Mercurial > octave
annotate scripts/linear-algebra/normest.m @ 22323:bac0d6f07a3e
maint: Update copyright notices for 2016.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 17 Aug 2016 01:05:19 -0400 |
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1 ## Copyright (C) 2006-2016 David Bateman and Marco Caliari |
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2 ## Copyright (C) 2009 VZLU Prague |
6212 | 3 ## |
7016 | 4 ## This file is part of Octave. |
6212 | 5 ## |
7016 | 6 ## Octave is free software; you can redistribute it and/or modify it |
7 ## under the terms of the GNU General Public License as published by | |
8 ## the Free Software Foundation; either version 3 of the License, or (at | |
9 ## your option) any later version. | |
10 ## | |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
6212 | 15 ## |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
6212 | 19 |
20 ## -*- texinfo -*- | |
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21 ## @deftypefn {} {@var{n} =} normest (@var{A}) |
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22 ## @deftypefnx {} {@var{n} =} normest (@var{A}, @var{tol}) |
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23 ## @deftypefnx {} {[@var{n}, @var{c}] =} normest (@dots{}) |
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24 ## Estimate the 2-norm of the matrix @var{A} using a power series analysis. |
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25 ## |
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26 ## This is typically used for large matrices, where the cost of calculating |
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27 ## @code{norm (@var{A})} is prohibitive and an approximation to the 2-norm is |
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28 ## acceptable. |
6212 | 29 ## |
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30 ## @var{tol} is the tolerance to which the 2-norm is calculated. By default |
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31 ## @var{tol} is 1e-6. |
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32 ## |
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33 ## The optional output @var{c} returns the number of iterations needed for |
6212 | 34 ## @code{normest} to converge. |
35 ## @end deftypefn | |
36 | |
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37 function [n, c] = normest (A, tol = 1e-6) |
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38 |
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39 if (nargin != 1 && nargin != 2) |
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40 print_usage (); |
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41 endif |
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42 |
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43 if (! (isnumeric (A) && ndims (A) == 2)) |
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44 error ("normest: A must be a numeric 2-D matrix"); |
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45 endif |
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46 |
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47 if (! (isscalar (tol) && isreal (tol))) |
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48 error ("normest: TOL must be a real scalar"); |
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49 endif |
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50 |
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51 if (! isfloat (A)) |
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52 A = double (A); |
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53 endif |
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54 |
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55 tol = max (tol, eps (class (A))); |
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56 ## Set random number generator to depend on target matrix |
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57 v = rand ("state"); |
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58 rand ("state", full (trace (A))); |
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59 ncols = columns (A); |
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60 ## Randomize y to avoid bad guesses for important matrices. |
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61 y = rand (ncols, 1); |
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63 n = 0; |
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64 do |
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65 n0 = n; |
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66 x = A * y; |
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67 normx = norm (x); |
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68 if (normx == 0) |
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69 x = rand (ncols, 1); |
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70 else |
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71 x /= normx; |
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72 endif |
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73 y = A' * x; |
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74 n = norm (y); |
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75 c += 1; |
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76 until (abs (n - n0) <= tol * n) |
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77 |
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78 rand ("state", v); # restore state of random number generator |
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79 |
6212 | 80 endfunction |
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81 |
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82 |
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83 %!test |
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84 %! A = toeplitz ([-2,1,0,0]); |
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85 %! assert (normest (A), norm (A), 1e-6); |
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86 |
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87 %!test |
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88 %! A = rand (10); |
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89 %! assert (normest (A), norm (A), 1e-6); |
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90 |
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91 ## Test input validation |
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92 %!error normest () |
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93 %!error normest (1, 2, 3) |
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94 %!error normest ([true true]) |
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95 %!error normest (ones (3,3,3)) |
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96 %!error normest (1, [1, 2]) |
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97 %!error normest (1, 1+1i) |
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98 |