from __future__ import annotations


import builtins
from collections.abc import Callable, Sequence
import os
from typing import Any, IO, Literal, NamedTuple, Protocol, TypeVar, Union, overload

from jax._src import core as _core
from jax._src import dtypes as _dtypes
from jax._src.lax.lax import PrecisionLike
from jax._src.lax.slicing import GatherScatterMode
from jax._src.lib import Device
from jax._src.numpy.index_tricks import _Mgrid, _Ogrid, CClass as _CClass, RClass as _RClass
from jax._src.numpy.array_api_metadata import ArrayNamespaceInfo
from jax._src.typing import (
    Array, ArrayLike, DType, DTypeLike, DeprecatedArg,
    DimSize, DuckTypedArray, Shape, StaticScalar, SupportsNdim, SupportsShape, SupportsSize,
)
from jax._src.sharding_impls import NamedSharding, PartitionSpec as P
from jax.numpy import fft as fft, linalg as linalg
from jax.sharding import Sharding as _Sharding
import numpy as _np

_T = TypeVar('_T')

_Axis = Union[None, int, Sequence[int]]

_Device = Device

ComplexWarning: type

class ufunc:
  def __init__(self, func: Callable[..., Any], /,
               nin: int, nout: int, *,
               name: str | None = None,
               nargs: int | None = None,
               identity: Any = None,
               call: Callable[..., Any] | None = None,
               reduce: Callable[..., Any] | None = None,
               accumulate: Callable[..., Any] | None = None,
               at: Callable[..., Any] | None = None,
               reduceat: Callable[..., Any] | None = None,
               ): ...
  @property
  def nin(self) -> int: ...
  @property
  def nout(self) -> int: ...
  @property
  def nargs(self) -> int: ...
  @property
  def identity(self) -> builtins.bool | int | float: ...
  def __call__(self, *args: ArrayLike) -> Any: ...
  def reduce(self, a: ArrayLike, /, *,
             axis: int | None = 0,
             dtype: DTypeLike | None = None,
             out: None = None,
             keepdims: builtins.bool = False,
             initial: ArrayLike | None = None,
             where: ArrayLike | None = None) -> Array: ...
  def accumulate(self, a: ArrayLike, /, *,
                 axis: int = 0,
                 dtype: DTypeLike | None = None,
                 out: None = None) -> Array: ...
  def at(self, a: ArrayLike, indices: Any, b: ArrayLike | None = None, /, *,
         inplace: builtins.bool = True) -> Array: ...
  def reduceat(self, a: ArrayLike, indices: Any, *,
               axis: int = 0,
               dtype: DTypeLike | None = None,
               out: None = None) -> Array: ...
  def outer(self, a: ArrayLike, b: ArrayLike, /) -> Array: ...

class BinaryUfunc(Protocol):
  @property
  def nin(self) -> int: ...
  @property
  def nout(self) -> int: ...
  @property
  def nargs(self) -> int: ...
  @property
  def identity(self) -> builtins.bool | int | float: ...
  def __call__(self, x: ArrayLike, y: ArrayLike, /) -> Array: ...
  def reduce(self, a: ArrayLike, /, *,
             axis: int | None = 0,
             dtype: DTypeLike | None = None,
             out: None = None,
             keepdims: builtins.bool = False,
             initial: ArrayLike | None = None,
             where: ArrayLike | None = None) -> Array: ...
  def accumulate(self, a: ArrayLike, /, *,
                 axis: int = 0,
                 dtype: DTypeLike | None = None,
                 out: None = None) -> Array: ...
  def at(self, a: ArrayLike, indices: Any, b: ArrayLike | None = None, /, *,
         inplace: builtins.bool = True) -> Array: ...
  def reduceat(self, a: ArrayLike, indices: Any, *,
               axis: int = 0,
               dtype: DTypeLike | None = None,
               out: None = None) -> Array: ...
  def outer(self, a: ArrayLike, b: ArrayLike, /) -> Array: ...

