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# dlaqps(3) [centos man page]

```dlaqps.f(3)							      LAPACK							       dlaqps.f(3)

NAME
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

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:
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
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dlaqps.f(3)```

## Check Out this Related Man Page

```DLAQPS(l)								 )								 DLAQPS(l)

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

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

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

INTEGER	  JPVT( * )

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

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.

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) 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(OFF-
SET+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) DOUBLE PRECISION array, dimension (KB)
The scalar factors of the elementary reflectors.

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

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

AUXV    (input/output) DOUBLE PRECISION array, dimension (NB)
Auxiliar vector.

F       (input/output) DOUBLE PRECISION 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

LAPACK version 3.0						   15 June 2000 							 DLAQPS(l)```