1DLAQP2(1)           LAPACK auxiliary routine (version 3.1)           DLAQP2(1)
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NAME

6       DLAQP2  -  a  QR factorization with column pivoting of the block A(OFF‐
7       SET+1:M,1:N)
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SYNOPSIS

10       SUBROUTINE DLAQP2( 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           DOUBLE         PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ),
17                          WORK( * )
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PURPOSE

20       DLAQP2  computes  a  QR factorization with column pivoting of the block
21       A(OFFSET+1:M,1:N).  The block A(1:OFFSET,1:N) is  accordingly  pivoted,
22       but not factorized.
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ARGUMENTS

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

65       Based on contributions by
66         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
67         X. Sun, Computer Science Dept., Duke University, USA
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69       Partial column norm updating strategy modified by
70         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
71         University of Zagreb, Croatia.
72         June 2006.
73       For more details see LAPACK Working Note 176.
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77 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLAQP2(1)