__array_api_version__: str
def __array_namespace_info__() -> ArrayNamespaceInfo: ...

_deprecations: dict[str, tuple[str, Any]]
def abs(x: ArrayLike, /) -> Array: ...
def absolute(x: ArrayLike, /) -> Array: ...
def acos(x: ArrayLike, /) -> Array: ...
def acosh(x: ArrayLike, /) -> Array: ...
add: BinaryUfunc
def amax(a: ArrayLike, axis: _Axis = ..., out: None = ...,
         keepdims: builtins.bool = ..., initial: ArrayLike | None = ...,
         where: ArrayLike | None = ...) -> Array: ...
def amin(a: ArrayLike, axis: _Axis = ..., out: None = ...,
         keepdims: builtins.bool = ..., initial: ArrayLike | None = ...,
         where: ArrayLike | None = ...) -> Array: ...
def all(a: ArrayLike, axis: _Axis = ..., out: None = ...,
        keepdims: builtins.bool = ..., *, where: ArrayLike | None = ...) -> Array: ...
def allclose(a: ArrayLike, b: ArrayLike, rtol: ArrayLike = ...,
             atol: ArrayLike = ..., equal_nan: builtins.bool = ...) -> Array: ...
def angle(z: ArrayLike, deg: builtins.bool = ...) -> Array: ...
def any(a: ArrayLike, axis: _Axis = ..., out: None = ...,
        keepdims: builtins.bool = ..., *, where: ArrayLike | None = ...) -> Array: ...
def append(
    arr: ArrayLike, values: ArrayLike, axis: int | None = ...
) -> Array: ...
def apply_along_axis(func1d: Callable, axis: int, arr: ArrayLike, *args,
                     **kwargs) -> Array: ...
def apply_over_axes(
    func: Callable, a: ArrayLike, axes: Sequence[int]
) -> Array: ...
def arange(
    start: ArrayLike | DimSize,
    stop: ArrayLike | DimSize | None = ...,
    step: ArrayLike | None = ...,
    dtype: DTypeLike | None = ..., *,
    device: _Device | _Sharding | None = ...,
) -> Array: ...
def arccos(x: ArrayLike, /) -> Array: ...
def arccosh(x: ArrayLike, /) -> Array: ...
def arcsin(x: ArrayLike, /) -> Array: ...
def arcsinh(x: ArrayLike, /) -> Array: ...
def arctan(x: ArrayLike, /) -> Array: ...
def arctan2(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def arctanh(x: ArrayLike, /) -> Array: ...
def argmax(
    a: ArrayLike,
    axis: int | None = ...,
    out: None = ...,
    keepdims: builtins.bool | None = ...,
) -> Array: ...
def argmin(
    a: ArrayLike,
    axis: int | None = ...,
    out: None = ...,
    keepdims: builtins.bool | None = ...,
) -> Array: ...
def argpartition(a: ArrayLike, kth: int, axis: int = ...) -> Array: ...
def argsort(
    a: ArrayLike,
    axis: int | None = ...,
    *,
    stable: builtins.bool = ...,
    descending: builtins.bool = ...,
    kind: str | None = ...,
    order: None = ...,
) -> Array: ...
def argwhere(
    a: ArrayLike,
    *,
    size: int | None = ...,
    fill_value: ArrayLike | None = ...,
) -> Array: ...
def around(a: ArrayLike, decimals: int = ..., out: None = ...) -> Array: ...
def array(object: Any, dtype: DTypeLike | None = ..., copy: builtins.bool = True,
          order: str | None = ..., ndmin: int = ..., *,
          device: _Device | _Sharding | None = None) -> Array: ...
def array_equal(
    a1: ArrayLike, a2: ArrayLike, equal_nan: builtins.bool = ...
) -> Array: ...
def array_equiv(a1: ArrayLike, a2: ArrayLike) -> Array: ...
array_repr = _np.array_repr
def array_split(
    ary: ArrayLike,
    indices_or_sections: int | Sequence[int] | ArrayLike,
    axis: int = ...,
) -> list[Array]: ...
array_str = _np.array_str
def asarray(
    a: Any, dtype: DTypeLike | None = ..., order: str | None = ...,
    *, copy: builtins.bool | None = ...,
    device: _Device | _Sharding | None = ...,
) -> Array: ...
def asin(x: ArrayLike, /) -> Array: ...
def asinh(x: ArrayLike, /) -> Array: ...
def astype(a: ArrayLike, dtype: DTypeLike | None, /, *, copy: builtins.bool = ..., device: _Device | _Sharding | None = ...) -> Array: ...
def atan(x: ArrayLike, /) -> Array: ...
def atan2(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def atanh(x: ArrayLike, /) -> Array: ...
@overload
def atleast_1d() -> list[Array]: ...
@overload
def atleast_1d(x: ArrayLike, /) -> Array: ...
@overload
def atleast_1d(x: ArrayLike, y: ArrayLike, /, *arys: ArrayLike) -> list[Array]: ...

@overload
def atleast_2d() -> list[Array]: ...
@overload
def atleast_2d(x: ArrayLike, /) -> Array: ...
@overload
def atleast_2d(x: ArrayLike, y: ArrayLike, /, *arys: ArrayLike) -> list[Array]: ...

@overload
def atleast_3d() -> list[Array]: ...
@overload
def atleast_3d(x: ArrayLike, /) -> Array: ...
@overload
def atleast_3d(x: ArrayLike, y: ArrayLike, /, *arys: ArrayLike) -> list[Array]: ...

@overload
def average(a: ArrayLike, axis: _Axis = ..., weights: ArrayLike | None = ...,
            returned: Literal[False] = False, keepdims: builtins.bool = False) -> Array: ...
@overload
def average(a: ArrayLike, axis: _Axis = ..., weights: ArrayLike | None = ..., *,
            returned: Literal[True], keepdims: builtins.bool = False) -> tuple[Array, Array]: ...
@overload
def average(a: ArrayLike, axis: _Axis = ..., weights: ArrayLike | None = ...,
            returned: builtins.bool = False, keepdims: builtins.bool = False) -> Array | tuple[Array, Array]: ...

def bartlett(M: int) -> Array: ...
bfloat16: Any
def bincount(x: ArrayLike, weights: ArrayLike | None = ...,
             minlength: int = ..., *, length: int | None = ...) -> Array: ...
bitwise_and: BinaryUfunc
def bitwise_count(x: ArrayLike, /) -> Array: ...
def bitwise_invert(x: ArrayLike, /) -> Array: ...
def bitwise_left_shift(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def bitwise_not(x: ArrayLike, /) -> Array: ...
bitwise_or: BinaryUfunc
def bitwise_right_shift(x: ArrayLike, y: ArrayLike, /) -> Array: ...
bitwise_xor: BinaryUfunc
def blackman(M: int) -> Array: ...
def block(arrays: ArrayLike | Sequence[ArrayLike] | Sequence[Sequence[ArrayLike]]) -> Array: ...
bool: Any
bool_: Any
def broadcast_arrays(*args: ArrayLike) -> list[Array]: ...

@overload
def broadcast_shapes(*shapes: Sequence[int]) -> tuple[int, ...]: ...

@overload
def broadcast_shapes(*shapes: Sequence[int | _core.Tracer]
                     ) -> tuple[int | _core.Tracer, ...]: ...

