zlaqps.f(3) LAPACK zlaqps.f(3)
NAME
zlaqps.f -
SYNOPSIS
Functions/Subroutines
subroutine zlaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
ZLAQPS
Function/Subroutine Documentation
subroutine zlaqps (integerM, integerN, integerOFFSET, integerNB, integerKB, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( *
)JPVT, complex*16, dimension( * )TAU, double precision, dimension( * )VN1, double precision, dimension( * )VN2, complex*16, dimension( *
)AUXV, complex*16, dimension( ldf, * )F, integerLDF)
ZLAQPS
Purpose:
ZLAQPS computes a step of QR factorization with column pivoting
of a complex 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (NB)
Auxiliar vector.
F
F is COMPLEX*16 array, dimension (LDF,NB)
Matrix F**H = L * Y**H * 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:
November 2011
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 zlaqps.f.
Author
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Version 3.4.1 Sun May 26 2013 zlaqps.f(3)