ZGEQP3(l)								 )								 ZGEQP3(l)

NAME

       ZGEQP3 - compute a QR factorization with column pivoting of a matrix A

SYNOPSIS

       SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO )

	   INTEGER	  INFO, LDA, LWORK, M, N

	   INTEGER	  JPVT( * )

	   DOUBLE	  PRECISION RWORK( * )

	   COMPLEX*16	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       ZGEQP3 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors.

       WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
	       On exit, if INFO=0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK. LWORK >= N+1.  For optimal performance LWORK >= ( 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.

       RWORK   (workspace) DOUBLE PRECISION array, dimension (2*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(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 							 ZGEQP3(l)