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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 )



     #include <sunperf.h>

     void cunmbr(char vect, char side, char trans, int m, int  n,
               int k, complex *ca, int lda, complex *tau, complex
               *cc, int ldc, int *info) ;

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 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  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 origi-
               nal  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  ele-
               mentary  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 ille-
               gal value

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