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dormbr

 NAME
      DORMBR - VECT = 'Q', DORMBR overwrites the general real M-
      by-N matrix C with  SIDE = 'L' SIDE = 'R' TRANS = 'N'

 SYNOPSIS
      SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU,
                         C, LDC, WORK, LWORK, INFO )

          CHARACTER      SIDE, TRANS, VECT

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

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

 PURPOSE
      If VECT = 'Q', DORMBR overwrites the general real M-by-N
      matrix C with
                      SIDE = 'L'     SIDE = 'R' TRANS = 'N':
      Q * C          C * Q TRANS = 'T':      Q**T * C       C *
      Q**T

      If VECT = 'P', DORMBR overwrites the general real M-by-N
      matrix C with
                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      P * C          C * P
      TRANS = 'T':      P**T * C       C * P**T

      Here Q and P**T are the orthogonal matrices 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) and G(i) respectively.

      Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq
      is the order of the orthogonal matrix Q or P**T 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) CHARACTER*1
              = 'Q': apply Q or Q**T;
              = 'P': apply P or P**T.

      SIDE    (input) CHARACTER*1

              = 'L': apply Q, Q**T, P or P**T from the Left;
              = 'R': apply Q, Q**T, P or P**T from the Right.

      TRANS   (input) CHARACTER*1
              = 'N':  No transpose, apply Q  or P;
              = 'T':  Transpose, apply Q**T or P**T.

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

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

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

      A       (input) DOUBLE PRECISION 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 DGEBRD.

      LDA     (input) 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) DOUBLE PRECISION array, dimension (min(nq,K))
              TAU(i) must contain the scalar factor of the elemen-
              tary reflector H(i) or G(i) which determines Q or P,
              as returned by DGEBRD in the array argument TAUQ or
              TAUP.

      C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
              On entry, the M-by-N matrix C.  On exit, C is
              overwritten by Q*C or Q**T*C or C*Q**T or C*Q or P*C
              or P**T*C or C*P or C*P**T.

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

      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.  If SIDE = 'L',
              LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M).

              For optimum performance LWORK >= N*NB if SIDE = 'L',
              and LWORK >= M*NB if SIDE = 'R', where NB is the
              optimal blocksize.

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