NAME

       zunmbr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zunmbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
           ZUNMBR

Function/Subroutine Documentation

   subroutine zunmbr (character VECT, character SIDE, character TRANS, integer M, integer N,
       integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU,
       complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer
       LWORK, integer INFO)
       ZUNMBR

       Purpose:

            If VECT = 'Q', ZUNMBR 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', ZUNMBR 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 ZGEBRD 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).

       Parameters:
           VECT

                     VECT is CHARACTER*1
                     = 'Q': apply Q or Q**H;
                     = 'P': apply P or P**H.

           SIDE

                     SIDE is 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

                     TRANS is CHARACTER*1
                     = 'N':  No transpose, apply Q or P;
                     = 'C':  Conjugate transpose, apply Q**H or P**H.

           M

                     M is INTEGER
                     The number of rows of the matrix C. M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix C. N >= 0.

           K

                     K is INTEGER
                     If VECT = 'Q', the number of columns in the original
                     matrix reduced by ZGEBRD.
                     If VECT = 'P', the number of rows in the original
                     matrix reduced by ZGEBRD.
                     K >= 0.

           A

                     A is COMPLEX*16 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 ZGEBRD.

           LDA

                     LDA is 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

                     TAU is COMPLEX*16 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 ZGEBRD in the array argument TAUQ or TAUP.

           C

                     C is COMPLEX*16 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

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

           WORK

                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     If SIDE = 'L', LWORK >= max(1,N);
                     if SIDE = 'R', LWORK >= max(1,M);
                     if N = 0 or M = 0, LWORK >= 1.
                     For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
                     and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
                     optimal blocksize. (NB = 0 if M = 0 or N = 0.)

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of 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

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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