linalg 1.7.4
A linear algebra library that provides a user-friendly interface to several BLAS and LAPACK routines.
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Modules List
Here is a list of all documented modules with brief descriptions:
[detail level 12]
 MblasA module providing explicit interfaces to BLAS routines
 Cdgbmv
 Cdgemm
 Cdgemv
 Cdscal
 Cdtrsm
 Cdtrsv
 Czdscal
 Czgbmv
 Czgemm
 Czgemv
 Czscal
 Cztrsm
 Cztrsv
 MlinalgProvides a set of common linear algebra routines
 Cband_diag_mtx_multMultiplies a banded matrix, A, with a diagonal matrix, B, such that A = alpha * A * B, or A = alpha * B * A
 Cband_mtx_multMultiplies a banded matrix, A, by a vector x such that alpha * op(A) * x + beta * y = y
 Cband_mtx_to_full_mtxConverts a banded matrix stored in dense form to a full matrix
 Ccholesky_factorComputes the Cholesky factorization of a symmetric, positive definite matrix
 Ccholesky_rank1_downdateComputes the rank 1 downdate to a Cholesky factored matrix (upper triangular)
 Ccholesky_rank1_updateComputes the rank 1 update to a Cholesky factored matrix (upper triangular)
 CdetComputes the determinant of a square matrix
 Cdiag_mtx_multMultiplies a diagonal matrix with another matrix or array
 CeigenComputes the eigenvalues, and optionally the eigenvectors, of a matrix
 Cform_lqForms the orthogonal matrix Q from the elementary reflectors returned by the LQ factorization algorithm
 Cform_luExtracts the L and U matrices from the condensed [L\U] storage format used by the lu_factor
 Cform_qrForms the full M-by-M orthogonal matrix Q from the elementary reflectors returned by the base QR factorization algorithm
 Clq_factorComputes the LQ factorization of an M-by-N matrix
 Clu_factorComputes the LU factorization of an M-by-N matrix
 Cmtx_inverseComputes the inverse of a square matrix
 Cmtx_multPerforms the matrix operation: \( C = \alpha op(A) op(B) + \beta C \)
 Cmtx_pinverseComputes the Moore-Penrose pseudo-inverse of a M-by-N matrix using the singular value decomposition of the matrix
 Cmtx_rankComputes the rank of a matrix
 Cmult_lqMultiplies a general matrix by the orthogonal matrix Q from a LQ factorization
 Cmult_qrMultiplies a general matrix by the orthogonal matrix Q from a QR factorization
 Cmult_rzMultiplies a general matrix by the orthogonal matrix Z from an RZ factorization
 Cqr_factorComputes the QR factorization of an M-by-N matrix
 Cqr_rank1_updateComputes 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_updatePerforms 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_arrayMultiplies a vector by the reciprocal of a real scalar
 Crz_factorFactors 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_choleskySolves a system of Cholesky factored equations
 Csolve_least_squaresSolves 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_fullSolves 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_svdSolves the overdetermined or underdetermined system \( A X = B \) of M equations of N unknowns using a singular value decomposition of matrix A
 Csolve_lqSolves a system of M LQ-factored equations of N unknowns. N must be greater than or equal to M
 Csolve_luSolves a system of LU-factored equations
 Csolve_qrSolves a system of M QR-factored equations of N unknowns
 Csolve_triangular_systemSolves a triangular system of equations
 CsortSorts an array
 CsvdComputes 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 \( V^T \)
 CswapSwaps the contents of two arrays
 CtraceComputes the trace of a matrix (the sum of the main diagonal elements)
 Ctri_mtx_multComputes 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
 MqrupdateA module providing explicit interfaces for the QRUPDATE library
 Cdch1dn
 Cdch1up
 Cdqr1up
 Czch1dn
 Czch1up
 Czqr1up