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@@ -4207,3 +4207,26 @@ tool_server/.venv/lib/python3.12/site-packages/triton/backends/nvidia/bin/cuobjd
 tool_server/.venv/lib/python3.12/site-packages/triton/backends/nvidia/bin/nvdisasm filter=lfs diff=lfs merge=lfs -text
 tool_server/.venv/lib/python3.12/site-packages/triton/backends/nvidia/bin/ptxas filter=lfs diff=lfs merge=lfs -text
 tool_server/.venv/lib/python3.12/site-packages/triton/backends/nvidia/bin/ptxas-blackwell filter=lfs diff=lfs merge=lfs -text
+tool_server/.venv/lib/python3.12/site-packages/triton/backends/nvidia/lib/libdevice.10.bc filter=lfs diff=lfs merge=lfs -text
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+tool_server/.venv/lib/python3.12/site-packages/triton/backends/nvidia/lib/cupti/libcupti.so.2025.1.0 filter=lfs diff=lfs merge=lfs -text
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+tool_server/.venv/lib/python3.12/site-packages/triton/backends/nvidia/lib/cupti/libnvperf_target.so filter=lfs diff=lfs merge=lfs -text
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+tool_server/.venv/lib/python3.12/site-packages/triton/language/__pycache__/semantic.cpython-312.pyc filter=lfs diff=lfs merge=lfs -text
+tool_server/.venv/lib/python3.12/site-packages/triton/runtime/__pycache__/interpreter.cpython-312.pyc filter=lfs diff=lfs merge=lfs -text
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+tool_server/.venv/lib/python3.12/site-packages/scipy/cluster/_vq.cpython-312-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
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+tool_server/.venv/lib/python3.12/site-packages/scipy/integrate/_lsoda.cpython-312-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
+tool_server/.venv/lib/python3.12/site-packages/scipy/integrate/_odepack.cpython-312-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
+tool_server/.venv/lib/python3.12/site-packages/scipy/integrate/_quadpack.cpython-312-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
+tool_server/.venv/lib/python3.12/site-packages/scipy/integrate/_test_odeint_banded.cpython-312-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
+tool_server/.venv/lib/python3.12/site-packages/scipy/integrate/_vode.cpython-312-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/__init__.py

@@ -0,0 +1,14 @@
+"""
+Module containing private utility functions
+===========================================
+
+The ``scipy._lib`` namespace is empty (for now). Tests for all
+utilities in submodules of ``_lib`` can be run with::
+
+    from scipy import _lib
+    _lib.test()
+
+"""
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_array_api.py

@@ -0,0 +1,931 @@
+"""Utility functions to use Python Array API compatible libraries.
+
+For the context about the Array API see:
+https://data-apis.org/array-api/latest/purpose_and_scope.html
+
+The SciPy use case of the Array API is described on the following page:
+https://data-apis.org/array-api/latest/use_cases.html#use-case-scipy
+"""
+import contextlib
+import dataclasses
+import functools
+import os
+import textwrap
+
+from collections.abc import Generator, Iterable, Iterator
+from contextlib import contextmanager
+from contextvars import ContextVar
+from types import ModuleType
+from typing import Any, Literal, TypeAlias
+
+import numpy as np
+import numpy.typing as npt
+
+from scipy._lib import array_api_compat
+from scipy._lib.array_api_compat import (
+    is_array_api_obj,
+    is_lazy_array,
+    size as xp_size,
+    numpy as np_compat,
+    device as xp_device,
+    is_numpy_namespace as is_numpy,
+    is_cupy_namespace as is_cupy,
+    is_torch_namespace as is_torch,
+    is_jax_namespace as is_jax,
+    is_dask_namespace as is_dask,
+    is_array_api_strict_namespace as is_array_api_strict
+)
+from scipy._lib._sparse import issparse
+from scipy._lib._docscrape import FunctionDoc
+
+__all__ = [
+    '_asarray', 'array_namespace', 'assert_almost_equal', 'assert_array_almost_equal',
+    'default_xp', 'eager_warns', 'is_lazy_array', 'is_marray',
+    'is_array_api_strict', 'is_complex', 'is_cupy', 'is_jax', 'is_numpy', 'is_torch',
+    'SCIPY_ARRAY_API', 'SCIPY_DEVICE', 'scipy_namespace_for',
+    'xp_assert_close', 'xp_assert_equal', 'xp_assert_less',
+    'xp_copy', 'xp_device', 'xp_ravel', 'xp_size',
+    'xp_unsupported_param_msg', 'xp_vector_norm', 'xp_capabilities',
+    'xp_result_type', 'xp_promote'
+]
+
+
+# To enable array API and strict array-like input validation
+SCIPY_ARRAY_API: str | bool = os.environ.get("SCIPY_ARRAY_API", False)
+# To control the default device - for use in the test suite only
+SCIPY_DEVICE = os.environ.get("SCIPY_DEVICE", "cpu")
+
+_GLOBAL_CONFIG = {
+    "SCIPY_ARRAY_API": SCIPY_ARRAY_API,
+    "SCIPY_DEVICE": SCIPY_DEVICE,
+}
+
+
+Array: TypeAlias = Any  # To be changed to a Protocol later (see array-api#589)
+ArrayLike: TypeAlias = Array | npt.ArrayLike
+
+
+def _compliance_scipy(arrays: Iterable[ArrayLike]) -> Iterator[Array]:
+    """Raise exceptions on known-bad subclasses. Discard 0-dimensional ArrayLikes
+    and convert 1+-dimensional ArrayLikes to numpy.
+
+    The following subclasses are not supported and raise and error:
+    - `numpy.ma.MaskedArray`
+    - `numpy.matrix`
+    - NumPy arrays which do not have a boolean or numerical dtype
+    - Any array-like which is neither array API compatible nor coercible by NumPy
+    - Any array-like which is coerced by NumPy to an unsupported dtype
+    """
+    for array in arrays:
+        if array is None:
+            continue
+
+        # this comes from `_util._asarray_validated`
+        if issparse(array):
+            msg = ('Sparse arrays/matrices are not supported by this function. '
+                   'Perhaps one of the `scipy.sparse.linalg` functions '
+                   'would work instead.')
+            raise ValueError(msg)
+
+        if isinstance(array, np.ma.MaskedArray):
+            raise TypeError("Inputs of type `numpy.ma.MaskedArray` are not supported.")
+
+        if isinstance(array, np.matrix):
+            raise TypeError("Inputs of type `numpy.matrix` are not supported.")
+
+        if isinstance(array, np.ndarray | np.generic):
+            dtype = array.dtype
+            if not (np.issubdtype(dtype, np.number) or np.issubdtype(dtype, np.bool_)):
+                raise TypeError(f"An argument has dtype `{dtype!r}`; "
+                                f"only boolean and numerical dtypes are supported.")
+
+        if is_array_api_obj(array):
+            yield array
+        else:
+            try:
+                array = np.asanyarray(array)
+            except TypeError:
+                raise TypeError("An argument is neither array API compatible nor "
+                                "coercible by NumPy.")
+            dtype = array.dtype
+            if not (np.issubdtype(dtype, np.number) or np.issubdtype(dtype, np.bool_)):
+                message = (
+                    f"An argument was coerced to an unsupported dtype `{dtype!r}`; "
+                    f"only boolean and numerical dtypes are supported."
+                )
+                raise TypeError(message)
+            # Ignore 0-dimensional arrays, coherently with array-api-compat.
+            # Raise if there are 1+-dimensional array-likes mixed with non-numpy
+            # Array API objects.
+            if array.ndim:
+                yield array
+
+
+def _check_finite(array: Array, xp: ModuleType) -> None:
+    """Check for NaNs or Infs."""
+    if not xp.all(xp.isfinite(array)):
+        msg = "array must not contain infs or NaNs"
+        raise ValueError(msg)
+
+
+def array_namespace(*arrays: Array) -> ModuleType:
+    """Get the array API compatible namespace for the arrays xs.
+
+    Parameters
+    ----------
+    *arrays : sequence of array_like
+        Arrays used to infer the common namespace.
+
+    Returns
+    -------
+    namespace : module
+        Common namespace.
+
+    Notes
+    -----
+    Thin wrapper around `array_api_compat.array_namespace`.
+
+    1. Check for the global switch: SCIPY_ARRAY_API. This can also be accessed
+       dynamically through ``_GLOBAL_CONFIG['SCIPY_ARRAY_API']``.
+    2. `_compliance_scipy` raise exceptions on known-bad subclasses. See
+       its definition for more details.
+
+    When the global switch is False, it defaults to the `numpy` namespace.
+    In that case, there is no compliance check. This is a convenience to
+    ease the adoption. Otherwise, arrays must comply with the new rules.
+    """
+    if not _GLOBAL_CONFIG["SCIPY_ARRAY_API"]:
+        # here we could wrap the namespace if needed
+        return np_compat
+
+    api_arrays = list(_compliance_scipy(arrays))
+    # In case of a mix of array API compliant arrays and scalars, return
+    # the array API namespace. If there are only ArrayLikes (e.g. lists),
+    # return NumPy (wrapped by array-api-compat).
+    if api_arrays:
+        return array_api_compat.array_namespace(*api_arrays)
+    return np_compat
+
+
+def _asarray(
+        array: ArrayLike,
+        dtype: Any = None,
+        order: Literal['K', 'A', 'C', 'F'] | None = None,
+        copy: bool | None = None,
+        *,
+        xp: ModuleType | None = None,
+        check_finite: bool = False,
+        subok: bool = False,
+    ) -> Array:
+    """SciPy-specific replacement for `np.asarray` with `order`, `check_finite`, and
+    `subok`.
+
+    Memory layout parameter `order` is not exposed in the Array API standard.
+    `order` is only enforced if the input array implementation
+    is NumPy based, otherwise `order` is just silently ignored.
+
+    `check_finite` is also not a keyword in the array API standard; included
+    here for convenience rather than that having to be a separate function
+    call inside SciPy functions.
+
+    `subok` is included to allow this function to preserve the behaviour of
+    `np.asanyarray` for NumPy based inputs.
+    """
+    if xp is None:
+        xp = array_namespace(array)
+    if is_numpy(xp):
+        # Use NumPy API to support order
+        if copy is True:
+            array = np.array(array, order=order, dtype=dtype, subok=subok)
+        elif subok:
+            array = np.asanyarray(array, order=order, dtype=dtype)
+        else:
+            array = np.asarray(array, order=order, dtype=dtype)
+    else:
+        try:
+            array = xp.asarray(array, dtype=dtype, copy=copy)
+        except TypeError:
+            coerced_xp = array_namespace(xp.asarray(3))
+            array = coerced_xp.asarray(array, dtype=dtype, copy=copy)
+
+    if check_finite:
+        _check_finite(array, xp)
+
+    return array
+
+
+def xp_copy(x: Array, *, xp: ModuleType | None = None) -> Array:
+    """
+    Copies an array.
+
+    Parameters
+    ----------
+    x : array
+
+    xp : array_namespace
+
+    Returns
+    -------
+    copy : array
+        Copied array
+
+    Notes
+    -----
+    This copy function does not offer all the semantics of `np.copy`, i.e. the
+    `subok` and `order` keywords are not used.
+    """
+    # Note: for older NumPy versions, `np.asarray` did not support the `copy` kwarg,
+    # so this uses our other helper `_asarray`.
+    if xp is None:
+        xp = array_namespace(x)
+
+    return _asarray(x, copy=True, xp=xp)
+
+
+_default_xp_ctxvar: ContextVar[ModuleType] = ContextVar("_default_xp")
+
+@contextmanager
+def default_xp(xp: ModuleType) -> Generator[None, None, None]:
+    """In all ``xp_assert_*`` and ``assert_*`` function calls executed within this
+    context manager, test by default that the array namespace is
+    the provided across all arrays, unless one explicitly passes the ``xp=``
+    parameter or ``check_namespace=False``.
+
+    Without this context manager, the default value for `xp` is the namespace
+    for the desired array (the second parameter of the tests).
+    """
+    token = _default_xp_ctxvar.set(xp)
+    try:
+        yield
+    finally:
+        _default_xp_ctxvar.reset(token)
+
+
+def eager_warns(x, warning_type, match=None):
+    """pytest.warns context manager, but only if x is not a lazy array."""
+    import pytest
+    # This attribute is interpreted by pytest-run-parallel, ensuring that tests that use
+    # `eager_warns` aren't run in parallel (since pytest.warns isn't thread-safe).
+    __thread_safe__ = False  # noqa: F841
+    if is_lazy_array(x):
+        return contextlib.nullcontext()
+    return pytest.warns(warning_type, match=match)
+
+
+def _strict_check(actual, desired, xp, *,
+                  check_namespace=True, check_dtype=True, check_shape=True,
+                  check_0d=True):
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    if xp is None:
+        try:
+            xp = _default_xp_ctxvar.get()
+        except LookupError:
+            xp = array_namespace(desired)
+
+    if check_namespace:
+        _assert_matching_namespace(actual, desired, xp)
+
+    # only NumPy distinguishes between scalars and arrays; we do if check_0d=True.
+    # do this first so we can then cast to array (and thus use the array API) below.
+    if is_numpy(xp) and check_0d:
+        _msg = ("Array-ness does not match:\n Actual: "
+                f"{type(actual)}\n Desired: {type(desired)}")
+        assert ((xp.isscalar(actual) and xp.isscalar(desired))
+                or (not xp.isscalar(actual) and not xp.isscalar(desired))), _msg
+
+    actual = xp.asarray(actual)
+    desired = xp.asarray(desired)
+
+    if check_dtype:
+        _msg = f"dtypes do not match.\nActual: {actual.dtype}\nDesired: {desired.dtype}"
+        assert actual.dtype == desired.dtype, _msg
+
+    if check_shape:
+        if is_dask(xp):
+            actual.compute_chunk_sizes()
+            desired.compute_chunk_sizes()
+        _msg = f"Shapes do not match.\nActual: {actual.shape}\nDesired: {desired.shape}"
+        assert actual.shape == desired.shape, _msg
+
+    desired = xp.broadcast_to(desired, actual.shape)
+    return actual, desired, xp
+
+
+def _assert_matching_namespace(actual, desired, xp):
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    desired_arr_space = array_namespace(desired)
+    _msg = ("Namespace of desired array does not match expectations "
+            "set by the `default_xp` context manager or by the `xp`"
+            "pytest fixture.\n"
+            f"Desired array's space: {desired_arr_space.__name__}\n"
+            f"Expected namespace: {xp.__name__}")
+    assert desired_arr_space == xp, _msg
+
+    actual_arr_space = array_namespace(actual)
+    _msg = ("Namespace of actual and desired arrays do not match.\n"
+            f"Actual: {actual_arr_space.__name__}\n"
+            f"Desired: {xp.__name__}")
+    assert actual_arr_space == xp, _msg
+
+
+def xp_assert_equal(actual, desired, *, check_namespace=True, check_dtype=True,
+                    check_shape=True, check_0d=True, err_msg='', xp=None):
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    actual, desired, xp = _strict_check(
+        actual, desired, xp, check_namespace=check_namespace,
+        check_dtype=check_dtype, check_shape=check_shape,
+        check_0d=check_0d
+    )
+
+    if is_cupy(xp):
+        return xp.testing.assert_array_equal(actual, desired, err_msg=err_msg)
+    elif is_torch(xp):
+        # PyTorch recommends using `rtol=0, atol=0` like this
+        # to test for exact equality
+        err_msg = None if err_msg == '' else err_msg
+        return xp.testing.assert_close(actual, desired, rtol=0, atol=0, equal_nan=True,
+                                       check_dtype=False, msg=err_msg)
+    # JAX uses `np.testing`
+    return np.testing.assert_array_equal(actual, desired, err_msg=err_msg)
+
+
+def xp_assert_close(actual, desired, *, rtol=None, atol=0, check_namespace=True,
+                    check_dtype=True, check_shape=True, check_0d=True,
+                    err_msg='', xp=None):
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    actual, desired, xp = _strict_check(
+        actual, desired, xp,
+        check_namespace=check_namespace, check_dtype=check_dtype,
+        check_shape=check_shape, check_0d=check_0d
+    )
+
+    floating = xp.isdtype(actual.dtype, ('real floating', 'complex floating'))
+    if rtol is None and floating:
+        # multiplier of 4 is used as for `np.float64` this puts the default `rtol`
+        # roughly half way between sqrt(eps) and the default for
+        # `numpy.testing.assert_allclose`, 1e-7
+        rtol = xp.finfo(actual.dtype).eps**0.5 * 4
+    elif rtol is None:
+        rtol = 1e-7
+
+    if is_cupy(xp):
+        return xp.testing.assert_allclose(actual, desired, rtol=rtol,
+                                          atol=atol, err_msg=err_msg)
+    elif is_torch(xp):
+        err_msg = None if err_msg == '' else err_msg
+        return xp.testing.assert_close(actual, desired, rtol=rtol, atol=atol,
+                                       equal_nan=True, check_dtype=False, msg=err_msg)
+    # JAX uses `np.testing`
+    return np.testing.assert_allclose(actual, desired, rtol=rtol,
+                                      atol=atol, err_msg=err_msg)
+
+
+def xp_assert_less(actual, desired, *, check_namespace=True, check_dtype=True,
+                   check_shape=True, check_0d=True, err_msg='', verbose=True, xp=None):
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    actual, desired, xp = _strict_check(
+        actual, desired, xp, check_namespace=check_namespace,
+        check_dtype=check_dtype, check_shape=check_shape,
+        check_0d=check_0d
+    )
+
+    if is_cupy(xp):
+        return xp.testing.assert_array_less(actual, desired,
+                                            err_msg=err_msg, verbose=verbose)
+    elif is_torch(xp):
+        if actual.device.type != 'cpu':
+            actual = actual.cpu()
+        if desired.device.type != 'cpu':
+            desired = desired.cpu()
+    # JAX uses `np.testing`
+    return np.testing.assert_array_less(actual, desired,
+                                        err_msg=err_msg, verbose=verbose)
+
+
+def assert_array_almost_equal(actual, desired, decimal=6, *args, **kwds):
+    """Backwards compatible replacement. In new code, use xp_assert_close instead.
+    """
+    rtol, atol = 0, 1.5*10**(-decimal)
+    return xp_assert_close(actual, desired,
+                           atol=atol, rtol=rtol, check_dtype=False, check_shape=False,
+                           *args, **kwds)
+
+
+def assert_almost_equal(actual, desired, decimal=7, *args, **kwds):
+    """Backwards compatible replacement. In new code, use xp_assert_close instead.
+    """
+    rtol, atol = 0, 1.5*10**(-decimal)
+    return xp_assert_close(actual, desired,
+                           atol=atol, rtol=rtol, check_dtype=False, check_shape=False,
+                           *args, **kwds)
+
+
+def xp_unsupported_param_msg(param: Any) -> str:
+    return f'Providing {param!r} is only supported for numpy arrays.'
+
+
+def is_complex(x: Array, xp: ModuleType) -> bool:
+    return xp.isdtype(x.dtype, 'complex floating')
+
+
+def scipy_namespace_for(xp: ModuleType) -> ModuleType | None:
+    """Return the `scipy`-like namespace of a non-NumPy backend
+
+    That is, return the namespace corresponding with backend `xp` that contains
+    `scipy` sub-namespaces like `linalg` and `special`. If no such namespace
+    exists, return ``None``. Useful for dispatching.
+    """
+
+    if is_cupy(xp):
+        import cupyx  # type: ignore[import-not-found,import-untyped]
+        return cupyx.scipy
+
+    if is_jax(xp):
+        import jax  # type: ignore[import-not-found]
+        return jax.scipy
+
+    if is_torch(xp):
+        return xp
+
+    return None
+
+
+# maybe use `scipy.linalg` if/when array API support is added
+def xp_vector_norm(x: Array, /, *,
+                   axis: int | tuple[int] | None = None,
+                   keepdims: bool = False,
+                   ord: int | float = 2,
+                   xp: ModuleType | None = None) -> Array:
+    xp = array_namespace(x) if xp is None else xp
+
+    if SCIPY_ARRAY_API:
+        # check for optional `linalg` extension
+        if hasattr(xp, 'linalg'):
+            return xp.linalg.vector_norm(x, axis=axis, keepdims=keepdims, ord=ord)
+        else:
+            if ord != 2:
+                raise ValueError(
+                    "only the Euclidean norm (`ord=2`) is currently supported in "
+                    "`xp_vector_norm` for backends not implementing the `linalg` "
+                    "extension."
+                )
+            # return (x @ x)**0.5
+            # or to get the right behavior with nd, complex arrays
+            return xp.sum(xp.conj(x) * x, axis=axis, keepdims=keepdims)**0.5
+    else:
+        # to maintain backwards compatibility
+        return np.linalg.norm(x, ord=ord, axis=axis, keepdims=keepdims)
+
+
+def xp_ravel(x: Array, /, *, xp: ModuleType | None = None) -> Array:
+    # Equivalent of np.ravel written in terms of array API
+    # Even though it's one line, it comes up so often that it's worth having
+    # this function for readability
+    xp = array_namespace(x) if xp is None else xp
+    return xp.reshape(x, (-1,))
+
+
+def xp_swapaxes(a, axis1, axis2, xp=None):
+    # Equivalent of np.swapaxes written in terms of array API
+    xp = array_namespace(a) if xp is None else xp
+    axes = list(range(a.ndim))
+    axes[axis1], axes[axis2] = axes[axis2], axes[axis1]
+    a = xp.permute_dims(a, axes)
+    return a
+
+
+# utility to find common dtype with option to force floating
+def xp_result_type(*args, force_floating=False, xp):
+    """
+    Returns the dtype that results from applying type promotion rules
+    (see Array API Standard Type Promotion Rules) to the arguments. Augments
+    standard `result_type` in a few ways:
+
+    - There is a `force_floating` argument that ensures that the result type
+      is floating point, even when all args are integer.
+    - When a TypeError is raised (e.g. due to an unsupported promotion)
+      and `force_floating=True`, we define a custom rule: use the result type
+      of the default float and any other floats passed. See
+      https://github.com/scipy/scipy/pull/22695/files#r1997905891
+      for rationale.
+    - This function accepts array-like iterables, which are immediately converted
+      to the namespace's arrays before result type calculation. Consequently, the
+      result dtype may be different when an argument is `1.` vs `[1.]`.
+
+    Typically, this function will be called shortly after `array_namespace`
+    on a subset of the arguments passed to `array_namespace`.
+    """
+    args = [(_asarray(arg, subok=True, xp=xp) if np.iterable(arg) else arg)
+            for arg in args]
+    args_not_none = [arg for arg in args if arg is not None]
+    if force_floating:
+        args_not_none.append(1.0)
+
+    if is_numpy(xp) and xp.__version__ < '2.0':
+        # Follow NEP 50 promotion rules anyway
+        args_not_none = [arg.dtype if getattr(arg, 'size', 0) == 1 else arg
+                         for arg in args_not_none]
+        return xp.result_type(*args_not_none)
+
+    try:  # follow library's preferred promotion rules
+        return xp.result_type(*args_not_none)
+    except TypeError:  # mixed type promotion isn't defined
+        if not force_floating:
+            raise
+        # use `result_type` of default floating point type and any floats present
+        # This can be revisited, but right now, the only backends that get here
+        # are array-api-strict (which is not for production use) and PyTorch
+        # (due to data-apis/array-api-compat#279).
+        float_args = []
+        for arg in args_not_none:
+            arg_array = xp.asarray(arg) if np.isscalar(arg) else arg
+            dtype = getattr(arg_array, 'dtype', arg)
+            if xp.isdtype(dtype, ('real floating', 'complex floating')):
+                float_args.append(arg)
+        return xp.result_type(*float_args, xp_default_dtype(xp))
+
+
+def xp_promote(*args, broadcast=False, force_floating=False, xp):
+    """
+    Promotes elements of *args to result dtype, ignoring `None`s.
+    Includes options for forcing promotion to floating point and
+    broadcasting the arrays, again ignoring `None`s.
+    Type promotion rules follow `xp_result_type` instead of `xp.result_type`.
+
+    Typically, this function will be called shortly after `array_namespace`
+    on a subset of the arguments passed to `array_namespace`.
+
+    This function accepts array-like iterables, which are immediately converted
+    to the namespace's arrays before result type calculation. Consequently, the
+    result dtype may be different when an argument is `1.` vs `[1.]`.
+
+    See Also
+    --------
+    xp_result_type
+    """
+    args = [(_asarray(arg, subok=True, xp=xp) if np.iterable(arg) else arg)
+            for arg in args]  # solely to prevent double conversion of iterable to array
+
+    dtype = xp_result_type(*args, force_floating=force_floating, xp=xp)
+
+    args = [(_asarray(arg, dtype=dtype, subok=True, xp=xp) if arg is not None else arg)
+            for arg in args]
+
+    if not broadcast:
+        return args[0] if len(args)==1 else tuple(args)
+
+    args_not_none = [arg for arg in args if arg is not None]
+
+    # determine result shape
+    shapes = {arg.shape for arg in args_not_none}
+    try:
+        shape = (np.broadcast_shapes(*shapes) if len(shapes) != 1
+                 else args_not_none[0].shape)
+    except ValueError as e:
+        message = "Array shapes are incompatible for broadcasting."
+        raise ValueError(message) from e
+
+    out = []
+    for arg in args:
+        if arg is None:
+            out.append(arg)
+            continue
+
+        # broadcast only if needed
+        # Even if two arguments need broadcasting, this is faster than
+        # `broadcast_arrays`, especially since we've already determined `shape`
+        if arg.shape != shape:
+            kwargs = {'subok': True} if is_numpy(xp) else {}
+            arg = xp.broadcast_to(arg, shape, **kwargs)
+
+        # This is much faster than xp.astype(arg, dtype, copy=False)
+        if arg.dtype != dtype:
+            arg = xp.astype(arg, dtype)
+
+        out.append(arg)
+
+    return out[0] if len(out)==1 else tuple(out)
+
+
+def xp_float_to_complex(arr: Array, xp: ModuleType | None = None) -> Array:
+    xp = array_namespace(arr) if xp is None else xp
+    arr_dtype = arr.dtype
+    # The standard float dtypes are float32 and float64.
+    # Convert float32 to complex64,
+    # and float64 (and non-standard real dtypes) to complex128
+    if xp.isdtype(arr_dtype, xp.float32):
+        arr = xp.astype(arr, xp.complex64)
+    elif xp.isdtype(arr_dtype, 'real floating'):
+        arr = xp.astype(arr, xp.complex128)
+
+    return arr
+
+
+def xp_default_dtype(xp):
+    """Query the namespace-dependent default floating-point dtype.
+    """
+    if is_torch(xp):
+        # historically, we allow pytorch to keep its default of float32
+        return xp.get_default_dtype()
+    else:
+        # we default to float64
+        return xp.float64
+
+
+def xp_result_device(*args):
+    """Return the device of an array in `args`, for the purpose of
+    input-output device propagation.
+    If there are multiple devices, return an arbitrary one.
+    If there are no arrays, return None (this typically happens only on NumPy).
+    """
+    for arg in args:
+        # Do not do a duck-type test for the .device attribute, as many backends today
+        # don't have it yet. See workarouunds in array_api_compat.device().
+        if is_array_api_obj(arg):
+            return xp_device(arg)
+    return None
+
+
+def is_marray(xp):
+    """Returns True if `xp` is an MArray namespace; False otherwise."""
+    return "marray" in xp.__name__
+
+
+@dataclasses.dataclass(repr=False)
+class _XPSphinxCapability:
+    cpu: bool | None  # None if not applicable
+    gpu: bool | None
+    warnings: list[str] = dataclasses.field(default_factory=list)
+
+    def _render(self, value):
+        if value is None:
+            return "n/a"
+        if not value:
+            return "⛔"
+        if self.warnings:
+            res = "⚠️ " + '; '.join(self.warnings)
+            assert len(res) <= 20, "Warnings too long"
+            return res
+        return "✅"
+
+    def __str__(self):
+        cpu = self._render(self.cpu)
+        gpu = self._render(self.gpu)
+        return f"{cpu:20}  {gpu:20}"
+
+
+def _make_sphinx_capabilities(
+    # lists of tuples [(module name, reason), ...]
+    skip_backends=(), xfail_backends=(),
+    # @pytest.mark.skip/xfail_xp_backends kwargs
+    cpu_only=False, np_only=False, exceptions=(),
+    # xpx.lazy_xp_backends kwargs
+    allow_dask_compute=False, jax_jit=True,
+    # list of tuples [(module name, reason), ...]
+    warnings = (),
+    # unused in documentation
+    reason=None,
+):
+    exceptions = set(exceptions)
+
+    # Default capabilities
+    capabilities = {
+        "numpy": _XPSphinxCapability(cpu=True, gpu=None),
+        "array_api_strict": _XPSphinxCapability(cpu=True, gpu=None),
+        "cupy": _XPSphinxCapability(cpu=None, gpu=True),
+        "torch": _XPSphinxCapability(cpu=True, gpu=True),
+        "jax.numpy": _XPSphinxCapability(cpu=True, gpu=True,
+            warnings=[] if jax_jit else ["no JIT"]),
+        # Note: Dask+CuPy is currently untested and unsupported
+        "dask.array": _XPSphinxCapability(cpu=True, gpu=None,
+            warnings=["computes graph"] if allow_dask_compute else []),
+    }
+
+    # documentation doesn't display the reason
+    for module, _ in list(skip_backends) + list(xfail_backends):
+        backend = capabilities[module]
+        if backend.cpu is not None:
+            backend.cpu = False
+        if backend.gpu is not None:
+            backend.gpu = False
+
+    for module, backend in capabilities.items():
+        if np_only and module not in exceptions | {"numpy"}:
+            if backend.cpu is not None:
+                backend.cpu = False
+            if backend.gpu is not None:
+                backend.gpu = False
+        elif cpu_only and module not in exceptions and backend.gpu is not None:
+            backend.gpu = False
+
+    for module, warning in warnings:
+        backend = capabilities[module]
+        backend.warnings.append(warning)
+
+    return capabilities
+
+
+def _make_capabilities_note(fun_name, capabilities):
+    # Note: deliberately not documenting array-api-strict
+    note = f"""
+    `{fun_name}` has experimental support for Python Array API Standard compatible
+    backends in addition to NumPy. Please consider testing these features
+    by setting an environment variable ``SCIPY_ARRAY_API=1`` and providing
+    CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following
+    combinations of backend and device (or other capability) are supported.
+
+    ====================  ====================  ====================
+    Library               CPU                   GPU
+    ====================  ====================  ====================
+    NumPy                 {capabilities['numpy']                   }
+    CuPy                  {capabilities['cupy']                    }
+    PyTorch               {capabilities['torch']                   }
+    JAX                   {capabilities['jax.numpy']               }
+    Dask                  {capabilities['dask.array']              }
+    ====================  ====================  ====================
+
+    See :ref:`dev-arrayapi` for more information.
+    """
+    return textwrap.dedent(note)
+
+
+def xp_capabilities(
+    *,
+    # Alternative capabilities table.
+    # Used only for testing this decorator.
+    capabilities_table=None,
+    # Generate pytest.mark.skip/xfail_xp_backends.
+    # See documentation in conftest.py.
+    # lists of tuples [(module name, reason), ...]
+    skip_backends=(), xfail_backends=(),
+    cpu_only=False, np_only=False, reason=None, exceptions=(),
+    # lists of tuples [(module name, reason), ...]
+    warnings=(),
+    # xpx.testing.lazy_xp_function kwargs.
+    # Refer to array-api-extra documentation.
+    allow_dask_compute=False, jax_jit=True,
+):
+    """Decorator for a function that states its support among various
+    Array API compatible backends.
+
+    This decorator has two effects:
+    1. It allows tagging tests with ``@make_xp_test_case`` or
+       ``make_xp_pytest_param`` (see below) to automatically generate
+       SKIP/XFAIL markers and perform additional backend-specific
+       testing, such as extra validation for Dask and JAX;
+    2. It automatically adds a note to the function's docstring, containing
+       a table matching what has been tested.    
+
+    See Also
+    --------
+    make_xp_test_case
+    make_xp_pytest_param
+    array_api_extra.testing.lazy_xp_function
+    """
+    capabilities_table = (xp_capabilities_table if capabilities_table is None
+                          else capabilities_table)
+
+    capabilities = dict(
+        skip_backends=skip_backends,
+        xfail_backends=xfail_backends,
+        cpu_only=cpu_only,
+        np_only=np_only,
+        reason=reason,
+        exceptions=exceptions,
+        allow_dask_compute=allow_dask_compute,
+        jax_jit=jax_jit,
+        warnings=warnings,
+    )
+    sphinx_capabilities = _make_sphinx_capabilities(**capabilities)
+
+    def decorator(f):
+        # Don't use a wrapper, as in some cases @xp_capabilities is
+        # applied to a ufunc
+        capabilities_table[f] = capabilities
+        note = _make_capabilities_note(f.__name__, sphinx_capabilities)
+        doc = FunctionDoc(f)
+        doc['Notes'].append(note)
+        doc = str(doc).split("\n", 1)[1]  # remove signature
+        try:
+            f.__doc__ = doc
+        except AttributeError:
+            # Can't update __doc__ on ufuncs if SciPy
+            # was compiled against NumPy < 2.2.
+            pass
+
+        return f
+    return decorator
+
+
+def _make_xp_pytest_marks(*funcs, capabilities_table=None):
+    capabilities_table = (xp_capabilities_table if capabilities_table is None
+                          else capabilities_table)
+    import pytest
+    from scipy._lib.array_api_extra.testing import lazy_xp_function
+
+    marks = []
+    for func in funcs:
+        capabilities = capabilities_table[func]
+        exceptions = capabilities['exceptions']
+        reason = capabilities['reason']
+
+        if capabilities['cpu_only']:
+            marks.append(pytest.mark.skip_xp_backends(
+                cpu_only=True, exceptions=exceptions, reason=reason))
+        if capabilities['np_only']:
+            marks.append(pytest.mark.skip_xp_backends(
+                np_only=True, exceptions=exceptions, reason=reason))
+
+        for mod_name, reason in capabilities['skip_backends']:
+            marks.append(pytest.mark.skip_xp_backends(mod_name, reason=reason))
+        for mod_name, reason in capabilities['xfail_backends']:
+            marks.append(pytest.mark.xfail_xp_backends(mod_name, reason=reason))
+
+        lazy_kwargs = {k: capabilities[k]
+                       for k in ('allow_dask_compute', 'jax_jit')}
+        lazy_xp_function(func, **lazy_kwargs)
+
+    return marks
+
+
+def make_xp_test_case(*funcs, capabilities_table=None):
+    capabilities_table = (xp_capabilities_table if capabilities_table is None
+                          else capabilities_table)
+    """Generate pytest decorator for a test function that tests functionality
+    of one or more Array API compatible functions.
+
+    Read the parameters of the ``@xp_capabilities`` decorator applied to the
+    listed functions and:
+
+    - Generate the ``@pytest.mark.skip_xp_backends`` and
+      ``@pytest.mark.xfail_xp_backends`` decorators
+      for the decorated test function
+    - Tag the function with `xpx.testing.lazy_xp_function`
+
+    See Also
+    --------
+    xp_capabilities
+    make_xp_pytest_param
+    array_api_extra.testing.lazy_xp_function
+    """
+    marks = _make_xp_pytest_marks(*funcs, capabilities_table=capabilities_table)
+    return lambda func: functools.reduce(lambda f, g: g(f), marks, func)
+
+
+def make_xp_pytest_param(func, *args, capabilities_table=None):
+    """Variant of ``make_xp_test_case`` that returns a pytest.param for a function,
+    with all necessary skip_xp_backends and xfail_xp_backends marks applied::
+    
+        @pytest.mark.parametrize(
+            "func", [make_xp_pytest_param(f1), make_xp_pytest_param(f2)]
+        )
+        def test(func, xp):
+            ...
+
+    The above is equivalent to::
+
+        @pytest.mark.parametrize(
+            "func", [
+                pytest.param(f1, marks=[
+                    pytest.mark.skip_xp_backends(...),
+                    pytest.mark.xfail_xp_backends(...), ...]),
+                pytest.param(f2, marks=[
+                    pytest.mark.skip_xp_backends(...),
+                    pytest.mark.xfail_xp_backends(...), ...]),
+        )
+        def test(func, xp):
+            ...
+
+    Parameters
+    ----------
+    func : Callable
+        Function to be tested. It must be decorated with ``@xp_capabilities``.
+    *args : Any, optional
+        Extra pytest parameters for the use case, e.g.::
+
+        @pytest.mark.parametrize("func,verb", [
+            make_xp_pytest_param(f1, "hello"),
+            make_xp_pytest_param(f2, "world")])
+        def test(func, verb, xp):
+            # iterates on (func=f1, verb="hello")
+            # and (func=f2, verb="world")
+
+    See Also
+    --------
+    xp_capabilities
+    make_xp_test_case
+    array_api_extra.testing.lazy_xp_function
+    """
+    import pytest
+
+    marks = _make_xp_pytest_marks(func, capabilities_table=capabilities_table)
+    return pytest.param(func, *args, marks=marks, id=func.__name__)
+
+
+# Is it OK to have a dictionary that is mutated (once upon import) in many places?
+xp_capabilities_table = {}  # type: ignore[var-annotated]

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_array_api_compat_vendor.py

@@ -0,0 +1,9 @@
+# DO NOT RENAME THIS FILE
+# This is a hook for array_api_extra/src/array_api_extra/_lib/_compat.py
+# to override functions of array_api_compat.
+
+from .array_api_compat import *  # noqa: F403
+from ._array_api import array_namespace as scipy_array_namespace
+
+# overrides array_api_compat.array_namespace inside array-api-extra
+array_namespace = scipy_array_namespace  # type: ignore[assignment]

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_array_api_no_0d.py

@@ -0,0 +1,103 @@
+"""
+Extra testing functions that forbid 0d-input, see #21044
+
+While the xp_assert_* functions generally aim to follow the conventions of the
+underlying `xp` library, NumPy in particular is inconsistent in its handling
+of scalars vs. 0d-arrays, see https://github.com/numpy/numpy/issues/24897.
+
+For example, this means that the following operations (as of v2.0.1) currently
+return scalars, even though a 0d-array would often be more appropriate:
+
+    import numpy as np
+    np.array(0) * 2     # scalar, not 0d array
+    - np.array(0)       # scalar, not 0d-array
+    np.sin(np.array(0)) # scalar, not 0d array
+    np.mean([1, 2, 3])  # scalar, not 0d array
+
+Libraries like CuPy tend to return a 0d-array in scenarios like those above,
+and even `xp.asarray(0)[()]` remains a 0d-array there. To deal with the reality
+of the inconsistencies present in NumPy, as well as 20+ years of code on top,
+the `xp_assert_*` functions here enforce consistency in the only way that
+doesn't go against the tide, i.e. by forbidding 0d-arrays as the return type.
+
+However, when scalars are not generally the expected NumPy return type,
+it remains preferable to use the assert functions from
+the `scipy._lib._array_api` module, which have less surprising behaviour.
+"""
+from scipy._lib._array_api import array_namespace, is_numpy
+from scipy._lib._array_api import (xp_assert_close as xp_assert_close_base,
+                                   xp_assert_equal as xp_assert_equal_base,
+                                   xp_assert_less as xp_assert_less_base)
+
+__all__: list[str] = []
+
+
+def _check_scalar(actual, desired, *, xp=None, **kwargs):
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    if xp is None:
+        xp = array_namespace(actual)
+
+    # necessary to handle non-numpy scalars, e.g. bare `0.0` has no shape
+    desired = xp.asarray(desired)
+
+    # Only NumPy distinguishes between scalars and arrays;
+    # shape check in xp_assert_* is sufficient except for shape == ()
+    if not (is_numpy(xp) and desired.shape == ()):
+        return
+
+    _msg = ("Result is a NumPy 0d-array. Many SciPy functions intend to follow "
+            "the convention of many NumPy functions, returning a scalar when a "
+            "0d-array would be correct. The specialized `xp_assert_*` functions "
+            "in the `scipy._lib._array_api_no_0d` module err on the side of "
+            "caution and do not accept 0d-arrays by default. If the correct "
+            "result may legitimately be a 0d-array, pass `check_0d=True`, "
+            "or use the `xp_assert_*` functions from `scipy._lib._array_api`.")
+    assert xp.isscalar(actual), _msg
+
+
+def xp_assert_equal(actual, desired, *, check_0d=False, **kwargs):
+    # in contrast to xp_assert_equal_base, this defaults to check_0d=False,
+    # but will do an extra check in that case, which forbids 0d-arrays for `actual`
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    # array-ness (check_0d == True) is taken care of by the *_base functions
+    if not check_0d:
+        _check_scalar(actual, desired, **kwargs)
+    return xp_assert_equal_base(actual, desired, check_0d=check_0d, **kwargs)
+
+
+def xp_assert_close(actual, desired, *, check_0d=False, **kwargs):
+    # as for xp_assert_equal
+    __tracebackhide__ = True
+
+    if not check_0d:
+        _check_scalar(actual, desired, **kwargs)
+    return xp_assert_close_base(actual, desired, check_0d=check_0d, **kwargs)
+
+
+def xp_assert_less(actual, desired, *, check_0d=False, **kwargs):
+    # as for xp_assert_equal
+    __tracebackhide__ = True
+
+    if not check_0d:
+        _check_scalar(actual, desired, **kwargs)
+    return xp_assert_less_base(actual, desired, check_0d=check_0d, **kwargs)
+
+
+def assert_array_almost_equal(actual, desired, decimal=6, *args, **kwds):
+    """Backwards compatible replacement. In new code, use xp_assert_close instead.
+    """
+    rtol, atol = 0, 1.5*10**(-decimal)
+    return xp_assert_close(actual, desired,
+                           atol=atol, rtol=rtol, check_dtype=False, check_shape=False,
+                           *args, **kwds)
+
+
+def assert_almost_equal(actual, desired, decimal=7, *args, **kwds):
+    """Backwards compatible replacement. In new code, use xp_assert_close instead.
+    """
+    rtol, atol = 0, 1.5*10**(-decimal)
+    return xp_assert_close(actual, desired,
+                           atol=atol, rtol=rtol, check_dtype=False, check_shape=False,
+                           *args, **kwds)

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_bunch.py

@@ -0,0 +1,229 @@
+import sys as _sys
+from keyword import iskeyword as _iskeyword
+
+
+def _validate_names(typename, field_names, extra_field_names):
+    """
+    Ensure that all the given names are valid Python identifiers that
+    do not start with '_'.  Also check that there are no duplicates
+    among field_names + extra_field_names.
+    """
+    for name in [typename] + field_names + extra_field_names:
+        if not isinstance(name, str):
+            raise TypeError('typename and all field names must be strings')
+        if not name.isidentifier():
+            raise ValueError('typename and all field names must be valid '
+                             f'identifiers: {name!r}')
+        if _iskeyword(name):
+            raise ValueError('typename and all field names cannot be a '
+                             f'keyword: {name!r}')
+
+    seen = set()
+    for name in field_names + extra_field_names:
+        if name.startswith('_'):
+            raise ValueError('Field names cannot start with an underscore: '
+                             f'{name!r}')
+        if name in seen:
+            raise ValueError(f'Duplicate field name: {name!r}')
+        seen.add(name)
+
+
+# Note: This code is adapted from CPython:Lib/collections/__init__.py
+def _make_tuple_bunch(typename, field_names, extra_field_names=None,
+                      module=None):
+    """
+    Create a namedtuple-like class with additional attributes.
+
+    This function creates a subclass of tuple that acts like a namedtuple
+    and that has additional attributes.
+
+    The additional attributes are listed in `extra_field_names`.  The
+    values assigned to these attributes are not part of the tuple.
+
+    The reason this function exists is to allow functions in SciPy
+    that currently return a tuple or a namedtuple to returned objects
+    that have additional attributes, while maintaining backwards
+    compatibility.
+
+    This should only be used to enhance *existing* functions in SciPy.
+    New functions are free to create objects as return values without
+    having to maintain backwards compatibility with an old tuple or
+    namedtuple return value.
+
+    Parameters
+    ----------
+    typename : str
+        The name of the type.
+    field_names : list of str
+        List of names of the values to be stored in the tuple. These names
+        will also be attributes of instances, so the values in the tuple
+        can be accessed by indexing or as attributes.  At least one name
+        is required.  See the Notes for additional restrictions.
+    extra_field_names : list of str, optional
+        List of names of values that will be stored as attributes of the
+        object.  See the notes for additional restrictions.
+
+    Returns
+    -------
+    cls : type
+        The new class.
+
+    Notes
+    -----
+    There are restrictions on the names that may be used in `field_names`
+    and `extra_field_names`:
+
+    * The names must be unique--no duplicates allowed.
+    * The names must be valid Python identifiers, and must not begin with
+      an underscore.
+    * The names must not be Python keywords (e.g. 'def', 'and', etc., are
+      not allowed).
+
+    Examples
+    --------
+    >>> from scipy._lib._bunch import _make_tuple_bunch
+
+    Create a class that acts like a namedtuple with length 2 (with field
+    names `x` and `y`) that will also have the attributes `w` and `beta`:
+
+    >>> Result = _make_tuple_bunch('Result', ['x', 'y'], ['w', 'beta'])
+
+    `Result` is the new class.  We call it with keyword arguments to create
+    a new instance with given values.
+
+    >>> result1 = Result(x=1, y=2, w=99, beta=0.5)
+    >>> result1
+    Result(x=1, y=2, w=99, beta=0.5)
+
+    `result1` acts like a tuple of length 2:
+
+    >>> len(result1)
+    2
+    >>> result1[:]
+    (1, 2)
+
+    The values assigned when the instance was created are available as
+    attributes:
+
+    >>> result1.y
+    2
+    >>> result1.beta
+    0.5
+    """
+    if len(field_names) == 0:
+        raise ValueError('field_names must contain at least one name')
+
+    if extra_field_names is None:
+        extra_field_names = []
+    _validate_names(typename, field_names, extra_field_names)
+
+    typename = _sys.intern(str(typename))
+    field_names = tuple(map(_sys.intern, field_names))
+    extra_field_names = tuple(map(_sys.intern, extra_field_names))
+
+    all_names = field_names + extra_field_names
+    arg_list = ', '.join(field_names)
+    full_list = ', '.join(all_names)
+    repr_fmt = ''.join(('(',
+                        ', '.join(f'{name}=%({name})r' for name in all_names),
+                        ')'))
+    tuple_new = tuple.__new__
+    _dict, _tuple, _zip = dict, tuple, zip
+
+    # Create all the named tuple methods to be added to the class namespace
+
+    s = f"""\
+def __new__(_cls, {arg_list}, **extra_fields):
+    return _tuple_new(_cls, ({arg_list},))
+
+def __init__(self, {arg_list}, **extra_fields):
+    for key in self._extra_fields:
+        if key not in extra_fields:
+            raise TypeError("missing keyword argument '%s'" % (key,))
+    for key, val in extra_fields.items():
+        if key not in self._extra_fields:
+            raise TypeError("unexpected keyword argument '%s'" % (key,))
+        self.__dict__[key] = val
+
+def __setattr__(self, key, val):
+    if key in {repr(field_names)}:
+        raise AttributeError("can't set attribute %r of class %r"
+                             % (key, self.__class__.__name__))
+    else:
+        self.__dict__[key] = val
+"""
+    del arg_list
+    namespace = {'_tuple_new': tuple_new,
+                 '__builtins__': dict(TypeError=TypeError,
+                                      AttributeError=AttributeError),
+                 '__name__': f'namedtuple_{typename}'}
+    exec(s, namespace)
+    __new__ = namespace['__new__']
+    __new__.__doc__ = f'Create new instance of {typename}({full_list})'
+    __init__ = namespace['__init__']
+    __init__.__doc__ = f'Instantiate instance of {typename}({full_list})'
+    __setattr__ = namespace['__setattr__']
+
+    def __repr__(self):
+        'Return a nicely formatted representation string'
+        return self.__class__.__name__ + repr_fmt % self._asdict()
+
+    def _asdict(self):
+        'Return a new dict which maps field names to their values.'
+        out = _dict(_zip(self._fields, self))
+        out.update(self.__dict__)
+        return out
+
+    def __getnewargs_ex__(self):
+        'Return self as a plain tuple.  Used by copy and pickle.'
+        return _tuple(self), self.__dict__
+
+    # Modify function metadata to help with introspection and debugging
+    for method in (__new__, __repr__, _asdict, __getnewargs_ex__):
+        method.__qualname__ = f'{typename}.{method.__name__}'
+
+    # Build-up the class namespace dictionary
+    # and use type() to build the result class
+    class_namespace = {
+        '__doc__': f'{typename}({full_list})',
+        '_fields': field_names,
+        '__new__': __new__,
+        '__init__': __init__,
+        '__repr__': __repr__,
+        '__setattr__': __setattr__,
+        '_asdict': _asdict,
+        '_extra_fields': extra_field_names,
+        '__getnewargs_ex__': __getnewargs_ex__,
+        # _field_defaults and _replace are added to get Polars to detect
+        # a bunch object as a namedtuple. See gh-22450
+        '_field_defaults': {},
+        '_replace': None,
+    }
+    for index, name in enumerate(field_names):
+
+        def _get(self, index=index):
+            return self[index]
+        class_namespace[name] = property(_get)
+    for name in extra_field_names:
+
+        def _get(self, name=name):
+            return self.__dict__[name]
+        class_namespace[name] = property(_get)
+
+    result = type(typename, (tuple,), class_namespace)
+
+    # For pickling to work, the __module__ variable needs to be set to the
+    # frame where the named tuple is created.  Bypass this step in environments
+    # where sys._getframe is not defined (Jython for example) or sys._getframe
+    # is not defined for arguments greater than 0 (IronPython), or where the
+    # user has specified a particular module.
+    if module is None:
+        try:
+            module = _sys._getframe(1).f_globals.get('__name__', '__main__')
+        except (AttributeError, ValueError):
+            pass
+    if module is not None:
+        result.__module__ = module
+        __new__.__module__ = module
+
+    return result

