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 subma
trix 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.
(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.
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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