dlaqps-f(3)

dlaqps.f –

Synopsis

Functions/Subroutines

subroutine dlaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
DLAQPS 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 dlaqps (integerM, integerN, integerOFFSET, integerNB, integerKB, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision, dimension( * )VN1, double precision, dimension( * )VN2, double precision, dimension( * )AUXV, double precision, dimension( ldf, * )F, integerLDF)

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

Purpose:

 DLAQPS 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (KB)
 The scalar factors of the elementary reflectors.

VN1

 VN1 is DOUBLE PRECISION array, dimension (N)
 The vector with the partial column norms.

VN2

 VN2 is DOUBLE PRECISION array, dimension (N)
 The vector with the exact column norms.

AUXV

 AUXV is DOUBLE PRECISION array, dimension (NB)
 Auxiliar vector.

 F is DOUBLE PRECISION 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.

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

Definition at line 177 of file dlaqps.f.

Author

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