zlaqps(l) [redhat man page]
ZLAQPS(l) ) ZLAQPS(l) NAME
ZLAQPS - compute a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3 SYNOPSIS
SUBROUTINE ZLAQPS( 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 VN1( * ), VN2( * ) COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ) 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 col- umns 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) 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(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) COMPLEX*16 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) COMPLEX*16 array, dimension (NB) Auxiliar vector. F (input/output) COMPLEX*16 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 ZLAQPS(l)
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claqps.f(3) LAPACK claqps.f(3) NAME
claqps.f - SYNOPSIS
Functions/Subroutines subroutine claqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF) CLAQPS Function/Subroutine Documentation subroutine claqps (integerM, integerN, integerOFFSET, integerNB, integerKB, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, complex, dimension( * )TAU, real, dimension( * )VN1, real, dimension( * )VN2, complex, dimension( * )AUXV, complex, dimension( ldf, * )F, integerLDF) CLAQPS 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 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 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 178 of file claqps.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 claqps.f(3)