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dorgbr examples
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Man Page Details
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NAME
       DORGBR  -  one  of the real orthogonal 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( * )

  Purpose
  =======

  DORGBR generates one of the real orthogonal 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
  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 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
          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.
          K >= 0.

  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 elementary
          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/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. LWORK >= max(1,min(M,N)).
          For optimum performance LWORK >= min(M,N)*NB, 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