def broadcast_to(array: ArrayLike, shape: DimSize | Shape, *,
                 out_sharding: NamedSharding | P | None = None) -> Array: ...
c_: _CClass
can_cast = _np.can_cast
def cbrt(x: ArrayLike, /) -> Array: ...
cdouble: Any
def ceil(x: ArrayLike, /) -> Array: ...
character = _np.character
def choose(a: ArrayLike, choices: Array | _np.ndarray | Sequence[ArrayLike],
           out: None = ..., mode: str = ...) -> Array: ...
def clip(
    x: ArrayLike | None = ...,
    /,
    min: ArrayLike | None = ...,
    max: ArrayLike | None = ...,
    *,
    a: ArrayLike | DeprecatedArg | None = ...,
    a_min: ArrayLike | DeprecatedArg | None = ...,
    a_max: ArrayLike | DeprecatedArg | None = ...
) -> Array: ...
def column_stack(
    tup: _np.ndarray | Array | Sequence[ArrayLike]
) -> Array: ...
complex128: Any
complex64: Any
complex_: Any
complexfloating = _np.complexfloating
def compress(condition: ArrayLike, a: ArrayLike, axis: int | None = ..., *,
             size: int | None = ..., fill_value: ArrayLike = ..., out: None = ...) -> Array: ...
def concat(arrays: Sequence[ArrayLike], /, *, axis: int | None = 0) -> Array: ...
def concatenate(
    arrays: _np.ndarray | Array | Sequence[ArrayLike],
    axis: int | None = ...,
    dtype: DTypeLike | None = ...,
) -> Array: ...
def conjugate(x: ArrayLike, /) -> Array: ...
def conj(x: ArrayLike, /) -> Array: ...
def convolve(a: ArrayLike, v: ArrayLike, mode: str = ..., *,
             precision: PrecisionLike = ...,
             preferred_element_type: DTypeLike | None = ...) -> Array: ...
def copy(a: ArrayLike, order: str | None = ...) -> Array: ...
def copysign(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def corrcoef(x: ArrayLike, y: ArrayLike | None = ..., rowvar: builtins.bool = ...) -> Array: ...
def correlate(a: ArrayLike, v: ArrayLike, mode: str = ..., *,
              precision: PrecisionLike = ...,
              preferred_element_type: DTypeLike | None = ...) -> Array: ...
def cos(x: ArrayLike, /) -> Array: ...
def cosh(x: ArrayLike, /) -> Array: ...
def count_nonzero(a: ArrayLike, axis: _Axis = ...,
                  keepdims: builtins.bool = ...) -> Array: ...
def cov(m: ArrayLike, y: ArrayLike | None = ..., rowvar: builtins.bool = ...,
        bias: builtins.bool = ..., ddof: int | None = ...,
        fweights: ArrayLike | None = ...,
        aweights: ArrayLike | None = ...) -> Array: ...
def cross(
    a: ArrayLike,
    b: ArrayLike,
    axisa: int = -1,
    axisb: int = -1,
    axisc: int = -1,
    axis: int | None = ...,
) -> Array: ...
csingle: Any
def cumprod(a: ArrayLike, axis: int | None = ..., dtype: DTypeLike | None = ...,
            out: None = ...) -> Array: ...
def cumsum(a: ArrayLike, axis: int | None = ..., dtype: DTypeLike | None = ...,
           out: None = ...) -> Array: ...
def cumulative_prod(x: ArrayLike, /, *, axis: int | None = ...,
                    dtype: DTypeLike | None = ...,
                    include_initial: builtins.bool = ...) -> Array: ...
def cumulative_sum(x: ArrayLike, /, *, axis: int | None = ...,
                   dtype: DTypeLike | None = ...,
                   include_initial: builtins.bool = ...) -> Array: ...

def deg2rad(x: ArrayLike, /) -> Array: ...
def degrees(x: ArrayLike, /) -> Array: ...
def delete(
    arr: ArrayLike,
    obj: ArrayLike | slice,
    axis: int | None = ...,
    *,
    assume_unique_indices: builtins.bool = ...,
) -> Array: ...
def diag(v: ArrayLike, k: int = 0) -> Array: ...
def diag_indices(n: int, ndim: int = ...) -> tuple[Array, ...]: ...
def diag_indices_from(arr: ArrayLike) -> tuple[Array, ...]: ...
def diagflat(v: ArrayLike, k: int = 0) -> Array: ...
def diagonal(
    a: ArrayLike, offset: ArrayLike = ..., axis1: int = ..., axis2: int = ...
): ...
def diff(a: ArrayLike, n: int = ..., axis: int = ...,
         prepend: ArrayLike | None = ...,
         append: ArrayLike | None = ...) -> Array: ...
def digitize(x: ArrayLike, bins: ArrayLike, right: builtins.bool = ..., *,
             method: str | None = ...) -> Array: ...
def divide(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def divmod(x: ArrayLike, y: ArrayLike, /) -> tuple[Array, Array]: ...
def dot(
    a: ArrayLike, b: ArrayLike, *, precision: PrecisionLike = ...,
    preferred_element_type: DTypeLike | None = ...,
    out_sharding: NamedSharding | P | None = ...) -> Array: ...
double: Any
def dsplit(
    ary: ArrayLike, indices_or_sections: int | ArrayLike
) -> list[Array]: ...

def dstack(tup: _np.ndarray | Array | Sequence[ArrayLike],
           dtype: DTypeLike | None = ...) -> Array: ...
dtype = _np.dtype
e: float
def ediff1d(ary: ArrayLike, to_end: ArrayLike | None = ...,
            to_begin: ArrayLike | None = ...) -> Array: ...
@overload
def einsum(
    subscript: str, /,
    *operands: ArrayLike,
    out: None = ...,
    optimize: str | builtins.bool | list[tuple[int, ...]] = ...,
    precision: PrecisionLike = ...,
    preferred_element_type: DTypeLike | None = ...,
    _dot_general: Callable[..., Array] = ...,
    out_sharding: NamedSharding | P | None = ...,
) -> Array: ...

@overload
def einsum(
    arr: ArrayLike,
    axes: Sequence[Any], /,
    *operands: ArrayLike | Sequence[Any],
    out: None = ...,
    optimize: str | builtins.bool | list[tuple[int, ...]] = ...,
    precision: PrecisionLike = ...,
    preferred_element_type: DTypeLike | None = ...,
    _dot_general: Callable[..., Array] = ...,
    out_sharding: NamedSharding | P | None = ...,
) -> Array: ...
@overload
def einsum(
    subscripts, /,
    *operands,
    out: None = ...,
    optimize: str | builtins.bool | list[tuple[int, ...]] = ...,
    precision: PrecisionLike = ...,
    preferred_element_type: DTypeLike | None = ...,
    _dot_general: Callable[..., Array] = ...,
    out_sharding: NamedSharding | P | None = ...,
) -> Array: ...

@overload
def einsum_path(
    subscripts: str, /,
    *operands: ArrayLike,
    optimize: str | builtins.bool | list[tuple[int, ...]] =  ...,
) -> tuple[list[tuple[int, ...]], Any]: ...
@overload
def einsum_path(
    arr: ArrayLike,
    axes: Sequence[Any], /,
    *operands: ArrayLike | Sequence[Any],
    optimize: str | builtins.bool | list[tuple[int, ...]] =  ...,
) -> tuple[list[tuple[int, ...]], Any]: ...
@overload
def einsum_path(
    subscripts, /,
    *operands: ArrayLike,
    optimize: str | builtins.bool | list[tuple[int, ...]] =  ...,
) -> tuple[list[tuple[int, ...]], Any]: ...

