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doc: Update documentation for norm, normest, normest1, condest. * data.cc (Fnorm): Add normest and normest1 to @seealso list. * condest.m: Delete extra space after colon. * normest.m: Rename output 'n' to 'nest' for norm estimate. Rename output 'c' to 'iter'. Add @seealso block. * normest1.m: Rewrite docstring.
author Rik <rik@octave.org>
date Thu, 24 Nov 2016 08:09:54 -0800
parents bac0d6f07a3e
children 41a751b19fd2 e9a0469dedd9
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1 ## Copyright (C) 2006-2016 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 {} {@var{nest} =} normest (@var{A})
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22 ## @deftypefnx {} {@var{nest} =} normest (@var{A}, @var{tol})
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23 ## @deftypefnx {} {[@var{nest}, @var{iter}] =} 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.
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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{iter} returns the number of iterations that were
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34 ## required for @code{normest} to converge.
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35 ## @seealso{normest1, norm, cond, condest}
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36 ## @end deftypefn
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37
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38 function [n, c] = normest (A, tol = 1e-6)
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39
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40 if (nargin != 1 && nargin != 2)
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41 print_usage ();
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42 endif
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43
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44 if (! (isnumeric (A) && ndims (A) == 2))
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45 error ("normest: A must be a numeric 2-D matrix");
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46 endif
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47
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48 if (! (isscalar (tol) && isreal (tol)))
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49 error ("normest: TOL must be a real scalar");
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50 endif
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51
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52 if (! isfloat (A))
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53 A = double (A);
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54 endif
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55
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56 tol = max (tol, eps (class (A)));
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57 ## Set random number generator to depend on target matrix
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58 v = rand ("state");
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59 rand ("state", full (trace (A)));
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60 ncols = columns (A);
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61 ## Randomize y to avoid bad guesses for important matrices.
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62 y = rand (ncols, 1);
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63 c = 0;
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64 n = 0;
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65 do
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66 n0 = n;
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67 x = A * y;
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68 normx = norm (x);
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69 if (normx == 0)
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70 x = rand (ncols, 1);
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71 else
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72 x /= normx;
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73 endif
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74 y = A' * x;
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75 n = norm (y);
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76 c += 1;
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77 until (abs (n - n0) <= tol * n)
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78
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79 rand ("state", v); # restore state of random number generator
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80
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81 endfunction
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82
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83
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84 %!test
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85 %! A = toeplitz ([-2,1,0,0]);
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86 %! assert (normest (A), norm (A), 1e-6);
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87
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88 %!test
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89 %! A = rand (10);
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90 %! assert (normest (A), norm (A), 1e-6);
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91
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92 ## Test input validation
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93 %!error normest ()
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94 %!error normest (1, 2, 3)
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95 %!error normest ([true true])
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96 %!error normest (ones (3,3,3))
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97 %!error normest (1, [1, 2])
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98 %!error normest (1, 1+1i)
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99