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python/user_packages/Python313/site-packages/numpy/_core/__init__.py

@@ -0,0 +1,203 @@
+"""
+Contains the core of NumPy: ndarray, ufuncs, dtypes, etc.
+
+Please note that this module is private.  All functions and objects
+are available in the main ``numpy`` namespace - use that instead.
+
+"""
+
+import os
+
+from numpy.version import version as __version__
+
+# disables OpenBLAS affinity setting of the main thread that limits
+# python threads or processes to one core
+env_added = []
+for envkey in ['OPENBLAS_MAIN_FREE']:
+    if envkey not in os.environ:
+        # Note: using `putenv` (and `unsetenv` further down) instead of updating
+        # `os.environ` on purpose to avoid a race condition, see gh-30627.
+        os.putenv(envkey, '1')
+        env_added.append(envkey)
+
+try:
+    from . import multiarray
+except ImportError as exc:
+    import sys
+
+    # Bypass for the module re-initialization opt-out
+    if exc.msg == "cannot load module more than once per process":
+        raise
+
+    # Basically always, the problem should be that the C module is wrong/missing...
+    if (
+        isinstance(exc, ModuleNotFoundError)
+        and exc.name == "numpy._core._multiarray_umath"
+    ):
+        import sys
+        candidates = []
+        for path in __path__:
+            candidates.extend(
+                f for f in os.listdir(path) if f.startswith("_multiarray_umath"))
+        if len(candidates) == 0:
+            bad_c_module_info = (
+                "We found no compiled module, did NumPy build successfully?\n")
+        else:
+            candidate_str = '\n  * '.join(candidates)
+            # cache_tag is documented to be possibly None, so just use name if it is
+            # this guesses at cache_tag being the same as the extension module scheme
+            tag = sys.implementation.cache_tag or sys.implementation.name
+            bad_c_module_info = (
+                f"The following compiled module files exist, but seem incompatible\n"
+                f"with with either python '{tag}' or the "
+                f"platform '{sys.platform}':\n\n  * {candidate_str}\n"
+            )
+    else:
+        bad_c_module_info = ""
+
+    major, minor, *_ = sys.version_info
+    msg = f"""
+
+IMPORTANT: PLEASE READ THIS FOR ADVICE ON HOW TO SOLVE THIS ISSUE!
+
+Importing the numpy C-extensions failed. This error can happen for
+many reasons, often due to issues with your setup or how NumPy was
+installed.
+{bad_c_module_info}
+We have compiled some common reasons and troubleshooting tips at:
+
+    https://numpy.org/devdocs/user/troubleshooting-importerror.html
+
+Please note and check the following:
+
+  * The Python version is: Python {major}.{minor} from "{sys.executable}"
+  * The NumPy version is: "{__version__}"
+
+and make sure that they are the versions you expect.
+
+Please carefully study the information and documentation linked above.
+This is unlikely to be a NumPy issue but will be caused by a bad install
+or environment on your machine.
+
+Original error was: {exc}
+"""
+
+    raise ImportError(msg) from exc
+finally:
+    for envkey in env_added:
+        os.unsetenv(envkey)
+del envkey
+del env_added
+del os
+
+from . import umath
+
+# Check that multiarray,umath are pure python modules wrapping
+# _multiarray_umath and not either of the old c-extension modules
+if not (hasattr(multiarray, '_multiarray_umath') and
+        hasattr(umath, '_multiarray_umath')):
+    import sys
+    path = sys.modules['numpy'].__path__
+    msg = ("Something is wrong with the numpy installation. "
+        "While importing we detected an older version of "
+        "numpy in {}. One method of fixing this is to repeatedly uninstall "
+        "numpy until none is found, then reinstall this version.")
+    raise ImportError(msg.format(path))
+
+from . import numerictypes as nt
+from .numerictypes import sctypeDict, sctypes
+
+multiarray.set_typeDict(nt.sctypeDict)
+from . import einsumfunc, fromnumeric, function_base, getlimits, numeric, shape_base
+from .einsumfunc import *
+from .fromnumeric import *
+from .function_base import *
+from .getlimits import *
+
+# Note: module name memmap is overwritten by a class with same name
+from .memmap import *
+from .numeric import *
+from .records import recarray, record
+from .shape_base import *
+
+del nt
+
+# do this after everything else, to minimize the chance of this misleadingly
+# appearing in an import-time traceback
+# add these for module-freeze analysis (like PyInstaller)
+from . import (
+    _add_newdocs,
+    _add_newdocs_scalars,
+    _dtype,
+    _dtype_ctypes,
+    _internal,
+    _methods,
+)
+from .numeric import absolute as abs
+
+acos = numeric.arccos
+acosh = numeric.arccosh
+asin = numeric.arcsin
+asinh = numeric.arcsinh
+atan = numeric.arctan
+atanh = numeric.arctanh
+atan2 = numeric.arctan2
+concat = numeric.concatenate
+bitwise_left_shift = numeric.left_shift
+bitwise_invert = numeric.invert
+bitwise_right_shift = numeric.right_shift
+permute_dims = numeric.transpose
+pow = numeric.power
+
+__all__ = [
+    "abs", "acos", "acosh", "asin", "asinh", "atan", "atanh", "atan2",
+    "bitwise_invert", "bitwise_left_shift", "bitwise_right_shift", "concat",
+    "pow", "permute_dims", "memmap", "sctypeDict", "record", "recarray"
+]
+__all__ += numeric.__all__
+__all__ += function_base.__all__
+__all__ += getlimits.__all__
+__all__ += shape_base.__all__
+__all__ += einsumfunc.__all__
+
+
+def _ufunc_reduce(func):
+    # Report the `__name__`. pickle will try to find the module. Note that
+    # pickle supports for this `__name__` to be a `__qualname__`. It may
+    # make sense to add a `__qualname__` to ufuncs, to allow this more
+    # explicitly (Numba has ufuncs as attributes).
+    # See also: https://github.com/dask/distributed/issues/3450
+    return func.__name__
+
+
+def _DType_reconstruct(scalar_type):
+    # This is a work-around to pickle type(np.dtype(np.float64)), etc.
+    # and it should eventually be replaced with a better solution, e.g. when
+    # DTypes become HeapTypes.
+    return type(dtype(scalar_type))
+
+
+def _DType_reduce(DType):
+    # As types/classes, most DTypes can simply be pickled by their name:
+    if not DType._legacy or DType.__module__ == "numpy.dtypes":
+        return DType.__name__
+
+    # However, user defined legacy dtypes (like rational) do not end up in
+    # `numpy.dtypes` as module and do not have a public class at all.
+    # For these, we pickle them by reconstructing them from the scalar type:
+    scalar_type = DType.type
+    return _DType_reconstruct, (scalar_type,)
+
+
+import copyreg
+
+copyreg.pickle(ufunc, _ufunc_reduce)
+copyreg.pickle(type(dtype), _DType_reduce, _DType_reconstruct)
+
+# Unclutter namespace (must keep _*_reconstruct for unpickling)
+del copyreg, _ufunc_reduce, _DType_reduce
+
+from numpy._pytesttester import PytestTester
+
+test = PytestTester(__name__)
+del PytestTester

python/user_packages/Python313/site-packages/numpy/_core/__init__.pyi

@@ -0,0 +1,666 @@
+# keep in sync with https://github.com/numpy/numtype/blob/main/src/numpy-stubs/_core/__init__.pyi
+
+from ._asarray import require
+from ._ufunc_config import (
+    errstate,
+    getbufsize,
+    geterr,
+    geterrcall,
+    setbufsize,
+    seterr,
+    seterrcall,
+)
+from .arrayprint import (
+    array2string,
+    array_repr,
+    array_str,
+    format_float_positional,
+    format_float_scientific,
+    get_printoptions,
+    printoptions,
+    set_printoptions,
+)
+from .einsumfunc import einsum, einsum_path
+from .fromnumeric import (
+    all,
+    amax,
+    amin,
+    any,
+    argmax,
+    argmin,
+    argpartition,
+    argsort,
+    around,
+    choose,
+    clip,
+    compress,
+    cumprod,
+    cumsum,
+    cumulative_prod,
+    cumulative_sum,
+    diagonal,
+    matrix_transpose,
+    max,
+    mean,
+    min,
+    ndim,
+    nonzero,
+    partition,
+    prod,
+    ptp,
+    put,
+    ravel,
+    repeat,
+    reshape,
+    resize,
+    round,
+    searchsorted,
+    shape,
+    size,
+    sort,
+    squeeze,
+    std,
+    sum,
+    swapaxes,
+    take,
+    trace,
+    transpose,
+    transpose as permute_dims,
+    var,
+)
+from .function_base import geomspace, linspace, logspace
+from .getlimits import finfo, iinfo
+from .memmap import memmap
+from .numeric import (
+    False_,
+    True_,
+    allclose,
+    arange,
+    argwhere,
+    array,
+    array_equal,
+    array_equiv,
+    asanyarray,
+    asarray,
+    ascontiguousarray,
+    asfortranarray,
+    astype,
+    base_repr,
+    binary_repr,
+    bitwise_not,
+    broadcast,
+    can_cast,
+    concatenate,
+    concatenate as concat,
+    convolve,
+    copyto,
+    correlate,
+    count_nonzero,
+    cross,
+    dot,
+    dtype,
+    empty,
+    empty_like,
+    flatiter,
+    flatnonzero,
+    from_dlpack,
+    frombuffer,
+    fromfile,
+    fromfunction,
+    fromiter,
+    fromstring,
+    full,
+    full_like,
+    identity,
+    indices,
+    inf,
+    inner,
+    isclose,
+    isfortran,
+    isscalar,
+    lexsort,
+    little_endian,
+    matmul,
+    may_share_memory,
+    min_scalar_type,
+    moveaxis,
+    nan,
+    ndarray,
+    nditer,
+    nested_iters,
+    newaxis,
+    ones,
+    ones_like,
+    outer,
+    promote_types,
+    putmask,
+    result_type,
+    roll,
+    rollaxis,
+    shares_memory,
+    tensordot,
+    ufunc,
+    vdot,
+    vecdot,
+    where,
+    zeros,
+    zeros_like,
+)
+from .numerictypes import (
+    ScalarType,
+    bool,
+    bool_,
+    busday_count,
+    busday_offset,
+    busdaycalendar,
+    byte,
+    bytes_,
+    cdouble,
+    character,
+    clongdouble,
+    complex64,
+    complex128,
+    complex192,
+    complex256,
+    complexfloating,
+    csingle,
+    datetime64,
+    datetime_as_string,
+    datetime_data,
+    double,
+    flexible,
+    float16,
+    float32,
+    float64,
+    float96,
+    float128,
+    floating,
+    generic,
+    half,
+    inexact,
+    int8,
+    int16,
+    int32,
+    int64,
+    int_,
+    intc,
+    integer,
+    intp,
+    is_busday,
+    isdtype,
+    issubdtype,
+    long,
+    longdouble,
+    longlong,
+    number,
+    object_,
+    sctypeDict,
+    short,
+    signedinteger,
+    single,
+    str_,
+    timedelta64,
+    typecodes,
+    ubyte,
+    uint,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+    uintc,
+    uintp,
+    ulong,
+    ulonglong,
+    unsignedinteger,
+    ushort,
+    void,
+)
+from .records import recarray, record
+from .shape_base import (
+    atleast_1d,
+    atleast_2d,
+    atleast_3d,
+    block,
+    hstack,
+    stack,
+    unstack,
+    vstack,
+)
+from .umath import (
+    absolute,
+    absolute as abs,
+    add,
+    arccos,
+    arccos as acos,
+    arccosh,
+    arccosh as acosh,
+    arcsin,
+    arcsin as asin,
+    arcsinh,
+    arcsinh as asinh,
+    arctan,
+    arctan as atan,
+    arctan2,
+    arctan2 as atan2,
+    arctanh,
+    arctanh as atanh,
+    bitwise_and,
+    bitwise_count,
+    bitwise_or,
+    bitwise_xor,
+    cbrt,
+    ceil,
+    conj,
+    conjugate,
+    copysign,
+    cos,
+    cosh,
+    deg2rad,
+    degrees,
+    divide,
+    divmod,
+    e,
+    equal,
+    euler_gamma,
+    exp,
+    exp2,
+    expm1,
+    fabs,
+    float_power,
+    floor,
+    floor_divide,
+    fmax,
+    fmin,
+    fmod,
+    frexp,
+    frompyfunc,
+    gcd,
+    greater,
+    greater_equal,
+    heaviside,
+    hypot,
+    invert,
+    invert as bitwise_invert,
+    isfinite,
+    isinf,
+    isnan,
+    isnat,
+    lcm,
+    ldexp,
+    left_shift,
+    left_shift as bitwise_left_shift,
+    less,
+    less_equal,
+    log,
+    log1p,
+    log2,
+    log10,
+    logaddexp,
+    logaddexp2,
+    logical_and,
+    logical_not,
+    logical_or,
+    logical_xor,
+    matvec,
+    maximum,
+    minimum,
+    mod,
+    modf,
+    multiply,
+    negative,
+    nextafter,
+    not_equal,
+    pi,
+    positive,
+    power,
+    power as pow,
+    rad2deg,
+    radians,
+    reciprocal,
+    remainder,
+    right_shift,
+    right_shift as bitwise_right_shift,
+    rint,
+    sign,
+    signbit,
+    sin,
+    sinh,
+    spacing,
+    sqrt,
+    square,
+    subtract,
+    tan,
+    tanh,
+    true_divide,
+    trunc,
+    vecmat,
+)
+
+__all__ = [
+    "False_",
+    "ScalarType",
+    "True_",
+    "abs",
+    "absolute",
+    "acos",
+    "acosh",
+    "add",
+    "all",
+    "allclose",
+    "amax",
+    "amin",
+    "any",
+    "arange",
+    "arccos",
+    "arccosh",
+    "arcsin",
+    "arcsinh",
+    "arctan",
+    "arctan2",
+    "arctanh",
+    "argmax",
+    "argmin",
+    "argpartition",
+    "argsort",
+    "argwhere",
+    "around",
+    "array",
+    "array2string",
+    "array_equal",
+    "array_equiv",
+    "array_repr",
+    "array_str",
+    "asanyarray",
+    "asarray",
+    "ascontiguousarray",
+    "asfortranarray",
+    "asin",
+    "asinh",
+    "astype",
+    "atan",
+    "atan2",
+    "atanh",
+    "atleast_1d",
+    "atleast_2d",
+    "atleast_3d",
+    "base_repr",
+    "binary_repr",
+    "bitwise_and",
+    "bitwise_count",
+    "bitwise_invert",
+    "bitwise_left_shift",
+    "bitwise_not",
+    "bitwise_or",
+    "bitwise_right_shift",
+    "bitwise_xor",
+    "block",
+    "bool",
+    "bool_",
+    "broadcast",
+    "busday_count",
+    "busday_offset",
+    "busdaycalendar",
+    "byte",
+    "bytes_",
+    "can_cast",
+    "cbrt",
+    "cdouble",
+    "ceil",
+    "character",
+    "choose",
+    "clip",
+    "clongdouble",
+    "complex64",
+    "complex128",
+    "complex192",
+    "complex256",
+    "complexfloating",
+    "compress",
+    "concat",
+    "concatenate",
+    "conj",
+    "conjugate",
+    "convolve",
+    "copysign",
+    "copyto",
+    "correlate",
+    "cos",
+    "cosh",
+    "count_nonzero",
+    "cross",
+    "csingle",
+    "cumprod",
+    "cumsum",
+    "cumulative_prod",
+    "cumulative_sum",
+    "datetime64",
+    "datetime_as_string",
+    "datetime_data",
+    "deg2rad",
+    "degrees",
+    "diagonal",
+    "divide",
+    "divmod",
+    "dot",
+    "double",
+    "dtype",
+    "e",
+    "einsum",
+    "einsum_path",
+    "empty",
+    "empty_like",
+    "equal",
+    "errstate",
+    "euler_gamma",
+    "exp",
+    "exp2",
+    "expm1",
+    "fabs",
+    "finfo",
+    "flatiter",
+    "flatnonzero",
+    "flexible",
+    "float16",
+    "float32",
+    "float64",
+    "float96",
+    "float128",
+    "float_power",
+    "floating",
+    "floor",
+    "floor_divide",
+    "fmax",
+    "fmin",
+    "fmod",
+    "format_float_positional",
+    "format_float_scientific",
+    "frexp",
+    "from_dlpack",
+    "frombuffer",
+    "fromfile",
+    "fromfunction",
+    "fromiter",
+    "frompyfunc",
+    "fromstring",
+    "full",
+    "full_like",
+    "gcd",
+    "generic",
+    "geomspace",
+    "get_printoptions",
+    "getbufsize",
+    "geterr",
+    "geterrcall",
+    "greater",
+    "greater_equal",
+    "half",
+    "heaviside",
+    "hstack",
+    "hypot",
+    "identity",
+    "iinfo",
+    "indices",
+    "inexact",
+    "inf",
+    "inner",
+    "int8",
+    "int16",
+    "int32",
+    "int64",
+    "int_",
+    "intc",
+    "integer",
+    "intp",
+    "invert",
+    "is_busday",
+    "isclose",
+    "isdtype",
+    "isfinite",
+    "isfortran",
+    "isinf",
+    "isnan",
+    "isnat",
+    "isscalar",
+    "issubdtype",
+    "lcm",
+    "ldexp",
+    "left_shift",
+    "less",
+    "less_equal",
+    "lexsort",
+    "linspace",
+    "little_endian",
+    "log",
+    "log1p",
+    "log2",
+    "log10",
+    "logaddexp",
+    "logaddexp2",
+    "logical_and",
+    "logical_not",
+    "logical_or",
+    "logical_xor",
+    "logspace",
+    "long",
+    "longdouble",
+    "longlong",
+    "matmul",
+    "matrix_transpose",
+    "matvec",
+    "max",
+    "maximum",
+    "may_share_memory",
+    "mean",
+    "memmap",
+    "min",
+    "min_scalar_type",
+    "minimum",
+    "mod",
+    "modf",
+    "moveaxis",
+    "multiply",
+    "nan",
+    "ndarray",
+    "ndim",
+    "nditer",
+    "negative",
+    "nested_iters",
+    "newaxis",
+    "nextafter",
+    "nonzero",
+    "not_equal",
+    "number",
+    "object_",
+    "ones",
+    "ones_like",
+    "outer",
+    "partition",
+    "permute_dims",
+    "pi",
+    "positive",
+    "pow",
+    "power",
+    "printoptions",
+    "prod",
+    "promote_types",
+    "ptp",
+    "put",
+    "putmask",
+    "rad2deg",
+    "radians",
+    "ravel",
+    "recarray",
+    "reciprocal",
+    "record",
+    "remainder",
+    "repeat",
+    "require",
+    "reshape",
+    "resize",
+    "result_type",
+    "right_shift",
+    "rint",
+    "roll",
+    "rollaxis",
+    "round",
+    "sctypeDict",
+    "searchsorted",
+    "set_printoptions",
+    "setbufsize",
+    "seterr",
+    "seterrcall",
+    "shape",
+    "shares_memory",
+    "short",
+    "sign",
+    "signbit",
+    "signedinteger",
+    "sin",
+    "single",
+    "sinh",
+    "size",
+    "sort",
+    "spacing",
+    "sqrt",
+    "square",
+    "squeeze",
+    "stack",
+    "std",
+    "str_",
+    "subtract",
+    "sum",
+    "swapaxes",
+    "take",
+    "tan",
+    "tanh",
+    "tensordot",
+    "timedelta64",
+    "trace",
+    "transpose",
+    "true_divide",
+    "trunc",
+    "typecodes",
+    "ubyte",
+    "ufunc",
+    "uint",
+    "uint8",
+    "uint16",
+    "uint32",
+    "uint64",
+    "uintc",
+    "uintp",
+    "ulong",
+    "ulonglong",
+    "unsignedinteger",
+    "unstack",
+    "ushort",
+    "var",
+    "vdot",
+    "vecdot",
+    "vecmat",
+    "void",
+    "vstack",
+    "where",
+    "zeros",
+    "zeros_like",
+]

python/user_packages/Python313/site-packages/numpy/_core/_add_newdocs.pyi

@@ -0,0 +1,2 @@
+from .function_base import add_newdoc as add_newdoc
+from .overrides import get_array_function_like_doc as get_array_function_like_doc

python/user_packages/Python313/site-packages/numpy/_core/_add_newdocs_scalars.py

@@ -0,0 +1,381 @@
+"""
+This file is separate from ``_add_newdocs.py`` so that it can be mocked out by
+our sphinx ``conf.py`` during doc builds, where we want to avoid showing
+platform-dependent information.
+"""
+import os
+import sys
+
+from numpy._core import dtype, numerictypes as _numerictypes
+from numpy._core.function_base import add_newdoc
+
+##############################################################################
+#
+# Documentation for concrete scalar classes
+#
+##############################################################################
+
+def numeric_type_aliases(aliases):
+    def type_aliases_gen():
+        for alias, doc in aliases:
+            try:
+                alias_type = getattr(_numerictypes, alias)
+            except AttributeError:
+                # The set of aliases that actually exist varies between platforms
+                pass
+            else:
+                yield (alias_type, alias, doc)
+    return list(type_aliases_gen())
+
+
+possible_aliases = numeric_type_aliases([
+    ('int8', '8-bit signed integer (``-128`` to ``127``)'),
+    ('int16', '16-bit signed integer (``-32_768`` to ``32_767``)'),
+    ('int32', '32-bit signed integer (``-2_147_483_648`` to ``2_147_483_647``)'),
+    ('int64', '64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``)'),
+    ('intp', 'Signed integer large enough to fit pointer, compatible with C ``intptr_t``'),
+    ('uint8', '8-bit unsigned integer (``0`` to ``255``)'),
+    ('uint16', '16-bit unsigned integer (``0`` to ``65_535``)'),
+    ('uint32', '32-bit unsigned integer (``0`` to ``4_294_967_295``)'),
+    ('uint64', '64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``)'),
+    ('uintp', 'Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``'),
+    ('float16', '16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa'),
+    ('float32', '32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa'),
+    ('float64', '64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa'),
+    ('float96', '96-bit extended-precision floating-point number type'),
+    ('float128', '128-bit extended-precision floating-point number type'),
+    ('complex64', 'Complex number type composed of 2 32-bit-precision floating-point numbers'),
+    ('complex128', 'Complex number type composed of 2 64-bit-precision floating-point numbers'),
+    ('complex192', 'Complex number type composed of 2 96-bit extended-precision floating-point numbers'),
+    ('complex256', 'Complex number type composed of 2 128-bit extended-precision floating-point numbers'),
+])
+
+
+def _get_platform_and_machine():
+    try:
+        system, _, _, _, machine = os.uname()
+    except AttributeError:
+        system = sys.platform
+        if system == 'win32':
+            machine = os.environ.get('PROCESSOR_ARCHITEW6432', '') \
+                    or os.environ.get('PROCESSOR_ARCHITECTURE', '')
+        else:
+            machine = 'unknown'
+    return system, machine
+
+
+_system, _machine = _get_platform_and_machine()
+_doc_alias_string = f":Alias on this platform ({_system} {_machine}):"
+
+# docstring prefix that cpython uses to populate `__text_signature__`
+_ARGUMENT_CLINIC_TEMPLATE = """{name}{signature}
+--
+
+{docstring}"""
+
+def add_newdoc_for_scalar_type(name: str, text_signature: str, doc: str) -> None:
+    # note: `:field: value` is rST syntax which renders as field lists.
+    cls = getattr(_numerictypes, name)
+    module = cls.__module__
+
+    lines_extra = [
+        "",  # blank line after main doc
+        f":Character code: ``{dtype(cls).char!r}``",
+    ]
+
+    if name != cls.__name__:
+        lines_extra.append(f":Canonical name: `{module}.{name}`")
+
+    lines_extra.extend(
+        f"{_doc_alias_string} `{module}.{alias}`: {doc}."
+        for alias_type, alias, doc in possible_aliases
+        if alias_type is cls
+    )
+
+    docstring = _ARGUMENT_CLINIC_TEMPLATE.format(
+        name=cls.__name__,  # must match the class name
+        signature=text_signature,
+        docstring="\n".join([doc.strip(), *lines_extra]),
+    )
+    add_newdoc('numpy._core.numerictypes', name, docstring)
+
+
+for bool_name in ('bool', 'bool_'):
+    add_newdoc_for_scalar_type(bool_name, '(value=False, /)', """
+Boolean type (True or False), stored as a byte.
+
+.. warning::
+
+    The :class:`bool` type is not a subclass of the :class:`int_` type
+    (the :class:`bool` is not even a number type). This is different
+    than Python's default implementation of :class:`bool` as a
+    sub-class of :class:`int`.
+""")
+
+add_newdoc_for_scalar_type('byte', '(value=0, /)', """
+Signed integer type, compatible with C ``char``.
+""")
+
+add_newdoc_for_scalar_type('short', '(value=0, /)', """
+Signed integer type, compatible with C ``short``.
+""")
+
+add_newdoc_for_scalar_type('intc', '(value=0, /)', """
+Signed integer type, compatible with C ``int``.
+""")
+
+add_newdoc_for_scalar_type('long', '(value=0, /)', """
+Signed integer type, compatible with C ``long``.
+""")
+
+# TODO: These docs probably need an if to highlight the default rather than
+#       the C-types (and be correct).
+add_newdoc_for_scalar_type('int_', '(value=0, /)', """
+Default signed integer type, 64bit on 64bit systems and 32bit on 32bit systems.
+""")
+
+add_newdoc_for_scalar_type('longlong', '(value=0, /)', """
+Signed integer type, compatible with C ``long long``.
+""")
+
+add_newdoc_for_scalar_type('ubyte', '(value=0, /)', """
+Unsigned integer type, compatible with C ``unsigned char``.
+""")
+
+add_newdoc_for_scalar_type('ushort', '(value=0, /)', """
+Unsigned integer type, compatible with C ``unsigned short``.
+""")
+
+add_newdoc_for_scalar_type('uintc', '(value=0, /)', """
+Unsigned integer type, compatible with C ``unsigned int``.
+""")
+
+add_newdoc_for_scalar_type('uint', '(value=0, /)', """
+Unsigned signed integer type, 64bit on 64bit systems and 32bit on 32bit systems.
+""")
+
+add_newdoc_for_scalar_type('ulong', '(value=0, /)', """
+Unsigned integer type, compatible with C ``unsigned long``.
+""")
+
+add_newdoc_for_scalar_type('ulonglong', '(value=0, /)', """
+Unsigned integer type, compatible with C ``unsigned long long``.
+""")
+
+add_newdoc_for_scalar_type('half', '(value=0, /)', """
+Half-precision floating-point number type.
+""")
+
+add_newdoc_for_scalar_type('single', '(value=0, /)', """
+Single-precision floating-point number type, compatible with C ``float``.
+""")
+
+add_newdoc_for_scalar_type('double', '(value=0, /)', """
+Double-precision floating-point number type, compatible with Python :class:`float` and C ``double``.
+""")
+
+add_newdoc_for_scalar_type('longdouble', '(value=0, /)', """
+Extended-precision floating-point number type, compatible with C ``long double``
+but not necessarily with IEEE 754 quadruple-precision.
+""")
+
+add_newdoc_for_scalar_type('csingle', '(real=0, imag=0, /)', """
+Complex number type composed of two single-precision floating-point numbers.
+""")
+
+add_newdoc_for_scalar_type('cdouble', '(real=0, imag=0, /)', """
+Complex number type composed of two double-precision floating-point numbers,
+compatible with Python :class:`complex`.
+""")
+
+add_newdoc_for_scalar_type('clongdouble', '(real=0, imag=0, /)', """
+Complex number type composed of two extended-precision floating-point numbers.
+""")
+
+add_newdoc_for_scalar_type('object_', '(value=None, /)', """
+Any Python object.
+""")
+
+add_newdoc_for_scalar_type('str_', '(value="", /, *args, **kwargs)', r"""
+A unicode string.
+
+This type strips trailing null codepoints.
+
+>>> s = np.str_("abc\x00")
+>>> s
+'abc'
+
+Unlike the builtin :class:`str`, this supports the
+:ref:`python:bufferobjects`, exposing its contents as UCS4:
+
+>>> m = memoryview(np.str_("abc"))
+>>> m.format
+'3w'
+>>> m.tobytes()
+b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00'
+""")
+
+add_newdoc_for_scalar_type('bytes_', '(value="", /, *args, **kwargs)', r"""
+A byte string.
+
+When used in arrays, this type strips trailing null bytes.
+""")
+
+add_newdoc_for_scalar_type('void', '(length_or_data, /, dtype=None)', r"""
+np.void(length_or_data, /, dtype=None)
+
+Create a new structured or unstructured void scalar.
+
+Parameters
+----------
+length_or_data : int, array-like, bytes-like, object
+    One of multiple meanings (see notes).  The length or
+    bytes data of an unstructured void.  Or alternatively,
+    the data to be stored in the new scalar when `dtype`
+    is provided.
+    This can be an array-like, in which case an array may
+    be returned.
+dtype : dtype, optional
+    If provided the dtype of the new scalar.  This dtype must
+    be "void" dtype (i.e. a structured or unstructured void,
+    see also :ref:`defining-structured-types`).
+
+    .. versionadded:: 1.24
+
+Notes
+-----
+For historical reasons and because void scalars can represent both
+arbitrary byte data and structured dtypes, the void constructor
+has three calling conventions:
+
+1. ``np.void(5)`` creates a ``dtype="V5"`` scalar filled with five
+    ``\0`` bytes.  The 5 can be a Python or NumPy integer.
+2. ``np.void(b"bytes-like")`` creates a void scalar from the byte string.
+    The dtype itemsize will match the byte string length, here ``"V10"``.
+3. When a ``dtype=`` is passed the call is roughly the same as an
+    array creation.  However, a void scalar rather than array is returned.
+
+Please see the examples which show all three different conventions.
+
+Examples
+--------
+>>> np.void(5)
+np.void(b'\x00\x00\x00\x00\x00')
+>>> np.void(b'abcd')
+np.void(b'\x61\x62\x63\x64')
+>>> np.void((3.2, b'eggs'), dtype="d,S5")
+np.void((3.2, b'eggs'), dtype=[('f0', '<f8'), ('f1', 'S5')])
+>>> np.void(3, dtype=[('x', np.int8), ('y', np.int8)])
+np.void((3, 3), dtype=[('x', 'i1'), ('y', 'i1')])
+""")
+
+add_newdoc_for_scalar_type('datetime64', '(value=None, /, *args)', """
+If created from a 64-bit integer, it represents an offset from ``1970-01-01T00:00:00``.
+If created from string, the string can be in ISO 8601 date or datetime format.
+
+When parsing a string to create a datetime object, if the string contains
+a trailing timezone (A 'Z' or a timezone offset), the timezone will be
+dropped and a User Warning is given.
+
+Datetime64 objects should be considered to be UTC and therefore have an
+offset of +0000.
+
+>>> np.datetime64(10, 'Y')
+np.datetime64('1980')
+>>> np.datetime64('1980', 'Y')
+np.datetime64('1980')
+>>> np.datetime64(10, 'D')
+np.datetime64('1970-01-11')
+
+See :ref:`arrays.datetime` for more information.
+""")
+
+add_newdoc_for_scalar_type('timedelta64', '(value=0, /, *args)', """
+A timedelta stored as a 64-bit integer.
+
+See :ref:`arrays.datetime` for more information.
+""")
+
+add_newdoc('numpy._core.numerictypes', "integer", ('is_integer',
+    """
+    is_integer($self, /)
+    --
+
+    integer.is_integer() -> bool
+
+    Return ``True`` if the number is finite with integral value.
+
+    .. versionadded:: 1.22
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.int64(-2).is_integer()
+    True
+    >>> np.uint32(5).is_integer()
+    True
+    """))
+
+# TODO: work out how to put this on the base class, np.floating
+for float_name in ('half', 'single', 'double', 'longdouble'):
+    add_newdoc('numpy._core.numerictypes', float_name, ('as_integer_ratio',
+        f"""
+        as_integer_ratio($self, /)
+        --
+
+        {float_name}.as_integer_ratio() -> (int, int)
+
+        Return a pair of integers, whose ratio is exactly equal to the original
+        floating point number, and with a positive denominator.
+        Raise `OverflowError` on infinities and a `ValueError` on NaNs.
+
+        >>> np.{float_name}(10.0).as_integer_ratio()
+        (10, 1)
+        >>> np.{float_name}(0.0).as_integer_ratio()
+        (0, 1)
+        >>> np.{float_name}(-.25).as_integer_ratio()
+        (-1, 4)
+        """))
+
+    add_newdoc('numpy._core.numerictypes', float_name, ('is_integer',
+        f"""
+        is_integer($self, /)
+        --
+
+        {float_name}.is_integer() -> bool
+
+        Return ``True`` if the floating point number is finite with integral
+        value, and ``False`` otherwise.
+
+        .. versionadded:: 1.22
+
+        Examples
+        --------
+        >>> np.{float_name}(-2.0).is_integer()
+        True
+        >>> np.{float_name}(3.2).is_integer()
+        False
+        """))
+
+for int_name in ('int8', 'uint8', 'int16', 'uint16', 'int32', 'uint32',
+                 'int64', 'uint64', 'int64', 'uint64', 'int64', 'uint64',
+                 'longlong', 'ulonglong'):
+    # Add negative examples for signed cases by checking typecode
+    add_newdoc('numpy._core.numerictypes', int_name, ('bit_count',
+        f"""
+        bit_count($self, /)
+        --
+
+        {int_name}.bit_count() -> int
+
+        Computes the number of 1-bits in the absolute value of the input.
+        Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
+
+        Examples
+        --------
+        >>> np.{int_name}(127).bit_count()
+        7""" +
+        (f"""
+        >>> np.{int_name}(-127).bit_count()
+        7
+        """ if dtype(int_name).char.islower() else "")))

python/user_packages/Python313/site-packages/numpy/_core/_add_newdocs_scalars.pyi

@@ -0,0 +1,16 @@
+from typing import Final
+
+import numpy as np
+
+possible_aliases: Final[list[tuple[type[np.number], str, str]]] = ...
+_system: Final[str] = ...
+_machine: Final[str] = ...
+_doc_alias_string: Final[str] = ...
+_bool_docstring: Final[str] = ...
+bool_name: str = ...
+int_name: str = ...
+float_name: str = ...
+
+def numeric_type_aliases(aliases: list[tuple[str, str]]) -> list[tuple[type[np.number], str, str]]: ...
+def add_newdoc_for_scalar_type(name: str, text_signature: str, doc: str) -> None: ...
+def _get_platform_and_machine() -> tuple[str, str]: ...

python/user_packages/Python313/site-packages/numpy/_core/_asarray.py

@@ -0,0 +1,130 @@
+"""
+Functions in the ``as*array`` family that promote array-likes into arrays.
+
+`require` fits this category despite its name not matching this pattern.
+"""
+from .multiarray import array, asanyarray
+from .overrides import array_function_dispatch, finalize_array_function_like, set_module
+
+__all__ = ["require"]
+
+
+POSSIBLE_FLAGS = {
+    'C': 'C', 'C_CONTIGUOUS': 'C', 'CONTIGUOUS': 'C',
+    'F': 'F', 'F_CONTIGUOUS': 'F', 'FORTRAN': 'F',
+    'A': 'A', 'ALIGNED': 'A',
+    'W': 'W', 'WRITEABLE': 'W',
+    'O': 'O', 'OWNDATA': 'O',
+    'E': 'E', 'ENSUREARRAY': 'E'
+}
+
+
+@finalize_array_function_like
+@set_module('numpy')
+def require(a, dtype=None, requirements=None, *, like=None):
+    """
+    Return an ndarray of the provided type that satisfies requirements.
+
+    This function is useful to be sure that an array with the correct flags
+    is returned for passing to compiled code (perhaps through ctypes).
+
+    Parameters
+    ----------
+    a : array_like
+       The object to be converted to a type-and-requirement-satisfying array.
+    dtype : data-type
+       The required data-type. If None preserve the current dtype. If your
+       application requires the data to be in native byteorder, include
+       a byteorder specification as a part of the dtype specification.
+    requirements : str or sequence of str
+       The requirements list can be any of the following
+
+       * 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array
+       * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array
+       * 'ALIGNED' ('A')      - ensure a data-type aligned array
+       * 'WRITEABLE' ('W')    - ensure a writable array
+       * 'OWNDATA' ('O')      - ensure an array that owns its own data
+       * 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Array with specified requirements and type if given.
+
+    See Also
+    --------
+    asarray : Convert input to an ndarray.
+    asanyarray : Convert to an ndarray, but pass through ndarray subclasses.
+    ascontiguousarray : Convert input to a contiguous array.
+    asfortranarray : Convert input to an ndarray with column-major
+                     memory order.
+    ndarray.flags : Information about the memory layout of the array.
+
+    Notes
+    -----
+    The returned array will be guaranteed to have the listed requirements
+    by making a copy if needed.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2,3)
+    >>> x.flags
+      C_CONTIGUOUS : True
+      F_CONTIGUOUS : False
+      OWNDATA : False
+      WRITEABLE : True
+      ALIGNED : True
+      WRITEBACKIFCOPY : False
+
+    >>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F'])
+    >>> y.flags
+      C_CONTIGUOUS : False
+      F_CONTIGUOUS : True
+      OWNDATA : True
+      WRITEABLE : True
+      ALIGNED : True
+      WRITEBACKIFCOPY : False
+
+    """
+    if like is not None:
+        return _require_with_like(
+            like,
+            a,
+            dtype=dtype,
+            requirements=requirements,
+        )
+
+    if not requirements:
+        return asanyarray(a, dtype=dtype)
+
+    requirements = {POSSIBLE_FLAGS[x.upper()] for x in requirements}
+
+    if 'E' in requirements:
+        requirements.remove('E')
+        subok = False
+    else:
+        subok = True
+
+    order = 'A'
+    if requirements >= {'C', 'F'}:
+        raise ValueError('Cannot specify both "C" and "F" order')
+    elif 'F' in requirements:
+        order = 'F'
+        requirements.remove('F')
+    elif 'C' in requirements:
+        order = 'C'
+        requirements.remove('C')
+
+    arr = array(a, dtype=dtype, order=order, copy=None, subok=subok)
+
+    for prop in requirements:
+        if not arr.flags[prop]:
+            return arr.copy(order)
+    return arr
+
+
+_require_with_like = array_function_dispatch()(require)

python/user_packages/Python313/site-packages/numpy/_core/_asarray.pyi

@@ -0,0 +1,43 @@
+from collections.abc import Iterable
+from typing import Any, Literal, TypeAlias, TypeVar, overload
+
+from numpy._typing import DTypeLike, NDArray, _SupportsArrayFunc
+
+__all__ = ["require"]
+
+_ArrayT = TypeVar("_ArrayT", bound=NDArray[Any])
+
+_Requirements: TypeAlias = Literal[
+    "C", "C_CONTIGUOUS", "CONTIGUOUS",
+    "F", "F_CONTIGUOUS", "FORTRAN",
+    "A", "ALIGNED",
+    "W", "WRITEABLE",
+    "O", "OWNDATA"
+]
+_E: TypeAlias = Literal["E", "ENSUREARRAY"]
+_RequirementsWithE: TypeAlias = _Requirements | _E
+
+@overload
+def require(
+    a: _ArrayT,
+    dtype: None = None,
+    requirements: _Requirements | Iterable[_Requirements] | None = None,
+    *,
+    like: _SupportsArrayFunc | None = None
+) -> _ArrayT: ...
+@overload
+def require(
+    a: object,
+    dtype: DTypeLike | None = None,
+    requirements: _E | Iterable[_RequirementsWithE] | None = None,
+    *,
+    like: _SupportsArrayFunc | None = None
+) -> NDArray[Any]: ...
+@overload
+def require(
+    a: object,
+    dtype: DTypeLike | None = None,
+    requirements: _Requirements | Iterable[_Requirements] | None = None,
+    *,
+    like: _SupportsArrayFunc | None = None
+) -> NDArray[Any]: ...

python/user_packages/Python313/site-packages/numpy/_core/_dtype.py

@@ -0,0 +1,366 @@
+"""
+A place for code to be called from the implementation of np.dtype
+
+String handling is much easier to do correctly in python.
+"""
+import numpy as np
+
+_kind_to_stem = {
+    'u': 'uint',
+    'i': 'int',
+    'c': 'complex',
+    'f': 'float',
+    'b': 'bool',
+    'V': 'void',
+    'O': 'object',
+    'M': 'datetime',
+    'm': 'timedelta',
+    'S': 'bytes',
+    'U': 'str',
+}
+
+
+def _kind_name(dtype):
+    try:
+        return _kind_to_stem[dtype.kind]
+    except KeyError as e:
+        raise RuntimeError(
+            f"internal dtype error, unknown kind {dtype.kind!r}"
+        ) from None
+
+
+def __str__(dtype):
+    if dtype.fields is not None:
+        return _struct_str(dtype, include_align=True)
+    elif dtype.subdtype:
+        return _subarray_str(dtype)
+    elif issubclass(dtype.type, np.flexible) or not dtype.isnative:
+        return dtype.str
+    else:
+        return dtype.name
+
+
+def __repr__(dtype):
+    arg_str = _construction_repr(dtype, include_align=False)
+    if dtype.isalignedstruct:
+        arg_str = arg_str + ", align=True"
+    return f"dtype({arg_str})"
+
+
+def _unpack_field(dtype, offset, title=None):
+    """
+    Helper function to normalize the items in dtype.fields.
+
+    Call as:
+
+    dtype, offset, title = _unpack_field(*dtype.fields[name])
+    """
+    return dtype, offset, title
+
+
+def _isunsized(dtype):
+    # PyDataType_ISUNSIZED
+    return dtype.itemsize == 0
+
+
+def _construction_repr(dtype, include_align=False, short=False):
+    """
+    Creates a string repr of the dtype, excluding the 'dtype()' part
+    surrounding the object. This object may be a string, a list, or
+    a dict depending on the nature of the dtype. This
+    is the object passed as the first parameter to the dtype
+    constructor, and if no additional constructor parameters are
+    given, will reproduce the exact memory layout.
+
+    Parameters
+    ----------
+    short : bool
+        If true, this creates a shorter repr using 'kind' and 'itemsize',
+        instead of the longer type name.
+
+    include_align : bool
+        If true, this includes the 'align=True' parameter
+        inside the struct dtype construction dict when needed. Use this flag
+        if you want a proper repr string without the 'dtype()' part around it.
+
+        If false, this does not preserve the
+        'align=True' parameter or sticky NPY_ALIGNED_STRUCT flag for
+        struct arrays like the regular repr does, because the 'align'
+        flag is not part of first dtype constructor parameter. This
+        mode is intended for a full 'repr', where the 'align=True' is
+        provided as the second parameter.
+    """
+    if dtype.fields is not None:
+        return _struct_str(dtype, include_align=include_align)
+    elif dtype.subdtype:
+        return _subarray_str(dtype)
+    else:
+        return _scalar_str(dtype, short=short)
+
+
+def _scalar_str(dtype, short):
+    byteorder = _byte_order_str(dtype)
+
+    if dtype.type == np.bool:
+        if short:
+            return "'?'"
+        else:
+            return "'bool'"
+
+    elif dtype.type == np.object_:
+        # The object reference may be different sizes on different
+        # platforms, so it should never include the itemsize here.
+        return "'O'"
+
+    elif dtype.type == np.bytes_:
+        if _isunsized(dtype):
+            return "'S'"
+        else:
+            return "'S%d'" % dtype.itemsize
+
+    elif dtype.type == np.str_:
+        if _isunsized(dtype):
+            return f"'{byteorder}U'"
+        else:
+            return "'%sU%d'" % (byteorder, dtype.itemsize / 4)
+
+    elif dtype.type == str:
+        return "'T'"
+
+    elif not type(dtype)._legacy:
+        return f"'{byteorder}{type(dtype).__name__}{dtype.itemsize * 8}'"
+
+    # unlike the other types, subclasses of void are preserved - but
+    # historically the repr does not actually reveal the subclass
+    elif issubclass(dtype.type, np.void):
+        if _isunsized(dtype):
+            return "'V'"
+        else:
+            return "'V%d'" % dtype.itemsize
+
+    elif dtype.type == np.datetime64:
+        return f"'{byteorder}M8{_datetime_metadata_str(dtype)}'"
+
+    elif dtype.type == np.timedelta64:
+        return f"'{byteorder}m8{_datetime_metadata_str(dtype)}'"
+
+    elif dtype.isbuiltin == 2:
+        return dtype.type.__name__
+
+    elif np.issubdtype(dtype, np.number):
+        # Short repr with endianness, like '<f8'
+        if short or dtype.byteorder not in ('=', '|'):
+            return "'%s%c%d'" % (byteorder, dtype.kind, dtype.itemsize)
+
+        # Longer repr, like 'float64'
+        else:
+            return "'%s%d'" % (_kind_name(dtype), 8 * dtype.itemsize)
+
+    else:
+        raise RuntimeError(
+            "Internal error: NumPy dtype unrecognized type number")
+
+
+def _byte_order_str(dtype):
+    """ Normalize byteorder to '<' or '>' """
+    # hack to obtain the native and swapped byte order characters
+    swapped = np.dtype(int).newbyteorder('S')
+    native = swapped.newbyteorder('S')
+
+    byteorder = dtype.byteorder
+    if byteorder == '=':
+        return native.byteorder
+    if byteorder == 'S':
+        # TODO: this path can never be reached
+        return swapped.byteorder
+    elif byteorder == '|':
+        return ''
+    else:
+        return byteorder
+
+
+def _datetime_metadata_str(dtype):
+    # TODO: this duplicates the C metastr_to_unicode functionality
+    unit, count = np.datetime_data(dtype)
+    if unit == 'generic':
+        return ''
+    elif count == 1:
+        return f'[{unit}]'
+    else:
+        return f'[{count}{unit}]'
+
+
+def _struct_dict_str(dtype, includealignedflag):
+    # unpack the fields dictionary into ls
+    names = dtype.names
+    fld_dtypes = []
+    offsets = []
+    titles = []
+    for name in names:
+        fld_dtype, offset, title = _unpack_field(*dtype.fields[name])
+        fld_dtypes.append(fld_dtype)
+        offsets.append(offset)
+        titles.append(title)
+
+    # Build up a string to make the dictionary
+
+    if np._core.arrayprint._get_legacy_print_mode() <= 121:
+        colon = ":"
+        fieldsep = ","
+    else:
+        colon = ": "
+        fieldsep = ", "
+
+    # First, the names
+    ret = "{'names'%s[" % colon
+    ret += fieldsep.join(repr(name) for name in names)
+
+    # Second, the formats
+    ret += f"], 'formats'{colon}["
+    ret += fieldsep.join(
+        _construction_repr(fld_dtype, short=True) for fld_dtype in fld_dtypes)
+
+    # Third, the offsets
+    ret += f"], 'offsets'{colon}["
+    ret += fieldsep.join("%d" % offset for offset in offsets)
+
+    # Fourth, the titles
+    if any(title is not None for title in titles):
+        ret += f"], 'titles'{colon}["
+        ret += fieldsep.join(repr(title) for title in titles)
+
+    # Fifth, the itemsize
+    ret += "], 'itemsize'%s%d" % (colon, dtype.itemsize)
+
+    if (includealignedflag and dtype.isalignedstruct):
+        # Finally, the aligned flag
+        ret += ", 'aligned'%sTrue}" % colon
+    else:
+        ret += "}"
+
+    return ret
+
+
+def _aligned_offset(offset, alignment):
+    # round up offset:
+    return - (-offset // alignment) * alignment
+
+
+def _is_packed(dtype):
+    """
+    Checks whether the structured data type in 'dtype'
+    has a simple layout, where all the fields are in order,
+    and follow each other with no alignment padding.
+
+    When this returns true, the dtype can be reconstructed
+    from a list of the field names and dtypes with no additional
+    dtype parameters.
+
+    Duplicates the C `is_dtype_struct_simple_unaligned_layout` function.
+    """
+    align = dtype.isalignedstruct
+    max_alignment = 1
+    total_offset = 0
+    for name in dtype.names:
+        fld_dtype, fld_offset, title = _unpack_field(*dtype.fields[name])
+
+        if align:
+            total_offset = _aligned_offset(total_offset, fld_dtype.alignment)
+            max_alignment = max(max_alignment, fld_dtype.alignment)
+
+        if fld_offset != total_offset:
+            return False
+        total_offset += fld_dtype.itemsize
+
+    if align:
+        total_offset = _aligned_offset(total_offset, max_alignment)
+
+    return total_offset == dtype.itemsize
+
+
+def _struct_list_str(dtype):
+    items = []
+    for name in dtype.names:
+        fld_dtype, fld_offset, title = _unpack_field(*dtype.fields[name])
+
+        item = "("
+        if title is not None:
+            item += f"({title!r}, {name!r}), "
+        else:
+            item += f"{name!r}, "
+        # Special case subarray handling here
+        if fld_dtype.subdtype is not None:
+            base, shape = fld_dtype.subdtype
+            item += f"{_construction_repr(base, short=True)}, {shape}"
+        else:
+            item += _construction_repr(fld_dtype, short=True)
+
+        item += ")"
+        items.append(item)
+
+    return "[" + ", ".join(items) + "]"
+
+
+def _struct_str(dtype, include_align):
+    # The list str representation can't include the 'align=' flag,
+    # so if it is requested and the struct has the aligned flag set,
+    # we must use the dict str instead.
+    if not (include_align and dtype.isalignedstruct) and _is_packed(dtype):
+        sub = _struct_list_str(dtype)
+
+    else:
+        sub = _struct_dict_str(dtype, include_align)
+
+    # If the data type isn't the default, void, show it
+    if dtype.type != np.void:
+        return f"({dtype.type.__module__}.{dtype.type.__name__}, {sub})"
+    else:
+        return sub
+
+
+def _subarray_str(dtype):
+    base, shape = dtype.subdtype
+    return f"({_construction_repr(base, short=True)}, {shape})"
+
+
+def _name_includes_bit_suffix(dtype):
+    if dtype.type == np.object_:
+        # pointer size varies by system, best to omit it
+        return False
+    elif dtype.type == np.bool:
+        # implied
+        return False
+    elif dtype.type is None:
+        return True
+    elif np.issubdtype(dtype, np.flexible) and _isunsized(dtype):
+        # unspecified
+        return False
+    else:
+        return True
+
+
+def _name_get(dtype):
+    # provides dtype.name.__get__, documented as returning a "bit name"
+
+    if dtype.isbuiltin == 2:
+        # user dtypes don't promise to do anything special
+        return dtype.type.__name__
+
+    if not type(dtype)._legacy:
+        name = type(dtype).__name__
+
+    elif issubclass(dtype.type, np.void):
+        # historically, void subclasses preserve their name, eg `record64`
+        name = dtype.type.__name__
+    else:
+        name = _kind_name(dtype)
+
+    # append bit counts
+    if _name_includes_bit_suffix(dtype):
+        name += f"{dtype.itemsize * 8}"
+
+    # append metadata to datetimes
+    if dtype.type in (np.datetime64, np.timedelta64):
+        name += _datetime_metadata_str(dtype)
+
+    return name

python/user_packages/Python313/site-packages/numpy/_core/_dtype.pyi

@@ -0,0 +1,56 @@
+from typing import Final, Literal as L, TypeAlias, TypedDict, overload, type_check_only
+from typing_extensions import ReadOnly, TypeVar
+
+import numpy as np
+
+###
+
+_T = TypeVar("_T")
+
+_Name: TypeAlias = L["uint", "int", "complex", "float", "bool", "void", "object", "datetime", "timedelta", "bytes", "str"]
+
+@type_check_only
+class _KindToStemType(TypedDict):
+    u: ReadOnly[L["uint"]]
+    i: ReadOnly[L["int"]]
+    c: ReadOnly[L["complex"]]
+    f: ReadOnly[L["float"]]
+    b: ReadOnly[L["bool"]]
+    V: ReadOnly[L["void"]]
+    O: ReadOnly[L["object"]]
+    M: ReadOnly[L["datetime"]]
+    m: ReadOnly[L["timedelta"]]
+    S: ReadOnly[L["bytes"]]
+    U: ReadOnly[L["str"]]
+
+###
+
+_kind_to_stem: Final[_KindToStemType] = ...
+
+#
+def _kind_name(dtype: np.dtype) -> _Name: ...
+def __str__(dtype: np.dtype) -> str: ...
+def __repr__(dtype: np.dtype) -> str: ...
+
+#
+def _isunsized(dtype: np.dtype) -> bool: ...
+def _is_packed(dtype: np.dtype) -> bool: ...
+def _name_includes_bit_suffix(dtype: np.dtype) -> bool: ...
+
+#
+def _construction_repr(dtype: np.dtype, include_align: bool = False, short: bool = False) -> str: ...
+def _scalar_str(dtype: np.dtype, short: bool) -> str: ...
+def _byte_order_str(dtype: np.dtype) -> str: ...
+def _datetime_metadata_str(dtype: np.dtype) -> str: ...
+def _struct_dict_str(dtype: np.dtype, includealignedflag: bool) -> str: ...
+def _struct_list_str(dtype: np.dtype) -> str: ...
+def _struct_str(dtype: np.dtype, include_align: bool) -> str: ...
+def _subarray_str(dtype: np.dtype) -> str: ...
+def _name_get(dtype: np.dtype) -> str: ...
+
+#
+@overload
+def _unpack_field(dtype: np.dtype, offset: int, title: _T) -> tuple[np.dtype, int, _T]: ...
+@overload
+def _unpack_field(dtype: np.dtype, offset: int, title: None = None) -> tuple[np.dtype, int, None]: ...
+def _aligned_offset(offset: int, alignment: int) -> int: ...

