DORMLQ(l) ) DORMLQ(l)NAME
DORMLQ - overwrite the general real M-by-N matrix C with SIDE = 'L'
SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
LWORK, INFO )
CHARACTER SIDE, TRANS
INTEGER INFO, K, LDA, LDC, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
* )
PURPOSE
DORMLQ overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE
= 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C *
Q**T
where Q is a real orthogonal matrix defined as the product of k elemen‐
tary reflectors
Q = H(k) . . . H(2)H(1)
as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N if
SIDE = 'R'.
ARGUMENTS
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
0.
A (input) DOUBLE PRECISION array, dimension
(LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
contain the vector which defines the elementary reflector H(i),
for i = 1,2,...,k, as returned by DGELQF in the first k rows of
its array argument A. A is modified by the routine but
restored on exit.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
TAU (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflec‐
tor H(i), as returned by DGELQF.
C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C. On exit, C is overwritten by
Q*C or Q**T*C or C*Q**T or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If SIDE = 'L', LWORK >=
max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
= 'R', where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK version 3.0 15 June 2000 DORMLQ(l)