dgerq2(l) [redhat man page]

DGERQ2(l)								 )								 DGERQ2(l)

NAME

       DGERQ2 - compute an RQ factorization of a real m by n matrix A

SYNOPSIS

       SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       DGERQ2 computes an RQ factorization of a real 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) DOUBLE PRECISION 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 orthogonal 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) DOUBLE PRECISION array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors (see Further Details).

       WORK    (workspace) DOUBLE PRECISION 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 real scalar, and v is a real vector with
       v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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 							 DGERQ2(l)