F08CXF (ZUNMRQ) multiplies a general complex
m by
n matrix
C by the complex unitary matrix
Q from an
RQ factorization computed by
F08CVF (ZGERQF).
SUBROUTINE F08CXF ( |
SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
INTEGER |
M, N, K, LDA, LDC, LWORK, INFO |
COMPLEX (KIND=nag_wp) |
A(LDA,*), TAU(*), C(LDC,*), WORK(max(1,LWORK)) |
CHARACTER(1) |
SIDE, TRANS |
|
F08CXF (ZUNMRQ) is intended to be used following a call to
F08CVF (ZGERQF), which performs an
RQ factorization of a complex matrix
A and represents the unitary matrix
Q as a product of elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
C, which may be any complex rectangular
m by
n matrix.
A common application of this routine is in solving underdetermined linear least squares problems, as described in the
F08 Chapter Introduction, and illustrated in
Section 9 in F08CVF (ZGERQF).
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999)
LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia
http://www.netlib.org/lapack/lug
Golub G H and Van Loan C F (1996)
Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
The computed result differs from the exact result by a matrix
E such that
where
ε is the
machine precision.
The real analogue of this routine is
F08CKF (DORMRQ).