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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 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 				SGEQP3(l)
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