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dormbr examples
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Man Page Details
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NAME
       DORMBR - = '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(
                          * )

  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 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 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
          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.
          K >= 0.

  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 elementary
          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/output) 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.

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