python/user_packages/Python313/site-packages/numpy/_core/_dtype_ctypes.py

@@ -0,0 +1,120 @@
+"""
+Conversion from ctypes to dtype.
+
+In an ideal world, we could achieve this through the PEP3118 buffer protocol,
+something like::
+
+    def dtype_from_ctypes_type(t):
+        # needed to ensure that the shape of `t` is within memoryview.format
+        class DummyStruct(ctypes.Structure):
+            _fields_ = [('a', t)]
+
+        # empty to avoid memory allocation
+        ctype_0 = (DummyStruct * 0)()
+        mv = memoryview(ctype_0)
+
+        # convert the struct, and slice back out the field
+        return _dtype_from_pep3118(mv.format)['a']
+
+Unfortunately, this fails because:
+
+* ctypes cannot handle length-0 arrays with PEP3118 (bpo-32782)
+* PEP3118 cannot represent unions, but both numpy and ctypes can
+* ctypes cannot handle big-endian structs with PEP3118 (bpo-32780)
+"""
+
+# We delay-import ctypes for distributions that do not include it.
+# While this module is not used unless the user passes in ctypes
+# members, it is eagerly imported from numpy/_core/__init__.py.
+import numpy as np
+
+
+def _from_ctypes_array(t):
+    return np.dtype((dtype_from_ctypes_type(t._type_), (t._length_,)))
+
+
+def _from_ctypes_structure(t):
+    for item in t._fields_:
+        if len(item) > 2:
+            raise TypeError(
+                "ctypes bitfields have no dtype equivalent")
+
+    if hasattr(t, "_pack_"):
+        import ctypes
+        formats = []
+        offsets = []
+        names = []
+        current_offset = 0
+        for fname, ftyp in t._fields_:
+            names.append(fname)
+            formats.append(dtype_from_ctypes_type(ftyp))
+            # Each type has a default offset, this is platform dependent
+            # for some types.
+            effective_pack = min(t._pack_, ctypes.alignment(ftyp))
+            current_offset = (
+                (current_offset + effective_pack - 1) // effective_pack
+            ) * effective_pack
+            offsets.append(current_offset)
+            current_offset += ctypes.sizeof(ftyp)
+
+        return np.dtype({
+            "formats": formats,
+            "offsets": offsets,
+            "names": names,
+            "itemsize": ctypes.sizeof(t)})
+    else:
+        fields = []
+        for fname, ftyp in t._fields_:
+            fields.append((fname, dtype_from_ctypes_type(ftyp)))
+
+        # by default, ctypes structs are aligned
+        return np.dtype(fields, align=True)
+
+
+def _from_ctypes_scalar(t):
+    """
+    Return the dtype type with endianness included if it's the case
+    """
+    if getattr(t, '__ctype_be__', None) is t:
+        return np.dtype('>' + t._type_)
+    elif getattr(t, '__ctype_le__', None) is t:
+        return np.dtype('<' + t._type_)
+    else:
+        return np.dtype(t._type_)
+
+
+def _from_ctypes_union(t):
+    import ctypes
+    formats = []
+    offsets = []
+    names = []
+    for fname, ftyp in t._fields_:
+        names.append(fname)
+        formats.append(dtype_from_ctypes_type(ftyp))
+        offsets.append(0)  # Union fields are offset to 0
+
+    return np.dtype({
+        "formats": formats,
+        "offsets": offsets,
+        "names": names,
+        "itemsize": ctypes.sizeof(t)})
+
+
+def dtype_from_ctypes_type(t):
+    """
+    Construct a dtype object from a ctypes type
+    """
+    import _ctypes
+    if issubclass(t, _ctypes.Array):
+        return _from_ctypes_array(t)
+    elif issubclass(t, _ctypes._Pointer):
+        raise TypeError("ctypes pointers have no dtype equivalent")
+    elif issubclass(t, _ctypes.Structure):
+        return _from_ctypes_structure(t)
+    elif issubclass(t, _ctypes.Union):
+        return _from_ctypes_union(t)
+    elif isinstance(getattr(t, '_type_', None), str):
+        return _from_ctypes_scalar(t)
+    else:
+        raise NotImplementedError(
+            f"Unknown ctypes type {t.__name__}")

python/user_packages/Python313/site-packages/numpy/_core/_dtype_ctypes.pyi

@@ -0,0 +1,83 @@
+import _ctypes
+import ctypes as ct
+from typing import Any, overload
+
+import numpy as np
+
+#
+@overload
+def dtype_from_ctypes_type(t: type[_ctypes.Array[Any] | _ctypes.Structure]) -> np.dtype[np.void]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_bool]) -> np.dtype[np.bool]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int8 | ct.c_byte]) -> np.dtype[np.int8]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint8 | ct.c_ubyte]) -> np.dtype[np.uint8]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int16 | ct.c_short]) -> np.dtype[np.int16]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint16 | ct.c_ushort]) -> np.dtype[np.uint16]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int32 | ct.c_int]) -> np.dtype[np.int32]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint32 | ct.c_uint]) -> np.dtype[np.uint32]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_ssize_t | ct.c_long]) -> np.dtype[np.int32 | np.int64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_size_t | ct.c_ulong]) -> np.dtype[np.uint32 | np.uint64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int64 | ct.c_longlong]) -> np.dtype[np.int64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint64 | ct.c_ulonglong]) -> np.dtype[np.uint64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_float]) -> np.dtype[np.float32]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_double]) -> np.dtype[np.float64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_longdouble]) -> np.dtype[np.longdouble]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_char]) -> np.dtype[np.bytes_]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.py_object[Any]]) -> np.dtype[np.object_]: ...
+
+# NOTE: the complex ctypes on python>=3.14 are not yet supported at runtim, see
+# https://github.com/numpy/numpy/issues/28360
+
+#
+def _from_ctypes_array(t: type[_ctypes.Array[Any]]) -> np.dtype[np.void]: ...
+def _from_ctypes_structure(t: type[_ctypes.Structure]) -> np.dtype[np.void]: ...
+def _from_ctypes_union(t: type[_ctypes.Union]) -> np.dtype[np.void]: ...
+
+# keep in sync with `dtype_from_ctypes_type` (minus the first overload)
+@overload
+def _from_ctypes_scalar(t: type[ct.c_bool]) -> np.dtype[np.bool]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int8 | ct.c_byte]) -> np.dtype[np.int8]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint8 | ct.c_ubyte]) -> np.dtype[np.uint8]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int16 | ct.c_short]) -> np.dtype[np.int16]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint16 | ct.c_ushort]) -> np.dtype[np.uint16]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int32 | ct.c_int]) -> np.dtype[np.int32]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint32 | ct.c_uint]) -> np.dtype[np.uint32]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_ssize_t | ct.c_long]) -> np.dtype[np.int32 | np.int64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_size_t | ct.c_ulong]) -> np.dtype[np.uint32 | np.uint64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int64 | ct.c_longlong]) -> np.dtype[np.int64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint64 | ct.c_ulonglong]) -> np.dtype[np.uint64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_float]) -> np.dtype[np.float32]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_double]) -> np.dtype[np.float64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_longdouble]) -> np.dtype[np.longdouble]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_char]) -> np.dtype[np.bytes_]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.py_object[Any]]) -> np.dtype[np.object_]: ...

python/user_packages/Python313/site-packages/numpy/_core/_exceptions.py

@@ -0,0 +1,162 @@
+"""
+Various richly-typed exceptions, that also help us deal with string formatting
+in python where it's easier.
+
+By putting the formatting in `__str__`, we also avoid paying the cost for
+users who silence the exceptions.
+"""
+
+def _unpack_tuple(tup):
+    if len(tup) == 1:
+        return tup[0]
+    else:
+        return tup
+
+
+def _display_as_base(cls):
+    """
+    A decorator that makes an exception class look like its base.
+
+    We use this to hide subclasses that are implementation details - the user
+    should catch the base type, which is what the traceback will show them.
+
+    Classes decorated with this decorator are subject to removal without a
+    deprecation warning.
+    """
+    assert issubclass(cls, Exception)
+    cls.__name__ = cls.__base__.__name__
+    return cls
+
+
+class UFuncTypeError(TypeError):
+    """ Base class for all ufunc exceptions """
+    def __init__(self, ufunc):
+        self.ufunc = ufunc
+
+
+@_display_as_base
+class _UFuncNoLoopError(UFuncTypeError):
+    """ Thrown when a ufunc loop cannot be found """
+    def __init__(self, ufunc, dtypes):
+        super().__init__(ufunc)
+        self.dtypes = tuple(dtypes)
+
+    def __str__(self):
+        return (
+            f"ufunc {self.ufunc.__name__!r} did not contain a loop with signature "
+            f"matching types {_unpack_tuple(self.dtypes[:self.ufunc.nin])!r} "
+            f"-> {_unpack_tuple(self.dtypes[self.ufunc.nin:])!r}"
+        )
+
+
+@_display_as_base
+class _UFuncBinaryResolutionError(_UFuncNoLoopError):
+    """ Thrown when a binary resolution fails """
+    def __init__(self, ufunc, dtypes):
+        super().__init__(ufunc, dtypes)
+        assert len(self.dtypes) == 2
+
+    def __str__(self):
+        return (
+            "ufunc {!r} cannot use operands with types {!r} and {!r}"
+        ).format(
+            self.ufunc.__name__, *self.dtypes
+        )
+
+
+@_display_as_base
+class _UFuncCastingError(UFuncTypeError):
+    def __init__(self, ufunc, casting, from_, to):
+        super().__init__(ufunc)
+        self.casting = casting
+        self.from_ = from_
+        self.to = to
+
+
+@_display_as_base
+class _UFuncInputCastingError(_UFuncCastingError):
+    """ Thrown when a ufunc input cannot be casted """
+    def __init__(self, ufunc, casting, from_, to, i):
+        super().__init__(ufunc, casting, from_, to)
+        self.in_i = i
+
+    def __str__(self):
+        # only show the number if more than one input exists
+        i_str = f"{self.in_i} " if self.ufunc.nin != 1 else ""
+        return (
+            f"Cannot cast ufunc {self.ufunc.__name__!r} input {i_str}from "
+            f"{self.from_!r} to {self.to!r} with casting rule {self.casting!r}"
+        )
+
+
+@_display_as_base
+class _UFuncOutputCastingError(_UFuncCastingError):
+    """ Thrown when a ufunc output cannot be casted """
+    def __init__(self, ufunc, casting, from_, to, i):
+        super().__init__(ufunc, casting, from_, to)
+        self.out_i = i
+
+    def __str__(self):
+        # only show the number if more than one output exists
+        i_str = f"{self.out_i} " if self.ufunc.nout != 1 else ""
+        return (
+            f"Cannot cast ufunc {self.ufunc.__name__!r} output {i_str}from "
+            f"{self.from_!r} to {self.to!r} with casting rule {self.casting!r}"
+        )
+
+
+@_display_as_base
+class _ArrayMemoryError(MemoryError):
+    """ Thrown when an array cannot be allocated"""
+    def __init__(self, shape, dtype):
+        self.shape = shape
+        self.dtype = dtype
+
+    @property
+    def _total_size(self):
+        num_bytes = self.dtype.itemsize
+        for dim in self.shape:
+            num_bytes *= dim
+        return num_bytes
+
+    @staticmethod
+    def _size_to_string(num_bytes):
+        """ Convert a number of bytes into a binary size string """
+
+        # https://en.wikipedia.org/wiki/Binary_prefix
+        LOG2_STEP = 10
+        STEP = 1024
+        units = ['bytes', 'KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB']
+
+        unit_i = max(num_bytes.bit_length() - 1, 1) // LOG2_STEP
+        unit_val = 1 << (unit_i * LOG2_STEP)
+        n_units = num_bytes / unit_val
+        del unit_val
+
+        # ensure we pick a unit that is correct after rounding
+        if round(n_units) == STEP:
+            unit_i += 1
+            n_units /= STEP
+
+        # deal with sizes so large that we don't have units for them
+        if unit_i >= len(units):
+            new_unit_i = len(units) - 1
+            n_units *= 1 << ((unit_i - new_unit_i) * LOG2_STEP)
+            unit_i = new_unit_i
+
+        unit_name = units[unit_i]
+        # format with a sensible number of digits
+        if unit_i == 0:
+            # no decimal point on bytes
+            return f'{n_units:.0f} {unit_name}'
+        elif round(n_units) < 1000:
+            # 3 significant figures, if none are dropped to the left of the .
+            return f'{n_units:#.3g} {unit_name}'
+        else:
+            # just give all the digits otherwise
+            return f'{n_units:#.0f} {unit_name}'
+
+    def __str__(self):
+        size_str = self._size_to_string(self._total_size)
+        return (f"Unable to allocate {size_str} for an array with shape "
+                f"{self.shape} and data type {self.dtype}")

python/user_packages/Python313/site-packages/numpy/_core/_exceptions.pyi

@@ -0,0 +1,54 @@
+from collections.abc import Iterable
+from typing import Any, Final, TypeVar, overload
+
+import numpy as np
+from numpy import _CastingKind
+
+###
+
+_T = TypeVar("_T")
+_TupleT = TypeVar("_TupleT", bound=tuple[()] | tuple[Any, Any, *tuple[Any, ...]])
+_ExceptionT = TypeVar("_ExceptionT", bound=Exception)
+
+###
+
+class UFuncTypeError(TypeError):
+    ufunc: Final[np.ufunc]
+    def __init__(self, /, ufunc: np.ufunc) -> None: ...
+
+class _UFuncNoLoopError(UFuncTypeError):
+    dtypes: tuple[np.dtype, ...]
+    def __init__(self, /, ufunc: np.ufunc, dtypes: Iterable[np.dtype]) -> None: ...
+
+class _UFuncBinaryResolutionError(_UFuncNoLoopError):
+    dtypes: tuple[np.dtype, np.dtype]
+    def __init__(self, /, ufunc: np.ufunc, dtypes: Iterable[np.dtype]) -> None: ...
+
+class _UFuncCastingError(UFuncTypeError):
+    casting: Final[_CastingKind]
+    from_: Final[np.dtype]
+    to: Final[np.dtype]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype) -> None: ...
+
+class _UFuncInputCastingError(_UFuncCastingError):
+    in_i: Final[int]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype, i: int) -> None: ...
+
+class _UFuncOutputCastingError(_UFuncCastingError):
+    out_i: Final[int]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype, i: int) -> None: ...
+
+class _ArrayMemoryError(MemoryError):
+    shape: tuple[int, ...]
+    dtype: np.dtype
+    def __init__(self, /, shape: tuple[int, ...], dtype: np.dtype) -> None: ...
+    @property
+    def _total_size(self) -> int: ...
+    @staticmethod
+    def _size_to_string(num_bytes: int) -> str: ...
+
+@overload
+def _unpack_tuple(tup: tuple[_T]) -> _T: ...
+@overload
+def _unpack_tuple(tup: _TupleT) -> _TupleT: ...
+def _display_as_base(cls: type[_ExceptionT]) -> type[_ExceptionT]: ...

python/user_packages/Python313/site-packages/numpy/_core/_internal.py

@@ -0,0 +1,968 @@
+"""
+A place for internal code
+
+Some things are more easily handled Python.
+
+"""
+import ast
+import math
+import re
+import sys
+import warnings
+
+from numpy import _NoValue
+from numpy.exceptions import DTypePromotionError
+
+from .multiarray import StringDType, array, dtype, promote_types
+
+try:
+    import ctypes
+except ImportError:
+    ctypes = None
+
+IS_PYPY = sys.implementation.name == 'pypy'
+
+if sys.byteorder == 'little':
+    _nbo = '<'
+else:
+    _nbo = '>'
+
+def _makenames_list(adict, align):
+    allfields = []
+
+    for fname, obj in adict.items():
+        n = len(obj)
+        if not isinstance(obj, tuple) or n not in (2, 3):
+            raise ValueError("entry not a 2- or 3- tuple")
+        if n > 2 and obj[2] == fname:
+            continue
+        num = int(obj[1])
+        if num < 0:
+            raise ValueError("invalid offset.")
+        format = dtype(obj[0], align=align)
+        if n > 2:
+            title = obj[2]
+        else:
+            title = None
+        allfields.append((fname, format, num, title))
+    # sort by offsets
+    allfields.sort(key=lambda x: x[2])
+    names = [x[0] for x in allfields]
+    formats = [x[1] for x in allfields]
+    offsets = [x[2] for x in allfields]
+    titles = [x[3] for x in allfields]
+
+    return names, formats, offsets, titles
+
+# Called in PyArray_DescrConverter function when
+#  a dictionary without "names" and "formats"
+#  fields is used as a data-type descriptor.
+def _usefields(adict, align):
+    try:
+        names = adict[-1]
+    except KeyError:
+        names = None
+    if names is None:
+        names, formats, offsets, titles = _makenames_list(adict, align)
+    else:
+        formats = []
+        offsets = []
+        titles = []
+        for name in names:
+            res = adict[name]
+            formats.append(res[0])
+            offsets.append(res[1])
+            if len(res) > 2:
+                titles.append(res[2])
+            else:
+                titles.append(None)
+
+    return dtype({"names": names,
+                  "formats": formats,
+                  "offsets": offsets,
+                  "titles": titles}, align)
+
+
+# construct an array_protocol descriptor list
+#  from the fields attribute of a descriptor
+# This calls itself recursively but should eventually hit
+#  a descriptor that has no fields and then return
+#  a simple typestring
+
+def _array_descr(descriptor):
+    fields = descriptor.fields
+    if fields is None:
+        subdtype = descriptor.subdtype
+        if subdtype is None:
+            if descriptor.metadata is None:
+                return descriptor.str
+            else:
+                new = descriptor.metadata.copy()
+                if new:
+                    return (descriptor.str, new)
+                else:
+                    return descriptor.str
+        else:
+            return (_array_descr(subdtype[0]), subdtype[1])
+
+    names = descriptor.names
+    ordered_fields = [fields[x] + (x,) for x in names]
+    result = []
+    offset = 0
+    for field in ordered_fields:
+        if field[1] > offset:
+            num = field[1] - offset
+            result.append(('', f'|V{num}'))
+            offset += num
+        elif field[1] < offset:
+            raise ValueError(
+                "dtype.descr is not defined for types with overlapping or "
+                "out-of-order fields")
+        if len(field) > 3:
+            name = (field[2], field[3])
+        else:
+            name = field[2]
+        if field[0].subdtype:
+            tup = (name, _array_descr(field[0].subdtype[0]),
+                   field[0].subdtype[1])
+        else:
+            tup = (name, _array_descr(field[0]))
+        offset += field[0].itemsize
+        result.append(tup)
+
+    if descriptor.itemsize > offset:
+        num = descriptor.itemsize - offset
+        result.append(('', f'|V{num}'))
+
+    return result
+
+
+# format_re was originally from numarray by J. Todd Miller
+
+format_re = re.compile(r'(?P<order1>[<>|=]?)'
+                       r'(?P<repeats> *[(]?[ ,0-9]*[)]? *)'
+                       r'(?P<order2>[<>|=]?)'
+                       r'(?P<dtype>[A-Za-z0-9.?]*(?:\[[a-zA-Z0-9,.]+\])?)')
+sep_re = re.compile(r'\s*,\s*')
+space_re = re.compile(r'\s+$')
+
+# astr is a string (perhaps comma separated)
+
+_convorder = {'=': _nbo}
+
+def _commastring(astr):
+    startindex = 0
+    result = []
+    islist = False
+    while startindex < len(astr):
+        mo = format_re.match(astr, pos=startindex)
+        try:
+            (order1, repeats, order2, dtype) = mo.groups()
+        except (TypeError, AttributeError):
+            raise ValueError(
+                f'format number {len(result) + 1} of "{astr}" is not recognized'
+                ) from None
+        startindex = mo.end()
+        # Separator or ending padding
+        if startindex < len(astr):
+            if space_re.match(astr, pos=startindex):
+                startindex = len(astr)
+            else:
+                mo = sep_re.match(astr, pos=startindex)
+                if not mo:
+                    raise ValueError(
+                        'format number %d of "%s" is not recognized' %
+                        (len(result) + 1, astr))
+                startindex = mo.end()
+                islist = True
+
+        if order2 == '':
+            order = order1
+        elif order1 == '':
+            order = order2
+        else:
+            order1 = _convorder.get(order1, order1)
+            order2 = _convorder.get(order2, order2)
+            if (order1 != order2):
+                raise ValueError(
+                    f'inconsistent byte-order specification {order1} and {order2}')
+            order = order1
+
+        if order in ('|', '=', _nbo):
+            order = ''
+        dtype = order + dtype
+        if repeats == '':
+            newitem = dtype
+        else:
+            if (repeats[0] == "(" and repeats[-1] == ")"
+                    and repeats[1:-1].strip() != ""
+                    and "," not in repeats):
+                warnings.warn(
+                    'Passing in a parenthesized single number for repeats '
+                    'is deprecated; pass either a single number or indicate '
+                    'a tuple with a comma, like "(2,)".', DeprecationWarning,
+                    stacklevel=2)
+            newitem = (dtype, ast.literal_eval(repeats))
+
+        result.append(newitem)
+
+    return result if islist else result[0]
+
+class dummy_ctype:
+
+    def __init__(self, cls):
+        self._cls = cls
+
+    def __mul__(self, other):
+        return self
+
+    def __call__(self, *other):
+        return self._cls(other)
+
+    def __eq__(self, other):
+        return self._cls == other._cls
+
+    def __ne__(self, other):
+        return self._cls != other._cls
+
+def _getintp_ctype():
+    val = _getintp_ctype.cache
+    if val is not None:
+        return val
+    if ctypes is None:
+        import numpy as np
+        val = dummy_ctype(np.intp)
+    else:
+        char = dtype('n').char
+        if char == 'i':
+            val = ctypes.c_int
+        elif char == 'l':
+            val = ctypes.c_long
+        elif char == 'q':
+            val = ctypes.c_longlong
+        else:
+            val = ctypes.c_long
+    _getintp_ctype.cache = val
+    return val
+
+
+_getintp_ctype.cache = None
+
+# Used for .ctypes attribute of ndarray
+
+class _missing_ctypes:
+    def cast(self, num, obj):
+        return num.value
+
+    class c_void_p:
+        def __init__(self, ptr):
+            self.value = ptr
+
+
+class _ctypes:
+    def __init__(self, array, ptr=None):
+        self._arr = array
+
+        if ctypes:
+            self._ctypes = ctypes
+            self._data = self._ctypes.c_void_p(ptr)
+        else:
+            # fake a pointer-like object that holds onto the reference
+            self._ctypes = _missing_ctypes()
+            self._data = self._ctypes.c_void_p(ptr)
+            self._data._objects = array
+
+        if self._arr.ndim == 0:
+            self._zerod = True
+        else:
+            self._zerod = False
+
+    def data_as(self, obj):
+        """
+        Return the data pointer cast to a particular c-types object.
+        For example, calling ``self._as_parameter_`` is equivalent to
+        ``self.data_as(ctypes.c_void_p)``. Perhaps you want to use
+        the data as a pointer to a ctypes array of floating-point data:
+        ``self.data_as(ctypes.POINTER(ctypes.c_double))``.
+
+        The returned pointer will keep a reference to the array.
+        """
+        # _ctypes.cast function causes a circular reference of self._data in
+        # self._data._objects. Attributes of self._data cannot be released
+        # until gc.collect is called. Make a copy of the pointer first then
+        # let it hold the array reference. This is a workaround to circumvent
+        # the CPython bug https://bugs.python.org/issue12836.
+        ptr = self._ctypes.cast(self._data, obj)
+        ptr._arr = self._arr
+        return ptr
+
+    def shape_as(self, obj):
+        """
+        Return the shape tuple as an array of some other c-types
+        type. For example: ``self.shape_as(ctypes.c_short)``.
+        """
+        if self._zerod:
+            return None
+        return (obj * self._arr.ndim)(*self._arr.shape)
+
+    def strides_as(self, obj):
+        """
+        Return the strides tuple as an array of some other
+        c-types type. For example: ``self.strides_as(ctypes.c_longlong)``.
+        """
+        if self._zerod:
+            return None
+        return (obj * self._arr.ndim)(*self._arr.strides)
+
+    @property
+    def data(self):
+        """
+        A pointer to the memory area of the array as a Python integer.
+        This memory area may contain data that is not aligned, or not in
+        correct byte-order. The memory area may not even be writeable.
+        The array flags and data-type of this array should be respected
+        when passing this attribute to arbitrary C-code to avoid trouble
+        that can include Python crashing. User Beware! The value of this
+        attribute is exactly the same as:
+        ``self._array_interface_['data'][0]``.
+
+        Note that unlike ``data_as``, a reference won't be kept to the array:
+        code like ``ctypes.c_void_p((a + b).ctypes.data)`` will result in a
+        pointer to a deallocated array, and should be spelt
+        ``(a + b).ctypes.data_as(ctypes.c_void_p)``
+        """
+        return self._data.value
+
+    @property
+    def shape(self):
+        """
+        (c_intp*self.ndim): A ctypes array of length self.ndim where
+        the basetype is the C-integer corresponding to ``dtype('p')`` on this
+        platform (see `~numpy.ctypeslib.c_intp`). This base-type could be
+        `ctypes.c_int`, `ctypes.c_long`, or `ctypes.c_longlong` depending on
+        the platform. The ctypes array contains the shape of
+        the underlying array.
+        """
+        return self.shape_as(_getintp_ctype())
+
+    @property
+    def strides(self):
+        """
+        (c_intp*self.ndim): A ctypes array of length self.ndim where
+        the basetype is the same as for the shape attribute. This ctypes
+        array contains the strides information from the underlying array.
+        This strides information is important for showing how many bytes
+        must be jumped to get to the next element in the array.
+        """
+        return self.strides_as(_getintp_ctype())
+
+    @property
+    def _as_parameter_(self):
+        """
+        Overrides the ctypes semi-magic method
+
+        Enables `c_func(some_array.ctypes)`
+        """
+        return self.data_as(ctypes.c_void_p)
+
+
+def _newnames(datatype, order):
+    """
+    Given a datatype and an order object, return a new names tuple, with the
+    order indicated
+    """
+    oldnames = datatype.names
+    nameslist = list(oldnames)
+    if isinstance(order, str):
+        order = [order]
+    seen = set()
+    if isinstance(order, (list, tuple)):
+        for name in order:
+            try:
+                nameslist.remove(name)
+            except ValueError:
+                if name in seen:
+                    raise ValueError(f"duplicate field name: {name}") from None
+                else:
+                    raise ValueError(f"unknown field name: {name}") from None
+            seen.add(name)
+        return tuple(list(order) + nameslist)
+    raise ValueError(f"unsupported order value: {order}")
+
+def _copy_fields(ary):
+    """Return copy of structured array with padding between fields removed.
+
+    Parameters
+    ----------
+    ary : ndarray
+       Structured array from which to remove padding bytes
+
+    Returns
+    -------
+    ary_copy : ndarray
+       Copy of ary with padding bytes removed
+    """
+    dt = ary.dtype
+    copy_dtype = {'names': dt.names,
+                  'formats': [dt.fields[name][0] for name in dt.names]}
+    return array(ary, dtype=copy_dtype, copy=True)
+
+def _promote_fields(dt1, dt2):
+    """ Perform type promotion for two structured dtypes.
+
+    Parameters
+    ----------
+    dt1 : structured dtype
+        First dtype.
+    dt2 : structured dtype
+        Second dtype.
+
+    Returns
+    -------
+    out : dtype
+        The promoted dtype
+
+    Notes
+    -----
+    If one of the inputs is aligned, the result will be.  The titles of
+    both descriptors must match (point to the same field).
+    """
+    # Both must be structured and have the same names in the same order
+    if (dt1.names is None or dt2.names is None) or dt1.names != dt2.names:
+        raise DTypePromotionError(
+                f"field names `{dt1.names}` and `{dt2.names}` mismatch.")
+
+    # if both are identical, we can (maybe!) just return the same dtype.
+    identical = dt1 is dt2
+    new_fields = []
+    for name in dt1.names:
+        field1 = dt1.fields[name]
+        field2 = dt2.fields[name]
+        new_descr = promote_types(field1[0], field2[0])
+        identical = identical and new_descr is field1[0]
+
+        # Check that the titles match (if given):
+        if field1[2:] != field2[2:]:
+            raise DTypePromotionError(
+                    f"field titles of field '{name}' mismatch")
+        if len(field1) == 2:
+            new_fields.append((name, new_descr))
+        else:
+            new_fields.append(((field1[2], name), new_descr))
+
+    res = dtype(new_fields, align=dt1.isalignedstruct or dt2.isalignedstruct)
+
+    # Might as well preserve identity (and metadata) if the dtype is identical
+    # and the itemsize, offsets are also unmodified.  This could probably be
+    # sped up, but also probably just be removed entirely.
+    if identical and res.itemsize == dt1.itemsize:
+        for name in dt1.names:
+            if dt1.fields[name][1] != res.fields[name][1]:
+                return res  # the dtype changed.
+        return dt1
+
+    return res
+
+
+def _getfield_is_safe(oldtype, newtype, offset):
+    """ Checks safety of getfield for object arrays.
+
+    As in _view_is_safe, we need to check that memory containing objects is not
+    reinterpreted as a non-object datatype and vice versa.
+
+    Parameters
+    ----------
+    oldtype : data-type
+        Data type of the original ndarray.
+    newtype : data-type
+        Data type of the field being accessed by ndarray.getfield
+    offset : int
+        Offset of the field being accessed by ndarray.getfield
+
+    Raises
+    ------
+    TypeError
+        If the field access is invalid
+
+    """
+    if newtype.hasobject or oldtype.hasobject:
+        if offset == 0 and newtype == oldtype:
+            return
+        if oldtype.names is not None:
+            for name in oldtype.names:
+                if (oldtype.fields[name][1] == offset and
+                        oldtype.fields[name][0] == newtype):
+                    return
+        raise TypeError("Cannot get/set field of an object array")
+    return
+
+def _view_is_safe(oldtype, newtype):
+    """ Checks safety of a view involving object arrays, for example when
+    doing::
+
+        np.zeros(10, dtype=oldtype).view(newtype)
+
+    Parameters
+    ----------
+    oldtype : data-type
+        Data type of original ndarray
+    newtype : data-type
+        Data type of the view
+
+    Raises
+    ------
+    TypeError
+        If the new type is incompatible with the old type.
+
+    """
+
+    # if the types are equivalent, there is no problem.
+    # for example: dtype((np.record, 'i4,i4')) == dtype((np.void, 'i4,i4'))
+    if oldtype == newtype:
+        return
+
+    if newtype.hasobject or oldtype.hasobject:
+        raise TypeError("Cannot change data-type for array of references.")
+    return
+
+
+# Given a string containing a PEP 3118 format specifier,
+# construct a NumPy dtype
+
+_pep3118_native_map = {
+    '?': '?',
+    'c': 'S1',
+    'b': 'b',
+    'B': 'B',
+    'h': 'h',
+    'H': 'H',
+    'i': 'i',
+    'I': 'I',
+    'l': 'l',
+    'L': 'L',
+    'q': 'q',
+    'Q': 'Q',
+    'e': 'e',
+    'f': 'f',
+    'd': 'd',
+    'g': 'g',
+    'Zf': 'F',
+    'Zd': 'D',
+    'Zg': 'G',
+    's': 'S',
+    'w': 'U',
+    'O': 'O',
+    'x': 'V',  # padding
+}
+_pep3118_native_typechars = ''.join(_pep3118_native_map.keys())
+
+_pep3118_standard_map = {
+    '?': '?',
+    'c': 'S1',
+    'b': 'b',
+    'B': 'B',
+    'h': 'i2',
+    'H': 'u2',
+    'i': 'i4',
+    'I': 'u4',
+    'l': 'i4',
+    'L': 'u4',
+    'q': 'i8',
+    'Q': 'u8',
+    'e': 'f2',
+    'f': 'f',
+    'd': 'd',
+    'Zf': 'F',
+    'Zd': 'D',
+    's': 'S',
+    'w': 'U',
+    'O': 'O',
+    'x': 'V',  # padding
+}
+_pep3118_standard_typechars = ''.join(_pep3118_standard_map.keys())
+
+_pep3118_unsupported_map = {
+    'u': 'UCS-2 strings',
+    '&': 'pointers',
+    't': 'bitfields',
+    'X': 'function pointers',
+}
+
+class _Stream:
+    def __init__(self, s):
+        self.s = s
+        self.byteorder = '@'
+
+    def advance(self, n):
+        res = self.s[:n]
+        self.s = self.s[n:]
+        return res
+
+    def consume(self, c):
+        if self.s[:len(c)] == c:
+            self.advance(len(c))
+            return True
+        return False
+
+    def consume_until(self, c):
+        if callable(c):
+            i = 0
+            while i < len(self.s) and not c(self.s[i]):
+                i = i + 1
+            return self.advance(i)
+        else:
+            i = self.s.index(c)
+            res = self.advance(i)
+            self.advance(len(c))
+            return res
+
+    @property
+    def next(self):
+        return self.s[0]
+
+    def __bool__(self):
+        return bool(self.s)
+
+
+def _dtype_from_pep3118(spec):
+    stream = _Stream(spec)
+    dtype, align = __dtype_from_pep3118(stream, is_subdtype=False)
+    return dtype
+
+def __dtype_from_pep3118(stream, is_subdtype):
+    field_spec = {
+        'names': [],
+        'formats': [],
+        'offsets': [],
+        'itemsize': 0
+    }
+    offset = 0
+    common_alignment = 1
+    is_padding = False
+
+    # Parse spec
+    while stream:
+        value = None
+
+        # End of structure, bail out to upper level
+        if stream.consume('}'):
+            break
+
+        # Sub-arrays (1)
+        shape = None
+        if stream.consume('('):
+            shape = stream.consume_until(')')
+            shape = tuple(map(int, shape.split(',')))
+
+        # Byte order
+        if stream.next in ('@', '=', '<', '>', '^', '!'):
+            byteorder = stream.advance(1)
+            if byteorder == '!':
+                byteorder = '>'
+            stream.byteorder = byteorder
+
+        # Byte order characters also control native vs. standard type sizes
+        if stream.byteorder in ('@', '^'):
+            type_map = _pep3118_native_map
+            type_map_chars = _pep3118_native_typechars
+        else:
+            type_map = _pep3118_standard_map
+            type_map_chars = _pep3118_standard_typechars
+
+        # Item sizes
+        itemsize_str = stream.consume_until(lambda c: not c.isdigit())
+        if itemsize_str:
+            itemsize = int(itemsize_str)
+        else:
+            itemsize = 1
+
+        # Data types
+        is_padding = False
+
+        if stream.consume('T{'):
+            value, align = __dtype_from_pep3118(
+                stream, is_subdtype=True)
+        elif stream.next in type_map_chars:
+            if stream.next == 'Z':
+                typechar = stream.advance(2)
+            else:
+                typechar = stream.advance(1)
+
+            is_padding = (typechar == 'x')
+            dtypechar = type_map[typechar]
+            if dtypechar in 'USV':
+                dtypechar += '%d' % itemsize
+                itemsize = 1
+            numpy_byteorder = {'@': '=', '^': '='}.get(
+                stream.byteorder, stream.byteorder)
+            value = dtype(numpy_byteorder + dtypechar)
+            align = value.alignment
+        elif stream.next in _pep3118_unsupported_map:
+            desc = _pep3118_unsupported_map[stream.next]
+            raise NotImplementedError(
+                f"Unrepresentable PEP 3118 data type {stream.next!r} ({desc})")
+        else:
+            raise ValueError(
+                f"Unknown PEP 3118 data type specifier {stream.s!r}"
+            )
+
+        #
+        # Native alignment may require padding
+        #
+        # Here we assume that the presence of a '@' character implicitly
+        # implies that the start of the array is *already* aligned.
+        #
+        extra_offset = 0
+        if stream.byteorder == '@':
+            start_padding = (-offset) % align
+            intra_padding = (-value.itemsize) % align
+
+            offset += start_padding
+
+            if intra_padding != 0:
+                if itemsize > 1 or (shape is not None and _prod(shape) > 1):
+                    # Inject internal padding to the end of the sub-item
+                    value = _add_trailing_padding(value, intra_padding)
+                else:
+                    # We can postpone the injection of internal padding,
+                    # as the item appears at most once
+                    extra_offset += intra_padding
+
+            # Update common alignment
+            common_alignment = _lcm(align, common_alignment)
+
+        # Convert itemsize to sub-array
+        if itemsize != 1:
+            value = dtype((value, (itemsize,)))
+
+        # Sub-arrays (2)
+        if shape is not None:
+            value = dtype((value, shape))
+
+        # Field name
+        if stream.consume(':'):
+            name = stream.consume_until(':')
+        else:
+            name = None
+
+        if not (is_padding and name is None):
+            if name is not None and name in field_spec['names']:
+                raise RuntimeError(
+                    f"Duplicate field name '{name}' in PEP3118 format"
+                )
+            field_spec['names'].append(name)
+            field_spec['formats'].append(value)
+            field_spec['offsets'].append(offset)
+
+        offset += value.itemsize
+        offset += extra_offset
+
+        field_spec['itemsize'] = offset
+
+    # extra final padding for aligned types
+    if stream.byteorder == '@':
+        field_spec['itemsize'] += (-offset) % common_alignment
+
+    # Check if this was a simple 1-item type, and unwrap it
+    if (field_spec['names'] == [None]
+            and field_spec['offsets'][0] == 0
+            and field_spec['itemsize'] == field_spec['formats'][0].itemsize
+            and not is_subdtype):
+        ret = field_spec['formats'][0]
+    else:
+        _fix_names(field_spec)
+        ret = dtype(field_spec)
+
+    # Finished
+    return ret, common_alignment
+
+def _fix_names(field_spec):
+    """ Replace names which are None with the next unused f%d name """
+    names = field_spec['names']
+    for i, name in enumerate(names):
+        if name is not None:
+            continue
+
+        j = 0
+        while True:
+            name = f'f{j}'
+            if name not in names:
+                break
+            j = j + 1
+        names[i] = name
+
+def _add_trailing_padding(value, padding):
+    """Inject the specified number of padding bytes at the end of a dtype"""
+    if value.fields is None:
+        field_spec = {
+            'names': ['f0'],
+            'formats': [value],
+            'offsets': [0],
+            'itemsize': value.itemsize
+        }
+    else:
+        fields = value.fields
+        names = value.names
+        field_spec = {
+            'names': names,
+            'formats': [fields[name][0] for name in names],
+            'offsets': [fields[name][1] for name in names],
+            'itemsize': value.itemsize
+        }
+
+    field_spec['itemsize'] += padding
+    return dtype(field_spec)
+
+def _prod(a):
+    p = 1
+    for x in a:
+        p *= x
+    return p
+
+def _gcd(a, b):
+    """Calculate the greatest common divisor of a and b"""
+    if not (math.isfinite(a) and math.isfinite(b)):
+        raise ValueError('Can only find greatest common divisor of '
+                         f'finite arguments, found "{a}" and "{b}"')
+    while b:
+        a, b = b, a % b
+    return a
+
+def _lcm(a, b):
+    return a // _gcd(a, b) * b
+
+def array_ufunc_errmsg_formatter(dummy, ufunc, method, *inputs, **kwargs):
+    """ Format the error message for when __array_ufunc__ gives up. """
+    args_string = ', '.join([f'{arg!r}' for arg in inputs] +
+                            [f'{k}={v!r}'
+                             for k, v in kwargs.items()])
+    args = inputs + kwargs.get('out', ())
+    types_string = ', '.join(repr(type(arg).__name__) for arg in args)
+    return ('operand type(s) all returned NotImplemented from '
+            f'__array_ufunc__({ufunc!r}, {method!r}, {args_string}): {types_string}'
+            )
+
+
+def array_function_errmsg_formatter(public_api, types):
+    """ Format the error message for when __array_ufunc__ gives up. """
+    func_name = f'{public_api.__module__}.{public_api.__name__}'
+    return (f"no implementation found for '{func_name}' on types that implement "
+            f'__array_function__: {list(types)}')
+
+
+def _ufunc_doc_signature_formatter(ufunc):
+    """
+    Builds a signature string which resembles PEP 457
+
+    This is used to construct the first line of the docstring
+
+    Keep in sync with `_ufunc_inspect_signature_builder`.
+    """
+
+    # input arguments are simple
+    if ufunc.nin == 1:
+        in_args = 'x'
+    else:
+        in_args = ', '.join(f'x{i + 1}' for i in range(ufunc.nin))
+
+    # output arguments are both keyword or positional
+    if ufunc.nout == 0:
+        out_args = ', /, out=()'
+    elif ufunc.nout == 1:
+        out_args = ', /, out=None'
+    else:
+        out_args = '[, {positional}], / [, out={default}]'.format(
+            positional=', '.join(
+                f'out{i + 1}' for i in range(ufunc.nout)),
+            default=repr((None,) * ufunc.nout)
+        )
+
+    # keyword only args depend on whether this is a gufunc
+    kwargs = (
+        ", casting='same_kind'"
+        ", order='K'"
+        ", dtype=None"
+        ", subok=True"
+    )
+
+    # NOTE: gufuncs may or may not support the `axis` parameter
+    if ufunc.signature is None:
+        kwargs = f", where=True{kwargs}[, signature]"
+    else:
+        kwargs += "[, signature, axes, axis]"
+
+    # join all the parts together
+    return f'{ufunc.__name__}({in_args}{out_args}, *{kwargs})'
+
+
+def _ufunc_inspect_signature_builder(ufunc):
+    """
+    Builds a ``__signature__`` string.
+
+    Should be kept in sync with `_ufunc_doc_signature_formatter`.
+    """
+
+    from inspect import Parameter, Signature
+
+    params = []
+
+    # positional-only input parameters
+    if ufunc.nin == 1:
+        params.append(Parameter("x", Parameter.POSITIONAL_ONLY))
+    else:
+        params.extend(
+            Parameter(f"x{i}", Parameter.POSITIONAL_ONLY)
+            for i in range(1, ufunc.nin + 1)
+        )
+
+    # for the sake of simplicity, we only consider a single output parameter
+    if ufunc.nout == 1:
+        out_default = None
+    else:
+        out_default = (None,) * ufunc.nout
+    params.append(
+        Parameter("out", Parameter.POSITIONAL_OR_KEYWORD, default=out_default),
+    )
+
+    if ufunc.signature is None:
+        params.append(Parameter("where", Parameter.KEYWORD_ONLY, default=True))
+    else:
+        # NOTE: not all gufuncs support the `axis` parameters
+        params.append(Parameter("axes", Parameter.KEYWORD_ONLY, default=_NoValue))
+        params.append(Parameter("axis", Parameter.KEYWORD_ONLY, default=_NoValue))
+        params.append(Parameter("keepdims", Parameter.KEYWORD_ONLY, default=False))
+
+    params.extend((
+        Parameter("casting", Parameter.KEYWORD_ONLY, default='same_kind'),
+        Parameter("order", Parameter.KEYWORD_ONLY, default='K'),
+        Parameter("dtype", Parameter.KEYWORD_ONLY, default=None),
+        Parameter("subok", Parameter.KEYWORD_ONLY, default=True),
+        Parameter("signature", Parameter.KEYWORD_ONLY, default=None),
+    ))
+
+    return Signature(params)
+
+
+def npy_ctypes_check(cls):
+    # determine if a class comes from ctypes, in order to work around
+    # a bug in the buffer protocol for those objects, bpo-10746
+    try:
+        # ctypes class are new-style, so have an __mro__. This probably fails
+        # for ctypes classes with multiple inheritance.
+        if IS_PYPY:
+            # (..., _ctypes.basics._CData, Bufferable, object)
+            ctype_base = cls.__mro__[-3]
+        else:
+            # # (..., _ctypes._CData, object)
+            ctype_base = cls.__mro__[-2]
+        # right now, they're part of the _ctypes module
+        return '_ctypes' in ctype_base.__module__
+    except Exception:
+        return False
+
+# used to handle the _NoValue default argument for na_object
+# in the C implementation of the __reduce__ method for stringdtype
+def _convert_to_stringdtype_kwargs(coerce, na_object=_NoValue):
+    if na_object is _NoValue:
+        return StringDType(coerce=coerce)
+    return StringDType(coerce=coerce, na_object=na_object)

python/user_packages/Python313/site-packages/numpy/_core/_internal.pyi

@@ -0,0 +1,61 @@
+import ctypes as ct
+import re
+from collections.abc import Callable, Iterable
+from typing import Any, Final, Generic, Self, overload
+from typing_extensions import TypeVar
+
+import numpy as np
+import numpy.typing as npt
+from numpy.ctypeslib import c_intp
+
+_CastT = TypeVar("_CastT", bound=ct._CanCastTo)
+_T_co = TypeVar("_T_co", covariant=True)
+_CT = TypeVar("_CT", bound=ct._CData)
+_PT_co = TypeVar("_PT_co", bound=int | None, default=None, covariant=True)
+
+###
+
+IS_PYPY: Final[bool] = ...
+
+format_re: Final[re.Pattern[str]] = ...
+sep_re: Final[re.Pattern[str]] = ...
+space_re: Final[re.Pattern[str]] = ...
+
+###
+
+# TODO: Let the likes of `shape_as` and `strides_as` return `None`
+# for 0D arrays once we've got shape-support
+
+class _ctypes(Generic[_PT_co]):
+    @overload
+    def __init__(self: _ctypes[None], /, array: npt.NDArray[Any], ptr: None = None) -> None: ...
+    @overload
+    def __init__(self, /, array: npt.NDArray[Any], ptr: _PT_co) -> None: ...
+
+    #
+    @property
+    def data(self) -> _PT_co: ...
+    @property
+    def shape(self) -> ct.Array[c_intp]: ...
+    @property
+    def strides(self) -> ct.Array[c_intp]: ...
+    @property
+    def _as_parameter_(self) -> ct.c_void_p: ...
+
+    #
+    def data_as(self, /, obj: type[_CastT]) -> _CastT: ...
+    def shape_as(self, /, obj: type[_CT]) -> ct.Array[_CT]: ...
+    def strides_as(self, /, obj: type[_CT]) -> ct.Array[_CT]: ...
+
+class dummy_ctype(Generic[_T_co]):
+    _cls: type[_T_co]
+
+    def __init__(self, /, cls: type[_T_co]) -> None: ...
+    def __eq__(self, other: Self, /) -> bool: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    def __ne__(self, other: Self, /) -> bool: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    def __mul__(self, other: object, /) -> Self: ...
+    def __call__(self, /, *other: object) -> _T_co: ...
+
+def array_ufunc_errmsg_formatter(dummy: object, ufunc: np.ufunc, method: str, *inputs: object, **kwargs: object) -> str: ...
+def array_function_errmsg_formatter(public_api: Callable[..., object], types: Iterable[str]) -> str: ...
+def npy_ctypes_check(cls: type) -> bool: ...