def empty(shape: Any, dtype: DTypeLike | None = ..., *,
          device: _Device | _Sharding | None = ...) -> Array: ...
def empty_like(prototype: ArrayLike | DuckTypedArray,
               dtype: DTypeLike | None = ...,
               shape: Any = ..., *,
               device: _Device | _Sharding | None = ...) -> Array: ...
def equal(x: ArrayLike, y: ArrayLike, /) -> Array: ...
euler_gamma: float
def exp(x: ArrayLike, /) -> Array: ...
def exp2(x: ArrayLike, /) -> Array: ...
def expand_dims(a: ArrayLike, axis: int | Sequence[int]) -> Array: ...
def expm1(x: ArrayLike, /) -> Array: ...
def extract(condition: ArrayLike, arr: ArrayLike, *,
            size: int | None = None, fill_value: ArrayLike = 0) -> Array: ...
def eye(N: DimSize, M: DimSize | None = ..., k: int | ArrayLike = ...,
        dtype: DTypeLike | None = ..., *,
        device: _Device | _Sharding | None = ...) -> Array: ...
def fabs(x: ArrayLike, /) -> Array: ...
finfo = _dtypes.finfo
def fix(x: ArrayLike, out: None = ...) -> Array: ...
def flatnonzero(
    a: ArrayLike,
    *,
    size: int | None = ...,
    fill_value: None | ArrayLike | tuple[ArrayLike] = ...,
) -> Array: ...
flexible = _np.flexible
def flip(
    m: ArrayLike, axis: int | Sequence[int] | None = ...
) -> Array: ...

def fliplr(m: ArrayLike) -> Array: ...
def flipud(m: ArrayLike) -> Array: ...
float16: Any
float32: Any
float4_e2m1fn: Any
float64: Any
float8_e3m4: Any
float8_e4m3: Any
float8_e4m3b11fnuz: Any
float8_e4m3fn: Any
float8_e4m3fnuz: Any
float8_e5m2: Any
float8_e5m2fnuz: Any
float8_e8m0fnu: Any
float_: Any
def float_power(x: ArrayLike, y: ArrayLike, /) -> Array: ...
floating = _np.floating
def floor(x: ArrayLike, /) -> Array: ...
def floor_divide(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def fmax(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def fmin(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def fmod(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def frexp(x: ArrayLike, /) -> tuple[Array, Array]: ...
def from_dlpack(x: Any, /, *, device: _Device | _Sharding | None = None,
                copy: builtins.bool | None = None) -> Array: ...
def frombuffer(buffer: bytes | Any, dtype: DTypeLike = ...,
               count: int = ..., offset: int = ...) -> Array: ...
def fromfile(*args, **kwargs): ...
def fromfunction(function: Callable[..., Array], shape: Any,
                 *, dtype: DTypeLike = ..., **kwargs) -> Array: ...
def fromiter(*args, **kwargs): ...
def frompyfunc(func: Callable[..., Any], /, nin: int, nout: int,
               *, identity: Any = None) -> ufunc: ...
def fromstring(
    string: str, dtype: DTypeLike = ..., count: int = ..., *, sep: str
) -> Array: ...
def full(shape: Any, fill_value: ArrayLike,
         dtype: DTypeLike | None = ..., *,
         device: _Device | _Sharding | None = ...) -> Array: ...
def full_like(a: ArrayLike | DuckTypedArray,
              fill_value: ArrayLike, dtype: DTypeLike | None = ...,
              shape: Any = ..., *,
              device: _Device | _Sharding | None = ...) -> Array: ...
def gcd(x1: ArrayLike, x2: ArrayLike) -> Array: ...
generic = _np.generic
def geomspace(
    start: ArrayLike,
    stop: ArrayLike,
    num: int = ...,
    endpoint: builtins.bool = ...,
    dtype: DTypeLike | None = ...,
    axis: int = ...,
) -> Array: ...
get_printoptions = _np.get_printoptions
def gradient(f: ArrayLike, *varargs: ArrayLike,
             axis: int | Sequence[int] | None = ...,
             edge_order: int | None = ...) -> Array | list[Array]: ...
def greater(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def greater_equal(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def hamming(M: int) -> Array: ...
def hanning(M: int) -> Array: ...
def heaviside(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def histogram(a: ArrayLike, bins: ArrayLike = ...,
              range: Sequence[ArrayLike] | None = ...,
              weights: ArrayLike | None = ...,
              density: builtins.bool | None = ...) -> tuple[Array, Array]: ...
def histogram2d(
    x: ArrayLike,
    y: ArrayLike,
    bins: ArrayLike | Sequence[ArrayLike] = ...,
    range: Sequence[None | Array | Sequence[ArrayLike]] | None = ...,
    weights: ArrayLike | None = ...,
    density: builtins.bool | None = ...,
) -> tuple[Array, Array, Array]: ...
def histogram_bin_edges(a: ArrayLike, bins: ArrayLike = ...,
                        range: None | Array | Sequence[ArrayLike] = ...,
                        weights: ArrayLike | None = ...) -> Array: ...
def histogramdd(
    sample: ArrayLike,
    bins: ArrayLike | Sequence[ArrayLike] = ...,
    range: Sequence[None | Array | Sequence[ArrayLike]] | None = ...,
    weights: ArrayLike | None = ...,
    density: builtins.bool | None = ...,
) -> tuple[Array, list[Array]]: ...
def hsplit(
    ary: ArrayLike, indices_or_sections: int | ArrayLike
) -> list[Array]: ...
def hstack(tup: _np.ndarray | Array | Sequence[ArrayLike],
           dtype: DTypeLike | None = ...) -> Array: ...
def hypot(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def i0(x: ArrayLike) -> Array: ...
def identity(n: DimSize, dtype: DTypeLike | None = ...) -> Array: ...
iinfo = _dtypes.iinfo
def imag(x: ArrayLike, /) -> Array: ...
index_exp = _np.index_exp

@overload
def indices(dimensions: Sequence[int], dtype: DTypeLike | None = None,
            sparse: Literal[False] = False) -> Array: ...
@overload
def indices(dimensions: Sequence[int], dtype: DTypeLike | None = None,
            *, sparse: Literal[True]) -> tuple[Array, ...]: ...
@overload
def indices(dimensions: Sequence[int], dtype: DTypeLike | None = None,
            sparse: builtins.bool = False) -> Array | tuple[Array, ...]: ...