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_ccallback.py

@@ -0,0 +1,251 @@
+from . import _ccallback_c
+
+import ctypes
+
+PyCFuncPtr = ctypes.CFUNCTYPE(ctypes.c_void_p).__bases__[0]
+
+ffi = None
+
+class CData:
+    pass
+
+def _import_cffi():
+    global ffi, CData
+
+    if ffi is not None:
+        return
+
+    try:
+        import cffi
+        ffi = cffi.FFI()
+        CData = ffi.CData
+    except ImportError:
+        ffi = False
+
+
+class LowLevelCallable(tuple):
+    """
+    Low-level callback function.
+
+    Some functions in SciPy take as arguments callback functions, which
+    can either be python callables or low-level compiled functions. Using
+    compiled callback functions can improve performance somewhat by
+    avoiding wrapping data in Python objects.
+
+    Such low-level functions in SciPy are wrapped in `LowLevelCallable`
+    objects, which can be constructed from function pointers obtained from
+    ctypes, cffi, Cython, or contained in Python `PyCapsule` objects.
+
+    .. seealso::
+
+       Functions accepting low-level callables:
+
+       `scipy.integrate.quad`, `scipy.ndimage.generic_filter`,
+       `scipy.ndimage.generic_filter1d`, `scipy.ndimage.geometric_transform`
+
+       Usage examples:
+
+       :ref:`ndimage-ccallbacks`, :ref:`quad-callbacks`
+
+    Parameters
+    ----------
+    function : {PyCapsule, ctypes function pointer, cffi function pointer}
+        Low-level callback function.
+    user_data : {PyCapsule, ctypes void pointer, cffi void pointer}
+        User data to pass on to the callback function.
+    signature : str, optional
+        Signature of the function. If omitted, determined from *function*,
+        if possible.
+
+    Attributes
+    ----------
+    function
+        Callback function given.
+    user_data
+        User data given.
+    signature
+        Signature of the function.
+
+    Methods
+    -------
+    from_cython
+        Class method for constructing callables from Cython C-exported
+        functions.
+
+    Notes
+    -----
+    The argument ``function`` can be one of:
+
+    - PyCapsule, whose name contains the C function signature
+    - ctypes function pointer
+    - cffi function pointer
+
+    The signature of the low-level callback must match one of those expected
+    by the routine it is passed to.
+
+    If constructing low-level functions from a PyCapsule, the name of the
+    capsule must be the corresponding signature, in the format::
+
+        return_type (arg1_type, arg2_type, ...)
+
+    For example::
+
+        "void (double)"
+        "double (double, int *, void *)"
+
+    The context of a PyCapsule passed in as ``function`` is used as ``user_data``,
+    if an explicit value for ``user_data`` was not given.
+
+    """
+
+    # Make the class immutable
+    __slots__ = ()
+
+    def __new__(cls, function, user_data=None, signature=None):
+        # We need to hold a reference to the function & user data,
+        # to prevent them going out of scope
+        item = cls._parse_callback(function, user_data, signature)
+        return tuple.__new__(cls, (item, function, user_data))
+
+    def __repr__(self):
+        return f"LowLevelCallable({self.function!r}, {self.user_data!r})"
+
+    @property
+    def function(self):
+        return tuple.__getitem__(self, 1)
+
+    @property
+    def user_data(self):
+        return tuple.__getitem__(self, 2)
+
+    @property
+    def signature(self):
+        return _ccallback_c.get_capsule_signature(tuple.__getitem__(self, 0))
+
+    def __getitem__(self, idx):
+        raise ValueError()
+
+    @classmethod
+    def from_cython(cls, module, name, user_data=None, signature=None):
+        """
+        Create a low-level callback function from an exported Cython function.
+
+        Parameters
+        ----------
+        module : module
+            Cython module where the exported function resides
+        name : str
+            Name of the exported function
+        user_data : {PyCapsule, ctypes void pointer, cffi void pointer}, optional
+            User data to pass on to the callback function.
+        signature : str, optional
+            Signature of the function. If omitted, determined from *function*.
+
+        """
+        try:
+            function = module.__pyx_capi__[name]
+        except AttributeError as e:
+            message = "Given module is not a Cython module with __pyx_capi__ attribute"
+            raise ValueError(message) from e
+        except KeyError as e:
+            message = f"No function {name!r} found in __pyx_capi__ of the module"
+            raise ValueError(message) from e
+        return cls(function, user_data, signature)
+
+    @classmethod
+    def _parse_callback(cls, obj, user_data=None, signature=None):
+        _import_cffi()
+
+        if isinstance(obj, LowLevelCallable):
+            func = tuple.__getitem__(obj, 0)
+        elif isinstance(obj, PyCFuncPtr):
+            func, signature = _get_ctypes_func(obj, signature)
+        elif isinstance(obj, CData):
+            func, signature = _get_cffi_func(obj, signature)
+        elif _ccallback_c.check_capsule(obj):
+            func = obj
+        else:
+            raise ValueError("Given input is not a callable or a "
+                             "low-level callable (pycapsule/ctypes/cffi)")
+
+        if isinstance(user_data, ctypes.c_void_p):
+            context = _get_ctypes_data(user_data)
+        elif isinstance(user_data, CData):
+            context = _get_cffi_data(user_data)
+        elif user_data is None:
+            context = 0
+        elif _ccallback_c.check_capsule(user_data):
+            context = user_data
+        else:
+            raise ValueError("Given user data is not a valid "
+                             "low-level void* pointer (pycapsule/ctypes/cffi)")
+
+        return _ccallback_c.get_raw_capsule(func, signature, context)
+
+
+#
+# ctypes helpers
+#
+
+def _get_ctypes_func(func, signature=None):
+    # Get function pointer
+    func_ptr = ctypes.cast(func, ctypes.c_void_p).value
+
+    # Construct function signature
+    if signature is None:
+        signature = _typename_from_ctypes(func.restype) + " ("
+        for j, arg in enumerate(func.argtypes):
+            if j == 0:
+                signature += _typename_from_ctypes(arg)
+            else:
+                signature += ", " + _typename_from_ctypes(arg)
+        signature += ")"
+
+    return func_ptr, signature
+
+
+def _typename_from_ctypes(item):
+    if item is None:
+        return "void"
+    elif item is ctypes.c_void_p:
+        return "void *"
+
+    name = item.__name__
+
+    pointer_level = 0
+    while name.startswith("LP_"):
+        pointer_level += 1
+        name = name[3:]
+
+    if name.startswith('c_'):
+        name = name[2:]
+
+    if pointer_level > 0:
+        name += " " + "*"*pointer_level
+
+    return name
+
+
+def _get_ctypes_data(data):
+    # Get voidp pointer
+    return ctypes.cast(data, ctypes.c_void_p).value
+
+
+#
+# CFFI helpers
+#
+
+def _get_cffi_func(func, signature=None):
+    # Get function pointer
+    func_ptr = ffi.cast('uintptr_t', func)
+
+    # Get signature
+    if signature is None:
+        signature = ffi.getctype(ffi.typeof(func)).replace('(*)', ' ')
+
+    return func_ptr, signature
+
+
+def _get_cffi_data(data):
+    # Get pointer
+    return ffi.cast('uintptr_t', data)

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_disjoint_set.py

@@ -0,0 +1,254 @@
+"""
+Disjoint set data structure
+"""
+
+
+class DisjointSet:
+    """ Disjoint set data structure for incremental connectivity queries.
+
+    .. versionadded:: 1.6.0
+
+    Attributes
+    ----------
+    n_subsets : int
+        The number of subsets.
+
+    Methods
+    -------
+    add
+    merge
+    connected
+    subset
+    subset_size
+    subsets
+    __getitem__
+
+    Notes
+    -----
+    This class implements the disjoint set [1]_, also known as the *union-find*
+    or *merge-find* data structure. The *find* operation (implemented in
+    `__getitem__`) implements the *path halving* variant. The *merge* method
+    implements the *merge by size* variant.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Disjoint-set_data_structure
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import DisjointSet
+
+    Initialize a disjoint set:
+
+    >>> disjoint_set = DisjointSet([1, 2, 3, 'a', 'b'])
+
+    Merge some subsets:
+
+    >>> disjoint_set.merge(1, 2)
+    True
+    >>> disjoint_set.merge(3, 'a')
+    True
+    >>> disjoint_set.merge('a', 'b')
+    True
+    >>> disjoint_set.merge('b', 'b')
+    False
+
+    Find root elements:
+
+    >>> disjoint_set[2]
+    1
+    >>> disjoint_set['b']
+    3
+
+    Test connectivity:
+
+    >>> disjoint_set.connected(1, 2)
+    True
+    >>> disjoint_set.connected(1, 'b')
+    False
+
+    List elements in disjoint set:
+
+    >>> list(disjoint_set)
+    [1, 2, 3, 'a', 'b']
+
+    Get the subset containing 'a':
+
+    >>> disjoint_set.subset('a')
+    {'a', 3, 'b'}
+
+    Get the size of the subset containing 'a' (without actually instantiating
+    the subset):
+
+    >>> disjoint_set.subset_size('a')
+    3
+
+    Get all subsets in the disjoint set:
+
+    >>> disjoint_set.subsets()
+    [{1, 2}, {'a', 3, 'b'}]
+    """
+    def __init__(self, elements=None):
+        self.n_subsets = 0
+        self._sizes = {}
+        self._parents = {}
+        # _nbrs is a circular linked list which links connected elements.
+        self._nbrs = {}
+        # _indices tracks the element insertion order in `__iter__`.
+        self._indices = {}
+        if elements is not None:
+            for x in elements:
+                self.add(x)
+
+    def __iter__(self):
+        """Returns an iterator of the elements in the disjoint set.
+
+        Elements are ordered by insertion order.
+        """
+        return iter(self._indices)
+
+    def __len__(self):
+        return len(self._indices)
+
+    def __contains__(self, x):
+        return x in self._indices
+
+    def __getitem__(self, x):
+        """Find the root element of `x`.
+
+        Parameters
+        ----------
+        x : hashable object
+            Input element.
+
+        Returns
+        -------
+        root : hashable object
+            Root element of `x`.
+        """
+        if x not in self._indices:
+            raise KeyError(x)
+
+        # find by "path halving"
+        parents = self._parents
+        while self._indices[x] != self._indices[parents[x]]:
+            parents[x] = parents[parents[x]]
+            x = parents[x]
+        return x
+
+    def add(self, x):
+        """Add element `x` to disjoint set
+        """
+        if x in self._indices:
+            return
+
+        self._sizes[x] = 1
+        self._parents[x] = x
+        self._nbrs[x] = x
+        self._indices[x] = len(self._indices)
+        self.n_subsets += 1
+
+    def merge(self, x, y):
+        """Merge the subsets of `x` and `y`.
+
+        The smaller subset (the child) is merged into the larger subset (the
+        parent). If the subsets are of equal size, the root element which was
+        first inserted into the disjoint set is selected as the parent.
+
+        Parameters
+        ----------
+        x, y : hashable object
+            Elements to merge.
+
+        Returns
+        -------
+        merged : bool
+            True if `x` and `y` were in disjoint sets, False otherwise.
+        """
+        xr = self[x]
+        yr = self[y]
+        if self._indices[xr] == self._indices[yr]:
+            return False
+
+        sizes = self._sizes
+        if (sizes[xr], self._indices[yr]) < (sizes[yr], self._indices[xr]):
+            xr, yr = yr, xr
+        self._parents[yr] = xr
+        self._sizes[xr] += self._sizes[yr]
+        self._nbrs[xr], self._nbrs[yr] = self._nbrs[yr], self._nbrs[xr]
+        self.n_subsets -= 1
+        return True
+
+    def connected(self, x, y):
+        """Test whether `x` and `y` are in the same subset.
+
+        Parameters
+        ----------
+        x, y : hashable object
+            Elements to test.
+
+        Returns
+        -------
+        result : bool
+            True if `x` and `y` are in the same set, False otherwise.
+        """
+        return self._indices[self[x]] == self._indices[self[y]]
+
+    def subset(self, x):
+        """Get the subset containing `x`.
+
+        Parameters
+        ----------
+        x : hashable object
+            Input element.
+
+        Returns
+        -------
+        result : set
+            Subset containing `x`.
+        """
+        if x not in self._indices:
+            raise KeyError(x)
+
+        result = [x]
+        nxt = self._nbrs[x]
+        while self._indices[nxt] != self._indices[x]:
+            result.append(nxt)
+            nxt = self._nbrs[nxt]
+        return set(result)
+
+    def subset_size(self, x):
+        """Get the size of the subset containing `x`.
+
+        Note that this method is faster than ``len(self.subset(x))`` because
+        the size is directly read off an internal field, without the need to
+        instantiate the full subset.
+
+        Parameters
+        ----------
+        x : hashable object
+            Input element.
+
+        Returns
+        -------
+        result : int
+            Size of the subset containing `x`.
+        """
+        return self._sizes[self[x]]
+
+    def subsets(self):
+        """Get all the subsets in the disjoint set.
+
+        Returns
+        -------
+        result : list
+            Subsets in the disjoint set.
+        """
+        result = []
+        visited = set()
+        for x in self:
+            if x not in visited:
+                xset = self.subset(x)
+                visited.update(xset)
+                result.append(xset)
+        return result

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_docscrape.py

@@ -0,0 +1,761 @@
+# copied from numpydoc/docscrape.py, commit 97a6026508e0dd5382865672e9563a72cc113bd2
+"""Extract reference documentation from the NumPy source tree."""
+
+import copy
+import inspect
+import pydoc
+import re
+import sys
+import textwrap
+from collections import namedtuple
+from collections.abc import Callable, Mapping
+from functools import cached_property
+from warnings import warn
+
+
+def strip_blank_lines(l):
+    "Remove leading and trailing blank lines from a list of lines"
+    while l and not l[0].strip():
+        del l[0]
+    while l and not l[-1].strip():
+        del l[-1]
+    return l
+
+
+class Reader:
+    """A line-based string reader."""
+
+    def __init__(self, data):
+        """
+        Parameters
+        ----------
+        data : str
+           String with lines separated by '\\n'.
+
+        """
+        if isinstance(data, list):
+            self._str = data
+        else:
+            self._str = data.split("\n")  # store string as list of lines
+
+        self.reset()
+
+    def __getitem__(self, n):
+        return self._str[n]
+
+    def reset(self):
+        self._l = 0  # current line nr
+
+    def read(self):
+        if not self.eof():
+            out = self[self._l]
+            self._l += 1
+            return out
+        else:
+            return ""
+
+    def seek_next_non_empty_line(self):
+        for l in self[self._l :]:
+            if l.strip():
+                break
+            else:
+                self._l += 1
+
+    def eof(self):
+        return self._l >= len(self._str)
+
+    def read_to_condition(self, condition_func):
+        start = self._l
+        for line in self[start:]:
+            if condition_func(line):
+                return self[start : self._l]
+            self._l += 1
+            if self.eof():
+                return self[start : self._l + 1]
+        return []
+
+    def read_to_next_empty_line(self):
+        self.seek_next_non_empty_line()
+
+        def is_empty(line):
+            return not line.strip()
+
+        return self.read_to_condition(is_empty)
+
+    def read_to_next_unindented_line(self):
+        def is_unindented(line):
+            return line.strip() and (len(line.lstrip()) == len(line))
+
+        return self.read_to_condition(is_unindented)
+
+    def peek(self, n=0):
+        if self._l + n < len(self._str):
+            return self[self._l + n]
+        else:
+            return ""
+
+    def is_empty(self):
+        return not "".join(self._str).strip()
+
+
+class ParseError(Exception):
+    def __str__(self):
+        message = self.args[0]
+        if hasattr(self, "docstring"):
+            message = f"{message} in {self.docstring!r}"
+        return message
+
+
+Parameter = namedtuple("Parameter", ["name", "type", "desc"])
+
+
+class NumpyDocString(Mapping):
+    """Parses a numpydoc string to an abstract representation
+
+    Instances define a mapping from section title to structured data.
+
+    """
+
+    sections = {
+        "Signature": "",
+        "Summary": [""],
+        "Extended Summary": [],
+        "Parameters": [],
+        "Attributes": [],
+        "Methods": [],
+        "Returns": [],
+        "Yields": [],
+        "Receives": [],
+        "Other Parameters": [],
+        "Raises": [],
+        "Warns": [],
+        "Warnings": [],
+        "See Also": [],
+        "Notes": [],
+        "References": "",
+        "Examples": "",
+        "index": {},
+    }
+
+    def __init__(self, docstring, config=None):
+        orig_docstring = docstring
+        docstring = textwrap.dedent(docstring).split("\n")
+
+        self._doc = Reader(docstring)
+        self._parsed_data = copy.deepcopy(self.sections)
+
+        try:
+            self._parse()
+        except ParseError as e:
+            e.docstring = orig_docstring
+            raise
+
+    def __getitem__(self, key):
+        return self._parsed_data[key]
+
+    def __setitem__(self, key, val):
+        if key not in self._parsed_data:
+            self._error_location(f"Unknown section {key}", error=False)
+        else:
+            self._parsed_data[key] = val
+
+    def __iter__(self):
+        return iter(self._parsed_data)
+
+    def __len__(self):
+        return len(self._parsed_data)
+
+    def _is_at_section(self):
+        self._doc.seek_next_non_empty_line()
+
+        if self._doc.eof():
+            return False
+
+        l1 = self._doc.peek().strip()  # e.g. Parameters
+
+        if l1.startswith(".. index::"):
+            return True
+
+        l2 = self._doc.peek(1).strip()  # ---------- or ==========
+        if len(l2) >= 3 and (set(l2) in ({"-"}, {"="})) and len(l2) != len(l1):
+            snip = "\n".join(self._doc._str[:2]) + "..."
+            self._error_location(
+                f"potentially wrong underline length... \n{l1} \n{l2} in \n{snip}",
+                error=False,
+            )
+        return l2.startswith("-" * len(l1)) or l2.startswith("=" * len(l1))
+
+    def _strip(self, doc):
+        i = 0
+        j = 0
+        for i, line in enumerate(doc):
+            if line.strip():
+                break
+
+        for j, line in enumerate(doc[::-1]):
+            if line.strip():
+                break
+
+        return doc[i : len(doc) - j]
+
+    def _read_to_next_section(self):
+        section = self._doc.read_to_next_empty_line()
+
+        while not self._is_at_section() and not self._doc.eof():
+            if not self._doc.peek(-1).strip():  # previous line was empty
+                section += [""]
+
+            section += self._doc.read_to_next_empty_line()
+
+        return section
+
+    def _read_sections(self):
+        while not self._doc.eof():
+            data = self._read_to_next_section()
+            name = data[0].strip()
+
+            if name.startswith(".."):  # index section
+                yield name, data[1:]
+            elif len(data) < 2:
+                yield StopIteration
+            else:
+                yield name, self._strip(data[2:])
+
+    def _parse_param_list(self, content, single_element_is_type=False):
+        content = dedent_lines(content)
+        r = Reader(content)
+        params = []
+        while not r.eof():
+            header = r.read().strip()
+            if " : " in header:
+                arg_name, arg_type = header.split(" : ", maxsplit=1)
+            else:
+                # NOTE: param line with single element should never have a
+                # a " :" before the description line, so this should probably
+                # warn.
+                if header.endswith(" :"):
+                    header = header[:-2]
+                if single_element_is_type:
+                    arg_name, arg_type = "", header
+                else:
+                    arg_name, arg_type = header, ""
+
+            desc = r.read_to_next_unindented_line()
+            desc = dedent_lines(desc)
+            desc = strip_blank_lines(desc)
+
+            params.append(Parameter(arg_name, arg_type, desc))
+
+        return params
+
+    # See also supports the following formats.
+    #
+    # <FUNCNAME>
+    # <FUNCNAME> SPACE* COLON SPACE+ <DESC> SPACE*
+    # <FUNCNAME> ( COMMA SPACE+ <FUNCNAME>)+ (COMMA | PERIOD)? SPACE*
+    # <FUNCNAME> ( COMMA SPACE+ <FUNCNAME>)* SPACE* COLON SPACE+ <DESC> SPACE*
+
+    # <FUNCNAME> is one of
+    #   <PLAIN_FUNCNAME>
+    #   COLON <ROLE> COLON BACKTICK <PLAIN_FUNCNAME> BACKTICK
+    # where
+    #   <PLAIN_FUNCNAME> is a legal function name, and
+    #   <ROLE> is any nonempty sequence of word characters.
+    # Examples: func_f1  :meth:`func_h1` :obj:`~baz.obj_r` :class:`class_j`
+    # <DESC> is a string describing the function.
+
+    _role = r":(?P<role>(py:)?\w+):"
+    _funcbacktick = r"`(?P<name>(?:~\w+\.)?[a-zA-Z0-9_\.-]+)`"
+    _funcplain = r"(?P<name2>[a-zA-Z0-9_\.-]+)"
+    _funcname = r"(" + _role + _funcbacktick + r"|" + _funcplain + r")"
+    _funcnamenext = _funcname.replace("role", "rolenext")
+    _funcnamenext = _funcnamenext.replace("name", "namenext")
+    _description = r"(?P<description>\s*:(\s+(?P<desc>\S+.*))?)?\s*$"
+    _func_rgx = re.compile(r"^\s*" + _funcname + r"\s*")
+    _line_rgx = re.compile(
+        r"^\s*"
+        + r"(?P<allfuncs>"
+        + _funcname  # group for all function names
+        + r"(?P<morefuncs>([,]\s+"
+        + _funcnamenext
+        + r")*)"
+        + r")"
+        + r"(?P<trailing>[,\.])?"  # end of "allfuncs"
+        + _description  # Some function lists have a trailing comma (or period)  '\s*'
+    )
+
+    # Empty <DESC> elements are replaced with '..'
+    empty_description = ".."
+
+    def _parse_see_also(self, content):
+        """
+        func_name : Descriptive text
+            continued text
+        another_func_name : Descriptive text
+        func_name1, func_name2, :meth:`func_name`, func_name3
+
+        """
+
+        content = dedent_lines(content)
+
+        items = []
+
+        def parse_item_name(text):
+            """Match ':role:`name`' or 'name'."""
+            m = self._func_rgx.match(text)
+            if not m:
+                self._error_location(f"Error parsing See Also entry {line!r}")
+            role = m.group("role")
+            name = m.group("name") if role else m.group("name2")
+            return name, role, m.end()
+
+        rest = []
+        for line in content:
+            if not line.strip():
+                continue
+
+            line_match = self._line_rgx.match(line)
+            description = None
+            if line_match:
+                description = line_match.group("desc")
+                if line_match.group("trailing") and description:
+                    self._error_location(
+                        "Unexpected comma or period after function list at index %d of "
+                        'line "%s"' % (line_match.end("trailing"), line),
+                        error=False,
+                    )
+            if not description and line.startswith(" "):
+                rest.append(line.strip())
+            elif line_match:
+                funcs = []
+                text = line_match.group("allfuncs")
+                while True:
+                    if not text.strip():
+                        break
+                    name, role, match_end = parse_item_name(text)
+                    funcs.append((name, role))
+                    text = text[match_end:].strip()
+                    if text and text[0] == ",":
+                        text = text[1:].strip()
+                rest = list(filter(None, [description]))
+                items.append((funcs, rest))
+            else:
+                self._error_location(f"Error parsing See Also entry {line!r}")
+        return items
+
+    def _parse_index(self, section, content):
+        """
+        .. index:: default
+           :refguide: something, else, and more
+
+        """
+
+        def strip_each_in(lst):
+            return [s.strip() for s in lst]
+
+        out = {}
+        section = section.split("::")
+        if len(section) > 1:
+            out["default"] = strip_each_in(section[1].split(","))[0]
+        for line in content:
+            line = line.split(":")
+            if len(line) > 2:
+                out[line[1]] = strip_each_in(line[2].split(","))
+        return out
+
+    def _parse_summary(self):
+        """Grab signature (if given) and summary"""
+        if self._is_at_section():
+            return
+
+        # If several signatures present, take the last one
+        while True:
+            summary = self._doc.read_to_next_empty_line()
+            summary_str = " ".join([s.strip() for s in summary]).strip()
+            compiled = re.compile(r"^([\w., ]+=)?\s*[\w\.]+\(.*\)$")
+            if compiled.match(summary_str):
+                self["Signature"] = summary_str
+                if not self._is_at_section():
+                    continue
+            break
+
+        if summary is not None:
+            self["Summary"] = summary
+
+        if not self._is_at_section():
+            self["Extended Summary"] = self._read_to_next_section()
+
+    def _parse(self):
+        self._doc.reset()
+        self._parse_summary()
+
+        sections = list(self._read_sections())
+        section_names = {section for section, content in sections}
+
+        has_yields = "Yields" in section_names
+        # We could do more tests, but we are not. Arbitrarily.
+        if not has_yields and "Receives" in section_names:
+            msg = "Docstring contains a Receives section but not Yields."
+            raise ValueError(msg)
+
+        for section, content in sections:
+            if not section.startswith(".."):
+                section = (s.capitalize() for s in section.split(" "))
+                section = " ".join(section)
+                if self.get(section):
+                    self._error_location(
+                        "The section %s appears twice in  %s"
+                        % (section, "\n".join(self._doc._str))
+                    )
+
+            if section in ("Parameters", "Other Parameters", "Attributes", "Methods"):
+                self[section] = self._parse_param_list(content)
+            elif section in ("Returns", "Yields", "Raises", "Warns", "Receives"):
+                self[section] = self._parse_param_list(
+                    content, single_element_is_type=True
+                )
+            elif section.startswith(".. index::"):
+                self["index"] = self._parse_index(section, content)
+            elif section == "See Also":
+                self["See Also"] = self._parse_see_also(content)
+            else:
+                self[section] = content
+
+    @property
+    def _obj(self):
+        if hasattr(self, "_cls"):
+            return self._cls
+        elif hasattr(self, "_f"):
+            return self._f
+        return None
+
+    def _error_location(self, msg, error=True):
+        if self._obj is not None:
+            # we know where the docs came from:
+            try:
+                filename = inspect.getsourcefile(self._obj)
+            except TypeError:
+                filename = None
+            # Make UserWarning more descriptive via object introspection.
+            # Skip if introspection fails
+            name = getattr(self._obj, "__name__", None)
+            if name is None:
+                name = getattr(getattr(self._obj, "__class__", None), "__name__", None)
+            if name is not None:
+                msg += f" in the docstring of {name}"
+            msg += f" in {filename}." if filename else ""
+        if error:
+            raise ValueError(msg)
+        else:
+            warn(msg, stacklevel=3)
+
+    # string conversion routines
+
+    def _str_header(self, name, symbol="-"):
+        return [name, len(name) * symbol]
+
+    def _str_indent(self, doc, indent=4):
+        return [" " * indent + line for line in doc]
+
+    def _str_signature(self):
+        if self["Signature"]:
+            return [self["Signature"].replace("*", r"\*")] + [""]
+        return [""]
+
+    def _str_summary(self):
+        if self["Summary"]:
+            return self["Summary"] + [""]
+        return []
+
+    def _str_extended_summary(self):
+        if self["Extended Summary"]:
+            return self["Extended Summary"] + [""]
+        return []
+
+    def _str_param_list(self, name):
+        out = []
+        if self[name]:
+            out += self._str_header(name)
+            for param in self[name]:
+                parts = []
+                if param.name:
+                    parts.append(param.name)
+                if param.type:
+                    parts.append(param.type)
+                out += [" : ".join(parts)]
+                if param.desc and "".join(param.desc).strip():
+                    out += self._str_indent(param.desc)
+            out += [""]
+        return out
+
+    def _str_section(self, name):
+        out = []
+        if self[name]:
+            out += self._str_header(name)
+            out += self[name]
+            out += [""]
+        return out
+
+    def _str_see_also(self, func_role):
+        if not self["See Also"]:
+            return []
+        out = []
+        out += self._str_header("See Also")
+        out += [""]
+        last_had_desc = True
+        for funcs, desc in self["See Also"]:
+            assert isinstance(funcs, list)
+            links = []
+            for func, role in funcs:
+                if role:
+                    link = f":{role}:`{func}`"
+                elif func_role:
+                    link = f":{func_role}:`{func}`"
+                else:
+                    link = f"`{func}`_"
+                links.append(link)
+            link = ", ".join(links)
+            out += [link]
+            if desc:
+                out += self._str_indent([" ".join(desc)])
+                last_had_desc = True
+            else:
+                last_had_desc = False
+                out += self._str_indent([self.empty_description])
+
+        if last_had_desc:
+            out += [""]
+        out += [""]
+        return out
+
+    def _str_index(self):
+        idx = self["index"]
+        out = []
+        output_index = False
+        default_index = idx.get("default", "")
+        if default_index:
+            output_index = True
+        out += [f".. index:: {default_index}"]
+        for section, references in idx.items():
+            if section == "default":
+                continue
+            output_index = True
+            out += [f"   :{section}: {', '.join(references)}"]
+        if output_index:
+            return out
+        return ""
+
+    def __str__(self, func_role=""):
+        out = []
+        out += self._str_signature()
+        out += self._str_summary()
+        out += self._str_extended_summary()
+        out += self._str_param_list("Parameters")
+        for param_list in ("Attributes", "Methods"):
+            out += self._str_param_list(param_list)
+        for param_list in (
+            "Returns",
+            "Yields",
+            "Receives",
+            "Other Parameters",
+            "Raises",
+            "Warns",
+        ):
+            out += self._str_param_list(param_list)
+        out += self._str_section("Warnings")
+        out += self._str_see_also(func_role)
+        for s in ("Notes", "References", "Examples"):
+            out += self._str_section(s)
+        out += self._str_index()
+        return "\n".join(out)
+
+
+def dedent_lines(lines):
+    """Deindent a list of lines maximally"""
+    return textwrap.dedent("\n".join(lines)).split("\n")
+
+
+class FunctionDoc(NumpyDocString):
+    def __init__(self, func, role="func", doc=None, config=None):
+        self._f = func
+        self._role = role  # e.g. "func" or "meth"
+
+        if doc is None:
+            if func is None:
+                raise ValueError("No function or docstring given")
+            doc = inspect.getdoc(func) or ""
+        if config is None:
+            config = {}
+        NumpyDocString.__init__(self, doc, config)
+
+    def get_func(self):
+        func_name = getattr(self._f, "__name__", self.__class__.__name__)
+        if inspect.isclass(self._f):
+            func = getattr(self._f, "__call__", self._f.__init__)
+        else:
+            func = self._f
+        return func, func_name
+
+    def __str__(self):
+        out = ""
+
+        func, func_name = self.get_func()
+
+        roles = {"func": "function", "meth": "method"}
+
+        if self._role:
+            if self._role not in roles:
+                print(f"Warning: invalid role {self._role}")
+            out += f".. {roles.get(self._role, '')}:: {func_name}\n    \n\n"
+
+        out += super().__str__(func_role=self._role)
+        return out
+
+
+class ObjDoc(NumpyDocString):
+    def __init__(self, obj, doc=None, config=None):
+        self._f = obj
+        if config is None:
+            config = {}
+        NumpyDocString.__init__(self, doc, config=config)
+
+
+class ClassDoc(NumpyDocString):
+    extra_public_methods = ["__call__"]
+
+    def __init__(self, cls, doc=None, modulename="", func_doc=FunctionDoc, config=None):
+        if not inspect.isclass(cls) and cls is not None:
+            raise ValueError(f"Expected a class or None, but got {cls!r}")
+        self._cls = cls
+
+        if "sphinx" in sys.modules:
+            from sphinx.ext.autodoc import ALL
+        else:
+            ALL = object()
+
+        if config is None:
+            config = {}
+        self.show_inherited_members = config.get("show_inherited_class_members", True)
+
+        if modulename and not modulename.endswith("."):
+            modulename += "."
+        self._mod = modulename
+
+        if doc is None:
+            if cls is None:
+                raise ValueError("No class or documentation string given")
+            doc = pydoc.getdoc(cls)
+
+        NumpyDocString.__init__(self, doc)
+
+        _members = config.get("members", [])
+        if _members is ALL:
+            _members = None
+        _exclude = config.get("exclude-members", [])
+
+        if config.get("show_class_members", True) and _exclude is not ALL:
+
+            def splitlines_x(s):
+                if not s:
+                    return []
+                else:
+                    return s.splitlines()
+
+            for field, items in [
+                ("Methods", self.methods),
+                ("Attributes", self.properties),
+            ]:
+                if not self[field]:
+                    doc_list = []
+                    for name in sorted(items):
+                        if name in _exclude or (_members and name not in _members):
+                            continue
+                        try:
+                            doc_item = pydoc.getdoc(getattr(self._cls, name))
+                            doc_list.append(Parameter(name, "", splitlines_x(doc_item)))
+                        except AttributeError:
+                            pass  # method doesn't exist
+                    self[field] = doc_list
+
+    @property
+    def methods(self):
+        if self._cls is None:
+            return []
+        return [
+            name
+            for name, func in inspect.getmembers(self._cls)
+            if (
+                (not name.startswith("_") or name in self.extra_public_methods)
+                and isinstance(func, Callable)
+                and self._is_show_member(name)
+            )
+        ]
+
+    @property
+    def properties(self):
+        if self._cls is None:
+            return []
+        return [
+            name
+            for name, func in inspect.getmembers(self._cls)
+            if (
+                not name.startswith("_")
+                and not self._should_skip_member(name, self._cls)
+                and (
+                    func is None
+                    or isinstance(func, property | cached_property)
+                    or inspect.isdatadescriptor(func)
+                )
+                and self._is_show_member(name)
+            )
+        ]
+
+    @staticmethod
+    def _should_skip_member(name, klass):
+        return (
+            # Namedtuples should skip everything in their ._fields as the
+            # docstrings for each of the members is: "Alias for field number X"
+            issubclass(klass, tuple)
+            and hasattr(klass, "_asdict")
+            and hasattr(klass, "_fields")
+            and name in klass._fields
+        )
+
+    def _is_show_member(self, name):
+        return (
+            # show all class members
+            self.show_inherited_members
+            # or class member is not inherited
+            or name in self._cls.__dict__
+        )
+
+
+def get_doc_object(
+    obj,
+    what=None,
+    doc=None,
+    config=None,
+    class_doc=ClassDoc,
+    func_doc=FunctionDoc,
+    obj_doc=ObjDoc,
+):
+    if what is None:
+        if inspect.isclass(obj):
+            what = "class"
+        elif inspect.ismodule(obj):
+            what = "module"
+        elif isinstance(obj, Callable):
+            what = "function"
+        else:
+            what = "object"
+    if config is None:
+        config = {}
+
+    if what == "class":
+        return class_doc(obj, func_doc=func_doc, doc=doc, config=config)
+    elif what in ("function", "method"):
+        return func_doc(obj, doc=doc, config=config)
+    else:
+        if doc is None:
+            doc = pydoc.getdoc(obj)
+        return obj_doc(obj, doc, config=config)

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_elementwise_iterative_method.py

@@ -0,0 +1,346 @@
+# `_elementwise_iterative_method.py` includes tools for writing functions that
+# - are vectorized to work elementwise on arrays,
+# - implement non-trivial, iterative algorithms with a callback interface, and
+# - return rich objects with iteration count, termination status, etc.
+#
+# Examples include:
+# `scipy.optimize._chandrupatla._chandrupatla for scalar rootfinding,
+# `scipy.optimize._chandrupatla._chandrupatla_minimize for scalar minimization,
+# `scipy.optimize._differentiate._differentiate for numerical differentiation,
+# `scipy.optimize._bracket._bracket_root for finding rootfinding brackets,
+# `scipy.optimize._bracket._bracket_minimize for finding minimization brackets,
+# `scipy.integrate._tanhsinh._tanhsinh` for numerical quadrature,
+# `scipy.differentiate.derivative` for finite difference based differentiation.
+
+import math
+import numpy as np
+from ._util import _RichResult, _call_callback_maybe_halt
+from ._array_api import array_namespace, xp_size, xp_result_type
+import scipy._lib.array_api_extra as xpx
+
+_ESIGNERR = -1
+_ECONVERR = -2
+_EVALUEERR = -3
+_ECALLBACK = -4
+_EINPUTERR = -5
+_ECONVERGED = 0
+_EINPROGRESS = 1
+
+def _initialize(func, xs, args, complex_ok=False, preserve_shape=None, xp=None):
+    """Initialize abscissa, function, and args arrays for elementwise function
+
+    Parameters
+    ----------
+    func : callable
+        An elementwise function with signature
+
+            func(x: ndarray, *args) -> ndarray
+
+        where each element of ``x`` is a finite real and ``args`` is a tuple,
+        which may contain an arbitrary number of arrays that are broadcastable
+        with ``x``.
+    xs : tuple of arrays
+        Finite real abscissa arrays. Must be broadcastable.
+    args : tuple, optional
+        Additional positional arguments to be passed to `func`.
+    preserve_shape : bool, default:False
+        When ``preserve_shape=False`` (default), `func` may be passed
+        arguments of any shape; `_scalar_optimization_loop` is permitted
+        to reshape and compress arguments at will. When
+        ``preserve_shape=False``, arguments passed to `func` must have shape
+        `shape` or ``shape + (n,)``, where ``n`` is any integer.
+    xp : namespace
+        Namespace of array arguments in `xs`.
+
+    Returns
+    -------
+    xs, fs, args : tuple of arrays
+        Broadcasted, writeable, 1D abscissa and function value arrays (or
+        NumPy floats, if appropriate). The dtypes of the `xs` and `fs` are
+        `xfat`; the dtype of the `args` are unchanged.
+    shape : tuple of ints
+        Original shape of broadcasted arrays.
+    xfat : NumPy dtype
+        Result dtype of abscissae, function values, and args determined using
+        `np.result_type`, except integer types are promoted to `np.float64`.
+
+    Raises
+    ------
+    ValueError
+        If the result dtype is not that of a real scalar
+
+    Notes
+    -----
+    Useful for initializing the input of SciPy functions that accept
+    an elementwise callable, abscissae, and arguments; e.g.
+    `scipy.optimize._chandrupatla`.
+    """
+    nx = len(xs)
+    xp = array_namespace(*xs) if xp is None else xp
+
+    # Try to preserve `dtype`, but we need to ensure that the arguments are at
+    # least floats before passing them into the function; integers can overflow
+    # and cause failure.
+    # There might be benefit to combining the `xs` into a single array and
+    # calling `func` once on the combined array. For now, keep them separate.
+    xat = xp_result_type(*xs, force_floating=True, xp=xp)
+    xas = xp.broadcast_arrays(*xs, *args)  # broadcast and rename
+    xs, args = xas[:nx], xas[nx:]
+    xs = [xp.asarray(x, dtype=xat) for x in xs]  # use copy=False when implemented
+    fs = [xp.asarray(func(x, *args)) for x in xs]
+    shape = xs[0].shape
+    fshape = fs[0].shape
+
+    if preserve_shape:
+        # bind original shape/func now to avoid late-binding gotcha
+        def func(x, *args, shape=shape, func=func,  **kwargs):
+            i = (0,)*(len(fshape) - len(shape))
+            return func(x[i], *args, **kwargs)
+        shape = np.broadcast_shapes(fshape, shape)  # just shapes; use of NumPy OK
+        xs = [xp.broadcast_to(x, shape) for x in xs]
+        args = [xp.broadcast_to(arg, shape) for arg in args]
+
+    message = ("The shape of the array returned by `func` must be the same as "
+               "the broadcasted shape of `x` and all other `args`.")
+    if preserve_shape is not None:  # only in tanhsinh for now
+        message = f"When `preserve_shape=False`, {message.lower()}"
+    shapes_equal = [f.shape == shape for f in fs]
+    if not all(shapes_equal):  # use Python all to reduce overhead
+        raise ValueError(message)
+
+    # These algorithms tend to mix the dtypes of the abscissae and function
+    # values, so figure out what the result will be and convert them all to
+    # that type from the outset.
+    xfat = xp.result_type(*([f.dtype for f in fs] + [xat]))
+    if not complex_ok and not xp.isdtype(xfat, "real floating"):
+        raise ValueError("Abscissae and function output must be real numbers.")
+    xs = [xp.asarray(x, dtype=xfat, copy=True) for x in xs]
+    fs = [xp.asarray(f, dtype=xfat, copy=True) for f in fs]
+
+    # To ensure that we can do indexing, we'll work with at least 1d arrays,
+    # but remember the appropriate shape of the output.
+    xs = [xp.reshape(x, (-1,)) for x in xs]
+    fs = [xp.reshape(f, (-1,)) for f in fs]
+    args = [xp.reshape(xp.asarray(arg, copy=True), (-1,)) for arg in args]
+    return func, xs, fs, args, shape, xfat, xp
+
+
+def _loop(work, callback, shape, maxiter, func, args, dtype, pre_func_eval,
+          post_func_eval, check_termination, post_termination_check,
+          customize_result, res_work_pairs, xp, preserve_shape=False):
+    """Main loop of a vectorized scalar optimization algorithm
+
+    Parameters
+    ----------
+    work : _RichResult
+        All variables that need to be retained between iterations. Must
+        contain attributes `nit`, `nfev`, and `success`. All arrays are
+        subject to being "compressed" if `preserve_shape is False`; nest
+        arrays that should not be compressed inside another object (e.g.
+        `dict` or `_RichResult`).
+    callback : callable
+        User-specified callback function
+    shape : tuple of ints
+        The shape of all output arrays
+    maxiter :
+        Maximum number of iterations of the algorithm
+    func : callable
+        The user-specified callable that is being optimized or solved
+    args : tuple
+        Additional positional arguments to be passed to `func`.
+    dtype : NumPy dtype
+        The common dtype of all abscissae and function values
+    pre_func_eval : callable
+        A function that accepts `work` and returns `x`, the active elements
+        of `x` at which `func` will be evaluated. May modify attributes
+        of `work` with any algorithmic steps that need to happen
+         at the beginning of an iteration, before `func` is evaluated,
+    post_func_eval : callable
+        A function that accepts `x`, `func(x)`, and `work`. May modify
+        attributes of `work` with any algorithmic steps that need to happen
+         in the middle of an iteration, after `func` is evaluated but before
+         the termination check.
+    check_termination : callable
+        A function that accepts `work` and returns `stop`, a boolean array
+        indicating which of the active elements have met a termination
+        condition.
+    post_termination_check : callable
+        A function that accepts `work`. May modify `work` with any algorithmic
+        steps that need to happen after the termination check and before the
+        end of the iteration.
+    customize_result : callable
+        A function that accepts `res` and `shape` and returns `shape`. May
+        modify `res` (in-place) according to preferences (e.g. rearrange
+        elements between attributes) and modify `shape` if needed.
+    res_work_pairs : list of (str, str)
+        Identifies correspondence between attributes of `res` and attributes
+        of `work`; i.e., attributes of active elements of `work` will be
+        copied to the appropriate indices of `res` when appropriate. The order
+        determines the order in which _RichResult attributes will be
+        pretty-printed.
+    preserve_shape : bool, default: False
+        Whether to compress the attributes of `work` (to avoid unnecessary
+        computation on elements that have already converged).
+
+    Returns
+    -------
+    res : _RichResult
+        The final result object
+
+    Notes
+    -----
+    Besides providing structure, this framework provides several important
+    services for a vectorized optimization algorithm.
+
+    - It handles common tasks involving iteration count, function evaluation
+      count, a user-specified callback, and associated termination conditions.
+    - It compresses the attributes of `work` to eliminate unnecessary
+      computation on elements that have already converged.
+
+    """
+    if xp is None:
+        raise NotImplementedError("Must provide xp.")
+
+    cb_terminate = False
+
+    # Initialize the result object and active element index array
+    n_elements = math.prod(shape)
+    active = xp.arange(n_elements)  # in-progress element indices
+    res_dict = {i: xp.zeros(n_elements, dtype=dtype) for i, j in res_work_pairs}
+    res_dict['success'] = xp.zeros(n_elements, dtype=xp.bool)
+    res_dict['status'] = xp.full(n_elements, xp.asarray(_EINPROGRESS), dtype=xp.int32)
+    res_dict['nit'] = xp.zeros(n_elements, dtype=xp.int32)
+    res_dict['nfev'] = xp.zeros(n_elements, dtype=xp.int32)
+    res = _RichResult(res_dict)
+    work.args = args
+
+    active = _check_termination(work, res, res_work_pairs, active,
+                                check_termination, preserve_shape, xp)
+
+    if callback is not None:
+        temp = _prepare_result(work, res, res_work_pairs, active, shape,
+                               customize_result, preserve_shape, xp)
+        if _call_callback_maybe_halt(callback, temp):
+            cb_terminate = True
+
+    while work.nit < maxiter and xp_size(active) and not cb_terminate and n_elements:
+        x = pre_func_eval(work)
+
+        if work.args and work.args[0].ndim != x.ndim:
+            # `x` always starts as 1D. If the SciPy function that uses
+            # _loop added dimensions to `x`, we need to
+            # add them to the elements of `args`.
+            args = []
+            for arg in work.args:
+                n_new_dims = x.ndim - arg.ndim
+                new_shape = arg.shape + (1,)*n_new_dims
+                args.append(xp.reshape(arg, new_shape))
+            work.args = args
+
+        x_shape = x.shape
+        if preserve_shape:
+            x = xp.reshape(x, (shape + (-1,)))
+        f = func(x, *work.args)
+        f = xp.asarray(f, dtype=dtype)
+        if preserve_shape:
+            x = xp.reshape(x, x_shape)
+            f = xp.reshape(f, x_shape)
+        work.nfev += 1 if x.ndim == 1 else x.shape[-1]
+
+        post_func_eval(x, f, work)
+
+        work.nit += 1
+        active = _check_termination(work, res, res_work_pairs, active,
+                                    check_termination, preserve_shape, xp)
+
+        if callback is not None:
+            temp = _prepare_result(work, res, res_work_pairs, active, shape,
+                                   customize_result, preserve_shape, xp)
+            if _call_callback_maybe_halt(callback, temp):
+                cb_terminate = True
+                break
+        if xp_size(active) == 0:
+            break
+
+        post_termination_check(work)
+
+    work.status = xpx.at(work.status)[:].set(_ECALLBACK if cb_terminate else _ECONVERR)
+    return _prepare_result(work, res, res_work_pairs, active, shape,
+                           customize_result, preserve_shape, xp)
+
+
+def _check_termination(work, res, res_work_pairs, active, check_termination,
+                       preserve_shape, xp):
+    # Checks termination conditions, updates elements of `res` with
+    # corresponding elements of `work`, and compresses `work`.
+
+    stop = check_termination(work)
+
+    if xp.any(stop):
+        # update the active elements of the result object with the active
+        # elements for which a termination condition has been met
+        _update_active(work, res, res_work_pairs, active, stop, preserve_shape, xp)
+
+        if preserve_shape:
+            stop = stop[active]
+
+        proceed = ~stop
+        active = active[proceed]
+
+        if not preserve_shape:
+            # compress the arrays to avoid unnecessary computation
+            for key, val in work.items():
+                # `continued_fraction` hacks `n`; improve if this becomes a problem
+                if key in {'args', 'n'}:
+                    continue
+                work[key] = val[proceed] if getattr(val, 'ndim', 0) > 0 else val
+            work.args = [arg[proceed] for arg in work.args]
+
+    return active
+
+
+def _update_active(work, res, res_work_pairs, active, mask, preserve_shape, xp):
+    # Update `active` indices of the arrays in result object `res` with the
+    # contents of the scalars and arrays in `update_dict`. When provided,
+    # `mask` is a boolean array applied both to the arrays in `update_dict`
+    # that are to be used and to the arrays in `res` that are to be updated.
+    update_dict = {key1: work[key2] for key1, key2 in res_work_pairs}
+    update_dict['success'] = work.status == 0
+
+    if mask is not None:
+        if preserve_shape:
+            active_mask = xp.zeros_like(mask)
+            active_mask = xpx.at(active_mask)[active].set(True)
+            active_mask = active_mask & mask
+            for key, val in update_dict.items():
+                val = val[active_mask] if getattr(val, 'ndim', 0) > 0 else val
+                res[key] = xpx.at(res[key])[active_mask].set(val)
+        else:
+            active_mask = active[mask]
+            for key, val in update_dict.items():
+                val = val[mask] if getattr(val, 'ndim', 0) > 0 else val
+                res[key] = xpx.at(res[key])[active_mask].set(val)
+    else:
+        for key, val in update_dict.items():
+            if preserve_shape and getattr(val, 'ndim', 0) > 0:
+                val = val[active]
+            res[key] = xpx.at(res[key])[active].set(val)
+
+
+def _prepare_result(work, res, res_work_pairs, active, shape, customize_result,
+                    preserve_shape, xp):
+    # Prepare the result object `res` by creating a copy, copying the latest
+    # data from work, running the provided result customization function,
+    # and reshaping the data to the original shapes.
+    res = res.copy()
+    _update_active(work, res, res_work_pairs, active, None, preserve_shape, xp)
+
+    shape = customize_result(res, shape)
+
+    for key, val in res.items():
+        # this looks like it won't work for xp != np if val is not numeric
+        temp = xp.reshape(val, shape)
+        res[key] = temp[()] if temp.ndim == 0 else temp
+
+    res['_order_keys'] = ['success'] + [i for i, j in res_work_pairs]
+    return _RichResult(**res)

