Next: Generalized Orthogonal Factorizations and Up: Orthogonal Factorizations and Linear Previous: Complete Orthogonal Factorization Contents Index

### Other Factorizations

The QL and RQ factorizations are given by

and

These factorizations are computed by xGEQLF and xGERQF, respectively; they are less commonly used than either the QR or LQ factorizations described above, but have applications in, for example, the computation of generalized QR factorizations [2].

All the factorization routines discussed here (except xTZRQF and xTZRZF) allow arbitrary m and n, so that in some cases the matrices R or L are trapezoidal rather than triangular. A routine that performs pivoting is provided only for the QR factorization.

Table 2.9: Computational routines for orthogonal factorizations
Type of factorization | Operation | Single precision | Double precision
and matrix |  | real | complex | real | complex
QR, general | factorize with pivoting | SGEQP3 | CGEQP3 | DGEQP3 | ZGEQP3
| factorize, no pivoting | SGEQRF | CGEQRF | DGEQRF | ZGEQRF
| generate Q | SORGQR | CUNGQR | DORGQR | ZUNGQR
| multiply matrix by Q | SORMQR | CUNMQR | DORMQR | ZUNMQR
LQ, general | factorize, no pivoting | SGELQF | CGELQF | DGELQF | ZGELQF
| generate Q | SORGLQ | CUNGLQ | DORGLQ | ZUNGLQ
| multiply matrix by Q | SORMLQ | CUNMLQ | DORMLQ | ZUNMLQ
QL, general | factorize, no pivoting | SGEQLF | CGEQLF | DGEQLF | ZGEQLF
| generate Q | SORGQL | CUNGQL | DORGQL | ZUNGQL
| multiply matrix by Q | SORMQL | CUNMQL | DORMQL | ZUNMQL
RQ, general | factorize, no pivoting | SGERQF | CGERQF | DGERQF | ZGERQF
| generate Q | SORGRQ | CUNGRQ | DORGRQ | ZUNGRQ
| multiply matrix by Q | SORMRQ | CUNMRQ | DORMRQ | ZUNMRQ
RZ, trapezoidal | factorize, no pivoting | STZRZF | CTZRZF | DTZRZF | ZTZRZF
| (blocked algorithm) |  |  |  |
| multiply matrix by Q | SORMRZ | CUNMRZ | DORMRZ | ZUNMRZ

Next: Generalized Orthogonal Factorizations and Up: Orthogonal Factorizations and Linear Previous: Complete Orthogonal Factorization Contents Index