NAME

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( LWORK )

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 elementary 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.

TRANS   (input) CHARACTER∗1
= ’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 original 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 elementary 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.

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