subroutine claqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
Purpose:
CLAQPS 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 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 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 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 COMPLEX array, dimension (NB) Auxiliar vector.
F
F is COMPLEX 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Contributors:
Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.
References:
Definition at line 180 of file claqps.f.
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