc_array(D) + where D is a 2-D ndarray + + csc_array(S) + with another sparse array or matrix S (equivalent to S.tocsc()) + + csc_array((M, N), [dtype]) + to construct an empty array with shape (M, N) + dtype is optional, defaulting to dtype='d'. + + csc_array((data, (row_ind, col_ind)), [shape=(M, N)]) + where ``data``, ``row_ind`` and ``col_ind`` satisfy the + relationship ``a[row_ind[k], col_ind[k]] = data[k]``. + + csc_array((data, indices, indptr), [shape=(M, N)]) + is the standard CSC representation where the row indices for + column i are stored in ``indices[indptr[i]:indptr[i+1]]`` + and their corresponding values are stored in + ``data[indptr[i]:indptr[i+1]]``. If the shape parameter is + not supplied, the array dimensions are inferred from + the index arrays. + + Attributes + ---------- + dtype : dtype + Data type of the array + shape : 2-tuple + Shape of the array + ndim : int + Number of dimensions (this is always 2) + nnz + size + data + CSC format data array of the array + indices + CSC format index array of the array + indptr + CSC format index pointer array of the array + has_sorted_indices + has_canonical_format + T + + Notes + ----- + + Sparse arrays can be used in arithmetic operations: they support + addition, subtraction, multiplication, division, and matrix power. + + Advantages of the CSC format + - efficient arithmetic operations CSC + CSC, CSC * CSC, etc. + - efficient column slicing + - fast matrix vector products (CSR, BSR may be faster) + + Disadvantages of the CSC format + - slow row slicing operations (consider CSR) + - changes to the sparsity structure are expensive (consider LIL or DOK) + + Canonical format + - Within each column, indices are sorted by row. + - There are no duplicate entries. + + Examples + -------- + + >>> import numpy as np + >>> from scipy.sparse import csc_array + >>> csc_array((3, 4), dtype=np.int8).toarray() + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int8) + + >>> row = np.array([0, 2, 2, 0, 1, 2]) + >>> col = np.array([0, 0, 1, 2, 2, 2]) + >>> data = np.array([1, 2, 3, 4, 5, 6]) + >>> csc_array((data, (row, col)), shape=(3, 3)).toarray() + array([[1, 0, 4], + [0, 0, 5], + [2, 3, 6]]) + + >>> indptr = np.array([0, 2, 3, 6]) + >>> indices = np.array([0, 2, 2, 0, 1, 2]) + >>> data = np.array([1, 2, 3, 4, 5, 6]) + >>> csc_array((data, indices, indptr), shape=(3, 3)).toarray() + array([[1, 0, 4], + [0, 0, 5], + [2, 3, 6]]) + + """ + + +class csc_matrix(spmatrix, _csc_base): + """ + Compressed Sparse Column matrix. + + This can be instantiated in several ways: + csc_matrix(D) + where D is a 2-D ndarray + + csc_matrix(S) + with another sparse array or matrix S (equivalent to S.tocsc()) + + csc_matrix((M, N), [dtype]) + to construct an empty matrix with shape (M, N) + dtype is optional, defaulting to dtype='d'. + + csc_matrix((data, (row_ind, col_ind)), [shape=(M, N)]) + where ``data``, ``row_ind`` and ``col_ind`` satisfy the + relationship ``a[row_ind[k], col_ind[k]] = data[k]``. + + csc_matrix((data, indices, indptr), [shape=(M, N)]) + is the standard CSC representation where the row indices for + column i are stored in ``indices[indptr[i]:indptr[i+1]]`` + and their corresponding values are stored in + ``data[indptr[i]:indptr[i+1]]``. If the shape parameter is + not supplied, the matrix dimensions are inferred from + the index arrays. + + Attributes + ---------- + dtype : dtype + Data type of the matrix + shape : 2-tuple + Shape of the matrix + ndim : int + Number of dimensions (this is always 2) + nnz + size + data + CSC format data array of the matrix + indices + CSC format index array of the matrix + indptr + CSC format index pointer array of the matrix + has_sorted_indices + has_canonical_format + T + + Notes + ----- + + Sparse matrices can be used in arithmetic operations: they support + addition, subtraction, multiplication, division, and matrix power. + + Advantages of the CSC format + - efficient arithmetic operations CSC + CSC, CSC * CSC, etc. + - efficient column slicing + - fast matrix vector products (CSR, BSR may be faster) + + Disadvantages of the CSC format + - slow row slicing operations (consider CSR) + - changes to the sparsity structure are expensive (consider LIL or DOK) + + Canonical format + - Within each column, indices are sorted by row. + - There are