slaqps()

subroutine slaqps	(	integer	M,
		integer	N,
		integer	OFFSET,
		integer	NB,
		integer	KB,
		real, dimension( lda, * )	A,
		integer	LDA,
		integer, dimension( * )	JPVT,
		real, dimension( * )	TAU,
		real, dimension( * )	VN1,
		real, dimension( * )	VN2,
		real, dimension( * )	AUXV,
		real, dimension( ldf, * )	F,
		integer	LDF
	)

SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Download SLAQPS + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 SLAQPS computes a step of QR factorization with column pivoting
 of a real M-by-N matrix A by using Blas-3.  It tries to factorize
 NB columns 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.

Parameters

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0
[in]	OFFSET	OFFSET is INTEGER The number of rows of A that have been factorized in previous steps.
[in]	NB	NB is INTEGER The number of columns to factorize.
[out]	KB	KB is INTEGER The number of columns actually factorized.
[in,out]	A	A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, block A(OFFSET+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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out]	JPVT	JPVT is INTEGER array, dimension (N) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP.
[out]	TAU	TAU is REAL array, dimension (KB) The scalar factors of the elementary reflectors.
[in,out]	VN1	VN1 is REAL array, dimension (N) The vector with the partial column norms.
[in,out]	VN2	VN2 is REAL array, dimension (N) The vector with the exact column norms.
[in,out]	AUXV	AUXV is REAL array, dimension (NB) Auxiliary vector.
[in,out]	F	F is REAL array, dimension (LDF,NB) Matrix F**T = L*Y**T*A.
[in]	LDF	LDF is INTEGER The leading dimension of the array F. LDF >= max(1,N).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA

Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

References:

LAPACK Working Note 176 [PDF]