NAME

SORMQR - overwrite the general real M-by-N matrix C with   SIDE = ’L’ SIDE = ’R’ TRANS = ’N’

SYNOPSIS

SUBROUTINE SORMQR(
SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS

INTEGER INFO, K, LDA, LDC, LWORK, M, N

REAL A( LDA, ∗ ), C( LDC, ∗ ), TAU( ∗ ), WORK( LWORK )

PURPOSE

SORMQR 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 SGEQRF. 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) REAL array, dimension (LDA,K)
The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRF in the first k columns 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. If SIDE = ’L’, LDA >= max(1,M); if SIDE = ’R’, LDA >= max(1,N).

TAU     (input) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQRF.

C       (input/output) REAL 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) REAL 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

  —  LAPACK version 2.0  —  08 October 1994