python/user_packages/Python313/site-packages/numpy/_core/_methods.py

@@ -0,0 +1,252 @@
+"""
+Array methods which are called by both the C-code for the method
+and the Python code for the NumPy-namespace function
+
+"""
+import os
+import pickle
+import warnings
+from contextlib import nullcontext
+
+import numpy as np
+from numpy._core import multiarray as mu, numerictypes as nt, umath as um
+from numpy._core.multiarray import asanyarray
+from numpy._globals import _NoValue
+
+# save those O(100) nanoseconds!
+bool_dt = mu.dtype("bool")
+umr_maximum = um.maximum.reduce
+umr_minimum = um.minimum.reduce
+umr_sum = um.add.reduce
+umr_prod = um.multiply.reduce
+umr_bitwise_count = um.bitwise_count
+umr_any = um.logical_or.reduce
+umr_all = um.logical_and.reduce
+
+# Complex types to -> (2,)float view for fast-path computation in _var()
+_complex_to_float = {
+    nt.dtype(nt.csingle): nt.dtype(nt.single),
+    nt.dtype(nt.cdouble): nt.dtype(nt.double),
+}
+# Special case for windows: ensure double takes precedence
+if nt.dtype(nt.longdouble) != nt.dtype(nt.double):
+    _complex_to_float.update({
+        nt.dtype(nt.clongdouble): nt.dtype(nt.longdouble),
+    })
+
+# avoid keyword arguments to speed up parsing, saves about 15%-20% for very
+# small reductions
+def _amax(a, axis=None, out=None, keepdims=False,
+          initial=_NoValue, where=True):
+    return umr_maximum(a, axis, None, out, keepdims, initial, where)
+
+def _amin(a, axis=None, out=None, keepdims=False,
+          initial=_NoValue, where=True):
+    return umr_minimum(a, axis, None, out, keepdims, initial, where)
+
+def _sum(a, axis=None, dtype=None, out=None, keepdims=False,
+         initial=_NoValue, where=True):
+    return umr_sum(a, axis, dtype, out, keepdims, initial, where)
+
+def _prod(a, axis=None, dtype=None, out=None, keepdims=False,
+          initial=_NoValue, where=True):
+    return umr_prod(a, axis, dtype, out, keepdims, initial, where)
+
+def _any(a, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
+    # By default, return a boolean for any and all
+    if dtype is None:
+        dtype = bool_dt
+    # Parsing keyword arguments is currently fairly slow, so avoid it for now
+    if where is True:
+        return umr_any(a, axis, dtype, out, keepdims)
+    return umr_any(a, axis, dtype, out, keepdims, where=where)
+
+def _all(a, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
+    # By default, return a boolean for any and all
+    if dtype is None:
+        dtype = bool_dt
+    # Parsing keyword arguments is currently fairly slow, so avoid it for now
+    if where is True:
+        return umr_all(a, axis, dtype, out, keepdims)
+    return umr_all(a, axis, dtype, out, keepdims, where=where)
+
+def _count_reduce_items(arr, axis, keepdims=False, where=True):
+    # fast-path for the default case
+    if where is True:
+        # no boolean mask given, calculate items according to axis
+        if axis is None:
+            axis = tuple(range(arr.ndim))
+        elif not isinstance(axis, tuple):
+            axis = (axis,)
+        items = 1
+        for ax in axis:
+            items *= arr.shape[mu.normalize_axis_index(ax, arr.ndim)]
+        items = nt.intp(items)
+    else:
+        # TODO: Optimize case when `where` is broadcast along a non-reduction
+        # axis and full sum is more excessive than needed.
+
+        # guarded to protect circular imports
+        from numpy.lib._stride_tricks_impl import broadcast_to
+        # count True values in (potentially broadcasted) boolean mask
+        items = umr_sum(broadcast_to(where, arr.shape), axis, nt.intp, None,
+                        keepdims)
+    return items
+
+def _clip(a, min=None, max=None, out=None, **kwargs):
+    if a.dtype.kind in "iu":
+        # If min/max is a Python integer, deal with out-of-bound values here.
+        # (This enforces NEP 50 rules as no value based promotion is done.)
+        if type(min) is int and min <= np.iinfo(a.dtype).min:
+            min = None
+        if type(max) is int and max >= np.iinfo(a.dtype).max:
+            max = None
+
+    if min is None and max is None:
+        # return identity
+        return um.positive(a, out=out, **kwargs)
+    elif min is None:
+        return um.minimum(a, max, out=out, **kwargs)
+    elif max is None:
+        return um.maximum(a, min, out=out, **kwargs)
+    else:
+        return um.clip(a, min, max, out=out, **kwargs)
+
+def _mean(a, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
+    arr = asanyarray(a)
+
+    is_float16_result = False
+
+    rcount = _count_reduce_items(arr, axis, keepdims=keepdims, where=where)
+    if rcount == 0 if where is True else umr_any(rcount == 0, axis=None):
+        warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=2)
+
+    # Cast bool, unsigned int, and int to float64 by default
+    if dtype is None:
+        if issubclass(arr.dtype.type, (nt.integer, nt.bool)):
+            dtype = mu.dtype('f8')
+        elif issubclass(arr.dtype.type, nt.float16):
+            dtype = mu.dtype('f4')
+            is_float16_result = True
+
+    ret = umr_sum(arr, axis, dtype, out, keepdims, where=where)
+    if isinstance(ret, mu.ndarray):
+        ret = um.true_divide(
+                ret, rcount, out=ret, casting='unsafe', subok=False)
+        if is_float16_result and out is None:
+            ret = arr.dtype.type(ret)
+    elif hasattr(ret, 'dtype'):
+        if is_float16_result:
+            ret = arr.dtype.type(ret / rcount)
+        else:
+            ret = ret.dtype.type(ret / rcount)
+    else:
+        ret = ret / rcount
+
+    return ret
+
+def _var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False, *,
+         where=True, mean=None):
+    arr = asanyarray(a)
+
+    rcount = _count_reduce_items(arr, axis, keepdims=keepdims, where=where)
+    # Make this warning show up on top.
+    if ddof >= rcount if where is True else umr_any(ddof >= rcount, axis=None):
+        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning,
+                      stacklevel=2)
+
+    # Cast bool, unsigned int, and int to float64 by default
+    if dtype is None and issubclass(arr.dtype.type, (nt.integer, nt.bool)):
+        dtype = mu.dtype('f8')
+
+    if mean is not None:
+        arrmean = mean
+    else:
+        # Compute the mean.
+        # Note that if dtype is not of inexact type then arraymean will
+        # not be either.
+        arrmean = umr_sum(arr, axis, dtype, keepdims=True, where=where)
+        # The shape of rcount has to match arrmean to not change the shape of
+        # out in broadcasting. Otherwise, it cannot be stored back to arrmean.
+        if rcount.ndim == 0:
+            # fast-path for default case when where is True
+            div = rcount
+        else:
+            # matching rcount to arrmean when where is specified as array
+            div = rcount.reshape(arrmean.shape)
+        if isinstance(arrmean, mu.ndarray):
+            arrmean = um.true_divide(arrmean, div, out=arrmean,
+                                     casting='unsafe', subok=False)
+        elif hasattr(arrmean, "dtype"):
+            arrmean = arrmean.dtype.type(arrmean / rcount)
+        else:
+            arrmean = arrmean / rcount
+
+    # Compute sum of squared deviations from mean
+    # Note that x may not be inexact and that we need it to be an array,
+    # not a scalar.
+    x = um.subtract(arr, arrmean, out=...)
+    if issubclass(arr.dtype.type, (nt.floating, nt.integer)):
+        x = um.square(x, out=x)
+    # Fast-paths for built-in complex types
+    elif (_float_dtype := _complex_to_float.get(x.dtype)) is not None:
+        xv = x.view(dtype=(_float_dtype, (2,)))
+        um.square(xv, out=xv)
+        x = um.add(xv[..., 0], xv[..., 1], out=x.real)
+    # Most general case; includes handling object arrays containing imaginary
+    # numbers and complex types with non-native byteorder
+    else:
+        x = um.multiply(x, um.conjugate(x), out=x).real
+
+    ret = umr_sum(x, axis, dtype, out, keepdims=keepdims, where=where)
+
+    # Compute degrees of freedom and make sure it is not negative.
+    rcount = um.maximum(rcount - ddof, 0)
+
+    # divide by degrees of freedom
+    if isinstance(ret, mu.ndarray):
+        ret = um.true_divide(
+                ret, rcount, out=ret, casting='unsafe', subok=False)
+    elif hasattr(ret, 'dtype'):
+        ret = ret.dtype.type(ret / rcount)
+    else:
+        ret = ret / rcount
+
+    return ret
+
+def _std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False, *,
+         where=True, mean=None):
+    ret = _var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+               keepdims=keepdims, where=where, mean=mean)
+
+    if isinstance(ret, mu.ndarray):
+        ret = um.sqrt(ret, out=ret)
+    elif hasattr(ret, 'dtype'):
+        ret = ret.dtype.type(um.sqrt(ret))
+    else:
+        ret = um.sqrt(ret)
+
+    return ret
+
+def _ptp(a, axis=None, out=None, keepdims=False):
+    return um.subtract(
+        umr_maximum(a, axis, None, out, keepdims),
+        umr_minimum(a, axis, None, None, keepdims),
+        out
+    )
+
+def _dump(self, file, protocol=2):
+    if hasattr(file, 'write'):
+        ctx = nullcontext(file)
+    else:
+        ctx = open(os.fspath(file), "wb")
+    with ctx as f:
+        pickle.dump(self, f, protocol=protocol)
+
+def _dumps(self, protocol=2):
+    return pickle.dumps(self, protocol=protocol)
+
+def _bitwise_count(a, out=None, *, where=True, casting='same_kind',
+          order='K', dtype=None, subok=True):
+    return umr_bitwise_count(a, out, where=where, casting=casting,
+            order=order, dtype=dtype, subok=subok)

python/user_packages/Python313/site-packages/numpy/_core/_methods.pyi

@@ -0,0 +1,22 @@
+from collections.abc import Callable
+from typing import Any, Concatenate, TypeAlias
+
+import numpy as np
+
+from . import _exceptions as _exceptions
+
+###
+
+_Reduce2: TypeAlias = Callable[Concatenate[object, ...], Any]
+
+###
+
+bool_dt: np.dtype[np.bool] = ...
+umr_maximum: _Reduce2 = ...
+umr_minimum: _Reduce2 = ...
+umr_sum: _Reduce2 = ...
+umr_prod: _Reduce2 = ...
+umr_bitwise_count = np.bitwise_count
+umr_any: _Reduce2 = ...
+umr_all: _Reduce2 = ...
+_complex_to_float: dict[np.dtype[np.complexfloating], np.dtype[np.floating]] = ...

python/user_packages/Python313/site-packages/numpy/_core/_simd.pyi

@@ -0,0 +1,35 @@
+from types import ModuleType
+from typing import TypedDict, type_check_only
+
+# NOTE: these 5 are only defined on systems with an intel processor
+SSE42: ModuleType | None = ...
+FMA3: ModuleType | None = ...
+AVX2: ModuleType | None = ...
+AVX512F: ModuleType | None = ...
+AVX512_SKX: ModuleType | None = ...
+
+# NOTE: these 2 are only defined on systems with an arm processor
+ASIMD: ModuleType | None = ...
+NEON: ModuleType | None = ...
+
+# NOTE: This is only defined on systems with an riscv64 processor.
+RVV: ModuleType | None = ...
+
+baseline: ModuleType | None = ...
+
+@type_check_only
+class SimdTargets(TypedDict):
+    SSE42: ModuleType | None
+    AVX2: ModuleType | None
+    FMA3: ModuleType | None
+    AVX512F: ModuleType | None
+    AVX512_SKX: ModuleType | None
+    ASIMD: ModuleType | None
+    NEON: ModuleType | None
+    RVV: ModuleType | None
+    baseline: ModuleType | None
+
+targets: SimdTargets = ...
+
+def clear_floatstatus() -> None: ...
+def get_floatstatus() -> int: ...

python/user_packages/Python313/site-packages/numpy/_core/_string_helpers.py

@@ -0,0 +1,100 @@
+"""
+String-handling utilities to avoid locale-dependence.
+
+Used primarily to generate type name aliases.
+"""
+# "import string" is costly to import!
+# Construct the translation tables directly
+#   "A" = chr(65), "a" = chr(97)
+_all_chars = tuple(map(chr, range(256)))
+_ascii_upper = _all_chars[65:65 + 26]
+_ascii_lower = _all_chars[97:97 + 26]
+LOWER_TABLE = _all_chars[:65] + _ascii_lower + _all_chars[65 + 26:]
+UPPER_TABLE = _all_chars[:97] + _ascii_upper + _all_chars[97 + 26:]
+
+
+def english_lower(s):
+    """ Apply English case rules to convert ASCII strings to all lower case.
+
+    This is an internal utility function to replace calls to str.lower() such
+    that we can avoid changing behavior with changing locales. In particular,
+    Turkish has distinct dotted and dotless variants of the Latin letter "I" in
+    both lowercase and uppercase. Thus, "I".lower() != "i" in a "tr" locale.
+
+    Parameters
+    ----------
+    s : str
+
+    Returns
+    -------
+    lowered : str
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import english_lower
+    >>> english_lower('ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_')
+    'abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz0123456789_'
+    >>> english_lower('')
+    ''
+    """
+    lowered = s.translate(LOWER_TABLE)
+    return lowered
+
+
+def english_upper(s):
+    """ Apply English case rules to convert ASCII strings to all upper case.
+
+    This is an internal utility function to replace calls to str.upper() such
+    that we can avoid changing behavior with changing locales. In particular,
+    Turkish has distinct dotted and dotless variants of the Latin letter "I" in
+    both lowercase and uppercase. Thus, "i".upper() != "I" in a "tr" locale.
+
+    Parameters
+    ----------
+    s : str
+
+    Returns
+    -------
+    uppered : str
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import english_upper
+    >>> english_upper('ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_')
+    'ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_'
+    >>> english_upper('')
+    ''
+    """
+    uppered = s.translate(UPPER_TABLE)
+    return uppered
+
+
+def english_capitalize(s):
+    """ Apply English case rules to convert the first character of an ASCII
+    string to upper case.
+
+    This is an internal utility function to replace calls to str.capitalize()
+    such that we can avoid changing behavior with changing locales.
+
+    Parameters
+    ----------
+    s : str
+
+    Returns
+    -------
+    capitalized : str
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import english_capitalize
+    >>> english_capitalize('int8')
+    'Int8'
+    >>> english_capitalize('Int8')
+    'Int8'
+    >>> english_capitalize('')
+    ''
+    """
+    if s:
+        return english_upper(s[0]) + s[1:]
+    else:
+        return s

python/user_packages/Python313/site-packages/numpy/_core/_string_helpers.pyi

@@ -0,0 +1,12 @@
+from typing import Final
+
+_all_chars: Final[tuple[str, ...]] = ...
+_ascii_upper: Final[tuple[str, ...]] = ...
+_ascii_lower: Final[tuple[str, ...]] = ...
+
+LOWER_TABLE: Final[tuple[str, ...]] = ...
+UPPER_TABLE: Final[tuple[str, ...]] = ...
+
+def english_lower(s: str) -> str: ...
+def english_upper(s: str) -> str: ...
+def english_capitalize(s: str) -> str: ...

python/user_packages/Python313/site-packages/numpy/_core/_type_aliases.py

@@ -0,0 +1,131 @@
+"""
+Due to compatibility, numpy has a very large number of different naming
+conventions for the scalar types (those subclassing from `numpy.generic`).
+This file produces a convoluted set of dictionaries mapping names to types,
+and sometimes other mappings too.
+
+.. data:: allTypes
+    A dictionary of names to types that will be exposed as attributes through
+    ``np._core.numerictypes.*``
+
+.. data:: sctypeDict
+    Similar to `allTypes`, but maps a broader set of aliases to their types.
+
+.. data:: sctypes
+    A dictionary keyed by a "type group" string, providing a list of types
+    under that group.
+
+"""
+
+import numpy._core.multiarray as ma
+from numpy._core.multiarray import dtype, typeinfo
+
+######################################
+# Building `sctypeDict` and `allTypes`
+######################################
+
+sctypeDict = {}
+allTypes = {}
+c_names_dict = {}
+
+_abstract_type_names = {
+    "generic", "integer", "inexact", "floating", "number",
+    "flexible", "character", "complexfloating", "unsignedinteger",
+    "signedinteger"
+}
+
+for _abstract_type_name in _abstract_type_names:
+    allTypes[_abstract_type_name] = getattr(ma, _abstract_type_name)
+    del _abstract_type_name
+
+for k, v in typeinfo.items():
+    if k.startswith("NPY_") and v not in c_names_dict:
+        c_names_dict[k[4:]] = v
+    else:
+        concrete_type = v.type
+        allTypes[k] = concrete_type
+        sctypeDict[k] = concrete_type
+        del concrete_type
+    del k, v
+
+_aliases = {
+    "double": "float64",
+    "cdouble": "complex128",
+    "single": "float32",
+    "csingle": "complex64",
+    "half": "float16",
+    "bool_": "bool",
+    # Default integer:
+    "int_": "intp",
+    "uint": "uintp",
+}
+
+for k, v in _aliases.items():
+    sctypeDict[k] = allTypes[v]
+    allTypes[k] = allTypes[v]
+    del k, v
+
+# extra aliases are added only to `sctypeDict`
+# to support dtype name access, such as`np.dtype("float")`
+_extra_aliases = {
+    "float": "float64",
+    "complex": "complex128",
+    "object": "object_",
+    "bytes": "bytes_",
+    "a": "bytes_",
+    "int": "int_",
+    "str": "str_",
+    "unicode": "str_",
+}
+
+for k, v in _extra_aliases.items():
+    sctypeDict[k] = allTypes[v]
+    del k, v
+
+# include extended precision sized aliases
+for is_complex, full_name in [(False, "longdouble"), (True, "clongdouble")]:
+    longdouble_type = allTypes[full_name]
+
+    bits = dtype(longdouble_type).itemsize * 8
+    base_name = "complex" if is_complex else "float"
+    extended_prec_name = f"{base_name}{bits}"
+    if extended_prec_name not in allTypes:
+        sctypeDict[extended_prec_name] = longdouble_type
+        allTypes[extended_prec_name] = longdouble_type
+
+    del is_complex, full_name, longdouble_type, bits, base_name, extended_prec_name
+
+
+####################
+# Building `sctypes`
+####################
+
+sctypes = {"int": set(), "uint": set(), "float": set(),
+           "complex": set(), "others": set()}
+
+for type_info in typeinfo.values():
+    if type_info.kind in ["M", "m"]:  # exclude timedelta and datetime
+        continue
+
+    concrete_type = type_info.type
+
+    # find proper group for each concrete type
+    for type_group, abstract_type in [
+        ("int", ma.signedinteger), ("uint", ma.unsignedinteger),
+        ("float", ma.floating), ("complex", ma.complexfloating),
+        ("others", ma.generic)
+    ]:
+        if issubclass(concrete_type, abstract_type):
+            sctypes[type_group].add(concrete_type)
+            del type_group, abstract_type
+            break
+
+    del type_info, concrete_type
+
+# sort sctype groups by bitsize
+for sctype_key in sctypes.keys():
+    sctype_list = list(sctypes[sctype_key])
+    sctype_list.sort(key=lambda x: dtype(x).itemsize)
+    sctypes[sctype_key] = sctype_list
+
+    del sctype_key, sctype_list

python/user_packages/Python313/site-packages/numpy/_core/_type_aliases.pyi

@@ -0,0 +1,86 @@
+from collections.abc import Collection
+from typing import Final, Literal as L, TypeAlias, TypedDict, type_check_only
+
+import numpy as np
+
+sctypeDict: Final[dict[str, type[np.generic]]]
+allTypes: Final[dict[str, type[np.generic]]]
+
+@type_check_only
+class _CNamesDict(TypedDict):
+    BOOL: np.dtype[np.bool]
+    HALF: np.dtype[np.half]
+    FLOAT: np.dtype[np.single]
+    DOUBLE: np.dtype[np.double]
+    LONGDOUBLE: np.dtype[np.longdouble]
+    CFLOAT: np.dtype[np.csingle]
+    CDOUBLE: np.dtype[np.cdouble]
+    CLONGDOUBLE: np.dtype[np.clongdouble]
+    STRING: np.dtype[np.bytes_]
+    UNICODE: np.dtype[np.str_]
+    VOID: np.dtype[np.void]
+    OBJECT: np.dtype[np.object_]
+    DATETIME: np.dtype[np.datetime64]
+    TIMEDELTA: np.dtype[np.timedelta64]
+    BYTE: np.dtype[np.byte]
+    UBYTE: np.dtype[np.ubyte]
+    SHORT: np.dtype[np.short]
+    USHORT: np.dtype[np.ushort]
+    INT: np.dtype[np.intc]
+    UINT: np.dtype[np.uintc]
+    LONG: np.dtype[np.long]
+    ULONG: np.dtype[np.ulong]
+    LONGLONG: np.dtype[np.longlong]
+    ULONGLONG: np.dtype[np.ulonglong]
+
+c_names_dict: Final[_CNamesDict]
+
+_AbstractTypeName: TypeAlias = L[
+    "generic",
+    "flexible",
+    "character",
+    "number",
+    "integer",
+    "inexact",
+    "unsignedinteger",
+    "signedinteger",
+    "floating",
+    "complexfloating",
+]
+_abstract_type_names: Final[set[_AbstractTypeName]]
+
+@type_check_only
+class _AliasesType(TypedDict):
+    double: L["float64"]
+    cdouble: L["complex128"]
+    single: L["float32"]
+    csingle: L["complex64"]
+    half: L["float16"]
+    bool_: L["bool"]
+    int_: L["intp"]
+    uint: L["intp"]
+
+_aliases: Final[_AliasesType]
+
+@type_check_only
+class _ExtraAliasesType(TypedDict):
+    float: L["float64"]
+    complex: L["complex128"]
+    object: L["object_"]
+    bytes: L["bytes_"]
+    a: L["bytes_"]
+    int: L["int_"]
+    str: L["str_"]
+    unicode: L["str_"]
+
+_extra_aliases: Final[_ExtraAliasesType]
+
+@type_check_only
+class _SCTypes(TypedDict):
+    int: Collection[type[np.signedinteger]]
+    uint: Collection[type[np.unsignedinteger]]
+    float: Collection[type[np.floating]]
+    complex: Collection[type[np.complexfloating]]
+    others: Collection[type[np.flexible | np.bool | np.object_]]
+
+sctypes: Final[_SCTypes]

python/user_packages/Python313/site-packages/numpy/_core/_ufunc_config.py

@@ -0,0 +1,515 @@
+"""
+Functions for changing global ufunc configuration
+
+This provides helpers which wrap `_get_extobj_dict` and `_make_extobj`, and
+`_extobj_contextvar` from umath.
+"""
+import functools
+
+from numpy._utils import set_module
+
+from .umath import _extobj_contextvar, _get_extobj_dict, _make_extobj
+
+__all__ = [
+    "seterr", "geterr", "setbufsize", "getbufsize", "seterrcall", "geterrcall",
+    "errstate"
+]
+
+
+@set_module('numpy')
+def seterr(all=None, divide=None, over=None, under=None, invalid=None):
+    """
+    Set how floating-point errors are handled.
+
+    Note that operations on integer scalar types (such as `int16`) are
+    handled like floating point, and are affected by these settings.
+
+    Parameters
+    ----------
+    all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Set treatment for all types of floating-point errors at once:
+
+        - ignore: Take no action when the exception occurs.
+        - warn: Print a :exc:`RuntimeWarning` (via the Python `warnings`
+          module).
+        - raise: Raise a :exc:`FloatingPointError`.
+        - call: Call a function specified using the `seterrcall` function.
+        - print: Print a warning directly to ``stdout``.
+        - log: Record error in a Log object specified by `seterrcall`.
+
+        The default is not to change the current behavior.
+    divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for division by zero.
+    over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for floating-point overflow.
+    under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for floating-point underflow.
+    invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for invalid floating-point operation.
+
+    Returns
+    -------
+    old_settings : dict
+        Dictionary containing the old settings.
+
+    See also
+    --------
+    seterrcall : Set a callback function for the 'call' mode.
+    geterr, geterrcall, errstate
+
+
+    Notes
+    -----
+    The floating-point exceptions are defined in the IEEE 754 standard [1]_:
+
+    - Division by zero: infinite result obtained from finite numbers.
+    - Overflow: result too large to be expressed.
+    - Underflow: result so close to zero that some precision
+      was lost.
+    - Invalid operation: result is not an expressible number, typically
+      indicates that a NaN was produced.
+
+    **Concurrency note:** see  :ref:`fp_error_handling`
+
+    .. [1] https://en.wikipedia.org/wiki/IEEE_754
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> orig_settings = np.seterr(all='ignore')  # seterr to known value
+    >>> np.int16(32000) * np.int16(3)
+    np.int16(30464)
+    >>> np.seterr(over='raise')
+    {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}
+    >>> old_settings = np.seterr(all='warn', over='raise')
+    >>> np.int16(32000) * np.int16(3)
+    Traceback (most recent call last):
+      File "<stdin>", line 1, in <module>
+    FloatingPointError: overflow encountered in scalar multiply
+
+    >>> old_settings = np.seterr(all='print')
+    >>> np.geterr()
+    {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'}
+    >>> np.int16(32000) * np.int16(3)
+    np.int16(30464)
+    >>> np.seterr(**orig_settings)  # restore original
+    {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'}
+
+    """
+
+    old = _get_extobj_dict()
+    # The errstate doesn't include call and bufsize, so pop them:
+    old.pop("call", None)
+    old.pop("bufsize", None)
+
+    extobj = _make_extobj(
+            all=all, divide=divide, over=over, under=under, invalid=invalid)
+    _extobj_contextvar.set(extobj)
+    return old
+
+
+@set_module('numpy')
+def geterr():
+    """
+    Get the current way of handling floating-point errors.
+
+    Returns
+    -------
+    res : dict
+        A dictionary with keys "divide", "over", "under", and "invalid",
+        whose values are from the strings "ignore", "print", "log", "warn",
+        "raise", and "call". The keys represent possible floating-point
+        exceptions, and the values define how these exceptions are handled.
+
+    See Also
+    --------
+    geterrcall, seterr, seterrcall
+
+    Notes
+    -----
+    For complete documentation of the types of floating-point exceptions and
+    treatment options, see `seterr`.
+
+    **Concurrency note:** see :doc:`/reference/routines.err`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.geterr()
+    {'divide': 'warn', 'over': 'warn', 'under': 'ignore', 'invalid': 'warn'}
+    >>> np.arange(3.) / np.arange(3.)  # doctest: +SKIP
+    array([nan,  1.,  1.])
+    RuntimeWarning: invalid value encountered in divide
+
+    >>> oldsettings = np.seterr(all='warn', invalid='raise')
+    >>> np.geterr()
+    {'divide': 'warn', 'over': 'warn', 'under': 'warn', 'invalid': 'raise'}
+    >>> np.arange(3.) / np.arange(3.)
+    Traceback (most recent call last):
+      ...
+    FloatingPointError: invalid value encountered in divide
+    >>> oldsettings = np.seterr(**oldsettings)  # restore original
+
+    """
+    res = _get_extobj_dict()
+    # The "geterr" doesn't include call and bufsize,:
+    res.pop("call", None)
+    res.pop("bufsize", None)
+    return res
+
+
+@set_module('numpy')
+def setbufsize(size):
+    """
+    Set the size of the buffer used in ufuncs.
+
+    .. versionchanged:: 2.0
+        The scope of setting the buffer is tied to the `numpy.errstate`
+        context.  Exiting a ``with errstate():`` will also restore the bufsize.
+
+    Parameters
+    ----------
+    size : int
+        Size of buffer.
+
+    Returns
+    -------
+    bufsize : int
+        Previous size of ufunc buffer in bytes.
+
+    Notes
+    -----
+    **Concurrency note:** see :doc:`/reference/routines.err`
+
+    Examples
+    --------
+    When exiting a `numpy.errstate` context manager the bufsize is restored:
+
+    >>> import numpy as np
+    >>> with np.errstate():
+    ...     np.setbufsize(4096)
+    ...     print(np.getbufsize())
+    ...
+    8192
+    4096
+    >>> np.getbufsize()
+    8192
+
+    """
+    if size < 0:
+        raise ValueError("buffer size must be non-negative")
+    old = _get_extobj_dict()["bufsize"]
+    extobj = _make_extobj(bufsize=size)
+    _extobj_contextvar.set(extobj)
+    return old
+
+
+@set_module('numpy')
+def getbufsize():
+    """
+    Return the size of the buffer used in ufuncs.
+
+    Returns
+    -------
+    getbufsize : int
+        Size of ufunc buffer in bytes.
+
+    Notes
+    -----
+
+    **Concurrency note:** see :doc:`/reference/routines.err`
+
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.getbufsize()
+    8192
+
+    """
+    return _get_extobj_dict()["bufsize"]
+
+
+@set_module('numpy')
+def seterrcall(func):
+    """
+    Set the floating-point error callback function or log object.
+
+    There are two ways to capture floating-point error messages.  The first
+    is to set the error-handler to 'call', using `seterr`.  Then, set
+    the function to call using this function.
+
+    The second is to set the error-handler to 'log', using `seterr`.
+    Floating-point errors then trigger a call to the 'write' method of
+    the provided object.
+
+    Parameters
+    ----------
+    func : callable f(err, flag) or object with write method
+        Function to call upon floating-point errors ('call'-mode) or
+        object whose 'write' method is used to log such message ('log'-mode).
+
+        The call function takes two arguments. The first is a string describing
+        the type of error (such as "divide by zero", "overflow", "underflow",
+        or "invalid value"), and the second is the status flag.  The flag is a
+        byte, whose four least-significant bits indicate the type of error, one
+        of "divide", "over", "under", "invalid"::
+
+          [0 0 0 0 divide over under invalid]
+
+        In other words, ``flags = divide + 2*over + 4*under + 8*invalid``.
+
+        If an object is provided, its write method should take one argument,
+        a string.
+
+    Returns
+    -------
+    h : callable, log instance or None
+        The old error handler.
+
+    See Also
+    --------
+    seterr, geterr, geterrcall
+
+    Notes
+    -----
+
+    **Concurrency note:** see :doc:`/reference/routines.err`
+
+    Examples
+    --------
+    Callback upon error:
+
+    >>> def err_handler(type, flag):
+    ...     print("Floating point error (%s), with flag %s" % (type, flag))
+    ...
+
+    >>> import numpy as np
+
+    >>> orig_handler = np.seterrcall(err_handler)
+    >>> orig_err = np.seterr(all='call')
+
+    >>> np.array([1, 2, 3]) / 0.0
+    Floating point error (divide by zero), with flag 1
+    array([inf, inf, inf])
+
+    >>> np.seterrcall(orig_handler)
+    <function err_handler at 0x...>
+    >>> np.seterr(**orig_err)
+    {'divide': 'call', 'over': 'call', 'under': 'call', 'invalid': 'call'}
+
+    Log error message:
+
+    >>> class Log:
+    ...     def write(self, msg):
+    ...         print("LOG: %s" % msg)
+    ...
+
+    >>> log = Log()
+    >>> saved_handler = np.seterrcall(log)
+    >>> save_err = np.seterr(all='log')
+
+    >>> np.array([1, 2, 3]) / 0.0
+    LOG: Warning: divide by zero encountered in divide
+    array([inf, inf, inf])
+
+    >>> np.seterrcall(orig_handler)
+    <numpy.Log object at 0x...>
+    >>> np.seterr(**orig_err)
+    {'divide': 'log', 'over': 'log', 'under': 'log', 'invalid': 'log'}
+
+    """
+    old = _get_extobj_dict()["call"]
+    extobj = _make_extobj(call=func)
+    _extobj_contextvar.set(extobj)
+    return old
+
+
+@set_module('numpy')
+def geterrcall():
+    """
+    Return the current callback function used on floating-point errors.
+
+    When the error handling for a floating-point error (one of "divide",
+    "over", "under", or "invalid") is set to 'call' or 'log', the function
+    that is called or the log instance that is written to is returned by
+    `geterrcall`. This function or log instance has been set with
+    `seterrcall`.
+
+    Returns
+    -------
+    errobj : callable, log instance or None
+        The current error handler. If no handler was set through `seterrcall`,
+        ``None`` is returned.
+
+    See Also
+    --------
+    seterrcall, seterr, geterr
+
+    Notes
+    -----
+    For complete documentation of the types of floating-point exceptions and
+    treatment options, see `seterr`.
+
+    **Concurrency note:** see :ref:`fp_error_handling`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.geterrcall()  # we did not yet set a handler, returns None
+
+    >>> orig_settings = np.seterr(all='call')
+    >>> def err_handler(type, flag):
+    ...     print("Floating point error (%s), with flag %s" % (type, flag))
+    >>> old_handler = np.seterrcall(err_handler)
+    >>> np.array([1, 2, 3]) / 0.0
+    Floating point error (divide by zero), with flag 1
+    array([inf, inf, inf])
+
+    >>> cur_handler = np.geterrcall()
+    >>> cur_handler is err_handler
+    True
+    >>> old_settings = np.seterr(**orig_settings)  # restore original
+    >>> old_handler = np.seterrcall(None)  # restore original
+
+    """
+    return _get_extobj_dict()["call"]
+
+
+class _unspecified:
+    pass
+
+
+_Unspecified = _unspecified()
+
+
+@set_module('numpy')
+class errstate:
+    """
+    errstate(**kwargs)
+
+    Context manager for floating-point error handling.
+
+    Using an instance of `errstate` as a context manager allows statements in
+    that context to execute with a known error handling behavior. Upon entering
+    the context the error handling is set with `seterr` and `seterrcall`, and
+    upon exiting it is reset to what it was before.
+
+    ..  versionchanged:: 1.17.0
+        `errstate` is also usable as a function decorator, saving
+        a level of indentation if an entire function is wrapped.
+
+    .. versionchanged:: 2.0
+        `errstate` is now fully thread and asyncio safe, but may not be
+        entered more than once.
+        It is not safe to decorate async functions using ``errstate``.
+
+    Parameters
+    ----------
+    kwargs : {divide, over, under, invalid}
+        Keyword arguments. The valid keywords are the possible floating-point
+        exceptions. Each keyword should have a string value that defines the
+        treatment for the particular error. Possible values are
+        {'ignore', 'warn', 'raise', 'call', 'print', 'log'}.
+
+    See Also
+    --------
+    seterr, geterr, seterrcall, geterrcall
+
+    Notes
+    -----
+    For complete documentation of the types of floating-point exceptions and
+    treatment options, see `seterr`.
+
+    **Concurrency note:** see :ref:`fp_error_handling`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> olderr = np.seterr(all='ignore')  # Set error handling to known state.
+
+    >>> np.arange(3) / 0.
+    array([nan, inf, inf])
+    >>> with np.errstate(divide='ignore'):
+    ...     np.arange(3) / 0.
+    array([nan, inf, inf])
+
+    >>> np.sqrt(-1)
+    np.float64(nan)
+    >>> with np.errstate(invalid='raise'):
+    ...     np.sqrt(-1)
+    Traceback (most recent call last):
+      File "<stdin>", line 2, in <module>
+    FloatingPointError: invalid value encountered in sqrt
+
+    Outside the context the error handling behavior has not changed:
+
+    >>> np.geterr()
+    {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}
+    >>> olderr = np.seterr(**olderr)  # restore original state
+
+    """
+    __slots__ = (
+        "_all",
+        "_call",
+        "_divide",
+        "_invalid",
+        "_over",
+        "_token",
+        "_under",
+    )
+
+    def __init__(self, *, call=_Unspecified,
+                 all=None, divide=None, over=None, under=None, invalid=None):
+        self._token = None
+        self._call = call
+        self._all = all
+        self._divide = divide
+        self._over = over
+        self._under = under
+        self._invalid = invalid
+
+    def __enter__(self):
+        # Note that __call__ duplicates much of this logic
+        if self._token is not None:
+            raise TypeError("Cannot enter `np.errstate` twice.")
+        if self._call is _Unspecified:
+            extobj = _make_extobj(
+                    all=self._all, divide=self._divide, over=self._over,
+                    under=self._under, invalid=self._invalid)
+        else:
+            extobj = _make_extobj(
+                    call=self._call,
+                    all=self._all, divide=self._divide, over=self._over,
+                    under=self._under, invalid=self._invalid)
+
+        self._token = _extobj_contextvar.set(extobj)
+
+    def __exit__(self, *exc_info):
+        _extobj_contextvar.reset(self._token)
+
+    def __call__(self, func):
+        # We need to customize `__call__` compared to `ContextDecorator`
+        # because we must store the token per-thread so cannot store it on
+        # the instance (we could create a new instance for this).
+        # This duplicates the code from `__enter__`.
+        @functools.wraps(func)
+        def inner(*args, **kwargs):
+            if self._call is _Unspecified:
+                extobj = _make_extobj(
+                        all=self._all, divide=self._divide, over=self._over,
+                        under=self._under, invalid=self._invalid)
+            else:
+                extobj = _make_extobj(
+                        call=self._call,
+                        all=self._all, divide=self._divide, over=self._over,
+                        under=self._under, invalid=self._invalid)
+
+            _token = _extobj_contextvar.set(extobj)
+            try:
+                # Call the original, decorated, function:
+                return func(*args, **kwargs)
+            finally:
+                _extobj_contextvar.reset(_token)
+
+        return inner

python/user_packages/Python313/site-packages/numpy/_core/_ufunc_config.pyi

@@ -0,0 +1,69 @@
+from _typeshed import SupportsWrite
+from collections.abc import Callable
+from types import TracebackType
+from typing import Any, Final, Literal, TypeAlias, TypedDict, TypeVar, type_check_only
+
+__all__ = [
+    "seterr",
+    "geterr",
+    "setbufsize",
+    "getbufsize",
+    "seterrcall",
+    "geterrcall",
+    "errstate",
+]
+
+_ErrKind: TypeAlias = Literal["ignore", "warn", "raise", "call", "print", "log"]
+_ErrCall: TypeAlias = Callable[[str, int], Any] | SupportsWrite[str]
+
+_CallableT = TypeVar("_CallableT", bound=Callable[..., object])
+
+@type_check_only
+class _ErrDict(TypedDict):
+    divide: _ErrKind
+    over: _ErrKind
+    under: _ErrKind
+    invalid: _ErrKind
+
+###
+
+class _unspecified: ...
+
+_Unspecified: Final[_unspecified]
+
+class errstate:
+    __slots__ = "_all", "_call", "_divide", "_invalid", "_over", "_token", "_under"
+
+    def __init__(
+        self,
+        /,
+        *,
+        call: _ErrCall | _unspecified = ...,  # = _Unspecified
+        all: _ErrKind | None = None,
+        divide: _ErrKind | None = None,
+        over: _ErrKind | None = None,
+        under: _ErrKind | None = None,
+        invalid: _ErrKind | None = None,
+    ) -> None: ...
+    def __call__(self, /, func: _CallableT) -> _CallableT: ...
+    def __enter__(self) -> None: ...
+    def __exit__(
+        self,
+        exc_type: type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
+        /,
+    ) -> None: ...
+
+def seterr(
+    all: _ErrKind | None = None,
+    divide: _ErrKind | None = None,
+    over: _ErrKind | None = None,
+    under: _ErrKind | None = None,
+    invalid: _ErrKind | None = None,
+) -> _ErrDict: ...
+def geterr() -> _ErrDict: ...
+def setbufsize(size: int) -> int: ...
+def getbufsize() -> int: ...
+def seterrcall(func: _ErrCall | None) -> _ErrCall | None: ...
+def geterrcall() -> _ErrCall | None: ...

python/user_packages/Python313/site-packages/numpy/_core/_umath_tests.pyi

@@ -0,0 +1,47 @@
+# undocumented internal testing module for ufunc features, defined in
+# numpy/_core/src/umath/_umath_tests.c.src
+
+from typing import Final, Literal as L, TypedDict, type_check_only
+
+import numpy as np
+from numpy._typing import _GUFunc_Nin2_Nout1, _UFunc_Nin1_Nout1, _UFunc_Nin2_Nout1
+
+@type_check_only
+class _TestDispatchResult(TypedDict):
+    func: str  # e.g. 'func_AVX2'
+    var: str  # e.g. 'var_AVX2'
+    func_xb: str  # e.g. 'func_AVX2'
+    var_xb: str  # e.g. 'var_AVX2'
+    all: list[str]  # e.g. ['func_AVX2', 'func_SSE41', 'func']
+
+###
+
+# undocumented
+def test_signature(
+    nin: int, nout: int, signature: str, /
+) -> tuple[
+    L[0, 1],  # core_enabled (0 for scalar ufunc; 1 for generalized ufunc)
+    tuple[int, ...] | None,  # core_num_dims
+    tuple[int, ...] | None,  # core_dim_ixs
+    tuple[int, ...] | None,  # core_dim_flags
+    tuple[int, ...] | None,  # core_dim_sizes
+]: ...
+
+# undocumented
+def test_dispatch() -> _TestDispatchResult: ...
+
+# undocumented ufuncs and gufuncs
+always_error: Final[_UFunc_Nin2_Nout1[L["always_error"], L[1], None]] = ...
+always_error_unary: Final[_UFunc_Nin1_Nout1[L["always_error_unary"], L[1], None]] = ...
+always_error_gufunc: Final[_GUFunc_Nin2_Nout1[L["always_error_gufunc"], L[1], None, L["(i),()->()"]]] = ...
+inner1d: Final[_GUFunc_Nin2_Nout1[L["inner1d"], L[2], None, L["(i),(i)->()"]]] = ...
+innerwt: Final[np.ufunc] = ...  # we have no specialized type for 3->1 gufuncs
+matrix_multiply: Final[_GUFunc_Nin2_Nout1[L["matrix_multiply"], L[3], None, L["(m,n),(n,p)->(m,p)"]]] = ...
+matmul: Final[_GUFunc_Nin2_Nout1[L["matmul"], L[3], None, L["(m?,n),(n,p?)->(m?,p?)"]]] = ...
+euclidean_pdist: Final[_GUFunc_Nin2_Nout1[L["euclidean_pdist"], L[2], None, L["(n,d)->(p)"]]] = ...
+cumsum: Final[np.ufunc] = ...  # we have no specialized type for 1->1 gufuncs
+inner1d_no_doc: Final[_GUFunc_Nin2_Nout1[L["inner1d_no_doc"], L[2], None, L["(i),(i)->()"]]] = ...
+cross1d: Final[_GUFunc_Nin2_Nout1[L["cross1d"], L[2], None, L["(3),(3)->(3)"]]] = ...
+_pickleable_module_global_ufunc: Final[np.ufunc] = ...  # 0->0 ufunc; segfaults if called
+indexed_negative: Final[_UFunc_Nin1_Nout1[L["indexed_negative"], L[0], L[0]]] = ...  # ntypes=0; can't be called
+conv1d_full: Final[_GUFunc_Nin2_Nout1[L["conv1d_full"], L[1], None, L["(m),(n)->(p)"]]] = ...

