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CLAQP2(1)	    LAPACK auxiliary routine (version 3.2)	     CLAQP2(1)

NAME
       CLAQP2  - computes a QR factorization with column pivoting of the block
       A(OFFSET+1:M,1:N)

SYNOPSIS
       SUBROUTINE CLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )

	   INTEGER	  LDA, M, N, OFFSET

	   INTEGER	  JPVT( * )

	   REAL		  VN1( * ), VN2( * )

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

PURPOSE
       CLAQP2 computes a QR factorization with column pivoting	of  the	 block
       A(OFFSET+1:M,1:N).   The	 block A(1:OFFSET,1:N) is accordingly pivoted,
       but not factorized.

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.

       OFFSET  (input) INTEGER
	       The number of rows of the matrix A that must be pivoted but  no
	       factorized. OFFSET >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
	       On  entry, the M-by-N matrix A.	On exit, the upper triangle of
	       block A(OFFSET+1:M,1:N) is the triangular factor obtained;  the
	       elements	  in   block  A(OFFSET+1:M,1:N)	 below	the  diagonal,
	       together with the array TAU, represent the orthogonal matrix  Q
	       as  a  product  of elementary reflectors. Block A(1:OFFSET,1:N)
	       has been accordingly pivoted, but no factorized.

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

       VN1     (input/output) REAL array, dimension (N)
	       The vector with the partial column norms.

       VN2     (input/output) REAL array, dimension (N)
	       The vector with the exact column norms.

       WORK    (workspace) COMPLEX array, dimension (N)

FURTHER DETAILS
       Based on contributions by
	 G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
	 X. Sun, Computer Science Dept., Duke University, USA
       Partial column norm updating strategy modified by
	 Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
	 University of Zagreb, Croatia.
	 June 2006.
       For more details see LAPACK Working Note 176.

 LAPACK auxiliary routine (versioNovember 2008			     CLAQP2(1)
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