"""
This type stub file was generated by pyright.
"""

from collections.abc import Iterable
from typing import Any, Literal as L, NamedTuple, SupportsIndex, SupportsInt, TypeVar, overload
from numpy import complex128, complexfloating, float64, floating, generic, int32
from numpy._typing import ArrayLike, NDArray, _ArrayLikeComplex_co, _ArrayLikeFloat_co, _ArrayLikeInt_co, _ArrayLikeObject_co, _ArrayLikeTD64_co

_T = TypeVar("_T")
_ArrayType = TypeVar("_ArrayType", bound=NDArray[Any])
_SCT = TypeVar("_SCT", bound=generic, covariant=True)
_SCT2 = TypeVar("_SCT2", bound=generic, covariant=True)
_2Tuple = tuple[_T, _T]
_ModeKind = L["reduced", "complete", "r", "raw"]
__all__: list[str]
class EigResult(NamedTuple):
    eigenvalues: NDArray[Any]
    eigenvectors: NDArray[Any]
    ...


class EighResult(NamedTuple):
    eigenvalues: NDArray[Any]
    eigenvectors: NDArray[Any]
    ...


class QRResult(NamedTuple):
    Q: NDArray[Any]
    R: NDArray[Any]
    ...


class SlogdetResult(NamedTuple):
    sign: Any
    logabsdet: Any
    ...


class SVDResult(NamedTuple):
    U: NDArray[Any]
    S: NDArray[Any]
    Vh: NDArray[Any]
    ...


@overload
def tensorsolve(a: _ArrayLikeInt_co, b: _ArrayLikeInt_co, axes: None | Iterable[int] = ...) -> NDArray[float64]:
    ...

@overload
def tensorsolve(a: _ArrayLikeFloat_co, b: _ArrayLikeFloat_co, axes: None | Iterable[int] = ...) -> NDArray[floating[Any]]:
    ...

@overload
def tensorsolve(a: _ArrayLikeComplex_co, b: _ArrayLikeComplex_co, axes: None | Iterable[int] = ...) -> NDArray[complexfloating[Any, Any]]:
    ...

@overload
def solve(a: _ArrayLikeInt_co, b: _ArrayLikeInt_co) -> NDArray[float64]:
    ...

@overload
def solve(a: _ArrayLikeFloat_co, b: _ArrayLikeFloat_co) -> NDArray[floating[Any]]:
    ...

@overload
def solve(a: _ArrayLikeComplex_co, b: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]:
    ...

@overload
def tensorinv(a: _ArrayLikeInt_co, ind: int = ...) -> NDArray[float64]:
    ...

@overload
def tensorinv(a: _ArrayLikeFloat_co, ind: int = ...) -> NDArray[floating[Any]]:
    ...

@overload
def tensorinv(a: _ArrayLikeComplex_co, ind: int = ...) -> NDArray[complexfloating[Any, Any]]:
    ...

@overload
def inv(a: _ArrayLikeInt_co) -> NDArray[float64]:
    ...

@overload
def inv(a: _ArrayLikeFloat_co) -> NDArray[floating[Any]]:
    ...

@overload
def inv(a: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]:
    ...

def matrix_power(a: _ArrayLikeComplex_co | _ArrayLikeObject_co, n: SupportsIndex) -> NDArray[Any]:
    ...

@overload
def cholesky(a: _ArrayLikeInt_co) -> NDArray[float64]:
    ...

@overload
def cholesky(a: _ArrayLikeFloat_co) -> NDArray[floating[Any]]:
    ...

@overload
def cholesky(a: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]:
    ...

@overload
def qr(a: _ArrayLikeInt_co, mode: _ModeKind = ...) -> QRResult:
    ...

@overload
def qr(a: _ArrayLikeFloat_co, mode: _ModeKind = ...) -> QRResult:
    ...

@overload
def qr(a: _ArrayLikeComplex_co, mode: _ModeKind = ...) -> QRResult:
    ...

@overload
def eigvals(a: _ArrayLikeInt_co) -> NDArray[float64] | NDArray[complex128]:
    ...

@overload
def eigvals(a: _ArrayLikeFloat_co) -> NDArray[floating[Any]] | NDArray[complexfloating[Any, Any]]:
    ...

@overload
def eigvals(a: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]:
    ...

@overload
def eigvalsh(a: _ArrayLikeInt_co, UPLO: L["L", "U", "l", "u"] = ...) -> NDArray[float64]:
    ...

