1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
.TH DLARRB l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
DLARRB - the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,
.SH SYNOPSIS
.TP 19
SUBROUTINE DLARRB(
N, D, L, LD, LLD, IFIRST, ILAST, SIGMA, RELTOL,
W, WGAP, WERR, WORK, IWORK, INFO )
.TP 19
.ti +4
INTEGER
IFIRST, ILAST, INFO, N
.TP 19
.ti +4
DOUBLE
PRECISION RELTOL, SIGMA
.TP 19
.ti +4
INTEGER
IWORK( * )
.TP 19
.ti +4
DOUBLE
PRECISION D( * ), L( * ), LD( * ), LLD( * ), W( * ),
WERR( * ), WGAP( * ), WORK( * )
.SH PURPOSE
Given the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T, W( IFIRST ) thru' W( ILAST ), to more accuracy. Intervals
[left, right] are maintained by storing their mid-points and
semi-widths in the arrays W and WERR respectively.
.br
.SH ARGUMENTS
.TP 8
N (input) INTEGER
The order of the matrix.
.TP 8
D (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D.
.TP 8
L (input) DOUBLE PRECISION array, dimension (N-1)
The n-1 subdiagonal elements of the unit bidiagonal matrix L.
.TP 8
LD (input) DOUBLE PRECISION array, dimension (N-1)
The n-1 elements L(i)*D(i).
.TP 8
LLD (input) DOUBLE PRECISION array, dimension (N-1)
The n-1 elements L(i)*L(i)*D(i).
.TP 8
IFIRST (input) INTEGER
The index of the first eigenvalue in the cluster.
.TP 8
ILAST (input) INTEGER
The index of the last eigenvalue in the cluster.
.TP 8
SIGMA (input) DOUBLE PRECISION
The shift used to form L D L^T (see DLARRF).
.TP 8
RELTOL (input) DOUBLE PRECISION
The relative tolerance.
.TP 8
W (input/output) DOUBLE PRECISION array, dimension (N)
On input, W( IFIRST ) thru' W( ILAST ) are estimates of the
corresponding eigenvalues of L D L^T.
On output, these estimates are ``refined''.
.TP 8
WGAP (input/output) DOUBLE PRECISION array, dimension (N)
The gaps between the eigenvalues of L D L^T. Very small
gaps are changed on output.
.TP 8
WERR (input/output) DOUBLE PRECISION array, dimension (N)
On input, WERR( IFIRST ) thru' WERR( ILAST ) are the errors
in the estimates W( IFIRST ) thru' W( ILAST ).
On output, these are the ``refined'' errors.
.TP 8
WORK (input) DOUBLE PRECISION array, dimension (???)
Workspace.
.TP 8
IWORK (input) INTEGER array, dimension (2*N)
Workspace.
.TP 8
INFO (output) INTEGER
Error flag.
.SH FURTHER DETAILS
Based on contributions by
.br
Inderjit Dhillon, IBM Almaden, USA
.br
Osni Marques, LBNL/NERSC, USA
.br
|
