DGEQPF(l)								 )								 DGEQPF(l)

NAME

       DGEQPF - routine is deprecated and has been replaced by routine DGEQP3

SYNOPSIS

       SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

	   INTEGER	  JPVT( * )

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

PURPOSE

       This  routine  is deprecated and has been replaced by routine DGEQP3.  DGEQPF computes a QR factorization with column pivoting of a real M-
       by-N matrix A: A*P = Q*R.

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, the upper triangle of the array contains the min(M,N)-by-N upper triangular matrix R;  the
	       elements  below	the  diagonal,	together with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary
	       reflectors.

       LDA     (input) INTEGER
	       The leading dimension of the array A. LDA >= max(1,M).

       JPVT    (input/output) INTEGER array, dimension (N)
	       On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th col-
	       umn of A is a free column.  On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.

       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors.

       WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

       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(n)

       Each H(i) has the form

	  H = I - tau * v * v'

       where tau is a real scalar, and v is a real vector with
       v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).

       The matrix P is represented in jpvt as follows: If
	  jpvt(j) = i
       then the jth column of P is the ith canonical unit vector.

LAPACK test version 3.0 					   15 June 2000 							 DGEQPF(l)