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annotate scripts/linear-algebra/vecnorm.m @ 26376:00f796120a6d stable

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maint: Update copyright dates in all source files.
author John W. Eaton <jwe@octave.org>
date Wed, 02 Jan 2019 16:32:43 -0500
parents 6652d3823428
children b442ec6dda5c
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
26376
00f796120a6d maint: Update copyright dates in all source files.
John W. Eaton <jwe@octave.org>
parents: 25054
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1 ## Copyright (C) 2017-2019 Marco Caliari
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2 ##
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3 ## This file is part of Octave.
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4 ##
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Rik <rik@octave.org>
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5 ## Octave is free software: you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation, either version 3 of the License, or
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8 ## (at your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 ## GNU General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <https://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {@var{n} =} vecnorm (@var{A})
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21 ## @deftypefnx {} {@var{n} =} vecnorm (@var{A}, @var{p})
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22 ## @deftypefnx {} {@var{n} =} vecnorm (@var{A}, @var{p}, @var{dim})
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23 ## Return the p-norm of the elements of @var{A} along dimension @var{dim}.
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24 ##
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25 ## The p-norm of a vector is defined as
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26 ##
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27 ## @tex
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28 ## $$ {\Vert A \Vert}_p = \left[ \sum_{i=1}^N {| A_i |}^p \right] ^ {1/p} $$
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29 ## @end tex
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30 ## @ifnottex
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31 ##
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32 ## @example
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33 ## @var{p-norm} (@var{A}, @var{p}) = sum (abs (@var{A}) .^ @var{p})) ^ (1/@var{p})
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34 ## @end example
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35 ##
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36 ## @end ifnottex
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37 ## If @var{p} is omitted it defaults to 2 (Euclidean norm). @var{p} can be
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38 ## @code{Inf} (absolute value of largest element).
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39 ##
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40 ## If @var{dim} is omitted the first non-singleton dimension is used.
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41 ##
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42 ## @seealso{norm}
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43 ## @end deftypefn
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44
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45 function n = vecnorm (A, p = 2, dim)
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46
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47 if (nargin < 1 || nargin > 3)
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48 print_usage ();
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49 endif
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50
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51 if (! isscalar (p) || ! isreal (p) || (p <= 0))
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52 error ("vecnorm: P must be positive real scalar or Inf");
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53 endif
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54
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55 sz = size (A);
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56 if (nargin <= 2)
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57 ## Find the first non-singleton dimension.
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58 (dim = find (sz > 1, 1)) || (dim = 1);
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59 elseif (! (isscalar (dim) && dim == fix (dim) && dim > 0))
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60 error ("vecnorm: DIM must be an integer and a valid dimension");
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61 endif
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62
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63 ## Calculate norm using the value of p to accelerate special cases
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64 switch (p)
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65 case {1}
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66 n = sum (abs (A), dim);
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67
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68 case {2}
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69 n = sqrt (sumsq (A, dim));
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70
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71 case {Inf}
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72 n = max (abs (A), [], dim);
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73
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74 otherwise
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75 if (rem (p,2) == 0)
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76 n = (sum ((real (A).^2 + imag (A).^2) .^ (p/2), dim)) .^ (1 / p);
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77 else
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78 n = (sum (abs (A) .^ p, dim)) .^ (1 / p);
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79 endif
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80
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81 endswitch
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82
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83 endfunction
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84
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85
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86 %!test
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87 %! A = [0 1 2; 3 4 5];
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88 %! c = vecnorm (A);
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89 %! r = vecnorm (A, 2, 2);
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90 %! i = vecnorm (A, Inf);
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91 %! assert (c, [3.0000, 4.1231, 5.3852], 1e-4);
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92 %! assert (r, [2.2361; 7.0711], 1e-4);
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93 %! assert (i, [3, 4, 5]);
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94 %!test
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95 %! A = [1, 2];
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96 %! assert (vecnorm (A), 2.2361, 1e-4);
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97 %!test
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98 %! A(:, :, 1) = [1, 2];
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99 %! A(:, :, 2) = [3, 4];
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100 %! A(:, :, 3) = [5, 6];
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101 %! ret(:, :, 1) = 2.2361;
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102 %! ret(:, :, 2) = 5;
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103 %! ret(:, :, 3) = 7.8102;
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104 %! assert (vecnorm (A), ret, 1e-4);
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105
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106 ## Test input validation
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107 %!error vecnorm ()
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108 %!error vecnorm (1,2,3,4)
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109 %!error <P must be positive real scalar> vecnorm (1, [1 2])
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110 %!error <P must be positive real scalar> vecnorm (1, i)
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111 %!error <P must be positive real scalar> vecnorm (1, -1)
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112 %!error <P must be positive real scalar> vecnorm (1, 0)
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113 %!error <DIM must be an integer and a valid dimension> vecnorm (1, 2, [1 2])
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114 %!error <DIM must be an integer and a valid dimension> vecnorm (1, 2, [1 2])
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115 %!error <DIM must be an integer and a valid dimension> vecnorm (1, 2, 0)
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116 %!error <DIM must be an integer and a valid dimension> vecnorm (1, 2, -1)