CUNMBR(3)      LAPACK routine of NEC Numeric Library Collection      CUNMBR(3)



NAME
       CUNMBR

SYNOPSIS
       SUBROUTINE CUNMBR (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
           WORK, LWORK, 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 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)
                     VECT is CHARACTER*1
                     = 'Q': apply Q or Q**H;
                     = 'P': apply P or P**H.

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

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

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

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

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

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



LAPACK routine                  31 October 2017                      CUNMBR(3)