inexact = _np.inexact
inf: float
def inner(
    a: ArrayLike, b: ArrayLike, *, precision: PrecisionLike = ...,
    preferred_element_type: DTypeLike | None = ...) -> Array: ...
def insert(arr: ArrayLike, obj: ArrayLike | slice, values: ArrayLike,
           axis: int | None = ...) -> Array: ...
int16: Any
int2: Any
int32: Any
int4: Any
int64: Any
int8: Any
int_: Any
integer = _np.integer
def interp(x: ArrayLike, xp: ArrayLike, fp: ArrayLike,
           left: ArrayLike | str | None = ...,
           right: ArrayLike | str | None = ...,
           period: ArrayLike | None = ...) -> Array: ...
def intersect1d(ar1: ArrayLike, ar2: ArrayLike, assume_unique: builtins.bool = ...,
                return_indices: builtins.bool = ..., *, size: int | None = ...,
                fill_value: ArrayLike | None = ...) -> Array | tuple[Array, Array, Array]: ...
def invert(x: ArrayLike, /) -> Array: ...
def isclose(a: ArrayLike, b: ArrayLike, rtol: ArrayLike = ...,
            atol: ArrayLike = ..., equal_nan: builtins.bool = ...) -> Array: ...
def iscomplex(x: ArrayLike) -> Array: ...
def iscomplexobj(x: Any) -> builtins.bool: ...
def isdtype(dtype: DTypeLike, kind: DType | str | tuple[DType | str, ...]) -> builtins.bool: ...
def isfinite(x: ArrayLike, /) -> Array: ...
def isin(element: ArrayLike, test_elements: ArrayLike, assume_unique: builtins.bool = ...,
         invert: builtins.bool = ..., *, method: str = ...) -> Array: ...
def isinf(x: ArrayLike, /) -> Array: ...
def isnan(x: ArrayLike, /) -> Array: ...
def isneginf(x: ArrayLike, /) -> Array: ...
def isposinf(x: ArrayLike, /) -> Array: ...
def isreal(x: ArrayLike) -> Array: ...
def isrealobj(x: Any) -> builtins.bool: ...
def isscalar(element: Any) -> builtins.bool: ...
def issubdtype(arg1: DTypeLike, arg2: DTypeLike) -> builtins.bool: ...
iterable = _np.iterable
def ix_(*args: ArrayLike) -> tuple[Array, ...]: ...
def kaiser(M: int, beta: ArrayLike) -> Array: ...
def kron(a: ArrayLike, b: ArrayLike) -> Array: ...
def lcm(x1: ArrayLike, x2: ArrayLike) -> Array: ...
def ldexp(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def left_shift(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def less(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def less_equal(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def lexsort(keys: Array | _np.ndarray | Sequence[ArrayLike], axis: int = ...) -> Array: ...

@overload
def linspace(start: ArrayLike, stop: ArrayLike, num: int = 50,
             endpoint: builtins.bool = True, retstep: Literal[False] = False,
             dtype: DTypeLike | None = ...,
             axis: int = 0,
             *, device: _Device | _Sharding | None = ...) -> Array: ...
@overload
def linspace(start: ArrayLike, stop: ArrayLike, num: int,
             endpoint: builtins.bool, retstep: Literal[True],
             dtype: DTypeLike | None = ...,
             axis: int = 0,
             *, device: _Device | _Sharding | None = ...) -> tuple[Array, Array]: ...
@overload
def linspace(start: ArrayLike, stop: ArrayLike, num: int = 50,
             endpoint: builtins.bool = True, *, retstep: Literal[True],
             dtype: DTypeLike | None = ...,
             axis: int = 0,
             device: _Device | _Sharding | None = ...) -> tuple[Array, Array]: ...
@overload
def linspace(start: ArrayLike, stop: ArrayLike, num: int = 50,
             endpoint: builtins.bool = True, retstep: builtins.bool = False,
             dtype: DTypeLike | None = ...,
             axis: int = 0,
             *, device: _Device | _Sharding | None = ...) -> Union[Array, tuple[Array, Array]]: ...

