Computational Routines for Orthogonal Factorization and Singular Value Decomposition

orthogonal factorization
Routine NameOperation
sgeqpf, dgeqpf
cgeqpf, zgeqpf
Computes a QR factorization with column pivoting of a general rectangular matrix
sgeqrf, dgeqrf
cgeqrf, zgeqrf
Computes a QR factorization of a general rectangular matrix
sorgqr, dorgqr
cungqr, zungqr
Generates all or part of the orthogonal/unitary matrix Q from a QR factorization determined by SGEQRF/CGEQRF
sormqr, dormqr
cunmqr, zunmqr
Multiplies a general matrix by the orthogonal/unitary matrix from a QR factorization determined by SGEQRF/CGEQRF
sgelqf, dgelqf
cgelqf, zgelqf
Computes an LQ factorization of a general rectangular matrix
sorglq, dorglq
cunglq, zunglq
Generates all or part of the orthogonal/unitary matrix Q from an LQ factorization determined by SGELQF/CGELQF
sormlq, dormlq
cunmlq, zunmlq
Multiplies a general matrix by the orthogonal/unitary matrix from an LQ factorization determined by SGELQF/CGELQF
sgeqlf, dgeqlf
cgeqlf, zgeqlf
Computes a QL factorization of a general rectangular matrix
sorgql, dorgql
cungql, zungql
Generates all or part of the orthogonal/unitary matrix Q from a QL factorization determined by SGEQLF/CGEQLF
sormql, dormql
cunmql, zunmql
Multiplies a general matrix by the orthogonal/unitary matrix from a QL factorization determined by SGEQLF/CGEQLF
sgerqf, dgerqf
cgerqf, zgerqf
Computes an RQ factorization of a general rectangular matrix
sorgrq, dorgrq
cungrq, zungrq
Generates all or part of the orthogonal/unitary matrix Q from an RQ factorization determined by SGERQF/CGERQF
sormrq, dormrq
cunmrq, zunmrq
Multiplies a general matrix by the orthogonal/unitary matrix from an RQ factorization determined by SGERQF/CGERQF
stzrqf, dtzrqf
ctzrqf, ztzrqf
Computes an RQ factorization of an upper trapezoidal matrix
singular value decomposition
sgebrd, dgebrd
cgebrd, zgebrd
Reduces a general rectangular matrix to real bidiagonal form by an orthogonal/ unitary transformation
sorgbr, dorgbr
cungbr, zungbr
Generates the orthogonal/unitary transformation matrices from a reduction to bidiagonal form determined by SGEBRD/CGEBRD
sormbr, dormbr
cunmbr, zunmbr
Multiplies a general matrix by one of the orthogonal/unitary transformation matrices from a reduction to bidiagonal form determined by SGEBRD/CGEBRD
sbdsqr, dbdsqr
cbdsqr, zbdsqr
Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using the bidiagonal QR algorithm
sggsvp, dggsvp
cggsvp, zggsvp
Computes orthogonal/unitary matrices as a preprocessing step for computing the generalized singular value decomposition
stgsja, dtgsja
ctgsja, ztgsja
Computes the generalized singular value decomposition of two real/complex upper "triangular (or trapezoidal)" matrices as output by xGGSVP

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