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annotate scripts/linear-algebra/normest.m @ 10687:a8ce6bdecce5

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author Rik <octave@nomad.inbox5.com>
date Tue, 08 Jun 2010 20:22:38 -0700
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1 ## Copyright (C) 2006, 2007, 2008, 2009 David Bateman and Marco Caliari
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2 ## Copyright (C) 2009 VZLU Prague
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {[@var{n}, @var{c}] =} normest (@var{a}, @var{tol})
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22 ## Estimate 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 [e, c] = normest (A, tol = 1e-6)
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33 if (! ismatrix (A) || ndims (A) != 2)
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34 error ("normest: A must be a matrix");
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35 endif
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36 if (! isfloat (A))
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37 A = double (A);
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38 endif
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39 tol = max (tol, eps (class (A)));
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40 c = 0;
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41 x = norm (A, "columns").';
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42 e = norm (x);
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43 if (e > 0)
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44 [m, n] = size (A);
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45 ## Randomize x to avoid bad guesses for important matrices.
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46 ## FIXME: can we do something smarter?
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47 x .*= randn (n, 1);
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48 e = norm (x);
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49 x /= e;
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50 e0 = 0;
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51 while (abs (e - e0) > tol * e)
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52 e0 = e;
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53 y = A*x;
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54 e = norm (y);
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55 if (e == 0)
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56 x = rand (n, 1);
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57 else
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58 x = A'*(y / e);
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59 endif
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60 x /= norm (x);
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61 c += 1;
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62 endwhile
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63 endif
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64 endfunction