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_gcutils.py

@@ -0,0 +1,105 @@
+"""
+Module for testing automatic garbage collection of objects
+
+.. autosummary::
+   :toctree: generated/
+
+   set_gc_state - enable or disable garbage collection
+   gc_state - context manager for given state of garbage collector
+   assert_deallocated - context manager to check for circular references on object
+
+"""
+import weakref
+import gc
+
+from contextlib import contextmanager
+from platform import python_implementation
+
+__all__ = ['set_gc_state', 'gc_state', 'assert_deallocated']
+
+
+IS_PYPY = python_implementation() == 'PyPy'
+
+
+class ReferenceError(AssertionError):
+    pass
+
+
+def set_gc_state(state):
+    """ Set status of garbage collector """
+    if gc.isenabled() == state:
+        return
+    if state:
+        gc.enable()
+    else:
+        gc.disable()
+
+
+@contextmanager
+def gc_state(state):
+    """ Context manager to set state of garbage collector to `state`
+
+    Parameters
+    ----------
+    state : bool
+        True for gc enabled, False for disabled
+
+    Examples
+    --------
+    >>> with gc_state(False):
+    ...     assert not gc.isenabled()
+    >>> with gc_state(True):
+    ...     assert gc.isenabled()
+    """
+    orig_state = gc.isenabled()
+    set_gc_state(state)
+    yield
+    set_gc_state(orig_state)
+
+
+@contextmanager
+def assert_deallocated(func, *args, **kwargs):
+    """Context manager to check that object is deallocated
+
+    This is useful for checking that an object can be freed directly by
+    reference counting, without requiring gc to break reference cycles.
+    GC is disabled inside the context manager.
+
+    This check is not available on PyPy.
+
+    Parameters
+    ----------
+    func : callable
+        Callable to create object to check
+    \\*args : sequence
+        positional arguments to `func` in order to create object to check
+    \\*\\*kwargs : dict
+        keyword arguments to `func` in order to create object to check
+
+    Examples
+    --------
+    >>> class C: pass
+    >>> with assert_deallocated(C) as c:
+    ...     # do something
+    ...     del c
+
+    >>> class C:
+    ...     def __init__(self):
+    ...         self._circular = self # Make circular reference
+    >>> with assert_deallocated(C) as c: #doctest: +IGNORE_EXCEPTION_DETAIL
+    ...     # do something
+    ...     del c
+    Traceback (most recent call last):
+        ...
+    ReferenceError: Remaining reference(s) to object
+    """
+    if IS_PYPY:
+        raise RuntimeError("assert_deallocated is unavailable on PyPy")
+
+    with gc_state(False):
+        obj = func(*args, **kwargs)
+        ref = weakref.ref(obj)
+        yield obj
+        del obj
+        if ref() is not None:
+            raise ReferenceError("Remaining reference(s) to object")

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_pep440.py

@@ -0,0 +1,487 @@
+"""Utility to compare pep440 compatible version strings.
+
+The LooseVersion and StrictVersion classes that distutils provides don't
+work; they don't recognize anything like alpha/beta/rc/dev versions.
+"""
+
+# Copyright (c) Donald Stufft and individual contributors.
+# All rights reserved.
+
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are met:
+
+#     1. Redistributions of source code must retain the above copyright notice,
+#        this list of conditions and the following disclaimer.
+
+#     2. 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.
+
+# 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 HOLDER 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 collections
+import itertools
+import re
+
+
+__all__ = [
+    "parse", "Version", "LegacyVersion", "InvalidVersion", "VERSION_PATTERN",
+]
+
+
+# BEGIN packaging/_structures.py
+
+
+class Infinity:
+    def __repr__(self):
+        return "Infinity"
+
+    def __hash__(self):
+        return hash(repr(self))
+
+    def __lt__(self, other):
+        return False
+
+    def __le__(self, other):
+        return False
+
+    def __eq__(self, other):
+        return isinstance(other, self.__class__)
+
+    def __ne__(self, other):
+        return not isinstance(other, self.__class__)
+
+    def __gt__(self, other):
+        return True
+
+    def __ge__(self, other):
+        return True
+
+    def __neg__(self):
+        return NegativeInfinity
+
+
+Infinity = Infinity()
+
+
+class NegativeInfinity:
+    def __repr__(self):
+        return "-Infinity"
+
+    def __hash__(self):
+        return hash(repr(self))
+
+    def __lt__(self, other):
+        return True
+
+    def __le__(self, other):
+        return True
+
+    def __eq__(self, other):
+        return isinstance(other, self.__class__)
+
+    def __ne__(self, other):
+        return not isinstance(other, self.__class__)
+
+    def __gt__(self, other):
+        return False
+
+    def __ge__(self, other):
+        return False
+
+    def __neg__(self):
+        return Infinity
+
+
+# BEGIN packaging/version.py
+
+
+NegativeInfinity = NegativeInfinity()
+
+_Version = collections.namedtuple(
+    "_Version",
+    ["epoch", "release", "dev", "pre", "post", "local"],
+)
+
+
+def parse(version):
+    """
+    Parse the given version string and return either a :class:`Version` object
+    or a :class:`LegacyVersion` object depending on if the given version is
+    a valid PEP 440 version or a legacy version.
+    """
+    try:
+        return Version(version)
+    except InvalidVersion:
+        return LegacyVersion(version)
+
+
+class InvalidVersion(ValueError):
+    """
+    An invalid version was found, users should refer to PEP 440.
+    """
+
+
+class _BaseVersion:
+
+    def __hash__(self):
+        return hash(self._key)
+
+    def __lt__(self, other):
+        return self._compare(other, lambda s, o: s < o)
+
+    def __le__(self, other):
+        return self._compare(other, lambda s, o: s <= o)
+
+    def __eq__(self, other):
+        return self._compare(other, lambda s, o: s == o)
+
+    def __ge__(self, other):
+        return self._compare(other, lambda s, o: s >= o)
+
+    def __gt__(self, other):
+        return self._compare(other, lambda s, o: s > o)
+
+    def __ne__(self, other):
+        return self._compare(other, lambda s, o: s != o)
+
+    def _compare(self, other, method):
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return method(self._key, other._key)
+
+
+class LegacyVersion(_BaseVersion):
+
+    def __init__(self, version):
+        self._version = str(version)
+        self._key = _legacy_cmpkey(self._version)
+
+    def __str__(self):
+        return self._version
+
+    def __repr__(self):
+        return f"<LegacyVersion({repr(str(self))})>"
+
+    @property
+    def public(self):
+        return self._version
+
+    @property
+    def base_version(self):
+        return self._version
+
+    @property
+    def local(self):
+        return None
+
+    @property
+    def is_prerelease(self):
+        return False
+
+    @property
+    def is_postrelease(self):
+        return False
+
+
+_legacy_version_component_re = re.compile(
+    r"(\d+ | [a-z]+ | \.| -)", re.VERBOSE,
+)
+
+_legacy_version_replacement_map = {
+    "pre": "c", "preview": "c", "-": "final-", "rc": "c", "dev": "@",
+}
+
+
+def _parse_version_parts(s):
+    for part in _legacy_version_component_re.split(s):
+        part = _legacy_version_replacement_map.get(part, part)
+
+        if not part or part == ".":
+            continue
+
+        if part[:1] in "0123456789":
+            # pad for numeric comparison
+            yield part.zfill(8)
+        else:
+            yield "*" + part
+
+    # ensure that alpha/beta/candidate are before final
+    yield "*final"
+
+
+def _legacy_cmpkey(version):
+    # We hardcode an epoch of -1 here. A PEP 440 version can only have an epoch
+    # greater than or equal to 0. This will effectively put the LegacyVersion,
+    # which uses the defacto standard originally implemented by setuptools,
+    # as before all PEP 440 versions.
+    epoch = -1
+
+    # This scheme is taken from pkg_resources.parse_version setuptools prior to
+    # its adoption of the packaging library.
+    parts = []
+    for part in _parse_version_parts(version.lower()):
+        if part.startswith("*"):
+            # remove "-" before a prerelease tag
+            if part < "*final":
+                while parts and parts[-1] == "*final-":
+                    parts.pop()
+
+            # remove trailing zeros from each series of numeric parts
+            while parts and parts[-1] == "00000000":
+                parts.pop()
+
+        parts.append(part)
+    parts = tuple(parts)
+
+    return epoch, parts
+
+
+# Deliberately not anchored to the start and end of the string, to make it
+# easier for 3rd party code to reuse
+VERSION_PATTERN = r"""
+    v?
+    (?:
+        (?:(?P<epoch>[0-9]+)!)?                           # epoch
+        (?P<release>[0-9]+(?:\.[0-9]+)*)                  # release segment
+        (?P<pre>                                          # pre-release
+            [-_\.]?
+            (?P<pre_l>(a|b|c|rc|alpha|beta|pre|preview))
+            [-_\.]?
+            (?P<pre_n>[0-9]+)?
+        )?
+        (?P<post>                                         # post release
+            (?:-(?P<post_n1>[0-9]+))
+            |
+            (?:
+                [-_\.]?
+                (?P<post_l>post|rev|r)
+                [-_\.]?
+                (?P<post_n2>[0-9]+)?
+            )
+        )?
+        (?P<dev>                                          # dev release
+            [-_\.]?
+            (?P<dev_l>dev)
+            [-_\.]?
+            (?P<dev_n>[0-9]+)?
+        )?
+    )
+    (?:\+(?P<local>[a-z0-9]+(?:[-_\.][a-z0-9]+)*))?       # local version
+"""
+
+
+class Version(_BaseVersion):
+
+    _regex = re.compile(
+        r"^\s*" + VERSION_PATTERN + r"\s*$",
+        re.VERBOSE | re.IGNORECASE,
+    )
+
+    def __init__(self, version):
+        # Validate the version and parse it into pieces
+        match = self._regex.search(version)
+        if not match:
+            raise InvalidVersion(f"Invalid version: '{version}'")
+
+        # Store the parsed out pieces of the version
+        self._version = _Version(
+            epoch=int(match.group("epoch")) if match.group("epoch") else 0,
+            release=tuple(int(i) for i in match.group("release").split(".")),
+            pre=_parse_letter_version(
+                match.group("pre_l"),
+                match.group("pre_n"),
+            ),
+            post=_parse_letter_version(
+                match.group("post_l"),
+                match.group("post_n1") or match.group("post_n2"),
+            ),
+            dev=_parse_letter_version(
+                match.group("dev_l"),
+                match.group("dev_n"),
+            ),
+            local=_parse_local_version(match.group("local")),
+        )
+
+        # Generate a key which will be used for sorting
+        self._key = _cmpkey(
+            self._version.epoch,
+            self._version.release,
+            self._version.pre,
+            self._version.post,
+            self._version.dev,
+            self._version.local,
+        )
+
+    def __repr__(self):
+        return f"<Version({repr(str(self))})>"
+
+    def __str__(self):
+        parts = []
+
+        # Epoch
+        if self._version.epoch != 0:
+            parts.append(f"{self._version.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self._version.release))
+
+        # Pre-release
+        if self._version.pre is not None:
+            parts.append("".join(str(x) for x in self._version.pre))
+
+        # Post-release
+        if self._version.post is not None:
+            parts.append(f".post{self._version.post[1]}")
+
+        # Development release
+        if self._version.dev is not None:
+            parts.append(f".dev{self._version.dev[1]}")
+
+        # Local version segment
+        if self._version.local is not None:
+            parts.append(
+                "+{}".format(".".join(str(x) for x in self._version.local))
+            )
+
+        return "".join(parts)
+
+    @property
+    def public(self):
+        return str(self).split("+", 1)[0]
+
+    @property
+    def base_version(self):
+        parts = []
+
+        # Epoch
+        if self._version.epoch != 0:
+            parts.append(f"{self._version.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self._version.release))
+
+        return "".join(parts)
+
+    @property
+    def local(self):
+        version_string = str(self)
+        if "+" in version_string:
+            return version_string.split("+", 1)[1]
+
+    @property
+    def is_prerelease(self):
+        return bool(self._version.dev or self._version.pre)
+
+    @property
+    def is_postrelease(self):
+        return bool(self._version.post)
+
+
+def _parse_letter_version(letter, number):
+    if letter:
+        # We assume there is an implicit 0 in a pre-release if there is
+        # no numeral associated with it.
+        if number is None:
+            number = 0
+
+        # We normalize any letters to their lower-case form
+        letter = letter.lower()
+
+        # We consider some words to be alternate spellings of other words and
+        # in those cases we want to normalize the spellings to our preferred
+        # spelling.
+        if letter == "alpha":
+            letter = "a"
+        elif letter == "beta":
+            letter = "b"
+        elif letter in ["c", "pre", "preview"]:
+            letter = "rc"
+        elif letter in ["rev", "r"]:
+            letter = "post"
+
+        return letter, int(number)
+    if not letter and number:
+        # We assume that if we are given a number but not given a letter,
+        # then this is using the implicit post release syntax (e.g., 1.0-1)
+        letter = "post"
+
+        return letter, int(number)
+
+
+_local_version_seperators = re.compile(r"[\._-]")
+
+
+def _parse_local_version(local):
+    """
+    Takes a string like abc.1.twelve and turns it into ("abc", 1, "twelve").
+    """
+    if local is not None:
+        return tuple(
+            part.lower() if not part.isdigit() else int(part)
+            for part in _local_version_seperators.split(local)
+        )
+
+
+def _cmpkey(epoch, release, pre, post, dev, local):
+    # When we compare a release version, we want to compare it with all of the
+    # trailing zeros removed. So we'll use a reverse the list, drop all the now
+    # leading zeros until we come to something non-zero, then take the rest,
+    # re-reverse it back into the correct order, and make it a tuple and use
+    # that for our sorting key.
+    release = tuple(
+        reversed(list(
+            itertools.dropwhile(
+                lambda x: x == 0,
+                reversed(release),
+            )
+        ))
+    )
+
+    # We need to "trick" the sorting algorithm to put 1.0.dev0 before 1.0a0.
+    # We'll do this by abusing the pre-segment, but we _only_ want to do this
+    # if there is no pre- or a post-segment. If we have one of those, then
+    # the normal sorting rules will handle this case correctly.
+    if pre is None and post is None and dev is not None:
+        pre = -Infinity
+    # Versions without a pre-release (except as noted above) should sort after
+    # those with one.
+    elif pre is None:
+        pre = Infinity
+
+    # Versions without a post-segment should sort before those with one.
+    if post is None:
+        post = -Infinity
+
+    # Versions without a development segment should sort after those with one.
+    if dev is None:
+        dev = Infinity
+
+    if local is None:
+        # Versions without a local segment should sort before those with one.
+        local = -Infinity
+    else:
+        # Versions with a local segment need that segment parsed to implement
+        # the sorting rules in PEP440.
+        # - Alphanumeric segments sort before numeric segments
+        # - Alphanumeric segments sort lexicographically
+        # - Numeric segments sort numerically
+        # - Shorter versions sort before longer versions when the prefixes
+        #   match exactly
+        local = tuple(
+            (i, "") if isinstance(i, int) else (-Infinity, i)
+            for i in local
+        )
+
+    return epoch, release, pre, post, dev, local

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_sparse.py

@@ -0,0 +1,41 @@
+from abc import ABC
+
+__all__ = ["SparseABC", "issparse"]
+
+
+class SparseABC(ABC):
+    pass
+
+
+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
+
+    Notes
+    -----
+    Use `isinstance(x, sp.sparse.sparray)` to check between an array or matrix.
+    Use `a.format` to check the sparse format, e.g. `a.format == 'csr'`.
+
+    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, SparseABC)

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_testutils.py

@@ -0,0 +1,373 @@
+"""
+Generic test utilities.
+
+"""
+
+import inspect
+import os
+import re
+import shutil
+import subprocess
+import sys
+import sysconfig
+import threading
+from importlib.util import module_from_spec, spec_from_file_location
+
+import numpy as np
+import scipy
+
+try:
+    # Need type: ignore[import-untyped] for mypy >= 1.6
+    import cython  # type: ignore[import-untyped]
+    from Cython.Compiler.Version import (  # type: ignore[import-untyped]
+        version as cython_version,
+    )
+except ImportError:
+    cython = None
+else:
+    from scipy._lib import _pep440
+    required_version = '3.0.8'
+    if _pep440.parse(cython_version) < _pep440.Version(required_version):
+        # too old or wrong cython, skip Cython API tests
+        cython = None
+
+
+__all__ = ['PytestTester', 'check_free_memory', '_TestPythranFunc', 'IS_MUSL']
+
+
+IS_MUSL = False
+# alternate way is
+# from packaging.tags import sys_tags
+#     _tags = list(sys_tags())
+#     if 'musllinux' in _tags[0].platform:
+_v = sysconfig.get_config_var('HOST_GNU_TYPE') or ''
+if 'musl' in _v:
+    IS_MUSL = True
+
+
+IS_EDITABLE = 'editable' in scipy.__path__[0]
+
+
+class FPUModeChangeWarning(RuntimeWarning):
+    """Warning about FPU mode change"""
+    pass
+
+
+class PytestTester:
+    """
+    Run tests for this namespace
+
+    ``scipy.test()`` runs tests for all of SciPy, with the default settings.
+    When used from a submodule (e.g., ``scipy.cluster.test()``, only the tests
+    for that namespace are run.
+
+    Parameters
+    ----------
+    label : {'fast', 'full'}, optional
+        Whether to run only the fast tests, or also those marked as slow.
+        Default is 'fast'.
+    verbose : int, optional
+        Test output verbosity. Default is 1.
+    extra_argv : list, optional
+        Arguments to pass through to Pytest.
+    doctests : bool, optional
+        Whether to run doctests or not. Default is False.
+    coverage : bool, optional
+        Whether to run tests with code coverage measurements enabled.
+        Default is False.
+    tests : list of str, optional
+        List of module names to run tests for. By default, uses the module
+        from which the ``test`` function is called.
+    parallel : int, optional
+        Run tests in parallel with pytest-xdist, if number given is larger than
+        1. Default is 1.
+
+    """
+    def __init__(self, module_name):
+        self.module_name = module_name
+
+    def __call__(self, label="fast", verbose=1, extra_argv=None, doctests=False,
+                 coverage=False, tests=None, parallel=None):
+        import pytest
+
+        module = sys.modules[self.module_name]
+        module_path = os.path.abspath(module.__path__[0])
+
+        pytest_args = ['--showlocals', '--tb=short']
+
+        if extra_argv is None:
+            extra_argv = []
+        pytest_args += extra_argv
+        if any(arg == "-m" or arg == "--markers" for arg in extra_argv):
+            # Likely conflict with default --mode=fast
+            raise ValueError("Must specify -m before --")
+
+        if verbose and int(verbose) > 1:
+            pytest_args += ["-" + "v"*(int(verbose)-1)]
+
+        if coverage:
+            pytest_args += ["--cov=" + module_path]
+
+        if label == "fast":
+            pytest_args += ["-m", "not slow"]
+        elif label != "full":
+            pytest_args += ["-m", label]
+
+        if tests is None:
+            tests = [self.module_name]
+
+        if parallel is not None and parallel > 1:
+            if _pytest_has_xdist():
+                pytest_args += ['-n', str(parallel)]
+            else:
+                import warnings
+                warnings.warn('Could not run tests in parallel because '
+                              'pytest-xdist plugin is not available.',
+                              stacklevel=2)
+
+        pytest_args += ['--pyargs'] + list(tests)
+
+        try:
+            code = pytest.main(pytest_args)
+        except SystemExit as exc:
+            code = exc.code
+
+        return (code == 0)
+
+
+class _TestPythranFunc:
+    '''
+    These are situations that can be tested in our pythran tests:
+    - A function with multiple array arguments and then
+      other positional and keyword arguments.
+    - A function with array-like keywords (e.g. `def somefunc(x0, x1=None)`.
+    Note: list/tuple input is not yet tested!
+
+    `self.arguments`: A dictionary which key is the index of the argument,
+                      value is tuple(array value, all supported dtypes)
+    `self.partialfunc`: A function used to freeze some non-array argument
+                        that of no interests in the original function
+    '''
+    ALL_INTEGER = [np.int8, np.int16, np.int32, np.int64, np.intc, np.intp]
+    ALL_FLOAT = [np.float32, np.float64]
+    ALL_COMPLEX = [np.complex64, np.complex128]
+
+    def setup_method(self):
+        self.arguments = {}
+        self.partialfunc = None
+        self.expected = None
+
+    def get_optional_args(self, func):
+        # get optional arguments with its default value,
+        # used for testing keywords
+        signature = inspect.signature(func)
+        optional_args = {}
+        for k, v in signature.parameters.items():
+            if v.default is not inspect.Parameter.empty:
+                optional_args[k] = v.default
+        return optional_args
+
+    def get_max_dtype_list_length(self):
+        # get the max supported dtypes list length in all arguments
+        max_len = 0
+        for arg_idx in self.arguments:
+            cur_len = len(self.arguments[arg_idx][1])
+            if cur_len > max_len:
+                max_len = cur_len
+        return max_len
+
+    def get_dtype(self, dtype_list, dtype_idx):
+        # get the dtype from dtype_list via index
+        # if the index is out of range, then return the last dtype
+        if dtype_idx > len(dtype_list)-1:
+            return dtype_list[-1]
+        else:
+            return dtype_list[dtype_idx]
+
+    def test_all_dtypes(self):
+        for type_idx in range(self.get_max_dtype_list_length()):
+            args_array = []
+            for arg_idx in self.arguments:
+                new_dtype = self.get_dtype(self.arguments[arg_idx][1],
+                                           type_idx)
+                args_array.append(self.arguments[arg_idx][0].astype(new_dtype))
+            self.pythranfunc(*args_array)
+
+    def test_views(self):
+        args_array = []
+        for arg_idx in self.arguments:
+            args_array.append(self.arguments[arg_idx][0][::-1][::-1])
+        self.pythranfunc(*args_array)
+
+    def test_strided(self):
+        args_array = []
+        for arg_idx in self.arguments:
+            args_array.append(np.repeat(self.arguments[arg_idx][0],
+                                        2, axis=0)[::2])
+        self.pythranfunc(*args_array)
+
+
+def _pytest_has_xdist():
+    """
+    Check if the pytest-xdist plugin is installed, providing parallel tests
+    """
+    # Check xdist exists without importing, otherwise pytests emits warnings
+    from importlib.util import find_spec
+    return find_spec('xdist') is not None
+
+
+def check_free_memory(free_mb):
+    """
+    Check *free_mb* of memory is available, otherwise do pytest.skip
+    """
+    import pytest
+
+    try:
+        mem_free = _parse_size(os.environ['SCIPY_AVAILABLE_MEM'])
+        msg = '{} MB memory required, but environment SCIPY_AVAILABLE_MEM={}'.format(
+            free_mb, os.environ['SCIPY_AVAILABLE_MEM'])
+    except KeyError:
+        mem_free = _get_mem_available()
+        if mem_free is None:
+            pytest.skip("Could not determine available memory; set SCIPY_AVAILABLE_MEM "
+                        "variable to free memory in MB to run the test.")
+        msg = f'{free_mb} MB memory required, but {mem_free/1e6} MB available'
+
+    if mem_free < free_mb * 1e6:
+        pytest.skip(msg)
+
+
+def _parse_size(size_str):
+    suffixes = {'': 1e6,
+                'b': 1.0,
+                'k': 1e3, 'M': 1e6, 'G': 1e9, 'T': 1e12,
+                'kb': 1e3, 'Mb': 1e6, 'Gb': 1e9, 'Tb': 1e12,
+                'kib': 1024.0, 'Mib': 1024.0**2, 'Gib': 1024.0**3, 'Tib': 1024.0**4}
+    m = re.match(r'^\s*(\d+)\s*({})\s*$'.format('|'.join(suffixes.keys())),
+                 size_str,
+                 re.I)
+    if not m or m.group(2) not in suffixes:
+        raise ValueError("Invalid size string")
+
+    return float(m.group(1)) * suffixes[m.group(2)]
+
+
+def _get_mem_available():
+    """
+    Get information about memory available, not counting swap.
+    """
+    try:
+        import psutil
+        return psutil.virtual_memory().available
+    except (ImportError, AttributeError):
+        pass
+
+    if sys.platform.startswith('linux'):
+        info = {}
+        with open('/proc/meminfo') as f:
+            for line in f:
+                p = line.split()
+                info[p[0].strip(':').lower()] = float(p[1]) * 1e3
+
+        if 'memavailable' in info:
+            # Linux >= 3.14
+            return info['memavailable']
+        else:
+            return info['memfree'] + info['cached']
+
+    return None
+
+def _test_cython_extension(tmp_path, srcdir):
+    """
+    Helper function to test building and importing Cython modules that
+    make use of the Cython APIs for BLAS, LAPACK, optimize, and special.
+    """
+    import pytest
+    try:
+        subprocess.check_call(["meson", "--version"])
+    except FileNotFoundError:
+        pytest.skip("No usable 'meson' found")
+
+    # Make safe for being called by multiple threads within one test
+    tmp_path = tmp_path / str(threading.get_ident())
+
+    # build the examples in a temporary directory
+    mod_name = os.path.split(srcdir)[1]
+    shutil.copytree(srcdir, tmp_path / mod_name)
+    build_dir = tmp_path / mod_name / 'tests' / '_cython_examples'
+    target_dir = build_dir / 'build'
+    os.makedirs(target_dir, exist_ok=True)
+
+    # Ensure we use the correct Python interpreter even when `meson` is
+    # installed in a different Python environment (see numpy#24956)
+    native_file = str(build_dir / 'interpreter-native-file.ini')
+    with open(native_file, 'w') as f:
+        f.write("[binaries]\n")
+        f.write(f"python = '{sys.executable}'")
+
+    if sys.platform == "win32":
+        subprocess.check_call(["meson", "setup",
+                               "--buildtype=release",
+                               "--native-file", native_file,
+                               "--vsenv", str(build_dir)],
+                              cwd=target_dir,
+                              )
+    else:
+        subprocess.check_call(["meson", "setup",
+                               "--native-file", native_file, str(build_dir)],
+                              cwd=target_dir
+                              )
+    subprocess.check_call(["meson", "compile", "-vv"], cwd=target_dir)
+
+    # import without adding the directory to sys.path
+    suffix = sysconfig.get_config_var('EXT_SUFFIX')
+
+    def load(modname):
+        so = (target_dir / modname).with_suffix(suffix)
+        spec = spec_from_file_location(modname, so)
+        mod = module_from_spec(spec)
+        spec.loader.exec_module(mod)
+        return mod
+
+    # test that the module can be imported
+    return load("extending"), load("extending_cpp")
+
+
+def _run_concurrent_barrier(n_workers, fn, *args, **kwargs):
+    """
+    Run a given function concurrently across a given number of threads.
+
+    This is equivalent to using a ThreadPoolExecutor, but using the threading
+    primitives instead. This function ensures that the closure passed by
+    parameter gets called concurrently by setting up a barrier before it gets
+    called before any of the threads.
+
+    Arguments
+    ---------
+    n_workers: int
+        Number of concurrent threads to spawn.
+    fn: callable
+        Function closure to execute concurrently. Its first argument will
+        be the thread id.
+    *args: tuple
+        Variable number of positional arguments to pass to the function.
+    **kwargs: dict
+        Keyword arguments to pass to the function.
+    """
+    barrier = threading.Barrier(n_workers)
+
+    def closure(i, *args, **kwargs):
+        barrier.wait()
+        fn(i, *args, **kwargs)
+
+    workers = []
+    for i in range(0, n_workers):
+        workers.append(threading.Thread(
+            target=closure,
+            args=(i,) + args, kwargs=kwargs))
+
+    for worker in workers:
+        worker.start()
+
+    for worker in workers:
+        worker.join()

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_threadsafety.py

@@ -0,0 +1,58 @@
+import threading
+
+import scipy._lib.decorator
+
+
+__all__ = ['ReentrancyError', 'ReentrancyLock', 'non_reentrant']
+
+
+class ReentrancyError(RuntimeError):
+    pass
+
+
+class ReentrancyLock:
+    """
+    Threading lock that raises an exception for reentrant calls.
+
+    Calls from different threads are serialized, and nested calls from the
+    same thread result to an error.
+
+    The object can be used as a context manager or to decorate functions
+    via the decorate() method.
+
+    """
+
+    def __init__(self, err_msg):
+        self._rlock = threading.RLock()
+        self._entered = False
+        self._err_msg = err_msg
+
+    def __enter__(self):
+        self._rlock.acquire()
+        if self._entered:
+            self._rlock.release()
+            raise ReentrancyError(self._err_msg)
+        self._entered = True
+
+    def __exit__(self, type, value, traceback):
+        self._entered = False
+        self._rlock.release()
+
+    def decorate(self, func):
+        def caller(func, *a, **kw):
+            with self:
+                return func(*a, **kw)
+        return scipy._lib.decorator.decorate(func, caller)
+
+
+def non_reentrant(err_msg=None):
+    """
+    Decorate a function with a threading lock and prevent reentrant calls.
+    """
+    def decorator(func):
+        msg = err_msg
+        if msg is None:
+            msg = f"{func.__name__} is not re-entrant"
+        lock = ReentrancyLock(msg)
+        return lock.decorate(func)
+    return decorator

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_tmpdirs.py

@@ -0,0 +1,86 @@
+''' Contexts for *with* statement providing temporary directories
+'''
+import os
+from contextlib import contextmanager
+from shutil import rmtree
+from tempfile import mkdtemp
+
+
+@contextmanager
+def tempdir():
+    """Create and return a temporary directory. This has the same
+    behavior as mkdtemp but can be used as a context manager.
+
+    Upon exiting the context, the directory and everything contained
+    in it are removed.
+
+    Examples
+    --------
+    >>> import os
+    >>> with tempdir() as tmpdir:
+    ...     fname = os.path.join(tmpdir, 'example_file.txt')
+    ...     with open(fname, 'wt') as fobj:
+    ...         _ = fobj.write('a string\\n')
+    >>> os.path.exists(tmpdir)
+    False
+    """
+    d = mkdtemp()
+    yield d
+    rmtree(d)
+
+
+@contextmanager
+def in_tempdir():
+    ''' Create, return, and change directory to a temporary directory
+
+    Examples
+    --------
+    >>> import os
+    >>> my_cwd = os.getcwd()
+    >>> with in_tempdir() as tmpdir:
+    ...     _ = open('test.txt', 'wt').write('some text')
+    ...     assert os.path.isfile('test.txt')
+    ...     assert os.path.isfile(os.path.join(tmpdir, 'test.txt'))
+    >>> os.path.exists(tmpdir)
+    False
+    >>> os.getcwd() == my_cwd
+    True
+    '''
+    pwd = os.getcwd()
+    d = mkdtemp()
+    os.chdir(d)
+    yield d
+    os.chdir(pwd)
+    rmtree(d)
+
+
+@contextmanager
+def in_dir(dir=None):
+    """ Change directory to given directory for duration of ``with`` block
+
+    Useful when you want to use `in_tempdir` for the final test, but
+    you are still debugging. For example, you may want to do this in the end:
+
+    >>> with in_tempdir() as tmpdir:
+    ...     # do something complicated which might break
+    ...     pass
+
+    But, indeed, the complicated thing does break, and meanwhile, the
+    ``in_tempdir`` context manager wiped out the directory with the
+    temporary files that you wanted for debugging. So, while debugging, you
+    replace with something like:
+
+    >>> with in_dir() as tmpdir: # Use working directory by default
+    ...     # do something complicated which might break
+    ...     pass
+
+    You can then look at the temporary file outputs to debug what is happening,
+    fix, and finally replace ``in_dir`` with ``in_tempdir`` again.
+    """
+    cwd = os.getcwd()
+    if dir is None:
+        yield cwd
+        return
+    os.chdir(dir)
+    yield dir
+    os.chdir(cwd)

