SORMBR - VECT = 'Q', SORMBR overwrites the general real M-
by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA,
TAU, C, LDC, WORK, LWORK, INFO )
CHARACTER SIDE, TRANS, VECT
INTEGER INFO, K, LDA, LDC, LWORK, M, N
REAL A( LDA, * ), C( LDC, * ), TAU( * ),
WORK( * )
PURPOSE
If VECT = 'Q', SORMBR 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
If VECT = 'P', SORMBR overwrites the general real M-by-N
matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'T': P**T * C C * P**T
Here Q and P**T are the orthogonal matrices determined by
SGEBRD when reducing a real matrix A to bidiagonal form: A
= Q * B * P**T. Q and P**T are defined as products of ele
mentary reflectors H(i) and G(i) respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq
is the order of the orthogonal matrix Q or P**T that is
applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K
matrix: if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
ARGUMENTS
VECT (input) CHARACTER*1
= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.
SIDE (input) CHARACTER*1
= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.
= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**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
If VECT = 'Q', the number of columns in the origi
nal matrix reduced by SGEBRD. If VECT = 'P', the
number of rows in the original matrix reduced by
SGEBRD. K >= 0.
A (input) REAL array, dimension
(LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if
VECT = 'P' The vectors which define the elementary
reflectors H(i) and G(i), whose products determine
the matrices Q and P, as returned by SGEBRD.
LDA (input) INTEGER
The leading dimension of the array A. If VECT =
'Q', LDA >= max(1,nq); if VECT = 'P', LDA >=
max(1,min(nq,K)).
TAU (input) REAL array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the ele
mentary reflector H(i) or G(i) which determines Q
or P, as returned by SGEBRD in the array argument
TAUQ or TAUP.
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 or
P*C or P**T*C or C*P or C*P**T.
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.
If LWORK = -1, then a workspace query is assumed;
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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