1ZLAQP2(1)           LAPACK auxiliary routine (version 3.2)           ZLAQP2(1)
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NAME

6       ZLAQP2  - computes a QR factorization with column pivoting of the block
7       A(OFFSET+1:M,1:N)
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SYNOPSIS

10       SUBROUTINE ZLAQP2( 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 VN1( * ), VN2( * )
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18           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

21       ZLAQP2 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

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) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 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
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.e2m)ber 2008                       ZLAQP2(1)