cunmbr(3F)

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

SYNOPSIS
     SUBROUTINE CUNMBR( 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

         COMPLEX        A( LDA, * ), C( LDC, * ), TAU( * ), WORK( LWORK )

PURPOSE
     If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with
                     SIDE = 'L'     SIDE = 'R' TRANS = 'N':      Q * C
     C * Q TRANS = 'C':      Q**H * C       C * Q**H

     If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C with
                     SIDE = 'L'     SIDE = 'R'
     TRANS = 'N':      P * C          C * P
     TRANS = 'C':      P**H * C       C * P**H

     Here Q and P**H are the unitary matrices determined by CGEBRD when
     reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and
     P**H 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 unitary matrix Q or P**H 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**H;
             = 'P': apply P or P**H.

     SIDE    (input) CHARACTER*1
             = 'L': apply Q, Q**H, P or P**H from the Left;
             = 'R': apply Q, Q**H, P or P**H from the Right.
     TRANS   (input) CHARACTER*1
             = 'N':  No transpose, apply Q or P;
             = 'C':  Conjugate transpose, apply Q**H or P**H.

     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 CGEBRD.  If VECT = 'P', the number of rows in the
             original matrix reduced by CGEBRD.  K >= 0.

     A       (input) COMPLEX 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
             CGEBRD.

     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) COMPLEX 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 CGEBRD in
             the array argument TAUQ or TAUP.

     C       (input/output) COMPLEX array, dimension (LDC,N)
             On entry, the M-by-N matrix C.  On exit, C is overwritten by Q*C
             or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H.

     LDC     (input) INTEGER
             The leading dimension of the array C. LDC >= max(1,M).

     WORK    (workspace/output) COMPLEX 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