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comparison scripts/sparse/normest.m @ 6212:cc34c0be7b00

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[project @ 2006-12-08 11:17:12 by dbateman]
author dbateman
date Fri, 08 Dec 2006 11:18:15 +0000
parents
children 0a259ae4375e
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6211:778fd090e505 6212:cc34c0be7b00
1 ## Copyright (C) 2006 David Bateman
2 ## Copyright (C) 2006 Marco Caliari
3 ##
4 ## This program is free software; you can redistribute it and/or modify
5 ## it under the terms of the GNU General Public License as published by
6 ## the Free Software Foundation; either version 2 of the License, or
7 ## (at your option) any later version.
8 ##
9 ## This program is distributed in the hope that it will be useful,
10 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
11 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 ## GNU General Public License for more details.
13 ##
14 ## You should have received a copy of the GNU General Public License
15 ## along with this program; if not, write to the Free Software
16 ## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
17 ## 02110-1301 USA
18
19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {[@var{n}, @var{c}] =} normest (@var{a}, @var{tol})
21 ##
22 ## Estimates the 2-norm of the matrix @var{a} using a power series
23 ## analysis. This is typically used for large matrices, where the cost
24 ## of calculating the @code{norm{@var{a})} is prohibitive and an approximation
25 ## to the 2-norm is acceptable.
26 ##
27 ## @var{tol} is the tolerance to which the 2-norm is calculated. By default
28 ## @var{tol} is 1e-6. @var{c} returns the number of iterations needed for
29 ## @code{normest} to converge.
30 ## @end deftypefn
31
32 function [e1, c] = normest(A, tol)
33 if (nargin < 2)
34 tol = 1e-6;
35 endif
36 if (tol < eps)
37 tol = eps
38 endif
39 if (ndims(A) != 2)
40 error("A must be a matrix");
41 endif
42 maxA = max(max(abs(A)));
43 c = 0;
44 if (maxA == 0)
45 e1 = 0
46 else
47 [m, n] = size(A);
48 B = A / maxA;
49 Bt = B';
50 if (m > n)
51 tmp = B;
52 B = Bt;
53 Bt = tmp;
54 endif
55 e0 = 0;
56 x = randn(min(m,n),1);
57 e1 = norm(x);
58 x = x / e1;
59 e1 = sqrt(e1);
60 if (issparse(A))
61 while (abs(e1 - e0) > tol * e1)
62 e0 = e1;
63 x = B * (Bt * x);
64 e1 = norm(x);
65 x = x / e1;
66 e1 = sqrt(e1);
67 c = c + 1;
68 endwhile
69 else
70 B = B * Bt
71 while (abs(e1 - e0) > tol * e1)
72 e0 = e1;
73 x = B * x;
74 e1 = norm(x);
75 x = x / e1;
76 e1 = sqrt(e1);
77 c = c + 1;
78 endwhile
79 endif
80 e1 = e1 * maxA;
81 endif
82 endfunction