python/user_packages/Python313/site-packages/numpy/_core/arrayprint.py

@@ -0,0 +1,1779 @@
+"""Array printing function
+
+$Id: arrayprint.py,v 1.9 2005/09/13 13:58:44 teoliphant Exp $
+
+"""
+__all__ = ["array2string", "array_str", "array_repr",
+           "set_printoptions", "get_printoptions", "printoptions",
+           "format_float_positional", "format_float_scientific"]
+__docformat__ = 'restructuredtext'
+
+#
+# Written by Konrad Hinsen <hinsenk@ere.umontreal.ca>
+# last revision: 1996-3-13
+# modified by Jim Hugunin 1997-3-3 for repr's and str's (and other details)
+# and by Perry Greenfield 2000-4-1 for numarray
+# and by Travis Oliphant  2005-8-22 for numpy
+
+
+# Note: Both scalartypes.c.src and arrayprint.py implement strs for numpy
+# scalars but for different purposes. scalartypes.c.src has str/reprs for when
+# the scalar is printed on its own, while arrayprint.py has strs for when
+# scalars are printed inside an ndarray. Only the latter strs are currently
+# user-customizable.
+
+import functools
+import numbers
+import sys
+
+try:
+    from _thread import get_ident
+except ImportError:
+    from _dummy_thread import get_ident
+
+import contextlib
+import operator
+import warnings
+
+import numpy as np
+
+from . import numerictypes as _nt
+from .fromnumeric import any
+from .multiarray import (
+    array,
+    datetime_as_string,
+    datetime_data,
+    dragon4_positional,
+    dragon4_scientific,
+    ndarray,
+)
+from .numeric import asarray, concatenate, errstate
+from .numerictypes import complex128, flexible, float64, int_
+from .overrides import array_function_dispatch, set_module
+from .printoptions import format_options
+from .umath import absolute, isfinite, isinf, isnat
+
+
+def _make_options_dict(precision=None, threshold=None, edgeitems=None,
+                       linewidth=None, suppress=None, nanstr=None, infstr=None,
+                       sign=None, formatter=None, floatmode=None, legacy=None,
+                       override_repr=None):
+    """
+    Make a dictionary out of the non-None arguments, plus conversion of
+    *legacy* and sanity checks.
+    """
+
+    options = {k: v for k, v in list(locals().items()) if v is not None}
+
+    if suppress is not None:
+        options['suppress'] = bool(suppress)
+
+    modes = ['fixed', 'unique', 'maxprec', 'maxprec_equal']
+    if floatmode not in modes + [None]:
+        raise ValueError("floatmode option must be one of " +
+                         ", ".join(f'"{m}"' for m in modes))
+
+    if sign not in [None, '-', '+', ' ']:
+        raise ValueError("sign option must be one of ' ', '+', or '-'")
+
+    if legacy is False:
+        options['legacy'] = sys.maxsize
+    elif legacy == False:  # noqa: E712
+        warnings.warn(
+            f"Passing `legacy={legacy!r}` is deprecated.",
+            FutureWarning, stacklevel=3
+        )
+        options['legacy'] = sys.maxsize
+    elif legacy == '1.13':
+        options['legacy'] = 113
+    elif legacy == '1.21':
+        options['legacy'] = 121
+    elif legacy == '1.25':
+        options['legacy'] = 125
+    elif legacy == '2.1':
+        options['legacy'] = 201
+    elif legacy == '2.2':
+        options['legacy'] = 202
+    elif legacy is None:
+        pass  # OK, do nothing.
+    else:
+        warnings.warn(
+            "legacy printing option can currently only be '1.13', '1.21', "
+            "'1.25', '2.1', '2.2' or `False`", stacklevel=3)
+
+    if threshold is not None:
+        # forbid the bad threshold arg suggested by stack overflow, gh-12351
+        if not isinstance(threshold, numbers.Number):
+            raise TypeError("threshold must be numeric")
+        if np.isnan(threshold):
+            raise ValueError("threshold must be non-NAN, try "
+                             "sys.maxsize for untruncated representation")
+
+    if precision is not None:
+        # forbid the bad precision arg as suggested by issue #18254
+        try:
+            options['precision'] = operator.index(precision)
+        except TypeError as e:
+            raise TypeError('precision must be an integer') from e
+
+    return options
+
+
+@set_module('numpy')
+def set_printoptions(precision=None, threshold=None, edgeitems=None,
+                     linewidth=None, suppress=None, nanstr=None,
+                     infstr=None, formatter=None, sign=None, floatmode=None,
+                     *, legacy=None, override_repr=None):
+    """
+    Set printing options.
+
+    These options determine the way floating point numbers, arrays and
+    other NumPy objects are displayed.
+
+    Parameters
+    ----------
+    precision : int or None, optional
+        Number of digits of precision for floating point output (default 8).
+        May be None if `floatmode` is not `fixed`, to print as many digits as
+        necessary to uniquely specify the value.
+    threshold : int, optional
+        Total number of array elements which trigger summarization
+        rather than full repr (default 1000).
+        To always use the full repr without summarization, pass `sys.maxsize`.
+    edgeitems : int, optional
+        Number of array items in summary at beginning and end of
+        each dimension (default 3).
+    linewidth : int, optional
+        The number of characters per line for the purpose of inserting
+        line breaks (default 75).
+    suppress : bool, optional
+        If True, always print floating point numbers using fixed point
+        notation, in which case numbers equal to zero in the current precision
+        will print as zero.  If False, then scientific notation is used when
+        absolute value of the smallest number is < 1e-4 or the ratio of the
+        maximum absolute value to the minimum is > 1e3. The default is False.
+    nanstr : str, optional
+        String representation of floating point not-a-number (default nan).
+    infstr : str, optional
+        String representation of floating point infinity (default inf).
+    sign : string, either '-', '+', or ' ', optional
+        Controls printing of the sign of floating-point types. If '+', always
+        print the sign of positive values. If ' ', always prints a space
+        (whitespace character) in the sign position of positive values.  If
+        '-', omit the sign character of positive values. (default '-')
+
+        .. versionchanged:: 2.0
+             The sign parameter can now be an integer type, previously
+             types were floating-point types.
+
+    formatter : dict of callables, optional
+        If not None, the keys should indicate the type(s) that the respective
+        formatting function applies to.  Callables should return a string.
+        Types that are not specified (by their corresponding keys) are handled
+        by the default formatters.  Individual types for which a formatter
+        can be set are:
+
+        - 'bool'
+        - 'int'
+        - 'timedelta' : a `numpy.timedelta64`
+        - 'datetime' : a `numpy.datetime64`
+        - 'float'
+        - 'longfloat' : 128-bit floats
+        - 'complexfloat'
+        - 'longcomplexfloat' : composed of two 128-bit floats
+        - 'numpystr' : types `numpy.bytes_` and `numpy.str_`
+        - 'object' : `np.object_` arrays
+
+        Other keys that can be used to set a group of types at once are:
+
+        - 'all' : sets all types
+        - 'int_kind' : sets 'int'
+        - 'float_kind' : sets 'float' and 'longfloat'
+        - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
+        - 'str_kind' : sets 'numpystr'
+    floatmode : str, optional
+        Controls the interpretation of the `precision` option for
+        floating-point types. Can take the following values
+        (default maxprec_equal):
+
+        * 'fixed': Always print exactly `precision` fractional digits,
+                even if this would print more or fewer digits than
+                necessary to specify the value uniquely.
+        * 'unique': Print the minimum number of fractional digits necessary
+                to represent each value uniquely. Different elements may
+                have a different number of digits. The value of the
+                `precision` option is ignored.
+        * 'maxprec': Print at most `precision` fractional digits, but if
+                an element can be uniquely represented with fewer digits
+                only print it with that many.
+        * 'maxprec_equal': Print at most `precision` fractional digits,
+                but if every element in the array can be uniquely
+                represented with an equal number of fewer digits, use that
+                many digits for all elements.
+    legacy : string or `False`, optional
+        If set to the string ``'1.13'`` enables 1.13 legacy printing mode. This
+        approximates numpy 1.13 print output by including a space in the sign
+        position of floats and different behavior for 0d arrays. This also
+        enables 1.21 legacy printing mode (described below).
+
+        If set to the string ``'1.21'`` enables 1.21 legacy printing mode. This
+        approximates numpy 1.21 print output of complex structured dtypes
+        by not inserting spaces after commas that separate fields and after
+        colons.
+
+        If set to ``'1.25'`` approximates printing of 1.25 which mainly means
+        that numeric scalars are printed without their type information, e.g.
+        as ``3.0`` rather than ``np.float64(3.0)``.
+
+        If set to ``'2.1'``, shape information is not given when arrays are
+        summarized (i.e., multiple elements replaced with ``...``).
+
+        If set to ``'2.2'``, the transition to use scientific notation for
+        printing ``np.float16`` and ``np.float32`` types may happen later or
+        not at all for larger values.
+
+        If set to `False`, disables legacy mode.
+
+        Unrecognized strings will be ignored with a warning for forward
+        compatibility.
+
+        .. versionchanged:: 1.22.0
+        .. versionchanged:: 2.2
+
+    override_repr: callable, optional
+        If set a passed function will be used for generating arrays' repr.
+        Other options will be ignored.
+
+    See Also
+    --------
+    get_printoptions, printoptions, array2string
+
+
+    Notes
+    -----
+
+    * ``formatter`` is always reset with a call to `set_printoptions`.
+    * Use `printoptions` as a context manager to set the values temporarily.
+    * These print options apply only to NumPy ndarrays, not to scalars.
+
+    **Concurrency note:** see :ref:`text_formatting_options`
+
+    Examples
+    --------
+    Floating point precision can be set:
+
+    >>> import numpy as np
+    >>> np.set_printoptions(precision=4)
+    >>> np.array([1.123456789])
+    [1.1235]
+
+    Long arrays can be summarised:
+
+    >>> np.set_printoptions(threshold=5)
+    >>> np.arange(10)
+    array([0, 1, 2, ..., 7, 8, 9], shape=(10,))
+
+    Small results can be suppressed:
+
+    >>> eps = np.finfo(float).eps
+    >>> x = np.arange(4.)
+    >>> x**2 - (x + eps)**2
+    array([-4.9304e-32, -4.4409e-16,  0.0000e+00,  0.0000e+00])
+    >>> np.set_printoptions(suppress=True)
+    >>> x**2 - (x + eps)**2
+    array([-0., -0.,  0.,  0.])
+
+    A custom formatter can be used to display array elements as desired:
+
+    >>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)})
+    >>> x = np.arange(3)
+    >>> x
+    array([int: 0, int: -1, int: -2])
+    >>> np.set_printoptions()  # formatter gets reset
+    >>> x
+    array([0, 1, 2])
+
+    To put back the default options, you can use:
+
+    >>> np.set_printoptions(edgeitems=3, infstr='inf',
+    ... linewidth=75, nanstr='nan', precision=8,
+    ... suppress=False, threshold=1000, formatter=None)
+
+    Also to temporarily override options, use `printoptions`
+    as a context manager:
+
+    >>> with np.printoptions(precision=2, suppress=True, threshold=5):
+    ...     np.linspace(0, 10, 10)
+    array([ 0.  ,  1.11,  2.22, ...,  7.78,  8.89, 10.  ], shape=(10,))
+
+    """
+    _set_printoptions(precision, threshold, edgeitems, linewidth, suppress,
+                      nanstr, infstr, formatter, sign, floatmode,
+                      legacy=legacy, override_repr=override_repr)
+
+
+def _set_printoptions(precision=None, threshold=None, edgeitems=None,
+                      linewidth=None, suppress=None, nanstr=None,
+                      infstr=None, formatter=None, sign=None, floatmode=None,
+                      *, legacy=None, override_repr=None):
+    new_opt = _make_options_dict(precision, threshold, edgeitems, linewidth,
+                                 suppress, nanstr, infstr, sign, formatter,
+                                 floatmode, legacy)
+    # formatter and override_repr are always reset
+    new_opt['formatter'] = formatter
+    new_opt['override_repr'] = override_repr
+
+    updated_opt = format_options.get() | new_opt
+    updated_opt.update(new_opt)
+
+    if updated_opt['legacy'] == 113:
+        updated_opt['sign'] = '-'
+
+    return format_options.set(updated_opt)
+
+
+@set_module('numpy')
+def get_printoptions():
+    """
+    Return the current print options.
+
+    Returns
+    -------
+    print_opts : dict
+        Dictionary of current print options with keys
+
+        - precision : int
+        - threshold : int
+        - edgeitems : int
+        - linewidth : int
+        - suppress : bool
+        - nanstr : str
+        - infstr : str
+        - sign : str
+        - formatter : dict of callables
+        - floatmode : str
+        - legacy : str or False
+
+        For a full description of these options, see `set_printoptions`.
+
+    Notes
+    -----
+    These print options apply only to NumPy ndarrays, not to scalars.
+
+    **Concurrency note:** see :ref:`text_formatting_options`
+
+    See Also
+    --------
+    set_printoptions, printoptions
+
+    Examples
+    --------
+    >>> import numpy as np
+
+    >>> np.get_printoptions()
+    {'edgeitems': 3, 'threshold': 1000, ..., 'override_repr': None}
+
+    >>> np.get_printoptions()['linewidth']
+    75
+    >>> np.set_printoptions(linewidth=100)
+    >>> np.get_printoptions()['linewidth']
+    100
+
+    """
+    opts = format_options.get().copy()
+    opts['legacy'] = {
+        113: '1.13', 121: '1.21', 125: '1.25', 201: '2.1',
+        202: '2.2', sys.maxsize: False,
+    }[opts['legacy']]
+    return opts
+
+
+def _get_legacy_print_mode():
+    """Return the legacy print mode as an int."""
+    return format_options.get()['legacy']
+
+
+@set_module('numpy')
+@contextlib.contextmanager
+def printoptions(*args, **kwargs):
+    """Context manager for setting print options.
+
+    Set print options for the scope of the `with` block, and restore the old
+    options at the end. See `set_printoptions` for the full description of
+    available options.
+
+    Examples
+    --------
+    >>> import numpy as np
+
+    >>> from numpy.testing import assert_equal
+    >>> with np.printoptions(precision=2):
+    ...     np.array([2.0]) / 3
+    array([0.67])
+
+    The `as`-clause of the `with`-statement gives the current print options:
+
+    >>> with np.printoptions(precision=2) as opts:
+    ...      assert_equal(opts, np.get_printoptions())
+
+    See Also
+    --------
+    set_printoptions, get_printoptions
+
+    Notes
+    -----
+    These print options apply only to NumPy ndarrays, not to scalars.
+
+    **Concurrency note:** see :ref:`text_formatting_options`
+
+    """
+    token = _set_printoptions(*args, **kwargs)
+
+    try:
+        yield get_printoptions()
+    finally:
+        format_options.reset(token)
+
+
+def _leading_trailing(a, edgeitems, index=()):
+    """
+    Keep only the N-D corners (leading and trailing edges) of an array.
+
+    Should be passed a base-class ndarray, since it makes no guarantees about
+    preserving subclasses.
+    """
+    axis = len(index)
+    if axis == a.ndim:
+        return a[index]
+
+    if a.shape[axis] > 2 * edgeitems:
+        return concatenate((
+            _leading_trailing(a, edgeitems, index + np.index_exp[:edgeitems]),
+            _leading_trailing(a, edgeitems, index + np.index_exp[-edgeitems:])
+        ), axis=axis)
+    else:
+        return _leading_trailing(a, edgeitems, index + np.index_exp[:])
+
+
+def _object_format(o):
+    """ Object arrays containing lists should be printed unambiguously """
+    if type(o) is list:
+        fmt = 'list({!r})'
+    else:
+        fmt = '{!r}'
+    return fmt.format(o)
+
+def repr_format(x):
+    if isinstance(x, (np.str_, np.bytes_)):
+        return repr(x.item())
+    return repr(x)
+
+def str_format(x):
+    if isinstance(x, (np.str_, np.bytes_)):
+        return str(x.item())
+    return str(x)
+
+def _get_formatdict(data, *, precision, floatmode, suppress, sign, legacy,
+                    formatter, **kwargs):
+    # note: extra arguments in kwargs are ignored
+
+    # wrapped in lambdas to avoid taking a code path
+    # with the wrong type of data
+    formatdict = {
+        'bool': lambda: BoolFormat(data),
+        'int': lambda: IntegerFormat(data, sign),
+        'float': lambda: FloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'longfloat': lambda: FloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'complexfloat': lambda: ComplexFloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'longcomplexfloat': lambda: ComplexFloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'datetime': lambda: DatetimeFormat(data, legacy=legacy),
+        'timedelta': lambda: TimedeltaFormat(data),
+        'object': lambda: _object_format,
+        'void': lambda: str_format,
+        'numpystr': lambda: repr_format}
+
+    # we need to wrap values in `formatter` in a lambda, so that the interface
+    # is the same as the above values.
+    def indirect(x):
+        return lambda: x
+
+    if formatter is not None:
+        fkeys = [k for k in formatter.keys() if formatter[k] is not None]
+        if 'all' in fkeys:
+            for key in formatdict.keys():
+                formatdict[key] = indirect(formatter['all'])
+        if 'int_kind' in fkeys:
+            for key in ['int']:
+                formatdict[key] = indirect(formatter['int_kind'])
+        if 'float_kind' in fkeys:
+            for key in ['float', 'longfloat']:
+                formatdict[key] = indirect(formatter['float_kind'])
+        if 'complex_kind' in fkeys:
+            for key in ['complexfloat', 'longcomplexfloat']:
+                formatdict[key] = indirect(formatter['complex_kind'])
+        if 'str_kind' in fkeys:
+            formatdict['numpystr'] = indirect(formatter['str_kind'])
+        for key in formatdict.keys():
+            if key in fkeys:
+                formatdict[key] = indirect(formatter[key])
+
+    return formatdict
+
+def _get_format_function(data, **options):
+    """
+    find the right formatting function for the dtype_
+    """
+    dtype_ = data.dtype
+    dtypeobj = dtype_.type
+    formatdict = _get_formatdict(data, **options)
+    if dtypeobj is None:
+        return formatdict["numpystr"]()
+    elif issubclass(dtypeobj, _nt.bool):
+        return formatdict['bool']()
+    elif issubclass(dtypeobj, _nt.integer):
+        if issubclass(dtypeobj, _nt.timedelta64):
+            return formatdict['timedelta']()
+        else:
+            return formatdict['int']()
+    elif issubclass(dtypeobj, _nt.floating):
+        if issubclass(dtypeobj, _nt.longdouble):
+            return formatdict['longfloat']()
+        else:
+            return formatdict['float']()
+    elif issubclass(dtypeobj, _nt.complexfloating):
+        if issubclass(dtypeobj, _nt.clongdouble):
+            return formatdict['longcomplexfloat']()
+        else:
+            return formatdict['complexfloat']()
+    elif issubclass(dtypeobj, (_nt.str_, _nt.bytes_)):
+        return formatdict['numpystr']()
+    elif issubclass(dtypeobj, _nt.datetime64):
+        return formatdict['datetime']()
+    elif issubclass(dtypeobj, _nt.object_):
+        return formatdict['object']()
+    elif issubclass(dtypeobj, _nt.void):
+        if dtype_.names is not None:
+            return StructuredVoidFormat.from_data(data, **options)
+        else:
+            return formatdict['void']()
+    else:
+        return formatdict['numpystr']()
+
+
+def _recursive_guard(fillvalue='...'):
+    """
+    Like the python 3.2 reprlib.recursive_repr, but forwards *args and **kwargs
+
+    Decorates a function such that if it calls itself with the same first
+    argument, it returns `fillvalue` instead of recursing.
+
+    Largely copied from reprlib.recursive_repr
+    """
+
+    def decorating_function(f):
+        repr_running = set()
+
+        @functools.wraps(f)
+        def wrapper(self, *args, **kwargs):
+            key = id(self), get_ident()
+            if key in repr_running:
+                return fillvalue
+            repr_running.add(key)
+            try:
+                return f(self, *args, **kwargs)
+            finally:
+                repr_running.discard(key)
+
+        return wrapper
+
+    return decorating_function
+
+
+# gracefully handle recursive calls, when object arrays contain themselves
+@_recursive_guard()
+def _array2string(a, options, separator=' ', prefix=""):
+    # The formatter __init__s in _get_format_function cannot deal with
+    # subclasses yet, and we also need to avoid recursion issues in
+    # _formatArray with subclasses which return 0d arrays in place of scalars
+    data = asarray(a)
+    if a.shape == ():
+        a = data
+
+    if a.size > options['threshold']:
+        summary_insert = "..."
+        data = _leading_trailing(data, options['edgeitems'])
+    else:
+        summary_insert = ""
+
+    # find the right formatting function for the array
+    format_function = _get_format_function(data, **options)
+
+    # skip over "["
+    next_line_prefix = " "
+    # skip over array(
+    next_line_prefix += " " * len(prefix)
+
+    lst = _formatArray(a, format_function, options['linewidth'],
+                       next_line_prefix, separator, options['edgeitems'],
+                       summary_insert, options['legacy'])
+    return lst
+
+
+def _array2string_dispatcher(
+        a, max_line_width=None, precision=None,
+        suppress_small=None, separator=None, prefix=None,
+        *, formatter=None, threshold=None,
+        edgeitems=None, sign=None, floatmode=None, suffix=None,
+        legacy=None):
+    return (a,)
+
+
+@array_function_dispatch(_array2string_dispatcher, module='numpy')
+def array2string(a, max_line_width=None, precision=None,
+                 suppress_small=None, separator=' ', prefix="",
+                 *, formatter=None, threshold=None,
+                 edgeitems=None, sign=None, floatmode=None, suffix="",
+                 legacy=None):
+    """
+    Return a string representation of an array.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+    max_line_width : int, optional
+        Inserts newlines if text is longer than `max_line_width`.
+        Defaults to ``numpy.get_printoptions()['linewidth']``.
+    precision : int or None, optional
+        Floating point precision.
+        Defaults to ``numpy.get_printoptions()['precision']``.
+    suppress_small : bool, optional
+        Represent numbers "very close" to zero as zero; default is False.
+        Very close is defined by precision: if the precision is 8, e.g.,
+        numbers smaller (in absolute value) than 5e-9 are represented as
+        zero.
+        Defaults to ``numpy.get_printoptions()['suppress']``.
+    separator : str, optional
+        Inserted between elements.
+    prefix : str, optional
+    suffix : str, optional
+        The length of the prefix and suffix strings are used to respectively
+        align and wrap the output. An array is typically printed as::
+
+          prefix + array2string(a) + suffix
+
+        The output is left-padded by the length of the prefix string, and
+        wrapping is forced at the column ``max_line_width - len(suffix)``.
+        It should be noted that the content of prefix and suffix strings are
+        not included in the output.
+    formatter : dict of callables, optional
+        If not None, the keys should indicate the type(s) that the respective
+        formatting function applies to.  Callables should return a string.
+        Types that are not specified (by their corresponding keys) are handled
+        by the default formatters.  Individual types for which a formatter
+        can be set are:
+
+        - 'bool'
+        - 'int'
+        - 'timedelta' : a `numpy.timedelta64`
+        - 'datetime' : a `numpy.datetime64`
+        - 'float'
+        - 'longfloat' : 128-bit floats
+        - 'complexfloat'
+        - 'longcomplexfloat' : composed of two 128-bit floats
+        - 'void' : type `numpy.void`
+        - 'numpystr' : types `numpy.bytes_` and `numpy.str_`
+
+        Other keys that can be used to set a group of types at once are:
+
+        - 'all' : sets all types
+        - 'int_kind' : sets 'int'
+        - 'float_kind' : sets 'float' and 'longfloat'
+        - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
+        - 'str_kind' : sets 'numpystr'
+    threshold : int, optional
+        Total number of array elements which trigger summarization
+        rather than full repr.
+        Defaults to ``numpy.get_printoptions()['threshold']``.
+    edgeitems : int, optional
+        Number of array items in summary at beginning and end of
+        each dimension.
+        Defaults to ``numpy.get_printoptions()['edgeitems']``.
+    sign : string, either '-', '+', or ' ', optional
+        Controls printing of the sign of floating-point types. If '+', always
+        print the sign of positive values. If ' ', always prints a space
+        (whitespace character) in the sign position of positive values.  If
+        '-', omit the sign character of positive values.
+        Defaults to ``numpy.get_printoptions()['sign']``.
+
+        .. versionchanged:: 2.0
+             The sign parameter can now be an integer type, previously
+             types were floating-point types.
+
+    floatmode : str, optional
+        Controls the interpretation of the `precision` option for
+        floating-point types.
+        Defaults to ``numpy.get_printoptions()['floatmode']``.
+        Can take the following values:
+
+        - 'fixed': Always print exactly `precision` fractional digits,
+          even if this would print more or fewer digits than
+          necessary to specify the value uniquely.
+        - 'unique': Print the minimum number of fractional digits necessary
+          to represent each value uniquely. Different elements may
+          have a different number of digits.  The value of the
+          `precision` option is ignored.
+        - 'maxprec': Print at most `precision` fractional digits, but if
+          an element can be uniquely represented with fewer digits
+          only print it with that many.
+        - 'maxprec_equal': Print at most `precision` fractional digits,
+          but if every element in the array can be uniquely
+          represented with an equal number of fewer digits, use that
+          many digits for all elements.
+    legacy : string or `False`, optional
+        If set to the string ``'1.13'`` enables 1.13 legacy printing mode. This
+        approximates numpy 1.13 print output by including a space in the sign
+        position of floats and different behavior for 0d arrays. If set to
+        `False`, disables legacy mode. Unrecognized strings will be ignored
+        with a warning for forward compatibility.
+
+    Returns
+    -------
+    array_str : str
+        String representation of the array.
+
+    Raises
+    ------
+    TypeError
+        if a callable in `formatter` does not return a string.
+
+    See Also
+    --------
+    array_str, array_repr, set_printoptions, get_printoptions
+
+    Notes
+    -----
+    If a formatter is specified for a certain type, the `precision` keyword is
+    ignored for that type.
+
+    This is a very flexible function; `array_repr` and `array_str` are using
+    `array2string` internally so keywords with the same name should work
+    identically in all three functions.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1e-16,1,2,3])
+    >>> np.array2string(x, precision=2, separator=',',
+    ...                       suppress_small=True)
+    '[0.,1.,2.,3.]'
+
+    >>> x  = np.arange(3.)
+    >>> np.array2string(x, formatter={'float_kind':lambda x: "%.2f" % x})
+    '[0.00 1.00 2.00]'
+
+    >>> x  = np.arange(3)
+    >>> np.array2string(x, formatter={'int':lambda x: hex(x)})
+    '[0x0 0x1 0x2]'
+
+    """
+
+    overrides = _make_options_dict(precision, threshold, edgeitems,
+                                   max_line_width, suppress_small, None, None,
+                                   sign, formatter, floatmode, legacy)
+    options = format_options.get().copy()
+    options.update(overrides)
+
+    if options['legacy'] <= 113:
+        if a.shape == () and a.dtype.names is None:
+            return repr(a.item())
+
+    if options['legacy'] > 113:
+        options['linewidth'] -= len(suffix)
+
+    # treat as a null array if any of shape elements == 0
+    if a.size == 0:
+        return "[]"
+
+    return _array2string(a, options, separator, prefix)
+
+
+def _extendLine(s, line, word, line_width, next_line_prefix, legacy):
+    needs_wrap = len(line) + len(word) > line_width
+    if legacy > 113:
+        # don't wrap lines if it won't help
+        if len(line) <= len(next_line_prefix):
+            needs_wrap = False
+
+    if needs_wrap:
+        s += line.rstrip() + "\n"
+        line = next_line_prefix
+    line += word
+    return s, line
+
+
+def _extendLine_pretty(s, line, word, line_width, next_line_prefix, legacy):
+    """
+    Extends line with nicely formatted (possibly multi-line) string ``word``.
+    """
+    words = word.splitlines()
+    if len(words) == 1 or legacy <= 113:
+        return _extendLine(s, line, word, line_width, next_line_prefix, legacy)
+
+    max_word_length = max(len(word) for word in words)
+    if (len(line) + max_word_length > line_width and
+            len(line) > len(next_line_prefix)):
+        s += line.rstrip() + '\n'
+        line = next_line_prefix + words[0]
+        indent = next_line_prefix
+    else:
+        indent = len(line) * ' '
+        line += words[0]
+
+    for word in words[1::]:
+        s += line.rstrip() + '\n'
+        line = indent + word
+
+    suffix_length = max_word_length - len(words[-1])
+    line += suffix_length * ' '
+
+    return s, line
+
+def _formatArray(a, format_function, line_width, next_line_prefix,
+                 separator, edge_items, summary_insert, legacy):
+    """formatArray is designed for two modes of operation:
+
+    1. Full output
+
+    2. Summarized output
+
+    """
+    def recurser(index, hanging_indent, curr_width):
+        """
+        By using this local function, we don't need to recurse with all the
+        arguments. Since this function is not created recursively, the cost is
+        not significant
+        """
+        axis = len(index)
+        axes_left = a.ndim - axis
+
+        if axes_left == 0:
+            return format_function(a[index])
+
+        # when recursing, add a space to align with the [ added, and reduce the
+        # length of the line by 1
+        next_hanging_indent = hanging_indent + ' '
+        if legacy <= 113:
+            next_width = curr_width
+        else:
+            next_width = curr_width - len(']')
+
+        a_len = a.shape[axis]
+        show_summary = summary_insert and 2 * edge_items < a_len
+        if show_summary:
+            leading_items = edge_items
+            trailing_items = edge_items
+        else:
+            leading_items = 0
+            trailing_items = a_len
+
+        # stringify the array with the hanging indent on the first line too
+        s = ''
+
+        # last axis (rows) - wrap elements if they would not fit on one line
+        if axes_left == 1:
+            # the length up until the beginning of the separator / bracket
+            if legacy <= 113:
+                elem_width = curr_width - len(separator.rstrip())
+            else:
+                elem_width = curr_width - max(
+                    len(separator.rstrip()), len(']')
+                )
+
+            line = hanging_indent
+            for i in range(leading_items):
+                word = recurser(index + (i,), next_hanging_indent, next_width)
+                s, line = _extendLine_pretty(
+                    s, line, word, elem_width, hanging_indent, legacy)
+                line += separator
+
+            if show_summary:
+                s, line = _extendLine(
+                    s, line, summary_insert, elem_width, hanging_indent, legacy
+                )
+                if legacy <= 113:
+                    line += ", "
+                else:
+                    line += separator
+
+            for i in range(trailing_items, 1, -1):
+                word = recurser(index + (-i,), next_hanging_indent, next_width)
+                s, line = _extendLine_pretty(
+                    s, line, word, elem_width, hanging_indent, legacy)
+                line += separator
+
+            if legacy <= 113:
+                # width of the separator is not considered on 1.13
+                elem_width = curr_width
+            word = recurser(index + (-1,), next_hanging_indent, next_width)
+            s, line = _extendLine_pretty(
+                s, line, word, elem_width, hanging_indent, legacy)
+
+            s += line
+
+        # other axes - insert newlines between rows
+        else:
+            s = ''
+            line_sep = separator.rstrip() + '\n' * (axes_left - 1)
+
+            for i in range(leading_items):
+                nested = recurser(
+                    index + (i,), next_hanging_indent, next_width
+                )
+                s += hanging_indent + nested + line_sep
+
+            if show_summary:
+                if legacy <= 113:
+                    # trailing space, fixed nbr of newlines,
+                    # and fixed separator
+                    s += hanging_indent + summary_insert + ", \n"
+                else:
+                    s += hanging_indent + summary_insert + line_sep
+
+            for i in range(trailing_items, 1, -1):
+                nested = recurser(index + (-i,), next_hanging_indent,
+                                  next_width)
+                s += hanging_indent + nested + line_sep
+
+            nested = recurser(index + (-1,), next_hanging_indent, next_width)
+            s += hanging_indent + nested
+
+        # remove the hanging indent, and wrap in []
+        s = '[' + s[len(hanging_indent):] + ']'
+        return s
+
+    try:
+        # invoke the recursive part with an initial index and prefix
+        return recurser(index=(),
+                        hanging_indent=next_line_prefix,
+                        curr_width=line_width)
+    finally:
+        # recursive closures have a cyclic reference to themselves, which
+        # requires gc to collect (gh-10620). To avoid this problem, for
+        # performance and PyPy friendliness, we break the cycle:
+        recurser = None
+
+def _none_or_positive_arg(x, name):
+    if x is None:
+        return -1
+    if x < 0:
+        raise ValueError(f"{name} must be >= 0")
+    return x
+
+class FloatingFormat:
+    """ Formatter for subtypes of np.floating """
+    def __init__(self, data, precision, floatmode, suppress_small, sign=False,
+                 *, legacy=None):
+        # for backcompatibility, accept bools
+        if isinstance(sign, bool):
+            sign = '+' if sign else '-'
+
+        self._legacy = legacy
+        if self._legacy <= 113:
+            # when not 0d, legacy does not support '-'
+            if data.shape != () and sign == '-':
+                sign = ' '
+
+        self.floatmode = floatmode
+        if floatmode == 'unique':
+            self.precision = None
+        else:
+            self.precision = precision
+
+        self.precision = _none_or_positive_arg(self.precision, 'precision')
+
+        self.suppress_small = suppress_small
+        self.sign = sign
+        self.exp_format = False
+        self.large_exponent = False
+        self.fillFormat(data)
+
+    def fillFormat(self, data):
+        # only the finite values are used to compute the number of digits
+        finite_vals = data[isfinite(data)]
+
+        # choose exponential mode based on the non-zero finite values:
+        abs_non_zero = absolute(finite_vals[finite_vals != 0])
+        if len(abs_non_zero) != 0:
+            max_val = np.max(abs_non_zero)
+            min_val = np.min(abs_non_zero)
+            if self._legacy <= 202:
+                exp_cutoff_max = 1.e8
+            else:
+                # consider data type while deciding the max cutoff for exp format
+                exp_cutoff_max = 10.**min(8, np.finfo(data.dtype).precision)
+            with errstate(over='ignore'):  # division can overflow
+                if max_val >= exp_cutoff_max or (not self.suppress_small and
+                        (min_val < 0.0001 or max_val / min_val > 1000.)):
+                    self.exp_format = True
+
+        # do a first pass of printing all the numbers, to determine sizes
+        if len(finite_vals) == 0:
+            self.pad_left = 0
+            self.pad_right = 0
+            self.trim = '.'
+            self.exp_size = -1
+            self.unique = True
+            self.min_digits = None
+        elif self.exp_format:
+            trim, unique = '.', True
+            if self.floatmode == 'fixed' or self._legacy <= 113:
+                trim, unique = 'k', False
+            strs = (dragon4_scientific(x, precision=self.precision,
+                               unique=unique, trim=trim, sign=self.sign == '+')
+                    for x in finite_vals)
+            frac_strs, _, exp_strs = zip(*(s.partition('e') for s in strs))
+            int_part, frac_part = zip(*(s.split('.') for s in frac_strs))
+            self.exp_size = max(len(s) for s in exp_strs) - 1
+
+            self.trim = 'k'
+            self.precision = max(len(s) for s in frac_part)
+            self.min_digits = self.precision
+            self.unique = unique
+
+            # for back-compat with np 1.13, use 2 spaces & sign and full prec
+            if self._legacy <= 113:
+                self.pad_left = 3
+            else:
+                # this should be only 1 or 2. Can be calculated from sign.
+                self.pad_left = max(len(s) for s in int_part)
+            # pad_right is only needed for nan length calculation
+            self.pad_right = self.exp_size + 2 + self.precision
+        else:
+            trim, unique = '.', True
+            if self.floatmode == 'fixed':
+                trim, unique = 'k', False
+            strs = (dragon4_positional(x, precision=self.precision,
+                                       fractional=True,
+                                       unique=unique, trim=trim,
+                                       sign=self.sign == '+')
+                    for x in finite_vals)
+            int_part, frac_part = zip(*(s.split('.') for s in strs))
+            if self._legacy <= 113:
+                self.pad_left = 1 + max(len(s.lstrip('-+')) for s in int_part)
+            else:
+                self.pad_left = max(len(s) for s in int_part)
+            self.pad_right = max(len(s) for s in frac_part)
+            self.exp_size = -1
+            self.unique = unique
+
+            if self.floatmode in ['fixed', 'maxprec_equal']:
+                self.precision = self.min_digits = self.pad_right
+                self.trim = 'k'
+            else:
+                self.trim = '.'
+                self.min_digits = 0
+
+        if self._legacy > 113:
+            # account for sign = ' ' by adding one to pad_left
+            if self.sign == ' ' and not any(np.signbit(finite_vals)):
+                self.pad_left += 1
+
+        # if there are non-finite values, may need to increase pad_left
+        if data.size != finite_vals.size:
+            neginf = self.sign != '-' or any(data[isinf(data)] < 0)
+            offset = self.pad_right + 1  # +1 for decimal pt
+            current_options = format_options.get()
+            self.pad_left = max(
+                self.pad_left, len(current_options['nanstr']) - offset,
+                len(current_options['infstr']) + neginf - offset
+            )
+
+    def __call__(self, x):
+        if not np.isfinite(x):
+            with errstate(invalid='ignore'):
+                current_options = format_options.get()
+                if np.isnan(x):
+                    sign = '+' if self.sign == '+' else ''
+                    ret = sign + current_options['nanstr']
+                else:  # isinf
+                    sign = '-' if x < 0 else '+' if self.sign == '+' else ''
+                    ret = sign + current_options['infstr']
+                return ' ' * (
+                    self.pad_left + self.pad_right + 1 - len(ret)
+                ) + ret
+
+        if self.exp_format:
+            return dragon4_scientific(x,
+                                      precision=self.precision,
+                                      min_digits=self.min_digits,
+                                      unique=self.unique,
+                                      trim=self.trim,
+                                      sign=self.sign == '+',
+                                      pad_left=self.pad_left,
+                                      exp_digits=self.exp_size)
+        else:
+            return dragon4_positional(x,
+                                      precision=self.precision,
+                                      min_digits=self.min_digits,
+                                      unique=self.unique,
+                                      fractional=True,
+                                      trim=self.trim,
+                                      sign=self.sign == '+',
+                                      pad_left=self.pad_left,
+                                      pad_right=self.pad_right)
+
+
+@set_module('numpy')
+def format_float_scientific(x, precision=None, unique=True, trim='k',
+                            sign=False, pad_left=None, exp_digits=None,
+                            min_digits=None):
+    """
+    Format a floating-point scalar as a decimal string in scientific notation.
+
+    Provides control over rounding, trimming and padding. Uses and assumes
+    IEEE unbiased rounding. Uses the "Dragon4" algorithm.
+
+    Parameters
+    ----------
+    x : python float or numpy floating scalar
+        Value to format.
+    precision : non-negative integer or None, optional
+        Maximum number of digits to print. May be None if `unique` is
+        `True`, but must be an integer if unique is `False`.
+    unique : boolean, optional
+        If `True`, use a digit-generation strategy which gives the shortest
+        representation which uniquely identifies the floating-point number from
+        other values of the same type, by judicious rounding. If `precision`
+        is given fewer digits than necessary can be printed. If `min_digits`
+        is given more can be printed, in which cases the last digit is rounded
+        with unbiased rounding.
+        If `False`, digits are generated as if printing an infinite-precision
+        value and stopping after `precision` digits, rounding the remaining
+        value with unbiased rounding
+    trim : one of 'k', '.', '0', '-', optional
+        Controls post-processing trimming of trailing digits, as follows:
+
+        * 'k' : keep trailing zeros, keep decimal point (no trimming)
+        * '.' : trim all trailing zeros, leave decimal point
+        * '0' : trim all but the zero before the decimal point. Insert the
+          zero if it is missing.
+        * '-' : trim trailing zeros and any trailing decimal point
+    sign : boolean, optional
+        Whether to show the sign for positive values.
+    pad_left : non-negative integer, optional
+        Pad the left side of the string with whitespace until at least that
+        many characters are to the left of the decimal point.
+    exp_digits : non-negative integer, optional
+        Pad the exponent with zeros until it contains at least this
+        many digits. If omitted, the exponent will be at least 2 digits.
+    min_digits : non-negative integer or None, optional
+        Minimum number of digits to print. This only has an effect for
+        `unique=True`. In that case more digits than necessary to uniquely
+        identify the value may be printed and rounded unbiased.
+
+        .. versionadded:: 1.21.0
+
+    Returns
+    -------
+    rep : string
+        The string representation of the floating point value
+
+    See Also
+    --------
+    format_float_positional
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.format_float_scientific(np.float32(np.pi))
+    '3.1415927e+00'
+    >>> s = np.float32(1.23e24)
+    >>> np.format_float_scientific(s, unique=False, precision=15)
+    '1.230000071797338e+24'
+    >>> np.format_float_scientific(s, exp_digits=4)
+    '1.23e+0024'
+    """
+    precision = _none_or_positive_arg(precision, 'precision')
+    pad_left = _none_or_positive_arg(pad_left, 'pad_left')
+    exp_digits = _none_or_positive_arg(exp_digits, 'exp_digits')
+    min_digits = _none_or_positive_arg(min_digits, 'min_digits')
+    if min_digits > 0 and precision > 0 and min_digits > precision:
+        raise ValueError("min_digits must be less than or equal to precision")
+    return dragon4_scientific(x, precision=precision, unique=unique,
+                              trim=trim, sign=sign, pad_left=pad_left,
+                              exp_digits=exp_digits, min_digits=min_digits)
+
+
+@set_module('numpy')
+def format_float_positional(x, precision=None, unique=True,
+                            fractional=True, trim='k', sign=False,
+                            pad_left=None, pad_right=None, min_digits=None):
+    """
+    Format a floating-point scalar as a decimal string in positional notation.
+
+    Provides control over rounding, trimming and padding. Uses and assumes
+    IEEE unbiased rounding. Uses the "Dragon4" algorithm.
+
+    Parameters
+    ----------
+    x : python float or numpy floating scalar
+        Value to format.
+    precision : non-negative integer or None, optional
+        Maximum number of digits to print. May be None if `unique` is
+        `True`, but must be an integer if unique is `False`.
+    unique : boolean, optional
+        If `True`, use a digit-generation strategy which gives the shortest
+        representation which uniquely identifies the floating-point number from
+        other values of the same type, by judicious rounding. If `precision`
+        is given fewer digits than necessary can be printed, or if `min_digits`
+        is given more can be printed, in which cases the last digit is rounded
+        with unbiased rounding.
+        If `False`, digits are generated as if printing an infinite-precision
+        value and stopping after `precision` digits, rounding the remaining
+        value with unbiased rounding
+    fractional : boolean, optional
+        If `True`, the cutoffs of `precision` and `min_digits` refer to the
+        total number of digits after the decimal point, including leading
+        zeros.
+        If `False`, `precision` and `min_digits` refer to the total number of
+        significant digits, before or after the decimal point, ignoring leading
+        zeros.
+    trim : one of 'k', '.', '0', '-', optional
+        Controls post-processing trimming of trailing digits, as follows:
+
+        * 'k' : keep trailing zeros, keep decimal point (no trimming)
+        * '.' : trim all trailing zeros, leave decimal point
+        * '0' : trim all but the zero before the decimal point. Insert the
+          zero if it is missing.
+        * '-' : trim trailing zeros and any trailing decimal point
+    sign : boolean, optional
+        Whether to show the sign for positive values.
+    pad_left : non-negative integer, optional
+        Pad the left side of the string with whitespace until at least that
+        many characters are to the left of the decimal point.
+    pad_right : non-negative integer, optional
+        Pad the right side of the string with whitespace until at least that
+        many characters are to the right of the decimal point.
+    min_digits : non-negative integer or None, optional
+        Minimum number of digits to print. Only has an effect if `unique=True`
+        in which case additional digits past those necessary to uniquely
+        identify the value may be printed, rounding the last additional digit.
+
+        .. versionadded:: 1.21.0
+
+    Returns
+    -------
+    rep : string
+        The string representation of the floating point value
+
+    See Also
+    --------
+    format_float_scientific
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.format_float_positional(np.float32(np.pi))
+    '3.1415927'
+    >>> np.format_float_positional(np.float16(np.pi))
+    '3.14'
+    >>> np.format_float_positional(np.float16(0.3))
+    '0.3'
+    >>> np.format_float_positional(np.float16(0.3), unique=False, precision=10)
+    '0.3000488281'
+    """
+    precision = _none_or_positive_arg(precision, 'precision')
+    pad_left = _none_or_positive_arg(pad_left, 'pad_left')
+    pad_right = _none_or_positive_arg(pad_right, 'pad_right')
+    min_digits = _none_or_positive_arg(min_digits, 'min_digits')
+    if not fractional and precision == 0:
+        raise ValueError("precision must be greater than 0 if "
+                         "fractional=False")
+    if min_digits > 0 and precision > 0 and min_digits > precision:
+        raise ValueError("min_digits must be less than or equal to precision")
+    return dragon4_positional(x, precision=precision, unique=unique,
+                              fractional=fractional, trim=trim,
+                              sign=sign, pad_left=pad_left,
+                              pad_right=pad_right, min_digits=min_digits)
+
+class IntegerFormat:
+    def __init__(self, data, sign='-'):
+        if data.size > 0:
+            data_max = np.max(data)
+            data_min = np.min(data)
+            data_max_str_len = len(str(data_max))
+            if sign == ' ' and data_min < 0:
+                sign = '-'
+            if data_max >= 0 and sign in "+ ":
+                data_max_str_len += 1
+            max_str_len = max(data_max_str_len,
+                              len(str(data_min)))
+        else:
+            max_str_len = 0
+        self.format = f'{{:{sign}{max_str_len}d}}'
+
+    def __call__(self, x):
+        return self.format.format(x)
+
+class BoolFormat:
+    def __init__(self, data, **kwargs):
+        # add an extra space so " True" and "False" have the same length and
+        # array elements align nicely when printed, except in 0d arrays
+        self.truestr = ' True' if data.shape != () else 'True'
+
+    def __call__(self, x):
+        return self.truestr if x else "False"
+
+
+class ComplexFloatingFormat:
+    """ Formatter for subtypes of np.complexfloating """
+    def __init__(self, x, precision, floatmode, suppress_small,
+                 sign=False, *, legacy=None):
+        # for backcompatibility, accept bools
+        if isinstance(sign, bool):
+            sign = '+' if sign else '-'
+
+        floatmode_real = floatmode_imag = floatmode
+        if legacy <= 113:
+            floatmode_real = 'maxprec_equal'
+            floatmode_imag = 'maxprec'
+
+        self.real_format = FloatingFormat(
+            x.real, precision, floatmode_real, suppress_small,
+            sign=sign, legacy=legacy
+        )
+        self.imag_format = FloatingFormat(
+            x.imag, precision, floatmode_imag, suppress_small,
+            sign='+', legacy=legacy
+        )
+
+    def __call__(self, x):
+        r = self.real_format(x.real)
+        i = self.imag_format(x.imag)
+
+        # add the 'j' before the terminal whitespace in i
+        sp = len(i.rstrip())
+        i = i[:sp] + 'j' + i[sp:]
+
+        return r + i
+
+
+class _TimelikeFormat:
+    def __init__(self, data):
+        non_nat = data[~isnat(data)]
+        if len(non_nat) > 0:
+            # Max str length of non-NaT elements
+            max_str_len = max(len(self._format_non_nat(np.max(non_nat))),
+                              len(self._format_non_nat(np.min(non_nat))))
+        else:
+            max_str_len = 0
+        if len(non_nat) < data.size:
+            # data contains a NaT
+            max_str_len = max(max_str_len, 5)
+        self._format = f'%{max_str_len}s'
+        self._nat = "'NaT'".rjust(max_str_len)
+
+    def _format_non_nat(self, x):
+        # override in subclass
+        raise NotImplementedError
+
+    def __call__(self, x):
+        if isnat(x):
+            return self._nat
+        else:
+            return self._format % self._format_non_nat(x)
+
+
+class DatetimeFormat(_TimelikeFormat):
+    def __init__(self, x, unit=None, timezone=None, casting='same_kind',
+                 legacy=False):
+        # Get the unit from the dtype
+        if unit is None:
+            if x.dtype.kind == 'M':
+                unit = datetime_data(x.dtype)[0]
+            else:
+                unit = 's'
+
+        if timezone is None:
+            timezone = 'naive'
+        self.timezone = timezone
+        self.unit = unit
+        self.casting = casting
+        self.legacy = legacy
+
+        # must be called after the above are configured
+        super().__init__(x)
+
+    def __call__(self, x):
+        if self.legacy <= 113:
+            return self._format_non_nat(x)
+        return super().__call__(x)
+
+    def _format_non_nat(self, x):
+        return "'%s'" % datetime_as_string(x,
+                                    unit=self.unit,
+                                    timezone=self.timezone,
+                                    casting=self.casting)
+
+
+class TimedeltaFormat(_TimelikeFormat):
+    def _format_non_nat(self, x):
+        return str(x.astype('i8'))
+
+
+class SubArrayFormat:
+    def __init__(self, format_function, **options):
+        self.format_function = format_function
+        self.threshold = options['threshold']
+        self.edge_items = options['edgeitems']
+
+    def __call__(self, a):
+        self.summary_insert = "..." if a.size > self.threshold else ""
+        return self.format_array(a)
+
+    def format_array(self, a):
+        if np.ndim(a) == 0:
+            return self.format_function(a)
+
+        if self.summary_insert and a.shape[0] > 2 * self.edge_items:
+            formatted = (
+                [self.format_array(a_) for a_ in a[:self.edge_items]]
+                + [self.summary_insert]
+                + [self.format_array(a_) for a_ in a[-self.edge_items:]]
+            )
+        else:
+            formatted = [self.format_array(a_) for a_ in a]
+
+        return "[" + ", ".join(formatted) + "]"
+
+
+class StructuredVoidFormat:
+    """
+    Formatter for structured np.void objects.
+
+    This does not work on structured alias types like
+    np.dtype(('i4', 'i2,i2')), as alias scalars lose their field information,
+    and the implementation relies upon np.void.__getitem__.
+    """
+    def __init__(self, format_functions):
+        self.format_functions = format_functions
+
+    @classmethod
+    def from_data(cls, data, **options):
+        """
+        This is a second way to initialize StructuredVoidFormat,
+        using the raw data as input. Added to avoid changing
+        the signature of __init__.
+        """
+        format_functions = []
+        for field_name in data.dtype.names:
+            format_function = _get_format_function(data[field_name], **options)
+            if data.dtype[field_name].shape != ():
+                format_function = SubArrayFormat(format_function, **options)
+            format_functions.append(format_function)
+        return cls(format_functions)
+
+    def __call__(self, x):
+        str_fields = [
+            format_function(field)
+            for field, format_function in zip(x, self.format_functions)
+        ]
+        if len(str_fields) == 1:
+            return f"({str_fields[0]},)"
+        else:
+            return f"({', '.join(str_fields)})"
+
+
+def _void_scalar_to_string(x, is_repr=True):
+    """
+    Implements the repr for structured-void scalars. It is called from the
+    scalartypes.c.src code, and is placed here because it uses the elementwise
+    formatters defined above.
+    """
+    options = format_options.get().copy()
+
+    if options["legacy"] <= 125:
+        return StructuredVoidFormat.from_data(array(x), **options)(x)
+
+    if options.get('formatter') is None:
+        options['formatter'] = {}
+    options['formatter'].setdefault('float_kind', str)
+    val_repr = StructuredVoidFormat.from_data(array(x), **options)(x)
+    if not is_repr:
+        return val_repr
+    cls = type(x)
+    cls_fqn = cls.__module__.replace("numpy", "np") + "." + cls.__name__
+    void_dtype = np.dtype((np.void, x.dtype))
+    return f"{cls_fqn}({val_repr}, dtype={void_dtype!s})"
+
+
+_typelessdata = [int_, float64, complex128, _nt.bool]
+
+
+def dtype_is_implied(dtype):
+    """
+    Determine if the given dtype is implied by the representation
+    of its values.
+
+    Parameters
+    ----------
+    dtype : dtype
+        Data type
+
+    Returns
+    -------
+    implied : bool
+        True if the dtype is implied by the representation of its values.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np._core.arrayprint.dtype_is_implied(int)
+    True
+    >>> np.array([1, 2, 3], int)
+    array([1, 2, 3])
+    >>> np._core.arrayprint.dtype_is_implied(np.int8)
+    False
+    >>> np.array([1, 2, 3], np.int8)
+    array([1, 2, 3], dtype=int8)
+    """
+    dtype = np.dtype(dtype)
+    if format_options.get()['legacy'] <= 113 and dtype.type == np.bool:
+        return False
+
+    # not just void types can be structured, and names are not part of the repr
+    if dtype.names is not None:
+        return False
+
+    # should care about endianness *unless size is 1* (e.g., int8, bool)
+    if not dtype.isnative:
+        return False
+
+    return dtype.type in _typelessdata
+
+
+def dtype_short_repr(dtype):
+    """
+    Convert a dtype to a short form which evaluates to the same dtype.
+
+    The intent is roughly that the following holds
+
+    >>> from numpy import *
+    >>> dt = np.int64([1, 2]).dtype
+    >>> assert eval(dtype_short_repr(dt)) == dt
+    """
+    if type(dtype).__repr__ != np.dtype.__repr__:
+        # TODO: Custom repr for user DTypes, logic should likely move.
+        return repr(dtype)
+    if dtype.names is not None:
+        # structured dtypes give a list or tuple repr
+        return str(dtype)
+    elif issubclass(dtype.type, flexible):
+        # handle these separately so they don't give garbage like str256
+        return f"'{str(dtype)}'"
+
+    typename = dtype.name
+    if not dtype.isnative:
+        # deal with cases like dtype('<u2') that are identical to an
+        # established dtype (in this case uint16)
+        # except that they have a different endianness.
+        return f"'{str(dtype)}'"
+    # quote typenames which can't be represented as python variable names
+    if typename and not (typename[0].isalpha() and typename.isalnum()):
+        typename = repr(typename)
+    return typename
+
+
+def _array_repr_implementation(
+        arr, max_line_width=None, precision=None, suppress_small=None,
+        array2string=array2string):
+    """Internal version of array_repr() that allows overriding array2string."""
+    current_options = format_options.get()
+    override_repr = current_options["override_repr"]
+    if override_repr is not None:
+        return override_repr(arr)
+
+    if max_line_width is None:
+        max_line_width = current_options['linewidth']
+
+    if type(arr) is not ndarray:
+        class_name = type(arr).__name__
+    else:
+        class_name = "array"
+
+    prefix = class_name + "("
+    if (current_options['legacy'] <= 113 and
+            arr.shape == () and not arr.dtype.names):
+        lst = repr(arr.item())
+    else:
+        lst = array2string(arr, max_line_width, precision, suppress_small,
+                           ', ', prefix, suffix=")")
+
+    # Add dtype and shape information if these cannot be inferred from
+    # the array string.
+    extras = []
+    if ((arr.size == 0 and arr.shape != (0,))
+            or (current_options['legacy'] > 210
+            and arr.size > current_options['threshold'])):
+        extras.append(f"shape={arr.shape}")
+    if not dtype_is_implied(arr.dtype) or arr.size == 0:
+        extras.append(f"dtype={dtype_short_repr(arr.dtype)}")
+
+    if not extras:
+        return prefix + lst + ")"
+
+    arr_str = prefix + lst + ","
+    extra_str = ", ".join(extras) + ")"
+    # compute whether we should put extras on a new line: Do so if adding the
+    # extras would extend the last line past max_line_width.
+    # Note: This line gives the correct result even when rfind returns -1.
+    last_line_len = len(arr_str) - (arr_str.rfind('\n') + 1)
+    spacer = " "
+    if current_options['legacy'] <= 113:
+        if issubclass(arr.dtype.type, flexible):
+            spacer = '\n' + ' ' * len(prefix)
+    elif last_line_len + len(extra_str) + 1 > max_line_width:
+        spacer = '\n' + ' ' * len(prefix)
+
+    return arr_str + spacer + extra_str
+
+
+def _array_repr_dispatcher(
+        arr, max_line_width=None, precision=None, suppress_small=None):
+    return (arr,)
+
+
+@array_function_dispatch(_array_repr_dispatcher, module='numpy')
+def array_repr(arr, max_line_width=None, precision=None, suppress_small=None):
+    """
+    Return the string representation of an array.
+
+    Parameters
+    ----------
+    arr : ndarray
+        Input array.
+    max_line_width : int, optional
+        Inserts newlines if text is longer than `max_line_width`.
+        Defaults to ``numpy.get_printoptions()['linewidth']``.
+    precision : int, optional
+        Floating point precision.
+        Defaults to ``numpy.get_printoptions()['precision']``.
+    suppress_small : bool, optional
+        Represent numbers "very close" to zero as zero; default is False.
+        Very close is defined by precision: if the precision is 8, e.g.,
+        numbers smaller (in absolute value) than 5e-9 are represented as
+        zero.
+        Defaults to ``numpy.get_printoptions()['suppress']``.
+
+    Returns
+    -------
+    string : str
+      The string representation of an array.
+
+    See Also
+    --------
+    array_str, array2string, set_printoptions
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.array_repr(np.array([1,2]))
+    'array([1, 2])'
+    >>> np.array_repr(np.ma.array([0.]))
+    'MaskedArray([0.])'
+    >>> np.array_repr(np.array([], np.int32))
+    'array([], dtype=int32)'
+
+    >>> x = np.array([1e-6, 4e-7, 2, 3])
+    >>> np.array_repr(x, precision=6, suppress_small=True)
+    'array([0.000001,  0.      ,  2.      ,  3.      ])'
+
+    """
+    return _array_repr_implementation(
+        arr, max_line_width, precision, suppress_small)
+
+
+@_recursive_guard()
+def _guarded_repr_or_str(v):
+    if isinstance(v, bytes):
+        return repr(v)
+    return str(v)
+
+
+def _array_str_implementation(
+        a, max_line_width=None, precision=None, suppress_small=None,
+        array2string=array2string):
+    """Internal version of array_str() that allows overriding array2string."""
+    if (format_options.get()['legacy'] <= 113 and
+            a.shape == () and not a.dtype.names):
+        return str(a.item())
+
+    # the str of 0d arrays is a special case: It should appear like a scalar,
+    # so floats are not truncated by `precision`, and strings are not wrapped
+    # in quotes. So we return the str of the scalar value.
+    if a.shape == ():
+        # obtain a scalar and call str on it, avoiding problems for subclasses
+        # for which indexing with () returns a 0d instead of a scalar by using
+        # ndarray's getindex. Also guard against recursive 0d object arrays.
+        return _guarded_repr_or_str(np.ndarray.__getitem__(a, ()))
+
+    return array2string(a, max_line_width, precision, suppress_small, ' ', "")
+
+
+def _array_str_dispatcher(
+        a, max_line_width=None, precision=None, suppress_small=None):
+    return (a,)
+
+
+@array_function_dispatch(_array_str_dispatcher, module='numpy')
+def array_str(a, max_line_width=None, precision=None, suppress_small=None):
+    """
+    Return a string representation of the data in an array.
+
+    The data in the array is returned as a single string.  This function is
+    similar to `array_repr`, the difference being that `array_repr` also
+    returns information on the kind of array and its data type.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+    max_line_width : int, optional
+        Inserts newlines if text is longer than `max_line_width`.
+        Defaults to ``numpy.get_printoptions()['linewidth']``.
+    precision : int, optional
+        Floating point precision.
+        Defaults to ``numpy.get_printoptions()['precision']``.
+    suppress_small : bool, optional
+        Represent numbers "very close" to zero as zero; default is False.
+        Very close is defined by precision: if the precision is 8, e.g.,
+        numbers smaller (in absolute value) than 5e-9 are represented as
+        zero.
+        Defaults to ``numpy.get_printoptions()['suppress']``.
+
+    See Also
+    --------
+    array2string, array_repr, set_printoptions
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.array_str(np.arange(3))
+    '[0 1 2]'
+
+    """
+    return _array_str_implementation(
+        a, max_line_width, precision, suppress_small)
+
+
+# needed if __array_function__ is disabled
+_array2string_impl = getattr(array2string, '__wrapped__', array2string)
+_default_array_str = functools.partial(_array_str_implementation,
+                                       array2string=_array2string_impl)
+_default_array_repr = functools.partial(_array_repr_implementation,
+                                        array2string=_array2string_impl)

