1DLAQP2(1)           LAPACK auxiliary routine (version 3.2)           DLAQP2(1)
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NAME

6       DLAQP2  - computes a QR factorization with column pivoting of the block
7       A(OFFSET+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

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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N))
53               The scalar factors of the elementary reflectors.
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55       VN1     (input/output) DOUBLE PRECISION array, dimension (N)
56               The vector with the partial column norms.
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58       VN2     (input/output) DOUBLE PRECISION array, dimension (N)
59               The vector with the exact column norms.
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61       WORK    (workspace) DOUBLE PRECISION 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
67       Partial column norm updating strategy modified by
68         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
69         University of Zagreb, Croatia.
70         June 2006.
71       For more details see LAPACK Working Note 176.
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75 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLAQP2(1)