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author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Mon, 27 May 2024 15:54:38 +0200 |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2006-2024 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
6212 | 7 ## |
7016 | 8 ## This file is part of Octave. |
6212 | 9 ## |
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10 ## Octave is free software: you can redistribute it and/or modify it |
7016 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
7016 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
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20 ## You should have received a copy of the GNU General Public License | |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
6212 | 25 |
26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {@var{nest} =} normest (@var{A}) |
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28 ## @deftypefnx {} {@var{nest} =} normest (@var{A}, @var{tol}) |
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29 ## @deftypefnx {} {[@var{nest}, @var{iter}] =} normest (@dots{}) |
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30 ## Estimate the 2-norm of the matrix @var{A} using a power series analysis. |
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31 ## |
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32 ## This is typically used for large matrices, where the cost of calculating |
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33 ## @code{norm (@var{A})} is prohibitive and an approximation to the 2-norm is |
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34 ## acceptable. |
6212 | 35 ## |
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36 ## @var{tol} is the tolerance to which the 2-norm is calculated. By default |
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37 ## @var{tol} is 1e-6. |
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38 ## |
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39 ## The optional output @var{iter} returns the number of iterations that were |
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40 ## required for @code{normest} to converge. |
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41 ## @seealso{normest1, norm, cond, condest} |
6212 | 42 ## @end deftypefn |
43 | |
22830 | 44 function [nest, iter] = normest (A, tol = 1e-6) |
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45 |
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46 if (nargin < 1) |
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47 print_usage (); |
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48 endif |
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49 |
22830 | 50 if (! isnumeric (A) || ndims (A) != 2) |
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51 error ("normest: A must be a numeric 2-D matrix"); |
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52 endif |
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53 |
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54 if (! (isscalar (tol) && isreal (tol))) |
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55 error ("normest: TOL must be a real scalar"); |
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56 endif |
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57 |
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58 if (! isfloat (A)) |
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59 A = double (A); |
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60 endif |
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61 |
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62 tol = max (tol, eps (class (A))); |
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63 ## Set random number generator to depend on target matrix |
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64 v = rand ("state"); |
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65 rand ("state", full (trace (A))); |
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66 ncols = columns (A); |
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67 ## Randomize y to avoid bad guesses for important matrices. |
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68 y = rand (ncols, 1); |
22830 | 69 iter = 0; |
70 nest = 0; | |
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71 do |
22830 | 72 n0 = nest; |
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73 x = A * y; |
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74 normx = norm (x); |
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75 if (normx == 0) |
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76 x = rand (ncols, 1); |
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77 else |
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78 x /= normx; |
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79 endif |
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80 y = A' * x; |
22830 | 81 nest = norm (y); |
82 iter += 1; | |
83 until (abs (nest - n0) <= tol * nest) | |
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84 |
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85 rand ("state", v); # restore state of random number generator |
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86 |
6212 | 87 endfunction |
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88 |
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89 |
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90 %!test |
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91 %! A = toeplitz ([-2,1,0,0]); |
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92 %! assert (normest (A), norm (A), 1e-6); |
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93 |
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94 %!test |
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95 %! A = rand (10); |
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96 %! assert (normest (A), norm (A), 1e-6); |
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97 |
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98 ## Test input validation |
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99 %!error <Invalid call> normest () |
22830 | 100 %!error <A must be a numeric .* matrix> normest ([true true]) |
101 %!error <A must be .* 2-D matrix> normest (ones (3,3,3)) | |
102 %!error <TOL must be a real scalar> normest (1, [1, 2]) | |
103 %!error <TOL must be a real scalar> normest (1, 1+1i) |