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LAPACK version 3.0
dorgrq(3)

PURPOSE
  DORGRQ - generate an M-by-N real matrix Q with orthonormal rows,

SYNTAX
  SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

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

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

DESCRIPTION
  DORGRQ generates an M-by-N real matrix Q with orthonormal rows, which is
  defined as the last M rows of a product of K elementary reflectors of order
  N

	Q  =  H(1) H(2) . . . H(k)

  as returned by DGERQF.

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

  N	  (input) INTEGER
	  The number of columns of the matrix Q. N >= M.

  K	  (input) INTEGER
	  The number of elementary reflectors whose product defines the
	  matrix Q. M >= K >= 0.

  A	  (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	  On entry, the (m-k+i)-th row must contain the vector which defines
	  the elementary reflector H(i), for i = 1,2,...,k, as returned by
	  DGERQF in the last k rows of its array argument A.  On exit, the
	  M-by-N matrix Q.

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

  TAU	  (input) DOUBLE PRECISION array, dimension (K)
	  TAU(i) must contain the scalar factor of the elementary reflector
	  H(i), as returned by DGERQF.

  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,M).  For optimum
	  performance LWORK >= M*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 has an illegal value