no duplicate entries. + + Examples + -------- + + >>> import numpy as np + >>> from scipy.sparse import csc_matrix + >>> csc_matrix((3, 4), dtype=np.int8).toarray() + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int8) + + >>> row = np.array([0, 2, 2, 0, 1, 2]) + >>> col = np.array([0, 0, 1, 2, 2, 2]) + >>> data = np.array([1, 2, 3, 4, 5, 6]) + >>> csc_matrix((data, (row, col)), shape=(3, 3)).toarray() + array([[1, 0, 4], + [0, 0, 5], + [2, 3, 6]]) + + >>> indptr = np.array([0, 2, 3, 6]) + >>> indices = np.array([0, 2, 2, 0, 1, 2]) + >>> data = np.array([1, 2, 3, 4, 5, 6]) + >>> csc_matrix((data, indices, indptr), shape=(3, 3)).toarray() + array([[1, 0, 4], + [0, 0, 5], + [2, 3, 6]]) + + """ + diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_extract.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_extract.py new file mode 100644 index 0000000000000000000000000000000000000000..349a056bd2f673b0a0b5379fa8b18d720eb5a86d --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_extract.py @@ -0,0 +1,178 @@ +"""Functions to extract parts of sparse matrices +""" + +__docformat__ = "restructuredtext en" + +__all__ = ['find', 'tril', 'triu'] + + +from ._coo import coo_matrix, coo_array +from ._base import sparray + + +def find(A): + """Return the indices and values of the nonzero elements of a matrix + + Parameters + ---------- + A : dense or sparse array or matrix + Matrix whose nonzero elements are desired. + + Returns + ------- + (I,J,V) : tuple of arrays + I,J, and V contain the row indices, column indices, and values + of the nonzero entries. + + + Examples + -------- + >>> from scipy.sparse import csr_array, find + >>> A = csr_array([[7.0, 8.0, 0],[0, 0, 9.0]]) + >>> find(A) + (array([0, 0, 1], dtype=int32), + array([0, 1, 2], dtype=int32), + array([ 7., 8., 9.])) + + """ + + A = coo_array(A, copy=True) + A.sum_duplicates() + # remove explicit zeros + nz_mask = A.data != 0 + return A.row[nz_mask], A.col[nz_mask], A.data[nz_mask] + + +def tril(A, k=0, format=None): + """Return the lower triangular portion of a sparse array or matrix + + Returns the elements on or below the k-th diagonal of A. + - k = 0 corresponds to the main diagonal + - k > 0 is above the main diagonal + - k < 0 is below the main diagonal + + Parameters + ---------- + A : dense or sparse array or matrix + Matrix whose lower trianglar portion is desired. + k : integer : optional + The top-most diagonal of the lower triangle. + format : string + Sparse format of the result, e.g. format="csr", etc. + + Returns + ------- + L : sparse matrix + Lower triangular portion of A in sparse format. + + See Also + -------- + triu : upper triangle in sparse format + + Examples + -------- + >>> from scipy.sparse import csr_array, tril + >>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]], + ... dtype='int32') + >>> A.toarray() + array([[1, 2, 0, 0, 3], + [4, 5, 0, 6, 7], + [0, 0, 8, 9, 0]]) + >>> tril(A).toarray() + array([[1, 0, 0, 0, 0], + [4, 5, 0, 0, 0], + [0, 0, 8, 0, 0]]) + >>> tril(A).nnz + 4 + >>> tril(A, k=1).toarray() + array([[1, 2, 0, 0, 0], + [4, 5, 0, 0, 0], + [0, 0, 8, 9, 0]]) + >>> tril(A, k=-1).toarray() + array([[0, 0, 0, 0, 0], + [4, 0, 0, 0, 0], + [0, 0, 0, 0, 0]]) + >>> tril(A, format='csc') + <3x5 sparse array of type '' + with 4 stored elements in Compressed Sparse Column format> + + """ + coo_sparse = coo_array if isinstance(A, sparray) else coo_matrix + + # convert to COOrdinate format where things are easy + A = coo_sparse(A, copy=False) + mask = A.row + k >= A.col + + row = A.row[mask] + col = A.col[mask] + data = A.data[mask] + new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype) + return new_coo.asformat(format) + + +def triu(A, k=0, format=None): + """Return the upper triangular portion of a sparse array or matrix + + Returns the elements on or above the k-th diagonal of A. + - k = 0 corresponds to the main diagonal + - k > 0 is above the main diagonal + - k < 0 is below the main diagonal + + Parameters + ---------- + A : dense or sparse array or matrix + Matrix whose upper trianglar portion is desired. + k : integer : optional + The bottom-most diagonal of the upper triangle. + format : string + Sparse format of the result, e.g. format="csr", etc. + + Returns + ------- + L : sparse array or matrix + Upper triangular portion of