NAME

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

SYNOPSIS

SUBROUTINE DORMHR(
SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS

INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N

DOUBLE PRECISION A( LDA, ∗ ), C( LDC, ∗ ), TAU( ∗ ), WORK( LWORK )

PURPOSE

DORMHR 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 of order nq, with nq = m if SIDE = ’L’ and nq = n if SIDE = ’R’. Q is defined as the product of IHI-ILO elementary reflectors, as returned by DGEHRD:
 
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
 

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.

ILO     (input) INTEGER
IHI     (input) INTEGER ILO and IHI must have the same values as in the previous call of DGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). If SIDE = ’L’, then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if SIDE = ’R’, then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and IHI = 0, if N = 0.

A       (input) DOUBLE PRECISION array, dimension
(LDA,M) if SIDE = ’L’ (LDA,N) if SIDE = ’R’ The vectors which define the elementary reflectors, as returned by DGEHRD.

LDA     (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M) if SIDE = ’L’; LDA >= max(1,N) if SIDE = ’R’.

TAU     (input) DOUBLE PRECISION array, dimension
(M-1) if SIDE = ’L’ (N-1) if SIDE = ’R’ TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEHRD.

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

  —  LAPACK version 2.0  —  08 October 1994