dormbr(3F)

NAME
     DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
     with  SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS
     SUBROUTINE DORMBR( 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

         DOUBLE         PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
                        LWORK )

PURPOSE
     If VECT = 'Q', DORMBR 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', DORMBR 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 DGEBRD 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 DGEBRD.  If VECT = 'P', the number of rows in the
             original matrix reduced by DGEBRD.  K >= 0.

     A       (input) DOUBLE PRECISION 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
             DGEBRD.

     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) DOUBLE PRECISION 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 DGEBRD in
             the array argument TAUQ or TAUP.

     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 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) 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.

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value