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linalg 1.8.2
A linear algebra library that provides a user-friendly interface to several BLAS and LAPACK routines.
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| ▼Mblas | A module providing explicit interfaces to BLAS routines |
| Cddot | |
| Cdgbmv | |
| Cdgemm | |
| Cdgemv | |
| Cdscal | |
| Cdtrsm | |
| Cdtrsv | |
| Czdscal | |
| Czgbmv | |
| Czgemm | |
| Czgemv | |
| Czscal | |
| Cztrsm | |
| Cztrsv | |
| ▼Mlinalg | Provides a set of common linear algebra routines |
| Cband_diag_mtx_mult | Multiplies a banded matrix, A, with a diagonal matrix, B, such that A = alpha * A * B, or A = alpha * B * A |
| Cband_mtx_mult | Multiplies a banded matrix, A, by a vector x such that alpha * op(A) * x + beta * y = y |
| Cband_mtx_to_full_mtx | Converts a banded matrix stored in dense form to a full matrix |
| Cbanded_to_dense | Converts a banded matrix to a dense matrix |
| 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) |
| Ccsr_matrix | A sparse matrix stored in compressed sparse row (CSR) format |
| Cdense_to_banded | Converts a dense matrix to a banded matrix |
| 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 |
| Cextract_diagonal | Extracts the diagonal 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 |
| Cmatmul | Performs sparse matrix multiplication C = A * B |
| Cmsr_matrix | A sparse matrix stored in modified sparse row format. This format is convenient for situations where the diagonal is fully populated |
| 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 |
| Cnonzero_count | Determines the number of nonzero entries in a sparse matrix |
| Coperator(*) | Multiplies a sparse matrix and a scalar |
| Coperator(+) | Adds two sparse matrices |
| Coperator(-) | Subtracts two sparse matrices |
| Coperator(/) | Multiplies a sparse matrix by a scalar |
| Cpgmres_solver | A preconditioned GMRES solver |
| 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 |
| Csize | Determines the size of the requested dimension of the supplied sparse 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 |
| Csparse_direct_solve | Provides a direct solution to a square, sparse system |
| 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) |
| Ctranspose | Provides the transpose of a sparse matrix |
| 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 |
| ▼Mqrupdate | A module providing explicit interfaces for the QRUPDATE library |
| Cdch1dn | |
| Cdch1up | |
| Cdqr1up | |
| Czch1dn | |
| Czch1up | |
| Czqr1up | |
| ▼Msparskit | An interface to the SPARSKIT library available at https://www-users.cse.umn.edu/~saad/software/SPARSKIT/ |
| Camub | Computes the matrix product: C = A * B |
| Caplb | Computes the matrix sum: C = A + B, where the matrices are given in CSR format |
| Caplsb | Computes the matrix sum: C = A + s * B, where the matrices are given in CSR format |
| Cbndcsr | Converts the LINPACK, BLAS, LAPACK banded matrix format into a CSR format |
| Cclncsr | @breif Cleans up a CSR matrix |
| Ccoocsr | Converte a matrix stored in coordinate format to CSR format |
| Ccsort | Sorces the elements of a CSR matrix in increasing order of their column indices within each row |
| Ccsrcsc2 | Converts a CSR matrix into a CSC matrix (transposition) |
| Ccsrmsr | Converts a CSR matrix to an MSR matrix |
| Cgetdia | Extracts the diagonal from a matrix |
| Cgetelm | Gets element A(i,j) of matrix A for any pair (i,j) |
| Cilud | Computes the incomplete LU factorization of a sparse matrix in CSR format with standard dropping strategy |
| Ciludp | Computes the incomplete LU factorization of a sparse matrix in CSR format with standard dropping strategy |
| Cilut | Computes the incomplete LU factorization of a sparse matrix in CSR format using a dual truncation mechanism |
| Cilutp | Computes the incomplete LU factorization of a sparse matrix in CSR format using a dual truncation mechanism and pivoting |
| Clusol | Solves the LU-factored system (LU) x = y |
| Cmsrcsr | Converts and MSR matrix to a CSR matrix |
| Cpgmres | An ILUT preconditioned GMRES algorithm. This routine utilizes the L and U matrices generated by the ILUT routine to precondition the GMRES algorithm. The stopping criteria utilized is based simply on reducing the residual norm to the requested tolerance |