Module lapack 

LAPACK decompositions and operations on ndarray types.

This module provides LAPACK decompositions (LU, QR, SVD, EVD, Cholesky) directly on ndarray types, using OxiBLAS-LAPACK as the backend.

Structs

CholeskyResult

Result of Cholesky decomposition.

Eigenvalue

Represents a real or complex eigenvalue.

GeneralEvdResult

Result of general eigenvalue decomposition.

LuResult

Result of LU decomposition.

QrResult

Result of QR decomposition.

RandomizedSvdResult

Result of randomized SVD.

SchurResult

Result of Schur decomposition.

SvdResult

Result of SVD decomposition.

SymEvdResult

Result of symmetric eigenvalue decomposition.

Enums

LapackError

Error type for LAPACK operations on ndarray.

Functions

cholesky_ndarray

Computes the Cholesky decomposition of a positive definite matrix.

cond_ndarray

Computes the condition number of a matrix (using 2-norm).

det_ndarray

Computes the determinant of a matrix.

eig_ndarray

Computes eigenvalues of a general (non-symmetric) matrix.

eig_symmetric

Computes the eigenvalue decomposition of a symmetric matrix.

eigvals_ndarray

Computes only the eigenvalues of a general matrix.

eigvals_symmetric

Computes only the eigenvalues of a symmetric matrix.

inv_ndarray

Computes the inverse of a matrix.

low_rank_approx_ndarray

Computes a low-rank approximation of a matrix.

lstsq_ndarray

Solves the least squares problem min ||Ax - b||.

lu_ndarray

Computes the LU decomposition of a matrix.

pinv_ndarray

Computes the Moore-Penrose pseudo-inverse.

qr_ndarray

Computes the QR decomposition of a matrix.

rank_ndarray

Computes the numerical rank of a matrix.

rsvd_ndarray

Computes a randomized SVD approximation of a matrix.

rsvd_power_ndarray

Computes randomized SVD with power iteration for improved accuracy.

schur_ndarray

Computes the real Schur decomposition of a square matrix.

solve_multiple_ndarray

Solves multiple linear systems AX = B.

solve_ndarray

Solves the linear system Ax = b.

svd_ndarray

Computes the SVD of a matrix.

svd_truncated

Computes the truncated SVD of a matrix.

tridiag_solve_multiple_ndarray

Solves multiple tridiagonal systems with the same matrix.

tridiag_solve_ndarray

Solves a tridiagonal system of equations.

tridiag_solve_spd_ndarray

Solves a symmetric positive definite tridiagonal system.

Type Aliases

LapackResult

Result type for LAPACK operations.