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/_util.py

@@ -0,0 +1,1283 @@
+import re
+from contextlib import contextmanager
+import functools
+import operator
+import warnings
+import numbers
+from collections import namedtuple
+import inspect
+import math
+from types import ModuleType
+from typing import Literal, TypeAlias, TypeVar
+
+import numpy as np
+from scipy._lib._array_api import (Array, array_namespace, is_lazy_array,
+                                   is_numpy, is_marray, xp_result_device,
+                                   xp_size, xp_result_type)
+from scipy._lib._docscrape import FunctionDoc, Parameter
+from scipy._lib._sparse import issparse
+
+from numpy.exceptions import AxisError
+
+
+np_long: type
+np_ulong: type
+
+if np.lib.NumpyVersion(np.__version__) >= "2.0.0.dev0":
+    try:
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                r".*In the future `np\.long` will be defined as.*",
+                FutureWarning,
+            )
+            np_long = np.long  # type: ignore[attr-defined]
+            np_ulong = np.ulong  # type: ignore[attr-defined]
+    except AttributeError:
+            np_long = np.int_
+            np_ulong = np.uint
+else:
+    np_long = np.int_
+    np_ulong = np.uint
+
+IntNumber = int | np.integer
+DecimalNumber = float | np.floating | np.integer
+
+copy_if_needed: bool | None
+
+if np.lib.NumpyVersion(np.__version__) >= "2.0.0":
+    copy_if_needed = None
+elif np.lib.NumpyVersion(np.__version__) < "1.28.0":
+    copy_if_needed = False
+else:
+    # 2.0.0 dev versions, handle cases where copy may or may not exist
+    try:
+        np.array([1]).__array__(copy=None)  # type: ignore[call-overload]
+        copy_if_needed = None
+    except TypeError:
+        copy_if_needed = False
+
+
+_RNG: TypeAlias = np.random.Generator | np.random.RandomState
+SeedType: TypeAlias = IntNumber | _RNG | None
+
+GeneratorType = TypeVar("GeneratorType", bound=_RNG)
+
+# Since Generator was introduced in numpy 1.17, the following condition is needed for
+# backward compatibility
+try:
+    from numpy.random import Generator as Generator
+except ImportError:
+    class Generator:  # type: ignore[no-redef]
+        pass
+
+
+def _lazyselect(condlist, choicelist, arrays, default=0):
+    """
+    Mimic `np.select(condlist, choicelist)`.
+
+    Notice, it assumes that all `arrays` are of the same shape or can be
+    broadcasted together.
+
+    All functions in `choicelist` must accept array arguments in the order
+    given in `arrays` and must return an array of the same shape as broadcasted
+    `arrays`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6)
+    >>> np.select([x <3, x > 3], [x**2, x**3], default=0)
+    array([  0,   1,   4,   0,  64, 125])
+
+    >>> _lazyselect([x < 3, x > 3], [lambda x: x**2, lambda x: x**3], (x,))
+    array([   0.,    1.,    4.,   0.,   64.,  125.])
+
+    >>> a = -np.ones_like(x)
+    >>> _lazyselect([x < 3, x > 3],
+    ...             [lambda x, a: x**2, lambda x, a: a * x**3],
+    ...             (x, a), default=np.nan)
+    array([   0.,    1.,    4.,   nan,  -64., -125.])
+
+    """
+    arrays = np.broadcast_arrays(*arrays)
+    tcode = np.mintypecode([a.dtype.char for a in arrays])
+    out = np.full(np.shape(arrays[0]), fill_value=default, dtype=tcode)
+    for func, cond in zip(choicelist, condlist):
+        if np.all(cond is False):
+            continue
+        cond, _ = np.broadcast_arrays(cond, arrays[0])
+        temp = tuple(np.extract(cond, arr) for arr in arrays)
+        np.place(out, cond, func(*temp))
+    return out
+
+
+def _aligned_zeros(shape, dtype=float, order="C", align=None):
+    """Allocate a new ndarray with aligned memory.
+
+    Primary use case for this currently is working around a f2py issue
+    in NumPy 1.9.1, where dtype.alignment is such that np.zeros() does
+    not necessarily create arrays aligned up to it.
+
+    """
+    dtype = np.dtype(dtype)
+    if align is None:
+        align = dtype.alignment
+    if not hasattr(shape, '__len__'):
+        shape = (shape,)
+    size = functools.reduce(operator.mul, shape) * dtype.itemsize
+    buf = np.empty(size + align + 1, np.uint8)
+    offset = buf.__array_interface__['data'][0] % align
+    if offset != 0:
+        offset = align - offset
+    # Note: slices producing 0-size arrays do not necessarily change
+    # data pointer --- so we use and allocate size+1
+    buf = buf[offset:offset+size+1][:-1]
+    data = np.ndarray(shape, dtype, buf, order=order)
+    data.fill(0)
+    return data
+
+
+def _prune_array(array):
+    """Return an array equivalent to the input array. If the input
+    array is a view of a much larger array, copy its contents to a
+    newly allocated array. Otherwise, return the input unchanged.
+    """
+    if array.base is not None and array.size < array.base.size // 2:
+        return array.copy()
+    return array
+
+
+def float_factorial(n: int) -> float:
+    """Compute the factorial and return as a float
+
+    Returns infinity when result is too large for a double
+    """
+    return float(math.factorial(n)) if n < 171 else np.inf
+
+
+_rng_desc = (
+    r"""If `rng` is passed by keyword, types other than `numpy.random.Generator` are
+    passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    If `rng` is already a ``Generator`` instance, then the provided instance is
+    used. Specify `rng` for repeatable function behavior.
+
+    If this argument is passed by position or `{old_name}` is passed by keyword,
+    legacy behavior for the argument `{old_name}` applies:
+
+    - If `{old_name}` is None (or `numpy.random`), the `numpy.random.RandomState`
+      singleton is used.
+    - If `{old_name}` is an int, a new ``RandomState`` instance is used,
+      seeded with `{old_name}`.
+    - If `{old_name}` is already a ``Generator`` or ``RandomState`` instance then
+      that instance is used.
+
+    .. versionchanged:: 1.15.0
+        As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+        transition from use of `numpy.random.RandomState` to
+        `numpy.random.Generator`, this keyword was changed from `{old_name}` to `rng`.
+        For an interim period, both keywords will continue to work, although only one
+        may be specified at a time. After the interim period, function calls using the
+        `{old_name}` keyword will emit warnings. The behavior of both `{old_name}` and
+        `rng` are outlined above, but only the `rng` keyword should be used in new code.
+        """
+)
+
+
+# SPEC 7
+def _transition_to_rng(old_name, *, position_num=None, end_version=None,
+                       replace_doc=True):
+    """Example decorator to transition from old PRNG usage to new `rng` behavior
+
+    Suppose the decorator is applied to a function that used to accept parameter
+    `old_name='random_state'` either by keyword or as a positional argument at
+    `position_num=1`. At the time of application, the name of the argument in the
+    function signature is manually changed to the new name, `rng`. If positional
+    use was allowed before, this is not changed.*
+
+    - If the function is called with both `random_state` and `rng`, the decorator
+      raises an error.
+    - If `random_state` is provided as a keyword argument, the decorator passes
+      `random_state` to the function's `rng` argument as a keyword. If `end_version`
+      is specified, the decorator will emit a `DeprecationWarning` about the
+      deprecation of keyword `random_state`.
+    - If `random_state` is provided as a positional argument, the decorator passes
+      `random_state` to the function's `rng` argument by position. If `end_version`
+      is specified, the decorator will emit a `FutureWarning` about the changing
+      interpretation of the argument.
+    - If `rng` is provided as a keyword argument, the decorator validates `rng` using
+      `numpy.random.default_rng` before passing it to the function.
+    - If `end_version` is specified and neither `random_state` nor `rng` is provided
+      by the user, the decorator checks whether `np.random.seed` has been used to set
+      the global seed. If so, it emits a `FutureWarning`, noting that usage of
+      `numpy.random.seed` will eventually have no effect. Either way, the decorator
+      calls the function without explicitly passing the `rng` argument.
+
+    If `end_version` is specified, a user must pass `rng` as a keyword to avoid
+    warnings.
+
+    After the deprecation period, the decorator can be removed, and the function
+    can simply validate the `rng` argument by calling `np.random.default_rng(rng)`.
+
+    * A `FutureWarning` is emitted when the PRNG argument is used by
+      position. It indicates that the "Hinsen principle" (same
+      code yielding different results in two versions of the software)
+      will be violated, unless positional use is deprecated. Specifically:
+
+      - If `None` is passed by position and `np.random.seed` has been used,
+        the function will change from being seeded to being unseeded.
+      - If an integer is passed by position, the random stream will change.
+      - If `np.random` or an instance of `RandomState` is passed by position,
+        an error will be raised.
+
+      We suggest that projects consider deprecating positional use of
+      `random_state`/`rng` (i.e., change their function signatures to
+      ``def my_func(..., *, rng=None)``); that might not make sense
+      for all projects, so this SPEC does not make that
+      recommendation, neither does this decorator enforce it.
+
+    Parameters
+    ----------
+    old_name : str
+        The old name of the PRNG argument (e.g. `seed` or `random_state`).
+    position_num : int, optional
+        The (0-indexed) position of the old PRNG argument (if accepted by position).
+        Maintainers are welcome to eliminate this argument and use, for example,
+        `inspect`, if preferred.
+    end_version : str, optional
+        The full version number of the library when the behavior described in
+        `DeprecationWarning`s and `FutureWarning`s will take effect. If left
+        unspecified, no warnings will be emitted by the decorator.
+    replace_doc : bool, default: True
+        Whether the decorator should replace the documentation for parameter `rng` with
+        `_rng_desc` (defined above), which documents both new `rng` keyword behavior
+        and typical legacy `random_state`/`seed` behavior. If True, manually replace
+        the first paragraph of the function's old `random_state`/`seed` documentation
+        with the desired *final* `rng` documentation; this way, no changes to
+        documentation are needed when the decorator is removed. Documentation of `rng`
+        after the first blank line is preserved. Use False if the function's old
+        `random_state`/`seed` behavior does not match that described by `_rng_desc`.
+
+    """
+    NEW_NAME = "rng"
+
+    cmn_msg = (
+        "To silence this warning and ensure consistent behavior in SciPy "
+        f"{end_version}, control the RNG using argument `{NEW_NAME}`. Arguments passed "
+        f"to keyword `{NEW_NAME}` will be validated by `np.random.default_rng`, so the "
+        "behavior corresponding with a given value may change compared to use of "
+        f"`{old_name}`. For example, "
+        "1) `None` will result in unpredictable random numbers, "
+        "2) an integer will result in a different stream of random numbers, (with the "
+        "same distribution), and "
+        "3) `np.random` or `RandomState` instances will result in an error. "
+        "See the documentation of `default_rng` for more information."
+    )
+
+    def decorator(fun):
+        @functools.wraps(fun)
+        def wrapper(*args, **kwargs):
+            # Determine how PRNG was passed
+            as_old_kwarg = old_name in kwargs
+            as_new_kwarg = NEW_NAME in kwargs
+            as_pos_arg = position_num is not None and len(args) >= position_num + 1
+            emit_warning = end_version is not None
+
+            # Can only specify PRNG one of the three ways
+            if int(as_old_kwarg) + int(as_new_kwarg) + int(as_pos_arg) > 1:
+                message = (
+                    f"{fun.__name__}() got multiple values for "
+                    f"argument now known as `{NEW_NAME}`. Specify one of "
+                    f"`{NEW_NAME}` or `{old_name}`."
+                )
+                raise TypeError(message)
+
+            # Check whether global random state has been set
+            global_seed_set = np.random.mtrand._rand._bit_generator._seed_seq is None
+
+            if as_old_kwarg:  # warn about deprecated use of old kwarg
+                kwargs[NEW_NAME] = kwargs.pop(old_name)
+                if emit_warning:
+                    message = (
+                        f"Use of keyword argument `{old_name}` is "
+                        f"deprecated and replaced by `{NEW_NAME}`.  "
+                        f"Support for `{old_name}` will be removed "
+                        f"in SciPy {end_version}. "
+                    ) + cmn_msg
+                    warnings.warn(message, DeprecationWarning, stacklevel=2)
+
+            elif as_pos_arg:
+                # Warn about changing meaning of positional arg
+
+                # Note that this decorator does not deprecate positional use of the
+                # argument; it only warns that the behavior will change in the future.
+                # Simultaneously transitioning to keyword-only use is another option.
+
+                arg = args[position_num]
+                # If the argument is None and the global seed wasn't set, or if the
+                # argument is one of a few new classes, the user will not notice change
+                # in behavior.
+                ok_classes = (
+                    np.random.Generator,
+                    np.random.SeedSequence,
+                    np.random.BitGenerator,
+                )
+                if (arg is None and not global_seed_set) or isinstance(arg, ok_classes):
+                    pass
+                elif emit_warning:
+                    message = (
+                        f"Positional use of `{NEW_NAME}` (formerly known as "
+                        f"`{old_name}`) is still allowed, but the behavior is "
+                        "changing: the argument will be normalized using "
+                        f"`np.random.default_rng` beginning in SciPy {end_version}, "
+                        "and the resulting `Generator` will be used to generate "
+                        "random numbers."
+                    ) + cmn_msg
+                    warnings.warn(message, FutureWarning, stacklevel=2)
+
+            elif as_new_kwarg:  # no warnings; this is the preferred use
+                # After the removal of the decorator, normalization with
+                # np.random.default_rng will be done inside the decorated function
+                kwargs[NEW_NAME] = np.random.default_rng(kwargs[NEW_NAME])
+
+            elif global_seed_set and emit_warning:
+                # Emit FutureWarning if `np.random.seed` was used and no PRNG was passed
+                message = (
+                    "The NumPy global RNG was seeded by calling "
+                    f"`np.random.seed`. Beginning in {end_version}, this "
+                    "function will no longer use the global RNG."
+                ) + cmn_msg
+                warnings.warn(message, FutureWarning, stacklevel=2)
+
+            return fun(*args, **kwargs)
+
+        # Add the old parameter name to the function signature
+        wrapped_signature = inspect.signature(fun)
+        wrapper.__signature__ = wrapped_signature.replace(parameters=[
+            *wrapped_signature.parameters.values(),
+            inspect.Parameter(old_name, inspect.Parameter.KEYWORD_ONLY, default=None),
+        ])
+
+        if replace_doc:
+            doc = FunctionDoc(wrapper)
+            parameter_names = [param.name for param in doc['Parameters']]
+            if 'rng' in parameter_names:
+                _type = "{None, int, `numpy.random.Generator`}, optional"
+                _desc = _rng_desc.replace("{old_name}", old_name)
+                old_doc = doc['Parameters'][parameter_names.index('rng')].desc
+                old_doc_keep = old_doc[old_doc.index("") + 1:] if "" in old_doc else []
+                new_doc = [_desc] + old_doc_keep
+                _rng_parameter_doc = Parameter('rng', _type, new_doc)
+                doc['Parameters'][parameter_names.index('rng')] = _rng_parameter_doc
+                doc = str(doc).split("\n", 1)[1]  # remove signature
+                wrapper.__doc__ = str(doc)
+        return wrapper
+
+    return decorator
+
+
+# copy-pasted from scikit-learn utils/validation.py
+def check_random_state(seed):
+    """Turn `seed` into a `np.random.RandomState` instance.
+
+    Parameters
+    ----------
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    seed : {`numpy.random.Generator`, `numpy.random.RandomState`}
+        Random number generator.
+
+    """
+    if seed is None or seed is np.random:
+        return np.random.mtrand._rand
+    if isinstance(seed, numbers.Integral | np.integer):
+        return np.random.RandomState(seed)
+    if isinstance(seed, np.random.RandomState | np.random.Generator):
+        return seed
+
+    raise ValueError(f"'{seed}' cannot be used to seed a numpy.random.RandomState"
+                     " instance")
+
+
+def _asarray_validated(a, check_finite=True,
+                       sparse_ok=False, objects_ok=False, mask_ok=False,
+                       as_inexact=False):
+    """
+    Helper function for SciPy argument validation.
+
+    Many SciPy linear algebra functions do support arbitrary array-like
+    input arguments. Examples of commonly unsupported inputs include
+    matrices containing inf/nan, sparse matrix representations, and
+    matrices with complicated elements.
+
+    Parameters
+    ----------
+    a : array_like
+        The array-like input.
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+    sparse_ok : bool, optional
+        True if scipy sparse matrices are allowed.
+    objects_ok : bool, optional
+        True if arrays with dype('O') are allowed.
+    mask_ok : bool, optional
+        True if masked arrays are allowed.
+    as_inexact : bool, optional
+        True to convert the input array to a np.inexact dtype.
+
+    Returns
+    -------
+    ret : ndarray
+        The converted validated array.
+
+    """
+    if not sparse_ok:
+        if issparse(a):
+            msg = ('Sparse arrays/matrices are not supported by this function. '
+                   'Perhaps one of the `scipy.sparse.linalg` functions '
+                   'would work instead.')
+            raise ValueError(msg)
+    if not mask_ok:
+        if np.ma.isMaskedArray(a):
+            raise ValueError('masked arrays are not supported')
+    toarray = np.asarray_chkfinite if check_finite else np.asarray
+    a = toarray(a)
+    if not objects_ok:
+        if a.dtype is np.dtype('O'):
+            raise ValueError('object arrays are not supported')
+    if as_inexact:
+        if not np.issubdtype(a.dtype, np.inexact):
+            a = toarray(a, dtype=np.float64)
+    return a
+
+
+def _validate_int(k, name, minimum=None):
+    """
+    Validate a scalar integer.
+
+    This function can be used to validate an argument to a function
+    that expects the value to be an integer.  It uses `operator.index`
+    to validate the value (so, for example, k=2.0 results in a
+    TypeError).
+
+    Parameters
+    ----------
+    k : int
+        The value to be validated.
+    name : str
+        The name of the parameter.
+    minimum : int, optional
+        An optional lower bound.
+    """
+    try:
+        k = operator.index(k)
+    except TypeError:
+        raise TypeError(f'{name} must be an integer.') from None
+    if minimum is not None and k < minimum:
+        raise ValueError(f'{name} must be an integer not less '
+                         f'than {minimum}') from None
+    return k
+
+
+# Add a replacement for inspect.getfullargspec()/
+# The version below is borrowed from Django,
+# https://github.com/django/django/pull/4846.
+
+# Note an inconsistency between inspect.getfullargspec(func) and
+# inspect.signature(func). If `func` is a bound method, the latter does *not*
+# list `self` as a first argument, while the former *does*.
+# Hence, cook up a common ground replacement: `getfullargspec_no_self` which
+# mimics `inspect.getfullargspec` but does not list `self`.
+#
+# This way, the caller code does not need to know whether it uses a legacy
+# .getfullargspec or a bright and shiny .signature.
+
+FullArgSpec = namedtuple('FullArgSpec',
+                         ['args', 'varargs', 'varkw', 'defaults',
+                          'kwonlyargs', 'kwonlydefaults', 'annotations'])
+
+
+def getfullargspec_no_self(func):
+    """inspect.getfullargspec replacement using inspect.signature.
+
+    If func is a bound method, do not list the 'self' parameter.
+
+    Parameters
+    ----------
+    func : callable
+        A callable to inspect
+
+    Returns
+    -------
+    fullargspec : FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
+                              kwonlydefaults, annotations)
+
+        NOTE: if the first argument of `func` is self, it is *not*, I repeat
+        *not*, included in fullargspec.args.
+        This is done for consistency between inspect.getargspec() under
+        Python 2.x, and inspect.signature() under Python 3.x.
+
+    """
+    sig = inspect.signature(func)
+    args = [
+        p.name for p in sig.parameters.values()
+        if p.kind in [inspect.Parameter.POSITIONAL_OR_KEYWORD,
+                      inspect.Parameter.POSITIONAL_ONLY]
+    ]
+    varargs = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.VAR_POSITIONAL
+    ]
+    varargs = varargs[0] if varargs else None
+    varkw = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.VAR_KEYWORD
+    ]
+    varkw = varkw[0] if varkw else None
+    defaults = tuple(
+        p.default for p in sig.parameters.values()
+        if (p.kind == inspect.Parameter.POSITIONAL_OR_KEYWORD and
+            p.default is not p.empty)
+    ) or None
+    kwonlyargs = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.KEYWORD_ONLY
+    ]
+    kwdefaults = {p.name: p.default for p in sig.parameters.values()
+                  if p.kind == inspect.Parameter.KEYWORD_ONLY and
+                  p.default is not p.empty}
+    annotations = {p.name: p.annotation for p in sig.parameters.values()
+                   if p.annotation is not p.empty}
+    return FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
+                       kwdefaults or None, annotations)
+
+
+class _FunctionWrapper:
+    """
+    Object to wrap user's function, allowing picklability
+    """
+    def __init__(self, f, args):
+        self.f = f
+        self.args = [] if args is None else args
+
+    def __call__(self, x):
+        return self.f(x, *self.args)
+
+
+class _ScalarFunctionWrapper:
+    """
+    Object to wrap scalar user function, allowing picklability
+    """
+    def __init__(self, f, args=None):
+        self.f = f
+        self.args = [] if args is None else args
+        self.nfev = 0
+
+    def __call__(self, x):
+        # Send a copy because the user may overwrite it.
+        # The user of this class might want `x` to remain unchanged.
+        fx = self.f(np.copy(x), *self.args)
+        self.nfev += 1
+
+        # Make sure the function returns a true scalar
+        if not np.isscalar(fx):
+            try:
+                fx = np.asarray(fx).item()
+            except (TypeError, ValueError) as e:
+                raise ValueError(
+                    "The user-provided objective function "
+                    "must return a scalar value."
+                ) from e
+        return fx
+
+class MapWrapper:
+    """
+    Parallelisation wrapper for working with map-like callables, such as
+    `multiprocessing.Pool.map`.
+
+    Parameters
+    ----------
+    pool : int or map-like callable
+        If `pool` is an integer, then it specifies the number of threads to
+        use for parallelization. If ``int(pool) == 1``, then no parallel
+        processing is used and the map builtin is used.
+        If ``pool == -1``, then the pool will utilize all available CPUs.
+        If `pool` is a map-like callable that follows the same
+        calling sequence as the built-in map function, then this callable is
+        used for parallelization.
+    """
+    def __init__(self, pool=1):
+        self.pool = None
+        self._mapfunc = map
+        self._own_pool = False
+
+        if callable(pool):
+            self.pool = pool
+            self._mapfunc = self.pool
+        else:
+            from multiprocessing import Pool
+            # user supplies a number
+            if int(pool) == -1:
+                # use as many processors as possible
+                self.pool = Pool()
+                self._mapfunc = self.pool.map
+                self._own_pool = True
+            elif int(pool) == 1:
+                pass
+            elif int(pool) > 1:
+                # use the number of processors requested
+                self.pool = Pool(processes=int(pool))
+                self._mapfunc = self.pool.map
+                self._own_pool = True
+            else:
+                raise RuntimeError("Number of workers specified must be -1,"
+                                   " an int >= 1, or an object with a 'map' "
+                                   "method")
+
+    def __enter__(self):
+        return self
+
+    def terminate(self):
+        if self._own_pool:
+            self.pool.terminate()
+
+    def join(self):
+        if self._own_pool:
+            self.pool.join()
+
+    def close(self):
+        if self._own_pool:
+            self.pool.close()
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        if self._own_pool:
+            self.pool.close()
+            self.pool.terminate()
+
+    def __call__(self, func, iterable):
+        # only accept one iterable because that's all Pool.map accepts
+        try:
+            return self._mapfunc(func, iterable)
+        except TypeError as e:
+            # wrong number of arguments
+            raise TypeError("The map-like callable must be of the"
+                            " form f(func, iterable)") from e
+
+
+def _workers_wrapper(func):
+    """
+    Wrapper to deal with setup-cleanup of workers outside a user function via a
+    ContextManager. It saves having to do the setup/tear down with within that
+    function, which can be messy.
+    """
+    @functools.wraps(func)
+    def inner(*args, **kwds):
+        kwargs = kwds.copy()
+        if 'workers' not in kwargs:
+            _workers = map
+        elif 'workers' in kwargs and kwargs['workers'] is None:
+            _workers = map
+        else:
+            _workers = kwargs['workers']
+
+        with MapWrapper(_workers) as mf:
+            kwargs['workers'] = mf
+            return func(*args, **kwargs)
+
+    return inner
+
+
+def rng_integers(gen, low, high=None, size=None, dtype='int64',
+                 endpoint=False):
+    """
+    Return random integers from low (inclusive) to high (exclusive), or if
+    endpoint=True, low (inclusive) to high (inclusive). Replaces
+    `RandomState.randint` (with endpoint=False) and
+    `RandomState.random_integers` (with endpoint=True).
+
+    Return random integers from the "discrete uniform" distribution of the
+    specified dtype. If high is None (the default), then results are from
+    0 to low.
+
+    Parameters
+    ----------
+    gen : {None, np.random.RandomState, np.random.Generator}
+        Random number generator. If None, then the np.random.RandomState
+        singleton is used.
+    low : int or array-like of ints
+        Lowest (signed) integers to be drawn from the distribution (unless
+        high=None, in which case this parameter is 0 and this value is used
+        for high).
+    high : int or array-like of ints
+        If provided, one above the largest (signed) integer to be drawn from
+        the distribution (see above for behavior if high=None). If array-like,
+        must contain integer values.
+    size : array-like of ints, optional
+        Output shape. If the given shape is, e.g., (m, n, k), then m * n * k
+        samples are drawn. Default is None, in which case a single value is
+        returned.
+    dtype : {str, dtype}, optional
+        Desired dtype of the result. All dtypes are determined by their name,
+        i.e., 'int64', 'int', etc, so byteorder is not available and a specific
+        precision may have different C types depending on the platform.
+        The default value is 'int64'.
+    endpoint : bool, optional
+        If True, sample from the interval [low, high] instead of the default
+        [low, high) Defaults to False.
+
+    Returns
+    -------
+    out: int or ndarray of ints
+        size-shaped array of random integers from the appropriate distribution,
+        or a single such random int if size not provided.
+    """
+    if isinstance(gen, Generator):
+        return gen.integers(low, high=high, size=size, dtype=dtype,
+                            endpoint=endpoint)
+    else:
+        if gen is None:
+            # default is RandomState singleton used by np.random.
+            gen = np.random.mtrand._rand
+        if endpoint:
+            # inclusive of endpoint
+            # remember that low and high can be arrays, so don't modify in
+            # place
+            if high is None:
+                return gen.randint(low + 1, size=size, dtype=dtype)
+            if high is not None:
+                return gen.randint(low, high=high + 1, size=size, dtype=dtype)
+
+        # exclusive
+        return gen.randint(low, high=high, size=size, dtype=dtype)
+
+
+@contextmanager
+def _fixed_default_rng(seed=1638083107694713882823079058616272161):
+    """Context with a fixed np.random.default_rng seed."""
+    orig_fun = np.random.default_rng
+    np.random.default_rng = lambda seed=seed: orig_fun(seed)
+    try:
+        yield
+    finally:
+        np.random.default_rng = orig_fun
+
+
+def _rng_html_rewrite(func):
+    """Rewrite the HTML rendering of ``np.random.default_rng``.
+
+    This is intended to decorate
+    ``numpydoc.docscrape_sphinx.SphinxDocString._str_examples``.
+
+    Examples are only run by Sphinx when there are plot involved. Even so,
+    it does not change the result values getting printed.
+    """
+    # hexadecimal or number seed, case-insensitive
+    pattern = re.compile(r'np.random.default_rng\((0x[0-9A-F]+|\d+)\)', re.I)
+
+    def _wrapped(*args, **kwargs):
+        res = func(*args, **kwargs)
+        lines = [
+            re.sub(pattern, 'np.random.default_rng()', line)
+            for line in res
+        ]
+        return lines
+
+    return _wrapped
+
+
+def _argmin(a, keepdims=False, axis=None):
+    """
+    argmin with a `keepdims` parameter.
+
+    See https://github.com/numpy/numpy/issues/8710
+
+    If axis is not None, a.shape[axis] must be greater than 0.
+    """
+    res = np.argmin(a, axis=axis)
+    if keepdims and axis is not None:
+        res = np.expand_dims(res, axis=axis)
+    return res
+
+
+def _first_nonnan(a, axis):
+    """
+    Return the first non-nan value along the given axis.
+
+    If a slice is all nan, nan is returned for that slice.
+
+    The shape of the return value corresponds to ``keepdims=True``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> nan = np.nan
+    >>> a = np.array([[ 3.,  3., nan,  3.],
+                      [ 1., nan,  2.,  4.],
+                      [nan, nan,  9., -1.],
+                      [nan,  5.,  4.,  3.],
+                      [ 2.,  2.,  2.,  2.],
+                      [nan, nan, nan, nan]])
+    >>> _first_nonnan(a, axis=0)
+    array([[3., 3., 2., 3.]])
+    >>> _first_nonnan(a, axis=1)
+    array([[ 3.],
+           [ 1.],
+           [ 9.],
+           [ 5.],
+           [ 2.],
+           [nan]])
+    """
+    k = _argmin(np.isnan(a), axis=axis, keepdims=True)
+    return np.take_along_axis(a, k, axis=axis)
+
+
+def _nan_allsame(a, axis, keepdims=False):
+    """
+    Determine if the values along an axis are all the same.
+
+    nan values are ignored.
+
+    `a` must be a numpy array.
+
+    `axis` is assumed to be normalized; that is, 0 <= axis < a.ndim.
+
+    For an axis of length 0, the result is True.  That is, we adopt the
+    convention that ``allsame([])`` is True. (There are no values in the
+    input that are different.)
+
+    `True` is returned for slices that are all nan--not because all the
+    values are the same, but because this is equivalent to ``allsame([])``.
+
+    Examples
+    --------
+    >>> from numpy import nan, array
+    >>> a = array([[ 3.,  3., nan,  3.],
+    ...            [ 1., nan,  2.,  4.],
+    ...            [nan, nan,  9., -1.],
+    ...            [nan,  5.,  4.,  3.],
+    ...            [ 2.,  2.,  2.,  2.],
+    ...            [nan, nan, nan, nan]])
+    >>> _nan_allsame(a, axis=1, keepdims=True)
+    array([[ True],
+           [False],
+           [False],
+           [False],
+           [ True],
+           [ True]])
+    """
+    if axis is None:
+        if a.size == 0:
+            return True
+        a = a.ravel()
+        axis = 0
+    else:
+        shp = a.shape
+        if shp[axis] == 0:
+            shp = shp[:axis] + (1,)*keepdims + shp[axis + 1:]
+            return np.full(shp, fill_value=True, dtype=bool)
+    a0 = _first_nonnan(a, axis=axis)
+    return ((a0 == a) | np.isnan(a)).all(axis=axis, keepdims=keepdims)
+
+
+def _contains_nan(
+    a: Array,
+    nan_policy: Literal["propagate", "raise", "omit"] = "propagate",
+    *,
+    xp_omit_okay: bool = False, 
+    xp: ModuleType | None = None,
+) -> Array | bool:
+    # Regarding `xp_omit_okay`: Temporarily, while `_axis_nan_policy` does not
+    # handle non-NumPy arrays, most functions that call `_contains_nan` want
+    # it to raise an error if `nan_policy='omit'` and `xp` is not `np`.
+    # Some functions support `nan_policy='omit'` natively, so setting this to
+    # `True` prevents the error from being raised.
+    policies = {"propagate", "raise", "omit"}
+    if nan_policy not in policies:
+        msg = f"nan_policy must be one of {policies}."
+        raise ValueError(msg)
+
+    if xp_size(a) == 0:
+        return False
+
+    if xp is None:
+        xp = array_namespace(a)
+
+    if xp.isdtype(a.dtype, "real floating"):
+        # Faster and less memory-intensive than xp.any(xp.isnan(a)), and unlike other
+        # reductions, `max`/`min` won't return NaN unless there is a NaN in the data.
+        contains_nan = xp.isnan(xp.max(a))
+    elif xp.isdtype(a.dtype, "complex floating"):
+        # Typically `real` and `imag` produce views; otherwise, `xp.any(xp.isnan(a))`
+        # would be more efficient.
+        contains_nan = xp.isnan(xp.max(xp.real(a))) | xp.isnan(xp.max(xp.imag(a)))
+    elif is_numpy(xp) and np.issubdtype(a.dtype, object):
+        contains_nan = False
+        for el in a.ravel():
+            # isnan doesn't work on non-numeric elements
+            if np.issubdtype(type(el), np.number) and np.isnan(el):
+                contains_nan = True
+                break
+    else:
+        # Only `object` and `inexact` arrays can have NaNs
+        return False
+
+    # The implicit call to bool(contains_nan) must happen after testing
+    # nan_policy to prevent lazy and device-bound xps from raising in the
+    # default policy='propagate' case.
+    if nan_policy == 'raise':
+        if is_lazy_array(a):
+            msg = "nan_policy='raise' is not supported for lazy arrays."
+            raise TypeError(msg)
+        if contains_nan:
+            msg = "The input contains nan values"
+            raise ValueError(msg)
+    elif nan_policy == 'omit' and not xp_omit_okay and not is_numpy(xp):
+        if is_lazy_array(a):
+            msg = "nan_policy='omit' is not supported for lazy arrays."
+            raise TypeError(msg)
+        if contains_nan:
+            msg = "nan_policy='omit' is incompatible with non-NumPy arrays."
+            raise ValueError(msg)
+
+    return contains_nan
+
+
+def _rename_parameter(old_name, new_name, dep_version=None):
+    """
+    Generate decorator for backward-compatible keyword renaming.
+
+    Apply the decorator generated by `_rename_parameter` to functions with a
+    recently renamed parameter to maintain backward-compatibility.
+
+    After decoration, the function behaves as follows:
+    If only the new parameter is passed into the function, behave as usual.
+    If only the old parameter is passed into the function (as a keyword), raise
+    a DeprecationWarning if `dep_version` is provided, and behave as usual
+    otherwise.
+    If both old and new parameters are passed into the function, raise a
+    DeprecationWarning if `dep_version` is provided, and raise the appropriate
+    TypeError (function got multiple values for argument).
+
+    Parameters
+    ----------
+    old_name : str
+        Old name of parameter
+    new_name : str
+        New name of parameter
+    dep_version : str, optional
+        Version of SciPy in which old parameter was deprecated in the format
+        'X.Y.Z'. If supplied, the deprecation message will indicate that
+        support for the old parameter will be removed in version 'X.Y+2.Z'
+
+    Notes
+    -----
+    Untested with functions that accept *args. Probably won't work as written.
+
+    """
+    def decorator(fun):
+        @functools.wraps(fun)
+        def wrapper(*args, **kwargs):
+            if old_name in kwargs:
+                if dep_version:
+                    end_version = dep_version.split('.')
+                    end_version[1] = str(int(end_version[1]) + 2)
+                    end_version = '.'.join(end_version)
+                    message = (f"Use of keyword argument `{old_name}` is "
+                               f"deprecated and replaced by `{new_name}`.  "
+                               f"Support for `{old_name}` will be removed "
+                               f"in SciPy {end_version}.")
+                    warnings.warn(message, DeprecationWarning, stacklevel=2)
+                if new_name in kwargs:
+                    message = (f"{fun.__name__}() got multiple values for "
+                               f"argument now known as `{new_name}`")
+                    raise TypeError(message)
+                kwargs[new_name] = kwargs.pop(old_name)
+            return fun(*args, **kwargs)
+        return wrapper
+    return decorator
+
+
+def _rng_spawn(rng, n_children):
+    # spawns independent RNGs from a parent RNG
+    bg = rng._bit_generator
+    ss = bg._seed_seq
+    child_rngs = [np.random.Generator(type(bg)(child_ss))
+                  for child_ss in ss.spawn(n_children)]
+    return child_rngs
+
+
+def _get_nan(*data, shape=(), xp=None):
+    xp = array_namespace(*data) if xp is None else xp
+    # Get NaN of appropriate dtype for data
+    dtype = xp_result_type(*data, force_floating=True, xp=xp)
+    device = xp_result_device(*data)
+    res = xp.full(shape, xp.nan, dtype=dtype, device=device)
+    if not shape:
+        res = res[()]
+    # whenever mdhaber/marray#89 is resolved, could just return `res`
+    return res.data if is_marray(xp) else res
+
+
+def normalize_axis_index(axis, ndim):
+    # Check if `axis` is in the correct range and normalize it
+    if axis < -ndim or axis >= ndim:
+        msg = f"axis {axis} is out of bounds for array of dimension {ndim}"
+        raise AxisError(msg)
+
+    if axis < 0:
+        axis = axis + ndim
+    return axis
+
+
+def _call_callback_maybe_halt(callback, res):
+    """Call wrapped callback; return True if algorithm should stop.
+
+    Parameters
+    ----------
+    callback : callable or None
+        A user-provided callback wrapped with `_wrap_callback`
+    res : OptimizeResult
+        Information about the current iterate
+
+    Returns
+    -------
+    halt : bool
+        True if minimization should stop
+
+    """
+    if callback is None:
+        return False
+    try:
+        callback(res)
+        return False
+    except StopIteration:
+        callback.stop_iteration = True
+        return True
+
+
+class _RichResult(dict):
+    """ Container for multiple outputs with pretty-printing """
+    def __getattr__(self, name):
+        try:
+            return self[name]
+        except KeyError as e:
+            raise AttributeError(name) from e
+
+    __setattr__ = dict.__setitem__  # type: ignore[assignment]
+    __delattr__ = dict.__delitem__  # type: ignore[assignment]
+
+    def __repr__(self):
+        order_keys = ['message', 'success', 'status', 'fun', 'funl', 'x', 'xl',
+                      'col_ind', 'nit', 'lower', 'upper', 'eqlin', 'ineqlin',
+                      'converged', 'flag', 'function_calls', 'iterations',
+                      'root']
+        order_keys = getattr(self, '_order_keys', order_keys)
+        # 'slack', 'con' are redundant with residuals
+        # 'crossover_nit' is probably not interesting to most users
+        omit_keys = {'slack', 'con', 'crossover_nit', '_order_keys'}
+
+        def key(item):
+            try:
+                return order_keys.index(item[0].lower())
+            except ValueError:  # item not in list
+                return np.inf
+
+        def omit_redundant(items):
+            for item in items:
+                if item[0] in omit_keys:
+                    continue
+                yield item
+
+        def item_sorter(d):
+            return sorted(omit_redundant(d.items()), key=key)
+
+        if self.keys():
+            return _dict_formatter(self, sorter=item_sorter)
+        else:
+            return self.__class__.__name__ + "()"
+
+    def __dir__(self):
+        return list(self.keys())
+
+
+def _indenter(s, n=0):
+    """
+    Ensures that lines after the first are indented by the specified amount
+    """
+    split = s.split("\n")
+    indent = " "*n
+    return ("\n" + indent).join(split)
+
+
+def _float_formatter_10(x):
+    """
+    Returns a string representation of a float with exactly ten characters
+    """
+    if np.isposinf(x):
+        return "       inf"
+    elif np.isneginf(x):
+        return "      -inf"
+    elif np.isnan(x):
+        return "       nan"
+    return np.format_float_scientific(x, precision=3, pad_left=2, unique=False)
+
+
+def _dict_formatter(d, n=0, mplus=1, sorter=None):
+    """
+    Pretty printer for dictionaries
+
+    `n` keeps track of the starting indentation;
+    lines are indented by this much after a line break.
+    `mplus` is additional left padding applied to keys
+    """
+    if isinstance(d, dict):
+        m = max(map(len, list(d.keys()))) + mplus  # width to print keys
+        s = '\n'.join([k.rjust(m) + ': ' +  # right justified, width m
+                       _indenter(_dict_formatter(v, m+n+2, 0, sorter), m+2)
+                       for k, v in sorter(d)])  # +2 for ': '
+    else:
+        # By default, NumPy arrays print with linewidth=76. `n` is
+        # the indent at which a line begins printing, so it is subtracted
+        # from the default to avoid exceeding 76 characters total.
+        # `edgeitems` is the number of elements to include before and after
+        # ellipses when arrays are not shown in full.
+        # `threshold` is the maximum number of elements for which an
+        # array is shown in full.
+        # These values tend to work well for use with OptimizeResult.
+        with np.printoptions(linewidth=76-n, edgeitems=2, threshold=12,
+                             formatter={'float_kind': _float_formatter_10}):
+            s = str(d)
+    return s
+
+
+_batch_note = """
+The documentation is written assuming array arguments are of specified
+"core" shapes. However, array argument(s) of this function may have additional
+"batch" dimensions prepended to the core shape. In this case, the array is treated
+as a batch of lower-dimensional slices; see :ref:`linalg_batch` for details.
+"""
+
+
+def _apply_over_batch(*argdefs):
+    """
+    Factory for decorator that applies a function over batched arguments.
+
+    Array arguments may have any number of core dimensions (typically 0,
+    1, or 2) and any broadcastable batch shapes. There may be any
+    number of array outputs of any number of dimensions. Assumptions
+    right now - which are satisfied by all functions of interest in `linalg` -
+    are that all array inputs are consecutive keyword or positional arguments,
+    and that the wrapped function returns either a single array or a tuple of
+    arrays. It's only as general as it needs to be right now - it can be extended.
+
+    Parameters
+    ----------
+    *argdefs : tuple of (str, int)
+        Definitions of array arguments: the keyword name of the argument, and
+        the number of core dimensions.
+
+    Example:
+    --------
+    `linalg.eig` accepts two matrices as the first two arguments `a` and `b`, where
+    `b` is optional, and returns one array or a tuple of arrays, depending on the
+    values of other positional or keyword arguments. To generate a wrapper that applies
+    the function over batches of `a` and optionally `b` :
+
+    >>> _apply_over_batch(('a', 2), ('b', 2))
+    """
+    names, ndims = list(zip(*argdefs))
+    n_arrays = len(names)
+
+    def decorator(f):
+        @functools.wraps(f)
+        def wrapper(*args, **kwargs):
+            args = list(args)
+
+            # Ensure all arrays in `arrays`, other arguments in `other_args`/`kwargs`
+            arrays, other_args = args[:n_arrays], args[n_arrays:]
+            for i, name in enumerate(names):
+                if name in kwargs:
+                    if i + 1 <= len(args):
+                        raise ValueError(f'{f.__name__}() got multiple values '
+                                         f'for argument `{name}`.')
+                    else:
+                        arrays.append(kwargs.pop(name))
+
+            # Determine core and batch shapes
+            batch_shapes = []
+            core_shapes = []
+            for i, (array, ndim) in enumerate(zip(arrays, ndims)):
+                array = None if array is None else np.asarray(array)
+                shape = () if array is None else array.shape
+
+                if ndim == "1|2":  # special case for `solve`, etc.
+                    ndim = 2 if array.ndim >= 2 else 1
+
+                arrays[i] = array
+                batch_shapes.append(shape[:-ndim] if ndim > 0 else shape)
+                core_shapes.append(shape[-ndim:] if ndim > 0 else ())
+
+            # Early exit if call is not batched
+            if not any(batch_shapes):
+                return f(*arrays, *other_args, **kwargs)
+
+            # Determine broadcasted batch shape
+            batch_shape = np.broadcast_shapes(*batch_shapes)  # Gives OK error message
+
+            # Broadcast arrays to appropriate shape
+            for i, (array, core_shape) in enumerate(zip(arrays, core_shapes)):
+                if array is None:
+                    continue
+                arrays[i] = np.broadcast_to(array, batch_shape + core_shape)
+
+            # Main loop
+            results = []
+            for index in np.ndindex(batch_shape):
+                result = f(*(array[index] for array in arrays), *other_args, **kwargs)
+                # Assume `result` is either a tuple or single array. This is easily
+                # generalized by allowing the contributor to pass an `unpack_result`
+                # callable to the decorator factory.
+                result = (result,) if not isinstance(result, tuple) else result
+                results.append(result)
+            results = list(zip(*results))
+
+            # Reshape results
+            for i, result in enumerate(results):
+                result = np.stack(result)
+                core_shape = result.shape[1:]
+                results[i] = np.reshape(result, batch_shape + core_shape)
+
+            # Assume `result` should be a single array if there is only one element or
+            # a `tuple` otherwise. This is easily generalized by allowing the
+            # contributor to pass an `pack_result` callable to the decorator factory.
+            return results[0] if len(results) == 1 else results
+
+        doc = FunctionDoc(wrapper)
+        doc['Extended Summary'].append(_batch_note.rstrip())
+        wrapper.__doc__ = str(doc).split("\n", 1)[1]  # remove signature
+
+        return wrapper
+    return decorator
+
+
+def np_vecdot(x1, x2, /, *, axis=-1):
+    # `np.vecdot` has advantages (e.g. see gh-22462), so let's use it when
+    # available. As functions are translated to Array API, `np_vecdot` can be
+    # replaced with `xp.vecdot`.
+    if np.__version__ > "2.0":
+        return np.vecdot(x1, x2, axis=axis)
+    else:
+        # of course there are other fancy ways of doing this (e.g. `einsum`)
+        # but let's keep it simple since it's temporary
+        return np.sum(x1 * x2, axis=axis)

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/decorator.py

@@ -0,0 +1,399 @@
+# #########################     LICENSE     ############################ #
+
+# Copyright (c) 2005-2015, Michele Simionato
+# All rights reserved.
+
+# 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 bytecode 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.
+
+# 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
+# HOLDERS 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.
+
+"""
+Decorator module, see https://pypi.python.org/pypi/decorator
+for the documentation.
+"""
+import re
+import sys
+import inspect
+import operator
+import itertools
+import collections
+
+from inspect import getfullargspec
+
+__version__ = '4.0.5'
+
+
+def get_init(cls):
+    return cls.__init__
+
+
+# getargspec has been deprecated in Python 3.5
+ArgSpec = collections.namedtuple(
+    'ArgSpec', 'args varargs varkw defaults')
+
+
+def getargspec(f):
+    """A replacement for inspect.getargspec"""
+    spec = getfullargspec(f)
+    return ArgSpec(spec.args, spec.varargs, spec.varkw, spec.defaults)
+
+
+DEF = re.compile(r'\s*def\s*([_\w][_\w\d]*)\s*\(')
+
+
+# basic functionality
+class FunctionMaker:
+    """
+    An object with the ability to create functions with a given signature.
+    It has attributes name, doc, module, signature, defaults, dict, and
+    methods update and make.
+    """
+
+    # Atomic get-and-increment provided by the GIL
+    _compile_count = itertools.count()
+
+    def __init__(self, func=None, name=None, signature=None,
+                 defaults=None, doc=None, module=None, funcdict=None):
+        self.shortsignature = signature
+        if func:
+            # func can be a class or a callable, but not an instance method
+            self.name = func.__name__
+            if self.name == '<lambda>':  # small hack for lambda functions
+                self.name = '_lambda_'
+            self.doc = func.__doc__
+            self.module = func.__module__
+            if inspect.isfunction(func):
+                argspec = getfullargspec(func)
+                self.annotations = getattr(func, '__annotations__', {})
+                for a in ('args', 'varargs', 'varkw', 'defaults', 'kwonlyargs',
+                          'kwonlydefaults'):
+                    setattr(self, a, getattr(argspec, a))
+                for i, arg in enumerate(self.args):
+                    setattr(self, f'arg{i}', arg)
+                allargs = list(self.args)
+                allshortargs = list(self.args)
+                if self.varargs:
+                    allargs.append('*' + self.varargs)
+                    allshortargs.append('*' + self.varargs)
+                elif self.kwonlyargs:
+                    allargs.append('*')  # single star syntax
+                for a in self.kwonlyargs:
+                    allargs.append(f'{a}=None')
+                    allshortargs.append(f'{a}={a}')
+                if self.varkw:
+                    allargs.append('**' + self.varkw)
+                    allshortargs.append('**' + self.varkw)
+                self.signature = ', '.join(allargs)
+                self.shortsignature = ', '.join(allshortargs)
+                self.dict = func.__dict__.copy()
+        # func=None happens when decorating a caller
+        if name:
+            self.name = name
+        if signature is not None:
+            self.signature = signature
+        if defaults:
+            self.defaults = defaults
+        if doc:
+            self.doc = doc
+        if module:
+            self.module = module
+        if funcdict:
+            self.dict = funcdict
+        # check existence required attributes
+        assert hasattr(self, 'name')
+        if not hasattr(self, 'signature'):
+            raise TypeError(f'You are decorating a non-function: {func}')
+
+    def update(self, func, **kw):
+        "Update the signature of func with the data in self"
+        func.__name__ = self.name
+        func.__doc__ = getattr(self, 'doc', None)
+        func.__dict__ = getattr(self, 'dict', {})
+        func.__defaults__ = getattr(self, 'defaults', ())
+        func.__kwdefaults__ = getattr(self, 'kwonlydefaults', None)
+        func.__annotations__ = getattr(self, 'annotations', None)
+        try:
+            frame = sys._getframe(3)
+        except AttributeError:  # for IronPython and similar implementations
+            callermodule = '?'
+        else:
+            callermodule = frame.f_globals.get('__name__', '?')
+        func.__module__ = getattr(self, 'module', callermodule)
+        func.__dict__.update(kw)
+
+    def make(self, src_templ, evaldict=None, addsource=False, **attrs):
+        "Make a new function from a given template and update the signature"
+        src = src_templ % vars(self)  # expand name and signature
+        evaldict = evaldict or {}
+        mo = DEF.match(src)
+        if mo is None:
+            raise SyntaxError(f'not a valid function template\n{src}')
+        name = mo.group(1)  # extract the function name
+        names = set([name] + [arg.strip(' *') for arg in
+                              self.shortsignature.split(',')])
+        for n in names:
+            if n in ('_func_', '_call_'):
+                raise NameError(f'{n} is overridden in\n{src}')
+        if not src.endswith('\n'):  # add a newline just for safety
+            src += '\n'  # this is needed in old versions of Python
+
+        # Ensure each generated function has a unique filename for profilers
+        # (such as cProfile) that depend on the tuple of (<filename>,
+        # <definition line>, <function name>) being unique.
+        filename = f'<decorator-gen-{next(self._compile_count)}>'
+        try:
+            code = compile(src, filename, 'single')
+            exec(code, evaldict)
+        except:  # noqa: E722
+            print('Error in generated code:', file=sys.stderr)
+            print(src, file=sys.stderr)
+            raise
+        func = evaldict[name]
+        if addsource:
+            attrs['__source__'] = src
+        self.update(func, **attrs)
+        return func
+
+    @classmethod
+    def create(cls, obj, body, evaldict, defaults=None,
+               doc=None, module=None, addsource=True, **attrs):
+        """
+        Create a function from the strings name, signature, and body.
+        evaldict is the evaluation dictionary. If addsource is true, an
+        attribute __source__ is added to the result. The attributes attrs
+        are added, if any.
+        """
+        if isinstance(obj, str):  # "name(signature)"
+            name, rest = obj.strip().split('(', 1)
+            signature = rest[:-1]  # strip a right parens
+            func = None
+        else:  # a function
+            name = None
+            signature = None
+            func = obj
+        self = cls(func, name, signature, defaults, doc, module)
+        ibody = '\n'.join('    ' + line for line in body.splitlines())
+        return self.make('def %(name)s(%(signature)s):\n' + ibody,
+                         evaldict, addsource, **attrs)
+
+
+def decorate(func, caller):
+    """
+    decorate(func, caller) decorates a function using a caller.
+    """
+    evaldict = func.__globals__.copy()
+    evaldict['_call_'] = caller
+    evaldict['_func_'] = func
+    fun = FunctionMaker.create(
+        func, "return _call_(_func_, %(shortsignature)s)",
+        evaldict, __wrapped__=func)
+    if hasattr(func, '__qualname__'):
+        fun.__qualname__ = func.__qualname__
+    return fun
+
+
+def decorator(caller, _func=None):
+    """decorator(caller) converts a caller function into a decorator"""
+    if _func is not None:  # return a decorated function
+        # this is obsolete behavior; you should use decorate instead
+        return decorate(_func, caller)
+    # else return a decorator function
+    if inspect.isclass(caller):
+        name = caller.__name__.lower()
+        callerfunc = get_init(caller)
+        doc = (f'decorator({caller.__name__}) converts functions/generators into ' 
+               f'factories of {caller.__name__} objects')
+    elif inspect.isfunction(caller):
+        if caller.__name__ == '<lambda>':
+            name = '_lambda_'
+        else:
+            name = caller.__name__
+        callerfunc = caller
+        doc = caller.__doc__
+    else:  # assume caller is an object with a __call__ method
+        name = caller.__class__.__name__.lower()
+        callerfunc = caller.__call__.__func__
+        doc = caller.__call__.__doc__
+    evaldict = callerfunc.__globals__.copy()
+    evaldict['_call_'] = caller
+    evaldict['_decorate_'] = decorate
+    return FunctionMaker.create(
+        f'{name}(func)', 'return _decorate_(func, _call_)',
+        evaldict, doc=doc, module=caller.__module__,
+        __wrapped__=caller)
+
+
+# ####################### contextmanager ####################### #
+
+try:  # Python >= 3.2
+    from contextlib import _GeneratorContextManager
+except ImportError:  # Python >= 2.5
+    from contextlib import GeneratorContextManager as _GeneratorContextManager
+
+
+class ContextManager(_GeneratorContextManager):
+    def __call__(self, func):
+        """Context manager decorator"""
+        return FunctionMaker.create(
+            func, "with _self_: return _func_(%(shortsignature)s)",
+            dict(_self_=self, _func_=func), __wrapped__=func)
+
+
+init = getfullargspec(_GeneratorContextManager.__init__)
+n_args = len(init.args)
+if n_args == 2 and not init.varargs:  # (self, genobj) Python 2.7
+    def __init__(self, g, *a, **k):
+        return _GeneratorContextManager.__init__(self, g(*a, **k))
+    ContextManager.__init__ = __init__
+elif n_args == 2 and init.varargs:  # (self, gen, *a, **k) Python 3.4
+    pass
+elif n_args == 4:  # (self, gen, args, kwds) Python 3.5
+    def __init__(self, g, *a, **k):
+        return _GeneratorContextManager.__init__(self, g, a, k)
+    ContextManager.__init__ = __init__
+
+contextmanager = decorator(ContextManager)
+
+
+# ############################ dispatch_on ############################ #
+
+def append(a, vancestors):
+    """
+    Append ``a`` to the list of the virtual ancestors, unless it is already
+    included.
+    """
+    add = True
+    for j, va in enumerate(vancestors):
+        if issubclass(va, a):
+            add = False
+            break
+        if issubclass(a, va):
+            vancestors[j] = a
+            add = False
+    if add:
+        vancestors.append(a)
+
+
+# inspired from simplegeneric by P.J. Eby and functools.singledispatch
+def dispatch_on(*dispatch_args):
+    """
+    Factory of decorators turning a function into a generic function
+    dispatching on the given arguments.
+    """
+    assert dispatch_args, 'No dispatch args passed'
+    dispatch_str = f"({', '.join(dispatch_args)},)"
+
+    def check(arguments, wrong=operator.ne, msg=''):
+        """Make sure one passes the expected number of arguments"""
+        if wrong(len(arguments), len(dispatch_args)):
+            raise TypeError(f'Expected {len(dispatch_args)} arguments, '
+                            'got {len(arguments)}{msg}')
+
+    def gen_func_dec(func):
+        """Decorator turning a function into a generic function"""
+
+        # first check the dispatch arguments
+        argset = set(getfullargspec(func).args)
+        if not set(dispatch_args) <= argset:
+            raise NameError(f'Unknown dispatch arguments {dispatch_str}')
+
+        typemap = {}
+
+        def vancestors(*types):
+            """
+            Get a list of sets of virtual ancestors for the given types
+            """
+            check(types)
+            ras = [[] for _ in range(len(dispatch_args))]
+            for types_ in typemap:
+                for t, type_, ra in zip(types, types_, ras):
+                    if issubclass(t, type_) and type_ not in t.__mro__:
+                        append(type_, ra)
+            return [set(ra) for ra in ras]
+
+        def ancestors(*types):
+            """
+            Get a list of virtual MROs, one for each type
+            """
+            check(types)
+            lists = []
+            for t, vas in zip(types, vancestors(*types)):
+                n_vas = len(vas)
+                if n_vas > 1:
+                    raise RuntimeError(
+                        f'Ambiguous dispatch for {t}: {vas}')
+                elif n_vas == 1:
+                    va, = vas
+                    mro = type('t', (t, va), {}).__mro__[1:]
+                else:
+                    mro = t.__mro__
+                lists.append(mro[:-1])  # discard t and object
+            return lists
+
+        def register(*types):
+            """
+            Decorator to register an implementation for the given types
+            """
+            check(types)
+
+            def dec(f):
+                check(getfullargspec(f).args, operator.lt, ' in ' + f.__name__)
+                typemap[types] = f
+                return f
+            return dec
+
+        def dispatch_info(*types):
+            """
+            An utility to introspect the dispatch algorithm
+            """
+            check(types)
+            lst = [tuple(a.__name__ for a in anc)
+                   for anc in itertools.product(*ancestors(*types))]
+            return lst
+
+        def _dispatch(dispatch_args, *args, **kw):
+            types = tuple(type(arg) for arg in dispatch_args)
+            try:  # fast path
+                f = typemap[types]
+            except KeyError:
+                pass
+            else:
+                return f(*args, **kw)
+            combinations = itertools.product(*ancestors(*types))
+            next(combinations)  # the first one has been already tried
+            for types_ in combinations:
+                f = typemap.get(types_)
+                if f is not None:
+                    return f(*args, **kw)
+
+            # else call the default implementation
+            return func(*args, **kw)
+
+        return FunctionMaker.create(
+            func, f'return _f_({dispatch_str}, %%(shortsignature)s)',
+            dict(_f_=_dispatch), register=register, default=func,
+            typemap=typemap, vancestors=vancestors, ancestors=ancestors,
+            dispatch_info=dispatch_info, __wrapped__=func)
+
+    gen_func_dec.__name__ = 'dispatch_on' + dispatch_str
+    return gen_func_dec

