SGEQP3(l)								 )								 SGEQP3(l)

NAME

       SGEQP3 - compute a QR factorization with column pivoting of a matrix A

SYNOPSIS

       SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )

	   INTEGER	  INFO, LDA, LWORK, M, N

	   INTEGER	  JPVT( * )

	   REAL 	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       SGEQP3 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) REAL 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) REAL array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors.

       WORK    (workspace/output) REAL 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  block-
	       size.

	       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 							 SGEQP3(l)