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DGEQP3(l)			       )			     DGEQP3(l)

NAME
       DGEQP3 - compute a QR factorization with column pivoting of a matrix A

SYNOPSIS
       SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )

	   INTEGER	  INFO, LDA, LWORK, M, N

	   INTEGER	  JPVT( * )

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

PURPOSE
       DGEQP3  computes a QR factorization with column pivoting of a matrix A:
       A*P = Q*R using Level 3 BLAS.

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 trapezoidal 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(J).ne.0, the J-th column of A is permuted  to
	       the  front  of  A*P  (a leading column); if JPVT(J)=0, the J-th
	       column of A is a free column.  On exit, if JPVT(J)=K, then  the
	       J-th column of A*P was the the K-th column of A.

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

       WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
	       On exit, if INFO=0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The  dimension  of the array WORK. LWORK >= 3*N+1.  For optimal
	       performance LWORK >= 2*N+( N+1 )*NB, where NB  is  the  optimal
	       blocksize.

	       If  LWORK  = -1, then a workspace query is assumed; the routine
	       only calculates the optimal size of  the	 WORK  array,  returns
	       this  value  as the first entry of the WORK array, and no error
	       message related to LWORK is issued by XERBLA.

       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/complex scalar, and v is a real/complex 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),
       and tau in TAU(i).

       Based on contributions by
	 G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
	 X. Sun, Computer Science Dept., Duke University, USA

LAPACK version 3.0		 15 June 2000			     DGEQP3(l)
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