.TH  SORMHR 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " 
.SH NAME
SORMHR - the general real M-by-N matrix C with   SIDE = \(aqL\(aq SIDE = \(aqR\(aq TRANS = \(aqN\(aq
.SH SYNOPSIS
.TP 19
SUBROUTINE SORMHR(
SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
LDC, WORK, LWORK, INFO )
.TP 19
.ti +4
CHARACTER
SIDE, TRANS
.TP 19
.ti +4
INTEGER
IHI, ILO, INFO, LDA, LDC, LWORK, M, N
.TP 19
.ti +4
REAL
A( LDA, * ), C( LDC, * ), TAU( * ),
WORK( * )
.SH PURPOSE
SORMHR overwrites the general real M-by-N matrix C with
TRANS = \(aqT\(aq:      Q**T * C       C * Q**T
.br

where Q is a real orthogonal matrix of order nq, with nq = m if
SIDE = \(aqL\(aq and nq = n if SIDE = \(aqR\(aq. Q is defined as the product of
IHI-ILO elementary reflectors, as returned by SGEHRD:
.br

Q = H(ilo) H(ilo+1) . . . H(ihi-1).
.br

.SH ARGUMENTS
.TP 8
SIDE    (input) CHARACTER*1
= \(aqL\(aq: apply Q or Q**T from the Left;
.br
= \(aqR\(aq: apply Q or Q**T from the Right.
.TP 8
TRANS   (input) CHARACTER*1
.br
= \(aqN\(aq:  No transpose, apply Q;
.br
= \(aqT\(aq:  Transpose, apply Q**T.
.TP 8
M       (input) INTEGER
The number of rows of the matrix C. M >= 0.
.TP 8
N       (input) INTEGER
The number of columns of the matrix C. N >= 0.
.TP 8
ILO     (input) INTEGER
IHI     (input) INTEGER
ILO and IHI must have the same values as in the previous call
of SGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
If SIDE = \(aqL\(aq, then 1 <= ILO <= IHI <= M, if M > 0, and
ILO = 1 and IHI = 0, if M = 0;
if SIDE = \(aqR\(aq, then 1 <= ILO <= IHI <= N, if N > 0, and
ILO = 1 and IHI = 0, if N = 0.
.TP 8
A       (input) REAL array, dimension
(LDA,M) if SIDE = \(aqL\(aq
(LDA,N) if SIDE = \(aqR\(aq
The vectors which define the elementary reflectors, as
returned by SGEHRD.
.TP 8
LDA     (input) INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = \(aqL\(aq; LDA >= max(1,N) if SIDE = \(aqR\(aq.
.TP 8
TAU     (input) REAL array, dimension
(M-1) if SIDE = \(aqL\(aq
(N-1) if SIDE = \(aqR\(aq
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEHRD.
.TP 8
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.
.TP 8
LDC     (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
.TP 8
WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
.TP 8
LWORK   (input) INTEGER
The dimension of the array WORK.
If SIDE = \(aqL\(aq, LWORK >= max(1,N);
if SIDE = \(aqR\(aq, LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = \(aqL\(aq, and
LWORK >= M*NB if SIDE = \(aqR\(aq, 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.
.TP 8
INFO    (output) INTEGER
= 0:  successful exit
.br
< 0:  if INFO = -i, the i-th argument had an illegal value
