redhat man page for zgerqf

ZGERQF(l)								 )								 ZGERQF(l)

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

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

	   INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE
       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 Fur-
	       ther 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).

LAPACK version 3.0						   15 June 2000 							 ZGERQF(l)