LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
slaqps.f File Reference

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## Functions/Subroutines

subroutine slaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

## Function/Subroutine Documentation

 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.

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) Auxiliar 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).```
Date:
September 2012
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]

Definition at line 178 of file slaqps.f.

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