python/user_packages/Python313/site-packages/numpy/_core/arrayprint.pyi

@@ -0,0 +1,158 @@
+from collections.abc import Callable
+
+# Using a private class is by no means ideal, but it is simply a consequence
+# of a `contextlib.context` returning an instance of aforementioned class
+from contextlib import _GeneratorContextManager
+from typing import (
+    Any,
+    Final,
+    Literal,
+    SupportsIndex,
+    TypeAlias,
+    TypedDict,
+    type_check_only,
+)
+
+import numpy as np
+from numpy._typing import NDArray, _CharLike_co, _FloatLike_co
+
+__all__ = [
+    "array2string",
+    "array_repr",
+    "array_str",
+    "format_float_positional",
+    "format_float_scientific",
+    "get_printoptions",
+    "printoptions",
+    "set_printoptions",
+]
+
+###
+
+_FloatMode: TypeAlias = Literal["fixed", "unique", "maxprec", "maxprec_equal"]
+_LegacyNoStyle: TypeAlias = Literal["1.21", "1.25", "2.1", False]
+_Legacy: TypeAlias = Literal["1.13", _LegacyNoStyle]
+_Sign: TypeAlias = Literal["-", "+", " "]
+_Trim: TypeAlias = Literal["k", ".", "0", "-"]
+_ReprFunc: TypeAlias = Callable[[NDArray[Any]], str]
+
+@type_check_only
+class _FormatDict(TypedDict, total=False):
+    bool: Callable[[np.bool], str]
+    int: Callable[[np.integer], str]
+    timedelta: Callable[[np.timedelta64], str]
+    datetime: Callable[[np.datetime64], str]
+    float: Callable[[np.floating], str]
+    longfloat: Callable[[np.longdouble], str]
+    complexfloat: Callable[[np.complexfloating], str]
+    longcomplexfloat: Callable[[np.clongdouble], str]
+    void: Callable[[np.void], str]
+    numpystr: Callable[[_CharLike_co], str]
+    object: Callable[[object], str]
+    all: Callable[[object], str]
+    int_kind: Callable[[np.integer], str]
+    float_kind: Callable[[np.floating], str]
+    complex_kind: Callable[[np.complexfloating], str]
+    str_kind: Callable[[_CharLike_co], str]
+
+@type_check_only
+class _FormatOptions(TypedDict):
+    precision: int
+    threshold: int
+    edgeitems: int
+    linewidth: int
+    suppress: bool
+    nanstr: str
+    infstr: str
+    formatter: _FormatDict | None
+    sign: _Sign
+    floatmode: _FloatMode
+    legacy: _Legacy
+
+###
+
+__docformat__: Final = "restructuredtext"  # undocumented
+
+def set_printoptions(
+    precision: SupportsIndex | None = None,
+    threshold: int | None = None,
+    edgeitems: int | None = None,
+    linewidth: int | None = None,
+    suppress: bool | None = None,
+    nanstr: str | None = None,
+    infstr: str | None = None,
+    formatter: _FormatDict | None = None,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    *,
+    legacy: _Legacy | None = None,
+    override_repr: _ReprFunc | None = None,
+) -> None: ...
+def get_printoptions() -> _FormatOptions: ...
+
+# public numpy export
+def array2string(
+    a: NDArray[Any],
+    max_line_width: int | None = None,
+    precision: SupportsIndex | None = None,
+    suppress_small: bool | None = None,
+    separator: str = " ",
+    prefix: str = "",
+    *,
+    formatter: _FormatDict | None = None,
+    threshold: int | None = None,
+    edgeitems: int | None = None,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    suffix: str = "",
+    legacy: _Legacy | None = None,
+) -> str: ...
+
+def format_float_scientific(
+    x: _FloatLike_co,
+    precision: int | None = None,
+    unique: bool = True,
+    trim: _Trim = "k",
+    sign: bool = False,
+    pad_left: int | None = None,
+    exp_digits: int | None = None,
+    min_digits: int | None = None,
+) -> str: ...
+def format_float_positional(
+    x: _FloatLike_co,
+    precision: int | None = None,
+    unique: bool = True,
+    fractional: bool = True,
+    trim: _Trim = "k",
+    sign: bool = False,
+    pad_left: int | None = None,
+    pad_right: int | None = None,
+    min_digits: int | None = None,
+) -> str: ...
+def array_repr(
+    arr: NDArray[Any],
+    max_line_width: int | None = None,
+    precision: SupportsIndex | None = None,
+    suppress_small: bool | None = None,
+) -> str: ...
+def array_str(
+    a: NDArray[Any],
+    max_line_width: int | None = None,
+    precision: SupportsIndex | None = None,
+    suppress_small: bool | None = None,
+) -> str: ...
+def printoptions(
+    precision: SupportsIndex | None = ...,
+    threshold: int | None = ...,
+    edgeitems: int | None = ...,
+    linewidth: int | None = ...,
+    suppress: bool | None = ...,
+    nanstr: str | None = ...,
+    infstr: str | None = ...,
+    formatter: _FormatDict | None = ...,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    *,
+    legacy: _Legacy | None = None,
+    override_repr: _ReprFunc | None = None,
+) -> _GeneratorContextManager[_FormatOptions]: ...

python/user_packages/Python313/site-packages/numpy/_core/cversions.py

@@ -0,0 +1,13 @@
+"""Simple script to compute the api hash of the current API.
+
+The API has is defined by numpy_api_order and ufunc_api_order.
+
+"""
+from os.path import dirname
+
+from code_generators.genapi import fullapi_hash
+from code_generators.numpy_api import full_api
+
+if __name__ == '__main__':
+    curdir = dirname(__file__)
+    print(fullapi_hash(full_api))

python/user_packages/Python313/site-packages/numpy/_core/defchararray.py

@@ -0,0 +1,1414 @@
+"""
+This module contains a set of functions for vectorized string
+operations and methods.
+
+.. note::
+   The `chararray` class exists for backwards compatibility with
+   Numarray, it is not recommended for new development. Starting from numpy
+   1.4, if one needs arrays of strings, it is recommended to use arrays of
+   `dtype` `object_`, `bytes_` or `str_`, and use the free functions
+   in the `numpy.char` module for fast vectorized string operations.
+
+Some methods will only be available if the corresponding string method is
+available in your version of Python.
+
+The preferred alias for `defchararray` is `numpy.char`.
+
+"""
+import functools
+
+import numpy as np
+from numpy._core import overrides
+from numpy._core.multiarray import compare_chararrays
+from numpy._core.strings import (
+    _join as join,
+    _rsplit as rsplit,
+    _split as split,
+    _splitlines as splitlines,
+)
+from numpy._utils import set_module
+from numpy.strings import *
+from numpy.strings import (
+    multiply as strings_multiply,
+    partition as strings_partition,
+    rpartition as strings_rpartition,
+)
+
+from .numeric import array as narray, asarray as asnarray, ndarray
+from .numerictypes import bytes_, character, str_
+
+__all__ = [
+    'equal', 'not_equal', 'greater_equal', 'less_equal',
+    'greater', 'less', 'str_len', 'add', 'multiply', 'mod', 'capitalize',
+    'center', 'count', 'decode', 'encode', 'endswith', 'expandtabs',
+    'find', 'index', 'isalnum', 'isalpha', 'isdigit', 'islower', 'isspace',
+    'istitle', 'isupper', 'join', 'ljust', 'lower', 'lstrip', 'partition',
+    'replace', 'rfind', 'rindex', 'rjust', 'rpartition', 'rsplit',
+    'rstrip', 'split', 'splitlines', 'startswith', 'strip', 'swapcase',
+    'title', 'translate', 'upper', 'zfill', 'isnumeric', 'isdecimal',
+    'array', 'asarray', 'compare_chararrays', 'chararray'
+    ]
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy.char')
+
+
+def _binary_op_dispatcher(x1, x2):
+    return (x1, x2)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def equal(x1, x2):
+    """
+    Return (x1 == x2) element-wise.
+
+    Unlike `numpy.equal`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> y = "aa "
+    >>> x = "aa"
+    >>> np.char.equal(x, y)
+    array(True)
+
+    See Also
+    --------
+    not_equal, greater_equal, less_equal, greater, less
+    """
+    return compare_chararrays(x1, x2, '==', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def not_equal(x1, x2):
+    """
+    Return (x1 != x2) element-wise.
+
+    Unlike `numpy.not_equal`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, greater_equal, less_equal, greater, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.not_equal(x1, 'b')
+    array([ True, False,  True])
+
+    """
+    return compare_chararrays(x1, x2, '!=', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def greater_equal(x1, x2):
+    """
+    Return (x1 >= x2) element-wise.
+
+    Unlike `numpy.greater_equal`, this comparison is performed by
+    first stripping whitespace characters from the end of the string.
+    This behavior is provided for backward-compatibility with
+    numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, less_equal, greater, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.greater_equal(x1, 'b')
+    array([False,  True,  True])
+
+    """
+    return compare_chararrays(x1, x2, '>=', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def less_equal(x1, x2):
+    """
+    Return (x1 <= x2) element-wise.
+
+    Unlike `numpy.less_equal`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, greater_equal, greater, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.less_equal(x1, 'b')
+    array([ True,  True, False])
+
+    """
+    return compare_chararrays(x1, x2, '<=', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def greater(x1, x2):
+    """
+    Return (x1 > x2) element-wise.
+
+    Unlike `numpy.greater`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, greater_equal, less_equal, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.greater(x1, 'b')
+    array([False, False,  True])
+
+    """
+    return compare_chararrays(x1, x2, '>', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def less(x1, x2):
+    """
+    Return (x1 < x2) element-wise.
+
+    Unlike `numpy.greater`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, greater_equal, less_equal, greater
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.less(x1, 'b')
+    array([True, False, False])
+
+    """
+    return compare_chararrays(x1, x2, '<', True)
+
+
+@set_module("numpy.char")
+def multiply(a, i):
+    """
+    Return (a * i), that is string multiple concatenation,
+    element-wise.
+
+    Values in ``i`` of less than 0 are treated as 0 (which yields an
+    empty string).
+
+    Parameters
+    ----------
+    a : array_like, with `np.bytes_` or `np.str_` dtype
+
+    i : array_like, with any integer dtype
+
+    Returns
+    -------
+    out : ndarray
+        Output array of str or unicode, depending on input types
+
+    Notes
+    -----
+    This is a thin wrapper around np.strings.multiply that raises
+    `ValueError` when ``i`` is not an integer. It only
+    exists for backwards-compatibility.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["a", "b", "c"])
+    >>> np.strings.multiply(a, 3)
+    array(['aaa', 'bbb', 'ccc'], dtype='<U3')
+    >>> i = np.array([1, 2, 3])
+    >>> np.strings.multiply(a, i)
+    array(['a', 'bb', 'ccc'], dtype='<U3')
+    >>> np.strings.multiply(np.array(['a']), i)
+    array(['a', 'aa', 'aaa'], dtype='<U3')
+    >>> a = np.array(['a', 'b', 'c', 'd', 'e', 'f']).reshape((2, 3))
+    >>> np.strings.multiply(a, 3)
+    array([['aaa', 'bbb', 'ccc'],
+           ['ddd', 'eee', 'fff']], dtype='<U3')
+    >>> np.strings.multiply(a, i)
+    array([['a', 'bb', 'ccc'],
+           ['d', 'ee', 'fff']], dtype='<U3')
+
+    """
+    try:
+        return strings_multiply(a, i)
+    except TypeError:
+        raise ValueError("Can only multiply by integers")
+
+
+@set_module("numpy.char")
+def partition(a, sep):
+    """
+    Partition each element in `a` around `sep`.
+
+    Calls :meth:`str.partition` element-wise.
+
+    For each element in `a`, split the element as the first
+    occurrence of `sep`, and return 3 strings containing the part
+    before the separator, the separator itself, and the part after
+    the separator. If the separator is not found, return 3 strings
+    containing the string itself, followed by two empty strings.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+    sep : {str, unicode}
+        Separator to split each string element in `a`.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types. The output array will have an extra
+        dimension with 3 elements per input element.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array(["Numpy is nice!"])
+    >>> np.char.partition(x, " ")
+    array([['Numpy', ' ', 'is nice!']], dtype='<U8')
+
+    See Also
+    --------
+    str.partition
+
+    """
+    return np.stack(strings_partition(a, sep), axis=-1)
+
+
+@set_module("numpy.char")
+def rpartition(a, sep):
+    """
+    Partition (split) each element around the right-most separator.
+
+    Calls :meth:`str.rpartition` element-wise.
+
+    For each element in `a`, split the element as the last
+    occurrence of `sep`, and return 3 strings containing the part
+    before the separator, the separator itself, and the part after
+    the separator. If the separator is not found, return 3 strings
+    containing the string itself, followed by two empty strings.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+    sep : str or unicode
+        Right-most separator to split each element in array.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types. The output array will have an extra
+        dimension with 3 elements per input element.
+
+    See Also
+    --------
+    str.rpartition
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> np.char.rpartition(a, 'A')
+    array([['aAaAa', 'A', ''],
+       ['  a', 'A', '  '],
+       ['abB', 'A', 'Bba']], dtype='<U5')
+
+    """
+    return np.stack(strings_rpartition(a, sep), axis=-1)
+
+
+@set_module("numpy.char")
+class chararray(ndarray):
+    """
+    chararray(shape, itemsize=1, unicode=False, buffer=None, offset=0,
+              strides=None, order=None)
+
+    Provides a convenient view on arrays of string and unicode values.
+
+    .. note::
+       The `chararray` class exists for backwards compatibility with
+       Numarray, it is not recommended for new development. Starting from numpy
+       1.4, if one needs arrays of strings, it is recommended to use arrays of
+       `dtype` `~numpy.object_`, `~numpy.bytes_` or `~numpy.str_`, and use
+       the free functions in the `numpy.char` module for fast vectorized
+       string operations.
+
+    Versus a NumPy array of dtype `~numpy.bytes_` or `~numpy.str_`, this
+    class adds the following functionality:
+
+    1) values automatically have whitespace removed from the end
+       when indexed
+
+    2) comparison operators automatically remove whitespace from the
+       end when comparing values
+
+    3) vectorized string operations are provided as methods
+       (e.g. `.endswith`) and infix operators (e.g. ``"+", "*", "%"``)
+
+    chararrays should be created using `numpy.char.array` or
+    `numpy.char.asarray`, rather than this constructor directly.
+
+    This constructor creates the array, using `buffer` (with `offset`
+    and `strides`) if it is not ``None``. If `buffer` is ``None``, then
+    constructs a new array with `strides` in "C order", unless both
+    ``len(shape) >= 2`` and ``order='F'``, in which case `strides`
+    is in "Fortran order".
+
+    Methods
+    -------
+    astype
+    argsort
+    copy
+    count
+    decode
+    dump
+    dumps
+    encode
+    endswith
+    expandtabs
+    fill
+    find
+    flatten
+    getfield
+    index
+    isalnum
+    isalpha
+    isdecimal
+    isdigit
+    islower
+    isnumeric
+    isspace
+    istitle
+    isupper
+    item
+    join
+    ljust
+    lower
+    lstrip
+    nonzero
+    put
+    ravel
+    repeat
+    replace
+    reshape
+    resize
+    rfind
+    rindex
+    rjust
+    rsplit
+    rstrip
+    searchsorted
+    setfield
+    setflags
+    sort
+    split
+    splitlines
+    squeeze
+    startswith
+    strip
+    swapaxes
+    swapcase
+    take
+    title
+    tofile
+    tolist
+    translate
+    transpose
+    upper
+    view
+    zfill
+
+    Parameters
+    ----------
+    shape : tuple
+        Shape of the array.
+    itemsize : int, optional
+        Length of each array element, in number of characters. Default is 1.
+    unicode : bool, optional
+        Are the array elements of type unicode (True) or string (False).
+        Default is False.
+    buffer : object exposing the buffer interface or str, optional
+        Memory address of the start of the array data.  Default is None,
+        in which case a new array is created.
+    offset : int, optional
+        Fixed stride displacement from the beginning of an axis?
+        Default is 0. Needs to be >=0.
+    strides : array_like of ints, optional
+        Strides for the array (see `~numpy.ndarray.strides` for
+        full description). Default is None.
+    order : {'C', 'F'}, optional
+        The order in which the array data is stored in memory: 'C' ->
+        "row major" order (the default), 'F' -> "column major"
+        (Fortran) order.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> charar = np.char.chararray((3, 3))
+    >>> charar[:] = 'a'
+    >>> charar
+    chararray([[b'a', b'a', b'a'],
+               [b'a', b'a', b'a'],
+               [b'a', b'a', b'a']], dtype='|S1')
+
+    >>> charar = np.char.chararray(charar.shape, itemsize=5)
+    >>> charar[:] = 'abc'
+    >>> charar
+    chararray([[b'abc', b'abc', b'abc'],
+               [b'abc', b'abc', b'abc'],
+               [b'abc', b'abc', b'abc']], dtype='|S5')
+
+    """
+    def __new__(subtype, shape, itemsize=1, unicode=False, buffer=None,
+                offset=0, strides=None, order='C'):
+        if unicode:
+            dtype = str_
+        else:
+            dtype = bytes_
+
+        # force itemsize to be a Python int, since using NumPy integer
+        # types results in itemsize.itemsize being used as the size of
+        # strings in the new array.
+        itemsize = int(itemsize)
+
+        if isinstance(buffer, str):
+            # unicode objects do not have the buffer interface
+            filler = buffer
+            buffer = None
+        else:
+            filler = None
+
+        if buffer is None:
+            self = ndarray.__new__(subtype, shape, (dtype, itemsize),
+                                   order=order)
+        else:
+            self = ndarray.__new__(subtype, shape, (dtype, itemsize),
+                                   buffer=buffer,
+                                   offset=offset, strides=strides,
+                                   order=order)
+        if filler is not None:
+            self[...] = filler
+
+        return self
+
+    def __array_wrap__(self, arr, context=None, return_scalar=False):
+        # When calling a ufunc (and some other functions), we return a
+        # chararray if the ufunc output is a string-like array,
+        # or an ndarray otherwise
+        if arr.dtype.char in "SUbc":
+            return arr.view(type(self))
+        return arr
+
+    def __array_finalize__(self, obj):
+        # The b is a special case because it is used for reconstructing.
+        if self.dtype.char not in 'VSUbc':
+            raise ValueError("Can only create a chararray from string data.")
+
+    def __getitem__(self, obj):
+        val = ndarray.__getitem__(self, obj)
+        if isinstance(val, character):
+            return val.rstrip()
+        return val
+
+    # IMPLEMENTATION NOTE: Most of the methods of this class are
+    # direct delegations to the free functions in this module.
+    # However, those that return an array of strings should instead
+    # return a chararray, so some extra wrapping is required.
+
+    def __eq__(self, other):
+        """
+        Return (self == other) element-wise.
+
+        See Also
+        --------
+        equal
+        """
+        return equal(self, other)
+
+    def __ne__(self, other):
+        """
+        Return (self != other) element-wise.
+
+        See Also
+        --------
+        not_equal
+        """
+        return not_equal(self, other)
+
+    def __ge__(self, other):
+        """
+        Return (self >= other) element-wise.
+
+        See Also
+        --------
+        greater_equal
+        """
+        return greater_equal(self, other)
+
+    def __le__(self, other):
+        """
+        Return (self <= other) element-wise.
+
+        See Also
+        --------
+        less_equal
+        """
+        return less_equal(self, other)
+
+    def __gt__(self, other):
+        """
+        Return (self > other) element-wise.
+
+        See Also
+        --------
+        greater
+        """
+        return greater(self, other)
+
+    def __lt__(self, other):
+        """
+        Return (self < other) element-wise.
+
+        See Also
+        --------
+        less
+        """
+        return less(self, other)
+
+    def __add__(self, other):
+        """
+        Return (self + other), that is string concatenation,
+        element-wise for a pair of array_likes of str or unicode.
+
+        See Also
+        --------
+        add
+        """
+        return add(self, other)
+
+    def __radd__(self, other):
+        """
+        Return (other + self), that is string concatenation,
+        element-wise for a pair of array_likes of `bytes_` or `str_`.
+
+        See Also
+        --------
+        add
+        """
+        return add(other, self)
+
+    def __mul__(self, i):
+        """
+        Return (self * i), that is string multiple concatenation,
+        element-wise.
+
+        See Also
+        --------
+        multiply
+        """
+        return asarray(multiply(self, i))
+
+    def __rmul__(self, i):
+        """
+        Return (self * i), that is string multiple concatenation,
+        element-wise.
+
+        See Also
+        --------
+        multiply
+        """
+        return asarray(multiply(self, i))
+
+    def __mod__(self, i):
+        """
+        Return (self % i), that is pre-Python 2.6 string formatting
+        (interpolation), element-wise for a pair of array_likes of `bytes_`
+        or `str_`.
+
+        See Also
+        --------
+        mod
+        """
+        return asarray(mod(self, i))
+
+    def __rmod__(self, other):
+        return NotImplemented
+
+    def argsort(self, axis=-1, kind=None, order=None, *, stable=None):
+        """
+        Return the indices that sort the array lexicographically.
+
+        For full documentation see `numpy.argsort`, for which this method is
+        in fact merely a "thin wrapper."
+
+        Examples
+        --------
+        >>> c = np.array(['a1b c', '1b ca', 'b ca1', 'Ca1b'], 'S5')
+        >>> c = c.view(np.char.chararray); c
+        chararray(['a1b c', '1b ca', 'b ca1', 'Ca1b'],
+              dtype='|S5')
+        >>> c[c.argsort()]
+        chararray(['1b ca', 'Ca1b', 'a1b c', 'b ca1'],
+              dtype='|S5')
+
+        """
+        return self.__array__().argsort(axis, kind, order, stable=stable)
+    argsort.__doc__ = ndarray.argsort.__doc__
+
+    def capitalize(self):
+        """
+        Return a copy of `self` with only the first character of each element
+        capitalized.
+
+        See Also
+        --------
+        char.capitalize
+
+        """
+        return asarray(capitalize(self))
+
+    def center(self, width, fillchar=' '):
+        """
+        Return a copy of `self` with its elements centered in a
+        string of length `width`.
+
+        See Also
+        --------
+        center
+        """
+        return asarray(center(self, width, fillchar))
+
+    def count(self, sub, start=0, end=None):
+        """
+        Returns an array with the number of non-overlapping occurrences of
+        substring `sub` in the range [`start`, `end`].
+
+        See Also
+        --------
+        char.count
+
+        """
+        return count(self, sub, start, end)
+
+    def decode(self, encoding=None, errors=None):
+        """
+        Calls ``bytes.decode`` element-wise.
+
+        See Also
+        --------
+        char.decode
+
+        """
+        return decode(self, encoding, errors)
+
+    def encode(self, encoding=None, errors=None):
+        """
+        Calls :meth:`str.encode` element-wise.
+
+        See Also
+        --------
+        char.encode
+
+        """
+        return encode(self, encoding, errors)
+
+    def endswith(self, suffix, start=0, end=None):
+        """
+        Returns a boolean array which is `True` where the string element
+        in `self` ends with `suffix`, otherwise `False`.
+
+        See Also
+        --------
+        char.endswith
+
+        """
+        return endswith(self, suffix, start, end)
+
+    def expandtabs(self, tabsize=8):
+        """
+        Return a copy of each string element where all tab characters are
+        replaced by one or more spaces.
+
+        See Also
+        --------
+        char.expandtabs
+
+        """
+        return asarray(expandtabs(self, tabsize))
+
+    def find(self, sub, start=0, end=None):
+        """
+        For each element, return the lowest index in the string where
+        substring `sub` is found.
+
+        See Also
+        --------
+        char.find
+
+        """
+        return find(self, sub, start, end)
+
+    def index(self, sub, start=0, end=None):
+        """
+        Like `find`, but raises :exc:`ValueError` when the substring is not
+        found.
+
+        See Also
+        --------
+        char.index
+
+        """
+        return index(self, sub, start, end)
+
+    def isalnum(self):
+        """
+        Returns true for each element if all characters in the string
+        are alphanumeric and there is at least one character, false
+        otherwise.
+
+        See Also
+        --------
+        char.isalnum
+
+        """
+        return isalnum(self)
+
+    def isalpha(self):
+        """
+        Returns true for each element if all characters in the string
+        are alphabetic and there is at least one character, false
+        otherwise.
+
+        See Also
+        --------
+        char.isalpha
+
+        """
+        return isalpha(self)
+
+    def isdigit(self):
+        """
+        Returns true for each element if all characters in the string are
+        digits and there is at least one character, false otherwise.
+
+        See Also
+        --------
+        char.isdigit
+
+        """
+        return isdigit(self)
+
+    def islower(self):
+        """
+        Returns true for each element if all cased characters in the
+        string are lowercase and there is at least one cased character,
+        false otherwise.
+
+        See Also
+        --------
+        char.islower
+
+        """
+        return islower(self)
+
+    def isspace(self):
+        """
+        Returns true for each element if there are only whitespace
+        characters in the string and there is at least one character,
+        false otherwise.
+
+        See Also
+        --------
+        char.isspace
+
+        """
+        return isspace(self)
+
+    def istitle(self):
+        """
+        Returns true for each element if the element is a titlecased
+        string and there is at least one character, false otherwise.
+
+        See Also
+        --------
+        char.istitle
+
+        """
+        return istitle(self)
+
+    def isupper(self):
+        """
+        Returns true for each element if all cased characters in the
+        string are uppercase and there is at least one character, false
+        otherwise.
+
+        See Also
+        --------
+        char.isupper
+
+        """
+        return isupper(self)
+
+    def join(self, seq):
+        """
+        Return a string which is the concatenation of the strings in the
+        sequence `seq`.
+
+        See Also
+        --------
+        char.join
+
+        """
+        return join(self, seq)
+
+    def ljust(self, width, fillchar=' '):
+        """
+        Return an array with the elements of `self` left-justified in a
+        string of length `width`.
+
+        See Also
+        --------
+        char.ljust
+
+        """
+        return asarray(ljust(self, width, fillchar))
+
+    def lower(self):
+        """
+        Return an array with the elements of `self` converted to
+        lowercase.
+
+        See Also
+        --------
+        char.lower
+
+        """
+        return asarray(lower(self))
+
+    def lstrip(self, chars=None):
+        """
+        For each element in `self`, return a copy with the leading characters
+        removed.
+
+        See Also
+        --------
+        char.lstrip
+
+        """
+        return lstrip(self, chars)
+
+    def partition(self, sep):
+        """
+        Partition each element in `self` around `sep`.
+
+        See Also
+        --------
+        partition
+        """
+        return asarray(partition(self, sep))
+
+    def replace(self, old, new, count=None):
+        """
+        For each element in `self`, return a copy of the string with all
+        occurrences of substring `old` replaced by `new`.
+
+        See Also
+        --------
+        char.replace
+
+        """
+        return replace(self, old, new, count if count is not None else -1)
+
+    def rfind(self, sub, start=0, end=None):
+        """
+        For each element in `self`, return the highest index in the string
+        where substring `sub` is found, such that `sub` is contained
+        within [`start`, `end`].
+
+        See Also
+        --------
+        char.rfind
+
+        """
+        return rfind(self, sub, start, end)
+
+    def rindex(self, sub, start=0, end=None):
+        """
+        Like `rfind`, but raises :exc:`ValueError` when the substring `sub` is
+        not found.
+
+        See Also
+        --------
+        char.rindex
+
+        """
+        return rindex(self, sub, start, end)
+
+    def rjust(self, width, fillchar=' '):
+        """
+        Return an array with the elements of `self`
+        right-justified in a string of length `width`.
+
+        See Also
+        --------
+        char.rjust
+
+        """
+        return asarray(rjust(self, width, fillchar))
+
+    def rpartition(self, sep):
+        """
+        Partition each element in `self` around `sep`.
+
+        See Also
+        --------
+        rpartition
+        """
+        return asarray(rpartition(self, sep))
+
+    def rsplit(self, sep=None, maxsplit=None):
+        """
+        For each element in `self`, return a list of the words in
+        the string, using `sep` as the delimiter string.
+
+        See Also
+        --------
+        char.rsplit
+
+        """
+        return rsplit(self, sep, maxsplit)
+
+    def rstrip(self, chars=None):
+        """
+        For each element in `self`, return a copy with the trailing
+        characters removed.
+
+        See Also
+        --------
+        char.rstrip
+
+        """
+        return rstrip(self, chars)
+
+    def split(self, sep=None, maxsplit=None):
+        """
+        For each element in `self`, return a list of the words in the
+        string, using `sep` as the delimiter string.
+
+        See Also
+        --------
+        char.split
+
+        """
+        return split(self, sep, maxsplit)
+
+    def splitlines(self, keepends=None):
+        """
+        For each element in `self`, return a list of the lines in the
+        element, breaking at line boundaries.
+
+        See Also
+        --------
+        char.splitlines
+
+        """
+        return splitlines(self, keepends)
+
+    def startswith(self, prefix, start=0, end=None):
+        """
+        Returns a boolean array which is `True` where the string element
+        in `self` starts with `prefix`, otherwise `False`.
+
+        See Also
+        --------
+        char.startswith
+
+        """
+        return startswith(self, prefix, start, end)
+
+    def strip(self, chars=None):
+        """
+        For each element in `self`, return a copy with the leading and
+        trailing characters removed.
+
+        See Also
+        --------
+        char.strip
+
+        """
+        return strip(self, chars)
+
+    def swapcase(self):
+        """
+        For each element in `self`, return a copy of the string with
+        uppercase characters converted to lowercase and vice versa.
+
+        See Also
+        --------
+        char.swapcase
+
+        """
+        return asarray(swapcase(self))
+
+    def title(self):
+        """
+        For each element in `self`, return a titlecased version of the
+        string: words start with uppercase characters, all remaining cased
+        characters are lowercase.
+
+        See Also
+        --------
+        char.title
+
+        """
+        return asarray(title(self))
+
+    def translate(self, table, deletechars=None):
+        """
+        For each element in `self`, return a copy of the string where
+        all characters occurring in the optional argument
+        `deletechars` are removed, and the remaining characters have
+        been mapped through the given translation table.
+
+        See Also
+        --------
+        char.translate
+
+        """
+        return asarray(translate(self, table, deletechars))
+
+    def upper(self):
+        """
+        Return an array with the elements of `self` converted to
+        uppercase.
+
+        See Also
+        --------
+        char.upper
+
+        """
+        return asarray(upper(self))
+
+    def zfill(self, width):
+        """
+        Return the numeric string left-filled with zeros in a string of
+        length `width`.
+
+        See Also
+        --------
+        char.zfill
+
+        """
+        return asarray(zfill(self, width))
+
+    def isnumeric(self):
+        """
+        For each element in `self`, return True if there are only
+        numeric characters in the element.
+
+        See Also
+        --------
+        char.isnumeric
+
+        """
+        return isnumeric(self)
+
+    def isdecimal(self):
+        """
+        For each element in `self`, return True if there are only
+        decimal characters in the element.
+
+        See Also
+        --------
+        char.isdecimal
+
+        """
+        return isdecimal(self)
+
+
+@set_module("numpy.char")
+def array(obj, itemsize=None, copy=True, unicode=None, order=None):
+    """
+    Create a `~numpy.char.chararray`.
+
+    .. note::
+       This class is provided for numarray backward-compatibility.
+       New code (not concerned with numarray compatibility) should use
+       arrays of type `bytes_` or `str_` and use the free functions
+       in :mod:`numpy.char` for fast vectorized string operations instead.
+
+    Versus a NumPy array of dtype `bytes_` or `str_`, this
+    class adds the following functionality:
+
+    1) values automatically have whitespace removed from the end
+       when indexed
+
+    2) comparison operators automatically remove whitespace from the
+       end when comparing values
+
+    3) vectorized string operations are provided as methods
+       (e.g. `chararray.endswith <numpy.char.chararray.endswith>`)
+       and infix operators (e.g. ``+, *, %``)
+
+    Parameters
+    ----------
+    obj : array of str or unicode-like
+
+    itemsize : int, optional
+        `itemsize` is the number of characters per scalar in the
+        resulting array.  If `itemsize` is None, and `obj` is an
+        object array or a Python list, the `itemsize` will be
+        automatically determined.  If `itemsize` is provided and `obj`
+        is of type str or unicode, then the `obj` string will be
+        chunked into `itemsize` pieces.
+
+    copy : bool, optional
+        If true (default), then the object is copied.  Otherwise, a copy
+        will only be made if ``__array__`` returns a copy, if obj is a
+        nested sequence, or if a copy is needed to satisfy any of the other
+        requirements (`itemsize`, unicode, `order`, etc.).
+
+    unicode : bool, optional
+        When true, the resulting `~numpy.char.chararray` can contain Unicode
+        characters, when false only 8-bit characters.  If unicode is
+        None and `obj` is one of the following:
+
+        - a `~numpy.char.chararray`,
+        - an ndarray of type :class:`str_` or :class:`bytes_`
+        - a Python :class:`str` or :class:`bytes` object,
+
+        then the unicode setting of the output array will be
+        automatically determined.
+
+    order : {'C', 'F', 'A'}, optional
+        Specify the order of the array.  If order is 'C' (default), then the
+        array will be in C-contiguous order (last-index varies the
+        fastest).  If order is 'F', then the returned array
+        will be in Fortran-contiguous order (first-index varies the
+        fastest).  If order is 'A', then the returned array may
+        be in any order (either C-, Fortran-contiguous, or even
+        discontiguous).
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> char_array = np.char.array(['hello', 'world', 'numpy','array'])
+    >>> char_array
+    chararray(['hello', 'world', 'numpy', 'array'], dtype='<U5')
+
+    """
+    if isinstance(obj, (bytes, str)):
+        if unicode is None:
+            if isinstance(obj, str):
+                unicode = True
+            else:
+                unicode = False
+
+        if itemsize is None:
+            itemsize = len(obj)
+        shape = len(obj) // itemsize
+
+        return chararray(shape, itemsize=itemsize, unicode=unicode,
+                         buffer=obj, order=order)
+
+    if isinstance(obj, (list, tuple)):
+        obj = asnarray(obj)
+
+    if isinstance(obj, ndarray) and issubclass(obj.dtype.type, character):
+        # If we just have a vanilla chararray, create a chararray
+        # view around it.
+        if not isinstance(obj, chararray):
+            obj = obj.view(chararray)
+
+        if itemsize is None:
+            itemsize = obj.itemsize
+            # itemsize is in 8-bit chars, so for Unicode, we need
+            # to divide by the size of a single Unicode character,
+            # which for NumPy is always 4
+            if issubclass(obj.dtype.type, str_):
+                itemsize //= 4
+
+        if unicode is None:
+            if issubclass(obj.dtype.type, str_):
+                unicode = True
+            else:
+                unicode = False
+
+        if unicode:
+            dtype = str_
+        else:
+            dtype = bytes_
+
+        if order is not None:
+            obj = asnarray(obj, order=order)
+        if (copy or
+                (itemsize != obj.itemsize) or
+                (not unicode and isinstance(obj, str_)) or
+                (unicode and isinstance(obj, bytes_))):
+            obj = obj.astype((dtype, int(itemsize)))
+        return obj
+
+    if isinstance(obj, ndarray) and issubclass(obj.dtype.type, object):
+        if itemsize is None:
+            # Since no itemsize was specified, convert the input array to
+            # a list so the ndarray constructor will automatically
+            # determine the itemsize for us.
+            obj = obj.tolist()
+            # Fall through to the default case
+
+    if unicode:
+        dtype = str_
+    else:
+        dtype = bytes_
+
+    if itemsize is None:
+        val = narray(obj, dtype=dtype, order=order, subok=True)
+    else:
+        val = narray(obj, dtype=(dtype, itemsize), order=order, subok=True)
+    return val.view(chararray)
+
+
+@set_module("numpy.char")
+def asarray(obj, itemsize=None, unicode=None, order=None):
+    """
+    Convert the input to a `~numpy.char.chararray`, copying the data only if
+    necessary.
+
+    Versus a NumPy array of dtype `bytes_` or `str_`, this
+    class adds the following functionality:
+
+    1) values automatically have whitespace removed from the end
+       when indexed
+
+    2) comparison operators automatically remove whitespace from the
+       end when comparing values
+
+    3) vectorized string operations are provided as methods
+       (e.g. `chararray.endswith <numpy.char.chararray.endswith>`)
+       and infix operators (e.g. ``+``, ``*``, ``%``)
+
+    Parameters
+    ----------
+    obj : array of str or unicode-like
+
+    itemsize : int, optional
+        `itemsize` is the number of characters per scalar in the
+        resulting array.  If `itemsize` is None, and `obj` is an
+        object array or a Python list, the `itemsize` will be
+        automatically determined.  If `itemsize` is provided and `obj`
+        is of type str or unicode, then the `obj` string will be
+        chunked into `itemsize` pieces.
+
+    unicode : bool, optional
+        When true, the resulting `~numpy.char.chararray` can contain Unicode
+        characters, when false only 8-bit characters.  If unicode is
+        None and `obj` is one of the following:
+
+        - a `~numpy.char.chararray`,
+        - an ndarray of type `str_` or `unicode_`
+        - a Python str or unicode object,
+
+        then the unicode setting of the output array will be
+        automatically determined.
+
+    order : {'C', 'F'}, optional
+        Specify the order of the array.  If order is 'C' (default), then the
+        array will be in C-contiguous order (last-index varies the
+        fastest).  If order is 'F', then the returned array
+        will be in Fortran-contiguous order (first-index varies the
+        fastest).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.char.asarray(['hello', 'world'])
+    chararray(['hello', 'world'], dtype='<U5')
+
+    """
+    return array(obj, itemsize, copy=False,
+                 unicode=unicode, order=order)

