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zungbr

 NAME
      ZUNGBR - generate one of the matrices Q or P**H determined
      by ZGEBRD when reducing a complex matrix A to bidiagonal
      form

 SYNOPSIS
      SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK,
                         INFO )

          CHARACTER      VECT

          INTEGER        INFO, K, LDA, LWORK, M, N

          COMPLEX*16     A( LDA, * ), TAU( * ), WORK( LWORK )

 PURPOSE
      ZUNGBR generates one of the matrices Q or P**H 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) or G(i) respectively.

      If VECT = 'Q', A is assumed to have been an M-by-K matrix,
      and Q is of order M:
      if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the
      first n columns of Q, where m >= n >= k;
      if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as
      an M-by-M matrix.

      If VECT = 'P', A is assumed to have been a K-by-N matrix,
      and P**H is of order N:
      if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the
      first m rows of P**H, where n >= m >= k;
      if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns
      P**H as an N-by-N matrix.

 ARGUMENTS
      VECT    (input) CHARACTER*1
              Specifies whether the matrix Q or the matrix P**H is
              required, as defined in the transformation applied
              by ZGEBRD:
              = 'Q':  generate Q;
              = 'P':  generate P**H.

      M       (input) INTEGER
              The number of rows of the matrix Q or P**H to be
              returned.  M >= 0.

      N       (input) INTEGER
              The number of columns of the matrix Q or P**H to be
              returned.  N >= 0.  If VECT = 'Q', M >= N >=

              min(M,K); if VECT = 'P', N >= M >= min(N,K).

      K       (input) INTEGER
              K >= 0.  If VECT = 'Q', the number of columns in the
              original M-by-K matrix reduced by ZGEBRD.  If VECT =
              'P', the number of rows in the original K-by-N
              matrix reduced by ZGEBRD.

      A       (input/output) COMPLEX*16 array, dimension (LDA,N)
              On entry, the vectors which define the elementary
              reflectors, as returned by ZGEBRD.  On exit, the M-
              by-N matrix Q or P**H.

      LDA     (input) INTEGER
              The leading dimension of the array A. LDA >= M.

      TAU     (input) COMPLEX*16 array, dimension
              (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P'
              TAU(i) must contain the scalar factor of the elemen-
              tary reflector H(i) or G(i), which determines Q or
              P**H, as returned by ZGEBRD in its array argument
              TAUQ or TAUP.

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

      LWORK   (input) INTEGER
              The dimension of the array WORK. LWORK >=
              max(1,min(M,N)).  For optimum performance LWORK >=
              min(M,N)*NB, where NB is the optimal blocksize.

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