| orthogonal factorization | |
|---|---|
| Routine Name | Operation |
| 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 |