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