def load(file: IO[bytes] | str | os.PathLike[Any], *args: Any, **kwargs: Any) -> Array: ...
def log(x: ArrayLike, /) -> Array: ...
def log10(x: ArrayLike, /) -> Array: ...
def log1p(x: ArrayLike, /) -> Array: ...
def log2(x: ArrayLike, /) -> Array: ...
logaddexp: BinaryUfunc
logaddexp2: BinaryUfunc
logical_and: BinaryUfunc
def logical_not(x: ArrayLike, /) -> Array: ...
logical_or: BinaryUfunc
logical_xor: BinaryUfunc
def logspace(start: ArrayLike, stop: ArrayLike, num: int = ...,
             endpoint: builtins.bool = ..., base: ArrayLike = ...,
             dtype: DTypeLike | None = ..., axis: int = ...) -> Array: ...
def mask_indices(
    n: int, mask_func: Callable, k: int = ..., *, size: int | None = ...
) -> tuple[Array, ...]: ...
def matmul(
    a: ArrayLike, b: ArrayLike, *, precision: PrecisionLike = ...,
    preferred_element_type: DTypeLike | None = ...) -> Array: ...
def matrix_transpose(x: ArrayLike, /) -> Array: ...
def matvec(x1: ArrayLike, x2: ArrayLike, /) -> Array: ...
def max(a: ArrayLike, axis: _Axis = ..., out: None = ...,
        keepdims: builtins.bool = ..., initial: ArrayLike | None = ...,
        where: ArrayLike | None = ...) -> Array: ...
maximum: BinaryUfunc
def mean(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
         out: None = ..., keepdims: builtins.bool = ..., *,
         where: ArrayLike | None = ...) -> Array: ...
def median(a: ArrayLike, axis: int | tuple[int, ...] | None = ...,
           out: None = ..., overwrite_input: builtins.bool = ...,
           keepdims: builtins.bool = ...) -> Array: ...
def meshgrid(*xi: ArrayLike, copy: builtins.bool = ..., sparse: builtins.bool = ...,
             indexing: str = ...) -> list[Array]: ...
mgrid: _Mgrid
def min(a: ArrayLike, axis: _Axis = ..., out: None = ...,
        keepdims: builtins.bool = ..., initial: ArrayLike | None = ...,
        where: ArrayLike | None = ...) -> Array: ...
minimum: BinaryUfunc
def mod(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def modf(x: ArrayLike, /, out=None) -> tuple[Array, Array]: ...
def moveaxis(a: ArrayLike, source: int | Sequence[int],
             destination: int | Sequence[int]) -> Array: ...
multiply: BinaryUfunc
nan: float
def nan_to_num(x: ArrayLike, copy: builtins.bool = ..., nan: ArrayLike = ...,
               posinf: ArrayLike | None = ...,
               neginf: ArrayLike | None = ...) -> Array: ...
def nanargmax(
    a: ArrayLike,
    axis: int | None = ...,
    out: None = ...,
    keepdims: builtins.bool | None = ...,
) -> Array: ...
def nanargmin(
    a: ArrayLike,
    axis: int | None = ...,
    out: None = ...,
    keepdims: builtins.bool | None = ...,
) -> Array: ...
def nancumprod(a: ArrayLike, axis: int | None = ..., dtype: DTypeLike | None = ...,
               out: None = ...) -> Array: ...
def nancumsum(a: ArrayLike, axis: int | None = ..., dtype: DTypeLike | None = ...,
               out: None = ...) -> Array: ...
def nanmax(a: ArrayLike, axis: _Axis = ..., out: None = ...,
           keepdims: builtins.bool = ..., initial: ArrayLike | None = ...,
           where: ArrayLike | None = ...) -> Array: ...
def nanmean(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
            out: None = ...,
            keepdims: builtins.bool = ...,
            where: ArrayLike | None = ...) -> Array: ...
def nanmedian(a: ArrayLike, axis: int | tuple[int, ...] | None = ...,
              out: None = ..., overwrite_input: builtins.bool = ...,
              keepdims: builtins.bool = ...) -> Array: ...
def nanmin(a: ArrayLike, axis: _Axis = ..., out: None = ...,
           keepdims: builtins.bool = ..., initial: ArrayLike | None = ...,
           where: ArrayLike | None = ...) -> Array: ...
def nanpercentile(a: ArrayLike, q: ArrayLike,
                  axis: int | tuple[int, ...] | None = ...,
                  out: None = ..., overwrite_input: builtins.bool = ..., method: str = ...,
                  keepdims: builtins.bool = ..., *, interpolation: DeprecatedArg | str = ...) -> Array: ...
def nanprod(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
            out: None = ...,
            keepdims: builtins.bool = ..., initial: ArrayLike | None = ...,
            where: ArrayLike | None = ...) -> Array: ...
def nanquantile(a: ArrayLike, q: ArrayLike, axis: int | tuple[int, ...] | None = ...,
                out: None = ..., overwrite_input: builtins.bool = ..., method: str = ...,
                keepdims: builtins.bool = ..., *, interpolation: DeprecatedArg | str = ...) -> Array: ...
def nanstd(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
           out: None = ..., ddof: int = ..., keepdims: builtins.bool = ...,
           where: ArrayLike | None = ...) -> Array: ...
def nansum(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
           out: None = ..., keepdims: builtins.bool = ...,
           initial: ArrayLike | None = ...,
           where: ArrayLike | None = ...) -> Array: ...
def nanvar(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
           out: None = ...,
           ddof: int = 0, keepdims: builtins.bool = False,
           where: ArrayLike | None = ...) -> Array: ...
ndarray = Array
def ndim(a: ArrayLike | SupportsNdim) -> int: ...
def negative(x: ArrayLike, /) -> Array: ...
newaxis = None
def nextafter(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def nonzero(a: ArrayLike, *, size: int | None = ...,
            fill_value: None | ArrayLike | tuple[ArrayLike, ...] = ...
    ) -> tuple[Array, ...]: ...
def not_equal(x: ArrayLike, y: ArrayLike, /) -> Array: ...
number = _np.number
object_ = _np.object_
ogrid: _Ogrid
def ones(shape: Any, dtype: DTypeLike | None = ..., *,
         device: _Device | _Sharding | None = ...) -> Array: ...
def ones_like(a: ArrayLike | DuckTypedArray,
              dtype: DTypeLike | None = ...,
              shape: Any = ..., *,
              device: _Device | _Sharding | None = ...) -> Array: ...
def outer(a: ArrayLike, b: Array, out: None = ...) -> Array: ...
def packbits(
    a: ArrayLike, axis: int | None = ..., bitorder: str = ...
) -> Array: ...

PadValueLike = Union[_T, Sequence[_T], Sequence[Sequence[_T]]]
def pad(array: ArrayLike, pad_width: PadValueLike[int | Array | _np.ndarray],
        mode: str | Callable[..., Any] = ..., **kwargs) -> Array: ...

def partition(a: ArrayLike, kth: int, axis: int = ...) -> Array: ...
def percentile(a: ArrayLike, q: ArrayLike,
               axis: int | tuple[int, ...] | None = ...,
               out: None = ..., overwrite_input: builtins.bool = ..., method: str = ...,
               keepdims: builtins.bool = ..., *, interpolation: DeprecatedArg | str = ...) -> Array: ...
def permute_dims(x: ArrayLike, /, axes: tuple[int, ...]) -> Array: ...
pi: float
def piecewise(x: ArrayLike, condlist: Array | Sequence[ArrayLike],
              funclist: Sequence[ArrayLike | Callable[..., Array]],
              *args, **kw) -> Array: ...
def place(arr: ArrayLike, mask: ArrayLike, vals: ArrayLike, *,
          inplace: builtins.bool = ...) -> Array: ...
def poly(seq_of_zeros: ArrayLike) -> Array: ...
def polyadd(a1: ArrayLike, a2: ArrayLike) -> Array: ...
def polyder(p: ArrayLike, m: int = ...) -> Array: ...
def polydiv(u: ArrayLike, v: ArrayLike, *, trim_leading_zeros: builtins.bool = ...) -> tuple[Array, Array]: ...
def polyfit(x: ArrayLike, y: ArrayLike, deg: int, rcond: float | None = ...,
            full: builtins.bool = ..., w: ArrayLike | None = ..., cov: builtins.bool = ...
            ) -> Array | tuple[Array, ...]: ...
def polyint(p: ArrayLike, m: int = ..., k: int | ArrayLike | None = ...) -> Array: ...
def polymul(a1: ArrayLike, a2: ArrayLike, *, trim_leading_zeros: builtins.bool = ...) -> Array: ...
def polysub(a1: ArrayLike, a2: ArrayLike) -> Array: ...
def polyval(p: ArrayLike, x: ArrayLike, *, unroll: int = ...) -> Array: ...
def positive(x: ArrayLike, /) -> Array: ...
def pow(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def power(x: ArrayLike, y: ArrayLike, /) -> Array: ...
printoptions = _np.printoptions
def prod(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
         out: None = ..., keepdims: builtins.bool = ...,
         initial: ArrayLike | None = ..., where: ArrayLike | None = ...,
         promote_integers: builtins.bool = ...) -> Array: ...
promote_types = _np.promote_types
def ptp(a: ArrayLike, axis: _Axis = ..., out: None = ...,
        keepdims: builtins.bool = ...) -> Array: ...
def put(a: ArrayLike, ind: ArrayLike, v: ArrayLike,
        mode: str | None = ..., *, inplace: builtins.bool = ...) -> Array: ...
def put_along_axis(arr: ArrayLike, indices: ArrayLike, values: ArrayLike,
        axis: int | None, inplace: bool = True, *, mode: str | None = None) -> Array: ...
def quantile(a: ArrayLike, q: ArrayLike, axis: int | tuple[int, ...] | None = ...,
             out: None = ..., overwrite_input: builtins.bool = ..., method: str = ...,
             keepdims: builtins.bool = ..., *, interpolation: DeprecatedArg | str = ...) -> Array: ...
r_: _RClass
def rad2deg(x: ArrayLike, /) -> Array: ...
def radians(x: ArrayLike, /) -> Array: ...
def ravel(a: ArrayLike, order: str = ..., *,
          out_sharding: NamedSharding | P | None = ...) -> Array: ...
def ravel_multi_index(multi_index: Sequence[ArrayLike], dims: Sequence[int],
                      mode: str = ..., order: str = ...) -> Array: ...
def real(x: ArrayLike, /) -> Array: ...
def reciprocal(x: ArrayLike, /) -> Array: ...
def remainder(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def repeat(a: ArrayLike, repeats: ArrayLike, axis: int | None = ..., *,
           total_repeat_length: int | None = ...,
           out_sharding: NamedSharding | P | None = None) -> Array: ...
def reshape(
    a: ArrayLike, shape: DimSize | Shape, order: str = ..., *, copy: bool | None = ...,
    out_sharding: NamedSharding | P | None = ...,
) -> Array: ...

