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zlaqps.f(3) LAPACK zlaqps.f(3)

zlaqps.f -


subroutine zlaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
 
ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
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:
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 zlaqps.f.

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