DGEQPF(l)	      LAPACK test routine (version 1.1)		    DGEQPF(l)

NAME
  DGEQPF - compute a QR	factorization with column pivoting of a	real M-by-N
  matrix A

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
  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 reflec-
	  tors.

  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
	  column 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.