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dorgbr

 NAME
      DORGBR - generate one of the matrices Q or P**T determined
      by DGEBRD when reducing a real matrix A to bidiagonal form

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

          CHARACTER      VECT

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

          DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK(
                         LWORK )

 PURPOSE
      DORGBR generates one of the matrices Q or P**T determined by
      DGEBRD when reducing a real matrix A to bidiagonal form: A =
      Q * B * P**T.  Q and P**T are defined as products of elemen-
      tary 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 DORGBR returns the
      first n columns of Q, where m >= n >= k;
      if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as
      an M-by-M matrix.

      If VECT = 'P', A is assumed to have been a K-by-N matrix,
      and P**T is of order N:
      if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the
      first m rows of P**T, where n >= m >= k;
      if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns
      P**T as an N-by-N matrix.

 ARGUMENTS
      VECT    (input) CHARACTER*1
              Specifies whether the matrix Q or the matrix P**T is
              required, as defined in the transformation applied
              by DGEBRD:
              = 'Q':  generate Q;
              = 'P':  generate P**T.

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

      N       (input) INTEGER
              The number of columns of the matrix Q or P**T 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 DGEBRD.  If VECT =
              'P', the number of rows in the original K-by-N
              matrix reduced by DGEBRD.

      A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the vectors which define the elementary
              reflectors, as returned by DGEBRD.  On exit, the M-
              by-N matrix Q or P**T.

      LDA     (input) INTEGER
              The leading dimension of the array A. LDA >=
              max(1,M).

      TAU     (input) DOUBLE PRECISION 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**T, as returned by DGEBRD in its array argument
              TAUQ or TAUP.

      WORK    (workspace) DOUBLE PRECISION 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