DORMRQ - overwrite the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE DORMRQ( 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
DORMRQ 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 elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGERQF. 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 DGERQF in the last k rows of its array
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 ele
mentary reflector H(i), as returned by DGERQF.
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 performance 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 ille
gal value
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