1CLAQPS(1)           LAPACK auxiliary routine (version 3.2)           CLAQPS(1)
2
3
4

NAME

6       CLAQPS  - computes a step of QR factorization with column pivoting of a
7       complex M-by-N matrix A by using Blas-3
8

SYNOPSIS

10       SUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU,  VN1,  VN2,
11                          AUXV, F, LDF )
12
13           INTEGER        KB, LDA, LDF, M, N, NB, OFFSET
14
15           INTEGER        JPVT( * )
16
17           REAL           VN1( * ), VN2( * )
18
19           COMPLEX        A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
20

PURPOSE

22       CLAQPS  computes  a  step of QR factorization with column pivoting of a
23       complex M-by-N matrix A by using Blas-3.  It tries to factorize NB col‐
24       umns  from  A  starting  from  the row OFFSET+1, and updates all of the
25       matrix with Blas-3 xGEMM.
26       In some cases, due to catastrophic cancellations, it  cannot  factorize
27       NB columns.  Hence, the actual number of factorized columns is returned
28       in KB.
29       Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
30

ARGUMENTS

32       M       (input) INTEGER
33               The number of rows of the matrix A. M >= 0.
34
35       N       (input) INTEGER
36               The number of columns of the matrix A. N >= 0
37
38       OFFSET  (input) INTEGER
39               The number of rows of A that have been factorized  in  previous
40               steps.
41
42       NB      (input) INTEGER
43               The number of columns to factorize.
44
45       KB      (output) INTEGER
46               The number of columns actually factorized.
47
48       A       (input/output) COMPLEX array, dimension (LDA,N)
49               On   entry,  the  M-by-N  matrix  A.   On  exit,  block  A(OFF‐
50               SET+1:M,1:KB) is the triangular
51               factor obtained and block A(1:OFFSET,1:N) has been  accordingly
52               pivoted,  but  no  factorized.   The  rest of the matrix, block
53               A(OFFSET+1:M,KB+1:N) has been updated.
54
55       LDA     (input) INTEGER
56               The leading dimension of the array A. LDA >= max(1,M).
57
58       JPVT    (input/output) INTEGER array, dimension (N)
59               JPVT(I) = K <==> Column K of the full matrix A  has  been  per‐
60               muted into position I in AP.
61
62       TAU     (output) COMPLEX array, dimension (KB)
63               The scalar factors of the elementary reflectors.
64
65       VN1     (input/output) REAL array, dimension (N)
66               The vector with the partial column norms.
67
68       VN2     (input/output) REAL array, dimension (N)
69               The vector with the exact column norms.
70
71       AUXV    (input/output) COMPLEX array, dimension (NB)
72               Auxiliar vector.
73
74       F       (input/output) COMPLEX array, dimension (LDF,NB)
75               Matrix F' = L*Y'*A.
76
77       LDF     (input) INTEGER
78               The leading dimension of the array F. LDF >= max(1,N).
79

FURTHER DETAILS

81       Based on contributions by
82         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
83         X. Sun, Computer Science Dept., Duke University, USA
84       Partial column norm updating strategy modified by
85         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
86         University of Zagreb, Croatia.
87         June 2006.
88       For more details see LAPACK Working Note 176.
89
90
91
92 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       CLAQPS(1)
Impressum