Other Factorizations     Next: Generalized Orthogonal Factorizations Up: Orthogonal Factorizations and Previous: Complete Orthogonal Factorization

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 .

All the factorization routines discussed here (except xTZRQF) 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.

---------------------------------------------------------------------------
Type of
factorization                            Single precision  Double precision
and matrix      Operation                real     complex  real     complex
---------------------------------------------------------------------------
QR, general     factorize with pivoting  SGEQPF   CGEQPF   DGEQPF   ZGEQPF
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
---------------------------------------------------------------------------
RQ, trapezoidal factorize, no pivoting   STZRQF   CTZRQF   DTZRQF   ZTZRQF
---------------------------------------------------------------------------
Table 2.9: Computational routines for orthogonal factorizations

Tue Nov 29 14:03:33 EST 1994