A in sparse format. + Sparse array if A is a sparse array, otherwise matrix. + + See Also + -------- + tril : lower triangle in sparse format + + Examples + -------- + >>> from scipy.sparse import csr_array, triu + >>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]], + ... dtype='int32') + >>> A.toarray() + array([[1, 2, 0, 0, 3], + [4, 5, 0, 6, 7], + [0, 0, 8, 9, 0]]) + >>> triu(A).toarray() + array([[1, 2, 0, 0, 3], + [0, 5, 0, 6, 7], + [0, 0, 8, 9, 0]]) + >>> triu(A).nnz + 8 + >>> triu(A, k=1).toarray() + array([[0, 2, 0, 0, 3], + [0, 0, 0, 6, 7], + [0, 0, 0, 9, 0]]) + >>> triu(A, k=-1).toarray() + array([[1, 2, 0, 0, 3], + [4, 5, 0, 6, 7], + [0, 0, 8, 9, 0]]) + >>> triu(A, format='csc') + <3x5 sparse array of type '' + with 8 stored elements in Compressed Sparse Column format> + + """ + coo_sparse = coo_array if isinstance(A, sparray) else coo_matrix + + # convert to COOrdinate format where things are easy + A = coo_sparse(A, copy=False) + mask = A.row + k <= A.col + + row = A.row[mask] + col = A.col[mask] + data = A.data[mask] + new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype) + return new_coo.asformat(format) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_lil.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_lil.py new file mode 100644 index 0000000000000000000000000000000000000000..b5590010386190fa5fadcdb3e9fae3cc236a3b0e --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_lil.py @@ -0,0 +1,618 @@ +"""List of Lists sparse matrix class +""" + +__docformat__ = "restructuredtext en" + +__all__ = ['lil_array', 'lil_matrix', 'isspmatrix_lil'] + +from bisect import bisect_left + +import numpy as np + +from ._matrix import spmatrix +from ._base import _spbase, sparray, issparse +from ._index import IndexMixin, INT_TYPES, _broadcast_arrays +from ._sputils import (getdtype, isshape, isscalarlike, upcast_scalar, + check_shape, check_reshape_kwargs) +from . import _csparsetools + + +class _lil_base(_spbase, IndexMixin): + _format = 'lil' + + def __init__(self, arg1, shape=None, dtype=None, copy=False): + _spbase.__init__(self) + self.dtype = getdtype(dtype, arg1, default=float) + + # First get the shape + if issparse(arg1): + if arg1.format == "lil" and copy: + A = arg1.copy() + else: + A = arg1.tolil() + + if dtype is not None: + A = A.astype(dtype, copy=False) + + self._shape = check_shape(A.shape) + self.dtype = A.dtype + self.rows = A.rows + self.data = A.data + elif isinstance(arg1,tuple): + if isshape(arg1): + if shape is not None: + raise ValueError('invalid use of shape parameter') + M, N = arg1 + self._shape = check_shape((M, N)) + self.rows = np.empty((M,), dtype=object) + self.data = np.empty((M,), dtype=object) + for i in range(M): + self.rows[i] = [] + self.data[i] = [] + else: + raise TypeError('unrecognized lil_array constructor usage') + else: + # assume A is dense + try: + A = self._ascontainer(arg1) + except TypeError as e: + raise TypeError('unsupported matrix type') from e + else: + A = self._csr_container(A, dtype=dtype).tolil() + + self._shape = check_shape(A.shape) + self.dtype = A.dtype + self.rows = A.rows + self.data = A.data + + def __iadd__(self,other): + self[:,:] = self + other + return self + + def __isub__(self,other): + self[:,:] = self - other + return self + + def __imul__(self,other): + if isscalarlike(other): + self[:,:] = self * other + return self + else: + return NotImplemented + + def __itruediv__(self,other): + if isscalarlike(other): + self[:,:] = self / other + return self + else: + return NotImplemented + + # Whenever the dimensions change, empty lists should be created for each + # row + + def _getnnz(self, axis=None): + if axis is None: + return sum([len(rowvals) for rowvals in self.data]) + if axis < 0: + axis += 2 + if axis == 0: + out = np.zeros(self.shape[1], dtype=np.intp) + for row in self.rows: + out[row] += 1 + return out + elif axis == 1: + return np.array([len(rowvals) for rowvals in self.data], dtype=np.intp) + else: + raise ValueError('axis out of bounds') + + def count_nonzero(self): + return sum(np.count_nonzero(rowvals) for rowvals in self.data) + + _getnnz.__doc__ = _spbase._getnnz.__doc__ + count_nonzero.__doc__ = _spbase.count_nonzero.