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/deprecation.py

@@ -0,0 +1,274 @@
+from inspect import Parameter, signature
+import functools
+import warnings
+from importlib import import_module
+from scipy._lib._docscrape import FunctionDoc
+
+
+__all__ = ["_deprecated"]
+
+
+# Object to use as default value for arguments to be deprecated. This should
+# be used over 'None' as the user could parse 'None' as a positional argument
+_NoValue = object()
+
+def _sub_module_deprecation(*, sub_package, module, private_modules, all,
+                            attribute, correct_module=None, dep_version="1.16.0"):
+    """Helper function for deprecating modules that are public but were
+    intended to be private.
+
+    Parameters
+    ----------
+    sub_package : str
+        Subpackage the module belongs to eg. stats
+    module : str
+        Public but intended private module to deprecate
+    private_modules : list
+        Private replacement(s) for `module`; should contain the
+        content of ``all``, possibly spread over several modules.
+    all : list
+        ``__all__`` belonging to `module`
+    attribute : str
+        The attribute in `module` being accessed
+    correct_module : str, optional
+        Module in `sub_package` that `attribute` should be imported from.
+        Default is that `attribute` should be imported from ``scipy.sub_package``.
+    dep_version : str, optional
+        Version in which deprecated attributes will be removed.
+    """
+    if correct_module is not None:
+        correct_import = f"scipy.{sub_package}.{correct_module}"
+    else:
+        correct_import = f"scipy.{sub_package}"
+
+    if attribute not in all:
+        raise AttributeError(
+            f"`scipy.{sub_package}.{module}` has no attribute `{attribute}`; "
+            f"furthermore, `scipy.{sub_package}.{module}` is deprecated "
+            f"and will be removed in SciPy 2.0.0."
+        )
+
+    attr = getattr(import_module(correct_import), attribute, None)
+
+    if attr is not None:
+        message = (
+            f"Please import `{attribute}` from the `{correct_import}` namespace; "
+            f"the `scipy.{sub_package}.{module}` namespace is deprecated "
+            f"and will be removed in SciPy 2.0.0."
+        )
+    else:
+        message = (
+            f"`scipy.{sub_package}.{module}.{attribute}` is deprecated along with "
+            f"the `scipy.{sub_package}.{module}` namespace. "
+            f"`scipy.{sub_package}.{module}.{attribute}` will be removed "
+            f"in SciPy {dep_version}, and the `scipy.{sub_package}.{module}` namespace "
+            f"will be removed in SciPy 2.0.0."
+        )
+
+    warnings.warn(message, category=DeprecationWarning, stacklevel=3)
+
+    for module in private_modules:
+        try:
+            return getattr(import_module(f"scipy.{sub_package}.{module}"), attribute)
+        except AttributeError as e:
+            # still raise an error if the attribute isn't in any of the expected
+            # private modules
+            if module == private_modules[-1]:
+                raise e
+            continue
+    
+
+def _deprecated(msg, stacklevel=2):
+    """Deprecate a function by emitting a warning on use."""
+    def wrap(fun):
+        if isinstance(fun, type):
+            warnings.warn(
+                f"Trying to deprecate class {fun!r}",
+                category=RuntimeWarning, stacklevel=2)
+            return fun
+
+        @functools.wraps(fun)
+        def call(*args, **kwargs):
+            warnings.warn(msg, category=DeprecationWarning,
+                          stacklevel=stacklevel)
+            return fun(*args, **kwargs)
+        call.__doc__ = fun.__doc__
+        return call
+
+    return wrap
+
+
+class _DeprecationHelperStr:
+    """
+    Helper class used by deprecate_cython_api
+    """
+    def __init__(self, content, message):
+        self._content = content
+        self._message = message
+
+    def __hash__(self):
+        return hash(self._content)
+
+    def __eq__(self, other):
+        res = (self._content == other)
+        if res:
+            warnings.warn(self._message, category=DeprecationWarning,
+                          stacklevel=2)
+        return res
+
+
+def deprecate_cython_api(module, routine_name, new_name=None, message=None):
+    """
+    Deprecate an exported cdef function in a public Cython API module.
+
+    Only functions can be deprecated; typedefs etc. cannot.
+
+    Parameters
+    ----------
+    module : module
+        Public Cython API module (e.g. scipy.linalg.cython_blas).
+    routine_name : str
+        Name of the routine to deprecate. May also be a fused-type
+        routine (in which case its all specializations are deprecated).
+    new_name : str
+        New name to include in the deprecation warning message
+    message : str
+        Additional text in the deprecation warning message
+
+    Examples
+    --------
+    Usually, this function would be used in the top-level of the
+    module ``.pyx`` file:
+
+    >>> from scipy._lib.deprecation import deprecate_cython_api
+    >>> import scipy.linalg.cython_blas as mod
+    >>> deprecate_cython_api(mod, "dgemm", "dgemm_new",
+    ...                      message="Deprecated in Scipy 1.5.0")
+    >>> del deprecate_cython_api, mod
+
+    After this, Cython modules that use the deprecated function emit a
+    deprecation warning when they are imported.
+
+    """
+    old_name = f"{module.__name__}.{routine_name}"
+
+    if new_name is None:
+        depdoc = f"`{old_name}` is deprecated!"
+    else:
+        depdoc = f"`{old_name}` is deprecated, use `{new_name}` instead!"
+
+    if message is not None:
+        depdoc += "\n" + message
+
+    d = module.__pyx_capi__
+
+    # Check if the function is a fused-type function with a mangled name
+    j = 0
+    has_fused = False
+    while True:
+        fused_name = f"__pyx_fuse_{j}{routine_name}"
+        if fused_name in d:
+            has_fused = True
+            d[_DeprecationHelperStr(fused_name, depdoc)] = d.pop(fused_name)
+            j += 1
+        else:
+            break
+
+    # If not, apply deprecation to the named routine
+    if not has_fused:
+        d[_DeprecationHelperStr(routine_name, depdoc)] = d.pop(routine_name)
+
+
+# taken from scikit-learn, see
+# https://github.com/scikit-learn/scikit-learn/blob/1.3.0/sklearn/utils/validation.py#L38
+def _deprecate_positional_args(func=None, *, version=None,
+                               deprecated_args=None, custom_message=""):
+    """Decorator for methods that issues warnings for positional arguments.
+
+    Using the keyword-only argument syntax in pep 3102, arguments after the
+    * will issue a warning when passed as a positional argument.
+
+    Parameters
+    ----------
+    func : callable, default=None
+        Function to check arguments on.
+    version : callable, default=None
+        The version when positional arguments will result in error.
+    deprecated_args : set of str, optional
+        Arguments to deprecate - whether passed by position or keyword.
+    custom_message : str, optional
+        Custom message to add to deprecation warning and documentation.
+    """
+    if version is None:
+        msg = "Need to specify a version where signature will be changed"
+        raise ValueError(msg)
+
+    deprecated_args = set() if deprecated_args is None else set(deprecated_args)
+
+    def _inner_deprecate_positional_args(f):
+        sig = signature(f)
+        kwonly_args = []
+        all_args = []
+
+        for name, param in sig.parameters.items():
+            if param.kind == Parameter.POSITIONAL_OR_KEYWORD:
+                all_args.append(name)
+            elif param.kind == Parameter.KEYWORD_ONLY:
+                kwonly_args.append(name)
+
+        def warn_deprecated_args(kwargs):
+            intersection = deprecated_args.intersection(kwargs)
+            if intersection:
+                message = (f"Arguments {intersection} are deprecated, whether passed "
+                           "by position or keyword. They will be removed in SciPy "
+                           f"{version}. ")
+                message += custom_message
+                warnings.warn(message, category=DeprecationWarning, stacklevel=3)
+
+        @functools.wraps(f)
+        def inner_f(*args, **kwargs):
+
+            extra_args = len(args) - len(all_args)
+            if extra_args <= 0:
+                warn_deprecated_args(kwargs)
+                return f(*args, **kwargs)
+
+            # extra_args > 0
+            kwonly_extra_args = set(kwonly_args[:extra_args]) - deprecated_args
+            args_msg = ", ".join(kwonly_extra_args)
+            warnings.warn(
+                (
+                    f"You are passing as positional arguments: {args_msg}. "
+                    "Please change your invocation to use keyword arguments. "
+                    f"From SciPy {version}, passing these as positional "
+                    "arguments will result in an error."
+                ),
+                DeprecationWarning,
+                stacklevel=2,
+            )
+            kwargs.update(zip(sig.parameters, args))
+            warn_deprecated_args(kwargs)
+            return f(**kwargs)
+
+        doc = FunctionDoc(inner_f)
+        kwonly_extra_args = set(kwonly_args) - deprecated_args
+        admonition = f"""
+.. deprecated:: {version}
+    Use of argument(s) ``{kwonly_extra_args}`` by position is deprecated; beginning in 
+    SciPy {version}, these will be keyword-only. """
+        if deprecated_args:
+            admonition += (f"Argument(s) ``{deprecated_args}`` are deprecated, whether "
+                           "passed by position or keyword; they will be removed in "
+                           f"SciPy {version}. ")
+        admonition += custom_message
+        doc['Extended Summary'] += [admonition]
+
+        doc = str(doc).split("\n", 1)[1]  # remove signature
+        inner_f.__doc__ = str(doc)
+
+        return inner_f
+
+    if func is not None:
+        return _inner_deprecate_positional_args(func)
+
+    return _inner_deprecate_positional_args

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/doccer.py

@@ -0,0 +1,366 @@
+"""Utilities to allow inserting docstring fragments for common
+parameters into function and method docstrings."""
+
+from collections.abc import Callable, Iterable, Mapping
+from typing import Protocol, TypeVar
+import sys
+
+__all__ = [
+    "docformat",
+    "inherit_docstring_from",
+    "indentcount_lines",
+    "filldoc",
+    "unindent_dict",
+    "unindent_string",
+    "extend_notes_in_docstring",
+    "replace_notes_in_docstring",
+    "doc_replace",
+]
+
+_F = TypeVar("_F", bound=Callable[..., object])
+
+
+class Decorator(Protocol):
+    """A decorator of a function."""
+
+    def __call__(self, func: _F, /) -> _F: ...
+
+
+def docformat(docstring: str, docdict: Mapping[str, str] | None = None) -> str:
+    """Fill a function docstring from variables in dictionary.
+
+    Adapt the indent of the inserted docs
+
+    Parameters
+    ----------
+    docstring : str
+        A docstring from a function, possibly with dict formatting strings.
+    docdict : dict[str, str], optional
+        A dictionary with keys that match the dict formatting strings
+        and values that are docstring fragments to be inserted. The
+        indentation of the inserted docstrings is set to match the
+        minimum indentation of the ``docstring`` by adding this
+        indentation to all lines of the inserted string, except the
+        first.
+
+    Returns
+    -------
+    docstring : str
+        string with requested ``docdict`` strings inserted.
+
+    Examples
+    --------
+    >>> docformat(' Test string with %(value)s', {'value':'inserted value'})
+    ' Test string with inserted value'
+    >>> docstring = 'First line\\n    Second line\\n    %(value)s'
+    >>> inserted_string = "indented\\nstring"
+    >>> docdict = {'value': inserted_string}
+    >>> docformat(docstring, docdict)
+    'First line\\n    Second line\\n    indented\\n    string'
+    """
+    if not docstring:
+        return docstring
+    if docdict is None:
+        docdict = {}
+    if not docdict:
+        return docstring
+    lines = docstring.expandtabs().splitlines()
+    # Find the minimum indent of the main docstring, after first line
+    if len(lines) < 2:
+        icount = 0
+    else:
+        icount = indentcount_lines(lines[1:])
+    indent = " " * icount
+    # Insert this indent to dictionary docstrings
+    indented = {}
+    for name, dstr in docdict.items():
+        lines = dstr.expandtabs().splitlines()
+        indented[name] = ("\n" + indent).join(lines)
+    return docstring % indented
+
+
+def inherit_docstring_from(cls: object) -> Decorator:
+    """This decorator modifies the decorated function's docstring by
+    replacing occurrences of '%(super)s' with the docstring of the
+    method of the same name from the class `cls`.
+
+    If the decorated method has no docstring, it is simply given the
+    docstring of `cls`s method.
+
+    Parameters
+    ----------
+    cls : type or object
+        A class with a method with the same name as the decorated method.
+        The docstring of the method in this class replaces '%(super)s' in the
+        docstring of the decorated method.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that modifies the __doc__ attribute
+        of its argument.
+
+    Examples
+    --------
+    In the following, the docstring for Bar.func created using the
+    docstring of `Foo.func`.
+
+    >>> class Foo:
+    ...     def func(self):
+    ...         '''Do something useful.'''
+    ...         return
+    ...
+    >>> class Bar(Foo):
+    ...     @inherit_docstring_from(Foo)
+    ...     def func(self):
+    ...         '''%(super)s
+    ...         Do it fast.
+    ...         '''
+    ...         return
+    ...
+    >>> b = Bar()
+    >>> b.func.__doc__
+    'Do something useful.\n        Do it fast.\n        '
+    """
+
+    def _doc(func: _F) -> _F:
+        cls_docstring = getattr(cls, func.__name__).__doc__
+        func_docstring = func.__doc__
+        if func_docstring is None:
+            func.__doc__ = cls_docstring
+        else:
+            new_docstring = func_docstring % dict(super=cls_docstring)
+            func.__doc__ = new_docstring
+        return func
+
+    return _doc
+
+
+def extend_notes_in_docstring(cls: object, notes: str) -> Decorator:
+    """This decorator replaces the decorated function's docstring
+    with the docstring from corresponding method in `cls`.
+    It extends the 'Notes' section of that docstring to include
+    the given `notes`.
+
+    Parameters
+    ----------
+    cls : type or object
+        A class with a method with the same name as the decorated method.
+        The docstring of the method in this class replaces the docstring of the
+        decorated method.
+    notes : str
+        Additional notes to append to the 'Notes' section of the docstring.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that modifies the __doc__ attribute
+        of its argument.
+    """
+
+    def _doc(func: _F) -> _F:
+        cls_docstring = getattr(cls, func.__name__).__doc__
+        # If python is called with -OO option,
+        # there is no docstring
+        if cls_docstring is None:
+            return func
+        end_of_notes = cls_docstring.find("        References\n")
+        if end_of_notes == -1:
+            end_of_notes = cls_docstring.find("        Examples\n")
+            if end_of_notes == -1:
+                end_of_notes = len(cls_docstring)
+        func.__doc__ = (
+            cls_docstring[:end_of_notes] + notes + cls_docstring[end_of_notes:]
+        )
+        return func
+
+    return _doc
+
+
+def replace_notes_in_docstring(cls: object, notes: str) -> Decorator:
+    """This decorator replaces the decorated function's docstring
+    with the docstring from corresponding method in `cls`.
+    It replaces the 'Notes' section of that docstring with
+    the given `notes`.
+
+    Parameters
+    ----------
+    cls : type or object
+        A class with a method with the same name as the decorated method.
+        The docstring of the method in this class replaces the docstring of the
+        decorated method.
+    notes : str
+        The notes to replace the existing 'Notes' section with.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that modifies the __doc__ attribute
+        of its argument.
+    """
+
+    def _doc(func: _F) -> _F:
+        cls_docstring = getattr(cls, func.__name__).__doc__
+        notes_header = "        Notes\n        -----\n"
+        # If python is called with -OO option,
+        # there is no docstring
+        if cls_docstring is None:
+            return func
+        start_of_notes = cls_docstring.find(notes_header)
+        end_of_notes = cls_docstring.find("        References\n")
+        if end_of_notes == -1:
+            end_of_notes = cls_docstring.find("        Examples\n")
+            if end_of_notes == -1:
+                end_of_notes = len(cls_docstring)
+        func.__doc__ = (
+            cls_docstring[: start_of_notes + len(notes_header)]
+            + notes
+            + cls_docstring[end_of_notes:]
+        )
+        return func
+
+    return _doc
+
+
+def indentcount_lines(lines: Iterable[str]) -> int:
+    """Minimum indent for all lines in line list
+
+    Parameters
+    ----------
+    lines : Iterable[str]
+        The lines to find the minimum indent of.
+
+    Returns
+    -------
+    indent : int
+        The minimum indent.
+
+
+    Examples
+    --------
+    >>> lines = [' one', '  two', '   three']
+    >>> indentcount_lines(lines)
+    1
+    >>> lines = []
+    >>> indentcount_lines(lines)
+    0
+    >>> lines = [' one']
+    >>> indentcount_lines(lines)
+    1
+    >>> indentcount_lines(['    '])
+    0
+    """
+    indentno = sys.maxsize
+    for line in lines:
+        stripped = line.lstrip()
+        if stripped:
+            indentno = min(indentno, len(line) - len(stripped))
+    if indentno == sys.maxsize:
+        return 0
+    return indentno
+
+
+def filldoc(docdict: Mapping[str, str], unindent_params: bool = True) -> Decorator:
+    """Return docstring decorator using docdict variable dictionary.
+
+    Parameters
+    ----------
+    docdict : dict[str, str]
+        A dictionary containing name, docstring fragment pairs.
+    unindent_params : bool, optional
+        If True, strip common indentation from all parameters in docdict.
+        Default is False.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that applies dictionary to its
+        argument's __doc__ attribute.
+    """
+    if unindent_params:
+        docdict = unindent_dict(docdict)
+
+    def decorate(func: _F) -> _F:
+        # __doc__ may be None for optimized Python (-OO)
+        doc = func.__doc__ or ""
+        func.__doc__ = docformat(doc, docdict)
+        return func
+
+    return decorate
+
+
+def unindent_dict(docdict: Mapping[str, str]) -> dict[str, str]:
+    """Unindent all strings in a docdict.
+
+    Parameters
+    ----------
+    docdict : dict[str, str]
+        A dictionary with string values to unindent.
+
+    Returns
+    -------
+    docdict : dict[str, str]
+        The `docdict` dictionary but each of its string values are unindented.
+    """
+    can_dict: dict[str, str] = {}
+    for name, dstr in docdict.items():
+        can_dict[name] = unindent_string(dstr)
+    return can_dict
+
+
+def unindent_string(docstring: str) -> str:
+    """Set docstring to minimum indent for all lines, including first.
+
+    Parameters
+    ----------
+    docstring : str
+        The input docstring to unindent.
+
+    Returns
+    -------
+    docstring : str
+        The unindented docstring.
+
+    Examples
+    --------
+    >>> unindent_string(' two')
+    'two'
+    >>> unindent_string('  two\\n   three')
+    'two\\n three'
+    """
+    lines = docstring.expandtabs().splitlines()
+    icount = indentcount_lines(lines)
+    if icount == 0:
+        return docstring
+    return "\n".join([line[icount:] for line in lines])
+
+
+def doc_replace(obj: object, oldval: str, newval: str) -> Decorator:
+    """Decorator to take the docstring from obj, with oldval replaced by newval
+
+    Equivalent to ``func.__doc__ = obj.__doc__.replace(oldval, newval)``
+
+    Parameters
+    ----------
+    obj : object
+        A class or object whose docstring will be used as the basis for the
+        replacement operation.
+    oldval : str
+        The string to search for in the docstring.
+    newval : str
+        The string to replace `oldval` with in the docstring.
+
+    Returns
+    -------
+    decfunc : function
+        A decorator function that replaces occurrences of `oldval` with `newval`
+        in the docstring of the decorated function.
+    """
+    # __doc__ may be None for optimized Python (-OO)
+    doc = (obj.__doc__ or "").replace(oldval, newval)
+
+    def inner(func: _F) -> _F:
+        func.__doc__ = doc
+        return func
+
+    return inner

tool_server/.venv/lib/python3.12/site-packages/scipy/_lib/uarray.py

@@ -0,0 +1,31 @@
+"""`uarray` provides functions for generating multimethods that dispatch to
+multiple different backends
+
+This should be imported, rather than `_uarray` so that an installed version could
+be used instead, if available. This means that users can call
+`uarray.set_backend` directly instead of going through SciPy.
+
+"""
+
+
+# Prefer an installed version of uarray, if available
+try:
+    import uarray as _uarray
+except ImportError:
+    _has_uarray = False
+else:
+    from scipy._lib._pep440 import Version as _Version
+
+    _has_uarray = _Version(_uarray.__version__) >= _Version("0.8")
+    del _uarray
+    del _Version
+
+
+if _has_uarray:
+    from uarray import *  # noqa: F403
+    from uarray import _Function
+else:
+    from ._uarray import *  # noqa: F403
+    from ._uarray import _Function  # noqa: F401
+
+del _has_uarray

tool_server/.venv/lib/python3.12/site-packages/scipy/cluster/__init__.py

@@ -0,0 +1,31 @@
+"""
+=========================================
+Clustering package (:mod:`scipy.cluster`)
+=========================================
+
+.. currentmodule:: scipy.cluster
+
+Clustering algorithms are useful in information theory, target detection,
+communications, compression, and other areas. The `vq` module only
+supports vector quantization and the k-means algorithms.
+
+The `hierarchy` module provides functions for hierarchical and
+agglomerative clustering.  Its features include generating hierarchical
+clusters from distance matrices,
+calculating statistics on clusters, cutting linkages
+to generate flat clusters, and visualizing clusters with dendrograms.
+
+.. toctree::
+   :maxdepth: 1
+
+   cluster.vq
+   cluster.hierarchy
+
+"""
+__all__ = ['vq', 'hierarchy']
+
+from . import vq, hierarchy
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

tool_server/.venv/lib/python3.12/site-packages/scipy/cluster/_hierarchy.cpython-312-x86_64-linux-gnu.so

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:06d7a371d04ebd6ebffb169e63c62b47c3647e97548f012b942d1cbcb32c1903
+size 300088

tool_server/.venv/lib/python3.12/site-packages/scipy/cluster/_optimal_leaf_ordering.cpython-312-x86_64-linux-gnu.so

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+version https://git-lfs.github.com/spec/v1
+oid sha256:a07f9f1b9bce7a39f0150194dc8bcacae4f8f53c47af21f9f672d38ed05c67c4
+size 195304

tool_server/.venv/lib/python3.12/site-packages/scipy/cluster/_vq.cpython-312-x86_64-linux-gnu.so

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:54a856896fc3b62956b45b0ec7c29b5fc5e338beb5dc078952e1950aaec24d43
+size 129872

tool_server/.venv/lib/python3.12/site-packages/scipy/cluster/vq.py

@@ -0,0 +1,832 @@
+"""
+K-means clustering and vector quantization (:mod:`scipy.cluster.vq`)
+====================================================================
+
+Provides routines for k-means clustering, generating code books
+from k-means models and quantizing vectors by comparing them with
+centroids in a code book.
+
+.. autosummary::
+   :toctree: generated/
+
+   whiten -- Normalize a group of observations so each feature has unit variance
+   vq -- Calculate code book membership of a set of observation vectors
+   kmeans -- Perform k-means on a set of observation vectors forming k clusters
+   kmeans2 -- A different implementation of k-means with more methods
+           -- for initializing centroids
+
+Background information
+----------------------
+The k-means algorithm takes as input the number of clusters to
+generate, k, and a set of observation vectors to cluster. It
+returns a set of centroids, one for each of the k clusters. An
+observation vector is classified with the cluster number or
+centroid index of the centroid closest to it.
+
+A vector v belongs to cluster i if it is closer to centroid i than
+any other centroid. If v belongs to i, we say centroid i is the
+dominating centroid of v. The k-means algorithm tries to
+minimize distortion, which is defined as the sum of the squared distances
+between each observation vector and its dominating centroid.
+The minimization is achieved by iteratively reclassifying
+the observations into clusters and recalculating the centroids until
+a configuration is reached in which the centroids are stable. One can
+also define a maximum number of iterations.
+
+Since vector quantization is a natural application for k-means,
+information theory terminology is often used. The centroid index
+or cluster index is also referred to as a "code" and the table
+mapping codes to centroids and, vice versa, is often referred to as a
+"code book". The result of k-means, a set of centroids, can be
+used to quantize vectors. Quantization aims to find an encoding of
+vectors that reduces the expected distortion.
+
+All routines expect obs to be an M by N array, where the rows are
+the observation vectors. The codebook is a k by N array, where the
+ith row is the centroid of code word i. The observation vectors
+and centroids have the same feature dimension.
+
+As an example, suppose we wish to compress a 24-bit color image
+(each pixel is represented by one byte for red, one for blue, and
+one for green) before sending it over the web. By using a smaller
+8-bit encoding, we can reduce the amount of data by two
+thirds. Ideally, the colors for each of the 256 possible 8-bit
+encoding values should be chosen to minimize distortion of the
+color. Running k-means with k=256 generates a code book of 256
+codes, which fills up all possible 8-bit sequences. Instead of
+sending a 3-byte value for each pixel, the 8-bit centroid index
+(or code word) of the dominating centroid is transmitted. The code
+book is also sent over the wire so each 8-bit code can be
+translated back to a 24-bit pixel value representation. If the
+image of interest was of an ocean, we would expect many 24-bit
+blues to be represented by 8-bit codes. If it was an image of a
+human face, more flesh-tone colors would be represented in the
+code book.
+
+"""
+import warnings
+import numpy as np
+from collections import deque
+from scipy._lib._array_api import (_asarray, array_namespace, is_lazy_array,
+                                   xp_capabilities, xp_copy, xp_size)
+from scipy._lib._util import (check_random_state, rng_integers,
+                              _transition_to_rng)
+from scipy._lib import array_api_extra as xpx
+from scipy.spatial.distance import cdist
+
+from . import _vq
+
+__docformat__ = 'restructuredtext'
+
+__all__ = ['whiten', 'vq', 'kmeans', 'kmeans2']
+
+
+class ClusterError(Exception):
+    pass
+
+
+@xp_capabilities()
+def whiten(obs, check_finite=None):
+    """
+    Normalize a group of observations on a per feature basis.
+
+    Before running k-means, it is beneficial to rescale each feature
+    dimension of the observation set by its standard deviation (i.e. "whiten"
+    it - as in "white noise" where each frequency has equal power).
+    Each feature is divided by its standard deviation across all observations
+    to give it unit variance.
+
+    Parameters
+    ----------
+    obs : ndarray
+        Each row of the array is an observation.  The
+        columns are the features seen during each observation::
+
+            #        f0  f1  f2
+            obs = [[ 1., 1., 1.],  #o0
+                   [ 2., 2., 2.],  #o1
+                   [ 3., 3., 3.],  #o2
+                   [ 4., 4., 4.]]  #o3
+
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True for eager backends and False for lazy ones.
+
+    Returns
+    -------
+    result : ndarray
+        Contains the values in `obs` scaled by the standard deviation
+        of each column.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import whiten
+    >>> features  = np.array([[1.9, 2.3, 1.7],
+    ...                       [1.5, 2.5, 2.2],
+    ...                       [0.8, 0.6, 1.7,]])
+    >>> whiten(features)
+    array([[ 4.17944278,  2.69811351,  7.21248917],
+           [ 3.29956009,  2.93273208,  9.33380951],
+           [ 1.75976538,  0.7038557 ,  7.21248917]])
+
+    """
+    xp = array_namespace(obs)
+    if check_finite is None:
+        check_finite = not is_lazy_array(obs)
+    obs = _asarray(obs, check_finite=check_finite, xp=xp)
+    std_dev = xp.std(obs, axis=0)
+    zero_std_mask = std_dev == 0
+    std_dev = xpx.at(std_dev, zero_std_mask).set(1.0)
+    if check_finite and xp.any(zero_std_mask):
+        warnings.warn("Some columns have standard deviation zero. "
+                      "The values of these columns will not change.",
+                      RuntimeWarning, stacklevel=2)
+    return obs / std_dev
+
+
+@xp_capabilities(cpu_only=True, reason="uses spatial.distance.cdist",
+                 jax_jit=False, allow_dask_compute=True)
+def vq(obs, code_book, check_finite=True):
+    """
+    Assign codes from a code book to observations.
+
+    Assigns a code from a code book to each observation. Each
+    observation vector in the 'M' by 'N' `obs` array is compared with the
+    centroids in the code book and assigned the code of the closest
+    centroid.
+
+    The features in `obs` should have unit variance, which can be
+    achieved by passing them through the whiten function. The code
+    book can be created with the k-means algorithm or a different
+    encoding algorithm.
+
+    Parameters
+    ----------
+    obs : ndarray
+        Each row of the 'M' x 'N' array is an observation. The columns are
+        the "features" seen during each observation. The features must be
+        whitened first using the whiten function or something equivalent.
+    code_book : ndarray
+        The code book is usually generated using the k-means algorithm.
+        Each row of the array holds a different code, and the columns are
+        the features of the code::
+
+            #              f0  f1  f2  f3
+            code_book = [[ 1., 2., 3., 4.],  #c0
+                         [ 1., 2., 3., 4.],  #c1
+                         [ 1., 2., 3., 4.]]  #c2
+
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+
+    Returns
+    -------
+    code : ndarray
+        A length M array holding the code book index for each observation.
+    dist : ndarray
+        The distortion (distance) between the observation and its nearest
+        code.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import vq
+    >>> code_book = np.array([[1., 1., 1.],
+    ...                       [2., 2., 2.]])
+    >>> features  = np.array([[1.9, 2.3, 1.7],
+    ...                       [1.5, 2.5, 2.2],
+    ...                       [0.8, 0.6, 1.7]])
+    >>> vq(features, code_book)
+    (array([1, 1, 0], dtype=int32), array([0.43588989, 0.73484692, 0.83066239]))
+
+    """
+    xp = array_namespace(obs, code_book)
+    obs = _asarray(obs, xp=xp, check_finite=check_finite)
+    code_book = _asarray(code_book, xp=xp, check_finite=check_finite)
+    ct = xp.result_type(obs, code_book)
+
+    if xp.isdtype(ct, kind='real floating'):
+        c_obs = xp.astype(obs, ct, copy=False)
+        c_code_book = xp.astype(code_book, ct, copy=False)
+        c_obs = np.asarray(c_obs)
+        c_code_book = np.asarray(c_code_book)
+        result = _vq.vq(c_obs, c_code_book)
+        return xp.asarray(result[0]), xp.asarray(result[1])
+    return py_vq(obs, code_book, check_finite=False)
+
+
+def py_vq(obs, code_book, check_finite=True):
+    """ Python version of vq algorithm.
+
+    The algorithm computes the Euclidean distance between each
+    observation and every frame in the code_book.
+
+    Parameters
+    ----------
+    obs : ndarray
+        Expects a rank 2 array. Each row is one observation.
+    code_book : ndarray
+        Code book to use. Same format than obs. Should have same number of
+        features (e.g., columns) than obs.
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+
+    Returns
+    -------
+    code : ndarray
+        code[i] gives the label of the ith obversation; its code is
+        code_book[code[i]].
+    mind_dist : ndarray
+        min_dist[i] gives the distance between the ith observation and its
+        corresponding code.
+
+    Notes
+    -----
+    This function is slower than the C version but works for
+    all input types. If the inputs have the wrong types for the
+    C versions of the function, this one is called as a last resort.
+
+    It is about 20 times slower than the C version.
+
+    """
+    xp = array_namespace(obs, code_book)
+    obs = _asarray(obs, xp=xp, check_finite=check_finite)
+    code_book = _asarray(code_book, xp=xp, check_finite=check_finite)
+
+    if obs.ndim != code_book.ndim:
+        raise ValueError("Observation and code_book should have the same rank")
+
+    if obs.ndim == 1:
+        obs = obs[:, xp.newaxis]
+        code_book = code_book[:, xp.newaxis]
+
+    # Once `cdist` has array API support, this `xp.asarray` call can be removed
+    dist = xp.asarray(cdist(obs, code_book))
+    code = xp.argmin(dist, axis=1)
+    min_dist = xp.min(dist, axis=1)
+    return code, min_dist
+
+
+def _kmeans(obs, guess, thresh=1e-5, xp=None):
+    """ "raw" version of k-means.
+
+    Returns
+    -------
+    code_book
+        The lowest distortion codebook found.
+    avg_dist
+        The average distance a observation is from a code in the book.
+        Lower means the code_book matches the data better.
+
+    See Also
+    --------
+    kmeans : wrapper around k-means
+
+    Examples
+    --------
+    Note: not whitened in this example.
+
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import _kmeans
+    >>> features  = np.array([[ 1.9,2.3],
+    ...                       [ 1.5,2.5],
+    ...                       [ 0.8,0.6],
+    ...                       [ 0.4,1.8],
+    ...                       [ 1.0,1.0]])
+    >>> book = np.array((features[0],features[2]))
+    >>> _kmeans(features,book)
+    (array([[ 1.7       ,  2.4       ],
+           [ 0.73333333,  1.13333333]]), 0.40563916697728591)
+
+    """
+    xp = np if xp is None else xp
+    code_book = guess
+    diff = xp.inf
+    prev_avg_dists = deque([diff], maxlen=2)
+
+    np_obs = np.asarray(obs)
+    while diff > thresh:
+        # compute membership and distances between obs and code_book
+        obs_code, distort = vq(obs, code_book, check_finite=False)
+        prev_avg_dists.append(xp.mean(distort, axis=-1))
+        # recalc code_book as centroids of associated obs
+        obs_code = np.asarray(obs_code)
+        code_book, has_members = _vq.update_cluster_means(np_obs, obs_code,
+                                                          code_book.shape[0])
+        code_book = code_book[has_members]
+        code_book = xp.asarray(code_book)
+        diff = xp.abs(prev_avg_dists[0] - prev_avg_dists[1])
+
+    return code_book, prev_avg_dists[1]
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False, allow_dask_compute=True)
+@_transition_to_rng("seed")
+def kmeans(obs, k_or_guess, iter=20, thresh=1e-5, check_finite=True,
+           *, rng=None):
+    """
+    Performs k-means on a set of observation vectors forming k clusters.
+
+    The k-means algorithm adjusts the classification of the observations
+    into clusters and updates the cluster centroids until the position of
+    the centroids is stable over successive iterations. In this
+    implementation of the algorithm, the stability of the centroids is
+    determined by comparing the absolute value of the change in the average
+    Euclidean distance between the observations and their corresponding
+    centroids against a threshold. This yields
+    a code book mapping centroids to codes and vice versa.
+
+    Parameters
+    ----------
+    obs : ndarray
+       Each row of the M by N array is an observation vector. The
+       columns are the features seen during each observation.
+       The features must be whitened first with the `whiten` function.
+
+    k_or_guess : int or ndarray
+       The number of centroids to generate. A code is assigned to
+       each centroid, which is also the row index of the centroid
+       in the code_book matrix generated.
+
+       The initial k centroids are chosen by randomly selecting
+       observations from the observation matrix. Alternatively,
+       passing a k by N array specifies the initial k centroids.
+
+    iter : int, optional
+       The number of times to run k-means, returning the codebook
+       with the lowest distortion. This argument is ignored if
+       initial centroids are specified with an array for the
+       ``k_or_guess`` parameter. This parameter does not represent the
+       number of iterations of the k-means algorithm.
+
+    thresh : float, optional
+       Terminates the k-means algorithm if the change in
+       distortion since the last k-means iteration is less than
+       or equal to threshold.
+
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    codebook : ndarray
+       A k by N array of k centroids. The ith centroid
+       codebook[i] is represented with the code i. The centroids
+       and codes generated represent the lowest distortion seen,
+       not necessarily the globally minimal distortion.
+       Note that the number of centroids is not necessarily the same as the
+       ``k_or_guess`` parameter, because centroids assigned to no observations
+       are removed during iterations.
+
+    distortion : float
+       The mean (non-squared) Euclidean distance between the observations
+       passed and the centroids generated. Note the difference to the standard
+       definition of distortion in the context of the k-means algorithm, which
+       is the sum of the squared distances.
+
+    See Also
+    --------
+    kmeans2 : a different implementation of k-means clustering
+       with more methods for generating initial centroids but without
+       using a distortion change threshold as a stopping criterion.
+
+    whiten : must be called prior to passing an observation matrix
+       to kmeans.
+
+    Notes
+    -----
+    For more functionalities or optimal performance, you can use
+    `sklearn.cluster.KMeans <https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html>`_.
+    `This <https://hdbscan.readthedocs.io/en/latest/performance_and_scalability.html#comparison-of-high-performance-implementations>`_
+    is a benchmark result of several implementations.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import vq, kmeans, whiten
+    >>> import matplotlib.pyplot as plt
+    >>> features  = np.array([[ 1.9,2.3],
+    ...                       [ 1.5,2.5],
+    ...                       [ 0.8,0.6],
+    ...                       [ 0.4,1.8],
+    ...                       [ 0.1,0.1],
+    ...                       [ 0.2,1.8],
+    ...                       [ 2.0,0.5],
+    ...                       [ 0.3,1.5],
+    ...                       [ 1.0,1.0]])
+    >>> whitened = whiten(features)
+    >>> book = np.array((whitened[0],whitened[2]))
+    >>> kmeans(whitened,book)
+    (array([[ 2.3110306 ,  2.86287398],    # random
+           [ 0.93218041,  1.24398691]]), 0.85684700941625547)
+
+    >>> codes = 3
+    >>> kmeans(whitened,codes)
+    (array([[ 2.3110306 ,  2.86287398],    # random
+           [ 1.32544402,  0.65607529],
+           [ 0.40782893,  2.02786907]]), 0.5196582527686241)
+
+    >>> # Create 50 datapoints in two clusters a and b
+    >>> pts = 50
+    >>> rng = np.random.default_rng()
+    >>> a = rng.multivariate_normal([0, 0], [[4, 1], [1, 4]], size=pts)
+    >>> b = rng.multivariate_normal([30, 10],
+    ...                             [[10, 2], [2, 1]],
+    ...                             size=pts)
+    >>> features = np.concatenate((a, b))
+    >>> # Whiten data
+    >>> whitened = whiten(features)
+    >>> # Find 2 clusters in the data
+    >>> codebook, distortion = kmeans(whitened, 2)
+    >>> # Plot whitened data and cluster centers in red
+    >>> plt.scatter(whitened[:, 0], whitened[:, 1])
+    >>> plt.scatter(codebook[:, 0], codebook[:, 1], c='r')
+    >>> plt.show()
+
+    """
+    if isinstance(k_or_guess, int):
+        xp = array_namespace(obs)
+    else:
+        xp = array_namespace(obs, k_or_guess)
+    obs = _asarray(obs, xp=xp, check_finite=check_finite)
+    guess = _asarray(k_or_guess, xp=xp, check_finite=check_finite)
+    if iter < 1:
+        raise ValueError(f"iter must be at least 1, got {iter}")
+
+    # Determine whether a count (scalar) or an initial guess (array) was passed.
+    if xp_size(guess) != 1:
+        if xp_size(guess) < 1:
+            raise ValueError(f"Asked for 0 clusters. Initial book was {guess}")
+        return _kmeans(obs, guess, thresh=thresh, xp=xp)
+
+    # k_or_guess is a scalar, now verify that it's an integer
+    k = int(guess)
+    if k != guess:
+        raise ValueError("If k_or_guess is a scalar, it must be an integer.")
+    if k < 1:
+        raise ValueError(f"Asked for {k} clusters.")
+
+    rng = check_random_state(rng)
+
+    # initialize best distance value to a large value
+    best_dist = xp.inf
+    for i in range(iter):
+        # the initial code book is randomly selected from observations
+        guess = _kpoints(obs, k, rng, xp)
+        book, dist = _kmeans(obs, guess, thresh=thresh, xp=xp)
+        if dist < best_dist:
+            best_book = book
+            best_dist = dist
+    return best_book, best_dist
+
+
+def _kpoints(data, k, rng, xp):
+    """Pick k points at random in data (one row = one observation).
+
+    Parameters
+    ----------
+    data : ndarray
+        Expect a rank 1 or 2 array. Rank 1 are assumed to describe one
+        dimensional data, rank 2 multidimensional data, in which case one
+        row is one observation.
+    k : int
+        Number of samples to generate.
+    rng : `numpy.random.Generator` or `numpy.random.RandomState`
+        Random number generator.
+
+    Returns
+    -------
+    x : ndarray
+        A 'k' by 'N' containing the initial centroids
+
+    """
+    idx = rng.choice(data.shape[0], size=int(k), replace=False)
+    # convert to array with default integer dtype (avoids numpy#25607)
+    idx = xp.asarray(idx, dtype=xp.asarray([1]).dtype)
+    return xp.take(data, idx, axis=0)
+
+
+def _krandinit(data, k, rng, xp):
+    """Returns k samples of a random variable whose parameters depend on data.
+
+    More precisely, it returns k observations sampled from a Gaussian random
+    variable whose mean and covariances are the ones estimated from the data.
+
+    Parameters
+    ----------
+    data : ndarray
+        Expect a rank 1 or 2 array. Rank 1 is assumed to describe 1-D
+        data, rank 2 multidimensional data, in which case one
+        row is one observation.
+    k : int
+        Number of samples to generate.
+    rng : `numpy.random.Generator` or `numpy.random.RandomState`
+        Random number generator.
+
+    Returns
+    -------
+    x : ndarray
+        A 'k' by 'N' containing the initial centroids
+
+    """
+    mu = xp.mean(data, axis=0)
+    k = np.asarray(k)
+
+    if data.ndim == 1:
+        _cov = xpx.cov(data, xp=xp)
+        x = rng.standard_normal(size=k)
+        x = xp.asarray(x)
+        x *= xp.sqrt(_cov)
+    elif data.shape[1] > data.shape[0]:
+        # initialize when the covariance matrix is rank deficient
+        _, s, vh = xp.linalg.svd(data - mu, full_matrices=False)
+        x = rng.standard_normal(size=(k, xp_size(s)))
+        x = xp.asarray(x)
+        sVh = s[:, None] * vh / xp.sqrt(data.shape[0] - xp.asarray(1.))
+        x = x @ sVh
+    else:
+        _cov = xpx.atleast_nd(xpx.cov(data.T, xp=xp), ndim=2, xp=xp)
+
+        # k rows, d cols (one row = one obs)
+        # Generate k sample of a random variable ~ Gaussian(mu, cov)
+        x = rng.standard_normal(size=(k, xp_size(mu)))
+        x = xp.asarray(x)
+        x = x @ xp.linalg.cholesky(_cov).T
+
+    x += mu
+    return x
+
+
+def _kpp(data, k, rng, xp):
+    """ Picks k points in the data based on the kmeans++ method.
+
+    Parameters
+    ----------
+    data : ndarray
+        Expect a rank 1 or 2 array. Rank 1 is assumed to describe 1-D
+        data, rank 2 multidimensional data, in which case one
+        row is one observation.
+    k : int
+        Number of samples to generate.
+    rng : `numpy.random.Generator` or `numpy.random.RandomState`
+        Random number generator.
+
+    Returns
+    -------
+    init : ndarray
+        A 'k' by 'N' containing the initial centroids.
+
+    References
+    ----------
+    .. [1] D. Arthur and S. Vassilvitskii, "k-means++: the advantages of
+       careful seeding", Proceedings of the Eighteenth Annual ACM-SIAM Symposium
+       on Discrete Algorithms, 2007.
+    """
+
+    ndim = len(data.shape)
+    if ndim == 1:
+        data = data[:, None]
+
+    dims = data.shape[1]
+
+    init = xp.empty((int(k), dims))
+
+    for i in range(k):
+        if i == 0:
+            data_idx = rng_integers(rng, data.shape[0])
+        else:
+            D2 = cdist(init[:i,:], data, metric='sqeuclidean').min(axis=0)
+            probs = D2/D2.sum()
+            cumprobs = probs.cumsum()
+            r = rng.uniform()
+            cumprobs = np.asarray(cumprobs)
+            data_idx = int(np.searchsorted(cumprobs, r))
+
+        init = xpx.at(init)[i, :].set(data[data_idx, :])
+
+    if ndim == 1:
+        init = init[:, 0]
+    return init
+
+
+_valid_init_meth = {'random': _krandinit, 'points': _kpoints, '++': _kpp}
+
+
+def _missing_warn():
+    """Print a warning when called."""
+    warnings.warn("One of the clusters is empty. "
+                  "Re-run kmeans with a different initialization.",
+                  stacklevel=3)
+
+
+def _missing_raise():
+    """Raise a ClusterError when called."""
+    raise ClusterError("One of the clusters is empty. "
+                       "Re-run kmeans with a different initialization.")
+
+
+_valid_miss_meth = {'warn': _missing_warn, 'raise': _missing_raise}
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False, allow_dask_compute=True)
+@_transition_to_rng("seed")
+def kmeans2(data, k, iter=10, thresh=1e-5, minit='random',
+            missing='warn', check_finite=True, *, rng=None):
+    """
+    Classify a set of observations into k clusters using the k-means algorithm.
+
+    The algorithm attempts to minimize the Euclidean distance between
+    observations and centroids. Several initialization methods are
+    included.
+
+    Parameters
+    ----------
+    data : ndarray
+        A 'M' by 'N' array of 'M' observations in 'N' dimensions or a length
+        'M' array of 'M' 1-D observations.
+    k : int or ndarray
+        The number of clusters to form as well as the number of
+        centroids to generate. If `minit` initialization string is
+        'matrix', or if a ndarray is given instead, it is
+        interpreted as initial cluster to use instead.
+    iter : int, optional
+        Number of iterations of the k-means algorithm to run. Note
+        that this differs in meaning from the iters parameter to
+        the kmeans function.
+    thresh : float, optional
+        (not used yet)
+    minit : str, optional
+        Method for initialization. Available methods are 'random',
+        'points', '++' and 'matrix':
+
+        'random': generate k centroids from a Gaussian with mean and
+        variance estimated from the data.
+
+        'points': choose k observations (rows) at random from data for
+        the initial centroids.
+
+        '++': choose k observations accordingly to the kmeans++ method
+        (careful seeding)
+
+        'matrix': interpret the k parameter as a k by M (or length k
+        array for 1-D data) array of initial centroids.
+    missing : str, optional
+        Method to deal with empty clusters. Available methods are
+        'warn' and 'raise':
+
+        'warn': give a warning and continue.
+
+        'raise': raise an ClusterError and terminate the algorithm.
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    centroid : ndarray
+        A 'k' by 'N' array of centroids found at the last iteration of
+        k-means.
+    label : ndarray
+        label[i] is the code or index of the centroid the
+        ith observation is closest to.
+
+    See Also
+    --------
+    kmeans
+
+    References
+    ----------
+    .. [1] D. Arthur and S. Vassilvitskii, "k-means++: the advantages of
+       careful seeding", Proceedings of the Eighteenth Annual ACM-SIAM Symposium
+       on Discrete Algorithms, 2007.
+
+    Examples
+    --------
+    >>> from scipy.cluster.vq import kmeans2
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    Create z, an array with shape (100, 2) containing a mixture of samples
+    from three multivariate normal distributions.
+
+    >>> rng = np.random.default_rng()
+    >>> a = rng.multivariate_normal([0, 6], [[2, 1], [1, 1.5]], size=45)
+    >>> b = rng.multivariate_normal([2, 0], [[1, -1], [-1, 3]], size=30)
+    >>> c = rng.multivariate_normal([6, 4], [[5, 0], [0, 1.2]], size=25)
+    >>> z = np.concatenate((a, b, c))
+    >>> rng.shuffle(z)
+
+    Compute three clusters.
+
+    >>> centroid, label = kmeans2(z, 3, minit='points')
+    >>> centroid
+    array([[ 2.22274463, -0.61666946],  # may vary
+           [ 0.54069047,  5.86541444],
+           [ 6.73846769,  4.01991898]])
+
+    How many points are in each cluster?
+
+    >>> counts = np.bincount(label)
+    >>> counts
+    array([29, 51, 20])  # may vary
+
+    Plot the clusters.
+
+    >>> w0 = z[label == 0]
+    >>> w1 = z[label == 1]
+    >>> w2 = z[label == 2]
+    >>> plt.plot(w0[:, 0], w0[:, 1], 'o', alpha=0.5, label='cluster 0')
+    >>> plt.plot(w1[:, 0], w1[:, 1], 'd', alpha=0.5, label='cluster 1')
+    >>> plt.plot(w2[:, 0], w2[:, 1], 's', alpha=0.5, label='cluster 2')
+    >>> plt.plot(centroid[:, 0], centroid[:, 1], 'k*', label='centroids')
+    >>> plt.axis('equal')
+    >>> plt.legend(shadow=True)
+    >>> plt.show()
+
+    """
+    if int(iter) < 1:
+        raise ValueError(f"Invalid iter ({iter}), must be a positive integer.")
+    try:
+        miss_meth = _valid_miss_meth[missing]
+    except KeyError as e:
+        raise ValueError(f"Unknown missing method {missing!r}") from e
+
+    if isinstance(k, int):
+        xp = array_namespace(data)
+    else:
+        xp = array_namespace(data, k)
+    data = _asarray(data, xp=xp, check_finite=check_finite)
+    code_book = xp_copy(k, xp=xp)
+    if data.ndim == 1:
+        d = 1
+    elif data.ndim == 2:
+        d = data.shape[1]
+    else:
+        raise ValueError("Input of rank > 2 is not supported.")
+
+    if xp_size(data) < 1 or xp_size(code_book) < 1:
+        raise ValueError("Empty input is not supported.")
+
+    # If k is not a single value, it should be compatible with data's shape
+    if minit == 'matrix' or xp_size(code_book) > 1:
+        if data.ndim != code_book.ndim:
+            raise ValueError("k array doesn't match data rank")
+        nc = code_book.shape[0]
+        if data.ndim > 1 and code_book.shape[1] != d:
+            raise ValueError("k array doesn't match data dimension")
+    else:
+        nc = int(code_book)
+
+        if nc < 1:
+            raise ValueError(
+                f"Cannot ask kmeans2 for {nc} clusters (k was {code_book})"
+            )
+        elif nc != code_book:
+            warnings.warn("k was not an integer, was converted.", stacklevel=2)
+
+        try:
+            init_meth = _valid_init_meth[minit]
+        except KeyError as e:
+            raise ValueError(f"Unknown init method {minit!r}") from e
+        else:
+            rng = check_random_state(rng)
+            code_book = init_meth(data, code_book, rng, xp)
+
+    data = np.asarray(data)
+    code_book = np.asarray(code_book)
+    for _ in range(iter):
+        # Compute the nearest neighbor for each obs using the current code book
+        label = vq(data, code_book, check_finite=check_finite)[0]
+        # Update the code book by computing centroids
+        new_code_book, has_members = _vq.update_cluster_means(data, label, nc)
+        if not has_members.all():
+            miss_meth()
+            # Set the empty clusters to their previous positions
+            new_code_book[~has_members] = code_book[~has_members]
+        code_book = new_code_book
+
+    return xp.asarray(code_book), xp.asarray(label)