python/user_packages/Python313/site-packages/numpy/_core/defchararray.pyi

@@ -0,0 +1,1150 @@
+from typing import (
+    Any,
+    Literal as L,
+    Self,
+    SupportsIndex,
+    SupportsInt,
+    TypeAlias,
+    overload,
+)
+from typing_extensions import Buffer, TypeVar
+
+import numpy as np
+from numpy import _OrderKACF, bytes_, dtype, int_, ndarray, object_, str_
+from numpy._core.multiarray import compare_chararrays
+from numpy._typing import (
+    NDArray,
+    _AnyShape,
+    _ArrayLikeAnyString_co as UST_co,
+    _ArrayLikeBool_co as b_co,
+    _ArrayLikeBytes_co as S_co,
+    _ArrayLikeInt_co as i_co,
+    _ArrayLikeStr_co as U_co,
+    _ArrayLikeString_co as T_co,
+    _Shape,
+    _ShapeLike,
+    _SupportsArray,
+)
+
+__all__ = [
+    "equal",
+    "not_equal",
+    "greater_equal",
+    "less_equal",
+    "greater",
+    "less",
+    "str_len",
+    "add",
+    "multiply",
+    "mod",
+    "capitalize",
+    "center",
+    "count",
+    "decode",
+    "encode",
+    "endswith",
+    "expandtabs",
+    "find",
+    "index",
+    "isalnum",
+    "isalpha",
+    "isdigit",
+    "islower",
+    "isspace",
+    "istitle",
+    "isupper",
+    "join",
+    "ljust",
+    "lower",
+    "lstrip",
+    "partition",
+    "replace",
+    "rfind",
+    "rindex",
+    "rjust",
+    "rpartition",
+    "rsplit",
+    "rstrip",
+    "split",
+    "splitlines",
+    "startswith",
+    "strip",
+    "swapcase",
+    "title",
+    "translate",
+    "upper",
+    "zfill",
+    "isnumeric",
+    "isdecimal",
+    "array",
+    "asarray",
+    "compare_chararrays",
+    "chararray",
+]
+
+_ShapeT_co = TypeVar("_ShapeT_co", bound=_Shape, default=_AnyShape, covariant=True)
+_CharacterT = TypeVar("_CharacterT", bound=np.character)
+_CharDTypeT_co = TypeVar("_CharDTypeT_co", bound=dtype[np.character], default=dtype, covariant=True)
+
+_CharArray: TypeAlias = chararray[_AnyShape, dtype[_CharacterT]]
+
+_StringDTypeArray: TypeAlias = np.ndarray[_AnyShape, np.dtypes.StringDType]
+_StringDTypeOrUnicodeArray: TypeAlias = _StringDTypeArray | NDArray[np.str_]
+_StringDTypeSupportsArray: TypeAlias = _SupportsArray[np.dtypes.StringDType]
+
+class chararray(ndarray[_ShapeT_co, _CharDTypeT_co]):
+    @overload
+    def __new__(
+        subtype,
+        shape: _ShapeLike,
+        itemsize: SupportsIndex | SupportsInt = 1,
+        unicode: L[False] = False,
+        buffer: Buffer | np.ndarray | None = None,
+        offset: SupportsIndex = 0,
+        strides: _ShapeLike | None = None,
+        order: _OrderKACF = "C",
+    ) -> _CharArray[bytes_]: ...
+    @overload
+    def __new__(
+        subtype,
+        shape: _ShapeLike,
+        itemsize: SupportsIndex | SupportsInt,
+        unicode: L[True],
+        buffer: Buffer | np.ndarray | None = None,
+        offset: SupportsIndex = 0,
+        strides: _ShapeLike | None = None,
+        order: _OrderKACF = "C",
+    ) -> _CharArray[str_]: ...
+    @overload
+    def __new__(
+        subtype,
+        shape: _ShapeLike,
+        itemsize: SupportsIndex | SupportsInt = 1,
+        *,
+        unicode: L[True],
+        buffer: Buffer | np.ndarray | None = None,
+        offset: SupportsIndex = 0,
+        strides: _ShapeLike | None = None,
+        order: _OrderKACF = "C",
+    ) -> _CharArray[str_]: ...
+
+    def __array_finalize__(self, obj: object) -> None: ...
+    def __mul__(self, other: i_co) -> chararray[_AnyShape, _CharDTypeT_co]: ...  # type: ignore[override]
+    def __rmul__(self, other: i_co) -> chararray[_AnyShape, _CharDTypeT_co]: ...  # type: ignore[override]
+    def __mod__(self, i: Any) -> chararray[_AnyShape, _CharDTypeT_co]: ...  # type: ignore[override]
+
+    @overload  # type: ignore[override]
+    def __eq__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __eq__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload  # type: ignore[override]
+    def __ne__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __ne__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload  # type: ignore[override]
+    def __ge__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __ge__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload  # type: ignore[override]
+    def __le__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __le__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload  # type: ignore[override]
+    def __gt__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __gt__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload  # type: ignore[override]
+    def __lt__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __lt__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload  # type: ignore[override]
+    def __add__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def __add__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload  # type: ignore[override]
+    def __radd__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def __radd__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def center(
+        self: _CharArray[str_],
+        width: i_co,
+        fillchar: U_co = " ",
+    ) -> _CharArray[str_]: ...
+    @overload
+    def center(
+        self: _CharArray[bytes_],
+        width: i_co,
+        fillchar: str | S_co = " ",
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def count(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+    @overload
+    def count(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+
+    def decode(
+        self: _CharArray[bytes_],
+        encoding: str | None = None,
+        errors: str | None = None,
+    ) -> _CharArray[str_]: ...
+
+    def encode(
+        self: _CharArray[str_],
+        encoding: str | None = None,
+        errors: str | None = None,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def endswith(
+        self: _CharArray[str_],
+        suffix: U_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def endswith(
+        self: _CharArray[bytes_],
+        suffix: S_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[np.bool]: ...
+
+    def expandtabs(
+        self,
+        tabsize: i_co = 8,
+    ) -> Self: ...
+
+    @overload
+    def find(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+    @overload
+    def find(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def index(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+    @overload
+    def index(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def join(
+        self: _CharArray[str_],
+        seq: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def join(
+        self: _CharArray[bytes_],
+        seq: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def ljust(
+        self: _CharArray[str_],
+        width: i_co,
+        fillchar: U_co = " ",
+    ) -> _CharArray[str_]: ...
+    @overload
+    def ljust(
+        self: _CharArray[bytes_],
+        width: i_co,
+        fillchar: str | S_co = " ",
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def lstrip(
+        self: _CharArray[str_],
+        chars: U_co | None = None,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def lstrip(
+        self: _CharArray[bytes_],
+        chars: S_co | None = None,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload  # type: ignore[override]
+    def partition(
+        self: _CharArray[str_],
+        sep: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def partition(
+        self: _CharArray[bytes_],
+        sep: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def replace(
+        self: _CharArray[str_],
+        old: U_co,
+        new: U_co,
+        count: i_co | None = None,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def replace(
+        self: _CharArray[bytes_],
+        old: S_co,
+        new: S_co,
+        count: i_co | None = None,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def rfind(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+    @overload
+    def rfind(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def rindex(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+    @overload
+    def rindex(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def rjust(
+        self: _CharArray[str_],
+        width: i_co,
+        fillchar: U_co = " ",
+    ) -> _CharArray[str_]: ...
+    @overload
+    def rjust(
+        self: _CharArray[bytes_],
+        width: i_co,
+        fillchar: str | S_co = " ",
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def rpartition(
+        self: _CharArray[str_],
+        sep: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def rpartition(
+        self: _CharArray[bytes_],
+        sep: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def rsplit(
+        self: _CharArray[str_],
+        sep: U_co | None = None,
+        maxsplit: i_co | None = None,
+    ) -> NDArray[object_]: ...
+    @overload
+    def rsplit(
+        self: _CharArray[bytes_],
+        sep: S_co | None = None,
+        maxsplit: i_co | None = None,
+    ) -> NDArray[object_]: ...
+
+    @overload
+    def rstrip(
+        self: _CharArray[str_],
+        chars: U_co | None = None,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def rstrip(
+        self: _CharArray[bytes_],
+        chars: S_co | None = None,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def split(
+        self: _CharArray[str_],
+        sep: U_co | None = None,
+        maxsplit: i_co | None = None,
+    ) -> NDArray[object_]: ...
+    @overload
+    def split(
+        self: _CharArray[bytes_],
+        sep: S_co | None = None,
+        maxsplit: i_co | None = None,
+    ) -> NDArray[object_]: ...
+
+    def splitlines(self, keepends: b_co | None = None) -> NDArray[object_]: ...
+
+    @overload
+    def startswith(
+        self: _CharArray[str_],
+        prefix: U_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def startswith(
+        self: _CharArray[bytes_],
+        prefix: S_co,
+        start: i_co = 0,
+        end: i_co | None = None,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def strip(
+        self: _CharArray[str_],
+        chars: U_co | None = None,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def strip(
+        self: _CharArray[bytes_],
+        chars: S_co | None = None,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def translate(
+        self: _CharArray[str_],
+        table: U_co,
+        deletechars: U_co | None = None,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def translate(
+        self: _CharArray[bytes_],
+        table: S_co,
+        deletechars: S_co | None = None,
+    ) -> _CharArray[bytes_]: ...
+
+    def zfill(self, width: i_co) -> Self: ...
+    def capitalize(self) -> Self: ...
+    def title(self) -> Self: ...
+    def swapcase(self) -> Self: ...
+    def lower(self) -> Self: ...
+    def upper(self) -> Self: ...
+    def isalnum(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isalpha(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isdigit(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def islower(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isspace(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def istitle(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isupper(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isnumeric(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isdecimal(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+
+# Comparison
+@overload
+def equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def not_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def not_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def not_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def greater_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def greater_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def greater_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def less_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def less_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def less_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def greater(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def greater(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def greater(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def less(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def less(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def less(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def add(x1: U_co, x2: U_co) -> NDArray[np.str_]: ...
+@overload
+def add(x1: S_co, x2: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def add(x1: _StringDTypeSupportsArray, x2: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def add(x1: T_co, x2: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def multiply(a: U_co, i: i_co) -> NDArray[np.str_]: ...
+@overload
+def multiply(a: S_co, i: i_co) -> NDArray[np.bytes_]: ...
+@overload
+def multiply(a: _StringDTypeSupportsArray, i: i_co) -> _StringDTypeArray: ...
+@overload
+def multiply(a: T_co, i: i_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def mod(a: U_co, value: Any) -> NDArray[np.str_]: ...
+@overload
+def mod(a: S_co, value: Any) -> NDArray[np.bytes_]: ...
+@overload
+def mod(a: _StringDTypeSupportsArray, value: Any) -> _StringDTypeArray: ...
+@overload
+def mod(a: T_co, value: Any) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def capitalize(a: U_co) -> NDArray[str_]: ...
+@overload
+def capitalize(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def capitalize(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def capitalize(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def center(a: U_co, width: i_co, fillchar: U_co = " ") -> NDArray[str_]: ...
+@overload
+def center(a: S_co, width: i_co, fillchar: str | S_co = " ") -> NDArray[bytes_]: ...
+@overload
+def center(a: _StringDTypeSupportsArray, width: i_co, fillchar: str | _StringDTypeSupportsArray = " ") -> _StringDTypeArray: ...
+@overload
+def center(a: T_co, width: i_co, fillchar: T_co = " ") -> _StringDTypeOrUnicodeArray: ...
+
+def decode(
+    a: S_co,
+    encoding: str | None = None,
+    errors: str | None = None,
+) -> NDArray[str_]: ...
+def encode(
+    a: U_co | T_co,
+    encoding: str | None = None,
+    errors: str | None = None,
+) -> NDArray[bytes_]: ...
+
+@overload
+def expandtabs(a: U_co, tabsize: i_co = 8) -> NDArray[str_]: ...
+@overload
+def expandtabs(a: S_co, tabsize: i_co = 8) -> NDArray[bytes_]: ...
+@overload
+def expandtabs(a: _StringDTypeSupportsArray, tabsize: i_co = 8) -> _StringDTypeArray: ...
+@overload
+def expandtabs(a: T_co, tabsize: i_co = 8) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def join(sep: U_co, seq: U_co) -> NDArray[str_]: ...
+@overload
+def join(sep: S_co, seq: S_co) -> NDArray[bytes_]: ...
+@overload
+def join(sep: _StringDTypeSupportsArray, seq: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def join(sep: T_co, seq: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def ljust(a: U_co, width: i_co, fillchar: U_co = " ") -> NDArray[str_]: ...
+@overload
+def ljust(a: S_co, width: i_co, fillchar: str | S_co = " ") -> NDArray[bytes_]: ...
+@overload
+def ljust(a: _StringDTypeSupportsArray, width: i_co, fillchar: str | _StringDTypeSupportsArray = " ") -> _StringDTypeArray: ...
+@overload
+def ljust(a: T_co, width: i_co, fillchar: T_co = " ") -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def lower(a: U_co) -> NDArray[str_]: ...
+@overload
+def lower(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def lower(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def lower(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def lstrip(a: U_co, chars: U_co | None = None) -> NDArray[str_]: ...
+@overload
+def lstrip(a: S_co, chars: S_co | None = None) -> NDArray[bytes_]: ...
+@overload
+def lstrip(a: _StringDTypeSupportsArray, chars: _StringDTypeSupportsArray | None = None) -> _StringDTypeArray: ...
+@overload
+def lstrip(a: T_co, chars: T_co | None = None) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def partition(a: U_co, sep: U_co) -> NDArray[str_]: ...
+@overload
+def partition(a: S_co, sep: S_co) -> NDArray[bytes_]: ...
+@overload
+def partition(a: _StringDTypeSupportsArray, sep: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def partition(a: T_co, sep: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def replace(
+    a: U_co,
+    old: U_co,
+    new: U_co,
+    count: i_co | None = -1,
+) -> NDArray[str_]: ...
+@overload
+def replace(
+    a: S_co,
+    old: S_co,
+    new: S_co,
+    count: i_co | None = -1,
+) -> NDArray[bytes_]: ...
+@overload
+def replace(
+    a: _StringDTypeSupportsArray,
+    old: _StringDTypeSupportsArray,
+    new: _StringDTypeSupportsArray,
+    count: i_co = -1,
+) -> _StringDTypeArray: ...
+@overload
+def replace(
+    a: T_co,
+    old: T_co,
+    new: T_co,
+    count: i_co = -1,
+) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rjust(
+    a: U_co,
+    width: i_co,
+    fillchar: U_co = " ",
+) -> NDArray[str_]: ...
+@overload
+def rjust(
+    a: S_co,
+    width: i_co,
+    fillchar: str | S_co = " ",
+) -> NDArray[bytes_]: ...
+@overload
+def rjust(
+    a: _StringDTypeSupportsArray,
+    width: i_co,
+    fillchar: str | _StringDTypeSupportsArray = " ",
+) -> _StringDTypeArray: ...
+@overload
+def rjust(
+    a: T_co,
+    width: i_co,
+    fillchar: T_co = " ",
+) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rpartition(a: U_co, sep: U_co) -> NDArray[str_]: ...
+@overload
+def rpartition(a: S_co, sep: S_co) -> NDArray[bytes_]: ...
+@overload
+def rpartition(a: _StringDTypeSupportsArray, sep: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def rpartition(a: T_co, sep: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rsplit(
+    a: U_co,
+    sep: U_co | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+@overload
+def rsplit(
+    a: S_co,
+    sep: S_co | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+@overload
+def rsplit(
+    a: _StringDTypeSupportsArray,
+    sep: _StringDTypeSupportsArray | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+@overload
+def rsplit(
+    a: T_co,
+    sep: T_co | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+
+@overload
+def rstrip(a: U_co, chars: U_co | None = None) -> NDArray[str_]: ...
+@overload
+def rstrip(a: S_co, chars: S_co | None = None) -> NDArray[bytes_]: ...
+@overload
+def rstrip(a: _StringDTypeSupportsArray, chars: _StringDTypeSupportsArray | None = None) -> _StringDTypeArray: ...
+@overload
+def rstrip(a: T_co, chars: T_co | None = None) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def split(
+    a: U_co,
+    sep: U_co | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+@overload
+def split(
+    a: S_co,
+    sep: S_co | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+@overload
+def split(
+    a: _StringDTypeSupportsArray,
+    sep: _StringDTypeSupportsArray | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+@overload
+def split(
+    a: T_co,
+    sep: T_co | None = None,
+    maxsplit: i_co | None = None,
+) -> NDArray[object_]: ...
+
+def splitlines(a: UST_co, keepends: b_co | None = None) -> NDArray[np.object_]: ...
+
+@overload
+def strip(a: U_co, chars: U_co | None = None) -> NDArray[str_]: ...
+@overload
+def strip(a: S_co, chars: S_co | None = None) -> NDArray[bytes_]: ...
+@overload
+def strip(a: _StringDTypeSupportsArray, chars: _StringDTypeSupportsArray | None = None) -> _StringDTypeArray: ...
+@overload
+def strip(a: T_co, chars: T_co | None = None) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def swapcase(a: U_co) -> NDArray[str_]: ...
+@overload
+def swapcase(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def swapcase(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def swapcase(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def title(a: U_co) -> NDArray[str_]: ...
+@overload
+def title(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def title(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def title(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def translate(
+    a: U_co,
+    table: str,
+    deletechars: str | None = None,
+) -> NDArray[str_]: ...
+@overload
+def translate(
+    a: S_co,
+    table: str,
+    deletechars: str | None = None,
+) -> NDArray[bytes_]: ...
+@overload
+def translate(
+    a: _StringDTypeSupportsArray,
+    table: str,
+    deletechars: str | None = None,
+) -> _StringDTypeArray: ...
+@overload
+def translate(
+    a: T_co,
+    table: str,
+    deletechars: str | None = None,
+) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def upper(a: U_co) -> NDArray[str_]: ...
+@overload
+def upper(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def upper(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def upper(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def zfill(a: U_co, width: i_co) -> NDArray[str_]: ...
+@overload
+def zfill(a: S_co, width: i_co) -> NDArray[bytes_]: ...
+@overload
+def zfill(a: _StringDTypeSupportsArray, width: i_co) -> _StringDTypeArray: ...
+@overload
+def zfill(a: T_co, width: i_co) -> _StringDTypeOrUnicodeArray: ...
+
+# String information
+@overload
+def count(
+    a: U_co,
+    sub: U_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def count(
+    a: S_co,
+    sub: S_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def count(
+    a: T_co,
+    sub: T_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.int_]: ...
+
+@overload
+def endswith(
+    a: U_co,
+    suffix: U_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.bool]: ...
+@overload
+def endswith(
+    a: S_co,
+    suffix: S_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.bool]: ...
+@overload
+def endswith(
+    a: T_co,
+    suffix: T_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.bool]: ...
+
+@overload
+def find(
+    a: U_co,
+    sub: U_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def find(
+    a: S_co,
+    sub: S_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def find(
+    a: T_co,
+    sub: T_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.int_]: ...
+
+@overload
+def index(
+    a: U_co,
+    sub: U_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def index(
+    a: S_co,
+    sub: S_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def index(
+    a: T_co,
+    sub: T_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.int_]: ...
+
+def isalpha(a: UST_co) -> NDArray[np.bool]: ...
+def isalnum(a: UST_co) -> NDArray[np.bool]: ...
+def isdecimal(a: U_co | T_co) -> NDArray[np.bool]: ...
+def isdigit(a: UST_co) -> NDArray[np.bool]: ...
+def islower(a: UST_co) -> NDArray[np.bool]: ...
+def isnumeric(a: U_co | T_co) -> NDArray[np.bool]: ...
+def isspace(a: UST_co) -> NDArray[np.bool]: ...
+def istitle(a: UST_co) -> NDArray[np.bool]: ...
+def isupper(a: UST_co) -> NDArray[np.bool]: ...
+
+@overload
+def rfind(
+    a: U_co,
+    sub: U_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def rfind(
+    a: S_co,
+    sub: S_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def rfind(
+    a: T_co,
+    sub: T_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.int_]: ...
+
+@overload
+def rindex(
+    a: U_co,
+    sub: U_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def rindex(
+    a: S_co,
+    sub: S_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[int_]: ...
+@overload
+def rindex(
+    a: T_co,
+    sub: T_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.int_]: ...
+
+@overload
+def startswith(
+    a: U_co,
+    prefix: U_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.bool]: ...
+@overload
+def startswith(
+    a: S_co,
+    prefix: S_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.bool]: ...
+@overload
+def startswith(
+    a: T_co,
+    prefix: T_co,
+    start: i_co = 0,
+    end: i_co | None = None,
+) -> NDArray[np.bool]: ...
+
+def str_len(A: UST_co) -> NDArray[int_]: ...
+
+# Overload 1 and 2: str- or bytes-based array-likes
+# overload 3 and 4: arbitrary object with unicode=False  (-> bytes_)
+# overload 5 and 6: arbitrary object with unicode=True  (-> str_)
+# overload 7: arbitrary object with unicode=None (default)  (-> str_ | bytes_)
+@overload
+def array(
+    obj: U_co,
+    itemsize: int | None = None,
+    copy: bool = True,
+    unicode: L[True] | None = None,
+    order: _OrderKACF = None,
+) -> _CharArray[str_]: ...
+@overload
+def array(
+    obj: S_co,
+    itemsize: int | None = None,
+    copy: bool = True,
+    unicode: L[False] | None = None,
+    order: _OrderKACF = None,
+) -> _CharArray[bytes_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None,
+    copy: bool,
+    unicode: L[False],
+    order: _OrderKACF = None,
+) -> _CharArray[bytes_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None = None,
+    copy: bool = True,
+    *,
+    unicode: L[False],
+    order: _OrderKACF = None,
+) -> _CharArray[bytes_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None,
+    copy: bool,
+    unicode: L[True],
+    order: _OrderKACF = None,
+) -> _CharArray[str_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None = None,
+    copy: bool = True,
+    *,
+    unicode: L[True],
+    order: _OrderKACF = None,
+) -> _CharArray[str_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None = None,
+    copy: bool = True,
+    unicode: bool | None = None,
+    order: _OrderKACF = None,
+) -> _CharArray[str_] | _CharArray[bytes_]: ...
+
+@overload
+def asarray(
+    obj: U_co,
+    itemsize: int | None = None,
+    unicode: L[True] | None = None,
+    order: _OrderKACF = None,
+) -> _CharArray[str_]: ...
+@overload
+def asarray(
+    obj: S_co,
+    itemsize: int | None = None,
+    unicode: L[False] | None = None,
+    order: _OrderKACF = None,
+) -> _CharArray[bytes_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None,
+    unicode: L[False],
+    order: _OrderKACF = None,
+) -> _CharArray[bytes_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None = None,
+    *,
+    unicode: L[False],
+    order: _OrderKACF = None,
+) -> _CharArray[bytes_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None,
+    unicode: L[True],
+    order: _OrderKACF = None,
+) -> _CharArray[str_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None = None,
+    *,
+    unicode: L[True],
+    order: _OrderKACF = None,
+) -> _CharArray[str_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None = None,
+    unicode: bool | None = None,
+    order: _OrderKACF = None,
+) -> _CharArray[str_] | _CharArray[bytes_]: ...

