linalg 1.7.2
A linear algebra library that provides a user-friendly interface to several BLAS and LAPACK routines.
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▼Nlinalg | Provides a set of common linear algebra routines |
Ccholesky_factor | Computes the Cholesky factorization of a symmetric, positive definite matrix |
Ccholesky_rank1_downdate | Computes the rank 1 downdate to a Cholesky factored matrix (upper triangular) |
Ccholesky_rank1_update | Computes the rank 1 update to a Cholesky factored matrix (upper triangular) |
Cdet | Computes the determinant of a square matrix |
Cdiag_mtx_mult | Multiplies a diagonal matrix with another matrix or array |
Ceigen | Computes the eigenvalues, and optionally the eigenvectors, of a matrix |
Cform_lq | Forms the orthogonal matrix Q from the elementary reflectors returned by the LQ factorization algorithm |
Cform_lu | Extracts the L and U matrices from the condensed [L\U] storage format used by the lu_factor |
Cform_qr | Forms the full M-by-M orthogonal matrix Q from the elementary reflectors returned by the base QR factorization algorithm |
Clq_factor | Computes the LQ factorization of an M-by-N matrix |
Clu_factor | Computes the LU factorization of an M-by-N matrix |
Cmtx_inverse | Computes the inverse of a square matrix |
Cmtx_mult | Performs the matrix operation: \( C = \alpha op(A) op(B) + \beta C \) |
Cmtx_pinverse | Computes the Moore-Penrose pseudo-inverse of a M-by-N matrix using the singular value decomposition of the matrix |
Cmtx_rank | Computes the rank of a matrix |
Cmult_lq | Multiplies a general matrix by the orthogonal matrix Q from a LQ factorization |
Cmult_qr | Multiplies a general matrix by the orthogonal matrix Q from a QR factorization |
Cmult_rz | Multiplies a general matrix by the orthogonal matrix Z from an RZ factorization |
Cqr_factor | Computes the QR factorization of an M-by-N matrix |
Cqr_rank1_update | Computes the rank 1 update to an M-by-N QR factored matrix A (M >= N) where \( A = Q R \), and \( A1 = A + U V^T \) such that \( A1 = Q1 R1 \). In the event \( V \) is complex-valued, \( V^H \) is computed instead of \( V^T \) |
Crank1_update | Performs the rank-1 update to matrix A such that: \( A = \alpha X Y^T + A \), where \( A \) is an M-by-N matrix, \( \alpha \)is a scalar, \( X \) is an M-element array, and \( Y \) is an N-element array. In the event that \( Y \) is complex, \( Y^H \) is used instead of \( Y^T \) |
Crecip_mult_array | Multiplies a vector by the reciprocal of a real scalar |
Crz_factor | Factors an upper trapezoidal matrix by means of orthogonal transformations such that \( A = R Z = (R 0) Z \). Z is an orthogonal matrix of dimension N-by-N, and R is an M-by-M upper triangular matrix |
Csolve_cholesky | Solves a system of Cholesky factored equations |
Csolve_least_squares | Solves the overdetermined or underdetermined system \( A X = B \) of M equations of N unknowns. Notice, it is assumed that matrix A has full rank |
Csolve_least_squares_full | Solves the overdetermined or underdetermined system \( A X = B \) of M equations of N unknowns, but uses a full orthogonal factorization of the system |
Csolve_least_squares_svd | Solves the overdetermined or underdetermined system \( A X = B \) of M equations of N unknowns using a singular value decomposition of matrix A |
Csolve_lq | Solves a system of M LQ-factored equations of N unknowns. N must be greater than or equal to M |
Csolve_lu | Solves a system of LU-factored equations |
Csolve_qr | Solves a system of M QR-factored equations of N unknowns |
Csolve_triangular_system | Solves a triangular system of equations |
Csort | Sorts an array |
Csvd | Computes the singular value decomposition of a matrix A. The SVD is defined as: \( A = U S V^T \), where \( U \) is an M-by-M orthogonal matrix, \( S \) is an M-by-N diagonal matrix, and \( V \) is an N-by-N orthogonal matrix. In the event that \( V \) is complex valued, \( V^H \) is computed instead of \( V^T \) |
Cswap | Swaps the contents of two arrays |
Ctrace | Computes the trace of a matrix (the sum of the main diagonal elements) |
Ctri_mtx_mult | Computes the triangular matrix operation: \( B = \alpha A^T A + \beta B \), or \( B = \alpha A A^T + \beta B \), where A is a triangular matrix |