tool_server/.venv/lib/python3.12/site-packages/scipy/constants/__init__.py

@@ -0,0 +1,358 @@
+r"""
+==================================
+Constants (:mod:`scipy.constants`)
+==================================
+
+.. currentmodule:: scipy.constants
+
+Physical and mathematical constants and units.
+
+
+Mathematical constants
+======================
+
+================  =================================================================
+``pi``            Pi
+``golden``        Golden ratio
+``golden_ratio``  Golden ratio
+================  =================================================================
+
+
+Physical constants
+==================
+The following physical constants are available as attributes of `scipy.constants`.
+All units are `SI <https://en.wikipedia.org/wiki/International_System_of_Units>`_.
+
+===========================  ================================================================  ===============
+Attribute                    Quantity                                                          Units
+===========================  ================================================================  ===============
+``c``                        speed of light in vacuum                                          m s^-1
+``speed_of_light``           speed of light in vacuum                                          m s^-1
+``mu_0``                     the magnetic constant :math:`\mu_0`                               N A^-2
+``epsilon_0``                the electric constant (vacuum permittivity), :math:`\epsilon_0`   F m^-1
+``h``                        the Planck constant :math:`h`                                     J Hz^-1
+``Planck``                   the Planck constant :math:`h`                                     J Hz^-1
+``hbar``                     the reduced Planck constant, :math:`\hbar = h/(2\pi)`             J s
+``G``                        Newtonian constant of gravitation                                 m^3 kg^-1 s^-2
+``gravitational_constant``   Newtonian constant of gravitation                                 m^3 kg^-1 s^-2
+``g``                        standard acceleration of gravity                                  m s^-2
+``e``                        elementary charge                                                 C
+``elementary_charge``        elementary charge                                                 C
+``R``                        molar gas constant                                                J mol^-1 K^-1
+``gas_constant``             molar gas constant                                                J mol^-1 K^-1
+``alpha``                    fine-structure constant                                           (unitless)
+``fine_structure``           fine-structure constant                                           (unitless)
+``N_A``                      Avogadro constant                                                 mol^-1
+``Avogadro``                 Avogadro constant                                                 mol^-1
+``k``                        Boltzmann constant                                                J K^-1
+``Boltzmann``                Boltzmann constant                                                J K^-1
+``sigma``                    Stefan-Boltzmann constant :math:`\sigma`                          W m^-2 K^-4
+``Stefan_Boltzmann``         Stefan-Boltzmann constant :math:`\sigma`                          W m^-2 K^-4
+``Wien``                     Wien wavelength displacement law constant                         m K
+``Rydberg``                  Rydberg constant                                                  m^-1
+``m_e``                      electron mass                                                     kg
+``electron_mass``            electron mass                                                     kg
+``m_p``                      proton mass                                                       kg
+``proton_mass``              proton mass                                                       kg
+``m_n``                      neutron mass                                                      kg
+``neutron_mass``             neutron mass                                                      kg
+===========================  ================================================================  ===============
+
+
+Constants database
+------------------
+
+In addition to the above variables, :mod:`scipy.constants` also contains the
+2022 CODATA recommended values [CODATA2022]_ database containing more physical
+constants.
+
+.. autosummary::
+   :toctree: generated/
+
+   value      -- Value in physical_constants indexed by key
+   unit       -- Unit in physical_constants indexed by key
+   precision  -- Relative precision in physical_constants indexed by key
+   find       -- Return list of physical_constant keys with a given string
+   ConstantWarning -- Constant sought not in newest CODATA data set
+
+.. data:: physical_constants
+
+   Dictionary of physical constants, of the format
+   ``physical_constants[name] = (value, unit, uncertainty)``.
+   The CODATA database uses ellipses to indicate that a value is defined
+   (exactly) in terms of others but cannot be represented exactly with the
+   allocated number of digits. In these cases, SciPy calculates the derived
+   value and reports it to the full precision of a Python ``float``. Although 
+   ``physical_constants`` lists the uncertainty as ``0.0`` to indicate that
+   the CODATA value is exact, the value in ``physical_constants`` is still
+   subject to the truncation error inherent in double-precision representation.
+
+Available constants:
+
+======================================================================  ====
+%(constant_names)s
+======================================================================  ====
+
+
+Units
+=====
+
+SI prefixes
+-----------
+
+============  =================================================================
+``quetta``    :math:`10^{30}`
+``ronna``     :math:`10^{27}`
+``yotta``     :math:`10^{24}`
+``zetta``     :math:`10^{21}`
+``exa``       :math:`10^{18}`
+``peta``      :math:`10^{15}`
+``tera``      :math:`10^{12}`
+``giga``      :math:`10^{9}`
+``mega``      :math:`10^{6}`
+``kilo``      :math:`10^{3}`
+``hecto``     :math:`10^{2}`
+``deka``      :math:`10^{1}`
+``deci``      :math:`10^{-1}`
+``centi``     :math:`10^{-2}`
+``milli``     :math:`10^{-3}`
+``micro``     :math:`10^{-6}`
+``nano``      :math:`10^{-9}`
+``pico``      :math:`10^{-12}`
+``femto``     :math:`10^{-15}`
+``atto``      :math:`10^{-18}`
+``zepto``     :math:`10^{-21}`
+``yocto``     :math:`10^{-24}`
+``ronto``     :math:`10^{-27}`
+``quecto``    :math:`10^{-30}`
+============  =================================================================
+
+Binary prefixes
+---------------
+
+============  =================================================================
+``kibi``      :math:`2^{10}`
+``mebi``      :math:`2^{20}`
+``gibi``      :math:`2^{30}`
+``tebi``      :math:`2^{40}`
+``pebi``      :math:`2^{50}`
+``exbi``      :math:`2^{60}`
+``zebi``      :math:`2^{70}`
+``yobi``      :math:`2^{80}`
+============  =================================================================
+
+Mass
+----
+
+=================  ============================================================
+``gram``           :math:`10^{-3}` kg
+``metric_ton``     :math:`10^{3}` kg
+``grain``          one grain in kg
+``lb``             one pound (avoirdupous) in kg
+``pound``          one pound (avoirdupous) in kg
+``blob``           one inch version of a slug in kg (added in 1.0.0)
+``slinch``         one inch version of a slug in kg (added in 1.0.0)
+``slug``           one slug in kg (added in 1.0.0)
+``oz``             one ounce in kg
+``ounce``          one ounce in kg
+``stone``          one stone in kg
+``grain``          one grain in kg
+``long_ton``       one long ton in kg
+``short_ton``      one short ton in kg
+``troy_ounce``     one Troy ounce in kg
+``troy_pound``     one Troy pound in kg
+``carat``          one carat in kg
+``m_u``            atomic mass constant (in kg)
+``u``              atomic mass constant (in kg)
+``atomic_mass``    atomic mass constant (in kg)
+=================  ============================================================
+
+Angle
+-----
+
+=================  ============================================================
+``degree``         degree in radians
+``arcmin``         arc minute in radians
+``arcminute``      arc minute in radians
+``arcsec``         arc second in radians
+``arcsecond``      arc second in radians
+=================  ============================================================
+
+
+Time
+----
+
+=================  ============================================================
+``minute``         one minute in seconds
+``hour``           one hour in seconds
+``day``            one day in seconds
+``week``           one week in seconds
+``year``           one year (365 days) in seconds
+``Julian_year``    one Julian year (365.25 days) in seconds
+=================  ============================================================
+
+
+Length
+------
+
+=====================  ============================================================
+``inch``               one inch in meters
+``foot``               one foot in meters
+``yard``               one yard in meters
+``mile``               one mile in meters
+``mil``                one mil in meters
+``pt``                 one point in meters
+``point``              one point in meters
+``survey_foot``        one survey foot in meters
+``survey_mile``        one survey mile in meters
+``nautical_mile``      one nautical mile in meters
+``fermi``              one Fermi in meters
+``angstrom``           one Angstrom in meters
+``micron``             one micron in meters
+``au``                 one astronomical unit in meters
+``astronomical_unit``  one astronomical unit in meters
+``light_year``         one light year in meters
+``parsec``             one parsec in meters
+=====================  ============================================================
+
+Pressure
+--------
+
+=================  ============================================================
+``atm``            standard atmosphere in pascals
+``atmosphere``     standard atmosphere in pascals
+``bar``            one bar in pascals
+``torr``           one torr (mmHg) in pascals
+``mmHg``           one torr (mmHg) in pascals
+``psi``            one psi in pascals
+=================  ============================================================
+
+Area
+----
+
+=================  ============================================================
+``hectare``        one hectare in square meters
+``acre``           one acre in square meters
+=================  ============================================================
+
+
+Volume
+------
+
+===================    ========================================================
+``liter``              one liter in cubic meters
+``litre``              one liter in cubic meters
+``gallon``             one gallon (US) in cubic meters
+``gallon_US``          one gallon (US) in cubic meters
+``gallon_imp``         one gallon (UK) in cubic meters
+``fluid_ounce``        one fluid ounce (US) in cubic meters
+``fluid_ounce_US``     one fluid ounce (US) in cubic meters
+``fluid_ounce_imp``    one fluid ounce (UK) in cubic meters
+``bbl``                one barrel in cubic meters
+``barrel``             one barrel in cubic meters
+===================    ========================================================
+
+Speed
+-----
+
+==================    ==========================================================
+``kmh``               kilometers per hour in meters per second
+``mph``               miles per hour in meters per second
+``mach``              one Mach (approx., at 15 C, 1 atm) in meters per second
+``speed_of_sound``    one Mach (approx., at 15 C, 1 atm) in meters per second
+``knot``              one knot in meters per second
+==================    ==========================================================
+
+
+Temperature
+-----------
+
+=====================  =======================================================
+``zero_Celsius``       zero of Celsius scale in Kelvin
+``degree_Fahrenheit``  one Fahrenheit (only differences) in Kelvins
+=====================  =======================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   convert_temperature
+
+Energy
+------
+
+====================  =======================================================
+``eV``                one electron volt in Joules
+``electron_volt``     one electron volt in Joules
+``calorie``           one calorie (thermochemical) in Joules
+``calorie_th``        one calorie (thermochemical) in Joules
+``calorie_IT``        one calorie (International Steam Table calorie, 1956) in Joules
+``erg``               one erg in Joules
+``Btu``               one British thermal unit (International Steam Table) in Joules
+``Btu_IT``            one British thermal unit (International Steam Table) in Joules
+``Btu_th``            one British thermal unit (thermochemical) in Joules
+``ton_TNT``           one ton of TNT in Joules
+====================  =======================================================
+
+Power
+-----
+
+====================  =======================================================
+``hp``                one horsepower in watts
+``horsepower``        one horsepower in watts
+====================  =======================================================
+
+Force
+-----
+
+====================  =======================================================
+``dyn``               one dyne in newtons
+``dyne``              one dyne in newtons
+``lbf``               one pound force in newtons
+``pound_force``       one pound force in newtons
+``kgf``               one kilogram force in newtons
+``kilogram_force``    one kilogram force in newtons
+====================  =======================================================
+
+Optics
+------
+
+.. autosummary::
+   :toctree: generated/
+
+   lambda2nu
+   nu2lambda
+
+References
+==========
+
+.. [CODATA2022] CODATA Recommended Values of the Fundamental
+   Physical Constants 2022.
+
+   https://physics.nist.gov/cuu/Constants/
+
+"""  # noqa: E501
+# Modules contributed by BasSw (wegwerp@gmail.com)
+from ._codata import *
+from ._constants import *
+from ._codata import _obsolete_constants, physical_constants
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import codata, constants
+
+_constant_names_list = [(_k.lower(), _k, _v)
+                        for _k, _v in physical_constants.items()
+                        if _k not in _obsolete_constants]
+_constant_names = "\n".join(["``{}``{}  {} {}".format(_x[1], " "*(66-len(_x[1])),
+                                                  _x[2][0], _x[2][1])
+                             for _x in sorted(_constant_names_list)])
+if __doc__:
+    __doc__ = __doc__ % dict(constant_names=_constant_names)
+
+del _constant_names
+del _constant_names_list
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

tool_server/.venv/lib/python3.12/site-packages/scipy/constants/_constants.py

@@ -0,0 +1,369 @@
+"""
+Collection of physical constants and conversion factors.
+
+Most constants are in SI units, so you can do
+print '10 mile per minute is', 10*mile/minute, 'm/s or', 10*mile/(minute*knot), 'knots'
+
+The list is not meant to be comprehensive, but just convenient for everyday use.
+"""
+
+import math as _math
+from typing import TYPE_CHECKING, Any
+
+from ._codata import value as _cd
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+from scipy._lib._array_api import array_namespace, _asarray, xp_capabilities
+
+
+"""
+BasSw 2006
+physical constants: imported from CODATA
+unit conversion: see e.g., NIST special publication 811
+Use at own risk: double-check values before calculating your Mars orbit-insertion burn.
+Some constants exist in a few variants, which are marked with suffixes.
+The ones without any suffix should be the most common ones.
+"""
+
+__all__ = [
+    'Avogadro', 'Boltzmann', 'Btu', 'Btu_IT', 'Btu_th', 'G',
+    'Julian_year', 'N_A', 'Planck', 'R', 'Rydberg',
+    'Stefan_Boltzmann', 'Wien', 'acre', 'alpha',
+    'angstrom', 'arcmin', 'arcminute', 'arcsec',
+    'arcsecond', 'astronomical_unit', 'atm',
+    'atmosphere', 'atomic_mass', 'atto', 'au', 'bar',
+    'barrel', 'bbl', 'blob', 'c', 'calorie',
+    'calorie_IT', 'calorie_th', 'carat', 'centi',
+    'convert_temperature', 'day', 'deci', 'degree',
+    'degree_Fahrenheit', 'deka', 'dyn', 'dyne', 'e',
+    'eV', 'electron_mass', 'electron_volt',
+    'elementary_charge', 'epsilon_0', 'erg',
+    'exa', 'exbi', 'femto', 'fermi', 'fine_structure',
+    'fluid_ounce', 'fluid_ounce_US', 'fluid_ounce_imp',
+    'foot', 'g', 'gallon', 'gallon_US', 'gallon_imp',
+    'gas_constant', 'gibi', 'giga', 'golden', 'golden_ratio',
+    'grain', 'gram', 'gravitational_constant', 'h', 'hbar',
+    'hectare', 'hecto', 'horsepower', 'hour', 'hp',
+    'inch', 'k', 'kgf', 'kibi', 'kilo', 'kilogram_force',
+    'kmh', 'knot', 'lambda2nu', 'lb', 'lbf',
+    'light_year', 'liter', 'litre', 'long_ton', 'm_e',
+    'm_n', 'm_p', 'm_u', 'mach', 'mebi', 'mega',
+    'metric_ton', 'micro', 'micron', 'mil', 'mile',
+    'milli', 'minute', 'mmHg', 'mph', 'mu_0', 'nano',
+    'nautical_mile', 'neutron_mass', 'nu2lambda',
+    'ounce', 'oz', 'parsec', 'pebi', 'peta',
+    'pi', 'pico', 'point', 'pound', 'pound_force',
+    'proton_mass', 'psi', 'pt', 'quecto', 'quetta', 'ronna', 'ronto',
+    'short_ton', 'sigma', 'slinch', 'slug', 'speed_of_light',
+    'speed_of_sound', 'stone', 'survey_foot',
+    'survey_mile', 'tebi', 'tera', 'ton_TNT',
+    'torr', 'troy_ounce', 'troy_pound', 'u',
+    'week', 'yard', 'year', 'yobi', 'yocto',
+    'yotta', 'zebi', 'zepto', 'zero_Celsius', 'zetta'
+]
+
+
+# mathematical constants
+pi = _math.pi
+golden = golden_ratio = (1 + _math.sqrt(5)) / 2
+
+# SI prefixes
+quetta = 1e30
+ronna = 1e27
+yotta = 1e24
+zetta = 1e21
+exa = 1e18
+peta = 1e15
+tera = 1e12
+giga = 1e9
+mega = 1e6
+kilo = 1e3
+hecto = 1e2
+deka = 1e1
+deci = 1e-1
+centi = 1e-2
+milli = 1e-3
+micro = 1e-6
+nano = 1e-9
+pico = 1e-12
+femto = 1e-15
+atto = 1e-18
+zepto = 1e-21
+yocto = 1e-24
+ronto = 1e-27
+quecto = 1e-30
+
+# binary prefixes
+kibi = 2**10
+mebi = 2**20
+gibi = 2**30
+tebi = 2**40
+pebi = 2**50
+exbi = 2**60
+zebi = 2**70
+yobi = 2**80
+
+# physical constants
+c = speed_of_light = _cd('speed of light in vacuum')
+mu_0 = _cd('vacuum mag. permeability')
+epsilon_0 = _cd('vacuum electric permittivity')
+h = Planck = _cd('Planck constant')
+hbar = _cd('reduced Planck constant')
+G = gravitational_constant = _cd('Newtonian constant of gravitation')
+g = _cd('standard acceleration of gravity')
+e = elementary_charge = _cd('elementary charge')
+R = gas_constant = _cd('molar gas constant')
+alpha = fine_structure = _cd('fine-structure constant')
+N_A = Avogadro = _cd('Avogadro constant')
+k = Boltzmann = _cd('Boltzmann constant')
+sigma = Stefan_Boltzmann = _cd('Stefan-Boltzmann constant')
+Wien = _cd('Wien wavelength displacement law constant')
+Rydberg = _cd('Rydberg constant')
+
+# mass in kg
+gram = 1e-3
+metric_ton = 1e3
+grain = 64.79891e-6
+lb = pound = 7000 * grain  # avoirdupois
+blob = slinch = pound * g / 0.0254  # lbf*s**2/in (added in 1.0.0)
+slug = blob / 12  # lbf*s**2/foot (added in 1.0.0)
+oz = ounce = pound / 16
+stone = 14 * pound
+long_ton = 2240 * pound
+short_ton = 2000 * pound
+
+troy_ounce = 480 * grain  # only for metals / gems
+troy_pound = 12 * troy_ounce
+carat = 200e-6
+
+m_e = electron_mass = _cd('electron mass')
+m_p = proton_mass = _cd('proton mass')
+m_n = neutron_mass = _cd('neutron mass')
+m_u = u = atomic_mass = _cd('atomic mass constant')
+
+# angle in rad
+degree = pi / 180
+arcmin = arcminute = degree / 60
+arcsec = arcsecond = arcmin / 60
+
+# time in second
+minute = 60.0
+hour = 60 * minute
+day = 24 * hour
+week = 7 * day
+year = 365 * day
+Julian_year = 365.25 * day
+
+# length in meter
+inch = 0.0254
+foot = 12 * inch
+yard = 3 * foot
+mile = 1760 * yard
+mil = inch / 1000
+pt = point = inch / 72  # typography
+survey_foot = 1200.0 / 3937
+survey_mile = 5280 * survey_foot
+nautical_mile = 1852.0
+fermi = 1e-15
+angstrom = 1e-10
+micron = 1e-6
+au = astronomical_unit = 149597870700.0
+light_year = Julian_year * c
+parsec = au / arcsec
+
+# pressure in pascal
+atm = atmosphere = _cd('standard atmosphere')
+bar = 1e5
+torr = mmHg = atm / 760
+psi = pound * g / (inch * inch)
+
+# area in meter**2
+hectare = 1e4
+acre = 43560 * foot**2
+
+# volume in meter**3
+litre = liter = 1e-3
+gallon = gallon_US = 231 * inch**3  # US
+# pint = gallon_US / 8
+fluid_ounce = fluid_ounce_US = gallon_US / 128
+bbl = barrel = 42 * gallon_US  # for oil
+
+gallon_imp = 4.54609e-3  # UK
+fluid_ounce_imp = gallon_imp / 160
+
+# speed in meter per second
+kmh = 1e3 / hour
+mph = mile / hour
+# approx value of mach at 15 degrees in 1 atm. Is this a common value?
+mach = speed_of_sound = 340.5
+knot = nautical_mile / hour
+
+# temperature in kelvin
+zero_Celsius = 273.15
+degree_Fahrenheit = 1/1.8  # only for differences
+
+# energy in joule
+eV = electron_volt = elementary_charge  # * 1 Volt
+calorie = calorie_th = 4.184
+calorie_IT = 4.1868
+erg = 1e-7
+Btu_th = pound * degree_Fahrenheit * calorie_th / gram
+Btu = Btu_IT = pound * degree_Fahrenheit * calorie_IT / gram
+ton_TNT = 1e9 * calorie_th
+# Wh = watt_hour
+
+# power in watt
+hp = horsepower = 550 * foot * pound * g
+
+# force in newton
+dyn = dyne = 1e-5
+lbf = pound_force = pound * g
+kgf = kilogram_force = g  # * 1 kg
+
+# functions for conversions that are not linear
+
+
+@xp_capabilities()
+def convert_temperature(
+    val: "npt.ArrayLike",
+    old_scale: str,
+    new_scale: str,
+) -> Any:
+    """
+    Convert from a temperature scale to another one among Celsius, Kelvin,
+    Fahrenheit, and Rankine scales.
+
+    Parameters
+    ----------
+    val : array_like
+        Value(s) of the temperature(s) to be converted expressed in the
+        original scale.
+    old_scale : str
+        Specifies as a string the original scale from which the temperature
+        value(s) will be converted. Supported scales are Celsius ('Celsius',
+        'celsius', 'C' or 'c'), Kelvin ('Kelvin', 'kelvin', 'K', 'k'),
+        Fahrenheit ('Fahrenheit', 'fahrenheit', 'F' or 'f'), and Rankine
+        ('Rankine', 'rankine', 'R', 'r').
+    new_scale : str
+        Specifies as a string the new scale to which the temperature
+        value(s) will be converted. Supported scales are Celsius ('Celsius',
+        'celsius', 'C' or 'c'), Kelvin ('Kelvin', 'kelvin', 'K', 'k'),
+        Fahrenheit ('Fahrenheit', 'fahrenheit', 'F' or 'f'), and Rankine
+        ('Rankine', 'rankine', 'R', 'r').
+
+    Returns
+    -------
+    res : float or array of floats
+        Value(s) of the converted temperature(s) expressed in the new scale.
+
+    Notes
+    -----
+    .. versionadded:: 0.18.0
+
+    Examples
+    --------
+    >>> from scipy.constants import convert_temperature
+    >>> import numpy as np
+    >>> convert_temperature(np.array([-40, 40]), 'Celsius', 'Kelvin')
+    array([ 233.15,  313.15])
+
+    """
+    xp = array_namespace(val)
+    _val = _asarray(val, xp=xp, subok=True)
+    # Convert from `old_scale` to Kelvin
+    if old_scale.lower() in ['celsius', 'c']:
+        tempo = _val + zero_Celsius
+    elif old_scale.lower() in ['kelvin', 'k']:
+        tempo = _val
+    elif old_scale.lower() in ['fahrenheit', 'f']:
+        tempo = (_val - 32) * 5 / 9 + zero_Celsius
+    elif old_scale.lower() in ['rankine', 'r']:
+        tempo = _val * 5 / 9
+    else:
+        raise NotImplementedError(f"{old_scale=} is unsupported: supported scales "
+                                   "are Celsius, Kelvin, Fahrenheit, and "
+                                   "Rankine")
+    # and from Kelvin to `new_scale`.
+    if new_scale.lower() in ['celsius', 'c']:
+        res = tempo - zero_Celsius
+    elif new_scale.lower() in ['kelvin', 'k']:
+        res = tempo
+    elif new_scale.lower() in ['fahrenheit', 'f']:
+        res = (tempo - zero_Celsius) * 9 / 5 + 32
+    elif new_scale.lower() in ['rankine', 'r']:
+        res = tempo * 9 / 5
+    else:
+        raise NotImplementedError(f"{new_scale=} is unsupported: supported "
+                                   "scales are 'Celsius', 'Kelvin', "
+                                   "'Fahrenheit', and 'Rankine'")
+
+    return res
+
+
+# optics
+
+
+@xp_capabilities()
+def lambda2nu(lambda_: "npt.ArrayLike") -> Any:
+    """
+    Convert wavelength to optical frequency
+
+    Parameters
+    ----------
+    lambda_ : array_like
+        Wavelength(s) to be converted.
+
+    Returns
+    -------
+    nu : float or array of floats
+        Equivalent optical frequency.
+
+    Notes
+    -----
+    Computes ``nu = c / lambda`` where c = 299792458.0, i.e., the
+    (vacuum) speed of light in meters/second.
+
+    Examples
+    --------
+    >>> from scipy.constants import lambda2nu, speed_of_light
+    >>> import numpy as np
+    >>> lambda2nu(np.array((1, speed_of_light)))
+    array([  2.99792458e+08,   1.00000000e+00])
+
+    """
+    xp = array_namespace(lambda_)
+    return c / _asarray(lambda_, xp=xp, subok=True)
+
+
+@xp_capabilities()
+def nu2lambda(nu: "npt.ArrayLike") -> Any:
+    """
+    Convert optical frequency to wavelength.
+
+    Parameters
+    ----------
+    nu : array_like
+        Optical frequency to be converted.
+
+    Returns
+    -------
+    lambda : float or array of floats
+        Equivalent wavelength(s).
+
+    Notes
+    -----
+    Computes ``lambda = c / nu`` where c = 299792458.0, i.e., the
+    (vacuum) speed of light in meters/second.
+
+    Examples
+    --------
+    >>> from scipy.constants import nu2lambda, speed_of_light
+    >>> import numpy as np
+    >>> nu2lambda(np.array((1, speed_of_light)))
+    array([  2.99792458e+08,   1.00000000e+00])
+
+    """
+    xp = array_namespace(nu)
+    return c / _asarray(nu, xp=xp, subok=True)

tool_server/.venv/lib/python3.12/site-packages/scipy/constants/codata.py

@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.constants` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'physical_constants', 'value', 'unit', 'precision', 'find',
+    'ConstantWarning', 'k', 'c',
+
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="constants", module="codata",
+                                   private_modules=["_codata"], all=__all__,
+                                   attribute=name)

tool_server/.venv/lib/python3.12/site-packages/scipy/constants/constants.py

@@ -0,0 +1,53 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.constants` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'Avogadro', 'Boltzmann', 'Btu', 'Btu_IT', 'Btu_th', 'G',
+    'Julian_year', 'N_A', 'Planck', 'R', 'Rydberg',
+    'Stefan_Boltzmann', 'Wien', 'acre', 'alpha',
+    'angstrom', 'arcmin', 'arcminute', 'arcsec',
+    'arcsecond', 'astronomical_unit', 'atm',
+    'atmosphere', 'atomic_mass', 'atto', 'au', 'bar',
+    'barrel', 'bbl', 'blob', 'c', 'calorie',
+    'calorie_IT', 'calorie_th', 'carat', 'centi',
+    'convert_temperature', 'day', 'deci', 'degree',
+    'degree_Fahrenheit', 'deka', 'dyn', 'dyne', 'e',
+    'eV', 'electron_mass', 'electron_volt',
+    'elementary_charge', 'epsilon_0', 'erg',
+    'exa', 'exbi', 'femto', 'fermi', 'fine_structure',
+    'fluid_ounce', 'fluid_ounce_US', 'fluid_ounce_imp',
+    'foot', 'g', 'gallon', 'gallon_US', 'gallon_imp',
+    'gas_constant', 'gibi', 'giga', 'golden', 'golden_ratio',
+    'grain', 'gram', 'gravitational_constant', 'h', 'hbar',
+    'hectare', 'hecto', 'horsepower', 'hour', 'hp',
+    'inch', 'k', 'kgf', 'kibi', 'kilo', 'kilogram_force',
+    'kmh', 'knot', 'lambda2nu', 'lb', 'lbf',
+    'light_year', 'liter', 'litre', 'long_ton', 'm_e',
+    'm_n', 'm_p', 'm_u', 'mach', 'mebi', 'mega',
+    'metric_ton', 'micro', 'micron', 'mil', 'mile',
+    'milli', 'minute', 'mmHg', 'mph', 'mu_0', 'nano',
+    'nautical_mile', 'neutron_mass', 'nu2lambda',
+    'ounce', 'oz', 'parsec', 'pebi', 'peta',
+    'pi', 'pico', 'point', 'pound', 'pound_force',
+    'proton_mass', 'psi', 'pt', 'short_ton',
+    'sigma', 'slinch', 'slug', 'speed_of_light',
+    'speed_of_sound', 'stone', 'survey_foot',
+    'survey_mile', 'tebi', 'tera', 'ton_TNT',
+    'torr', 'troy_ounce', 'troy_pound', 'u',
+    'week', 'yard', 'year', 'yobi', 'yocto',
+    'yotta', 'zebi', 'zepto', 'zero_Celsius', 'zetta'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="constants", module="constants",
+                                   private_modules=["_constants"], all=__all__,
+                                   attribute=name)

tool_server/.venv/lib/python3.12/site-packages/scipy/datasets/__init__.py

@@ -0,0 +1,90 @@
+"""
+================================
+Datasets (:mod:`scipy.datasets`)
+================================
+
+.. currentmodule:: scipy.datasets
+
+Dataset Methods
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   ascent
+   face
+   electrocardiogram
+
+Utility Methods
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   download_all    -- Download all the dataset files to specified path.
+   clear_cache     -- Clear cached dataset directory.
+
+
+Usage of Datasets
+=================
+
+SciPy dataset methods can be simply called as follows: ``'<dataset-name>()'``
+This downloads the dataset files over the network once, and saves the cache,
+before returning a `numpy.ndarray` object representing the dataset.
+
+Note that the return data structure and data type might be different for
+different dataset methods. For a more detailed example on usage, please look
+into the particular dataset method documentation above.
+
+
+How dataset retrieval and storage works
+=======================================
+
+SciPy dataset files are stored within individual GitHub repositories under the
+SciPy GitHub organization, following a naming convention as
+``'dataset-<name>'``, for example `scipy.datasets.face` files live at
+https://github.com/scipy/dataset-face.  The `scipy.datasets` submodule utilizes
+and depends on `Pooch <https://www.fatiando.org/pooch/latest/>`_, a Python
+package built to simplify fetching data files. Pooch uses these repos to
+retrieve the respective dataset files when calling the dataset function.
+
+A registry of all the datasets, essentially a mapping of filenames with their
+SHA256 hash and repo urls are maintained, which Pooch uses to handle and verify
+the downloads on function call. After downloading the dataset once, the files
+are saved in the system cache directory under ``'scipy-data'``.
+
+Dataset cache locations may vary on different platforms.
+
+For macOS::
+
+    '~/Library/Caches/scipy-data'
+
+For Linux and other Unix-like platforms::
+
+    '~/.cache/scipy-data'  # or the value of the XDG_CACHE_HOME env var, if defined
+
+For Windows::
+
+    'C:\\Users\\<user>\\AppData\\Local\\<AppAuthor>\\scipy-data\\Cache'
+
+
+In environments with constrained network connectivity for various security
+reasons or on systems without continuous internet connections, one may manually
+load the cache of the datasets by placing the contents of the dataset repo in
+the above mentioned cache directory to avoid fetching dataset errors without
+the internet connectivity.
+
+"""
+
+
+from ._fetchers import face, ascent, electrocardiogram
+from ._download_all import download_all
+from ._utils import clear_cache
+
+__all__ = ['ascent', 'electrocardiogram', 'face',
+           'download_all', 'clear_cache']
+
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

tool_server/.venv/lib/python3.12/site-packages/scipy/datasets/_download_all.py

@@ -0,0 +1,71 @@
+"""
+Platform independent script to download all the
+`scipy.datasets` module data files.
+This doesn't require a full scipy build.
+
+Run: python _download_all.py <download_dir>
+"""
+
+import argparse
+try:
+    import pooch
+except ImportError:
+    pooch = None
+
+
+if __package__ is None or __package__ == '':
+    # Running as python script, use absolute import
+    import _registry  # type: ignore
+else:
+    # Running as python module, use relative import
+    from . import _registry
+
+
+def download_all(path=None):
+    """
+    Utility method to download all the dataset files
+    for `scipy.datasets` module.
+
+    Parameters
+    ----------
+    path : str, optional
+        Directory path to download all the dataset files.
+        If None, default to the system cache_dir detected by pooch.
+    
+    Examples
+    --------
+    Download the datasets to the default cache location:
+
+    >>> from scipy import datasets
+    >>> datasets.download_all()
+
+    Download the datasets to the current directory:
+
+    >>> datasets.download_all(".")
+    
+    """
+    if pooch is None:
+        raise ImportError("Missing optional dependency 'pooch' required "
+                          "for scipy.datasets module. Please use pip or "
+                          "conda to install 'pooch'.")
+    if path is None:
+        path = pooch.os_cache('scipy-data')
+    # https://github.com/scipy/scipy/issues/21879
+    downloader = pooch.HTTPDownloader(headers={"User-Agent": "SciPy"})
+    for dataset_name, dataset_hash in _registry.registry.items():
+        pooch.retrieve(url=_registry.registry_urls[dataset_name],
+                       known_hash=dataset_hash,
+                       fname=dataset_name, path=path, downloader=downloader)
+
+
+def main():
+    parser = argparse.ArgumentParser(description='Download SciPy data files.')
+    parser.add_argument("path", nargs='?', type=str,
+                        default=pooch.os_cache('scipy-data'),
+                        help="Directory path to download all the data files.")
+    args = parser.parse_args()
+    download_all(args.path)
+
+
+if __name__ == "__main__":
+    main()

tool_server/.venv/lib/python3.12/site-packages/scipy/datasets/_fetchers.py

@@ -0,0 +1,225 @@
+import sys
+
+from numpy import array, frombuffer, load
+from ._registry import registry, registry_urls
+
+try:
+    import pooch
+except ImportError:
+    pooch = None
+    data_fetcher = None
+else:
+    data_fetcher = pooch.create(
+        # Use the default cache folder for the operating system
+        # Pooch uses appdirs (https://github.com/ActiveState/appdirs) to
+        # select an appropriate directory for the cache on each platform.
+        path=pooch.os_cache("scipy-data"),
+
+        # The remote data is on Github
+        # base_url is a required param, even though we override this
+        # using individual urls in the registry.
+        base_url="https://github.com/scipy/",
+        registry=registry,
+        urls=registry_urls
+    )
+
+
+def fetch_data(dataset_name, data_fetcher=data_fetcher):
+    if data_fetcher is None:
+        raise ImportError("Missing optional dependency 'pooch' required "
+                          "for scipy.datasets module. Please use pip or "
+                          "conda to install 'pooch'.")
+    # https://github.com/scipy/scipy/issues/21879
+    downloader = pooch.HTTPDownloader(
+        headers={"User-Agent": f"SciPy {sys.modules['scipy'].__version__}"}
+    )
+    # The "fetch" method returns the full path to the downloaded data file.
+    return data_fetcher.fetch(dataset_name, downloader=downloader)
+
+
+def ascent():
+    """
+    Get an 8-bit grayscale bit-depth, 512 x 512 derived image for easy
+    use in demos.
+
+    The image is derived from
+    https://pixnio.com/people/accent-to-the-top
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    ascent : ndarray
+       convenient image to use for testing and demonstration
+
+    Examples
+    --------
+    >>> import scipy.datasets
+    >>> ascent = scipy.datasets.ascent()
+    >>> ascent.shape
+    (512, 512)
+    >>> ascent.max()
+    np.uint8(255)
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.gray()
+    >>> plt.imshow(ascent)
+    >>> plt.show()
+
+    """
+    import pickle
+
+    # The file will be downloaded automatically the first time this is run,
+    # returning the path to the downloaded file. Afterwards, Pooch finds
+    # it in the local cache and doesn't repeat the download.
+    fname = fetch_data("ascent.dat")
+    # Now we just need to load it with our standard Python tools.
+    with open(fname, 'rb') as f:
+        ascent = array(pickle.load(f))
+    return ascent
+
+
+def electrocardiogram():
+    """
+    Load an electrocardiogram as an example for a 1-D signal.
+
+    The returned signal is a 5 minute long electrocardiogram (ECG), a medical
+    recording of the heart's electrical activity, sampled at 360 Hz.
+
+    Returns
+    -------
+    ecg : ndarray
+        The electrocardiogram in millivolt (mV) sampled at 360 Hz.
+
+    Notes
+    -----
+    The provided signal is an excerpt (19:35 to 24:35) from the `record 208`_
+    (lead MLII) provided by the MIT-BIH Arrhythmia Database [1]_ on
+    PhysioNet [2]_. The excerpt includes noise induced artifacts, typical
+    heartbeats as well as pathological changes.
+
+    .. _record 208: https://physionet.org/physiobank/database/html/mitdbdir/records.htm#208
+
+    .. versionadded:: 1.1.0
+
+    References
+    ----------
+    .. [1] Moody GB, Mark RG. The impact of the MIT-BIH Arrhythmia Database.
+           IEEE Eng in Med and Biol 20(3):45-50 (May-June 2001).
+           (PMID: 11446209); :doi:`10.13026/C2F305`
+    .. [2] Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh,
+           Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank,
+           PhysioToolkit, and PhysioNet: Components of a New Research Resource
+           for Complex Physiologic Signals. Circulation 101(23):e215-e220;
+           :doi:`10.1161/01.CIR.101.23.e215`
+
+    Examples
+    --------
+    >>> from scipy.datasets import electrocardiogram
+    >>> ecg = electrocardiogram()
+    >>> ecg
+    array([-0.245, -0.215, -0.185, ..., -0.405, -0.395, -0.385], shape=(108000,))
+    >>> ecg.shape, ecg.mean(), ecg.std()
+    ((108000,), -0.16510875, 0.5992473991177294)
+
+    As stated the signal features several areas with a different morphology.
+    E.g., the first few seconds show the electrical activity of a heart in
+    normal sinus rhythm as seen below.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> fs = 360
+    >>> time = np.arange(ecg.size) / fs
+    >>> plt.plot(time, ecg)
+    >>> plt.xlabel("time in s")
+    >>> plt.ylabel("ECG in mV")
+    >>> plt.xlim(9, 10.2)
+    >>> plt.ylim(-1, 1.5)
+    >>> plt.show()
+
+    After second 16, however, the first premature ventricular contractions,
+    also called extrasystoles, appear. These have a different morphology
+    compared to typical heartbeats. The difference can easily be observed
+    in the following plot.
+
+    >>> plt.plot(time, ecg)
+    >>> plt.xlabel("time in s")
+    >>> plt.ylabel("ECG in mV")
+    >>> plt.xlim(46.5, 50)
+    >>> plt.ylim(-2, 1.5)
+    >>> plt.show()
+
+    At several points large artifacts disturb the recording, e.g.:
+
+    >>> plt.plot(time, ecg)
+    >>> plt.xlabel("time in s")
+    >>> plt.ylabel("ECG in mV")
+    >>> plt.xlim(207, 215)
+    >>> plt.ylim(-2, 3.5)
+    >>> plt.show()
+
+    Finally, examining the power spectrum reveals that most of the biosignal is
+    made up of lower frequencies. At 60 Hz the noise induced by the mains
+    electricity can be clearly observed.
+
+    >>> from scipy.signal import welch
+    >>> f, Pxx = welch(ecg, fs=fs, nperseg=2048, scaling="spectrum")
+    >>> plt.semilogy(f, Pxx)
+    >>> plt.xlabel("Frequency in Hz")
+    >>> plt.ylabel("Power spectrum of the ECG in mV**2")
+    >>> plt.xlim(f[[0, -1]])
+    >>> plt.show()
+    """
+    fname = fetch_data("ecg.dat")
+    with load(fname) as file:
+        ecg = file["ecg"].astype(int)  # np.uint16 -> int
+    # Convert raw output of ADC to mV: (ecg - adc_zero) / adc_gain
+    ecg = (ecg - 1024) / 200.0
+    return ecg
+
+
+def face(gray=False):
+    """
+    Get a 1024 x 768, color image of a raccoon face.
+
+    The image is derived from
+    https://pixnio.com/fauna-animals/raccoons/raccoon-procyon-lotor
+
+    Parameters
+    ----------
+    gray : bool, optional
+        If True return 8-bit grey-scale image, otherwise return a color image
+
+    Returns
+    -------
+    face : ndarray
+        image of a raccoon face
+
+    Examples
+    --------
+    >>> import scipy.datasets
+    >>> face = scipy.datasets.face()
+    >>> face.shape
+    (768, 1024, 3)
+    >>> face.max()
+    np.uint8(255)
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.gray()
+    >>> plt.imshow(face)
+    >>> plt.show()
+
+    """
+    import bz2
+    fname = fetch_data("face.dat")
+    with open(fname, 'rb') as f:
+        rawdata = f.read()
+    face_data = bz2.decompress(rawdata)
+    face = frombuffer(face_data, dtype='uint8')
+    face.shape = (768, 1024, 3)
+    if gray is True:
+        face = (0.21 * face[:, :, 0] + 0.71 * face[:, :, 1] +
+                0.07 * face[:, :, 2]).astype('uint8')
+    return face

tool_server/.venv/lib/python3.12/site-packages/scipy/datasets/_registry.py

@@ -0,0 +1,26 @@
+##########################################################################
+# This file serves as the dataset registry for SciPy Datasets SubModule.
+##########################################################################
+
+
+# To generate the SHA256 hash, use the command
+# openssl sha256 <filename>
+registry = {
+    "ascent.dat": "03ce124c1afc880f87b55f6b061110e2e1e939679184f5614e38dacc6c1957e2",
+    "ecg.dat": "f20ad3365fb9b7f845d0e5c48b6fe67081377ee466c3a220b7f69f35c8958baf",
+    "face.dat": "9d8b0b4d081313e2b485748c770472e5a95ed1738146883d84c7030493e82886"
+}
+
+registry_urls = {
+    "ascent.dat": "https://raw.githubusercontent.com/scipy/dataset-ascent/main/ascent.dat",
+    "ecg.dat": "https://raw.githubusercontent.com/scipy/dataset-ecg/main/ecg.dat",
+    "face.dat": "https://raw.githubusercontent.com/scipy/dataset-face/main/face.dat"
+}
+
+# dataset method mapping with their associated filenames
+# <method_name> : ["filename1", "filename2", ...]
+method_files_map = {
+    "ascent": ["ascent.dat"],
+    "electrocardiogram": ["ecg.dat"],
+    "face": ["face.dat"]
+}

tool_server/.venv/lib/python3.12/site-packages/scipy/datasets/_utils.py

@@ -0,0 +1,81 @@
+import os
+import shutil
+from ._registry import method_files_map
+
+try:
+    import platformdirs
+except ImportError:
+    platformdirs = None  # type: ignore[assignment]
+
+
+def _clear_cache(datasets, cache_dir=None, method_map=None):
+    if method_map is None:
+        # Use SciPy Datasets method map
+        method_map = method_files_map
+    if cache_dir is None:
+        # Use default cache_dir path
+        if platformdirs is None:
+            # platformdirs is pooch dependency
+            raise ImportError("Missing optional dependency 'pooch' required "
+                              "for scipy.datasets module. Please use pip or "
+                              "conda to install 'pooch'.")
+        cache_dir = platformdirs.user_cache_dir("scipy-data")
+
+    if not os.path.exists(cache_dir):
+        print(f"Cache Directory {cache_dir} doesn't exist. Nothing to clear.")
+        return
+
+    if datasets is None:
+        print(f"Cleaning the cache directory {cache_dir}!")
+        shutil.rmtree(cache_dir)
+    else:
+        if not isinstance(datasets, list | tuple):
+            # single dataset method passed should be converted to list
+            datasets = [datasets, ]
+        for dataset in datasets:
+            assert callable(dataset)
+            dataset_name = dataset.__name__  # Name of the dataset method
+            if dataset_name not in method_map:
+                raise ValueError(f"Dataset method {dataset_name} doesn't "
+                                 "exist. Please check if the passed dataset "
+                                 "is a subset of the following dataset "
+                                 f"methods: {list(method_map.keys())}")
+
+            data_files = method_map[dataset_name]
+            data_filepaths = [os.path.join(cache_dir, file)
+                              for file in data_files]
+            for data_filepath in data_filepaths:
+                if os.path.exists(data_filepath):
+                    print("Cleaning the file "
+                          f"{os.path.split(data_filepath)[1]} "
+                          f"for dataset {dataset_name}")
+                    os.remove(data_filepath)
+                else:
+                    print(f"Path {data_filepath} doesn't exist. "
+                          "Nothing to clear.")
+
+
+def clear_cache(datasets=None):
+    """
+    Cleans the scipy datasets cache directory.
+
+    If a scipy.datasets method or a list/tuple of the same is
+    provided, then clear_cache removes all the data files
+    associated to the passed dataset method callable(s).
+
+    By default, it removes all the cached data files.
+
+    Parameters
+    ----------
+    datasets : callable or list/tuple of callable or None
+
+    Examples
+    --------
+    >>> from scipy import datasets
+    >>> ascent_array = datasets.ascent()
+    >>> ascent_array.shape
+    (512, 512)
+    >>> datasets.clear_cache([datasets.ascent])
+    Cleaning the file ascent.dat for dataset ascent
+    """
+    _clear_cache(datasets)

tool_server/.venv/lib/python3.12/site-packages/scipy/differentiate/__init__.py

@@ -0,0 +1,27 @@
+"""
+==============================================================
+Finite Difference Differentiation (:mod:`scipy.differentiate`)
+==============================================================
+
+.. currentmodule:: scipy.differentiate
+
+SciPy ``differentiate`` provides functions for performing finite difference
+numerical differentiation of black-box functions.
+
+.. autosummary::
+   :toctree: generated/
+
+   derivative
+   jacobian
+   hessian
+
+"""
+
+
+from ._differentiate import *
+
+__all__ = ['derivative', 'jacobian', 'hessian']
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

tool_server/.venv/lib/python3.12/site-packages/scipy/differentiate/_differentiate.py