__doc__ + + def __str__(self): + val = '' + for i, row in enumerate(self.rows): + for pos, j in enumerate(row): + val += f" {str((i, j))}\t{str(self.data[i][pos])}\n" + return val[:-1] + + def getrowview(self, i): + """Returns a view of the 'i'th row (without copying). + """ + new = self._lil_container((1, self.shape[1]), dtype=self.dtype) + new.rows[0] = self.rows[i] + new.data[0] = self.data[i] + return new + + def getrow(self, i): + """Returns a copy of the 'i'th row. + """ + M, N = self.shape + if i < 0: + i += M + if i < 0 or i >= M: + raise IndexError('row index out of bounds') + new = self._lil_container((1, N), dtype=self.dtype) + new.rows[0] = self.rows[i][:] + new.data[0] = self.data[i][:] + return new + + def __getitem__(self, key): + # Fast path for simple (int, int) indexing. + if (isinstance(key, tuple) and len(key) == 2 and + isinstance(key[0], INT_TYPES) and + isinstance(key[1], INT_TYPES)): + # lil_get1 handles validation for us. + return self._get_intXint(*key) + # Everything else takes the normal path. + return IndexMixin.__getitem__(self, key) + + def _asindices(self, idx, N): + # LIL routines handle bounds-checking for us, so don't do it here. + try: + x = np.asarray(idx) + except (ValueError, TypeError, MemoryError) as e: + raise IndexError('invalid index') from e + if x.ndim not in (1, 2): + raise IndexError('Index dimension must be <= 2') + return x + + def _get_intXint(self, row, col): + v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows, + self.data, row, col) + return self.dtype.type(v) + + def _get_sliceXint(self, row, col): + row = range(*row.indices(self.shape[0])) + return self._get_row_ranges(row, slice(col, col+1)) + + def _get_arrayXint(self, row, col): + row = row.squeeze() + return self._get_row_ranges(row, slice(col, col+1)) + + def _get_intXslice(self, row, col): + return self._get_row_ranges((row,), col) + + def _get_sliceXslice(self, row, col): + row = range(*row.indices(self.shape[0])) + return self._get_row_ranges(row, col) + + def _get_arrayXslice(self, row, col): + return self._get_row_ranges(row, col) + + def _get_intXarray(self, row, col): + row = np.array(row, dtype=col.dtype, ndmin=1) + return self._get_columnXarray(row, col) + + def _get_sliceXarray(self, row, col): + row = np.arange(*row.indices(self.shape[0])) + return self._get_columnXarray(row, col) + + def _get_columnXarray(self, row, col): + # outer indexing + row, col = _broadcast_arrays(row[:,None], col) + return self._get_arrayXarray(row, col) + + def _get_arrayXarray(self, row, col): + # inner indexing + i, j = map(np.atleast_2d, _prepare_index_for_memoryview(row, col)) + new = self._lil_container(i.shape, dtype=self.dtype) + _csparsetools.lil_fancy_get(self.shape[0], self.shape[1], + self.rows, self.data, + new.rows, new.data, + i, j) + return new + + def _get_row_ranges(self, rows, col_slice): + """ + Fast path for indexing in the case where column index is slice. + + This gains performance improvement over brute force by more + efficient skipping of zeros, by accessing the elements + column-wise in order. + + Parameters + ---------- + rows : sequence or range + Rows indexed. If range, must be within valid bounds. + col_slice : slice + Columns indexed + + """ + j_start, j_stop, j_stride = col_slice.indices(self.shape[1]) + col_range = range(j_start, j_stop, j_stride) + nj = len(col_range) + new = self._lil_container((len(rows), nj), dtype=self.dtype) + + _csparsetools.lil_get_row_ranges(self.shape[0], self.shape[1], + self.rows, self.data, + new.rows, new.data, + rows, + j_start, j_stop, j_stride, nj) + + return new + + def _set_intXint(self, row, col, x): + _csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows, + self.data, row, col, x) + + def _set_arrayXarray(self, row, col, x): + i, j, x = map(np.atleast_2d, _prepare_index_for_memoryview(row, col, x)) + _csparsetools.lil_fancy_set(self.shape[0], self.shape[1], + self.rows, self.data, + i, j, x) + + def _set_arrayXarray_sparse(self, row, col, x): + # Fall back to densifying x + x = np.asarray(x.toarray(), dtype=self.dtype) + x, _ = _broadcast_arrays(x, row) + self._set_arrayXarray(row, col, x) + + def __setitem__(self, key, x): + if isinstance(key, tuple) and len(key) == 2: + row, col = key + # Fast path for simple (int, int) indexing. + if isinstance(row, INT_TYPES) and isinstance(col, INT_TYPES): + x = self.dtype.type(x) + if x.size > 1: + raise ValueError("Trying to assign a sequence to an item") + return self._set_intXint(row, col, x) + # Fast path for full-matrix sparse assignment. + if (isinstance(row, slice) and isinstance(col, slice) and + row == slice(None) and col == slice(None) and + issparse(x) and x.shape == self.shape): + x = self._lil_container(x, dtype=self.dtype) + self.rows = x.rows + self.data = x.data + return + # Everything else takes the normal path. + IndexMixin.