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RedHat 9 (Linux i386) - man page for cgerq2 (redhat section l)

CGERQ2(l)					)					CGERQ2(l)

NAME
       CGERQ2 - compute an RQ factorization of a complex m by n matrix A

SYNOPSIS
       SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

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

PURPOSE
       CGERQ2 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 sub-
	       array 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 trape-
	       zoidal matrix R; the remaining elements, with the array TAU, represent the unitary
	       matrix Q as a product of 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) COMPLEX array, dimension (M)

       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 				CGERQ2(l)


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