# slaqps.f man page

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

*N*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*NB is INTEGER The number of columns to factorize.

*KB*KB is INTEGER The number of columns actually factorized.

*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.

*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*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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slaqps(3) is an alias of slaqps.f(3).