@@ -0,0 +1,1129 @@
+# mypy: disable-error-code="attr-defined"
+import warnings
+import numpy as np
+import scipy._lib._elementwise_iterative_method as eim
+from scipy._lib._util import _RichResult
+from scipy._lib._array_api import array_namespace, xp_copy, xp_promote
+import scipy._lib.array_api_extra as xpx
+
+_EERRORINCREASE = -1  # used in derivative
+
+def _derivative_iv(f, x, args, tolerances, maxiter, order, initial_step,
+                   step_factor, step_direction, preserve_shape, callback):
+    # Input validation for `derivative`
+    xp = array_namespace(x)
+
+    if not callable(f):
+        raise ValueError('`f` must be callable.')
+
+    if not np.iterable(args):
+        args = (args,)
+
+    tolerances = {} if tolerances is None else tolerances
+    atol = tolerances.get('atol', None)
+    rtol = tolerances.get('rtol', None)
+
+    # tolerances are floats, not arrays; OK to use NumPy
+    message = 'Tolerances and step parameters must be non-negative scalars.'
+    tols = np.asarray([atol if atol is not None else 1,
+                       rtol if rtol is not None else 1,
+                       step_factor])
+    if (not np.issubdtype(tols.dtype, np.number) or np.any(tols < 0)
+            or np.any(np.isnan(tols)) or tols.shape != (3,)):
+        raise ValueError(message)
+    step_factor = float(tols[2])
+
+    maxiter_int = int(maxiter)
+    if maxiter != maxiter_int or maxiter <= 0:
+        raise ValueError('`maxiter` must be a positive integer.')
+
+    order_int = int(order)
+    if order_int != order or order <= 0:
+        raise ValueError('`order` must be a positive integer.')
+
+    step_direction = xp.asarray(step_direction)
+    initial_step = xp.asarray(initial_step)
+    temp = xp.broadcast_arrays(x, step_direction, initial_step)
+    x, step_direction, initial_step = temp
+
+    message = '`preserve_shape` must be True or False.'
+    if preserve_shape not in {True, False}:
+        raise ValueError(message)
+
+    if callback is not None and not callable(callback):
+        raise ValueError('`callback` must be callable.')
+
+    return (f, x, args, atol, rtol, maxiter_int, order_int, initial_step,
+            step_factor, step_direction, preserve_shape, callback)
+
+
+def derivative(f, x, *, args=(), tolerances=None, maxiter=10,
+               order=8, initial_step=0.5, step_factor=2.0,
+               step_direction=0, preserve_shape=False, callback=None):
+    """Evaluate the derivative of a elementwise, real scalar function numerically.
+
+    For each element of the output of `f`, `derivative` approximates the first
+    derivative of `f` at the corresponding element of `x` using finite difference
+    differentiation.
+
+    This function works elementwise when `x`, `step_direction`, and `args` contain
+    (broadcastable) arrays.
+
+    Parameters
+    ----------
+    f : callable
+        The function whose derivative is desired. The signature must be::
+
+            f(xi: ndarray, *argsi) -> ndarray
+
+        where each element of ``xi`` is a finite real number and ``argsi`` is a tuple,
+        which may contain an arbitrary number of arrays that are broadcastable with
+        ``xi``. `f` must be an elementwise function: each scalar element ``f(xi)[j]``
+        must equal ``f(xi[j])`` for valid indices ``j``. It must not mutate the array
+        ``xi`` or the arrays in ``argsi``.
+    x : float array_like
+        Abscissae at which to evaluate the derivative. Must be broadcastable with
+        `args` and `step_direction`.
+    args : tuple of array_like, optional
+        Additional positional array arguments to be passed to `f`. Arrays
+        must be broadcastable with one another and the arrays of `init`.
+        If the callable for which the root is desired requires arguments that are
+        not broadcastable with `x`, wrap that callable with `f` such that `f`
+        accepts only `x` and broadcastable ``*args``.
+    tolerances : dictionary of floats, optional
+        Absolute and relative tolerances. Valid keys of the dictionary are:
+
+        - ``atol`` - absolute tolerance on the derivative
+        - ``rtol`` - relative tolerance on the derivative
+
+        Iteration will stop when ``res.error < atol + rtol * abs(res.df)``. The default
+        `atol` is the smallest normal number of the appropriate dtype, and
+        the default `rtol` is the square root of the precision of the
+        appropriate dtype.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float array_like, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform. See
+        Notes.
+    step_direction : integer array_like
+        An array representing the direction of the finite difference steps (for
+        use when `x` lies near to the boundary of the domain of the function.)
+        Must be broadcastable with `x` and all `args`.
+        Where 0 (default), central differences are used; where negative (e.g.
+        -1), steps are non-positive; and where positive (e.g. 1), all steps are
+        non-negative.
+    preserve_shape : bool, default: False
+        In the following, "arguments of `f`" refers to the array ``xi`` and
+        any arrays within ``argsi``. Let ``shape`` be the broadcasted shape
+        of `x` and all elements of `args` (which is conceptually
+        distinct from ``xi` and ``argsi`` passed into `f`).
+
+        - When ``preserve_shape=False`` (default), `f` must accept arguments
+          of *any* broadcastable shapes.
+
+        - When ``preserve_shape=True``, `f` must accept arguments of shape
+          ``shape`` *or* ``shape + (n,)``, where ``(n,)`` is the number of
+          abscissae at which the function is being evaluated.
+
+        In either case, for each scalar element ``xi[j]`` within ``xi``, the array
+        returned by `f` must include the scalar ``f(xi[j])`` at the same index.
+        Consequently, the shape of the output is always the shape of the input
+        ``xi``.
+
+        See Examples.
+    callback : callable, optional
+        An optional user-supplied function to be called before the first
+        iteration and after each iteration.
+        Called as ``callback(res)``, where ``res`` is a ``_RichResult``
+        similar to that returned by `derivative` (but containing the current
+        iterate's values of all variables). If `callback` raises a
+        ``StopIteration``, the algorithm will terminate immediately and
+        `derivative` will return a result. `callback` must not mutate
+        `res` or its attributes.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-1`` : The error estimate increased, so iteration was terminated.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+            - ``-4`` : Iteration was terminated by `callback`.
+            - ``1`` : The algorithm is proceeding normally (in `callback` only).
+
+        df : float array
+            The derivative of `f` at `x`, if the algorithm terminated
+            successfully.
+        error : float array
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the derivative and the estimate in the
+            previous iteration.
+        nit : int array
+            The number of iterations of the algorithm that were performed.
+        nfev : int array
+            The number of points at which `f` was evaluated.
+        x : float array
+            The value at which the derivative of `f` was evaluated
+            (after broadcasting with `args` and `step_direction`).
+
+    See Also
+    --------
+    jacobian, hessian
+
+    Notes
+    -----
+    The implementation was inspired by jacobi [1]_, numdifftools [2]_, and
+    DERIVEST [3]_, but the implementation follows the theory of Taylor series
+    more straightforwardly (and arguably naively so).
+    In the first iteration, the derivative is estimated using a finite
+    difference formula of order `order` with maximum step size `initial_step`.
+    Each subsequent iteration, the maximum step size is reduced by
+    `step_factor`, and the derivative is estimated again until a termination
+    condition is reached. The error estimate is the magnitude of the difference
+    between the current derivative approximation and that of the previous
+    iteration.
+
+    The stencils of the finite difference formulae are designed such that
+    abscissae are "nested": after `f` is evaluated at ``order + 1``
+    points in the first iteration, `f` is evaluated at only two new points
+    in each subsequent iteration; ``order - 1`` previously evaluated function
+    values required by the finite difference formula are reused, and two
+    function values (evaluations at the points furthest from `x`) are unused.
+
+    Step sizes are absolute. When the step size is small relative to the
+    magnitude of `x`, precision is lost; for example, if `x` is ``1e20``, the
+    default initial step size of ``0.5`` cannot be resolved. Accordingly,
+    consider using larger initial step sizes for large magnitudes of `x`.
+
+    The default tolerances are challenging to satisfy at points where the
+    true derivative is exactly zero. If the derivative may be exactly zero,
+    consider specifying an absolute tolerance (e.g. ``atol=1e-12``) to
+    improve convergence.
+
+    References
+    ----------
+    .. [1] Hans Dembinski (@HDembinski). jacobi.
+           https://github.com/HDembinski/jacobi
+    .. [2] Per A. Brodtkorb and John D'Errico. numdifftools.
+           https://numdifftools.readthedocs.io/en/latest/
+    .. [3] John D'Errico. DERIVEST: Adaptive Robust Numerical Differentiation.
+           https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation
+    .. [4] Numerical Differentition. Wikipedia.
+           https://en.wikipedia.org/wiki/Numerical_differentiation
+
+    Examples
+    --------
+    Evaluate the derivative of ``np.exp`` at several points ``x``.
+
+    >>> import numpy as np
+    >>> from scipy.differentiate import derivative
+    >>> f = np.exp
+    >>> df = np.exp  # true derivative
+    >>> x = np.linspace(1, 2, 5)
+    >>> res = derivative(f, x)
+    >>> res.df  # approximation of the derivative
+    array([2.71828183, 3.49034296, 4.48168907, 5.75460268, 7.3890561 ])
+    >>> res.error  # estimate of the error
+    array([7.13740178e-12, 9.16600129e-12, 1.17594823e-11, 1.51061386e-11,
+           1.94262384e-11])
+    >>> abs(res.df - df(x))  # true error
+    array([2.53130850e-14, 3.55271368e-14, 5.77315973e-14, 5.59552404e-14,
+           6.92779167e-14])
+
+    Show the convergence of the approximation as the step size is reduced.
+    Each iteration, the step size is reduced by `step_factor`, so for
+    sufficiently small initial step, each iteration reduces the error by a
+    factor of ``1/step_factor**order`` until finite precision arithmetic
+    inhibits further improvement.
+
+    >>> import matplotlib.pyplot as plt
+    >>> iter = list(range(1, 12))  # maximum iterations
+    >>> hfac = 2  # step size reduction per iteration
+    >>> hdir = [-1, 0, 1]  # compare left-, central-, and right- steps
+    >>> order = 4  # order of differentiation formula
+    >>> x = 1
+    >>> ref = df(x)
+    >>> errors = []  # true error
+    >>> for i in iter:
+    ...     res = derivative(f, x, maxiter=i, step_factor=hfac,
+    ...                      step_direction=hdir, order=order,
+    ...                      # prevent early termination
+    ...                      tolerances=dict(atol=0, rtol=0))
+    ...     errors.append(abs(res.df - ref))
+    >>> errors = np.array(errors)
+    >>> plt.semilogy(iter, errors[:, 0], label='left differences')
+    >>> plt.semilogy(iter, errors[:, 1], label='central differences')
+    >>> plt.semilogy(iter, errors[:, 2], label='right differences')
+    >>> plt.xlabel('iteration')
+    >>> plt.ylabel('error')
+    >>> plt.legend()
+    >>> plt.show()
+    >>> (errors[1, 1] / errors[0, 1], 1 / hfac**order)
+    (0.06215223140159822, 0.0625)
+
+    The implementation is vectorized over `x`, `step_direction`, and `args`.
+    The function is evaluated once before the first iteration to perform input
+    validation and standardization, and once per iteration thereafter.
+
+    >>> def f(x, p):
+    ...     f.nit += 1
+    ...     return x**p
+    >>> f.nit = 0
+    >>> def df(x, p):
+    ...     return p*x**(p-1)
+    >>> x = np.arange(1, 5)
+    >>> p = np.arange(1, 6).reshape((-1, 1))
+    >>> hdir = np.arange(-1, 2).reshape((-1, 1, 1))
+    >>> res = derivative(f, x, args=(p,), step_direction=hdir, maxiter=1)
+    >>> np.allclose(res.df, df(x, p))
+    True
+    >>> res.df.shape
+    (3, 5, 4)
+    >>> f.nit
+    2
+
+    By default, `preserve_shape` is False, and therefore the callable
+    `f` may be called with arrays of any broadcastable shapes.
+    For example:
+
+    >>> shapes = []
+    >>> def f(x, c):
+    ...    shape = np.broadcast_shapes(x.shape, c.shape)
+    ...    shapes.append(shape)
+    ...    return np.sin(c*x)
+    >>>
+    >>> c = [1, 5, 10, 20]
+    >>> res = derivative(f, 0, args=(c,))
+    >>> shapes
+    [(4,), (4, 8), (4, 2), (3, 2), (2, 2), (1, 2)]
+
+    To understand where these shapes are coming from - and to better
+    understand how `derivative` computes accurate results - note that
+    higher values of ``c`` correspond with higher frequency sinusoids.
+    The higher frequency sinusoids make the function's derivative change
+    faster, so more function evaluations are required to achieve the target
+    accuracy:
+
+    >>> res.nfev
+    array([11, 13, 15, 17], dtype=int32)
+
+    The initial ``shape``, ``(4,)``, corresponds with evaluating the
+    function at a single abscissa and all four frequencies; this is used
+    for input validation and to determine the size and dtype of the arrays
+    that store results. The next shape corresponds with evaluating the
+    function at an initial grid of abscissae and all four frequencies.
+    Successive calls to the function evaluate the function at two more
+    abscissae, increasing the effective order of the approximation by two.
+    However, in later function evaluations, the function is evaluated at
+    fewer frequencies because the corresponding derivative has already
+    converged to the required tolerance. This saves function evaluations to
+    improve performance, but it requires the function to accept arguments of
+    any shape.
+
+    "Vector-valued" functions are unlikely to satisfy this requirement.
+    For example, consider
+
+    >>> def f(x):
+    ...    return [x, np.sin(3*x), x+np.sin(10*x), np.sin(20*x)*(x-1)**2]
+
+    This integrand is not compatible with `derivative` as written; for instance,
+    the shape of the output will not be the same as the shape of ``x``. Such a
+    function *could* be converted to a compatible form with the introduction of
+    additional parameters, but this would be inconvenient. In such cases,
+    a simpler solution would be to use `preserve_shape`.
+
+    >>> shapes = []
+    >>> def f(x):
+    ...     shapes.append(x.shape)
+    ...     x0, x1, x2, x3 = x
+    ...     return [x0, np.sin(3*x1), x2+np.sin(10*x2), np.sin(20*x3)*(x3-1)**2]
+    >>>
+    >>> x = np.zeros(4)
+    >>> res = derivative(f, x, preserve_shape=True)
+    >>> shapes
+    [(4,), (4, 8), (4, 2), (4, 2), (4, 2), (4, 2)]
+
+    Here, the shape of ``x`` is ``(4,)``. With ``preserve_shape=True``, the
+    function may be called with argument ``x`` of shape ``(4,)`` or ``(4, n)``,
+    and this is what we observe.
+
+    """
+    # TODO (followup):
+    #  - investigate behavior at saddle points
+    #  - multivariate functions?
+    #  - relative steps?
+    #  - show example of `np.vectorize`
+
+    res = _derivative_iv(f, x, args, tolerances, maxiter, order, initial_step,
+                            step_factor, step_direction, preserve_shape, callback)
+    (func, x, args, atol, rtol, maxiter, order,
+     h0, fac, hdir, preserve_shape, callback) = res
+
+    # Initialization
+    # Since f(x) (no step) is not needed for central differences, it may be
+    # possible to eliminate this function evaluation. However, it's useful for
+    # input validation and standardization, and everything else is designed to
+    # reduce function calls, so let's keep it simple.
+    temp = eim._initialize(func, (x,), args, preserve_shape=preserve_shape)
+    func, xs, fs, args, shape, dtype, xp = temp
+
+    finfo = xp.finfo(dtype)
+    atol = finfo.smallest_normal if atol is None else atol
+    rtol = finfo.eps**0.5 if rtol is None else rtol  # keep same as `hessian`
+
+    x, f = xs[0], fs[0]
+    df = xp.full_like(f, xp.nan)
+
+    # Ideally we'd broadcast the shape of `hdir` in `_elementwise_algo_init`, but
+    # it's simpler to do it here than to generalize `_elementwise_algo_init` further.
+    # `hdir` and `x` are already broadcasted in `_derivative_iv`, so we know
+    # that `hdir` can be broadcasted to the final shape. Same with `h0`.
+    hdir = xp.broadcast_to(hdir, shape)
+    hdir = xp.reshape(hdir, (-1,))
+    hdir = xp.astype(xp.sign(hdir), dtype)
+    h0 = xp.broadcast_to(h0, shape)
+    h0 = xp.reshape(h0, (-1,))
+    h0 = xp.astype(h0, dtype)
+    h0 = xpx.at(h0)[h0 <= 0].set(xp.nan)
+
+    status = xp.full_like(x, eim._EINPROGRESS, dtype=xp.int32)  # in progress
+    nit, nfev = 0, 1  # one function evaluations performed above
+    # Boolean indices of left, central, right, and (all) one-sided steps
+    il = hdir < 0
+    ic = hdir == 0
+    ir = hdir > 0
+    io = il | ir
+
+    # Most of these attributes are reasonably obvious, but:
+    # - `fs` holds all the function values of all active `x`. The zeroth
+    #   axis corresponds with active points `x`, the first axis corresponds
+    #   with the different steps (in the order described in
+    #   `_derivative_weights`).
+    # - `terms` (which could probably use a better name) is half the `order`,
+    #   which is always even.
+    work = _RichResult(x=x, df=df, fs=f[:, xp.newaxis], error=xp.nan, h=h0,
+                       df_last=xp.nan, error_last=xp.nan, fac=fac,
+                       atol=atol, rtol=rtol, nit=nit, nfev=nfev,
+                       status=status, dtype=dtype, terms=(order+1)//2,
+                       hdir=hdir, il=il, ic=ic, ir=ir, io=io,
+                       # Store the weights in an object so they can't get compressed
+                       # Using RichResult to allow dot notation, but a dict would work
+                       diff_state=_RichResult(central=[], right=[], fac=None))
+
+    # This is the correspondence between terms in the `work` object and the
+    # final result. In this case, the mapping is trivial. Note that `success`
+    # is prepended automatically.
+    res_work_pairs = [('status', 'status'), ('df', 'df'), ('error', 'error'),
+                      ('nit', 'nit'), ('nfev', 'nfev'), ('x', 'x')]
+
+    def pre_func_eval(work):
+        """Determine the abscissae at which the function needs to be evaluated.
+
+        See `_derivative_weights` for a description of the stencil (pattern
+        of the abscissae).
+
+        In the first iteration, there is only one stored function value in
+        `work.fs`, `f(x)`, so we need to evaluate at `order` new points. In
+        subsequent iterations, we evaluate at two new points. Note that
+        `work.x` is always flattened into a 1D array after broadcasting with
+        all `args`, so we add a new axis at the end and evaluate all point
+        in one call to the function.
+
+        For improvement:
+        - Consider measuring the step size actually taken, since ``(x + h) - x``
+          is not identically equal to `h` with floating point arithmetic.
+        - Adjust the step size automatically if `x` is too big to resolve the
+          step.
+        - We could probably save some work if there are no central difference
+          steps or no one-sided steps.
+        """
+        n = work.terms  # half the order
+        h = work.h[:, xp.newaxis]  # step size
+        c = work.fac  # step reduction factor
+        d = c**0.5  # square root of step reduction factor (one-sided stencil)
+        # Note - no need to be careful about dtypes until we allocate `x_eval`
+
+        if work.nit == 0:
+            hc = h / c**xp.arange(n, dtype=work.dtype)
+            hc = xp.concat((-xp.flip(hc, axis=-1), hc), axis=-1)
+        else:
+            hc = xp.concat((-h, h), axis=-1) / c**(n-1)
+
+        if work.nit == 0:
+            hr = h / d**xp.arange(2*n, dtype=work.dtype)
+        else:
+            hr = xp.concat((h, h/d), axis=-1) / c**(n-1)
+
+        n_new = 2*n if work.nit == 0 else 2  # number of new abscissae
+        x_eval = xp.zeros((work.hdir.shape[0], n_new), dtype=work.dtype)
+        il, ic, ir = work.il, work.ic, work.ir
+        x_eval = xpx.at(x_eval)[ir].set(work.x[ir][:, xp.newaxis] + hr[ir])
+        x_eval = xpx.at(x_eval)[ic].set(work.x[ic][:, xp.newaxis] + hc[ic])
+        x_eval = xpx.at(x_eval)[il].set(work.x[il][:, xp.newaxis] - hr[il])
+        return x_eval
+
+    def post_func_eval(x, f, work):
+        """ Estimate the derivative and error from the function evaluations
+
+        As in `pre_func_eval`: in the first iteration, there is only one stored
+        function value in `work.fs`, `f(x)`, so we need to add the `order` new
+        points. In subsequent iterations, we add two new points. The tricky
+        part is getting the order to match that of the weights, which is
+        described in `_derivative_weights`.
+
+        For improvement:
+        - Change the order of the weights (and steps in `pre_func_eval`) to
+          simplify `work_fc` concatenation and eliminate `fc` concatenation.
+        - It would be simple to do one-step Richardson extrapolation with `df`
+          and `df_last` to increase the order of the estimate and/or improve
+          the error estimate.
+        - Process the function evaluations in a more numerically favorable
+          way. For instance, combining the pairs of central difference evals
+          into a second-order approximation and using Richardson extrapolation
+          to produce a higher order approximation seemed to retain accuracy up
+          to very high order.
+        - Alternatively, we could use `polyfit` like Jacobi. An advantage of
+          fitting polynomial to more points than necessary is improved noise
+          tolerance.
+        """
+        n = work.terms
+        n_new = n if work.nit == 0 else 1
+        il, ic, io = work.il, work.ic, work.io
+
+        # Central difference
+        # `work_fc` is *all* the points at which the function has been evaluated
+        # `fc` is the points we're using *this iteration* to produce the estimate
+        work_fc = (f[ic][:, :n_new], work.fs[ic], f[ic][:, -n_new:])
+        work_fc = xp.concat(work_fc, axis=-1)
+        if work.nit == 0:
+            fc = work_fc
+        else:
+            fc = (work_fc[:, :n], work_fc[:, n:n+1], work_fc[:, -n:])
+            fc = xp.concat(fc, axis=-1)
+
+        # One-sided difference
+        work_fo = xp.concat((work.fs[io], f[io]), axis=-1)
+        if work.nit == 0:
+            fo = work_fo
+        else:
+            fo = xp.concat((work_fo[:, 0:1], work_fo[:, -2*n:]), axis=-1)
+
+        work.fs = xp.zeros((ic.shape[0], work.fs.shape[-1] + 2*n_new), dtype=work.dtype)
+        work.fs = xpx.at(work.fs)[ic].set(work_fc)
+        work.fs = xpx.at(work.fs)[io].set(work_fo)
+
+        wc, wo = _derivative_weights(work, n, xp)
+        work.df_last = xp.asarray(work.df, copy=True)
+        work.df = xpx.at(work.df)[ic].set(fc @ wc / work.h[ic])
+        work.df = xpx.at(work.df)[io].set(fo @ wo / work.h[io])
+        work.df = xpx.at(work.df)[il].multiply(-1)
+
+        work.h /= work.fac
+        work.error_last = work.error
+        # Simple error estimate - the difference in derivative estimates between
+        # this iteration and the last. This is typically conservative because if
+        # convergence has begin, the true error is much closer to the difference
+        # between the current estimate and the *next* error estimate. However,
+        # we could use Richarson extrapolation to produce an error estimate that
+        # is one order higher, and take the difference between that and
+        # `work.df` (which would just be constant factor that depends on `fac`.)
+        work.error = xp.abs(work.df - work.df_last)
+
+    def check_termination(work):
+        """Terminate due to convergence, non-finite values, or error increase"""
+        stop = xp.astype(xp.zeros_like(work.df), xp.bool)
+
+        i = work.error < work.atol + work.rtol*abs(work.df)
+        work.status = xpx.at(work.status)[i].set(eim._ECONVERGED)
+        stop = xpx.at(stop)[i].set(True)
+
+        if work.nit > 0:
+            i = ~((xp.isfinite(work.x) & xp.isfinite(work.df)) | stop)
+            work.df = xpx.at(work.df)[i].set(xp.nan)
+            work.status = xpx.at(work.status)[i].set(eim._EVALUEERR)
+            stop = xpx.at(stop)[i].set(True)
+
+        # With infinite precision, there is a step size below which
+        # all smaller step sizes will reduce the error. But in floating point
+        # arithmetic, catastrophic cancellation will begin to cause the error
+        # to increase again. This heuristic tries to avoid step sizes that are
+        # too small. There may be more theoretically sound approaches for
+        # detecting a step size that minimizes the total error, but this
+        # heuristic seems simple and effective.
+        i = (work.error > work.error_last*10) & ~stop
+        work.status = xpx.at(work.status)[i].set(_EERRORINCREASE)
+        stop = xpx.at(stop)[i].set(True)
+
+        return stop
+
+    def post_termination_check(work):
+        return
+
+    def customize_result(res, shape):
+        return shape
+
+    return eim._loop(work, callback, shape, maxiter, func, args, dtype,
+                     pre_func_eval, post_func_eval, check_termination,
+                     post_termination_check, customize_result, res_work_pairs,
+                     xp, preserve_shape)
+
+
+def _derivative_weights(work, n, xp):
+    # This produces the weights of the finite difference formula for a given
+    # stencil. In experiments, use of a second-order central difference formula
+    # with Richardson extrapolation was more accurate numerically, but it was
+    # more complicated, and it would have become even more complicated when
+    # adding support for one-sided differences. However, now that all the
+    # function evaluation values are stored, they can be processed in whatever
+    # way is desired to produce the derivative estimate. We leave alternative
+    # approaches to future work. To be more self-contained, here is the theory
+    # for deriving the weights below.
+    #
+    # Recall that the Taylor expansion of a univariate, scalar-values function
+    # about a point `x` may be expressed as:
+    #      f(x + h)  =     f(x) + f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    # Suppose we evaluate f(x), f(x+h), and f(x-h).  We have:
+    #      f(x)      =     f(x)
+    #      f(x + h)  =     f(x) + f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    #      f(x - h)  =     f(x) - f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    # We can solve for weights `wi` such that:
+    #   w1*f(x)      = w1*(f(x))
+    # + w2*f(x + h)  = w2*(f(x) + f'(x)*h + f''(x)/2!*h**2) + O(h**3)
+    # + w3*f(x - h)  = w3*(f(x) - f'(x)*h + f''(x)/2!*h**2) + O(h**3)
+    #                =     0    + f'(x)*h + 0               + O(h**3)
+    # Then
+    #     f'(x) ~ (w1*f(x) + w2*f(x+h) + w3*f(x-h))/h
+    # is a finite difference derivative approximation with error O(h**2),
+    # and so it is said to be a "second-order" approximation. Under certain
+    # conditions (e.g. well-behaved function, `h` sufficiently small), the
+    # error in the approximation will decrease with h**2; that is, if `h` is
+    # reduced by a factor of 2, the error is reduced by a factor of 4.
+    #
+    # By default, we use eighth-order formulae. Our central-difference formula
+    # uses abscissae:
+    #   x-h/c**3, x-h/c**2, x-h/c, x-h, x, x+h, x+h/c, x+h/c**2, x+h/c**3
+    # where `c` is the step factor. (Typically, the step factor is greater than
+    # one, so the outermost points - as written above - are actually closest to
+    # `x`.) This "stencil" is chosen so that each iteration, the step can be
+    # reduced by the factor `c`, and most of the function evaluations can be
+    # reused with the new step size. For example, in the next iteration, we
+    # will have:
+    #   x-h/c**4, x-h/c**3, x-h/c**2, x-h/c, x, x+h/c, x+h/c**2, x+h/c**3, x+h/c**4
+    # We do not reuse `x-h` and `x+h` for the new derivative estimate.
+    # While this would increase the order of the formula and thus the
+    # theoretical convergence rate, it is also less stable numerically.
+    # (As noted above, there are other ways of processing the values that are
+    # more stable. Thus, even now we store `f(x-h)` and `f(x+h)` in `work.fs`
+    # to simplify future development of this sort of improvement.)
+    #
+    # The (right) one-sided formula is produced similarly using abscissae
+    #   x, x+h, x+h/d, x+h/d**2, ..., x+h/d**6, x+h/d**7, x+h/d**7
+    # where `d` is the square root of `c`. (The left one-sided formula simply
+    # uses -h.) When the step size is reduced by factor `c = d**2`, we have
+    # abscissae:
+    #   x, x+h/d**2, x+h/d**3..., x+h/d**8, x+h/d**9, x+h/d**9
+    # `d` is chosen as the square root of `c` so that the rate of the step-size
+    # reduction is the same per iteration as in the central difference case.
+    # Note that because the central difference formulas are inherently of even
+    # order, for simplicity, we use only even-order formulas for one-sided
+    # differences, too.
+
+    # It's possible for the user to specify `fac` in, say, double precision but
+    # `x` and `args` in single precision. `fac` gets converted to single
+    # precision, but we should always use double precision for the intermediate
+    # calculations here to avoid additional error in the weights.
+    fac = float(work.fac)
+
+    # Note that if the user switches back to floating point precision with
+    # `x` and `args`, then `fac` will not necessarily equal the (lower
+    # precision) cached `_derivative_weights.fac`, and the weights will
+    # need to be recalculated. This could be fixed, but it's late, and of
+    # low consequence.
+
+    diff_state = work.diff_state
+    if fac != diff_state.fac:
+        diff_state.central = []
+        diff_state.right = []
+        diff_state.fac = fac
+
+    if len(diff_state.central) != 2*n + 1:
+        # Central difference weights. Consider refactoring this; it could
+        # probably be more compact.
+        # Note: Using NumPy here is OK; we convert to xp-type at the end
+        i = np.arange(-n, n + 1)
+        p = np.abs(i) - 1.  # center point has power `p` -1, but sign `s` is 0
+        s = np.sign(i)
+
+        h = s / fac ** p
+        A = np.vander(h, increasing=True).T
+        b = np.zeros(2*n + 1)
+        b[1] = 1
+        weights = np.linalg.solve(A, b)
+
+        # Enforce identities to improve accuracy
+        weights[n] = 0
+        for i in range(n):
+            weights[-i-1] = -weights[i]
+
+        # Cache the weights. We only need to calculate them once unless
+        # the step factor changes.
+        diff_state.central = weights
+
+        # One-sided difference weights. The left one-sided weights (with
+        # negative steps) are simply the negative of the right one-sided
+        # weights, so no need to compute them separately.
+        i = np.arange(2*n + 1)
+        p = i - 1.
+        s = np.sign(i)
+
+        h = s / np.sqrt(fac) ** p
+        A = np.vander(h, increasing=True).T
+        b = np.zeros(2 * n + 1)
+        b[1] = 1
+        weights = np.linalg.solve(A, b)
+
+        diff_state.right = weights
+
+    return (xp.asarray(diff_state.central, dtype=work.dtype),
+            xp.asarray(diff_state.right, dtype=work.dtype))
+
+
+def jacobian(f, x, *, tolerances=None, maxiter=10, order=8, initial_step=0.5,
+             step_factor=2.0, step_direction=0):
+    r"""Evaluate the Jacobian of a function numerically.
+
+    Parameters
+    ----------
+    f : callable
+        The function whose Jacobian is desired. The signature must be::
+
+            f(xi: ndarray) -> ndarray
+
+        where each element of ``xi`` is a finite real. If the function to be
+        differentiated accepts additional arguments, wrap it (e.g. using
+        `functools.partial` or ``lambda``) and pass the wrapped callable
+        into `jacobian`. `f` must not mutate the array ``xi``. See Notes
+        regarding vectorization and the dimensionality of the input and output.
+    x : float array_like
+        Points at which to evaluate the Jacobian. Must have at least one dimension.
+        See Notes regarding the dimensionality and vectorization.
+    tolerances : dictionary of floats, optional
+        Absolute and relative tolerances. Valid keys of the dictionary are:
+
+        - ``atol`` - absolute tolerance on the derivative
+        - ``rtol`` - relative tolerance on the derivative
+
+        Iteration will stop when ``res.error < atol + rtol * abs(res.df)``. The default
+        `atol` is the smallest normal number of the appropriate dtype, and
+        the default `rtol` is the square root of the precision of the
+        appropriate dtype.
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform. See
+        Notes.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float array_like, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation. Must be broadcastable with `x` and `step_direction`.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    step_direction : integer array_like
+        An array representing the direction of the finite difference steps (e.g.
+        for use when `x` lies near to the boundary of the domain of the function.)
+        Must be broadcastable with `x` and `initial_step`.
+        Where 0 (default), central differences are used; where negative (e.g.
+        -1), steps are non-positive; and where positive (e.g. 1), all steps are
+        non-negative.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-1`` : The error estimate increased, so iteration was terminated.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+
+        df : float array
+            The Jacobian of `f` at `x`, if the algorithm terminated
+            successfully.
+        error : float array
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the Jacobian and the estimate in the
+            previous iteration.
+        nit : int array
+            The number of iterations of the algorithm that were performed.
+        nfev : int array
+            The number of points at which `f` was evaluated.
+
+        Each element of an attribute is associated with the corresponding
+        element of `df`. For instance, element ``i`` of `nfev` is the
+        number of points at which `f` was evaluated for the sake of
+        computing element ``i`` of `df`.
+
+    See Also
+    --------
+    derivative, hessian
+
+    Notes
+    -----
+    Suppose we wish to evaluate the Jacobian of a function
+    :math:`f: \mathbf{R}^m \rightarrow \mathbf{R}^n`. Assign to variables
+    ``m`` and ``n`` the positive integer values of :math:`m` and :math:`n`,
+    respectively, and let ``...`` represent an arbitrary tuple of integers.
+    If we wish to evaluate the Jacobian at a single point, then:
+
+    - argument `x` must be an array of shape ``(m,)``
+    - argument `f` must be vectorized to accept an array of shape ``(m, ...)``.
+      The first axis represents the :math:`m` inputs of :math:`f`; the remainder
+      are for evaluating the function at multiple points in a single call.
+    - argument `f` must return an array of shape ``(n, ...)``. The first
+      axis represents the :math:`n` outputs of :math:`f`; the remainder
+      are for the result of evaluating the function at multiple points.
+    - attribute ``df`` of the result object will be an array of shape ``(n, m)``,
+      the Jacobian.
+
+    This function is also vectorized in the sense that the Jacobian can be
+    evaluated at ``k`` points in a single call. In this case, `x` would be an
+    array of shape ``(m, k)``, `f` would accept an array of shape
+    ``(m, k, ...)`` and return an array of shape ``(n, k, ...)``, and the ``df``
+    attribute of the result would have shape ``(n, m, k)``.
+
+    Suppose the desired callable ``f_not_vectorized`` is not vectorized; it can
+    only accept an array of shape ``(m,)``. A simple solution to satisfy the required
+    interface is to wrap ``f_not_vectorized`` as follows::
+
+        def f(x):
+            return np.apply_along_axis(f_not_vectorized, axis=0, arr=x)
+
+    Alternatively, suppose the desired callable ``f_vec_q`` is vectorized, but
+    only for 2-D arrays of shape ``(m, q)``. To satisfy the required interface,
+    consider::
+
+        def f(x):
+            m, batch = x.shape[0], x.shape[1:]  # x.shape is (m, ...)
+            x = np.reshape(x, (m, -1))  # `-1` is short for q = prod(batch)
+            res = f_vec_q(x)  # pass shape (m, q) to function
+            n = res.shape[0]
+            return np.reshape(res, (n,) + batch)  # return shape (n, ...)
+
+    Then pass the wrapped callable ``f`` as the first argument of `jacobian`.
+
+    References
+    ----------
+    .. [1] Jacobian matrix and determinant, *Wikipedia*,
+           https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant
+
+    Examples
+    --------
+    The Rosenbrock function maps from :math:`\mathbf{R}^m \rightarrow \mathbf{R}`;
+    the SciPy implementation `scipy.optimize.rosen` is vectorized to accept an
+    array of shape ``(m, p)`` and return an array of shape ``p``. Suppose we wish
+    to evaluate the Jacobian (AKA the gradient because the function returns a scalar)
+    at ``[0.5, 0.5, 0.5]``.
+
+    >>> import numpy as np
+    >>> from scipy.differentiate import jacobian
+    >>> from scipy.optimize import rosen, rosen_der
+    >>> m = 3
+    >>> x = np.full(m, 0.5)
+    >>> res = jacobian(rosen, x)
+    >>> ref = rosen_der(x)  # reference value of the gradient
+    >>> res.df, ref
+    (array([-51.,  -1.,  50.]), array([-51.,  -1.,  50.]))
+
+    As an example of a function with multiple outputs, consider Example 4
+    from [1]_.
+
+    >>> def f(x):
+    ...     x1, x2, x3 = x
+    ...     return [x1, 5*x3, 4*x2**2 - 2*x3, x3*np.sin(x1)]
+
+    The true Jacobian is given by:
+
+    >>> def df(x):
+    ...         x1, x2, x3 = x
+    ...         one = np.ones_like(x1)
+    ...         return [[one, 0*one, 0*one],
+    ...                 [0*one, 0*one, 5*one],
+    ...                 [0*one, 8*x2, -2*one],
+    ...                 [x3*np.cos(x1), 0*one, np.sin(x1)]]
+
+    Evaluate the Jacobian at an arbitrary point.
+
+    >>> rng = np.random.default_rng(389252938452)
+    >>> x = rng.random(size=3)
+    >>> res = jacobian(f, x)
+    >>> ref = df(x)
+    >>> res.df.shape == (4, 3)
+    True
+    >>> np.allclose(res.df, ref)
+    True
+
+    Evaluate the Jacobian at 10 arbitrary points in a single call.
+
+    >>> x = rng.random(size=(3, 10))
+    >>> res = jacobian(f, x)
+    >>> ref = df(x)
+    >>> res.df.shape == (4, 3, 10)
+    True
+    >>> np.allclose(res.df, ref)
+    True
+
+    """
+    xp = array_namespace(x)
+    x0 = xp_promote(x, force_floating=True, xp=xp)
+
+    if x0.ndim < 1:
+        message = "Argument `x` must be at least 1-D."
+        raise ValueError(message)
+
+    m = x0.shape[0]
+    i = xp.arange(m)
+
+    def wrapped(x):
+        p = () if x.ndim == x0.ndim else (x.shape[-1],)  # number of abscissae
+
+        new_shape = (m, m) + x0.shape[1:] + p
+        xph = xp.expand_dims(x0, axis=1)
+        if x.ndim != x0.ndim:
+            xph = xp.expand_dims(xph, axis=-1)
+        xph = xp_copy(xp.broadcast_to(xph, new_shape), xp=xp)
+        xph = xpx.at(xph)[i, i].set(x)
+        return f(xph)
+
+    res = derivative(wrapped, x, tolerances=tolerances,
+                     maxiter=maxiter, order=order, initial_step=initial_step,
+                     step_factor=step_factor, preserve_shape=True,
+                     step_direction=step_direction)
+
+    del res.x  # the user knows `x`, and the way it gets broadcasted is meaningless here
+    return res
+
+
+def hessian(f, x, *, tolerances=None, maxiter=10,
+            order=8, initial_step=0.5, step_factor=2.0):
+    r"""Evaluate the Hessian of a function numerically.
+
+    Parameters
+    ----------
+    f : callable
+        The function whose Hessian is desired. The signature must be::
+
+            f(xi: ndarray) -> ndarray
+
+        where each element of ``xi`` is a finite real. If the function to be
+        differentiated accepts additional arguments, wrap it (e.g. using
+        `functools.partial` or ``lambda``) and pass the wrapped callable
+        into `hessian`. `f` must not mutate the array ``xi``. See Notes
+        regarding vectorization and the dimensionality of the input and output.
+    x : float array_like
+        Points at which to evaluate the Hessian. Must have at least one dimension.
+        See Notes regarding the dimensionality and vectorization.
+    tolerances : dictionary of floats, optional
+        Absolute and relative tolerances. Valid keys of the dictionary are:
+
+        - ``atol`` - absolute tolerance on the derivative
+        - ``rtol`` - relative tolerance on the derivative
+
+        Iteration will stop when ``res.error < atol + rtol * abs(res.df)``. The default
+        `atol` is the smallest normal number of the appropriate dtype, and
+        the default `rtol` is the square root of the precision of the
+        appropriate dtype.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform. See
+        Notes.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-1`` : The error estimate increased, so iteration was terminated.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+
+        ddf : float array
+            The Hessian of `f` at `x`, if the algorithm terminated
+            successfully.
+        error : float array
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the Hessian and the estimate in the
+            previous iteration.
+        nfev : int array
+            The number of points at which `f` was evaluated.
+
+        Each element of an attribute is associated with the corresponding
+        element of `ddf`. For instance, element ``[i, j]`` of `nfev` is the
+        number of points at which `f` was evaluated for the sake of
+        computing element ``[i, j]`` of `ddf`.
+
+    See Also
+    --------
+    derivative, jacobian
+
+    Notes
+    -----
+    Suppose we wish to evaluate the Hessian of a function
+    :math:`f: \mathbf{R}^m \rightarrow \mathbf{R}`, and we assign to variable
+    ``m`` the positive integer value of :math:`m`. If we wish to evaluate
+    the Hessian at a single point, then:
+
+    - argument `x` must be an array of shape ``(m,)``
+    - argument `f` must be vectorized to accept an array of shape
+      ``(m, ...)``. The first axis represents the :math:`m` inputs of
+      :math:`f`; the remaining axes indicated by ellipses are for evaluating
+      the function at several abscissae in a single call.
+    - argument `f` must return an array of shape ``(...)``.
+    - attribute ``dff`` of the result object will be an array of shape ``(m, m)``,
+      the Hessian.
+
+    This function is also vectorized in the sense that the Hessian can be
+    evaluated at ``k`` points in a single call. In this case, `x` would be an
+    array of shape ``(m, k)``, `f` would accept an array of shape
+    ``(m, ...)`` and return an array of shape ``(...)``, and the ``ddf``
+    attribute of the result would have shape ``(m, m, k)``. Note that the
+    axis associated with the ``k`` points is included within the axes
+    denoted by ``(...)``.
+
+    Currently, `hessian` is implemented by nesting calls to `jacobian`.
+    All options passed to `hessian` are used for both the inner and outer
+    calls with one exception: the `rtol` used in the inner `jacobian` call
+    is tightened by a factor of 100 with the expectation that the inner
+    error can be ignored. A consequence is that `rtol` should not be set
+    less than 100 times the precision of the dtype of `x`; a warning is
+    emitted otherwise.
+
+    References
+    ----------
+    .. [1] Hessian matrix, *Wikipedia*,
+           https://en.wikipedia.org/wiki/Hessian_matrix
+
+    Examples
+    --------
+    The Rosenbrock function maps from :math:`\mathbf{R}^m \rightarrow \mathbf{R}`;
+    the SciPy implementation `scipy.optimize.rosen` is vectorized to accept an
+    array of shape ``(m, ...)`` and return an array of shape ``...``. Suppose we
+    wish to evaluate the Hessian at ``[0.5, 0.5, 0.5]``.
+
+    >>> import numpy as np
+    >>> from scipy.differentiate import hessian
+    >>> from scipy.optimize import rosen, rosen_hess
+    >>> m = 3
+    >>> x = np.full(m, 0.5)
+    >>> res = hessian(rosen, x)
+    >>> ref = rosen_hess(x)  # reference value of the Hessian
+    >>> np.allclose(res.ddf, ref)
+    True
+
+    `hessian` is vectorized to evaluate the Hessian at multiple points
+    in a single call.
+
+    >>> rng = np.random.default_rng(4589245925010)
+    >>> x = rng.random((m, 10))
+    >>> res = hessian(rosen, x)
+    >>> ref = [rosen_hess(xi) for xi in x.T]
+    >>> ref = np.moveaxis(ref, 0, -1)
+    >>> np.allclose(res.ddf, ref)
+    True
+
+    """
+    # todo:
+    # - add ability to vectorize over additional parameters (*args?)
+    # - error estimate stack with inner jacobian (or use legit 2D stencil)
+
+    kwargs = dict(maxiter=maxiter, order=order, initial_step=initial_step,
+                  step_factor=step_factor)
+    tolerances = {} if tolerances is None else tolerances
+    atol = tolerances.get('atol', None)
+    rtol = tolerances.get('rtol', None)
+
+    xp = array_namespace(x)
+    x0 = xp_promote(x, force_floating=True, xp=xp)
+
+    finfo = xp.finfo(x0.dtype)
+    rtol = finfo.eps**0.5 if rtol is None else rtol  # keep same as `derivative`
+
+    # tighten the inner tolerance to make the inner error negligible
+    rtol_min = finfo.eps * 100
+    message = (f"The specified `{rtol=}`, but error estimates are likely to be "
+               f"unreliable when `rtol < {rtol_min}`.")
+    if 0 < rtol < rtol_min:  # rtol <= 0 is an error
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+        rtol = rtol_min
+
+    def df(x):
+        tolerances = dict(rtol=rtol/100, atol=atol)
+        temp = jacobian(f, x, tolerances=tolerances, **kwargs)
+        nfev.append(temp.nfev if len(nfev) == 0 else temp.nfev.sum(axis=-1))
+        return temp.df
+
+    nfev = []  # track inner function evaluations
+    res = jacobian(df, x, tolerances=tolerances, **kwargs)  # jacobian of jacobian
+
+    nfev = xp.cumulative_sum(xp.stack(nfev), axis=0)
+    res_nit = xp.astype(res.nit[xp.newaxis, ...], xp.int64)  # appease torch
+    res.nfev = xp.take_along_axis(nfev, res_nit, axis=0)[0]
+    res.ddf = res.df
+    del res.df  # this is renamed to ddf
+    del res.nit  # this is only the outer-jacobian nit
+
+    return res

tool_server/.venv/lib/python3.12/site-packages/scipy/fft/__init__.py

@@ -0,0 +1,114 @@
+"""
+==============================================
+Discrete Fourier transforms (:mod:`scipy.fft`)
+==============================================
+
+.. currentmodule:: scipy.fft
+
+Fast Fourier Transforms (FFTs)
+==============================
+
+.. autosummary::
+   :toctree: generated/
+
+   fft - Fast (discrete) Fourier Transform (FFT)
+   ifft - Inverse FFT
+   fft2 - 2-D FFT
+   ifft2 - 2-D inverse FFT
+   fftn - N-D FFT
+   ifftn - N-D inverse FFT
+   rfft - FFT of strictly real-valued sequence
+   irfft - Inverse of rfft
+   rfft2 - 2-D FFT of real sequence
+   irfft2 - Inverse of rfft2
+   rfftn - N-D FFT of real sequence
+   irfftn - Inverse of rfftn
+   hfft - FFT of a Hermitian sequence (real spectrum)
+   ihfft - Inverse of hfft
+   hfft2 - 2-D FFT of a Hermitian sequence
+   ihfft2 - Inverse of hfft2
+   hfftn - N-D FFT of a Hermitian sequence
+   ihfftn - Inverse of hfftn
+
+Discrete Sin and Cosine Transforms (DST and DCT)
+================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   dct - Discrete cosine transform
+   idct - Inverse discrete cosine transform
+   dctn - N-D Discrete cosine transform
+   idctn - N-D Inverse discrete cosine transform
+   dst - Discrete sine transform
+   idst - Inverse discrete sine transform
+   dstn - N-D Discrete sine transform
+   idstn - N-D Inverse discrete sine transform
+
+Fast Hankel Transforms
+======================
+
+.. autosummary::
+   :toctree: generated/
+
+   fht - Fast Hankel transform
+   ifht - Inverse of fht
+
+Helper functions
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   fftshift - Shift the zero-frequency component to the center of the spectrum
+   ifftshift - The inverse of `fftshift`
+   fftfreq - Return the Discrete Fourier Transform sample frequencies
+   rfftfreq - DFT sample frequencies (for usage with rfft, irfft)
+   fhtoffset - Compute an optimal offset for the Fast Hankel Transform
+   next_fast_len - Find the optimal length to zero-pad an FFT for speed
+   prev_fast_len - Find the maximum slice length that results in a fast FFT
+   set_workers - Context manager to set default number of workers
+   get_workers - Get the current default number of workers
+
+Backend control
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   set_backend - Context manager to set the backend within a fixed scope
+   skip_backend - Context manager to skip a backend within a fixed scope
+   set_global_backend - Sets the global fft backend
+   register_backend - Register a backend for permanent use
+
+"""
+
+from ._basic import (
+    fft, ifft, fft2, ifft2, fftn, ifftn,
+    rfft, irfft, rfft2, irfft2, rfftn, irfftn,
+    hfft, ihfft, hfft2, ihfft2, hfftn, ihfftn)
+from ._realtransforms import dct, idct, dst, idst, dctn, idctn, dstn, idstn
+from ._fftlog import fht, ifht, fhtoffset
+from ._helper import (
+    next_fast_len, prev_fast_len, fftfreq,
+    rfftfreq, fftshift, ifftshift)
+from ._backend import (set_backend, skip_backend, set_global_backend,
+                       register_backend)
+from ._pocketfft.helper import set_workers, get_workers
+
+__all__ = [
+    'fft', 'ifft', 'fft2', 'ifft2', 'fftn', 'ifftn',
+    'rfft', 'irfft', 'rfft2', 'irfft2', 'rfftn', 'irfftn',
+    'hfft', 'ihfft', 'hfft2', 'ihfft2', 'hfftn', 'ihfftn',
+    'fftfreq', 'rfftfreq', 'fftshift', 'ifftshift',
+    'next_fast_len', 'prev_fast_len',
+    'dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn',
+    'fht', 'ifht',
+    'fhtoffset',
+    'set_backend', 'skip_backend', 'set_global_backend', 'register_backend',
+    'get_workers', 'set_workers']
+
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

