DORMHR(l) ) DORMHR(l)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(
* )
PURPOSE
DORMHR 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 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 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 DORMHR(l)