__setitem__(self, key, x) + + def _mul_scalar(self, other): + if other == 0: + # Multiply by zero: return the zero matrix + new = self._lil_container(self.shape, dtype=self.dtype) + else: + res_dtype = upcast_scalar(self.dtype, other) + + new = self.copy() + new = new.astype(res_dtype) + # Multiply this scalar by every element. + for j, rowvals in enumerate(new.data): + new.data[j] = [val*other for val in rowvals] + return new + + def __truediv__(self, other): # self / other + if isscalarlike(other): + new = self.copy() + new.dtype = np.result_type(self, other) + # Divide every element by this scalar + for j, rowvals in enumerate(new.data): + new.data[j] = [val/other for val in rowvals] + return new + else: + return self.tocsr() / other + + def copy(self): + M, N = self.shape + new = self._lil_container(self.shape, dtype=self.dtype) + # This is ~14x faster than calling deepcopy() on rows and data. + _csparsetools.lil_get_row_ranges(M, N, self.rows, self.data, + new.rows, new.data, range(M), + 0, N, 1, N) + return new + + copy.__doc__ = _spbase.copy.__doc__ + + def reshape(self, *args, **kwargs): + shape = check_shape(args, self.shape) + order, copy = check_reshape_kwargs(kwargs) + + # Return early if reshape is not required + if shape == self.shape: + if copy: + return self.copy() + else: + return self + + new = self._lil_container(shape, dtype=self.dtype) + + if order == 'C': + ncols = self.shape[1] + for i, row in enumerate(self.rows): + for col, j in enumerate(row): + new_r, new_c = np.unravel_index(i * ncols + j, shape) + new[new_r, new_c] = self[i, j] + elif order == 'F': + nrows = self.shape[0] + for i, row in enumerate(self.rows): + for col, j in enumerate(row): + new_r, new_c = np.unravel_index(i + j * nrows, shape, order) + new[new_r, new_c] = self[i, j] + else: + raise ValueError("'order' must be 'C' or 'F'") + + return new + + reshape.__doc__ = _spbase.reshape.__doc__ + + def resize(self, *shape): + shape = check_shape(shape) + new_M, new_N = shape + M, N = self.shape + + if new_M < M: + self.rows = self.rows[:new_M] + self.data = self.data[:new_M] + elif new_M > M: + self.rows = np.resize(self.rows, new_M) + self.data = np.resize(self.data, new_M) + for i in range(M, new_M): + self.rows[i] = [] + self.data[i] = [] + + if new_N < N: + for row, data in zip(self.rows, self.data): + trunc = bisect_left(row, new_N) + del row[trunc:] + del data[trunc:] + + self._shape = shape + + resize.__doc__ = _spbase.resize.__doc__ + + def toarray(self, order=None, out=None): + d = self._process_toarray_args(order, out) + for i, row in enumerate(self.rows): + for pos, j in enumerate(row): + d[i, j] = self.data[i][pos] + return d + + toarray.__doc__ = _spbase.toarray.__doc__ + + def transpose(self, axes=None, copy=False): + return self.tocsr(copy=copy).transpose(axes=axes, copy=False).tolil(copy=False) + + transpose.__doc__ = _spbase.transpose.__doc__ + + def tolil(self, copy=False): + if copy: + return self.copy() + else: + return self + + tolil.__doc__ = _spbase.tolil.__doc__ + + def tocsr(self, copy=False): + M, N = self.shape + if M == 0 or N == 0: + return self._csr_container((M, N), dtype=self.dtype) + + # construct indptr array + if M*N <= np.iinfo(np.int32).max: + # fast path: it is known that 64-bit indexing will not be needed. + idx_dtype = np.int32 + indptr = np.empty(M + 1, dtype=idx_dtype) + indptr[0] = 0 + _csparsetools.lil_get_lengths(self.rows, indptr[1:]) + np.cumsum(indptr, out=indptr) + nnz = indptr[-1] + else: + idx_dtype = self._get_index_dtype(maxval=N) + lengths = np.empty(M, dtype=idx_dtype) + _csparsetools.lil_get_lengths(self.rows, lengths) + nnz = lengths.sum(dtype=np.int64) + idx_dtype = self._get_index_dtype(maxval=max(N, nnz)) + indptr = np.empty(M + 1, dtype=idx_dtype) + indptr[0] = 0 + np.cumsum(lengths, dtype=idx_dtype, out=indptr[1:]) + + indices = np.empty(nnz, dtype=idx_dtype) + data = np.empty(nnz, dtype=self.dtype) + _csparsetools.lil_flatten_to_array(self.rows, indices) + _csparsetools.lil_flatten_to_array(self.data, data) + + # init csr matrix + return self._csr_container((data, indices, indptr), shape=self.shape) + + tocsr.