def resize(a: ArrayLike, new_shape: Shape) -> Array: ...
def result_type(*args: Any) -> DType: ...
def right_shift(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def rint(x: ArrayLike, /) -> Array: ...
def roll(a: ArrayLike, shift: ArrayLike | Sequence[int],
         axis: int | Sequence[int] | None = ...) -> Array: ...
def rollaxis(a: ArrayLike, axis: int, start: int = 0) -> Array: ...
def roots(p: ArrayLike, *, strip_zeros: builtins.bool = ...) -> Array: ...
def rot90(m: ArrayLike, k: int = ..., axes: tuple[int, int] = ...) -> Array: ...
def round(a: ArrayLike, decimals: int = ..., out: None = ...) -> Array: ...
s_ = _np.s_
save = _np.save
savez = _np.savez
def searchsorted(a: ArrayLike, v: ArrayLike, side: str = ...,
                 sorter: ArrayLike | None = ..., *, method: str = ...) -> Array: ...
def select(
    condlist: Sequence[ArrayLike],
    choicelist: Sequence[ArrayLike],
    default: ArrayLike = ...,
) -> Array: ...
set_printoptions = _np.set_printoptions
def setdiff1d(
    ar1: ArrayLike,
    ar2: ArrayLike,
    assume_unique: builtins.bool = ...,
    *,
    size: int | None = ...,
    fill_value: ArrayLike | None = ...,
) -> Array: ...
def setxor1d(ar1: ArrayLike, ar2: ArrayLike, assume_unique: builtins.bool = ..., *,
             size: int | None = ..., fill_value: ArrayLike | None = ...) -> Array: ...
def shape(a: ArrayLike | SupportsShape) -> tuple[int, ...]: ...
def sign(x: ArrayLike, /) -> Array: ...
def signbit(x: ArrayLike, /) -> Array: ...
signedinteger = _np.signedinteger
def sin(x: ArrayLike, /) -> Array: ...
def sinc(x: ArrayLike, /) -> Array: ...
single: Any
def sinh(x: ArrayLike, /) -> Array: ...
def size(a: ArrayLike | SupportsSize, axis: int | None = None) -> int: ...
def sort(
    a: ArrayLike,
    axis: int | None = ...,
    *,
    stable: builtins.bool = ...,
    descending: builtins.bool = ...,
    kind: str | None = ...,
    order: None = ...,
) -> Array: ...
def sort_complex(a: ArrayLike) -> Array: ...
def spacing(x: ArrayLike, /) -> Array: ...
def split(
    ary: ArrayLike,
    indices_or_sections: int | Sequence[int] | ArrayLike,
    axis: int = ...,
) -> list[Array]: ...

