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LAPACK version 3.0
zungrq(3)

PURPOSE
  ZUNGRQ - generate an M-by-N complex matrix Q with orthonormal rows,

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

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

      COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

DESCRIPTION
  ZUNGRQ generates an M-by-N complex 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 ZGERQF.

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) COMPLEX*16 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
	  ZGERQF 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) COMPLEX*16 array, dimension (K)
	  TAU(i) must contain the scalar factor of the elementary reflector
	  H(i), as returned by ZGERQF.

  WORK	  (workspace/output) COMPLEX*16 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