__doc__ = _spbase.tocsr.__doc__ + + +def _prepare_index_for_memoryview(i, j, x=None): + """ + Convert index and data arrays to form suitable for passing to the + Cython fancy getset routines. + + The conversions are necessary since to (i) ensure the integer + index arrays are in one of the accepted types, and (ii) to ensure + the arrays are writable so that Cython memoryview support doesn't + choke on them. + + Parameters + ---------- + i, j + Index arrays + x : optional + Data arrays + + Returns + ------- + i, j, x + Re-formatted arrays (x is omitted, if input was None) + + """ + if i.dtype > j.dtype: + j = j.astype(i.dtype) + elif i.dtype < j.dtype: + i = i.astype(j.dtype) + + if not i.flags.writeable or i.dtype not in (np.int32, np.int64): + i = i.astype(np.intp) + if not j.flags.writeable or j.dtype not in (np.int32, np.int64): + j = j.astype(np.intp) + + if x is not None: + if not x.flags.writeable: + x = x.copy() + return i, j, x + else: + return i, j + + +def isspmatrix_lil(x): + """Is `x` of lil_matrix type? + + Parameters + ---------- + x + object to check for being a lil matrix + + Returns + ------- + bool + True if `x` is a lil matrix, False otherwise + + Examples + -------- + >>> from scipy.sparse import lil_array, lil_matrix, coo_matrix, isspmatrix_lil + >>> isspmatrix_lil(lil_matrix([[5]])) + True + >>> isspmatrix_lil(lil_array([[5]])) + False + >>> isspmatrix_lil(coo_matrix([[5]])) + False + """ + return isinstance(x, lil_matrix) + + +# This namespace class separates array from matrix with isinstance +class lil_array(_lil_base, sparray): + """ + Row-based LIst of Lists sparse array. + + This is a structure for constructing sparse arrays incrementally. + Note that inserting a single item can take linear time in the worst case; + to construct the array efficiently, make sure the items are pre-sorted by + index, per row. + + This can be instantiated in several ways: + lil_array(D) + where D is a 2-D ndarray + + lil_array(S) + with another sparse array or matrix S (equivalent to S.tolil()) + + lil_array((M, N), [dtype]) + to construct an empty array with shape (M, N) + dtype is optional, defaulting to dtype='d'. + + Attributes + ---------- + dtype : dtype + Data type of the array + shape : 2-tuple + Shape of the array + ndim : int + Number of dimensions (this is always 2) + nnz + size + data + LIL format data array of the array + rows + LIL format row index array of the array + T + + Notes + ----- + Sparse arrays can be used in arithmetic operations: they support + addition, subtraction, multiplication, division, and matrix power. + + Advantages of the LIL format + - supports flexible slicing + - changes to the array sparsity structure are efficient + + Disadvantages of the LIL format + - arithmetic operations LIL + LIL are slow (consider CSR or CSC) + - slow column slicing (consider CSC) + - slow matrix vector products (consider CSR or CSC) + + Intended Usage + - LIL is a convenient format for constructing sparse arrays + - once an array has been constructed, convert to CSR or + CSC format for fast arithmetic and matrix vector operations + - consider using the COO format when constructing large arrays + + Data Structure + - An array (``self.rows``) of rows, each of which is a sorted + list of column indices of non-zero elements. + - The corresponding nonzero values are stored in similar + fashion in ``self.data``. + + """ + + +class lil_matrix(spmatrix, _lil_base): + """ + Row-based LIst of Lists sparse matrix. + + This is a structure for constructing sparse matrices incrementally. + Note that inserting a single item can take linear time in the worst case; + to construct the matrix efficiently, make sure the items are pre-sorted by + index, per row. + + This can be instantiated in several ways: + lil_matrix(D) + where D is a 2-D ndarray + + lil_matrix(S) + with another sparse array or matrix S (equivalent to S.tolil()) + + lil_matrix((M, N), [dtype]) + to construct an empty matrix with shape (M, N) + dtype is optional, defaulting to dtype='d'. + + Attributes + ---------- + dtype : dtype + Data type of the matrix + shape : 2-tuple + Shape of the matrix + ndim : int + Number of dimensions (this is always 2) + nnz + size + data + LIL format data array of the matrix + rows + LIL format row index array of the matrix + T + + Notes + ----- + Sparse matrices can be used in arithmetic operations: they support + addition, subtraction, multiplication, division, and matrix power. + + Advantages of the LIL format + - supports flexible slicing + - changes to the matrix sparsity structure are efficient + + Disadvantages of the LIL format + - arithmetic operations LIL + LIL are slow (consider CSR or CSC) + - slow column slicing (consider CSC) + - slow matrix vector products (consider CSR or CSC) + + Intended Usage + - LIL is a convenient format for constructing sparse matrices + - once a matrix has been constructed, convert to CSR or + CSC format for fast arithmetic and matrix vector operations + - consider using the COO format when constructing large matrices + + Data Structure + - An array (``self.rows``) of rows, each of which is a sorted + list of column indices of non-zero elements. + - The corresponding nonzero values are stored in similar + fashion in ``self.data``. + + """ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_spfuncs.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_spfuncs.py new file mode 100644 index 0000000000000000000000000000000000000000..8e9b0abcede6387e74538baf839a303c6cc1b6be --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/_spfuncs.py @@ -0,0 +1,76 @@ +""" Functions that operate on sparse matrices +""" + +__all__ = ['count_blocks','estimate_blocksize'] + +from ._base import issparse +from ._csr import csr_array +from ._sparsetools import csr_count_blocks + + +def estimate_blocksize(A,efficiency=0.7): + """Attempt to determine the blocksize of a sparse matrix + + Returns a blocksize=(r,c) such that + - A.nnz / A.tobsr( (r,c) ).nnz > efficiency + """ + if not (issparse(A) and A.format in ("csc", "csr")): + A = csr_array(A) + + if A.nnz == 0: + return (1,1) + + if not 0 < efficiency < 1.0: + raise ValueError('efficiency must satisfy 0.0 < efficiency < 1.0') + + high_efficiency = (1.0 + efficiency) / 2.0 + nnz = float(A.nnz) + M,N = A.shape + + if M % 2 == 0 and N % 2 == 0: + e22 = nnz / (4 * count_blocks(A,(2,2))) + else: + e22 = 0.0 + + if M % 3 == 0 and N % 3 == 0: + e33 = nnz / (9 * count_blocks(A,(3,3))) + else: + e33 = 0.0 + + if e22 > high_efficiency and e33 > high_efficiency: + e66 = nnz / (36 * count_blocks(A,(6,6))) + if e66 > efficiency: + return (6,6) + else: + return (3,3) + else: + if M % 4 == 0 and N % 4 == 0: + e44 = nnz / (16 * count_blocks(A,(4,4))) + else: + e44 = 0.0 + + if e44 > efficiency: + return (4,4) + elif e33 > efficiency: + return (3,3) + elif e22 > efficiency: + return (2,2) + else: + return (1,1) + + +def count_blocks(A,blocksize): + """For a given blocksize=(r,c) count the number of occupied + blocks in a sparse matrix A + """ + r,c = blocksize + if r < 1 or c < 1: + raise ValueError('r and c must be positive') + + if issparse(A): + if A.format == "csr": + M,N = A.shape + return csr_count_blocks(M,N,r,c,A.indptr,A.indices) + elif A.format == "csc": + return count_blocks(A.T,(c,r)) + return count_blocks(csr_array(A),blocksize) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/construct.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/construct.py new file mode 100644 index 0000000000000000000000000000000000000000..c3d34d2fd38887877980727bceaaa215129bf283 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/construct.py @@ -0,0 +1,44 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.sparse` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'block_diag', + 'bmat', + 'bsr_matrix', + 'check_random_state', + 'coo_matrix', + 'csc_matrix', + 'csr_hstack', + 'csr_matrix', + 'dia_matrix', + 'diags', + 'eye', + 'get_index_dtype', + 'hstack', + 'identity', + 'isscalarlike', + 'issparse', + 'kron', + 'kronsum', + 'numbers', + 'rand', + 'random', + 'rng_integers', + 'spdiags', + 'upcast', + 'vstack', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="sparse", module="construct", + private_modules=["_construct"], all=__all__, + attribute=name) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/lil.