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CLAQPS(l)) CLAQPS(l)NAMECLAQPS - compute a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3SYNOPSISSUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF ) INTEGER KB, LDA, LDF, M, N, NB, OFFSET INTEGER JPVT( * ) REAL VN1( * ), VN2( * ) COMPLEX A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )PURPOSECLAQPS 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.ARGUMENTSM (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 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, block A(OFFSET+1:M,1:KB) is the triangu- lar 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 (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 array, dimension (KB) The scalar factors of the elementary reflectors. VN1 (input/output) REAL array, dimension (N) The vector with the partial column norms. VN2 (input/output) REAL array, dimension (N) The vector with the exact column norms. AUXV (input/output) COMPLEX array, dimension (NB) Auxiliar vector. F (input/output) COMPLEX array, dimension (LDF,NB) Matrix F' = L*Y'*A. LDF (input) INTEGER The leading dimension of the array F. LDF >= max(1,N).FURTHER DETAILSBased on contributions by G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USALAPACK version 3.015 June 2000 CLAQPS(l)

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