NAME

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( LWORK )

#include <sunperf.h>

void dormrq(char side, char trans, int m, int n, int k, double ∗da, int lda, double ∗tau, double ∗dc, int ldc, int ∗info) ;

PURPOSE

DORMRQ overwrites the general real M-by-N matrix C with 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 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 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.

INFO (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

SunOS 5.0  —  Last change: 10 Dec 1998