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/lil.py new file mode 100644 index 0000000000000000000000000000000000000000..31e5f20e4887c4e163aa2d807c89fe0768e3afb0 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/lil.py @@ -0,0 +1,31 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.sparse` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'INT_TYPES', + 'IndexMixin', + 'bisect_left', + 'check_reshape_kwargs', + 'check_shape', + 'getdtype', + 'isscalarlike', + 'isshape', + 'isspmatrix_lil', + 'lil_matrix', + 'spmatrix', + 'upcast_scalar', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="sparse", module="lil", + private_modules=["_lil"], all=__all__, + attribute=name) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/sparsetools.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/sparsetools.py new file mode 100644 index 0000000000000000000000000000000000000000..47ac80adae7145a6192f9fb9b225a1762ff830ce --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/sparsetools.py @@ -0,0 +1,98 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.sparse` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'bsr_diagonal', + 'bsr_eldiv_bsr', + 'bsr_elmul_bsr', + 'bsr_ge_bsr', + 'bsr_gt_bsr', + 'bsr_le_bsr', + 'bsr_lt_bsr', + 'bsr_matmat', + 'bsr_matvec', + 'bsr_matvecs', + 'bsr_maximum_bsr', + 'bsr_minimum_bsr', + 'bsr_minus_bsr', + 'bsr_ne_bsr', + 'bsr_plus_bsr', + 'bsr_scale_columns', + 'bsr_scale_rows', + 'bsr_sort_indices', + 'bsr_tocsr', + 'bsr_transpose', + 'coo_matvec', + 'coo_tocsr', + 'coo_todense', + 'cs_graph_components', + 'csc_diagonal', + 'csc_eldiv_csc', + 'csc_elmul_csc', + 'csc_ge_csc', + 'csc_gt_csc', + 'csc_le_csc', + 'csc_lt_csc', + 'csc_matmat', + 'csc_matmat_maxnnz', + 'csc_matvec', + 'csc_matvecs', + 'csc_maximum_csc', + 'csc_minimum_csc', + 'csc_minus_csc', + 'csc_ne_csc', + 'csc_plus_csc', + 'csc_tocsr', + 'csr_column_index1', + 'csr_column_index2', + 'csr_count_blocks', + 'csr_diagonal', + 'csr_eldiv_csr', + 'csr_eliminate_zeros', + 'csr_elmul_csr', + 'csr_ge_csr', + 'csr_gt_csr', + 'csr_has_canonical_format', + 'csr_has_sorted_indices', + 'csr_hstack', + 'csr_le_csr', + 'csr_lt_csr', + 'csr_matmat', + 'csr_matmat_maxnnz', + 'csr_matvec', + 'csr_matvecs', + 'csr_maximum_csr', + 'csr_minimum_csr', + 'csr_minus_csr', + 'csr_ne_csr', + 'csr_plus_csr', + 'csr_row_index', + 'csr_row_slice', + 'csr_sample_offsets', + 'csr_sample_values', + 'csr_scale_columns', + 'csr_scale_rows', + 'csr_sort_indices', + 'csr_sum_duplicates', + 'csr_tobsr', + 'csr_tocsc', + 'csr_todense', + 'dia_matvec', + 'expandptr', + 'get_csr_submatrix', + 'test_throw_error', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="sparse", module="sparsetools", + private_modules=["_sparsetools"], all=__all__, + attribute=name) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/sparse/sputils.py b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/sputils.py new file mode 100644 index 0000000000000000000000000000000000000000..bdacb42dd0fb23b956fb95f2eea913cfb933d029 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/sparse/sputils.py @@ -0,0 +1,44 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.sparse` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'asmatrix', + 'check_reshape_kwargs', + 'check_shape', + 'downcast_intp_index', + 'get_index_dtype', + 'get_sum_dtype', + 'getdata', + 'getdtype', + 'is_pydata_spmatrix', + 'isdense', + 'isintlike', + 'ismatrix', + 'isscalarlike', + 'issequence', + 'isshape', + 'matrix', + 'operator', + 'prod', + 'supported_dtypes', + 'sys', + 'to_native', + 'upcast', + 'upcast_char', + 'upcast_scalar', + 'validateaxis', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="sparse", module="sputils", + private_modules=["_sputils"], all=__all__, + attribute=name) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/version.py b/env-llmeval/lib/python3.10/site-packages/scipy/version.py new file mode 100644 index 0000000000000000000000000000000000000000..db73d1943ef5d7a2fcdd510aea849c3b4901984b --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/version.py @@ -0,0 +1,12 @@ +# THIS FILE IS GENERATED DURING THE SCIPY BUILD +# See tools/version_utils.py for details + +short_version = '1.13.0' +version = '1.13.0' +full_version = '1.13.0' +git_revision = '7dcd8c5' +commit_count = '1580' +release = True + +if not release: + version = full_version