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

NAME
       CLAQPS  - computes a step of QR factorization with column pivoting of a
       complex M-by-N matrix A by using Blas-3

SYNOPSIS
       SUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU,  VN1,  VN2,
			  AUXV, F, LDF )

	   INTEGER	  KB, LDA, LDF, M, N, NB, OFFSET

	   INTEGER	  JPVT( * )

	   REAL		  VN1( * ), VN2( * )

	   COMPLEX	  A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )

PURPOSE
       CLAQPS  computes	 a  step of QR factorization with column pivoting of a
       complex M-by-N matrix A by using Blas-3.	 It tries to factorize NB col‐
       umns  from  A  starting	from  the row OFFSET+1, and updates all of the
       matrix with Blas-3 xGEMM.
       In some cases, due to catastrophic cancellations, it  cannot  factorize
       NB columns.  Hence, the actual number of factorized columns is returned
       in KB.
       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 A that have been factorized  in  previous
	       steps.

       NB      (input) INTEGER
	       The number of columns to factorize.

       KB      (output) INTEGER
	       The number of columns actually factorized.

       A       (input/output) COMPLEX array, dimension (LDA,N)
	       On   entry,  the	 M-by-N	 matrix	 A.   On  exit,	 block	A(OFF‐
	       SET+1:M,1:KB) is the triangular
	       factor obtained and block A(1:OFFSET,1:N) has been  accordingly
	       pivoted,	 but  no  factorized.	The  rest of the matrix, block
	       A(OFFSET+1:M,KB+1:N) has been updated.

       LDA     (input) INTEGER
	       The leading dimension of the array A. LDA >= max(1,M).

       JPVT    (input/output) INTEGER array, dimension (N)
	       JPVT(I) = K <==> Column K of the full matrix A  has  been  per‐
	       muted into position I in AP.

       TAU     (output) COMPLEX array, dimension (KB)
	       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.

       AUXV    (input/output) COMPLEX array, dimension (NB)
	       Auxiliar vector.

       F       (input/output) COMPLEX array, dimension (LDF,NB)
	       Matrix F' = L*Y'*A.

       LDF     (input) INTEGER
	       The leading dimension of the array F. LDF >= max(1,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			     CLAQPS(1)

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