def sqrt(x: ArrayLike, /) -> Array: ...
def square(x: ArrayLike, /) -> Array: ...
def squeeze(
    a: ArrayLike, axis: int | Sequence[int] | None = ...
) -> Array: ...
def stack(
    arrays: _np.ndarray | Array | Sequence[ArrayLike],
    axis: int = ...,
    out: None = ...,
    dtype: DTypeLike | None = ...,
) -> Array: ...
def std(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
        out: None = ..., ddof: int = ..., keepdims: builtins.bool = ..., *,
        where: ArrayLike | None = ..., correction: int | float | None = ...) -> Array: ...
subtract: BinaryUfunc
def sum(
    a: ArrayLike,
    axis: _Axis = ...,
    dtype: DTypeLike | None = ...,
    out: None = ...,
    keepdims: builtins.bool = ...,
    initial: ArrayLike | None = ...,
    where: ArrayLike | None = ...,
    promote_integers: builtins.bool = ...,
) -> Array: ...
def swapaxes(a: ArrayLike, axis1: int, axis2: int) -> Array: ...
def take(
    a: ArrayLike,
    indices: ArrayLike,
    axis: int | None = ...,
    out: None = ...,
    mode: str | None = ...,
    unique_indices: builtins.bool = ...,
    indices_are_sorted: builtins.bool = ...,
    fill_value: StaticScalar | None = ...,
) -> Array: ...
def take_along_axis(
    arr: ArrayLike,
    indices: ArrayLike,
    axis: int | None,
    mode: str | GatherScatterMode | None = ...,
    fill_value: StaticScalar | None = None,
) -> Array: ...
def tan(x: ArrayLike, /) -> Array: ...
def tanh(x: ArrayLike, /) -> Array: ...
def tensordot(a: ArrayLike, b: ArrayLike,
              axes: int | Sequence[int] | Sequence[Sequence[int]] = ...,
              *, precision: PrecisionLike = ...,
              preferred_element_type: DTypeLike | None = ...) -> Array: ...
def tile(A: ArrayLike, reps: DimSize | Sequence[DimSize]) -> Array: ...
def trace(a: ArrayLike, offset: int | ArrayLike = ..., axis1: int = ..., axis2: int = ...,
          dtype: DTypeLike | None = ..., out: None = ...) -> Array: ...
def transpose(a: ArrayLike, axes: Sequence[int] | None = ...) -> Array: ...
def trapezoid(y: ArrayLike, x: ArrayLike | None = None, dx: ArrayLike = ...,
              axis: int = ...) -> Array: ...
def tri(
    N: int, M: int | None = ..., k: int = ..., dtype: DTypeLike | None = ...
) -> Array: ...
def tril(m: ArrayLike, k: int = ...) -> Array: ...
def tril_indices(
    n: int, k: int = ..., m: int | None = ...
) -> tuple[Array, Array]: ...
def tril_indices_from(arr: ArrayLike | SupportsShape, k: int = ...) -> tuple[Array, Array]: ...
def fill_diagonal(a: ArrayLike, val: ArrayLike, wrap: builtins.bool = ..., *, inplace: builtins.bool = ...) -> Array: ...
def trim_zeros(filt: ArrayLike, trim: str = ...) -> Array: ...
def triu(m: ArrayLike, k: int = ...) -> Array: ...
def triu_indices(
    n: int, k: int = ..., m: int | None = ...
) -> tuple[Array, Array]: ...
def triu_indices_from(arr: ArrayLike | SupportsShape, k: int = ...) -> tuple[Array, Array]: ...
def true_divide(x: ArrayLike, y: ArrayLike, /) -> Array: ...
def trunc(x: ArrayLike, /) -> Array: ...
uint: Any
uint16: Any
uint2: Any
uint32: Any
uint4: Any
uint64: Any
uint8: Any
def union1d(
    ar1: ArrayLike,
    ar2: ArrayLike,
    *,
    size: int | None = ...,
    fill_value: ArrayLike | None = ...,
) -> Array: ...
class _UniqueAllResult(NamedTuple):
  values: Array
  indices: Array
  inverse_indices: Array
  counts: Array
class _UniqueCountsResult(NamedTuple):
    values: Array
    counts: Array
class _UniqueInverseResult(NamedTuple):
    values: Array
    inverse_indices: Array
def unique(ar: ArrayLike, return_index: builtins.bool = ..., return_inverse: builtins.bool = ...,
           return_counts: builtins.bool = ..., axis: int | None = ...,
           *, equal_nan: builtins.bool = ..., size: int | None = ...,
           fill_value: ArrayLike | None = ..., sorted: bool = ...,
): ...
def unique_all(x: ArrayLike, /, *, size: int | None = ...,
               fill_value: ArrayLike | None = ...) -> _UniqueAllResult: ...
def unique_counts(x: ArrayLike, /, *, size: int | None = ...,
                  fill_value: ArrayLike | None = ...) -> _UniqueCountsResult: ...
def unique_inverse(x: ArrayLike, /, *, size: int | None = ...,
                   fill_value: ArrayLike | None = ...) -> _UniqueInverseResult: ...
def unique_values(x: ArrayLike, /, *, size: int | None = ...,
                  fill_value: ArrayLike | None = ...) -> Array: ...
def unpackbits(
    a: ArrayLike,
    axis: int | None = ...,
    count: ArrayLike | None = ...,
    bitorder: str = ...,
) -> Array: ...
def unravel_index(indices: ArrayLike, shape: Shape) -> tuple[Array, ...]: ...
unsignedinteger = _np.unsignedinteger
def unstack(x: ArrayLike , /, *, axis: int = ...) -> tuple[Array, ...]: ...
def unwrap(p: ArrayLike, discont: ArrayLike | None = ...,
           axis: int = ..., period: ArrayLike = ...) -> Array: ...
def vander(
    x: ArrayLike, N: int | None = ..., increasing: builtins.bool = ...
) -> Array: ...
def var(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike | None = ...,
        out: None = ..., ddof: int = ..., keepdims: builtins.bool = ..., *,
        where: ArrayLike | None = ..., correction: int | float | None = ...) -> Array: ...
def vdot(
    a: ArrayLike, b: ArrayLike, *, precision: PrecisionLike = ...,
    preferred_element_type: DTypeLike | None = ...) -> Array: ...
def vecdot(x1: ArrayLike, x2: ArrayLike, /, *, axis: int = ...,
           precision: PrecisionLike = ...,
           preferred_element_type: DTypeLike | None = ...) -> Array: ...
def vecmat(x1: ArrayLike, x2: ArrayLike, /) -> Array: ...
def vsplit(
    ary: ArrayLike, indices_or_sections: int | ArrayLike
) -> list[Array]: ...

def vstack(tup: _np.ndarray | Array | Sequence[ArrayLike],
           dtype: DTypeLike | None = ...) -> Array: ...

@overload
def where(condition: ArrayLike, x: Literal[None] = ..., y: Literal[None] = ...,
          /, *, size: int | None = ...,
          fill_value: None | ArrayLike | tuple[ArrayLike, ...] = ...
          ) -> tuple[Array, ...]: ...

@overload
def where(condition: ArrayLike, x: ArrayLike, y: ArrayLike, /, *,
          size: int | None = ...,
          fill_value: None | ArrayLike | tuple[ArrayLike, ...] = ...
          ) -> Array: ...

@overload
def where(condition: ArrayLike, x: ArrayLike | None = ...,
          y: ArrayLike | None = ..., /, *, size: int | None = ...,
          fill_value: None | ArrayLike | tuple[ArrayLike, ...] = ...
          ) -> Array | tuple[Array, ...]: ...

def zeros(shape: Any, dtype: DTypeLike | None = ..., *,
          device: _Device | _Sharding | None = ...) -> Array: ...
def zeros_like(a: ArrayLike | DuckTypedArray,
               dtype: DTypeLike | None = ...,
               shape: Any = ..., *,
               device: _Device | _Sharding | None = ...) -> Array: ...

def vectorize(pyfunc, *, excluded = ..., signature = ...) -> Callable: ...