tool_server/.venv/lib/python3.12/site-packages/scipy/fft/_backend.py

@@ -0,0 +1,196 @@
+import scipy._lib.uarray as ua
+from . import _basic_backend
+from . import _realtransforms_backend
+from . import _fftlog_backend
+
+
+class _ScipyBackend:
+    """The default backend for fft calculations
+
+    Notes
+    -----
+    We use the domain ``numpy.scipy`` rather than ``scipy`` because ``uarray``
+    treats the domain as a hierarchy. This means the user can install a single
+    backend for ``numpy`` and have it implement ``numpy.scipy.fft`` as well.
+    """
+    __ua_domain__ = "numpy.scipy.fft"
+
+    @staticmethod
+    def __ua_function__(method, args, kwargs):
+
+        fn = getattr(_basic_backend, method.__name__, None)
+        if fn is None:
+            fn = getattr(_realtransforms_backend, method.__name__, None)
+        if fn is None:
+            fn = getattr(_fftlog_backend, method.__name__, None)
+        if fn is None:
+            return NotImplemented
+        return fn(*args, **kwargs)
+
+
+_named_backends = {
+    'scipy': _ScipyBackend,
+}
+
+
+def _backend_from_arg(backend):
+    """Maps strings to known backends and validates the backend"""
+
+    if isinstance(backend, str):
+        try:
+            backend = _named_backends[backend]
+        except KeyError as e:
+            raise ValueError(f'Unknown backend {backend}') from e
+
+    if backend.__ua_domain__ != 'numpy.scipy.fft':
+        raise ValueError('Backend does not implement "numpy.scipy.fft"')
+
+    return backend
+
+
+def set_global_backend(backend, coerce=False, only=False, try_last=False):
+    """Sets the global fft backend
+
+    This utility method replaces the default backend for permanent use. It
+    will be tried in the list of backends automatically, unless the
+    ``only`` flag is set on a backend. This will be the first tried
+    backend outside the :obj:`set_backend` context manager.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to use.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+    coerce : bool
+        Whether to coerce input types when trying this backend.
+    only : bool
+        If ``True``, no more backends will be tried if this fails.
+        Implied by ``coerce=True``.
+    try_last : bool
+        If ``True``, the global backend is tried after registered backends.
+
+    Raises
+    ------
+    ValueError: If the backend does not implement ``numpy.scipy.fft``.
+
+    Notes
+    -----
+    This will overwrite the previously set global backend, which, by default, is
+    the SciPy implementation.
+
+    Examples
+    --------
+    We can set the global fft backend:
+
+    >>> from scipy.fft import fft, set_global_backend
+    >>> set_global_backend("scipy")  # Sets global backend (default is "scipy").
+    >>> fft([1])  # Calls the global backend
+    array([1.+0.j])
+    """
+    backend = _backend_from_arg(backend)
+    ua.set_global_backend(backend, coerce=coerce, only=only, try_last=try_last)
+
+
+def register_backend(backend):
+    """
+    Register a backend for permanent use.
+
+    Registered backends have the lowest priority and will be tried after the
+    global backend.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to use.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+
+    Raises
+    ------
+    ValueError: If the backend does not implement ``numpy.scipy.fft``.
+
+    Examples
+    --------
+    We can register a new fft backend:
+
+    >>> from scipy.fft import fft, register_backend, set_global_backend
+    >>> class NoopBackend:  # Define an invalid Backend
+    ...     __ua_domain__ = "numpy.scipy.fft"
+    ...     def __ua_function__(self, func, args, kwargs):
+    ...          return NotImplemented
+    >>> set_global_backend(NoopBackend())  # Set the invalid backend as global
+    >>> register_backend("scipy")  # Register a new backend
+    # The registered backend is called because
+    # the global backend returns `NotImplemented`
+    >>> fft([1])
+    array([1.+0.j])
+    >>> set_global_backend("scipy")  # Restore global backend to default
+
+    """
+    backend = _backend_from_arg(backend)
+    ua.register_backend(backend)
+
+
+def set_backend(backend, coerce=False, only=False):
+    """Context manager to set the backend within a fixed scope.
+
+    Upon entering the ``with`` statement, the given backend will be added to
+    the list of available backends with the highest priority. Upon exit, the
+    backend is reset to the state before entering the scope.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to use.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+    coerce : bool, optional
+        Whether to allow expensive conversions for the ``x`` parameter. e.g.,
+        copying a NumPy array to the GPU for a CuPy backend. Implies ``only``.
+    only : bool, optional
+        If only is ``True`` and this backend returns ``NotImplemented``, then a
+        BackendNotImplemented error will be raised immediately. Ignoring any
+        lower priority backends.
+
+    Examples
+    --------
+    >>> import scipy.fft as fft
+    >>> with fft.set_backend('scipy', only=True):
+    ...     fft.fft([1])  # Always calls the scipy implementation
+    array([1.+0.j])
+    """
+    backend = _backend_from_arg(backend)
+    return ua.set_backend(backend, coerce=coerce, only=only)
+
+
+def skip_backend(backend):
+    """Context manager to skip a backend within a fixed scope.
+
+    Within the context of a ``with`` statement, the given backend will not be
+    called. This covers backends registered both locally and globally. Upon
+    exit, the backend will again be considered.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to skip.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+
+    Examples
+    --------
+    >>> import scipy.fft as fft
+    >>> fft.fft([1])  # Calls default SciPy backend
+    array([1.+0.j])
+    >>> with fft.skip_backend('scipy'):  # We explicitly skip the SciPy backend
+    ...     fft.fft([1])                 # leaving no implementation available
+    Traceback (most recent call last):
+        ...
+    BackendNotImplementedError: No selected backends had an implementation ...
+    """
+    backend = _backend_from_arg(backend)
+    return ua.skip_backend(backend)
+
+
+set_global_backend('scipy', try_last=True)

tool_server/.venv/lib/python3.12/site-packages/scipy/fft/_basic.py

@@ -0,0 +1,1650 @@
+from scipy._lib.uarray import generate_multimethod, Dispatchable
+import numpy as np
+
+
+def _x_replacer(args, kwargs, dispatchables):
+    """
+    uarray argument replacer to replace the transform input array (``x``)
+    """
+    if len(args) > 0:
+        return (dispatchables[0],) + args[1:], kwargs
+    kw = kwargs.copy()
+    kw['x'] = dispatchables[0]
+    return args, kw
+
+
+def _dispatch(func):
+    """
+    Function annotation that creates a uarray multimethod from the function
+    """
+    return generate_multimethod(func, _x_replacer, domain="numpy.scipy.fft")
+
+
+@_dispatch
+def fft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+        plan=None):
+    """
+    Compute the 1-D discrete Fourier Transform.
+
+    This function computes the 1-D *n*-point discrete Fourier
+    Transform (DFT) with the efficient Fast Fourier Transform (FFT)
+    algorithm [1]_.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    n : int, optional
+        Length of the transformed axis of the output.
+        If `n` is smaller than the length of the input, the input is cropped.
+        If it is larger, the input is padded with zeros. If `n` is not given,
+        the length of the input along the axis specified by `axis` is used.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last axis is
+        used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode. Default is "backward", meaning no normalization on
+        the forward transforms and scaling by ``1/n`` on the `ifft`.
+        "forward" instead applies the ``1/n`` factor on the forward transform.
+        For ``norm="ortho"``, both directions are scaled by ``1/sqrt(n)``.
+
+        .. versionadded:: 1.6.0
+           ``norm={"forward", "backward"}`` options were added
+
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See the notes below for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``. See below for more
+        details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+
+    Raises
+    ------
+    IndexError
+        if `axes` is larger than the last axis of `x`.
+
+    See Also
+    --------
+    ifft : The inverse of `fft`.
+    fft2 : The 2-D FFT.
+    fftn : The N-D FFT.
+    rfftn : The N-D FFT of real input.
+    fftfreq : Frequency bins for given FFT parameters.
+    next_fast_len : Size to pad input to for most efficient transforms
+
+    Notes
+    -----
+    FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform
+    (DFT) can be calculated efficiently, by using symmetries in the calculated
+    terms. The symmetry is highest when `n` is a power of 2, and the transform
+    is therefore most efficient for these sizes. For poorly factorizable sizes,
+    `scipy.fft` uses Bluestein's algorithm [2]_ and so is never worse than
+    O(`n` log `n`). Further performance improvements may be seen by zero-padding
+    the input using `next_fast_len`.
+
+    If ``x`` is a 1d array, then the `fft` is equivalent to ::
+
+        y[k] = np.sum(x * np.exp(-2j * np.pi * k * np.arange(n)/n))
+
+    The frequency term ``f=k/n`` is found at ``y[k]``. At ``y[n/2]`` we reach
+    the Nyquist frequency and wrap around to the negative-frequency terms. So,
+    for an 8-point transform, the frequencies of the result are
+    [0, 1, 2, 3, -4, -3, -2, -1]. To rearrange the fft output so that the
+    zero-frequency component is centered, like [-4, -3, -2, -1, 0, 1, 2, 3],
+    use `fftshift`.
+
+    Transforms can be done in single, double, or extended precision (long
+    double) floating point. Half precision inputs will be converted to single
+    precision and non-floating-point inputs will be converted to double
+    precision.
+
+    If the data type of ``x`` is real, a "real FFT" algorithm is automatically
+    used, which roughly halves the computation time. To increase efficiency
+    a little further, use `rfft`, which does the same calculation, but only
+    outputs half of the symmetrical spectrum. If the data are both real and
+    symmetrical, the `dct` can again double the efficiency, by generating
+    half of the spectrum from half of the signal.
+
+    When ``overwrite_x=True`` is specified, the memory referenced by ``x`` may
+    be used by the implementation in any way. This may include reusing the
+    memory for the result, but this is in no way guaranteed. You should not
+    rely on the contents of ``x`` after the transform as this may change in
+    future without warning.
+
+    The ``workers`` argument specifies the maximum number of parallel jobs to
+    split the FFT computation into. This will execute independent 1-D
+    FFTs within ``x``. So, ``x`` must be at least 2-D and the
+    non-transformed axes must be large enough to split into chunks. If ``x`` is
+    too small, fewer jobs may be used than requested.
+
+    References
+    ----------
+    .. [1] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
+           machine calculation of complex Fourier series," *Math. Comput.*
+           19: 297-301.
+    .. [2] Bluestein, L., 1970, "A linear filtering approach to the
+           computation of discrete Fourier transform". *IEEE Transactions on
+           Audio and Electroacoustics.* 18 (4): 451-455.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> scipy.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
+    array([-2.33486982e-16+1.14423775e-17j,  8.00000000e+00-1.25557246e-15j,
+            2.33486982e-16+2.33486982e-16j,  0.00000000e+00+1.22464680e-16j,
+           -1.14423775e-17+2.33486982e-16j,  0.00000000e+00+5.20784380e-16j,
+            1.14423775e-17+1.14423775e-17j,  0.00000000e+00+1.22464680e-16j])
+
+    In this example, real input has an FFT which is Hermitian, i.e., symmetric
+    in the real part and anti-symmetric in the imaginary part:
+
+    >>> from scipy.fft import fft, fftfreq, fftshift
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.arange(256)
+    >>> sp = fftshift(fft(np.sin(t)))
+    >>> freq = fftshift(fftfreq(t.shape[-1]))
+    >>> plt.plot(freq, sp.real, freq, sp.imag)
+    [<matplotlib.lines.Line2D object at 0x...>,
+     <matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def ifft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the 1-D inverse discrete Fourier Transform.
+
+    This function computes the inverse of the 1-D *n*-point
+    discrete Fourier transform computed by `fft`.  In other words,
+    ``ifft(fft(x)) == x`` to within numerical accuracy.
+
+    The input should be ordered in the same way as is returned by `fft`,
+    i.e.,
+
+    * ``x[0]`` should contain the zero frequency term,
+    * ``x[1:n//2]`` should contain the positive-frequency terms,
+    * ``x[n//2 + 1:]`` should contain the negative-frequency terms, in
+      increasing order starting from the most negative frequency.
+
+    For an even number of input points, ``x[n//2]`` represents the sum of
+    the values at the positive and negative Nyquist frequencies, as the two
+    are aliased together. See `fft` for details.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    n : int, optional
+        Length of the transformed axis of the output.
+        If `n` is smaller than the length of the input, the input is cropped.
+        If it is larger, the input is padded with zeros. If `n` is not given,
+        the length of the input along the axis specified by `axis` is used.
+        See notes about padding issues.
+    axis : int, optional
+        Axis over which to compute the inverse DFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+
+    Raises
+    ------
+    IndexError
+        If `axes` is larger than the last axis of `x`.
+
+    See Also
+    --------
+    fft : The 1-D (forward) FFT, of which `ifft` is the inverse.
+    ifft2 : The 2-D inverse FFT.
+    ifftn : The N-D inverse FFT.
+
+    Notes
+    -----
+    If the input parameter `n` is larger than the size of the input, the input
+    is padded by appending zeros at the end. Even though this is the common
+    approach, it might lead to surprising results. If a different padding is
+    desired, it must be performed before calling `ifft`.
+
+    If ``x`` is a 1-D array, then the `ifft` is equivalent to ::
+
+        y[k] = np.sum(x * np.exp(2j * np.pi * k * np.arange(n)/n)) / len(x)
+
+    As with `fft`, `ifft` has support for all floating point types and is
+    optimized for real input.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> scipy.fft.ifft([0, 4, 0, 0])
+    array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j]) # may vary
+
+    Create and plot a band-limited signal with random phases:
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> t = np.arange(400)
+    >>> n = np.zeros((400,), dtype=complex)
+    >>> n[40:60] = np.exp(1j*rng.uniform(0, 2*np.pi, (20,)))
+    >>> s = scipy.fft.ifft(n)
+    >>> plt.plot(t, s.real, 'b-', t, s.imag, 'r--')
+    [<matplotlib.lines.Line2D object at ...>, <matplotlib.lines.Line2D object at ...>]
+    >>> plt.legend(('real', 'imaginary'))
+    <matplotlib.legend.Legend object at ...>
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def rfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the 1-D discrete Fourier Transform for real input.
+
+    This function computes the 1-D *n*-point discrete Fourier
+    Transform (DFT) of a real-valued array by means of an efficient algorithm
+    called the Fast Fourier Transform (FFT).
+
+    Parameters
+    ----------
+    x : array_like
+        Input array
+    n : int, optional
+        Number of points along transformation axis in the input to use.
+        If `n` is smaller than the length of the input, the input is cropped.
+        If it is larger, the input is padded with zeros. If `n` is not given,
+        the length of the input along the axis specified by `axis` is used.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last axis is
+        used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        If `n` is even, the length of the transformed axis is ``(n/2)+1``.
+        If `n` is odd, the length is ``(n+1)/2``.
+
+    Raises
+    ------
+    IndexError
+        If `axis` is larger than the last axis of `a`.
+
+    See Also
+    --------
+    irfft : The inverse of `rfft`.
+    fft : The 1-D FFT of general (complex) input.
+    fftn : The N-D FFT.
+    rfft2 : The 2-D FFT of real input.
+    rfftn : The N-D FFT of real input.
+
+    Notes
+    -----
+    When the DFT is computed for purely real input, the output is
+    Hermitian-symmetric, i.e., the negative frequency terms are just the complex
+    conjugates of the corresponding positive-frequency terms, and the
+    negative-frequency terms are therefore redundant. This function does not
+    compute the negative frequency terms, and the length of the transformed
+    axis of the output is therefore ``n//2 + 1``.
+
+    When ``X = rfft(x)`` and fs is the sampling frequency, ``X[0]`` contains
+    the zero-frequency term 0*fs, which is real due to Hermitian symmetry.
+
+    If `n` is even, ``A[-1]`` contains the term representing both positive
+    and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely
+    real. If `n` is odd, there is no term at fs/2; ``A[-1]`` contains
+    the largest positive frequency (fs/2*(n-1)/n), and is complex in the
+    general case.
+
+    If the input `a` contains an imaginary part, it is silently discarded.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> scipy.fft.fft([0, 1, 0, 0])
+    array([ 1.+0.j,  0.-1.j, -1.+0.j,  0.+1.j]) # may vary
+    >>> scipy.fft.rfft([0, 1, 0, 0])
+    array([ 1.+0.j,  0.-1.j, -1.+0.j]) # may vary
+
+    Notice how the final element of the `fft` output is the complex conjugate
+    of the second element, for real input. For `rfft`, this symmetry is
+    exploited to compute only the non-negative frequency terms.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def irfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Computes the inverse of `rfft`.
+
+    This function computes the inverse of the 1-D *n*-point
+    discrete Fourier Transform of real input computed by `rfft`.
+    In other words, ``irfft(rfft(x), len(x)) == x`` to within numerical
+    accuracy. (See Notes below for why ``len(a)`` is necessary here.)
+
+    The input is expected to be in the form returned by `rfft`, i.e., the
+    real zero-frequency term followed by the complex positive frequency terms
+    in order of increasing frequency. Since the discrete Fourier Transform of
+    real input is Hermitian-symmetric, the negative frequency terms are taken
+    to be the complex conjugates of the corresponding positive frequency terms.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    n : int, optional
+        Length of the transformed axis of the output.
+        For `n` output points, ``n//2+1`` input points are necessary. If the
+        input is longer than this, it is cropped. If it is shorter than this,
+        it is padded with zeros. If `n` is not given, it is taken to be
+        ``2*(m-1)``, where ``m`` is the length of the input along the axis
+        specified by `axis`.
+    axis : int, optional
+        Axis over which to compute the inverse FFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        The length of the transformed axis is `n`, or, if `n` is not given,
+        ``2*(m-1)`` where ``m`` is the length of the transformed axis of the
+        input. To get an odd number of output points, `n` must be specified.
+
+    Raises
+    ------
+    IndexError
+        If `axis` is larger than the last axis of `x`.
+
+    See Also
+    --------
+    rfft : The 1-D FFT of real input, of which `irfft` is inverse.
+    fft : The 1-D FFT.
+    irfft2 : The inverse of the 2-D FFT of real input.
+    irfftn : The inverse of the N-D FFT of real input.
+
+    Notes
+    -----
+    Returns the real valued `n`-point inverse discrete Fourier transform
+    of `x`, where `x` contains the non-negative frequency terms of a
+    Hermitian-symmetric sequence. `n` is the length of the result, not the
+    input.
+
+    If you specify an `n` such that `a` must be zero-padded or truncated, the
+    extra/removed values will be added/removed at high frequencies. One can
+    thus resample a series to `m` points via Fourier interpolation by:
+    ``a_resamp = irfft(rfft(a), m)``.
+
+    The default value of `n` assumes an even output length. By the Hermitian
+    symmetry, the last imaginary component must be 0 and so is ignored. To
+    avoid losing information, the correct length of the real input *must* be
+    given.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> scipy.fft.ifft([1, -1j, -1, 1j])
+    array([0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]) # may vary
+    >>> scipy.fft.irfft([1, -1j, -1])
+    array([0.,  1.,  0.,  0.])
+
+    Notice how the last term in the input to the ordinary `ifft` is the
+    complex conjugate of the second term, and the output has zero imaginary
+    part everywhere. When calling `irfft`, the negative frequencies are not
+    specified, and the output array is purely real.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def hfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the FFT of a signal that has Hermitian symmetry, i.e., a real
+    spectrum.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    n : int, optional
+        Length of the transformed axis of the output. For `n` output
+        points, ``n//2 + 1`` input points are necessary. If the input is
+        longer than this, it is cropped. If it is shorter than this, it is
+        padded with zeros. If `n` is not given, it is taken to be ``2*(m-1)``,
+        where ``m`` is the length of the input along the axis specified by
+        `axis`.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See `fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        The length of the transformed axis is `n`, or, if `n` is not given,
+        ``2*m - 2``, where ``m`` is the length of the transformed axis of
+        the input. To get an odd number of output points, `n` must be
+        specified, for instance, as ``2*m - 1`` in the typical case,
+
+    Raises
+    ------
+    IndexError
+        If `axis` is larger than the last axis of `a`.
+
+    See Also
+    --------
+    rfft : Compute the 1-D FFT for real input.
+    ihfft : The inverse of `hfft`.
+    hfftn : Compute the N-D FFT of a Hermitian signal.
+
+    Notes
+    -----
+    `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
+    opposite case: here the signal has Hermitian symmetry in the time
+    domain and is real in the frequency domain. So, here, it's `hfft`, for
+    which you must supply the length of the result if it is to be odd.
+    * even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error,
+    * odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error.
+
+    Examples
+    --------
+    >>> from scipy.fft import fft, hfft
+    >>> import numpy as np
+    >>> a = 2 * np.pi * np.arange(10) / 10
+    >>> signal = np.cos(a) + 3j * np.sin(3 * a)
+    >>> fft(signal).round(10)
+    array([ -0.+0.j,   5.+0.j,  -0.+0.j,  15.-0.j,   0.+0.j,   0.+0.j,
+            -0.+0.j, -15.-0.j,   0.+0.j,   5.+0.j])
+    >>> hfft(signal[:6]).round(10) # Input first half of signal
+    array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])
+    >>> hfft(signal, 10)  # Input entire signal and truncate
+    array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def ihfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the inverse FFT of a signal that has Hermitian symmetry.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    n : int, optional
+        Length of the inverse FFT, the number of points along
+        transformation axis in the input to use.  If `n` is smaller than
+        the length of the input, the input is cropped. If it is larger,
+        the input is padded with zeros. If `n` is not given, the length of
+        the input along the axis specified by `axis` is used.
+    axis : int, optional
+        Axis over which to compute the inverse FFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See `fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        The length of the transformed axis is ``n//2 + 1``.
+
+    See Also
+    --------
+    hfft, irfft
+
+    Notes
+    -----
+    `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
+    opposite case: here, the signal has Hermitian symmetry in the time
+    domain and is real in the frequency domain. So, here, it's `hfft`, for
+    which you must supply the length of the result if it is to be odd:
+    * even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error,
+    * odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error.
+
+    Examples
+    --------
+    >>> from scipy.fft import ifft, ihfft
+    >>> import numpy as np
+    >>> spectrum = np.array([ 15, -4, 0, -1, 0, -4])
+    >>> ifft(spectrum)
+    array([1.+0.j,  2.+0.j,  3.+0.j,  4.+0.j,  3.+0.j,  2.+0.j]) # may vary
+    >>> ihfft(spectrum)
+    array([ 1.-0.j,  2.-0.j,  3.-0.j,  4.-0.j]) # may vary
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def fftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the N-D discrete Fourier Transform.
+
+    This function computes the N-D discrete Fourier Transform over
+    any number of axes in an M-D array by means of the Fast Fourier
+    Transform (FFT).
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        This corresponds to ``n`` for ``fft(x, n)``.
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` and `x`,
+        as explained in the parameters section above.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    ifftn : The inverse of `fftn`, the inverse N-D FFT.
+    fft : The 1-D FFT, with definitions and conventions used.
+    rfftn : The N-D FFT of real input.
+    fft2 : The 2-D FFT.
+    fftshift : Shifts zero-frequency terms to centre of array.
+
+    Notes
+    -----
+    The output, analogously to `fft`, contains the term for zero frequency in
+    the low-order corner of all axes, the positive frequency terms in the
+    first half of all axes, the term for the Nyquist frequency in the middle
+    of all axes and the negative frequency terms in the second half of all
+    axes, in order of decreasingly negative frequency.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.mgrid[:3, :3, :3][0]
+    >>> scipy.fft.fftn(x, axes=(1, 2))
+    array([[[ 0.+0.j,   0.+0.j,   0.+0.j], # may vary
+            [ 0.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j]],
+           [[ 9.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j]],
+           [[18.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j]]])
+    >>> scipy.fft.fftn(x, (2, 2), axes=(0, 1))
+    array([[[ 2.+0.j,  2.+0.j,  2.+0.j], # may vary
+            [ 0.+0.j,  0.+0.j,  0.+0.j]],
+           [[-2.+0.j, -2.+0.j, -2.+0.j],
+            [ 0.+0.j,  0.+0.j,  0.+0.j]]])
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> [X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12,
+    ...                      2 * np.pi * np.arange(200) / 34)
+    >>> S = np.sin(X) + np.cos(Y) + rng.uniform(0, 1, X.shape)
+    >>> FS = scipy.fft.fftn(S)
+    >>> plt.imshow(np.log(np.abs(scipy.fft.fftshift(FS))**2))
+    <matplotlib.image.AxesImage object at 0x...>
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def ifftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the N-D inverse discrete Fourier Transform.
+
+    This function computes the inverse of the N-D discrete
+    Fourier Transform over any number of axes in an M-D array by
+    means of the Fast Fourier Transform (FFT).  In other words,
+    ``ifftn(fftn(x)) == x`` to within numerical accuracy.
+
+    The input, analogously to `ifft`, should be ordered in the same way as is
+    returned by `fftn`, i.e., it should have the term for zero frequency
+    in all axes in the low-order corner, the positive frequency terms in the
+    first half of all axes, the term for the Nyquist frequency in the middle
+    of all axes and the negative frequency terms in the second half of all
+    axes, in order of decreasingly negative frequency.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        This corresponds to ``n`` for ``ifft(x, n)``.
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used. See notes for issue on `ifft` zero padding.
+    axes : sequence of ints, optional
+        Axes over which to compute the IFFT.  If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` or `x`,
+        as explained in the parameters section above.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    fftn : The forward N-D FFT, of which `ifftn` is the inverse.
+    ifft : The 1-D inverse FFT.
+    ifft2 : The 2-D inverse FFT.
+    ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning
+        of array.
+
+    Notes
+    -----
+    Zero-padding, analogously with `ifft`, is performed by appending zeros to
+    the input along the specified dimension. Although this is the common
+    approach, it might lead to surprising results. If another form of zero
+    padding is desired, it must be performed before `ifftn` is called.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.eye(4)
+    >>> scipy.fft.ifftn(scipy.fft.fftn(x, axes=(0,)), axes=(1,))
+    array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary
+           [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],
+           [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
+           [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j]])
+
+
+    Create and plot an image with band-limited frequency content:
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> n = np.zeros((200,200), dtype=complex)
+    >>> n[60:80, 20:40] = np.exp(1j*rng.uniform(0, 2*np.pi, (20, 20)))
+    >>> im = scipy.fft.ifftn(n).real
+    >>> plt.imshow(im)
+    <matplotlib.image.AxesImage object at 0x...>
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def fft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the 2-D discrete Fourier Transform
+
+    This function computes the N-D discrete Fourier Transform
+    over any axes in an M-D array by means of the
+    Fast Fourier Transform (FFT). By default, the transform is computed over
+    the last two axes of the input array, i.e., a 2-dimensional FFT.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        This corresponds to ``n`` for ``fft(x, n)``.
+        Along each axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last two axes are
+        used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or the last two axes if `axes` is not given.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length, or `axes` not given and
+        ``len(s) != 2``.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    ifft2 : The inverse 2-D FFT.
+    fft : The 1-D FFT.
+    fftn : The N-D FFT.
+    fftshift : Shifts zero-frequency terms to the center of the array.
+        For 2-D input, swaps first and third quadrants, and second
+        and fourth quadrants.
+
+    Notes
+    -----
+    `fft2` is just `fftn` with a different default for `axes`.
+
+    The output, analogously to `fft`, contains the term for zero frequency in
+    the low-order corner of the transformed axes, the positive frequency terms
+    in the first half of these axes, the term for the Nyquist frequency in the
+    middle of the axes and the negative frequency terms in the second half of
+    the axes, in order of decreasingly negative frequency.
+
+    See `fftn` for details and a plotting example, and `fft` for
+    definitions and conventions used.
+
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.mgrid[:5, :5][0]
+    >>> scipy.fft.fft2(x)
+    array([[ 50.  +0.j        ,   0.  +0.j        ,   0.  +0.j        , # may vary
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5+17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5 +4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5 -4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5-17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def ifft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the 2-D inverse discrete Fourier Transform.
+
+    This function computes the inverse of the 2-D discrete Fourier
+    Transform over any number of axes in an M-D array by means of
+    the Fast Fourier Transform (FFT). In other words, ``ifft2(fft2(x)) == x``
+    to within numerical accuracy. By default, the inverse transform is
+    computed over the last two axes of the input array.
+
+    The input, analogously to `ifft`, should be ordered in the same way as is
+    returned by `fft2`, i.e., it should have the term for zero frequency
+    in the low-order corner of the two axes, the positive frequency terms in
+    the first half of these axes, the term for the Nyquist frequency in the
+    middle of the axes and the negative frequency terms in the second half of
+    both axes, in order of decreasingly negative frequency.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    s : sequence of ints, optional
+        Shape (length of each axis) of the output (``s[0]`` refers to axis 0,
+        ``s[1]`` to axis 1, etc.). This corresponds to `n` for ``ifft(x, n)``.
+        Along each axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.  See notes for issue on `ifft` zero padding.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last two
+        axes are used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or the last two axes if `axes` is not given.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length, or `axes` not given and
+        ``len(s) != 2``.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    fft2 : The forward 2-D FFT, of which `ifft2` is the inverse.
+    ifftn : The inverse of the N-D FFT.
+    fft : The 1-D FFT.
+    ifft : The 1-D inverse FFT.
+
+    Notes
+    -----
+    `ifft2` is just `ifftn` with a different default for `axes`.
+
+    See `ifftn` for details and a plotting example, and `fft` for
+    definition and conventions used.
+
+    Zero-padding, analogously with `ifft`, is performed by appending zeros to
+    the input along the specified dimension. Although this is the common
+    approach, it might lead to surprising results. If another form of zero
+    padding is desired, it must be performed before `ifft2` is called.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = 4 * np.eye(4)
+    >>> scipy.fft.ifft2(x)
+    array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary
+           [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],
+           [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
+           [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def rfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the N-D discrete Fourier Transform for real input.
+
+    This function computes the N-D discrete Fourier Transform over
+    any number of axes in an M-D real array by means of the Fast
+    Fourier Transform (FFT). By default, all axes are transformed, with the
+    real transform performed over the last axis, while the remaining
+    transforms are complex.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, taken to be real.
+    s : sequence of ints, optional
+        Shape (length along each transformed axis) to use from the input.
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        The final element of `s` corresponds to `n` for ``rfft(x, n)``, while
+        for the remaining axes, it corresponds to `n` for ``fft(x, n)``.
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` and `x`,
+        as explained in the parameters section above.
+        The length of the last axis transformed will be ``s[-1]//2+1``,
+        while the remaining transformed axes will have lengths according to
+        `s`, or unchanged from the input.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    irfftn : The inverse of `rfftn`, i.e., the inverse of the N-D FFT
+         of real input.
+    fft : The 1-D FFT, with definitions and conventions used.
+    rfft : The 1-D FFT of real input.
+    fftn : The N-D FFT.
+    rfft2 : The 2-D FFT of real input.
+
+    Notes
+    -----
+    The transform for real input is performed over the last transformation
+    axis, as by `rfft`, then the transform over the remaining axes is
+    performed as by `fftn`. The order of the output is as for `rfft` for the
+    final transformation axis, and as for `fftn` for the remaining
+    transformation axes.
+
+    See `fft` for details, definitions and conventions used.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.ones((2, 2, 2))
+    >>> scipy.fft.rfftn(x)
+    array([[[8.+0.j,  0.+0.j], # may vary
+            [0.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+
+    >>> scipy.fft.rfftn(x, axes=(2, 0))
+    array([[[4.+0.j,  0.+0.j], # may vary
+            [4.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def rfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the 2-D FFT of a real array.
+
+    Parameters
+    ----------
+    x : array
+        Input array, taken to be real.
+    s : sequence of ints, optional
+        Shape of the FFT.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The result of the real 2-D FFT.
+
+    See Also
+    --------
+    irfft2 : The inverse of the 2-D FFT of real input.
+    rfft : The 1-D FFT of real input.
+    rfftn : Compute the N-D discrete Fourier Transform for real
+            input.
+
+    Notes
+    -----
+    This is really just `rfftn` with different default behavior.
+    For more details see `rfftn`.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.broadcast_to([1, 0, -1, 0], (4, 4))
+    >>> scipy.fft.rfft2(x)
+    array([[0.+0.j, 8.+0.j, 0.+0.j],
+           [0.+0.j, 0.+0.j, 0.+0.j],
+           [0.+0.j, 0.+0.j, 0.+0.j],
+           [0.+0.j, 0.+0.j, 0.+0.j]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def irfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Computes the inverse of `rfftn`
+
+    This function computes the inverse of the N-D discrete
+    Fourier Transform for real input over any number of axes in an
+    M-D array by means of the Fast Fourier Transform (FFT). In
+    other words, ``irfftn(rfftn(x), x.shape) == x`` to within numerical
+    accuracy. (The ``a.shape`` is necessary like ``len(a)`` is for `irfft`,
+    and for the same reason.)
+
+    The input should be ordered in the same way as is returned by `rfftn`,
+    i.e., as for `irfft` for the final transformation axis, and as for `ifftn`
+    along all the other axes.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
+        number of input points used along this axis, except for the last axis,
+        where ``s[-1]//2+1`` points of the input are used.
+        Along any axis, if the shape indicated by `s` is smaller than that of
+        the input, the input is cropped. If it is larger, the input is padded
+        with zeros. If `s` is not given, the shape of the input along the axes
+        specified by axes is used. Except for the last axis which is taken to be
+        ``2*(m-1)``, where ``m`` is the length of the input along that axis.
+    axes : sequence of ints, optional
+        Axes over which to compute the inverse FFT. If not given, the last
+        `len(s)` axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` or `x`,
+        as explained in the parameters section above.
+        The length of each transformed axis is as given by the corresponding
+        element of `s`, or the length of the input in every axis except for the
+        last one if `s` is not given. In the final transformed axis the length
+        of the output when `s` is not given is ``2*(m-1)``, where ``m`` is the
+        length of the final transformed axis of the input. To get an odd
+        number of output points in the final axis, `s` must be specified.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    rfftn : The forward N-D FFT of real input,
+            of which `ifftn` is the inverse.
+    fft : The 1-D FFT, with definitions and conventions used.
+    irfft : The inverse of the 1-D FFT of real input.
+    irfft2 : The inverse of the 2-D FFT of real input.
+
+    Notes
+    -----
+    See `fft` for definitions and conventions used.
+
+    See `rfft` for definitions and conventions used for real input.
+
+    The default value of `s` assumes an even output length in the final
+    transformation axis. When performing the final complex to real
+    transformation, the Hermitian symmetry requires that the last imaginary
+    component along that axis must be 0 and so it is ignored. To avoid losing
+    information, the correct length of the real input *must* be given.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.zeros((3, 2, 2))
+    >>> x[0, 0, 0] = 3 * 2 * 2
+    >>> scipy.fft.irfftn(x)
+    array([[[1.,  1.],
+            [1.,  1.]],
+           [[1.,  1.],
+            [1.,  1.]],
+           [[1.,  1.],
+            [1.,  1.]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def irfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Computes the inverse of `rfft2`
+
+    Parameters
+    ----------
+    x : array_like
+        The input array
+    s : sequence of ints, optional
+        Shape of the real output to the inverse FFT.
+    axes : sequence of ints, optional
+        The axes over which to compute the inverse fft.
+        Default is the last two axes.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The result of the inverse real 2-D FFT.
+
+    See Also
+    --------
+    rfft2 : The 2-D FFT of real input.
+    irfft : The inverse of the 1-D FFT of real input.
+    irfftn : The inverse of the N-D FFT of real input.
+
+    Notes
+    -----
+    This is really `irfftn` with different defaults.
+    For more details see `irfftn`.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def hfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the N-D FFT of Hermitian symmetric complex input, i.e., a
+    signal with a real spectrum.
+
+    This function computes the N-D discrete Fourier Transform for a
+    Hermitian symmetric complex input over any number of axes in an
+    M-D array by means of the Fast Fourier Transform (FFT). In other
+    words, ``ihfftn(hfftn(x, s)) == x`` to within numerical accuracy. (``s``
+    here is ``x.shape`` with ``s[-1] = x.shape[-1] * 2 - 1``, this is necessary
+    for the same reason ``x.shape`` would be necessary for `irfft`.)
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
+        number of input points used along this axis, except for the last axis,
+        where ``s[-1]//2+1`` points of the input are used.
+        Along any axis, if the shape indicated by `s` is smaller than that of
+        the input, the input is cropped. If it is larger, the input is padded
+        with zeros. If `s` is not given, the shape of the input along the axes
+        specified by axes is used. Except for the last axis which is taken to be
+        ``2*(m-1)`` where ``m`` is the length of the input along that axis.
+    axes : sequence of ints, optional
+        Axes over which to compute the inverse FFT. If not given, the last
+        `len(s)` axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` or `x`,
+        as explained in the parameters section above.
+        The length of each transformed axis is as given by the corresponding
+        element of `s`, or the length of the input in every axis except for the
+        last one if `s` is not given.  In the final transformed axis the length
+        of the output when `s` is not given is ``2*(m-1)`` where ``m`` is the
+        length of the final transformed axis of the input.  To get an odd
+        number of output points in the final axis, `s` must be specified.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    ihfftn : The inverse N-D FFT with real spectrum. Inverse of `hfftn`.
+    fft : The 1-D FFT, with definitions and conventions used.
+    rfft : Forward FFT of real input.
+
+    Notes
+    -----
+    For a 1-D signal ``x`` to have a real spectrum, it must satisfy
+    the Hermitian property::
+
+        x[i] == np.conj(x[-i]) for all i
+
+    This generalizes into higher dimensions by reflecting over each axis in
+    turn::
+
+        x[i, j, k, ...] == np.conj(x[-i, -j, -k, ...]) for all i, j, k, ...
+
+    This should not be confused with a Hermitian matrix, for which the
+    transpose is its own conjugate::
+
+        x[i, j] == np.conj(x[j, i]) for all i, j
+
+
+    The default value of `s` assumes an even output length in the final
+    transformation axis. When performing the final complex to real
+    transformation, the Hermitian symmetry requires that the last imaginary
+    component along that axis must be 0 and so it is ignored. To avoid losing
+    information, the correct length of the real input *must* be given.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.ones((3, 2, 2))
+    >>> scipy.fft.hfftn(x)
+    array([[[12.,  0.],
+            [ 0.,  0.]],
+           [[ 0.,  0.],
+            [ 0.,  0.]],
+           [[ 0.,  0.],
+            [ 0.,  0.]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def hfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the 2-D FFT of a Hermitian complex array.
+
+    Parameters
+    ----------
+    x : array
+        Input array, taken to be Hermitian complex.
+    s : sequence of ints, optional
+        Shape of the real output.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See `fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The real result of the 2-D Hermitian complex real FFT.
+
+    See Also
+    --------
+    hfftn : Compute the N-D discrete Fourier Transform for Hermitian
+            complex input.
+
+    Notes
+    -----
+    This is really just `hfftn` with different default behavior.
+    For more details see `hfftn`.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.array([[1+0j, 2+0j], [2+0j, 1+0j]])  # Hermitian-symmetric input
+    >>> scipy.fft.hfft2(x, s=(2, 2))
+    array([[ 6.,  0.],
+           [ 0., -2.]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def ihfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Compute the N-D inverse discrete Fourier Transform for a real
+    spectrum.
+
+    This function computes the N-D inverse discrete Fourier Transform
+    over any number of axes in an M-D real array by means of the Fast
+    Fourier Transform (FFT). By default, all axes are transformed, with the
+    real transform performed over the last axis, while the remaining transforms
+    are complex.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, taken to be real.
+    s : sequence of ints, optional
+        Shape (length along each transformed axis) to use from the input.
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` and `x`,
+        as explained in the parameters section above.
+        The length of the last axis transformed will be ``s[-1]//2+1``,
+        while the remaining transformed axes will have lengths according to
+        `s`, or unchanged from the input.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    hfftn : The forward N-D FFT of Hermitian input.
+    hfft : The 1-D FFT of Hermitian input.
+    fft : The 1-D FFT, with definitions and conventions used.
+    fftn : The N-D FFT.
+    hfft2 : The 2-D FFT of Hermitian input.
+
+    Notes
+    -----
+    The transform for real input is performed over the last transformation
+    axis, as by `ihfft`, then the transform over the remaining axes is
+    performed as by `ifftn`. The order of the output is the positive part of
+    the Hermitian output signal, in the same format as `rfft`.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.ones((2, 2, 2))
+    >>> scipy.fft.ihfftn(x)
+    array([[[1.+0.j,  0.+0.j], # may vary
+            [0.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+    >>> scipy.fft.ihfftn(x, axes=(2, 0))
+    array([[[1.+0.j,  0.+0.j], # may vary
+            [1.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@_dispatch
+def ihfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Compute the 2-D inverse FFT of a real spectrum.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array
+    s : sequence of ints, optional
+        Shape of the real input to the inverse FFT.
+    axes : sequence of ints, optional
+        The axes over which to compute the inverse fft.
+        Default is the last two axes.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The result of the inverse real 2-D FFT.
+
+    See Also
+    --------
+    ihfftn : Compute the inverse of the N-D FFT of Hermitian input.
+
+    Notes
+    -----
+    This is really `ihfftn` with different defaults.
+    For more details see `ihfftn`.
+
+    """
+    return (Dispatchable(x, np.ndarray),)

tool_server/.venv/lib/python3.12/site-packages/scipy/fft/_basic_backend.py

@@ -0,0 +1,197 @@
+from scipy._lib._array_api import (
+    array_namespace, is_numpy, xp_unsupported_param_msg, is_complex, xp_float_to_complex
+)
+from . import _pocketfft
+import numpy as np
+
+
+def _validate_fft_args(workers, plan, norm):
+    if workers is not None:
+        raise ValueError(xp_unsupported_param_msg("workers"))
+    if plan is not None:
+        raise ValueError(xp_unsupported_param_msg("plan"))
+    if norm is None:
+        norm = 'backward'
+    return norm
+
+
+# these functions expect complex input in the fft standard extension
+complex_funcs = {'fft', 'ifft', 'fftn', 'ifftn', 'hfft', 'irfft', 'irfftn'}
+
+# pocketfft is used whenever SCIPY_ARRAY_API is not set,
+# or x is a NumPy array or array-like.
+# When SCIPY_ARRAY_API is set, we try to use xp.fft for CuPy arrays,
+# PyTorch arrays and other array API standard supporting objects.
+# If xp.fft does not exist, we attempt to convert to np and back to use pocketfft.
+
+def _execute_1D(func_str, pocketfft_func, x, n, axis, norm, overwrite_x, workers, plan):
+    xp = array_namespace(x)
+
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return pocketfft_func(x, n=n, axis=axis, norm=norm,
+                              overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+    norm = _validate_fft_args(workers, plan, norm)
+    if hasattr(xp, 'fft'):
+        xp_func = getattr(xp.fft, func_str)
+        if func_str in complex_funcs:
+            try:
+                res = xp_func(x, n=n, axis=axis, norm=norm)
+            except: # backends may require complex input  # noqa: E722
+                x = xp_float_to_complex(x, xp)
+                res = xp_func(x, n=n, axis=axis, norm=norm)
+            return res
+        return xp_func(x, n=n, axis=axis, norm=norm)
+
+    x = np.asarray(x)
+    y = pocketfft_func(x, n=n, axis=axis, norm=norm)
+    return xp.asarray(y)
+
+
+def _execute_nD(func_str, pocketfft_func, x, s, axes, norm, overwrite_x, workers, plan):
+    xp = array_namespace(x)
+    
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return pocketfft_func(x, s=s, axes=axes, norm=norm,
+                              overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+    norm = _validate_fft_args(workers, plan, norm)
+    if hasattr(xp, 'fft'):
+        xp_func = getattr(xp.fft, func_str)
+        if func_str in complex_funcs:
+            try:
+                res = xp_func(x, s=s, axes=axes, norm=norm)
+            except: # backends may require complex input  # noqa: E722
+                x = xp_float_to_complex(x, xp)
+                res = xp_func(x, s=s, axes=axes, norm=norm)
+            return res
+        return xp_func(x, s=s, axes=axes, norm=norm)
+
+    x = np.asarray(x)
+    y = pocketfft_func(x, s=s, axes=axes, norm=norm)
+    return xp.asarray(y)
+
+
+def fft(x, n=None, axis=-1, norm=None,
+        overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('fft', _pocketfft.fft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def ifft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    return _execute_1D('ifft', _pocketfft.ifft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def rfft(x, n=None, axis=-1, norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('rfft', _pocketfft.rfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def irfft(x, n=None, axis=-1, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('irfft', _pocketfft.irfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def hfft(x, n=None, axis=-1, norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('hfft', _pocketfft.hfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def ihfft(x, n=None, axis=-1, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('ihfft', _pocketfft.ihfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def fftn(x, s=None, axes=None, norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('fftn', _pocketfft.fftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+
+def ifftn(x, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('ifftn', _pocketfft.ifftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def fft2(x, s=None, axes=(-2, -1), norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return fftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def ifft2(x, s=None, axes=(-2, -1), norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return ifftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def rfftn(x, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('rfftn', _pocketfft.rfftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def rfft2(x, s=None, axes=(-2, -1), norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return rfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def irfftn(x, s=None, axes=None, norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('irfftn', _pocketfft.irfftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def irfft2(x, s=None, axes=(-2, -1), norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    return irfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def _swap_direction(norm):
+    if norm in (None, 'backward'):
+        norm = 'forward'
+    elif norm == 'forward':
+        norm = 'backward'
+    elif norm != 'ortho':
+        raise ValueError(f'Invalid norm value {norm}; should be "backward", '
+                         '"ortho", or "forward".')
+    return norm
+
+
+def hfftn(x, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    xp = array_namespace(x)
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return _pocketfft.hfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+    if is_complex(x, xp):
+        x = xp.conj(x)
+    return irfftn(x, s, axes, _swap_direction(norm),
+                  overwrite_x, workers, plan=plan)
+
+
+def hfft2(x, s=None, axes=(-2, -1), norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return hfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def ihfftn(x, s=None, axes=None, norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    xp = array_namespace(x)
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return _pocketfft.ihfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+    return xp.conj(rfftn(x, s, axes, _swap_direction(norm),
+                         overwrite_x, workers, plan=plan))
+
+def ihfft2(x, s=None, axes=(-2, -1), norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    return ihfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)

tool_server/.venv/lib/python3.12/site-packages/scipy/fft/_debug_backends.py

@@ -0,0 +1,22 @@
+import numpy as np
+
+class NumPyBackend:
+    """Backend that uses numpy.fft"""
+    __ua_domain__ = "numpy.scipy.fft"
+
+    @staticmethod
+    def __ua_function__(method, args, kwargs):
+        kwargs.pop("overwrite_x", None)
+
+        fn = getattr(np.fft, method.__name__, None)
+        return (NotImplemented if fn is None
+                else fn(*args, **kwargs))
+
+
+class EchoBackend:
+    """Backend that just prints the __ua_function__ arguments"""
+    __ua_domain__ = "numpy.scipy.fft"
+
+    @staticmethod
+    def __ua_function__(method, args, kwargs):
+        print(method, args, kwargs, sep='\n')