.TH ZLAQPS 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME ZLAQPS - a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3 .SH SYNOPSIS .TP 19 SUBROUTINE ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF ) .TP 19 .ti +4 INTEGER KB, LDA, LDF, M, N, NB, OFFSET .TP 19 .ti +4 INTEGER JPVT( * ) .TP 19 .ti +4 DOUBLE PRECISION VN1( * ), VN2( * ) .TP 19 .ti +4 COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ) .SH 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. .br In some cases, due to catastrophic cancellations, it cannot factorize NB columns. Hence, the actual number of factorized columns is returned in KB. .br Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. .SH ARGUMENTS .TP 8 M (input) INTEGER The number of rows of the matrix A. M >= 0. .TP 8 N (input) INTEGER The number of columns of the matrix A. N >= 0 .TP 8 OFFSET (input) INTEGER The number of rows of A that have been factorized in previous steps. .TP 8 NB (input) INTEGER The number of columns to factorize. .TP 8 KB (output) INTEGER The number of columns actually factorized. .TP 8 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 .br 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. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). .TP 8 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. .TP 8 TAU (output) COMPLEX*16 array, dimension (KB) The scalar factors of the elementary reflectors. .TP 8 VN1 (input/output) DOUBLE PRECISION array, dimension (N) The vector with the partial column norms. .TP 8 VN2 (input/output) DOUBLE PRECISION array, dimension (N) The vector with the exact column norms. .TP 8 AUXV (input/output) COMPLEX*16 array, dimension (NB) Auxiliar vector. .TP 8 F (input/output) COMPLEX*16 array, dimension (LDF,NB) Matrix F\(aq = L*Y\(aq*A. .TP 8 LDF (input) INTEGER The leading dimension of the array F. LDF >= max(1,N). .SH FURTHER DETAILS Based on contributions by .br G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA .br