annotate scripts/linear-algebra/issymmetric.m @ 33632:fed0dc6fd44c default tip @

remove unused variable from libgui/module.mk * libgui/module.mk: remove empty variable OCTAVE_GUI_EDITOR_MOC
author Torsten Lilge <ttl-octave@mailbox.org>
date Mon, 27 May 2024 19:42:05 +0200
parents 0b8f3470d1fb
children
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1996-2024 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/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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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.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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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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19 ##
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20 ## You should have received a copy of the GNU General Public License
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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 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{tf} =} issymmetric (@var{A})
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28 ## @deftypefnx {} {@var{tf} =} issymmetric (@var{A}, @var{tol})
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29 ## @deftypefnx {} {@var{tf} =} issymmetric (@var{A}, @qcode{"skew"})
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30 ## @deftypefnx {} {@var{tf} =} issymmetric (@var{A}, @qcode{"skew"}, @var{tol})
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31 ## Return true if @var{A} is a symmetric or skew-symmetric numeric matrix
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32 ## within the tolerance specified by @var{tol}.
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33 ##
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34 ## The default tolerance is zero (uses faster code).
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35 ##
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36 ## The type of symmetry to check may be specified with the additional input
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37 ## @qcode{"nonskew"} (default) for regular symmetry or @qcode{"skew"} for
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38 ## skew-symmetry.
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39 ##
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40 ## Background: A matrix is symmetric if the transpose of the matrix is equal
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41 ## to the original matrix: @w{@tcode{@var{A} == @var{A}.'}}. If a tolerance
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42 ## is given then symmetry is determined by
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43 ## @code{norm (@var{A} - @var{A}.', Inf) / norm (@var{A}, Inf) < @var{tol}}.
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44 ##
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45 ## A matrix is skew-symmetric if the transpose of the matrix is equal to the
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46 ## negative of the original matrix: @w{@tcode{@var{A} == -@var{A}.'}}. If a
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47 ## tolerance is given then skew-symmetry is determined by
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48 ## @code{norm (@var{A} + @var{A}.', Inf) / norm (@var{A}, Inf) < @var{tol}}.
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49 ## @seealso{ishermitian, isdefinite}
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50 ## @end deftypefn
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51
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52 function tf = issymmetric (A, skewopt = "nonskew", tol = 0)
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53
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54 if (nargin < 1)
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55 print_usage ();
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56 endif
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57
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58 if (nargin == 2)
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59 ## Decode whether second argument is skewopt or tol
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60 if (isnumeric (skewopt))
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61 tol = skewopt;
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62 skewopt = "nonskew";
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63 elseif (! ischar (skewopt))
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64 error ("issymmetric: second argument must be a non-negative scalar TOL, or one of the strings: 'skew' / 'nonskew'");
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65 endif
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66 endif
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67
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68 ## Validate inputs
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69 if (! (isnumeric (A) || islogical (A) || ischar (A)))
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70 error ("issymmetric: A must be a numeric, logical, or character matrix");
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71 endif
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72
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73 if (! (strcmp (skewopt, "skew") || strcmp (skewopt, "nonskew")))
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74 error ("issymmetric: SKEWOPT must be 'skew' or 'nonskew'");
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75 endif
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76
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77 if (! (isnumeric (tol) && isscalar (tol) && tol >= 0))
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78 error ("issymmetric: TOL must be a scalar >= 0");
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79 endif
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80
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81 if (! issquare (A))
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82 tf = false;
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83 return;
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84 endif
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85
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86 ## Calculate symmetry
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87 if (strcmp (skewopt, "nonskew"))
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88 if (tol == 0)
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89 ## check for exact symmetry
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90 tf = full (! any ((A != A.')(:)));
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91 else
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92 if (! isnumeric (A))
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93 ## Hack to allow norm to work. Choose single to minimize memory.
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94 A = single (A);
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95 endif
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96 norm_x = norm (A, Inf);
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97 tf = norm_x == 0 || norm (A - A.', Inf) / norm_x <= tol;
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98 endif
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99 else
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100 ## skew symmetry
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101 if (tol == 0)
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102 tf = full (! any ((A != -A.')(:)));
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103 else
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104 if (! isnumeric (A))
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105 ## Hack to allow norm to work. Choose single to minimize memory.
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106 A = single (A);
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107 endif
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108 norm_x = norm (A, Inf);
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109 tf = norm_x == 0 || norm (A + A.', Inf) / norm_x <= tol;
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110 endif
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111 endif
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112
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113 endfunction
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114
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115
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116 %!assert (issymmetric (1))
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117 %!assert (! issymmetric ([1, 2]))
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118 %!assert (issymmetric ([]))
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119 %!assert (issymmetric ([1, 2; 2, 1]))
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120 %!assert (issymmetric ([1, 2.1; 2, 1.1], 0.2))
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121 %!assert (issymmetric ([1, 2i; 2i, 1]))
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122 %!assert (issymmetric (speye (100)), true) # Return full logical value.
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123 %!assert (! issymmetric ([0, 2; -2, 0], "nonskew"))
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124 %!assert (issymmetric ([0, 2; -2, 0], "skew"))
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125 %!assert (! issymmetric ([0, 2; -2, eps], "skew"))
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126 %!assert (issymmetric ([0, 2; -2, eps], "skew", eps))
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127 %!assert (issymmetric (logical (eye (2))))
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128 %!assert (! issymmetric (logical ([1 1; 0 1])))
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129 %!assert (issymmetric (logical ([1 1; 0 1]), 0.5))
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130 %!assert (! issymmetric ("test"))
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131 %!assert (issymmetric ("t"))
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132 %!assert (issymmetric (["te"; "et"]))
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f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
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133
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134 ## Test input validation
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135 %!error <Invalid call> issymmetric ()
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136 %!error <second argument must be> issymmetric (1, {"skew"})
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137 %!error <A must be a numeric,.* matrix> issymmetric ({1})
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138 %!error <SKEWOPT must be 'skew' or 'nonskew'> issymmetric (1, "foobar")
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139 %!error <TOL must be a scalar .= 0> issymmetric (1, "skew", {1})
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140 %!error <TOL must be a scalar .= 0> issymmetric (1, "skew", [1 1])
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141 %!error <TOL must be a scalar .= 0> issymmetric (1, -1)