@overload
def eigvalsh(a: _ArrayLikeComplex_co, UPLO: L["L", "U", "l", "u"] = ...) -> NDArray[floating[Any]]:
    ...

@overload
def eig(a: _ArrayLikeInt_co) -> EigResult:
    ...

@overload
def eig(a: _ArrayLikeFloat_co) -> EigResult:
    ...

@overload
def eig(a: _ArrayLikeComplex_co) -> EigResult:
    ...

@overload
def eigh(a: _ArrayLikeInt_co, UPLO: L["L", "U", "l", "u"] = ...) -> EighResult:
    ...

@overload
def eigh(a: _ArrayLikeFloat_co, UPLO: L["L", "U", "l", "u"] = ...) -> EighResult:
    ...

@overload
def eigh(a: _ArrayLikeComplex_co, UPLO: L["L", "U", "l", "u"] = ...) -> EighResult:
    ...

@overload
def svd(a: _ArrayLikeInt_co, full_matrices: bool = ..., compute_uv: L[True] = ..., hermitian: bool = ...) -> SVDResult:
    ...

@overload
def svd(a: _ArrayLikeFloat_co, full_matrices: bool = ..., compute_uv: L[True] = ..., hermitian: bool = ...) -> SVDResult:
    ...

@overload
def svd(a: _ArrayLikeComplex_co, full_matrices: bool = ..., compute_uv: L[True] = ..., hermitian: bool = ...) -> SVDResult:
    ...

@overload
def svd(a: _ArrayLikeInt_co, full_matrices: bool = ..., compute_uv: L[False] = ..., hermitian: bool = ...) -> NDArray[float64]:
    ...

@overload
def svd(a: _ArrayLikeComplex_co, full_matrices: bool = ..., compute_uv: L[False] = ..., hermitian: bool = ...) -> NDArray[floating[Any]]:
    ...

def cond(x: _ArrayLikeComplex_co, p: None | float | L["fro", "nuc"] = ...) -> Any:
    ...

def matrix_rank(A: _ArrayLikeComplex_co, tol: None | _ArrayLikeFloat_co = ..., hermitian: bool = ...) -> Any:
    ...

@overload
def pinv(a: _ArrayLikeInt_co, rcond: _ArrayLikeFloat_co = ..., hermitian: bool = ...) -> NDArray[float64]:
    ...

@overload
def pinv(a: _ArrayLikeFloat_co, rcond: _ArrayLikeFloat_co = ..., hermitian: bool = ...) -> NDArray[floating[Any]]:
    ...

@overload
def pinv(a: _ArrayLikeComplex_co, rcond: _ArrayLikeFloat_co = ..., hermitian: bool = ...) -> NDArray[complexfloating[Any, Any]]:
    ...

def slogdet(a: _ArrayLikeComplex_co) -> SlogdetResult:
    ...

def det(a: _ArrayLikeComplex_co) -> Any:
    ...

@overload
def lstsq(a: _ArrayLikeInt_co, b: _ArrayLikeInt_co, rcond: None | float = ...) -> tuple[NDArray[float64], NDArray[float64], int32, NDArray[float64],]:
    ...

@overload
def lstsq(a: _ArrayLikeFloat_co, b: _ArrayLikeFloat_co, rcond: None | float = ...) -> tuple[NDArray[floating[Any]], NDArray[floating[Any]], int32, NDArray[floating[Any]],]:
    ...

@overload
def lstsq(a: _ArrayLikeComplex_co, b: _ArrayLikeComplex_co, rcond: None | float = ...) -> tuple[NDArray[complexfloating[Any, Any]], NDArray[floating[Any]], int32, NDArray[floating[Any]],]:
    ...

@overload
def norm(x: ArrayLike, ord: None | float | L["fro", "nuc"] = ..., axis: None = ..., keepdims: bool = ...) -> floating[Any]:
    ...

@overload
def norm(x: ArrayLike, ord: None | float | L["fro", "nuc"] = ..., axis: SupportsInt | SupportsIndex | tuple[int, ...] = ..., keepdims: bool = ...) -> Any:
    ...

def multi_dot(arrays: Iterable[_ArrayLikeComplex_co | _ArrayLikeObject_co | _ArrayLikeTD64_co], *, out: None | NDArray[Any] = ...) -> Any:
    ...