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LAPACK version 3.0
zgerqf(3)

PURPOSE
  ZGERQF - compute an RQ factorization of a complex M-by-N matrix A

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

      INTEGER	     INFO, LDA, LWORK, M, N

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

DESCRIPTION
  ZGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R *
  Q.

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

  N	  (input) INTEGER
	  The number of columns of the matrix A.  N >= 0.

  A	  (input/output) COMPLEX*16 array, dimension (LDA,N)
	  On entry, the M-by-N matrix A.  On exit, if m <= n, the upper
	  triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper
	  triangular matrix R; if m >= n, the elements on and above the (m-
	  n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R;
	  the remaining elements, with the array TAU, represent the unitary
	  matrix Q as a product of min(m,n) elementary reflectors (see
	  Further Details).  LDA     (input) INTEGER The leading dimension of
	  the array A.	LDA >= max(1,M).

  TAU	  (output) COMPLEX*16 array, dimension (min(M,N))
	  The scalar factors of the elementary reflectors (see Further
	  Details).

  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 had an illegal value

FURTHER DETAILS
  The matrix Q is represented as a product of elementary reflectors

     Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v'

  where tau is a complex scalar, and v is a complex vector with v(n-k+i+1:n)
  = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-
  k+i,1:n-k+i-1), and tau in TAU(i).