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## man page of LAPACK-3

### LAPACK-3: computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

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LAPACK-3 - computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)## SYNOPSIS

SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK ) INTEGER LDA, M, N, OFFSET INTEGER JPVT( * ) DOUBLE PRECISION VN1( * ), VN2( * ) COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )## PURPOSE

ZLAQP2 computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N). The 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT (input/output) INTEGER array, dimension (N) On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A. TAU (output) COMPLEX*16 array, dimension (min(M,N)) 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. WORK (workspace) COMPLEX*16 array, dimension (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 Partial column norm updating strategy modified by Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia. June 2010 For more details see LAPACK Working Note 176. LAPACK auxiliary routine (versionMarch22011 LAPACK-3(3)

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