python/user_packages/Python313/site-packages/numpy/_core/einsumfunc.py

@@ -0,0 +1,1650 @@
+"""
+Implementation of optimized einsum.
+
+"""
+import functools
+import itertools
+import operator
+
+from numpy._core.multiarray import c_einsum, matmul
+from numpy._core.numeric import asanyarray, reshape
+from numpy._core.overrides import array_function_dispatch
+from numpy._core.umath import multiply
+
+__all__ = ['einsum', 'einsum_path']
+
+# importing string for string.ascii_letters would be too slow
+# the first import before caching has been measured to take 800 µs (#23777)
+# imports begin with uppercase to mimic ASCII values to avoid sorting issues
+einsum_symbols = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'
+einsum_symbols_set = set(einsum_symbols)
+
+
+def _flop_count(idx_contraction, inner, num_terms, size_dictionary):
+    """
+    Computes the number of FLOPS in the contraction.
+
+    Parameters
+    ----------
+    idx_contraction : iterable
+        The indices involved in the contraction
+    inner : bool
+        Does this contraction require an inner product?
+    num_terms : int
+        The number of terms in a contraction
+    size_dictionary : dict
+        The size of each of the indices in idx_contraction
+
+    Returns
+    -------
+    flop_count : int
+        The total number of FLOPS required for the contraction.
+
+    Examples
+    --------
+
+    >>> _flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5})
+    30
+
+    >>> _flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5})
+    60
+
+    """
+
+    overall_size = _compute_size_by_dict(idx_contraction, size_dictionary)
+    op_factor = max(1, num_terms - 1)
+    if inner:
+        op_factor += 1
+
+    return overall_size * op_factor
+
+def _compute_size_by_dict(indices, idx_dict):
+    """
+    Computes the product of the elements in indices based on the dictionary
+    idx_dict.
+
+    Parameters
+    ----------
+    indices : iterable
+        Indices to base the product on.
+    idx_dict : dictionary
+        Dictionary of index sizes
+
+    Returns
+    -------
+    ret : int
+        The resulting product.
+
+    Examples
+    --------
+    >>> _compute_size_by_dict('abbc', {'a': 2, 'b':3, 'c':5})
+    90
+
+    """
+    ret = 1
+    for i in indices:
+        ret *= idx_dict[i]
+    return ret
+
+
+def _find_contraction(positions, input_sets, output_set):
+    """
+    Finds the contraction for a given set of input and output sets.
+
+    Parameters
+    ----------
+    positions : iterable
+        Integer positions of terms used in the contraction.
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+
+    Returns
+    -------
+    new_result : set
+        The indices of the resulting contraction
+    remaining : list
+        List of sets that have not been contracted, the new set is appended to
+        the end of this list
+    idx_removed : set
+        Indices removed from the entire contraction
+    idx_contraction : set
+        The indices used in the current contraction
+
+    Examples
+    --------
+
+    # A simple dot product test case
+    >>> pos = (0, 1)
+    >>> isets = [set('ab'), set('bc')]
+    >>> oset = set('ac')
+    >>> _find_contraction(pos, isets, oset)
+    ({'a', 'c'}, [{'a', 'c'}], {'b'}, {'a', 'b', 'c'})
+
+    # A more complex case with additional terms in the contraction
+    >>> pos = (0, 2)
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set('ac')
+    >>> _find_contraction(pos, isets, oset)
+    ({'a', 'c'}, [{'a', 'c'}, {'a', 'c'}], {'b', 'd'}, {'a', 'b', 'c', 'd'})
+    """
+
+    idx_contract = set()
+    idx_remain = output_set.copy()
+    remaining = []
+    for ind, value in enumerate(input_sets):
+        if ind in positions:
+            idx_contract |= value
+        else:
+            remaining.append(value)
+            idx_remain |= value
+
+    new_result = idx_remain & idx_contract
+    idx_removed = (idx_contract - new_result)
+    remaining.append(new_result)
+
+    return (new_result, remaining, idx_removed, idx_contract)
+
+
+def _optimal_path(input_sets, output_set, idx_dict, memory_limit):
+    """
+    Computes all possible pair contractions, sieves the results based
+    on ``memory_limit`` and returns the lowest cost path. This algorithm
+    scales factorial with respect to the elements in the list ``input_sets``.
+
+    Parameters
+    ----------
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+    idx_dict : dictionary
+        Dictionary of index sizes
+    memory_limit : int
+        The maximum number of elements in a temporary array
+
+    Returns
+    -------
+    path : list
+        The optimal contraction order within the memory limit constraint.
+
+    Examples
+    --------
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set()
+    >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    >>> _optimal_path(isets, oset, idx_sizes, 5000)
+    [(0, 2), (0, 1)]
+    """
+
+    full_results = [(0, [], input_sets)]
+    for iteration in range(len(input_sets) - 1):
+        iter_results = []
+
+        # Compute all unique pairs
+        for curr in full_results:
+            cost, positions, remaining = curr
+            for con in itertools.combinations(
+                range(len(input_sets) - iteration), 2
+            ):
+
+                # Find the contraction
+                cont = _find_contraction(con, remaining, output_set)
+                new_result, new_input_sets, idx_removed, idx_contract = cont
+
+                # Sieve the results based on memory_limit
+                new_size = _compute_size_by_dict(new_result, idx_dict)
+                if new_size > memory_limit:
+                    continue
+
+                # Build (total_cost, positions, indices_remaining)
+                total_cost = cost + _flop_count(
+                    idx_contract, idx_removed, len(con), idx_dict
+                )
+                new_pos = positions + [con]
+                iter_results.append((total_cost, new_pos, new_input_sets))
+
+        # Update combinatorial list, if we did not find anything return best
+        # path + remaining contractions
+        if iter_results:
+            full_results = iter_results
+        else:
+            path = min(full_results, key=lambda x: x[0])[1]
+            path += [tuple(range(len(input_sets) - iteration))]
+            return path
+
+    # If we have not found anything return single einsum contraction
+    if len(full_results) == 0:
+        return [tuple(range(len(input_sets)))]
+
+    path = min(full_results, key=lambda x: x[0])[1]
+    return path
+
+def _parse_possible_contraction(
+        positions, input_sets, output_set, idx_dict,
+        memory_limit, path_cost, naive_cost
+    ):
+    """Compute the cost (removed size + flops) and resultant indices for
+    performing the contraction specified by ``positions``.
+
+    Parameters
+    ----------
+    positions : tuple of int
+        The locations of the proposed tensors to contract.
+    input_sets : list of sets
+        The indices found on each tensors.
+    output_set : set
+        The output indices of the expression.
+    idx_dict : dict
+        Mapping of each index to its size.
+    memory_limit : int
+        The total allowed size for an intermediary tensor.
+    path_cost : int
+        The contraction cost so far.
+    naive_cost : int
+        The cost of the unoptimized expression.
+
+    Returns
+    -------
+    cost : (int, int)
+        A tuple containing the size of any indices removed, and the flop cost.
+    positions : tuple of int
+        The locations of the proposed tensors to contract.
+    new_input_sets : list of sets
+        The resulting new list of indices if this proposed contraction
+        is performed.
+
+    """
+
+    # Find the contraction
+    contract = _find_contraction(positions, input_sets, output_set)
+    idx_result, new_input_sets, idx_removed, idx_contract = contract
+
+    # Sieve the results based on memory_limit
+    new_size = _compute_size_by_dict(idx_result, idx_dict)
+    if new_size > memory_limit:
+        return None
+
+    # Build sort tuple
+    old_sizes = (
+        _compute_size_by_dict(input_sets[p], idx_dict) for p in positions
+    )
+    removed_size = sum(old_sizes) - new_size
+
+    # NB: removed_size used to be just the size of any removed indices i.e.:
+    #     helpers.compute_size_by_dict(idx_removed, idx_dict)
+    cost = _flop_count(idx_contract, idx_removed, len(positions), idx_dict)
+    sort = (-removed_size, cost)
+
+    # Sieve based on total cost as well
+    if (path_cost + cost) > naive_cost:
+        return None
+
+    # Add contraction to possible choices
+    return [sort, positions, new_input_sets]
+
+
+def _update_other_results(results, best):
+    """Update the positions and provisional input_sets of ``results``
+    based on performing the contraction result ``best``. Remove any
+    involving the tensors contracted.
+
+    Parameters
+    ----------
+    results : list
+        List of contraction results produced by
+        ``_parse_possible_contraction``.
+    best : list
+        The best contraction of ``results`` i.e. the one that
+        will be performed.
+
+    Returns
+    -------
+    mod_results : list
+        The list of modified results, updated with outcome of
+        ``best`` contraction.
+    """
+
+    best_con = best[1]
+    bx, by = best_con
+    mod_results = []
+
+    for cost, (x, y), con_sets in results:
+
+        # Ignore results involving tensors just contracted
+        if x in best_con or y in best_con:
+            continue
+
+        # Update the input_sets
+        del con_sets[by - int(by > x) - int(by > y)]
+        del con_sets[bx - int(bx > x) - int(bx > y)]
+        con_sets.insert(-1, best[2][-1])
+
+        # Update the position indices
+        mod_con = x - int(x > bx) - int(x > by), y - int(y > bx) - int(y > by)
+        mod_results.append((cost, mod_con, con_sets))
+
+    return mod_results
+
+def _greedy_path(input_sets, output_set, idx_dict, memory_limit):
+    """
+    Finds the path by contracting the best pair until the input list is
+    exhausted. The best pair is found by minimizing the tuple
+    ``(-prod(indices_removed), cost)``.  What this amounts to is prioritizing
+    matrix multiplication or inner product operations, then Hadamard like
+    operations, and finally outer operations. Outer products are limited by
+    ``memory_limit``. This algorithm scales cubically with respect to the
+    number of elements in the list ``input_sets``.
+
+    Parameters
+    ----------
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+    idx_dict : dictionary
+        Dictionary of index sizes
+    memory_limit : int
+        The maximum number of elements in a temporary array
+
+    Returns
+    -------
+    path : list
+        The greedy contraction order within the memory limit constraint.
+
+    Examples
+    --------
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set()
+    >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    >>> _greedy_path(isets, oset, idx_sizes, 5000)
+    [(0, 2), (0, 1)]
+    """
+
+    # Handle trivial cases that leaked through
+    if len(input_sets) == 1:
+        return [(0,)]
+    elif len(input_sets) == 2:
+        return [(0, 1)]
+
+    # Build up a naive cost
+    contract = _find_contraction(
+        range(len(input_sets)), input_sets, output_set
+    )
+    idx_result, new_input_sets, idx_removed, idx_contract = contract
+    naive_cost = _flop_count(
+        idx_contract, idx_removed, len(input_sets), idx_dict
+    )
+
+    # Initially iterate over all pairs
+    comb_iter = itertools.combinations(range(len(input_sets)), 2)
+    known_contractions = []
+
+    path_cost = 0
+    path = []
+
+    for iteration in range(len(input_sets) - 1):
+
+        # Iterate over all pairs on the first step, only previously
+        # found pairs on subsequent steps
+        for positions in comb_iter:
+
+            # Always initially ignore outer products
+            if input_sets[positions[0]].isdisjoint(input_sets[positions[1]]):
+                continue
+
+            result = _parse_possible_contraction(
+                positions, input_sets, output_set, idx_dict,
+                memory_limit, path_cost, naive_cost
+            )
+            if result is not None:
+                known_contractions.append(result)
+
+        # If we do not have a inner contraction, rescan pairs
+        # including outer products
+        if len(known_contractions) == 0:
+
+            # Then check the outer products
+            for positions in itertools.combinations(
+                range(len(input_sets)), 2
+            ):
+                result = _parse_possible_contraction(
+                    positions, input_sets, output_set, idx_dict,
+                    memory_limit, path_cost, naive_cost
+                )
+                if result is not None:
+                    known_contractions.append(result)
+
+            # If we still did not find any remaining contractions,
+            # default back to einsum like behavior
+            if len(known_contractions) == 0:
+                path.append(tuple(range(len(input_sets))))
+                break
+
+        # Sort based on first index
+        best = min(known_contractions, key=lambda x: x[0])
+
+        # Now propagate as many unused contractions as possible
+        # to the next iteration
+        known_contractions = _update_other_results(known_contractions, best)
+
+        # Next iteration only compute contractions with the new tensor
+        # All other contractions have been accounted for
+        input_sets = best[2]
+        new_tensor_pos = len(input_sets) - 1
+        comb_iter = ((i, new_tensor_pos) for i in range(new_tensor_pos))
+
+        # Update path and total cost
+        path.append(best[1])
+        path_cost += best[0][1]
+
+    return path
+
+
+def _parse_einsum_input(operands):
+    """
+    A reproduction of einsum c side einsum parsing in python.
+
+    Returns
+    -------
+    input_strings : str
+        Parsed input strings
+    output_string : str
+        Parsed output string
+    operands : list of array_like
+        The operands to use in the numpy contraction
+
+    Examples
+    --------
+    The operand list is simplified to reduce printing:
+
+    >>> np.random.seed(123)
+    >>> a = np.random.rand(4, 4)
+    >>> b = np.random.rand(4, 4, 4)
+    >>> _parse_einsum_input(('...a,...a->...', a, b))
+    ('za,xza', 'xz', [a, b]) # may vary
+
+    >>> _parse_einsum_input((a, [Ellipsis, 0], b, [Ellipsis, 0]))
+    ('za,xza', 'xz', [a, b]) # may vary
+    """
+
+    if len(operands) == 0:
+        raise ValueError("No input operands")
+
+    if isinstance(operands[0], str):
+        subscripts = operands[0].replace(" ", "")
+        operands = [asanyarray(v) for v in operands[1:]]
+
+        # Ensure all characters are valid
+        for s in subscripts:
+            if s in '.,->':
+                continue
+            if s not in einsum_symbols:
+                raise ValueError(f"Character {s} is not a valid symbol.")
+
+    else:
+        tmp_operands = list(operands)
+        operand_list = []
+        subscript_list = []
+        for p in range(len(operands) // 2):
+            operand_list.append(tmp_operands.pop(0))
+            subscript_list.append(tmp_operands.pop(0))
+
+        output_list = tmp_operands[-1] if len(tmp_operands) else None
+        operands = [asanyarray(v) for v in operand_list]
+        subscripts = ""
+        last = len(subscript_list) - 1
+        for num, sub in enumerate(subscript_list):
+            for s in sub:
+                if s is Ellipsis:
+                    subscripts += "..."
+                else:
+                    try:
+                        s = operator.index(s)
+                    except TypeError as e:
+                        raise TypeError(
+                            "For this input type lists must contain "
+                            "either int or Ellipsis"
+                        ) from e
+                    subscripts += einsum_symbols[s]
+            if num != last:
+                subscripts += ","
+
+        if output_list is not None:
+            subscripts += "->"
+            for s in output_list:
+                if s is Ellipsis:
+                    subscripts += "..."
+                else:
+                    try:
+                        s = operator.index(s)
+                    except TypeError as e:
+                        raise TypeError(
+                            "For this input type lists must contain "
+                            "either int or Ellipsis"
+                        ) from e
+                    subscripts += einsum_symbols[s]
+    # Check for proper "->"
+    if ("-" in subscripts) or (">" in subscripts):
+        invalid = (subscripts.count("-") > 1) or (subscripts.count(">") > 1)
+        if invalid or (subscripts.count("->") != 1):
+            raise ValueError("Subscripts can only contain one '->'.")
+
+    # Parse ellipses
+    if "." in subscripts:
+        used = subscripts.replace(".", "").replace(",", "").replace("->", "")
+        unused = list(einsum_symbols_set - set(used))
+        ellipse_inds = "".join(unused)
+        longest = 0
+
+        if "->" in subscripts:
+            input_tmp, output_sub = subscripts.split("->")
+            split_subscripts = input_tmp.split(",")
+            out_sub = True
+        else:
+            split_subscripts = subscripts.split(',')
+            out_sub = False
+
+        for num, sub in enumerate(split_subscripts):
+            if "." in sub:
+                if (sub.count(".") != 3) or (sub.count("...") != 1):
+                    raise ValueError("Invalid Ellipses.")
+
+                # Take into account numerical values
+                if operands[num].shape == ():
+                    ellipse_count = 0
+                else:
+                    ellipse_count = max(operands[num].ndim, 1)
+                    ellipse_count -= (len(sub) - 3)
+
+                if ellipse_count > longest:
+                    longest = ellipse_count
+
+                if ellipse_count < 0:
+                    raise ValueError("Ellipses lengths do not match.")
+                elif ellipse_count == 0:
+                    split_subscripts[num] = sub.replace('...', '')
+                else:
+                    rep_inds = ellipse_inds[-ellipse_count:]
+                    split_subscripts[num] = sub.replace('...', rep_inds)
+
+        subscripts = ",".join(split_subscripts)
+        if longest == 0:
+            out_ellipse = ""
+        else:
+            out_ellipse = ellipse_inds[-longest:]
+
+        if out_sub:
+            subscripts += "->" + output_sub.replace("...", out_ellipse)
+        else:
+            # Special care for outputless ellipses
+            output_subscript = ""
+            tmp_subscripts = subscripts.replace(",", "")
+            for s in sorted(set(tmp_subscripts)):
+                if s not in (einsum_symbols):
+                    raise ValueError(f"Character {s} is not a valid symbol.")
+                if tmp_subscripts.count(s) == 1:
+                    output_subscript += s
+            normal_inds = ''.join(sorted(set(output_subscript) -
+                                         set(out_ellipse)))
+
+            subscripts += "->" + out_ellipse + normal_inds
+
+    # Build output string if does not exist
+    if "->" in subscripts:
+        input_subscripts, output_subscript = subscripts.split("->")
+    else:
+        input_subscripts = subscripts
+        # Build output subscripts
+        tmp_subscripts = subscripts.replace(",", "")
+        output_subscript = ""
+        for s in sorted(set(tmp_subscripts)):
+            if s not in einsum_symbols:
+                raise ValueError(f"Character {s} is not a valid symbol.")
+            if tmp_subscripts.count(s) == 1:
+                output_subscript += s
+
+    # Make sure output subscripts are in the input
+    for char in output_subscript:
+        if output_subscript.count(char) != 1:
+            raise ValueError("Output character %s appeared more than once in "
+                             "the output." % char)
+        if char not in input_subscripts:
+            raise ValueError(f"Output character {char} did not appear in the input")
+
+    # Make sure number operands is equivalent to the number of terms
+    if len(input_subscripts.split(',')) != len(operands):
+        raise ValueError("Number of einsum subscripts must be equal to the "
+                         "number of operands.")
+
+    return (input_subscripts, output_subscript, operands)
+
+
+def _einsum_path_dispatcher(*operands, optimize=None, einsum_call=None):
+    # NOTE: technically, we should only dispatch on array-like arguments, not
+    # subscripts (given as strings). But separating operands into
+    # arrays/subscripts is a little tricky/slow (given einsum's two supported
+    # signatures), so as a practical shortcut we dispatch on everything.
+    # Strings will be ignored for dispatching since they don't define
+    # __array_function__.
+    return operands
+
+
+@array_function_dispatch(_einsum_path_dispatcher, module='numpy')
+def einsum_path(*operands, optimize='greedy', einsum_call=False):
+    """
+    einsum_path(subscripts, *operands, optimize='greedy')
+
+    Evaluates the lowest cost contraction order for an einsum expression by
+    considering the creation of intermediate arrays.
+
+    Parameters
+    ----------
+    subscripts : str
+        Specifies the subscripts for summation.
+    *operands : list of array_like
+        These are the arrays for the operation.
+    optimize : {bool, list, tuple, 'greedy', 'optimal'}
+        Choose the type of path. If a tuple is provided, the second argument is
+        assumed to be the maximum intermediate size created. If only a single
+        argument is provided the largest input or output array size is used
+        as a maximum intermediate size.
+
+        * if a list is given that starts with ``einsum_path``, uses this as the
+          contraction path
+        * if False no optimization is taken
+        * if True defaults to the 'greedy' algorithm
+        * 'optimal' An algorithm that combinatorially explores all possible
+          ways of contracting the listed tensors and chooses the least costly
+          path. Scales exponentially with the number of terms in the
+          contraction.
+        * 'greedy' An algorithm that chooses the best pair contraction
+          at each step. Effectively, this algorithm searches the largest inner,
+          Hadamard, and then outer products at each step. Scales cubically with
+          the number of terms in the contraction. Equivalent to the 'optimal'
+          path for most contractions.
+
+        Default is 'greedy'.
+
+    Returns
+    -------
+    path : list of tuples
+        A list representation of the einsum path.
+    string_repr : str
+        A printable representation of the einsum path.
+
+    Notes
+    -----
+    The resulting path indicates which terms of the input contraction should be
+    contracted first, the result of this contraction is then appended to the
+    end of the contraction list. This list can then be iterated over until all
+    intermediate contractions are complete.
+
+    See Also
+    --------
+    einsum, linalg.multi_dot
+
+    Examples
+    --------
+
+    We can begin with a chain dot example. In this case, it is optimal to
+    contract the ``b`` and ``c`` tensors first as represented by the first
+    element of the path ``(1, 2)``. The resulting tensor is added to the end
+    of the contraction and the remaining contraction ``(0, 1)`` is then
+    completed.
+
+    >>> np.random.seed(123)
+    >>> a = np.random.rand(2, 2)
+    >>> b = np.random.rand(2, 5)
+    >>> c = np.random.rand(5, 2)
+    >>> path_info = np.einsum_path('ij,jk,kl->il', a, b, c, optimize='greedy')
+    >>> print(path_info[0])
+    ['einsum_path', (1, 2), (0, 1)]
+    >>> print(path_info[1])
+      Complete contraction:  ij,jk,kl->il # may vary
+             Naive scaling:  4
+         Optimized scaling:  3
+          Naive FLOP count:  1.600e+02
+      Optimized FLOP count:  5.600e+01
+       Theoretical speedup:  2.857
+      Largest intermediate:  4.000e+00 elements
+    -------------------------------------------------------------------------
+    scaling                  current                                remaining
+    -------------------------------------------------------------------------
+       3                   kl,jk->jl                                ij,jl->il
+       3                   jl,ij->il                                   il->il
+
+
+    A more complex index transformation example.
+
+    >>> I = np.random.rand(10, 10, 10, 10)
+    >>> C = np.random.rand(10, 10)
+    >>> path_info = np.einsum_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C,
+    ...                            optimize='greedy')
+
+    >>> print(path_info[0])
+    ['einsum_path', (0, 2), (0, 3), (0, 2), (0, 1)]
+    >>> print(path_info[1])
+      Complete contraction:  ea,fb,abcd,gc,hd->efgh # may vary
+             Naive scaling:  8
+         Optimized scaling:  5
+          Naive FLOP count:  8.000e+08
+      Optimized FLOP count:  8.000e+05
+       Theoretical speedup:  1000.000
+      Largest intermediate:  1.000e+04 elements
+    --------------------------------------------------------------------------
+    scaling                  current                                remaining
+    --------------------------------------------------------------------------
+       5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
+       5               bcde,fb->cdef                         gc,hd,cdef->efgh
+       5               cdef,gc->defg                            hd,defg->efgh
+       5               defg,hd->efgh                               efgh->efgh
+    """
+
+    # Figure out what the path really is
+    path_type = optimize
+    if path_type is True:
+        path_type = 'greedy'
+    if path_type is None:
+        path_type = False
+
+    explicit_einsum_path = False
+    memory_limit = None
+
+    # No optimization or a named path algorithm
+    if (path_type is False) or isinstance(path_type, str):
+        pass
+
+    # Given an explicit path
+    elif len(path_type) and (path_type[0] == 'einsum_path'):
+        explicit_einsum_path = True
+
+    # Path tuple with memory limit
+    elif ((len(path_type) == 2) and isinstance(path_type[0], str) and
+            isinstance(path_type[1], (int, float))):
+        memory_limit = int(path_type[1])
+        path_type = path_type[0]
+
+    else:
+        raise TypeError(f"Did not understand the path: {str(path_type)}")
+
+    # Hidden option, only einsum should call this
+    einsum_call_arg = einsum_call
+
+    # Python side parsing
+    input_subscripts, output_subscript, operands = (
+        _parse_einsum_input(operands)
+    )
+
+    # Build a few useful list and sets
+    input_list = input_subscripts.split(',')
+    num_inputs = len(input_list)
+    input_sets = [set(x) for x in input_list]
+    output_set = set(output_subscript)
+    indices = set(input_subscripts.replace(',', ''))
+    num_indices = len(indices)
+
+    # Get length of each unique dimension and ensure all dimensions are correct
+    dimension_dict = {}
+    for tnum, term in enumerate(input_list):
+        sh = operands[tnum].shape
+        if len(sh) != len(term):
+            raise ValueError("Einstein sum subscript %s does not contain the "
+                             "correct number of indices for operand %d."
+                             % (input_subscripts[tnum], tnum))
+        for cnum, char in enumerate(term):
+            dim = sh[cnum]
+
+            if char in dimension_dict.keys():
+                # For broadcasting cases we always want the largest dim size
+                if dimension_dict[char] == 1:
+                    dimension_dict[char] = dim
+                elif dim not in (1, dimension_dict[char]):
+                    raise ValueError("Size of label '%s' for operand %d (%d) "
+                                     "does not match previous terms (%d)."
+                                     % (char, tnum, dimension_dict[char], dim))
+            else:
+                dimension_dict[char] = dim
+
+    # Compute size of each input array plus the output array
+    size_list = [_compute_size_by_dict(term, dimension_dict)
+                 for term in input_list + [output_subscript]]
+    max_size = max(size_list)
+
+    if memory_limit is None:
+        memory_arg = max_size
+    else:
+        memory_arg = memory_limit
+
+    # Compute the path
+    if explicit_einsum_path:
+        path = path_type[1:]
+    elif (
+        (path_type is False)
+        or (num_inputs in [1, 2])
+        or (indices == output_set)
+    ):
+        # Nothing to be optimized, leave it to einsum
+        path = [tuple(range(num_inputs))]
+    elif path_type == "greedy":
+        path = _greedy_path(
+            input_sets, output_set, dimension_dict, memory_arg
+        )
+    elif path_type == "optimal":
+        path = _optimal_path(
+            input_sets, output_set, dimension_dict, memory_arg
+        )
+    else:
+        raise KeyError("Path name %s not found", path_type)
+
+    cost_list, scale_list, size_list, contraction_list = [], [], [], []
+
+    # Build contraction tuple (positions, gemm, einsum_str, remaining)
+    for cnum, contract_inds in enumerate(path):
+        # Make sure we remove inds from right to left
+        contract_inds = tuple(sorted(contract_inds, reverse=True))
+
+        contract = _find_contraction(contract_inds, input_sets, output_set)
+        out_inds, input_sets, idx_removed, idx_contract = contract
+
+        if not einsum_call_arg:
+            # these are only needed for printing info
+            cost = _flop_count(
+                idx_contract, idx_removed, len(contract_inds), dimension_dict
+            )
+            cost_list.append(cost)
+            scale_list.append(len(idx_contract))
+            size_list.append(_compute_size_by_dict(out_inds, dimension_dict))
+
+        tmp_inputs = []
+        for x in contract_inds:
+            tmp_inputs.append(input_list.pop(x))
+
+        # Last contraction
+        if (cnum - len(path)) == -1:
+            idx_result = output_subscript
+        else:
+            sort_result = [(dimension_dict[ind], ind) for ind in out_inds]
+            idx_result = "".join([x[1] for x in sorted(sort_result)])
+
+        input_list.append(idx_result)
+        einsum_str = ",".join(tmp_inputs) + "->" + idx_result
+
+        contraction = (contract_inds, einsum_str, input_list[:])
+        contraction_list.append(contraction)
+
+    if len(input_list) != 1:
+        # Explicit "einsum_path" is usually trusted, but we detect this kind of
+        # mistake in order to prevent from returning an intermediate value.
+        raise RuntimeError(
+            f"Invalid einsum_path is specified: {len(input_list) - 1} more "
+            "operands has to be contracted.")
+
+    if einsum_call_arg:
+        return (operands, contraction_list)
+
+    # Return the path along with a nice string representation
+    overall_contraction = input_subscripts + "->" + output_subscript
+    header = ("scaling", "current", "remaining")
+
+    # Compute naive cost
+    # This isn't quite right, need to look into exactly how einsum does this
+    inner_product = (
+        sum(len(set(x)) for x in input_subscripts.split(',')) - num_indices
+    ) > 0
+    naive_cost = _flop_count(
+        indices, inner_product, num_inputs, dimension_dict
+    )
+
+    opt_cost = sum(cost_list) + 1
+    speedup = naive_cost / opt_cost
+    max_i = max(size_list)
+
+    path_print = f"  Complete contraction:  {overall_contraction}\n"
+    path_print += f"         Naive scaling:  {num_indices}\n"
+    path_print += "     Optimized scaling:  %d\n" % max(scale_list)
+    path_print += f"      Naive FLOP count:  {naive_cost:.3e}\n"
+    path_print += f"  Optimized FLOP count:  {opt_cost:.3e}\n"
+    path_print += f"   Theoretical speedup:  {speedup:3.3f}\n"
+    path_print += f"  Largest intermediate:  {max_i:.3e} elements\n"
+    path_print += "-" * 74 + "\n"
+    path_print += "%6s %24s %40s\n" % header
+    path_print += "-" * 74
+
+    for n, contraction in enumerate(contraction_list):
+        _, einsum_str, remaining = contraction
+        remaining_str = ",".join(remaining) + "->" + output_subscript
+        path_run = (scale_list[n], einsum_str, remaining_str)
+        path_print += "\n%4d    %24s %40s" % path_run
+
+    path = ['einsum_path'] + path
+    return (path, path_print)
+
+
+def _parse_eq_to_pure_multiplication(a_term, shape_a, b_term, shape_b, out):
+    """If there are no contracted indices, then we can directly transpose and
+    insert singleton dimensions into ``a`` and ``b`` such that (broadcast)
+    elementwise multiplication performs the einsum.
+
+    No need to cache this as it is within the cached
+    ``_parse_eq_to_batch_matmul``.
+
+    """
+    desired_a = ""
+    desired_b = ""
+    new_shape_a = []
+    new_shape_b = []
+    for ix in out:
+        if ix in a_term:
+            desired_a += ix
+            new_shape_a.append(shape_a[a_term.index(ix)])
+        else:
+            new_shape_a.append(1)
+        if ix in b_term:
+            desired_b += ix
+            new_shape_b.append(shape_b[b_term.index(ix)])
+        else:
+            new_shape_b.append(1)
+
+    if desired_a != a_term:
+        eq_a = f"{a_term}->{desired_a}"
+    else:
+        eq_a = None
+    if desired_b != b_term:
+        eq_b = f"{b_term}->{desired_b}"
+    else:
+        eq_b = None
+
+    return (
+        eq_a,
+        eq_b,
+        new_shape_a,
+        new_shape_b,
+        None,  # new_shape_ab, not needed since not fusing
+        None,  # perm_ab, not needed as we transpose a and b first
+        True,  # pure_multiplication=True
+    )
+
+
+@functools.lru_cache(2**12)
+def _parse_eq_to_batch_matmul(eq, shape_a, shape_b):
+    """Cached parsing of a two term einsum equation into the necessary
+    sequence of arguments for contracttion via batched matrix multiplication.
+    The steps we need to specify are:
+
+        1. Remove repeated and trivial indices from the left and right terms,
+           and transpose them, done as a single einsum.
+        2. Fuse the remaining indices so we have two 3D tensors.
+        3. Perform the batched matrix multiplication.
+        4. Unfuse the output to get the desired final index order.
+
+    """
+    lhs, out = eq.split("->")
+    a_term, b_term = lhs.split(",")
+
+    if len(a_term) != len(shape_a):
+        raise ValueError(f"Term '{a_term}' does not match shape {shape_a}.")
+    if len(b_term) != len(shape_b):
+        raise ValueError(f"Term '{b_term}' does not match shape {shape_b}.")
+
+    sizes = {}
+    singletons = set()
+
+    # parse left term to unique indices with size > 1
+    left = {}
+    for ix, d in zip(a_term, shape_a):
+        if d == 1:
+            # everything (including broadcasting) works nicely if simply ignore
+            # such dimensions, but we do need to track if they appear in output
+            # and thus should be reintroduced later
+            singletons.add(ix)
+            continue
+        if sizes.setdefault(ix, d) != d:
+            # set and check size
+            raise ValueError(
+                f"Index {ix} has mismatched sizes {sizes[ix]} and {d}."
+            )
+        left[ix] = True
+
+    # parse right term to unique indices with size > 1
+    right = {}
+    for ix, d in zip(b_term, shape_b):
+        # broadcast indices (size 1 on one input and size != 1
+        # on the other) should not be treated as singletons
+        if d == 1:
+            if ix not in left:
+                singletons.add(ix)
+            continue
+        singletons.discard(ix)
+
+        if sizes.setdefault(ix, d) != d:
+            # set and check size
+            raise ValueError(
+                f"Index {ix} has mismatched sizes {sizes[ix]} and {d}."
+            )
+        right[ix] = True
+
+    # now we classify the unique size > 1 indices only
+    bat_inds = []  # appears on A, B, O
+    con_inds = []  # appears on A, B, .
+    a_keep = []  # appears on A, ., O
+    b_keep = []  # appears on ., B, O
+    # other indices (appearing on A or B only) will
+    # be summed or traced out prior to the matmul
+    for ix in left:
+        if right.pop(ix, False):
+            if ix in out:
+                bat_inds.append(ix)
+            else:
+                con_inds.append(ix)
+        elif ix in out:
+            a_keep.append(ix)
+    # now only indices unique to right remain
+    for ix in right:
+        if ix in out:
+            b_keep.append(ix)
+
+    if not con_inds:
+        # contraction is pure multiplication, prepare inputs differently
+        return _parse_eq_to_pure_multiplication(
+            a_term, shape_a, b_term, shape_b, out
+        )
+
+    # only need the size one indices that appear in the output
+    singletons = [ix for ix in out if ix in singletons]
+
+    # take diagonal, remove any trivial axes and transpose left
+    desired_a = "".join((*bat_inds, *a_keep, *con_inds))
+    if a_term != desired_a:
+        eq_a = f"{a_term}->{desired_a}"
+    else:
+        eq_a = None
+
+    # take diagonal, remove any trivial axes and transpose right
+    desired_b = "".join((*bat_inds, *con_inds, *b_keep))
+    if b_term != desired_b:
+        eq_b = f"{b_term}->{desired_b}"
+    else:
+        eq_b = None
+
+    # then we want to reshape
+    if bat_inds:
+        lgroups = (bat_inds, a_keep, con_inds)
+        rgroups = (bat_inds, con_inds, b_keep)
+        ogroups = (bat_inds, a_keep, b_keep)
+    else:
+        # avoid size 1 batch dimension if no batch indices
+        lgroups = (a_keep, con_inds)
+        rgroups = (con_inds, b_keep)
+        ogroups = (a_keep, b_keep)
+
+    if any(len(group) != 1 for group in lgroups):
+        # need to fuse 'kept' and contracted indices
+        # (though could allow batch indices to be broadcast)
+        new_shape_a = tuple(
+            functools.reduce(operator.mul, (sizes[ix] for ix in ix_group), 1)
+            for ix_group in lgroups
+        )
+    else:
+        new_shape_a = None
+
+    if any(len(group) != 1 for group in rgroups):
+        # need to fuse 'kept' and contracted indices
+        # (though could allow batch indices to be broadcast)
+        new_shape_b = tuple(
+            functools.reduce(operator.mul, (sizes[ix] for ix in ix_group), 1)
+            for ix_group in rgroups
+        )
+    else:
+        new_shape_b = None
+
+    if any(len(group) != 1 for group in ogroups) or singletons:
+        new_shape_ab = (1,) * len(singletons) + tuple(
+            sizes[ix] for ix_group in ogroups for ix in ix_group
+        )
+    else:
+        new_shape_ab = None
+
+    # then we might need to permute the matmul produced output:
+    out_produced = "".join((*singletons, *bat_inds, *a_keep, *b_keep))
+    if out_produced != out:
+        perm_ab = tuple(out_produced.index(ix) for ix in out)
+    else:
+        perm_ab = None
+
+    return (
+        eq_a,
+        eq_b,
+        new_shape_a,
+        new_shape_b,
+        new_shape_ab,
+        perm_ab,
+        False,  # pure_multiplication=False
+    )
+
+
+@functools.lru_cache(maxsize=64)
+def _parse_output_order(order, a_is_fcontig, b_is_fcontig):
+    order = order.upper()
+    if order == "K":
+        return None
+    elif order in "CF":
+        return order
+    elif order == "A":
+        if a_is_fcontig and b_is_fcontig:
+            return "F"
+        else:
+            return "C"
+    else:
+        raise ValueError(
+            "ValueError: order must be one of "
+            f"'C', 'F', 'A', or 'K' (got '{order}')"
+        )
+
+
+def bmm_einsum(eq, a, b, out=None, **kwargs):
+    """Perform arbitrary pairwise einsums using only ``matmul``, or
+    ``multiply`` if no contracted indices are involved (plus maybe single term
+    ``einsum`` to prepare the terms individually). The logic for each is cached
+    based on the equation and array shape, and each step is only performed if
+    necessary.
+
+    Parameters
+    ----------
+    eq : str
+        The einsum equation.
+    a : array_like
+        The first array to contract.
+    b : array_like
+        The second array to contract.
+
+    Returns
+    -------
+    array_like
+
+    Notes
+    -----
+    A fuller description of this algorithm, and original source for this
+    implementation, can be found at https://github.com/jcmgray/einsum_bmm.
+    """
+    (
+        eq_a,
+        eq_b,
+        new_shape_a,
+        new_shape_b,
+        new_shape_ab,
+        perm_ab,
+        pure_multiplication,
+    ) = _parse_eq_to_batch_matmul(eq, a.shape, b.shape)
+
+    # n.b. one could special case various cases to call c_einsum directly here
+
+    # need to handle `order` a little manually, since we do transpose
+    # operations before and potentially after the ufunc calls
+    output_order = _parse_output_order(
+        kwargs.pop("order", "K"), a.flags.f_contiguous, b.flags.f_contiguous
+    )
+
+    # prepare left
+    if eq_a is not None:
+        # diagonals, sums, and tranpose
+        a = c_einsum(eq_a, a)
+    if new_shape_a is not None:
+        a = reshape(a, new_shape_a)
+
+    # prepare right
+    if eq_b is not None:
+        # diagonals, sums, and tranpose
+        b = c_einsum(eq_b, b)
+    if new_shape_b is not None:
+        b = reshape(b, new_shape_b)
+
+    if pure_multiplication:
+        # no contracted indices
+        if output_order is not None:
+            kwargs["order"] = output_order
+
+        # do the 'contraction' via multiplication!
+        return multiply(a, b, out=out, **kwargs)
+
+    # can only supply out here if no other reshaping / transposing
+    matmul_out_compatible = (new_shape_ab is None) and (perm_ab is None)
+    if matmul_out_compatible:
+        kwargs["out"] = out
+
+    # do the contraction!
+    ab = matmul(a, b, **kwargs)
+
+    # prepare the output
+    if new_shape_ab is not None:
+        ab = reshape(ab, new_shape_ab)
+    if perm_ab is not None:
+        ab = ab.transpose(perm_ab)
+
+    if (out is not None) and (not matmul_out_compatible):
+        # handle case where out is specified, but we also needed
+        # to reshape / transpose ``ab`` after the matmul
+        out[:] = ab
+        ab = out
+    elif output_order is not None:
+        ab = asanyarray(ab, order=output_order)
+
+    return ab
+
+
+def _einsum_dispatcher(*operands, out=None, optimize=None, **kwargs):
+    # Arguably we dispatch on more arguments than we really should; see note in
+    # _einsum_path_dispatcher for why.
+    yield from operands
+    yield out
+
+
+# Rewrite einsum to handle different cases
+@array_function_dispatch(_einsum_dispatcher, module='numpy')
+def einsum(*operands, out=None, optimize=False, **kwargs):
+    """
+    einsum(subscripts, *operands, out=None, dtype=None, order='K',
+           casting='safe', optimize=False)
+
+    Evaluates the Einstein summation convention on the operands.
+
+    Using the Einstein summation convention, many common multi-dimensional,
+    linear algebraic array operations can be represented in a simple fashion.
+    In *implicit* mode `einsum` computes these values.
+
+    In *explicit* mode, `einsum` provides further flexibility to compute
+    other array operations that might not be considered classical Einstein
+    summation operations, by disabling, or forcing summation over specified
+    subscript labels.
+
+    See the notes and examples for clarification.
+
+    Parameters
+    ----------
+    subscripts : str
+        Specifies the subscripts for summation as comma separated list of
+        subscript labels. An implicit (classical Einstein summation)
+        calculation is performed unless the explicit indicator '->' is
+        included as well as subscript labels of the precise output form.
+    operands : list of array_like
+        These are the arrays for the operation.
+    out : ndarray, optional
+        If provided, the calculation is done into this array.
+    dtype : {data-type, None}, optional
+        If provided, forces the calculation to use the data type specified.
+        Note that you may have to also give a more liberal `casting`
+        parameter to allow the conversions. Default is None.
+    order : {'C', 'F', 'A', 'K'}, optional
+        Controls the memory layout of the output. 'C' means it should
+        be C contiguous. 'F' means it should be Fortran contiguous,
+        'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
+        'K' means it should be as close to the layout as the inputs as
+        is possible, including arbitrarily permuted axes.
+        Default is 'K'.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur.  Setting this to
+        'unsafe' is not recommended, as it can adversely affect accumulations.
+
+        * 'no' means the data types should not be cast at all.
+        * 'equiv' means only byte-order changes are allowed.
+        * 'safe' means only casts which can preserve values are allowed.
+        * 'same_kind' means only safe casts or casts within a kind,
+          like float64 to float32, are allowed.
+        * 'unsafe' means any data conversions may be done.
+
+        Default is 'safe'.
+    optimize : {False, True, 'greedy', 'optimal'}, optional
+        Controls if intermediate optimization should occur. No optimization
+        will occur if False and True will default to the 'greedy' algorithm.
+        Also accepts an explicit contraction list from the ``np.einsum_path``
+        function. See ``np.einsum_path`` for more details. Defaults to False.
+
+    Returns
+    -------
+    output : ndarray
+        The calculation based on the Einstein summation convention.
+
+    See Also
+    --------
+    einsum_path, dot, inner, outer, tensordot, linalg.multi_dot
+    einsum:
+        Similar verbose interface is provided by the
+        `einops <https://github.com/arogozhnikov/einops>`_ package to cover
+        additional operations: transpose, reshape/flatten, repeat/tile,
+        squeeze/unsqueeze and reductions.
+        The `opt_einsum <https://optimized-einsum.readthedocs.io/en/stable/>`_
+        optimizes contraction order for einsum-like expressions
+        in backend-agnostic manner.
+
+    Notes
+    -----
+    The Einstein summation convention can be used to compute
+    many multi-dimensional, linear algebraic array operations. `einsum`
+    provides a succinct way of representing these.
+
+    A non-exhaustive list of these operations,
+    which can be computed by `einsum`, is shown below along with examples:
+
+    * Trace of an array, :py:func:`numpy.trace`.
+    * Return a diagonal, :py:func:`numpy.diag`.
+    * Array axis summations, :py:func:`numpy.sum`.
+    * Transpositions and permutations, :py:func:`numpy.transpose`.
+    * Matrix multiplication and dot product, :py:func:`numpy.matmul`
+        :py:func:`numpy.dot`.
+    * Vector inner and outer products, :py:func:`numpy.inner`
+        :py:func:`numpy.outer`.
+    * Broadcasting, element-wise and scalar multiplication,
+        :py:func:`numpy.multiply`.
+    * Tensor contractions, :py:func:`numpy.tensordot`.
+    * Chained array operations, in efficient calculation order,
+        :py:func:`numpy.einsum_path`.
+
+    The subscripts string is a comma-separated list of subscript labels,
+    where each label refers to a dimension of the corresponding operand.
+    Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
+    is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label
+    appears only once, it is not summed, so ``np.einsum('i', a)``
+    produces a view of ``a`` with no changes. A further example
+    ``np.einsum('ij,jk', a, b)`` describes traditional matrix multiplication
+    and is equivalent to :py:func:`np.matmul(a,b) <numpy.matmul>`.
+    Repeated subscript labels in one operand take the diagonal.
+    For example, ``np.einsum('ii', a)`` is equivalent to
+    :py:func:`np.trace(a) <numpy.trace>`.
+
+    In *implicit mode*, the chosen subscripts are important
+    since the axes of the output are reordered alphabetically.  This
+    means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
+    ``np.einsum('ji', a)`` takes its transpose. Additionally,
+    ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
+    ``np.einsum('ij,jh', a, b)`` returns the transpose of the
+    multiplication since subscript 'h' precedes subscript 'i'.
+
+    In *explicit mode* the output can be directly controlled by
+    specifying output subscript labels.  This requires the
+    identifier '->' as well as the list of output subscript labels.
+    This feature increases the flexibility of the function since
+    summing can be disabled or forced when required. The call
+    ``np.einsum('i->', a)`` is like :py:func:`np.sum(a) <numpy.sum>`
+    if ``a`` is a 1-D array, and ``np.einsum('ii->i', a)``
+    is like :py:func:`np.diag(a) <numpy.diag>` if ``a`` is a square 2-D array.
+    The difference is that `einsum` does not allow broadcasting by default.
+    Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
+    order of the output subscript labels and therefore returns matrix
+    multiplication, unlike the example above in implicit mode.
+
+    To enable and control broadcasting, use an ellipsis.  Default
+    NumPy-style broadcasting is done by adding an ellipsis
+    to the left of each term, like ``np.einsum('...ii->...i', a)``.
+    ``np.einsum('...i->...', a)`` is like
+    :py:func:`np.sum(a, axis=-1) <numpy.sum>` for array ``a`` of any shape.
+    To take the trace along the first and last axes,
+    you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
+    product with the left-most indices instead of rightmost, one can do
+    ``np.einsum('ij...,jk...->ik...', a, b)``.
+
+    When there is only one operand, no axes are summed, and no output
+    parameter is provided, a view into the operand is returned instead
+    of a new array.  Thus, taking the diagonal as ``np.einsum('ii->i', a)``
+    produces a view (changed in version 1.10.0).
+
+    `einsum` also provides an alternative way to provide the subscripts and
+    operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.
+    If the output shape is not provided in this format `einsum` will be
+    calculated in implicit mode, otherwise it will be performed explicitly.
+    The examples below have corresponding `einsum` calls with the two
+    parameter methods.
+
+    Views returned from einsum are now writeable whenever the input array
+    is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
+    have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`
+    and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
+    of a 2D array.
+
+    Added the ``optimize`` argument which will optimize the contraction order
+    of an einsum expression. For a contraction with three or more operands
+    this can greatly increase the computational efficiency at the cost of
+    a larger memory footprint during computation.
+
+    Typically a 'greedy' algorithm is applied which empirical tests have shown
+    returns the optimal path in the majority of cases. In some cases 'optimal'
+    will return the superlative path through a more expensive, exhaustive
+    search. For iterative calculations it may be advisable to calculate
+    the optimal path once and reuse that path by supplying it as an argument.
+    An example is given below.
+
+    See :py:func:`numpy.einsum_path` for more details.
+
+    Examples
+    --------
+    >>> a = np.arange(25).reshape(5,5)
+    >>> b = np.arange(5)
+    >>> c = np.arange(6).reshape(2,3)
+
+    Trace of a matrix:
+
+    >>> np.einsum('ii', a)
+    60
+    >>> np.einsum(a, [0,0])
+    60
+    >>> np.trace(a)
+    60
+
+    Extract the diagonal (requires explicit form):
+
+    >>> np.einsum('ii->i', a)
+    array([ 0,  6, 12, 18, 24])
+    >>> np.einsum(a, [0,0], [0])
+    array([ 0,  6, 12, 18, 24])
+    >>> np.diag(a)
+    array([ 0,  6, 12, 18, 24])
+
+    Sum over an axis (requires explicit form):
+
+    >>> np.einsum('ij->i', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [0,1], [0])
+    array([ 10,  35,  60,  85, 110])
+    >>> np.sum(a, axis=1)
+    array([ 10,  35,  60,  85, 110])
+
+    For higher dimensional arrays summing a single axis can be done
+    with ellipsis:
+
+    >>> np.einsum('...j->...', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [Ellipsis,1], [Ellipsis])
+    array([ 10,  35,  60,  85, 110])
+
+    Compute a matrix transpose, or reorder any number of axes:
+
+    >>> np.einsum('ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum('ij->ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum(c, [1,0])
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.transpose(c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+
+    Vector inner products:
+
+    >>> np.einsum('i,i', b, b)
+    30
+    >>> np.einsum(b, [0], b, [0])
+    30
+    >>> np.inner(b,b)
+    30
+
+    Matrix vector multiplication:
+
+    >>> np.einsum('ij,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum(a, [0,1], b, [1])
+    array([ 30,  80, 130, 180, 230])
+    >>> np.dot(a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum('...j,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+
+    Broadcasting and scalar multiplication:
+
+    >>> np.einsum('..., ...', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(',ij', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(3, [Ellipsis], c, [Ellipsis])
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.multiply(3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+
+    Vector outer product:
+
+    >>> np.einsum('i,j', np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.einsum(np.arange(2)+1, [0], b, [1])
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.outer(np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+
+    Tensor contraction:
+
+    >>> a = np.arange(60.).reshape(3,4,5)
+    >>> b = np.arange(24.).reshape(4,3,2)
+    >>> np.einsum('ijk,jil->kl', a, b)
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+    >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+    >>> np.tensordot(a,b, axes=([1,0],[0,1]))
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+
+    Writeable returned arrays (since version 1.10.0):
+
+    >>> a = np.zeros((3, 3))
+    >>> np.einsum('ii->i', a)[:] = 1
+    >>> a
+    array([[1., 0., 0.],
+           [0., 1., 0.],
+           [0., 0., 1.]])
+
+    Example of ellipsis use:
+
+    >>> a = np.arange(6).reshape((3,2))
+    >>> b = np.arange(12).reshape((4,3))
+    >>> np.einsum('ki,jk->ij', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('ki,...k->i...', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('k...,jk', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+
+    Chained array operations. For more complicated contractions, speed ups
+    might be achieved by repeatedly computing a 'greedy' path or pre-computing
+    the 'optimal' path and repeatedly applying it, using an `einsum_path`
+    insertion (since version 1.12.0). Performance improvements can be
+    particularly significant with larger arrays:
+
+    >>> a = np.ones(64).reshape(2,4,8)
+
+    Basic `einsum`: ~1520ms  (benchmarked on 3.1GHz Intel i5.)
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)
+
+    Sub-optimal `einsum` (due to repeated path calculation time): ~330ms
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a,
+    ...         optimize='optimal')
+
+    Greedy `einsum` (faster optimal path approximation): ~160ms
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy')
+
+    Optimal `einsum` (best usage pattern in some use cases): ~110ms
+
+    >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a,
+    ...     optimize='optimal')[0]
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path)
+
+    """
+    # Special handling if out is specified
+    specified_out = out is not None
+
+    # If no optimization, run pure einsum
+    if optimize is False:
+        if specified_out:
+            kwargs['out'] = out
+        return c_einsum(*operands, **kwargs)
+
+    # Check the kwargs to avoid a more cryptic error later, without having to
+    # repeat default values here
+    valid_einsum_kwargs = ['dtype', 'order', 'casting']
+    unknown_kwargs = [k for (k, v) in kwargs.items() if
+                      k not in valid_einsum_kwargs]
+    if len(unknown_kwargs):
+        raise TypeError(f"Did not understand the following kwargs: {unknown_kwargs}")
+
+    # Build the contraction list and operand
+    operands, contraction_list = einsum_path(*operands, optimize=optimize,
+                                             einsum_call=True)
+
+    # Start contraction loop
+    for num, contraction in enumerate(contraction_list):
+        inds, einsum_str, _ = contraction
+        tmp_operands = [operands.pop(x) for x in inds]
+
+        # Do we need to deal with the output?
+        handle_out = specified_out and ((num + 1) == len(contraction_list))
+
+        # If out was specified
+        if handle_out:
+            kwargs["out"] = out
+
+        if len(tmp_operands) == 2:
+            # Call (batched) matrix multiplication if possible
+            new_view = bmm_einsum(einsum_str, *tmp_operands, **kwargs)
+        else:
+            # Call einsum
+            new_view = c_einsum(einsum_str, *tmp_operands, **kwargs)
+
+        # Append new items and dereference what we can
+        operands.append(new_view)
+        del tmp_operands, new_view
+
+    if specified_out:
+        return out
+    else:
+        return operands[0]

python/user_packages/Python313/site-packages/numpy/_core/einsumfunc.pyi

@@ -0,0 +1,184 @@
+from collections.abc import Sequence
+from typing import Any, Literal, TypeAlias, TypeVar, overload
+
+import numpy as np
+from numpy import _OrderKACF, number
+from numpy._typing import (
+    NDArray,
+    _ArrayLikeBool_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeInt_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeUInt_co,
+    _DTypeLikeBool,
+    _DTypeLikeComplex,
+    _DTypeLikeComplex_co,
+    _DTypeLikeFloat,
+    _DTypeLikeInt,
+    _DTypeLikeObject,
+    _DTypeLikeUInt,
+)
+
+__all__ = ["einsum", "einsum_path"]
+
+_ArrayT = TypeVar(
+    "_ArrayT",
+    bound=NDArray[np.bool | number],
+)
+
+_OptimizeKind: TypeAlias = bool | Literal["greedy", "optimal"] | Sequence[Any] | None
+_CastingSafe: TypeAlias = Literal["no", "equiv", "safe", "same_kind"]
+_CastingUnsafe: TypeAlias = Literal["unsafe"]
+
+# TODO: Properly handle the `casting`-based combinatorics
+# TODO: We need to evaluate the content `__subscripts` in order
+# to identify whether or an array or scalar is returned. At a cursory
+# glance this seems like something that can quite easily be done with
+# a mypy plugin.
+# Something like `is_scalar = bool(__subscripts.partition("->")[-1])`
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeBool_co,
+    out: None = None,
+    dtype: _DTypeLikeBool | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeUInt_co,
+    out: None = None,
+    dtype: _DTypeLikeUInt | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeInt_co,
+    out: None = None,
+    dtype: _DTypeLikeInt | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeFloat_co,
+    out: None = None,
+    dtype: _DTypeLikeFloat | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeComplex_co,
+    out: None = None,
+    dtype: _DTypeLikeComplex | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeComplex_co | None = ...,
+    out: None = None,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeComplex_co,
+    out: _ArrayT,
+    dtype: _DTypeLikeComplex_co | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> _ArrayT: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    out: _ArrayT,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeComplex_co | None = ...,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = False,
+) -> _ArrayT: ...
+
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeObject_co,
+    out: None = None,
+    dtype: _DTypeLikeObject | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeObject | None = ...,
+    out: None = None,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = False,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeObject_co,
+    out: _ArrayT,
+    dtype: _DTypeLikeObject | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = False,
+) -> _ArrayT: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    out: _ArrayT,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeObject | None = ...,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = False,
+) -> _ArrayT: ...
+
+# NOTE: `einsum_call` is a hidden kwarg unavailable for public use.
+# It is therefore excluded from the signatures below.
+# NOTE: In practice the list consists of a `str` (first element)
+# and a variable number of integer tuples.
+def einsum_path(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeComplex_co | _DTypeLikeObject,
+    optimize: _OptimizeKind = "greedy",
+    einsum_call: Literal[False] = False,
+) -> tuple[list[Any], str]: ...

python/user_packages/Python313/site-packages/numpy/_core/fromnumeric.pyi

@@ -0,0 +1,1735 @@
+# ruff: noqa: ANN401
+from _typeshed import Incomplete
+from collections.abc import Sequence
+from typing import (
+    Any,
+    Literal,
+    Never,
+    Protocol,
+    SupportsIndex,
+    TypeAlias,
+    TypedDict,
+    TypeVar,
+    Unpack,
+    overload,
+    type_check_only,
+)
+
+import numpy as np
+from numpy import (
+    _AnyShapeT,
+    _CastingKind,
+    _ModeKind,
+    _OrderACF,
+    _OrderKACF,
+    _PartitionKind,
+    _SortKind,
+    _SortSide,
+    complexfloating,
+    float16,
+    floating,
+    generic,
+    int64,
+    int_,
+    intp,
+    object_,
+    timedelta64,
+    uint64,
+)
+from numpy._globals import _NoValueType
+from numpy._typing import (
+    ArrayLike,
+    DTypeLike,
+    NDArray,
+    _AnyShape,
+    _ArrayLike,
+    _ArrayLikeBool_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeInt,
+    _ArrayLikeInt_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeUInt_co,
+    _BoolLike_co,
+    _ComplexLike_co,
+    _DTypeLike,
+    _IntLike_co,
+    _NestedSequence,
+    _NumberLike_co,
+    _ScalarLike_co,
+    _ShapeLike,
+)
+
+__all__ = [
+    "all",
+    "amax",
+    "amin",
+    "any",
+    "argmax",
+    "argmin",
+    "argpartition",
+    "argsort",
+    "around",
+    "choose",
+    "clip",
+    "compress",
+    "cumprod",
+    "cumsum",
+    "cumulative_prod",
+    "cumulative_sum",
+    "diagonal",
+    "mean",
+    "max",
+    "min",
+    "matrix_transpose",
+    "ndim",
+    "nonzero",
+    "partition",
+    "prod",
+    "ptp",
+    "put",
+    "ravel",
+    "repeat",
+    "reshape",
+    "resize",
+    "round",
+    "searchsorted",
+    "shape",
+    "size",
+    "sort",
+    "squeeze",
+    "std",
+    "sum",
+    "swapaxes",
+    "take",
+    "trace",
+    "transpose",
+    "var",
+]
+
+_ScalarT = TypeVar("_ScalarT", bound=generic)
+_NumberOrObjectT = TypeVar("_NumberOrObjectT", bound=np.number | np.object_)
+_ArrayT = TypeVar("_ArrayT", bound=np.ndarray[Any, Any])
+_ShapeT = TypeVar("_ShapeT", bound=tuple[int, ...])
+_ShapeT_co = TypeVar("_ShapeT_co", bound=tuple[int, ...], covariant=True)
+_BoolOrIntArrayT = TypeVar("_BoolOrIntArrayT", bound=NDArray[np.integer | np.bool])
+
+@type_check_only
+class _SupportsShape(Protocol[_ShapeT_co]):
+    # NOTE: it matters that `self` is positional only
+    @property
+    def shape(self, /) -> _ShapeT_co: ...
+
+@type_check_only
+class _UFuncKwargs(TypedDict, total=False):
+    where: _ArrayLikeBool_co | None
+    order: _OrderKACF
+    subok: bool
+    signature: str | tuple[str | None, ...]
+    casting: _CastingKind
+
+# a "sequence" that isn't a string, bytes, bytearray, or memoryview
+_T = TypeVar("_T")
+_PyArray: TypeAlias = list[_T] | tuple[_T, ...]
+# `int` also covers `bool`
+_PyScalar: TypeAlias = complex | bytes | str
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def take(
+    a: _ArrayLike[_ScalarT],
+    indices: _IntLike_co,
+    axis: None = None,
+    out: None = None,
+    mode: _ModeKind = "raise",
+) -> _ScalarT: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _IntLike_co,
+    axis: SupportsIndex | None = None,
+    out: None = None,
+    mode: _ModeKind = "raise",
+) -> Any: ...
+@overload
+def take(
+    a: _ArrayLike[_ScalarT],
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = None,
+    out: None = None,
+    mode: _ModeKind = "raise",
+) -> NDArray[_ScalarT]: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = None,
+    out: None = None,
+    mode: _ModeKind = "raise",
+) -> NDArray[Any]: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None,
+    out: _ArrayT,
+    mode: _ModeKind = "raise",
+) -> _ArrayT: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = None,
+    *,
+    out: _ArrayT,
+    mode: _ModeKind = "raise",
+) -> _ArrayT: ...
+
+@overload
+def reshape(  # shape: index
+    a: _ArrayLike[_ScalarT],
+    /,
+    shape: SupportsIndex,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[tuple[int], np.dtype[_ScalarT]]: ...
+@overload
+def reshape(  # shape: (int, ...) @ _AnyShapeT
+    a: _ArrayLike[_ScalarT],
+    /,
+    shape: _AnyShapeT,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[_AnyShapeT, np.dtype[_ScalarT]]: ...
+@overload  # shape: Sequence[index]
+def reshape(
+    a: _ArrayLike[_ScalarT],
+    /,
+    shape: Sequence[SupportsIndex],
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload  # shape: index
+def reshape(
+    a: ArrayLike,
+    /,
+    shape: SupportsIndex,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[tuple[int], np.dtype]: ...
+@overload
+def reshape(  # shape: (int, ...) @ _AnyShapeT
+    a: ArrayLike,
+    /,
+    shape: _AnyShapeT,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[_AnyShapeT, np.dtype]: ...
+@overload  # shape: Sequence[index]
+def reshape(
+    a: ArrayLike,
+    /,
+    shape: Sequence[SupportsIndex],
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> NDArray[Any]: ...
+
+@overload
+def choose(
+    a: _IntLike_co,
+    choices: ArrayLike,
+    out: None = None,
+    mode: _ModeKind = "raise",
+) -> Any: ...
+@overload
+def choose(
+    a: _ArrayLikeInt_co,
+    choices: _ArrayLike[_ScalarT],
+    out: None = None,
+    mode: _ModeKind = "raise",
+) -> NDArray[_ScalarT]: ...
+@overload
+def choose(
+    a: _ArrayLikeInt_co,
+    choices: ArrayLike,
+    out: None = None,
+    mode: _ModeKind = "raise",
+) -> NDArray[Any]: ...
+@overload
+def choose(
+    a: _ArrayLikeInt_co,
+    choices: ArrayLike,
+    out: _ArrayT,
+    mode: _ModeKind = "raise",
+) -> _ArrayT: ...
+
+# keep in sync with `ma.core.repeat`
+@overload
+def repeat(
+    a: _ArrayLike[_ScalarT],
+    repeats: _ArrayLikeInt_co,
+    axis: None = None,
+) -> np.ndarray[tuple[int], np.dtype[_ScalarT]]: ...
+@overload
+def repeat(
+    a: _ArrayLike[_ScalarT],
+    repeats: _ArrayLikeInt_co,
+    axis: SupportsIndex,
+) -> NDArray[_ScalarT]: ...
+@overload
+def repeat(
+    a: ArrayLike,
+    repeats: _ArrayLikeInt_co,
+    axis: None = None,
+) -> np.ndarray[tuple[int], np.dtype[Any]]: ...
+@overload
+def repeat(
+    a: ArrayLike,
+    repeats: _ArrayLikeInt_co,
+    axis: SupportsIndex,
+) -> NDArray[Any]: ...
+
+#
+def put(
+    a: NDArray[Any],
+    ind: _ArrayLikeInt_co,
+    v: ArrayLike,
+    mode: _ModeKind = "raise",
+) -> None: ...
+
+# keep in sync with `ndarray.swapaxes` and `ma.core.swapaxes`
+@overload
+def swapaxes(a: _ArrayT, axis1: SupportsIndex, axis2: SupportsIndex) -> _ArrayT: ...
+@overload
+def swapaxes(a: _ArrayLike[_ScalarT], axis1: SupportsIndex, axis2: SupportsIndex) -> NDArray[_ScalarT]: ...
+@overload
+def swapaxes(a: ArrayLike, axis1: SupportsIndex, axis2: SupportsIndex) -> NDArray[Any]: ...
+
+@overload
+def transpose(
+    a: _ArrayLike[_ScalarT],
+    axes: _ShapeLike | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def transpose(
+    a: ArrayLike,
+    axes: _ShapeLike | None = None,
+) -> NDArray[Any]: ...
+
+@overload
+def matrix_transpose(x: _ArrayLike[_ScalarT], /) -> NDArray[_ScalarT]: ...
+@overload
+def matrix_transpose(x: ArrayLike, /) -> NDArray[Any]: ...
+
+#
+@overload
+def partition(
+    a: _ArrayLike[_ScalarT],
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def partition(
+    a: _ArrayLike[np.void],
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: str | Sequence[str] | None = None,
+) -> NDArray[np.void]: ...
+@overload
+def partition(
+    a: ArrayLike,
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: str | Sequence[str] | None = None,
+) -> NDArray[Any]: ...
+
+#
+def argpartition(
+    a: ArrayLike,
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: str | Sequence[str] | None = None,
+) -> NDArray[intp]: ...
+
+#
+@overload
+def sort(
+    a: _ArrayLike[_ScalarT],
+    axis: SupportsIndex | None = -1,
+    kind: _SortKind | None = None,
+    order: str | Sequence[str] | None = None,
+    *,
+    stable: bool | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def sort(
+    a: ArrayLike,
+    axis: SupportsIndex | None = -1,
+    kind: _SortKind | None = None,
+    order: str | Sequence[str] | None = None,
+    *,
+    stable: bool | None = None,
+) -> NDArray[Any]: ...
+
+def argsort(
+    a: ArrayLike,
+    axis: SupportsIndex | None = -1,
+    kind: _SortKind | None = None,
+    order: str | Sequence[str] | None = None,
+    *,
+    stable: bool | None = None,
+) -> NDArray[intp]: ...
+
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: None = None,
+    out: None = None,
+    *,
+    keepdims: Literal[False] | _NoValueType = ...,
+) -> intp: ...
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    out: None = None,
+    *,
+    keepdims: bool | _NoValueType = ...,
+) -> Any: ...
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    out: _BoolOrIntArrayT,
+    *,
+    keepdims: bool | _NoValueType = ...,
+) -> _BoolOrIntArrayT: ...
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    *,
+    out: _BoolOrIntArrayT,
+    keepdims: bool | _NoValueType = ...,
+) -> _BoolOrIntArrayT: ...
+
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: None = None,
+    out: None = None,
+    *,
+    keepdims: Literal[False] | _NoValueType = ...,
+) -> intp: ...
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    out: None = None,
+    *,
+    keepdims: bool | _NoValueType = ...,
+) -> Any: ...
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    out: _BoolOrIntArrayT,
+    *,
+    keepdims: bool | _NoValueType = ...,
+) -> _BoolOrIntArrayT: ...
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    *,
+    out: _BoolOrIntArrayT,
+    keepdims: bool | _NoValueType = ...,
+) -> _BoolOrIntArrayT: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def searchsorted(
+    a: ArrayLike,
+    v: _ScalarLike_co,
+    side: _SortSide = "left",
+    sorter: _ArrayLikeInt_co | None = None,  # 1D int array
+) -> intp: ...
+@overload
+def searchsorted(
+    a: ArrayLike,
+    v: ArrayLike,
+    side: _SortSide = "left",
+    sorter: _ArrayLikeInt_co | None = None,  # 1D int array
+) -> NDArray[intp]: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def resize(a: _ArrayLike[_ScalarT], new_shape: SupportsIndex | tuple[SupportsIndex]) -> np.ndarray[tuple[int], np.dtype[_ScalarT]]: ...
+@overload
+def resize(a: _ArrayLike[_ScalarT], new_shape: _AnyShapeT) -> np.ndarray[_AnyShapeT, np.dtype[_ScalarT]]: ...
+@overload
+def resize(a: _ArrayLike[_ScalarT], new_shape: _ShapeLike) -> NDArray[_ScalarT]: ...
+@overload
+def resize(a: ArrayLike, new_shape: SupportsIndex | tuple[SupportsIndex]) -> np.ndarray[tuple[int], np.dtype]: ...
+@overload
+def resize(a: ArrayLike, new_shape: _AnyShapeT) -> np.ndarray[_AnyShapeT, np.dtype]: ...
+@overload
+def resize(a: ArrayLike, new_shape: _ShapeLike) -> NDArray[Any]: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def squeeze(
+    a: _ScalarT,
+    axis: _ShapeLike | None = None,
+) -> _ScalarT: ...
+@overload
+def squeeze(
+    a: _ArrayLike[_ScalarT],
+    axis: _ShapeLike | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def squeeze(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+) -> NDArray[Any]: ...
+
+# keep in sync with `ma.core.diagonal`
+@overload
+def diagonal(
+    a: _ArrayLike[_ScalarT],
+    offset: SupportsIndex = 0,
+    axis1: SupportsIndex = 0,
+    axis2: SupportsIndex = 1,  # >= 2D array
+) -> NDArray[_ScalarT]: ...
+@overload
+def diagonal(
+    a: ArrayLike,
+    offset: SupportsIndex = 0,
+    axis1: SupportsIndex = 0,
+    axis2: SupportsIndex = 1,  # >= 2D array
+) -> NDArray[Any]: ...
+
+# keep in sync with `ma.core.trace`
+@overload
+def trace(
+    a: ArrayLike,  # >= 2D array
+    offset: SupportsIndex = 0,
+    axis1: SupportsIndex = 0,
+    axis2: SupportsIndex = 1,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+) -> Any: ...
+@overload
+def trace(
+    a: ArrayLike,  # >= 2D array
+    offset: SupportsIndex,
+    axis1: SupportsIndex,
+    axis2: SupportsIndex,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def trace(
+    a: ArrayLike,  # >= 2D array
+    offset: SupportsIndex = 0,
+    axis1: SupportsIndex = 0,
+    axis2: SupportsIndex = 1,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+_Array1D: TypeAlias = np.ndarray[tuple[int], np.dtype[_ScalarT]]
+
+@overload
+def ravel(a: _ArrayLike[_ScalarT], order: _OrderKACF = "C") -> _Array1D[_ScalarT]: ...
+@overload
+def ravel(a: bytes | _NestedSequence[bytes], order: _OrderKACF = "C") -> _Array1D[np.bytes_]: ...
+@overload
+def ravel(a: str | _NestedSequence[str], order: _OrderKACF = "C") -> _Array1D[np.str_]: ...
+@overload
+def ravel(a: bool | _NestedSequence[bool], order: _OrderKACF = "C") -> _Array1D[np.bool]: ...
+@overload
+def ravel(a: int | _NestedSequence[int], order: _OrderKACF = "C") -> _Array1D[np.int_ | Any]: ...
+@overload
+def ravel(a: float | _NestedSequence[float], order: _OrderKACF = "C") -> _Array1D[np.float64 | Any]: ...
+@overload
+def ravel(a: complex | _NestedSequence[complex], order: _OrderKACF = "C") -> _Array1D[np.complex128 | Any]: ...
+@overload
+def ravel(a: ArrayLike, order: _OrderKACF = "C") -> np.ndarray[tuple[int], np.dtype]: ...
+
+def nonzero(a: _ArrayLike[Any]) -> tuple[np.ndarray[tuple[int], np.dtype[intp]], ...]: ...
+
+# this prevents `Any` from being returned with Pyright
+@overload
+def shape(a: _SupportsShape[Never]) -> _AnyShape: ...
+@overload
+def shape(a: _SupportsShape[_ShapeT]) -> _ShapeT: ...
+@overload
+def shape(a: _PyScalar) -> tuple[()]: ...
+# `collections.abc.Sequence` can't be used hesre, since `bytes` and `str` are
+# subtypes of it, which would make the return types incompatible.
+@overload
+def shape(a: _PyArray[_PyScalar]) -> tuple[int]: ...
+@overload
+def shape(a: _PyArray[_PyArray[_PyScalar]]) -> tuple[int, int]: ...
+# this overload will be skipped by typecheckers that don't support PEP 688
+@overload
+def shape(a: memoryview | bytearray) -> tuple[int]: ...
+@overload
+def shape(a: ArrayLike) -> _AnyShape: ...
+
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: _ArrayLike[_ScalarT],
+    axis: SupportsIndex | None = None,
+    out: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    out: None = None,
+) -> NDArray[Any]: ...
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def clip(
+    a: _ScalarT,
+    a_min: ArrayLike | _NoValueType | None = ...,
+    a_max: ArrayLike | _NoValueType | None = ...,
+    out: None = None,
+    *,
+    min: ArrayLike | _NoValueType | None = ...,
+    max: ArrayLike | _NoValueType | None = ...,
+    dtype: None = None,
+    **kwargs: Unpack[_UFuncKwargs],
+) -> _ScalarT: ...
+@overload
+def clip(
+    a: _ScalarLike_co,
+    a_min: ArrayLike | _NoValueType | None = ...,
+    a_max: ArrayLike | _NoValueType | None = ...,
+    out: None = None,
+    *,
+    min: ArrayLike | _NoValueType | None = ...,
+    max: ArrayLike | _NoValueType | None = ...,
+    dtype: None = None,
+    **kwargs: Unpack[_UFuncKwargs],
+) -> Any: ...
+@overload
+def clip(
+    a: _ArrayLike[_ScalarT],
+    a_min: ArrayLike | _NoValueType | None = ...,
+    a_max: ArrayLike | _NoValueType | None = ...,
+    out: None = None,
+    *,
+    min: ArrayLike | _NoValueType | None = ...,
+    max: ArrayLike | _NoValueType | None = ...,
+    dtype: None = None,
+    **kwargs: Unpack[_UFuncKwargs],
+) -> NDArray[_ScalarT]: ...
+@overload
+def clip(
+    a: ArrayLike,
+    a_min: ArrayLike | _NoValueType | None = ...,
+    a_max: ArrayLike | _NoValueType | None = ...,
+    out: None = None,
+    *,
+    min: ArrayLike | _NoValueType | None = ...,
+    max: ArrayLike | _NoValueType | None = ...,
+    dtype: None = None,
+    **kwargs: Unpack[_UFuncKwargs],
+) -> NDArray[Any]: ...
+@overload
+def clip(
+    a: ArrayLike,
+    a_min: ArrayLike | None,
+    a_max: ArrayLike | None,
+    out: _ArrayT,
+    *,
+    min: ArrayLike | _NoValueType | None = ...,
+    max: ArrayLike | _NoValueType | None = ...,
+    dtype: DTypeLike | None = None,
+    **kwargs: Unpack[_UFuncKwargs],
+) -> _ArrayT: ...
+@overload
+def clip(
+    a: ArrayLike,
+    a_min: ArrayLike | _NoValueType | None = ...,
+    a_max: ArrayLike | _NoValueType | None = ...,
+    *,
+    out: _ArrayT,
+    min: ArrayLike | _NoValueType | None = ...,
+    max: ArrayLike | _NoValueType | None = ...,
+    dtype: DTypeLike | None = None,
+    **kwargs: Unpack[_UFuncKwargs],
+) -> _ArrayT: ...
+@overload
+def clip(
+    a: ArrayLike,
+    a_min: ArrayLike | _NoValueType | None = ...,
+    a_max: ArrayLike | _NoValueType | None = ...,
+    out: None = None,
+    *,
+    min: ArrayLike | _NoValueType | None = ...,
+    max: ArrayLike | _NoValueType | None = ...,
+    dtype: DTypeLike | None = None,
+    **kwargs: Unpack[_UFuncKwargs],
+) -> Any: ...
+
+@overload
+def sum(
+    a: _ArrayLike[_ScalarT],
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def sum(
+    a: _ArrayLike[_ScalarT],
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Any: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+# keep in sync with `any`
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: None = None,
+    out: None = None,
+    keepdims: Literal[False, 0] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> np.bool: ...
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    out: None = None,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Incomplete: ...
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+# keep in sync with `all`
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: None = None,
+    out: None = None,
+    keepdims: Literal[False, 0] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> np.bool: ...
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    out: None = None,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Incomplete: ...
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+#
+@overload
+def cumsum(
+    a: _ArrayLike[_ScalarT],
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[Any]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+) -> NDArray[Any]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+@overload
+def cumulative_sum(
+    x: _ArrayLike[_ScalarT],
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[Any]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[Any]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    out: _ArrayT,
+    include_initial: bool = False,
+) -> _ArrayT: ...
+
+@overload
+def ptp(
+    a: _ArrayLike[_ScalarT],
+    axis: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def ptp(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+) -> Any: ...
+@overload
+def ptp(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def ptp(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+) -> _ArrayT: ...
+
+@overload
+def amax(
+    a: _ArrayLike[_ScalarT],
+    axis: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def amax(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Any: ...
+@overload
+def amax(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def amax(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+@overload
+def amin(
+    a: _ArrayLike[_ScalarT],
+    axis: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def amin(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Any: ...
+@overload
+def amin(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def amin(
+    a: ArrayLike,
+    axis: _ShapeLike | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+# TODO: `np.prod()``: For object arrays `initial` does not necessarily
+# have to be a numerical scalar.
+# The only requirement is that it is compatible
+# with the `.__mul__()` method(s) of the passed array's elements.
+# Note that the same situation holds for all wrappers around
+# `np.ufunc.reduce`, e.g. `np.sum()` (`.__add__()`).
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def prod(
+    a: _ArrayLikeBool_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> int_: ...
+@overload
+def prod(
+    a: _ArrayLikeUInt_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> uint64: ...
+@overload
+def prod(
+    a: _ArrayLikeInt_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> int64: ...
+@overload
+def prod(
+    a: _ArrayLikeFloat_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> floating: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> complexfloating: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Any: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Any: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    initial: _NumberLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def cumprod(
+    a: _ArrayLikeBool_co,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[int_]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeUInt_co,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[uint64]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[int64]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeFloat_co,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[floating]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[complexfloating]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeObject_co,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+) -> NDArray[object_]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+) -> NDArray[Any]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def cumulative_prod(
+    x: _ArrayLikeBool_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[int_]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeUInt_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[uint64]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeInt_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[int64]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeFloat_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[floating]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[complexfloating]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[object_]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+    include_initial: bool = False,
+) -> NDArray[Any]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = None,
+    dtype: DTypeLike | None = None,
+    out: _ArrayT,
+    include_initial: bool = False,
+) -> _ArrayT: ...
+
+def ndim(a: ArrayLike) -> int: ...
+
+def size(a: ArrayLike, axis: int | tuple[int, ...] | None = None) -> int: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def around(
+    a: _BoolLike_co,
+    decimals: SupportsIndex = 0,
+    out: None = None,
+) -> float16: ...
+@overload
+def around(
+    a: _NumberOrObjectT,
+    decimals: SupportsIndex = 0,
+    out: None = None,
+) -> _NumberOrObjectT: ...
+@overload
+def around(
+    a: _ComplexLike_co | object_,
+    decimals: SupportsIndex = 0,
+    out: None = None,
+) -> Any: ...
+@overload
+def around(
+    a: _ArrayLikeBool_co,
+    decimals: SupportsIndex = 0,
+    out: None = None,
+) -> NDArray[float16]: ...
+@overload
+def around(
+    a: _ArrayLike[_NumberOrObjectT],
+    decimals: SupportsIndex = 0,
+    out: None = None,
+) -> NDArray[_NumberOrObjectT]: ...
+@overload
+def around(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    decimals: SupportsIndex = 0,
+    out: None = None,
+) -> NDArray[Any]: ...
+@overload
+def around(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    decimals: SupportsIndex,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def around(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    decimals: SupportsIndex = 0,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+# TODO: Fix overlapping overloads: https://github.com/numpy/numpy/issues/27032
+@overload
+def mean(
+    a: _ArrayLikeFloat_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> floating: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> complexfloating: ...
+@overload
+def mean(
+    a: _ArrayLike[np.timedelta64],
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> timedelta64: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: Literal[False] | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None,
+    keepdims: Literal[True, 1],
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    *,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Incomplete: ...
+
+@overload
+def std(
+    a: _ArrayLikeComplex_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    ddof: float = 0,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> floating: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: None = None,
+    out: None = None,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    ddof: float = 0,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    ddof: float = 0,
+    keepdims: Literal[False] | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+
+@overload
+def var(
+    a: _ArrayLikeComplex_co,
+    axis: None = None,
+    dtype: None = None,
+    out: None = None,
+    ddof: float = 0,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> floating: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: None = None,
+    out: None = None,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    ddof: float = 0,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = None,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = None,
+    ddof: float = 0,
+    keepdims: Literal[False] | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    out: None = None,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = None,
+    dtype: DTypeLike | None = None,
+    *,
+    out: _ArrayT,
+    ddof: float = 0,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+
+max = amax
+min = amin
+round = around

python/user_packages/Python313/site-packages/numpy/_core/function_base.py

@@ -0,0 +1,547 @@
+import functools
+import inspect
+import operator
+import types
+import warnings
+
+import numpy as np
+from numpy._core import overrides
+from numpy._core._multiarray_umath import _array_converter
+from numpy._core.multiarray import add_docstring
+
+from . import numeric as _nx
+from .numeric import asanyarray, nan, ndim, result_type
+
+__all__ = ['logspace', 'linspace', 'geomspace']
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+def _linspace_dispatcher(start, stop, num=None, endpoint=None, retstep=None,
+                         dtype=None, axis=None, *, device=None):
+    return (start, stop)
+
+
+@array_function_dispatch(_linspace_dispatcher)
+def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None,
+             axis=0, *, device=None):
+    """
+    Return evenly spaced numbers over a specified interval.
+
+    Returns `num` evenly spaced samples, calculated over the
+    interval [`start`, `stop`].
+
+    The endpoint of the interval can optionally be excluded.
+
+    .. versionchanged:: 1.20.0
+        Values are rounded towards ``-inf`` instead of ``0`` when an
+        integer ``dtype`` is specified. The old behavior can
+        still be obtained with ``np.linspace(start, stop, num).astype(int)``
+
+    Parameters
+    ----------
+    start : array_like
+        The starting value of the sequence.
+    stop : array_like
+        The end value of the sequence, unless `endpoint` is set to False.
+        In that case, the sequence consists of all but the last of ``num + 1``
+        evenly spaced samples, so that `stop` is excluded.  Note that the step
+        size changes when `endpoint` is False.
+    num : int, optional
+        Number of samples to generate. Default is 50. Must be non-negative.
+    endpoint : bool, optional
+        If True, `stop` is the last sample. Otherwise, it is not included.
+        Default is True.
+    retstep : bool, optional
+        If True, return (`samples`, `step`), where `step` is the spacing
+        between samples.
+    dtype : dtype, optional
+        The type of the output array.  If `dtype` is not given, the data type
+        is inferred from `start` and `stop`. The inferred dtype will never be
+        an integer; `float` is chosen even if the arguments would produce an
+        array of integers.
+    axis : int, optional
+        The axis in the result to store the samples.  Relevant only if start
+        or stop are array-like.  By default (0), the samples will be along a
+        new axis inserted at the beginning. Use -1 to get an axis at the end.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    samples : ndarray
+        There are `num` equally spaced samples in the closed interval
+        ``[start, stop]`` or the half-open interval ``[start, stop)``
+        (depending on whether `endpoint` is True or False).
+    step : float, optional
+        Only returned if `retstep` is True
+
+        Size of spacing between samples.
+
+
+    See Also
+    --------
+    arange : Similar to `linspace`, but uses a step size (instead of the
+             number of samples).
+    geomspace : Similar to `linspace`, but with numbers spaced evenly on a log
+                scale (a geometric progression).
+    logspace : Similar to `geomspace`, but with the end points specified as
+               logarithms.
+    :ref:`how-to-partition`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.linspace(2.0, 3.0, num=5)
+    array([2.  , 2.25, 2.5 , 2.75, 3.  ])
+    >>> np.linspace(2.0, 3.0, num=5, endpoint=False)
+    array([2. ,  2.2,  2.4,  2.6,  2.8])
+    >>> np.linspace(2.0, 3.0, num=5, retstep=True)
+    (array([2.  ,  2.25,  2.5 ,  2.75,  3.  ]), 0.25)
+
+    Graphical illustration:
+
+    >>> import matplotlib.pyplot as plt
+    >>> N = 8
+    >>> y = np.zeros(N)
+    >>> x1 = np.linspace(0, 10, N, endpoint=True)
+    >>> x2 = np.linspace(0, 10, N, endpoint=False)
+    >>> plt.plot(x1, y, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.plot(x2, y + 0.5, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.ylim([-0.5, 1])
+    (-0.5, 1)
+    >>> plt.show()
+
+    """
+    num = operator.index(num)
+    if num < 0:
+        raise ValueError(
+            f"Number of samples, {num}, must be non-negative."
+        )
+    div = (num - 1) if endpoint else num
+
+    conv = _array_converter(start, stop)
+    start, stop = conv.as_arrays()
+    dt = conv.result_type(ensure_inexact=True)
+
+    if dtype is None:
+        dtype = dt
+        integer_dtype = False
+    else:
+        integer_dtype = _nx.issubdtype(dtype, _nx.integer)
+
+    # Use `dtype=type(dt)` to enforce a floating point evaluation:
+    delta = np.subtract(stop, start, dtype=type(dt))
+    y = _nx.arange(
+        0, num, dtype=dt, device=device
+    ).reshape((-1,) + (1,) * ndim(delta))
+
+    # In-place multiplication y *= delta/div is faster, but prevents
+    # the multiplicant from overriding what class is produced, and thus
+    # prevents, e.g. use of Quantities, see gh-7142. Hence, we multiply
+    # in place only for standard scalar types.
+    if div > 0:
+        _mult_inplace = _nx.isscalar(delta)
+        step = delta / div
+        any_step_zero = (
+            step == 0 if _mult_inplace else _nx.asanyarray(step == 0).any())
+        if any_step_zero:
+            # Special handling for denormal numbers, gh-5437
+            y /= div
+            if _mult_inplace:
+                y *= delta
+            else:
+                y = y * delta
+        elif _mult_inplace:
+            y *= step
+        else:
+            y = y * step
+    else:
+        # sequences with 0 items or 1 item with endpoint=True (i.e. div <= 0)
+        # have an undefined step
+        step = nan
+        # Multiply with delta to allow possible override of output class.
+        y = y * delta
+
+    y += start
+
+    if endpoint and num > 1:
+        y[-1, ...] = stop
+
+    if axis != 0:
+        y = _nx.moveaxis(y, 0, axis)
+
+    if integer_dtype:
+        _nx.floor(y, out=y)
+
+    y = conv.wrap(y.astype(dtype, copy=False))
+    if retstep:
+        return y, step
+    else:
+        return y
+
+
+def _logspace_dispatcher(start, stop, num=None, endpoint=None, base=None,
+                         dtype=None, axis=None):
+    return (start, stop, base)
+
+
+@array_function_dispatch(_logspace_dispatcher)
+def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None,
+             axis=0):
+    """
+    Return numbers spaced evenly on a log scale.
+
+    In linear space, the sequence starts at ``base ** start``
+    (`base` to the power of `start`) and ends with ``base ** stop``
+    (see `endpoint` below).
+
+    .. versionchanged:: 1.25.0
+        Non-scalar 'base` is now supported
+
+    Parameters
+    ----------
+    start : array_like
+        ``base ** start`` is the starting value of the sequence.
+    stop : array_like
+        ``base ** stop`` is the final value of the sequence, unless `endpoint`
+        is False.  In that case, ``num + 1`` values are spaced over the
+        interval in log-space, of which all but the last (a sequence of
+        length `num`) are returned.
+    num : integer, optional
+        Number of samples to generate.  Default is 50.
+    endpoint : boolean, optional
+        If true, `stop` is the last sample. Otherwise, it is not included.
+        Default is True.
+    base : array_like, optional
+        The base of the log space. The step size between the elements in
+        ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform.
+        Default is 10.0.
+    dtype : dtype
+        The type of the output array.  If `dtype` is not given, the data type
+        is inferred from `start` and `stop`. The inferred type will never be
+        an integer; `float` is chosen even if the arguments would produce an
+        array of integers.
+    axis : int, optional
+        The axis in the result to store the samples.  Relevant only if start,
+        stop, or base are array-like.  By default (0), the samples will be
+        along a new axis inserted at the beginning. Use -1 to get an axis at
+        the end.
+
+    Returns
+    -------
+    samples : ndarray
+        `num` samples, equally spaced on a log scale.
+
+    See Also
+    --------
+    arange : Similar to linspace, with the step size specified instead of the
+             number of samples. Note that, when used with a float endpoint, the
+             endpoint may or may not be included.
+    linspace : Similar to logspace, but with the samples uniformly distributed
+               in linear space, instead of log space.
+    geomspace : Similar to logspace, but with endpoints specified directly.
+    :ref:`how-to-partition`
+
+    Notes
+    -----
+    If base is a scalar, logspace is equivalent to the code
+
+    >>> y = np.linspace(start, stop, num=num, endpoint=endpoint)
+    ... # doctest: +SKIP
+    >>> power(base, y).astype(dtype)
+    ... # doctest: +SKIP
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.logspace(2.0, 3.0, num=4)
+    array([ 100.        ,  215.443469  ,  464.15888336, 1000.        ])
+    >>> np.logspace(2.0, 3.0, num=4, endpoint=False)
+    array([100.        ,  177.827941  ,  316.22776602,  562.34132519])
+    >>> np.logspace(2.0, 3.0, num=4, base=2.0)
+    array([4.        ,  5.0396842 ,  6.34960421,  8.        ])
+    >>> np.logspace(2.0, 3.0, num=4, base=[2.0, 3.0], axis=-1)
+    array([[ 4.        ,  5.0396842 ,  6.34960421,  8.        ],
+           [ 9.        , 12.98024613, 18.72075441, 27.        ]])
+
+    Graphical illustration:
+
+    >>> import matplotlib.pyplot as plt
+    >>> N = 10
+    >>> x1 = np.logspace(0.1, 1, N, endpoint=True)
+    >>> x2 = np.logspace(0.1, 1, N, endpoint=False)
+    >>> y = np.zeros(N)
+    >>> plt.plot(x1, y, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.plot(x2, y + 0.5, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.ylim([-0.5, 1])
+    (-0.5, 1)
+    >>> plt.show()
+
+    """
+    if not isinstance(base, (float, int)) and np.ndim(base):
+        # If base is non-scalar, broadcast it with the others, since it
+        # may influence how axis is interpreted.
+        ndmax = np.broadcast(start, stop, base).ndim
+        start, stop, base = (
+            np.array(a, copy=None, subok=True, ndmin=ndmax)
+            for a in (start, stop, base)
+        )
+        base = np.expand_dims(base, axis=axis)
+    y = linspace(start, stop, num=num, endpoint=endpoint, axis=axis)
+    if dtype is None:
+        return _nx.power(base, y)
+    return _nx.power(base, y).astype(dtype, copy=False)
+
+
+def _geomspace_dispatcher(start, stop, num=None, endpoint=None, dtype=None,
+                          axis=None):
+    return (start, stop)
+
+
+@array_function_dispatch(_geomspace_dispatcher)
+def geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0):
+    """
+    Return numbers spaced evenly on a log scale (a geometric progression).
+
+    This is similar to `logspace`, but with endpoints specified directly.
+    Each output sample is a constant multiple of the previous.
+
+    Parameters
+    ----------
+    start : array_like
+        The starting value of the sequence.
+    stop : array_like
+        The final value of the sequence, unless `endpoint` is False.
+        In that case, ``num + 1`` values are spaced over the
+        interval in log-space, of which all but the last (a sequence of
+        length `num`) are returned.
+    num : integer, optional
+        Number of samples to generate.  Default is 50.
+    endpoint : boolean, optional
+        If true, `stop` is the last sample. Otherwise, it is not included.
+        Default is True.
+    dtype : dtype
+        The type of the output array.  If `dtype` is not given, the data type
+        is inferred from `start` and `stop`. The inferred dtype will never be
+        an integer; `float` is chosen even if the arguments would produce an
+        array of integers.
+    axis : int, optional
+        The axis in the result to store the samples.  Relevant only if start
+        or stop are array-like.  By default (0), the samples will be along a
+        new axis inserted at the beginning. Use -1 to get an axis at the end.
+
+    Returns
+    -------
+    samples : ndarray
+        `num` samples, equally spaced on a log scale.
+
+    See Also
+    --------
+    logspace : Similar to geomspace, but with endpoints specified using log
+               and base.
+    linspace : Similar to geomspace, but with arithmetic instead of geometric
+               progression.
+    arange : Similar to linspace, with the step size specified instead of the
+             number of samples.
+    :ref:`how-to-partition`
+
+    Notes
+    -----
+    If the inputs or dtype are complex, the output will follow a logarithmic
+    spiral in the complex plane.  (There are an infinite number of spirals
+    passing through two points; the output will follow the shortest such path.)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.geomspace(1, 1000, num=4)
+    array([    1.,    10.,   100.,  1000.])
+    >>> np.geomspace(1, 1000, num=3, endpoint=False)
+    array([   1.,   10.,  100.])
+    >>> np.geomspace(1, 1000, num=4, endpoint=False)
+    array([   1.        ,    5.62341325,   31.6227766 ,  177.827941  ])
+    >>> np.geomspace(1, 256, num=9)
+    array([   1.,    2.,    4.,    8.,   16.,   32.,   64.,  128.,  256.])
+
+    Note that the above may not produce exact integers:
+
+    >>> np.geomspace(1, 256, num=9, dtype=int)
+    array([  1,   2,   4,   7,  16,  32,  63, 127, 256])
+    >>> np.around(np.geomspace(1, 256, num=9)).astype(int)
+    array([  1,   2,   4,   8,  16,  32,  64, 128, 256])
+
+    Negative, decreasing, and complex inputs are allowed:
+
+    >>> np.geomspace(1000, 1, num=4)
+    array([1000.,  100.,   10.,    1.])
+    >>> np.geomspace(-1000, -1, num=4)
+    array([-1000.,  -100.,   -10.,    -1.])
+    >>> np.geomspace(1j, 1000j, num=4)  # Straight line
+    array([0.   +1.j, 0.  +10.j, 0. +100.j, 0.+1000.j])
+    >>> np.geomspace(-1+0j, 1+0j, num=5)  # Circle
+    array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j,
+            6.12323400e-17+1.00000000e+00j,  7.07106781e-01+7.07106781e-01j,
+            1.00000000e+00+0.00000000e+00j])
+
+    Graphical illustration of `endpoint` parameter:
+
+    >>> import matplotlib.pyplot as plt
+    >>> N = 10
+    >>> y = np.zeros(N)
+    >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.axis([0.5, 2000, 0, 3])
+    [0.5, 2000, 0, 3]
+    >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both')
+    >>> plt.show()
+
+    """
+    start = asanyarray(start)
+    stop = asanyarray(stop)
+    if _nx.any(start == 0) or _nx.any(stop == 0):
+        raise ValueError('Geometric sequence cannot include zero')
+
+    dt = result_type(start, stop, float(num), _nx.zeros((), dtype))
+    if dtype is None:
+        dtype = dt
+    else:
+        # complex to dtype('complex128'), for instance
+        dtype = _nx.dtype(dtype)
+
+    # Promote both arguments to the same dtype in case, for instance, one is
+    # complex and another is negative and log would produce NaN otherwise.
+    # Copy since we may change things in-place further down.
+    start = start.astype(dt, copy=True)
+    stop = stop.astype(dt, copy=True)
+
+    # Allow negative real values and ensure a consistent result for complex
+    # (including avoiding negligible real or imaginary parts in output) by
+    # rotating start to positive real, calculating, then undoing rotation.
+    out_sign = _nx.sign(start)
+    start /= out_sign
+    stop = stop / out_sign
+
+    log_start = _nx.log10(start)
+    log_stop = _nx.log10(stop)
+    result = logspace(log_start, log_stop, num=num,
+                      endpoint=endpoint, base=10.0, dtype=dt)
+
+    # Make sure the endpoints match the start and stop arguments. This is
+    # necessary because np.exp(np.log(x)) is not necessarily equal to x.
+    if num > 0:
+        result[0] = start
+        if num > 1 and endpoint:
+            result[-1] = stop
+
+    result *= out_sign
+
+    if axis != 0:
+        result = _nx.moveaxis(result, 0, axis)
+
+    return result.astype(dtype, copy=False)
+
+
+def _needs_add_docstring(obj):
+    """
+    Returns true if the only way to set the docstring of `obj` from python is
+    via add_docstring.
+
+    This function errs on the side of being overly conservative.
+    """
+    Py_TPFLAGS_HEAPTYPE = 1 << 9
+
+    if isinstance(obj, (types.FunctionType, types.MethodType, property)):
+        return False
+
+    if isinstance(obj, type) and obj.__flags__ & Py_TPFLAGS_HEAPTYPE:
+        return False
+
+    return True
+
+
+def _add_docstring(obj, doc, warn_on_python):
+    if warn_on_python and not _needs_add_docstring(obj):
+        warnings.warn(
+            f"add_newdoc was used on a pure-python object {obj}. "
+            "Prefer to attach it directly to the source.",
+            UserWarning,
+            stacklevel=3)
+
+    doc = inspect.cleandoc(doc)
+
+    try:
+        add_docstring(obj, doc)
+    except Exception:
+        pass
+
+
+def add_newdoc(place, obj, doc, warn_on_python=True):
+    """
+    Add documentation to an existing object, typically one defined in C
+
+    The purpose is to allow easier editing of the docstrings without requiring
+    a re-compile. This exists primarily for internal use within numpy itself.
+
+    Parameters
+    ----------
+    place : str
+        The absolute name of the module to import from
+    obj : str | None
+        The name of the object to add documentation to, typically a class or
+        function name.
+    doc : str | tuple[str, str] | list[tuple[str, str]]
+        If a string, the documentation to apply to `obj`
+
+        If a tuple, then the first element is interpreted as an attribute
+        of `obj` and the second as the docstring to apply -
+        ``(method, docstring)``
+
+        If a list, then each element of the list should be a tuple of length
+        two - ``[(method1, docstring1), (method2, docstring2), ...]``
+    warn_on_python : bool
+        If True, the default, emit `UserWarning` if this is used to attach
+        documentation to a pure-python object.
+
+    Notes
+    -----
+    This routine never raises an error if the docstring can't be written, but
+    will raise an error if the object being documented does not exist.
+
+    This routine cannot modify read-only docstrings, as appear
+    in new-style classes or built-in functions. Because this
+    routine never raises an error the caller must check manually
+    that the docstrings were changed.
+
+    Since this function grabs the ``char *`` from a c-level str object and puts
+    it into the ``tp_doc`` slot of the type of `obj`, it violates a number of
+    C-API best-practices, by:
+
+    - modifying a `PyTypeObject` after calling `PyType_Ready`
+    - calling `Py_INCREF` on the str and losing the reference, so the str
+      will never be released
+
+    If possible it should be avoided.
+    """
+    new = getattr(__import__(place, globals(), {}, [obj]), obj)
+    if isinstance(doc, str):
+        if "${ARRAY_FUNCTION_LIKE}" in doc:
+            doc = overrides.get_array_function_like_doc(new, doc)
+        _add_docstring(new, doc, warn_on_python)
+    elif isinstance(doc, tuple):
+        attr, docstring = doc
+        _add_docstring(getattr(new, attr), docstring, warn_on_python)
+    elif isinstance(doc, list):
+        for attr, docstring in doc:
+            _add_docstring(getattr(new, attr), docstring, warn_on_python)

python/user_packages/Python313/site-packages/numpy/_core/function_base.pyi

@@ -0,0 +1,276 @@
+from _typeshed import Incomplete
+from typing import Literal as L, SupportsIndex, TypeAlias, TypeVar, overload
+
+import numpy as np
+from numpy._typing import (
+    DTypeLike,
+    NDArray,
+    _ArrayLikeComplex_co,
+    _ArrayLikeFloat_co,
+    _DTypeLike,
+)
+from numpy._typing._array_like import _DualArrayLike
+
+__all__ = ["geomspace", "linspace", "logspace"]
+
+_ScalarT = TypeVar("_ScalarT", bound=np.generic)
+
+_ToArrayFloat64: TypeAlias = _DualArrayLike[np.dtype[np.float64 | np.integer | np.bool], float]
+
+@overload
+def linspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[np.float64]: ...
+@overload
+def linspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[np.floating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[np.complexfloating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex,
+    endpoint: bool,
+    retstep: L[False],
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[Incomplete]: ...
+@overload
+def linspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[np.float64], np.float64]: ...
+@overload
+def linspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[np.floating], np.floating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[np.complexfloating], np.complexfloating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[_ScalarT], _ScalarT]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[Incomplete], Incomplete]: ...
+
+@overload
+def logspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ToArrayFloat64 = 10.0,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.float64]: ...
+@overload
+def logspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeFloat_co = 10.0,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.floating]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeComplex_co = 10.0,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.complexfloating]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex,
+    endpoint: bool,
+    base: _ArrayLikeComplex_co,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeComplex_co = 10.0,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeComplex_co = 10.0,
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[Incomplete]: ...
+
+@overload
+def geomspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.float64]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.floating]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.complexfloating]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex,
+    endpoint: bool,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[Incomplete]: ...
+
+def add_newdoc(
+    place: str,
+    obj: str,
+    doc: str | tuple[str, str] | list[tuple[str, str]],
+    warn_on_python: bool = True,
+) -> None: ...

python/user_packages/Python313/site-packages/numpy/_core/getlimits.py

@@ -0,0 +1,462 @@
+"""Machine limits for Float32 and Float64 and (long double) if available...
+
+"""
+__all__ = ['finfo', 'iinfo']
+
+import math
+import types
+import warnings
+from functools import cached_property
+
+from numpy._utils import set_module
+
+from . import numeric, numerictypes as ntypes
+from ._multiarray_umath import _populate_finfo_constants
+
+
+def _fr0(a):
+    """fix rank-0 --> rank-1"""
+    if a.ndim == 0:
+        a = a.copy()
+        a.shape = (1,)
+    return a
+
+
+def _fr1(a):
+    """fix rank > 0 --> rank-0"""
+    if a.size == 1:
+        a = a.copy()
+        a.shape = ()
+    return a
+
+
+_convert_to_float = {
+    ntypes.csingle: ntypes.single,
+    ntypes.complex128: ntypes.float64,
+    ntypes.clongdouble: ntypes.longdouble
+    }
+
+# Parameters for creating MachAr / MachAr-like objects
+_title_fmt = 'numpy {} precision floating point number'
+_MACHAR_PARAMS = {
+    ntypes.double: {
+        'itype': ntypes.int64,
+        'fmt': '%24.16e',
+        'title': _title_fmt.format('double')},
+    ntypes.single: {
+        'itype': ntypes.int32,
+        'fmt': '%15.7e',
+        'title': _title_fmt.format('single')},
+    ntypes.longdouble: {
+        'itype': ntypes.longlong,
+        'fmt': '%s',
+        'title': _title_fmt.format('long double')},
+    ntypes.half: {
+        'itype': ntypes.int16,
+        'fmt': '%12.5e',
+        'title': _title_fmt.format('half')}}
+
+
+@set_module('numpy')
+class finfo:
+    """
+    finfo(dtype)
+
+    Machine limits for floating point types.
+
+    Attributes
+    ----------
+    bits : int
+        The number of bits occupied by the type.
+    dtype : dtype
+        Returns the dtype for which `finfo` returns information. For complex
+        input, the returned dtype is the associated ``float*`` dtype for its
+        real and complex components.
+    eps : float
+        The difference between 1.0 and the next smallest representable float
+        larger than 1.0. For example, for 64-bit binary floats in the IEEE-754
+        standard, ``eps = 2**-52``, approximately 2.22e-16.
+    epsneg : float
+        The difference between 1.0 and the next smallest representable float
+        less than 1.0. For example, for 64-bit binary floats in the IEEE-754
+        standard, ``epsneg = 2**-53``, approximately 1.11e-16.
+    iexp : int
+        The number of bits in the exponent portion of the floating point
+        representation.
+    machep : int
+        The exponent that yields `eps`.
+    max : floating point number of the appropriate type
+        The largest representable number.
+    maxexp : int
+        The smallest positive power of the base (2) that causes overflow.
+        Corresponds to the C standard MAX_EXP.
+    min : floating point number of the appropriate type
+        The smallest representable number, typically ``-max``.
+    minexp : int
+        The most negative power of the base (2) consistent with there
+        being no leading 0's in the mantissa. Corresponds to the C
+        standard MIN_EXP - 1.
+    negep : int
+        The exponent that yields `epsneg`.
+    nexp : int
+        The number of bits in the exponent including its sign and bias.
+    nmant : int
+        The number of explicit bits in the mantissa (excluding the implicit
+        leading bit for normalized numbers).
+    precision : int
+        The approximate number of decimal digits to which this kind of
+        float is precise.
+    resolution : floating point number of the appropriate type
+        The approximate decimal resolution of this type, i.e.,
+        ``10**-precision``.
+    tiny : float
+        An alias for `smallest_normal`, kept for backwards compatibility.
+    smallest_normal : float
+        The smallest positive floating point number with 1 as leading bit in
+        the mantissa following IEEE-754 (see Notes).
+    smallest_subnormal : float
+        The smallest positive floating point number with 0 as leading bit in
+        the mantissa following IEEE-754.
+
+    Parameters
+    ----------
+    dtype : float, dtype, or instance
+        Kind of floating point or complex floating point
+        data-type about which to get information.
+
+    See Also
+    --------
+    iinfo : The equivalent for integer data types.
+    spacing : The distance between a value and the nearest adjacent number
+    nextafter : The next floating point value after x1 towards x2
+
+    Notes
+    -----
+    For developers of NumPy: do not instantiate this at the module level.
+    The initial calculation of these parameters is expensive and negatively
+    impacts import times.  These objects are cached, so calling ``finfo()``
+    repeatedly inside your functions is not a problem.
+
+    Note that ``smallest_normal`` is not actually the smallest positive
+    representable value in a NumPy floating point type. As in the IEEE-754
+    standard [1]_, NumPy floating point types make use of subnormal numbers to
+    fill the gap between 0 and ``smallest_normal``. However, subnormal numbers
+    may have significantly reduced precision [2]_.
+
+    For ``longdouble``, the representation varies across platforms. On most
+    platforms it is IEEE 754 binary128 (quad precision) or binary64-extended
+    (80-bit extended precision). On PowerPC systems, it may use the IBM
+    double-double format (a pair of float64 values), which has special
+    characteristics for precision and range.
+
+    This function can also be used for complex data types as well. If used,
+    the output will be the same as the corresponding real float type
+    (e.g. numpy.finfo(numpy.csingle) is the same as numpy.finfo(numpy.single)).
+    However, the output is true for the real and imaginary components.
+
+    References
+    ----------
+    .. [1] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008,
+           pp.1-70, 2008, https://doi.org/10.1109/IEEESTD.2008.4610935
+    .. [2] Wikipedia, "Denormal Numbers",
+           https://en.wikipedia.org/wiki/Denormal_number
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.finfo(np.float64).dtype
+    dtype('float64')
+    >>> np.finfo(np.complex64).dtype
+    dtype('float32')
+
+    """
+
+    _finfo_cache = {}
+
+    __class_getitem__ = classmethod(types.GenericAlias)
+
+    def __new__(cls, dtype):
+        try:
+            obj = cls._finfo_cache.get(dtype)  # most common path
+            if obj is not None:
+                return obj
+        except TypeError:
+            pass
+
+        if dtype is None:
+            # Deprecated in NumPy 1.25, 2023-01-16
+            warnings.warn(
+                "finfo() dtype cannot be None. This behavior will "
+                "raise an error in the future. (Deprecated in NumPy 1.25)",
+                DeprecationWarning,
+                stacklevel=2
+            )
+
+        try:
+            dtype = numeric.dtype(dtype)
+        except TypeError:
+            # In case a float instance was given
+            dtype = numeric.dtype(type(dtype))
+
+        obj = cls._finfo_cache.get(dtype)
+        if obj is not None:
+            return obj
+        dtypes = [dtype]
+        newdtype = ntypes.obj2sctype(dtype)
+        if newdtype is not dtype:
+            dtypes.append(newdtype)
+            dtype = newdtype
+        if not issubclass(dtype, numeric.inexact):
+            raise ValueError(f"data type {dtype!r} not inexact")
+        obj = cls._finfo_cache.get(dtype)
+        if obj is not None:
+            return obj
+        if not issubclass(dtype, numeric.floating):
+            newdtype = _convert_to_float[dtype]
+            if newdtype is not dtype:
+                # dtype changed, for example from complex128 to float64
+                dtypes.append(newdtype)
+                dtype = newdtype
+
+                obj = cls._finfo_cache.get(dtype, None)
+                if obj is not None:
+                    # the original dtype was not in the cache, but the new
+                    # dtype is in the cache. we add the original dtypes to
+                    # the cache and return the result
+                    for dt in dtypes:
+                        cls._finfo_cache[dt] = obj
+                    return obj
+        obj = object.__new__(cls)._init(dtype)
+        for dt in dtypes:
+            cls._finfo_cache[dt] = obj
+        return obj
+
+    def _init(self, dtype):
+        self.dtype = numeric.dtype(dtype)
+        self.bits = self.dtype.itemsize * 8
+        self._fmt = None
+        self._repr = None
+        _populate_finfo_constants(self, self.dtype)
+        return self
+
+    @cached_property
+    def epsneg(self):
+        # Assume typical floating point logic.  Could also use nextafter.
+        return self.eps / self._radix
+
+    @cached_property
+    def resolution(self):
+        return self.dtype.type(10)**-self.precision
+
+    @cached_property
+    def machep(self):
+        return int(math.log2(self.eps))
+
+    @cached_property
+    def negep(self):
+        return int(math.log2(self.epsneg))
+
+    @cached_property
+    def nexp(self):
+        # considering all ones (inf/nan) and all zeros (subnormal/zero)
+        return math.ceil(math.log2(self.maxexp - self.minexp + 2))
+
+    @cached_property
+    def iexp(self):
+        # Calculate exponent bits from it's range:
+        return math.ceil(math.log2(self.maxexp - self.minexp))
+
+    def __str__(self):
+        if (fmt := getattr(self, "_fmt", None)) is not None:
+            return fmt
+
+        def get_str(name, pad=None):
+            if (val := getattr(self, name, None)) is None:
+                return "<undefined>"
+            if pad is not None:
+                s = str(val).ljust(pad)
+            return str(val)
+
+        precision = get_str("precision", 3)
+        machep = get_str("machep", 6)
+        negep = get_str("negep", 6)
+        minexp = get_str("minexp", 6)
+        maxexp = get_str("maxexp", 6)
+        resolution = get_str("resolution")
+        eps = get_str("eps")
+        epsneg = get_str("epsneg")
+        tiny = get_str("tiny")
+        smallest_normal = get_str("smallest_normal")
+        smallest_subnormal = get_str("smallest_subnormal")
+        nexp = get_str("nexp", 6)
+        max_ = get_str("max")
+        if hasattr(self, "min") and hasattr(self, "max") and -self.min == self.max:
+            min_ = "-max"
+        else:
+            min_ = get_str("min")
+
+        fmt = (
+            f'Machine parameters for {self.dtype}\n'
+            f'---------------------------------------------------------------\n'
+            f'precision = {precision}   resolution = {resolution}\n'
+            f'machep = {machep}   eps =        {eps}\n'
+            f'negep =  {negep}   epsneg =     {epsneg}\n'
+            f'minexp = {minexp}   tiny =       {tiny}\n'
+            f'maxexp = {maxexp}   max =        {max_}\n'
+            f'nexp =   {nexp}   min =        {min_}\n'
+            f'smallest_normal = {smallest_normal}   '
+            f'smallest_subnormal = {smallest_subnormal}\n'
+            f'---------------------------------------------------------------\n'
+        )
+        self._fmt = fmt
+        return fmt
+
+    def __repr__(self):
+        if (repr_str := getattr(self, "_repr", None)) is not None:
+            return repr_str
+
+        c = self.__class__.__name__
+
+        # Use precision+1 digits in exponential notation
+        fmt_str = _MACHAR_PARAMS.get(self.dtype.type, {}).get('fmt', '%s')
+        if fmt_str != '%s' and hasattr(self, 'max') and hasattr(self, 'min'):
+            max_str = (fmt_str % self.max).strip()
+            min_str = (fmt_str % self.min).strip()
+        else:
+            max_str = str(self.max)
+            min_str = str(self.min)
+
+        resolution_str = str(self.resolution)
+
+        repr_str = (f"{c}(resolution={resolution_str}, min={min_str},"
+                    f" max={max_str}, dtype={self.dtype})")
+        self._repr = repr_str
+        return repr_str
+
+    @cached_property
+    def tiny(self):
+        """Return the value for tiny, alias of smallest_normal.
+
+        Returns
+        -------
+        tiny : float
+            Value for the smallest normal, alias of smallest_normal.
+
+        Warns
+        -----
+        UserWarning
+            If the calculated value for the smallest normal is requested for
+            double-double.
+        """
+        return self.smallest_normal
+
+
+@set_module('numpy')
+class iinfo:
+    """
+    iinfo(type)
+
+    Machine limits for integer types.
+
+    Attributes
+    ----------
+    bits : int
+        The number of bits occupied by the type.
+    dtype : dtype
+        Returns the dtype for which `iinfo` returns information.
+    min : int
+        The smallest integer expressible by the type.
+    max : int
+        The largest integer expressible by the type.
+
+    Parameters
+    ----------
+    int_type : integer type, dtype, or instance
+        The kind of integer data type to get information about.
+
+    See Also
+    --------
+    finfo : The equivalent for floating point data types.
+
+    Examples
+    --------
+    With types:
+
+    >>> import numpy as np
+    >>> ii16 = np.iinfo(np.int16)
+    >>> ii16.min
+    -32768
+    >>> ii16.max
+    32767
+    >>> ii32 = np.iinfo(np.int32)
+    >>> ii32.min
+    -2147483648
+    >>> ii32.max
+    2147483647
+
+    With instances:
+
+    >>> ii32 = np.iinfo(np.int32(10))
+    >>> ii32.min
+    -2147483648
+    >>> ii32.max
+    2147483647
+
+    """
+
+    _min_vals = {}
+    _max_vals = {}
+
+    __class_getitem__ = classmethod(types.GenericAlias)
+
+    def __init__(self, int_type):
+        try:
+            self.dtype = numeric.dtype(int_type)
+        except TypeError:
+            self.dtype = numeric.dtype(type(int_type))
+        self.kind = self.dtype.kind
+        self.bits = self.dtype.itemsize * 8
+        self.key = "%s%d" % (self.kind, self.bits)
+        if self.kind not in 'iu':
+            raise ValueError(f"Invalid integer data type {self.kind!r}.")
+
+    @property
+    def min(self):
+        """Minimum value of given dtype."""
+        if self.kind == 'u':
+            return 0
+        else:
+            try:
+                val = iinfo._min_vals[self.key]
+            except KeyError:
+                val = int(-(1 << (self.bits - 1)))
+                iinfo._min_vals[self.key] = val
+            return val
+
+    @property
+    def max(self):
+        """Maximum value of given dtype."""
+        try:
+            val = iinfo._max_vals[self.key]
+        except KeyError:
+            if self.kind == 'u':
+                val = int((1 << self.bits) - 1)
+            else:
+                val = int((1 << (self.bits - 1)) - 1)
+            iinfo._max_vals[self.key] = val
+        return val
+
+    def __str__(self):
+        """String representation."""
+        fmt = (
+            'Machine parameters for %(dtype)s\n'
+            '---------------------------------------------------------------\n'
+            'min = %(min)s\n'
+            'max = %(max)s\n'
+            '---------------------------------------------------------------\n'
+            )
+        return fmt % {'dtype': self.dtype, 'min': self.min, 'max': self.max}
+
+    def __repr__(self):
+        return "%s(min=%s, max=%s, dtype=%s)" % (self.__class__.__name__,
+                                    self.min, self.max, self.dtype)