cgerqf man page on YellowDog

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CGERQF(l)			       )			     CGERQF(l)

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

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

	   INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE
       CGERQF 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 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 array, dimension (min(M,N))
	       The  scalar  factors  of the elementary reflectors (see Further
	       Details).

       WORK    (workspace/output) COMPLEX 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 opti‐
	       mum  performance	 LWORK >= M*NB, where NB is the optimal block‐
	       size.

	       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			     CGERQF(l)
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