---
name: "slaqps"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slaqps/3lapack"
---

# slaqps(3lapack)

computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3

## NAME

SLAQPS - computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3

## SYNOPSIS

- SUBROUTINE SLAQPS(

  M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF )

- INTEGER

  KB, LDA, LDF, M, N, NB, OFFSET

- INTEGER

  JPVT( \* )

- REAL

  A( LDA, \* ), AUXV( \* ), F( LDF, \* ), TAU( \* ), VN1( \* ), VN2( \* )

## 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.

## ARGUMENTS

- M (input) INTEGER

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

- N (input) INTEGER

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

- OFFSET (input) INTEGER

  The number of rows of A that have been factorized in previous steps.

- NB (input) INTEGER

  The number of columns to factorize.

- KB (output) INTEGER

  The number of columns actually factorized.

- A (input/output) 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 (input) INTEGER

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

- JPVT (input/output) INTEGER array, dimension (N)

  JPVT(I) = K \<==\> Column K of the full matrix A has been permuted into position I in AP.

- TAU (output) REAL array, dimension (KB)

  The scalar factors of the elementary reflectors.

- VN1 (input/output) REAL array, dimension (N)

  The vector with the partial column norms.

- VN2 (input/output) REAL array, dimension (N)

  The vector with the exact column norms.

- AUXV (input/output) REAL array, dimension (NB)

  Auxiliar vector.

- F (input/output) REAL array, dimension (LDF,NB)

  Matrix F' = L\*Y'\*A.

- LDF (input) INTEGER

  The leading dimension of the array F. LDF \>= max(1,N).

## FURTHER DETAILS

Based on contributions by\
\
   G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain\
   X. Sun, Computer Science Dept., Duke University, USA\
 Partial column norm updating strategy modified by\
\
   Z. Drmac and Z. Bujanovic, Dept. of Mathematics,\
\
   University of Zagreb, Croatia.\
\
   June 2006.\
 For more details see LAPACK Working Note 176.\