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numpy
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linalg
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linalg.pyi
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from collections.abc import Iterable from typing import ( Literal as L, overload, TypeVar, Any, SupportsIndex, SupportsInt, NamedTuple, Generic, ) from numpy import ( generic, floating, complexfloating, int32, float64, complex128, ) from numpy.linalg import LinAlgError as LinAlgError from numpy._typing import ( NDArray, ArrayLike, _ArrayLikeInt_co, _ArrayLikeFloat_co, _ArrayLikeComplex_co, _ArrayLikeTD64_co, _ArrayLikeObject_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): # TODO: `sign` and `logabsdet` are scalars for input 2D arrays and # a `(x.ndim - 2)`` dimensionl arrays otherwise 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]]: ... # TODO: The supported input and output dtypes are dependent on the value of `n`. # For example: `n < 0` always casts integer types to float64 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]]: ... # TODO: Returns a scalar for 2D arrays and # a `(x.ndim - 2)`` dimensionl array otherwise def cond(x: _ArrayLikeComplex_co, p: None | float | L["fro", "nuc"] = ...) -> Any: ... # TODO: Returns `int` for <2D arrays and `intp` otherwise 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]]: ... # TODO: Returns a 2-tuple of scalars for 2D arrays and # a 2-tuple of `(a.ndim - 2)`` dimensionl arrays otherwise def slogdet(a: _ArrayLikeComplex_co) -> SlogdetResult: ... # TODO: Returns a 2-tuple of scalars for 2D arrays and # a 2-tuple of `(a.ndim - 2)`` dimensionl arrays otherwise 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: ... # TODO: Returns a scalar or array def multi_dot( arrays: Iterable[_ArrayLikeComplex_co | _ArrayLikeObject_co | _ArrayLikeTD64_co], *, out: None | NDArray[Any] = ..., ) -> Any: ...