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qttools.kernels.linalg#

source package qttools.kernels.linalg

Functions

  • eig — Computes the eigenvalues and eigenvectors of matrices on a given location.

  • inv — Computes the (batched) inverse of a matrix.

  • svd — Computes the singular value decomposition of a matrix on a given location.

  • eigvalsh — Compute eigenvalues of a hermitain generalized eigenvalue problem.

  • qr — Computes the QR decomposition of a batch of matrices.

source eig(A: NDArray | list[NDArray], compute_module: str = 'numpy', output_module: str | None = None, use_pinned_memory: bool = True) → tuple[NDArray, NDArray] | tuple[list[NDArray], list[NDArray]]

Computes the eigenvalues and eigenvectors of matrices on a given location.

To compute the eigenvalues and eigenvectors on the device with cupy is only possible if the cupy.linalg.eig function is available.

A list of matrices is beneficial if not all the matrices have the same shape. Then the host numba implementation will still parallelize, but not the cupy implementation. Only over the list will be parallelized, further extra dimensions are not allowed.

Assumes that all the input matrices are at the same location.

Parameters

  • A : NDArray | list[NDArray] — The matrices.

  • compute_module : str, optional — The location where to compute the eigenvalues and eigenvectors. Can be either "numpy" or "cupy".

  • output_module : str, optional — The location where to store the eigenvalues and eigenvectors. Can be either "numpy" or "cupy". If None, the output location is the same as the input location

  • use_pinned_memory : bool, optional — Whether to use pinnend memory if cupy is used. Default is True.

Returns

  • NDArray | list[NDArray] — The eigenvalues.

  • NDArray | list[NDArray] — The eigenvectors.

Raises

  • ValueError

source inv(a: NDArray) → NDArray

Computes the (batched) inverse of a matrix.

Parameters

  • a : NDArray — The (batched) matrix.

Returns

  • NDArray — The inverse (batched) of the matrix.

source svd(A: NDArray, full_matrices: bool = True, compute_module: str = 'numpy', output_module: str | None = None, use_pinned_memory: bool = True) → tuple[NDArray, NDArray, NDArray]

Computes the singular value decomposition of a matrix on a given location.

The kwargs compute_uv and hermitian are not supported. They are implicitly set to True and False, respectively.

Parameters

  • A : NDArray — The matrix.

  • full_matrices : bool, optional — Whether to compute the full matrices u and vh (see numpy.linalg.svd).

  • compute_module : str, optional — The location where to compute the singular value decomposition. Can be either "numpy" or "cupy".

  • output_module : str, optional — The location where to store the singular value decomposition. Can be either "numpy" or "cupy". If None, the output location is the same as the input location

  • use_pinned_memory : bool, optional — Whether to use pinnend memory if cupy is used. Default is True.

Returns

  • NDArray : NDArray — The left singular vectors.

  • NDArray : NDArray — The singular values.

  • NDArray : NDArray — The right singular vectors.

Raises

  • ValueError

source eigvalsh(A: NDArray, B: NDArray | None = None, compute_module: str = 'cupy', output_module: str | None = None, use_pinned_memory: bool = True) → NDArray

Compute eigenvalues of a hermitain generalized eigenvalue problem.

TODO: only type 1 generalized problems are supported, Only a subset of keywords of scipy.linalg.eigvalsh are supported.

Parameters

  • A : NDArray — A complex or real symmetric or hermitian matrix.

  • B : NDArray, optional — A complex or real symmetric or hermitian positive definite matrix. If omitted, identity matrix is assumed.

  • compute_module : str, optional — The location where to compute the eigenvalues.

  • output_module : str, optional — The location where to store the resulting eigenvalues.

  • use_pinned_memory : bool, optional — Whether to use pinnend memory if cupy is used. Default is True.

Returns

  • NDArray — The eigenvalues of the generalized eigenvalue problem.

Raises

  • ValueError

source qr(A: NDArray, compute_module: str = 'numpy', output_module: str | None = None, use_pinned_memory: bool = True) → tuple[NDArray, NDArray]

Computes the QR decomposition of a batch of matrices.

If compute_module is "numpy", the computation is done with numpy and parallelized with numba. Only mode 'reduced' is supported due to numba limitations.

Parameters

  • A : NDArray — The matrices.

  • compute_module : str, optional — The location where to compute the QR decomposition. Can be either "numpy" or "cupy".

  • output_module : str, optional — The location where to store the QR decomposition. Can be either "numpy" or "cupy". If None, the output location is the same as the input location

  • use_pinned_memory : bool, optional — Whether to use pinnend memory if cupy is used. Default is True.

Returns

  • NDArray : NDArray — Unitary matrix Q in the QR decomposition.

  • NDArray : NDArray — Upper triangular matrix R in the QR decomposition.

Raises

  • ValueError