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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
Susan Blackford
19991001