DORGBR (3lapack)

generate 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( LWORK )

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.

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