SRC/zunmbr.f(3)

NAME
SRC/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.

Definition at line 194 of file zunmbr.f.

Author

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