# dlaqps.f - Man Page

## 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 (integer M, integer N, integer OFFSET, integer NB, integer KB, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) JPVT, double precision, dimension( * ) TAU, double precision, dimension( * ) VN1, double precision, dimension( * ) VN2, double precision, dimension( * ) AUXV, double precision, dimension( ldf, * ) F, integer LDF)

**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*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 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*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:**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 179 of file dlaqps.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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