dgerq2 man page on IRIX

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DGERQ2(3F)							    DGERQ2(3F)

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'

									Page 1

DGERQ2(3F)							    DGERQ2(3F)

     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).

									Page 2

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