1CLAQP2(1)           LAPACK auxiliary routine (version 3.1)           CLAQP2(1)
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NAME

6       CLAQP2  -  a  QR factorization with column pivoting of the block A(OFF‐
7       SET+1:M,1:N)
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SYNOPSIS

10       SUBROUTINE CLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )
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12           INTEGER        LDA, M, N, OFFSET
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14           INTEGER        JPVT( * )
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16           REAL           VN1( * ), VN2( * )
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18           COMPLEX        A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

21       CLAQP2 computes a QR factorization with column pivoting  of  the  block
22       A(OFFSET+1:M,1:N).   The  block A(1:OFFSET,1:N) is accordingly pivoted,
23       but not factorized.
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ARGUMENTS

27       M       (input) INTEGER
28               The number of rows of the matrix A. M >= 0.
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30       N       (input) INTEGER
31               The number of columns of the matrix A. N >= 0.
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33       OFFSET  (input) INTEGER
34               The number of rows of the matrix A that must be pivoted but  no
35               factorized. OFFSET >= 0.
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37       A       (input/output) COMPLEX array, dimension (LDA,N)
38               On  entry, the M-by-N matrix A.  On exit, the upper triangle of
39               block A(OFFSET+1:M,1:N) is the triangular factor obtained;  the
40               elements   in   block  A(OFFSET+1:M,1:N)  below  the  diagonal,
41               together with the array TAU, represent the orthogonal matrix  Q
42               as  a  product  of elementary reflectors. Block A(1:OFFSET,1:N)
43               has been accordingly pivoted, but no factorized.
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45       LDA     (input) INTEGER
46               The leading dimension of the array A. LDA >= max(1,M).
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48       JPVT    (input/output) INTEGER array, dimension (N)
49               On entry, if JPVT(i) .ne. 0, the i-th column of A  is  permuted
50               to  the front of A*P (a leading column); if JPVT(i) = 0, the i-
51               th column of A is a free column.  On exit, if JPVT(i) = k, then
52               the i-th column of A*P was the k-th column of A.
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54       TAU     (output) COMPLEX array, dimension (min(M,N))
55               The scalar factors of the elementary reflectors.
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57       VN1     (input/output) REAL array, dimension (N)
58               The vector with the partial column norms.
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60       VN2     (input/output) REAL array, dimension (N)
61               The vector with the exact column norms.
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63       WORK    (workspace) COMPLEX array, dimension (N)
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FURTHER DETAILS

66       Based on contributions by
67         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
68         X. Sun, Computer Science Dept., Duke University, USA
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70       Partial column norm updating strategy modified by
71         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
72         University of Zagreb, Croatia.
73         June 2006.
74       For more details see LAPACK Working Note 176.
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78 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLAQP2(1)
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