slaqps.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

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)
          Auxiliar 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.

Date:

: December 2016

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 180 of file slaqps.f.

Author

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