NAME

SRC/slaqps.f

SYNOPSIS

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



          M is INTEGER


          The number of rows of the matrix A. M >= 0.



          N is INTEGER


          The number of columns of the matrix A. N >= 0

OFFSET



          OFFSET is INTEGER


          The number of rows of A that have been factorized in


          previous steps.



          NB is INTEGER


          The number of columns to factorize.



          KB is INTEGER


          The number of columns actually factorized.



          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.

LDA



          LDA is INTEGER


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

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.

TAU



          TAU is REAL array, dimension (KB)


          The scalar factors of the elementary reflectors.

VN1



          VN1 is REAL array, dimension (N)


          The vector with the partial column norms.

VN2



          VN2 is REAL array, dimension (N)


          The vector with the exact column norms.

AUXV



          AUXV is REAL array, dimension (NB)


          Auxiliary vector.



          F is REAL array, dimension (LDF,NB)


          Matrix F**T = L*Y**T*A.

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

Definition at line 176 of file slaqps.f.

Author

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