1SLAQP2(1)           LAPACK auxiliary routine (version 3.1)           SLAQP2(1)
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NAME

6       SLAQP2  -  a  QR factorization with column pivoting of the block A(OFF‐
7       SET+1:M,1:N)
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SYNOPSIS

10       SUBROUTINE SLAQP2( 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           A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), WORK( * )
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PURPOSE

19       SLAQP2 computes a QR factorization with column pivoting  of  the  block
20       A(OFFSET+1:M,1:N).   The  block A(1:OFFSET,1:N) is accordingly pivoted,
21       but not factorized.
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ARGUMENTS

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

64       Based on contributions by
65         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
66         X. Sun, Computer Science Dept., Duke University, USA
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68       Partial column norm updating strategy modified by
69         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
70         University of Zagreb, Croatia.
71         June 2006.
72       For more details see LAPACK Working Note 176.
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76 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLAQP2(1)