F08CKF (DORMRQ) multiplies a general real
by
matrix
by the real orthogonal matrix
from an
factorization computed by
F08CHF (DGERQF).
SUBROUTINE F08CKF ( |
SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
INTEGER |
M, N, K, LDA, LDC, LWORK, INFO |
REAL (KIND=nag_wp) |
A(LDA,*), TAU(*), C(LDC,*), WORK(max(1,LWORK)) |
CHARACTER(1) |
SIDE, TRANS |
|
F08CKF (DORMRQ) is intended to be used following a call to
F08CHF (DGERQF), which performs an
factorization of a real matrix
and represents the orthogonal matrix
as a product of elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
, which may be any real rectangular
by
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 F08CHF (DGERQF).
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
The computed result differs from the exact result by a matrix
such that
where
is the
machine precision.
The complex analogue of this routine is
F08CXF (ZUNMRQ).