annotate scripts/linear-algebra/issymmetric.m @ 25224:1f1aef87e136

issymmetric.m: Fix calculation of skew matrices (bug in 0f98040552de). * issymmetric.m: Reshape comparison matrix into column vector before using any().
author Rik <rik@octave.org>
date Wed, 11 Apr 2018 21:50:38 -0700
parents 0f98040552de
children a937ffe7dfd9
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1 ## Copyright (C) 1996-2018 John W. Eaton
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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
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9 ## (at 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
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14 ## GNU 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 ## <https://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {} {} issymmetric (@var{A})
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22 ## @deftypefnx {} {} issymmetric (@var{A}, @var{tol})
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23 ## @deftypefnx {} {} issymmetric (@var{A}, @qcode{"skew"})
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24 ## @deftypefnx {} {} issymmetric (@var{A}, @qcode{"skew"}, @var{tol})
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25 ## Return true if @var{A} is a symmetric or skew-symmetric matrix within the
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26 ## tolerance specified by @var{tol}.
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27 ##
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28 ## The default tolerance is zero (uses faster code).
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29 ##
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30 ## The type of symmetry to check may be specified with the additional input
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31 ## @qcode{"nonskew"} (default) for regular symmetry or @qcode{"skew"} for
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32 ## skew-symmetry.
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33 ##
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34 ## Background: A matrix is symmetric if the transpose of the matrix is equal
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35 ## to the original matrix: @w{@acode{@var{A} == @var{A}.'}}. If a tolerance
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36 ## is given then symmetry is determined by
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37 ## @code{norm (@var{A} - @var{A}.', Inf) / norm (@var{A}, Inf) < @var{tol}}.
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38 ##
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39 ## A matrix is skew-symmetric if the transpose of the matrix is equal to the
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40 ## negative of the original matrix: @w{@acode{@var{A} == -@var{A}.'}}. If a
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41 ## tolerance is given then skew-symmetry is determined by
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42 ## @code{norm (@var{A} + @var{A}.', Inf) / norm (@var{A}, Inf) < @var{tol}}.
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43 ## @seealso{ishermitian, isdefinite}
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44 ## @end deftypefn
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45
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46 ## Author: A. S. Hodel <scotte@eng.auburn.edu>
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47 ## Created: August 1993
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48 ## Adapted-By: jwe
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49
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50 function retval = issymmetric (A, skewopt = "nonskew", tol = 0)
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51
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52 if (nargin < 1 || nargin > 3)
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53 print_usage ();
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54 endif
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55
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56 if (nargin == 2)
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57 ## Decode whether second argument is skewopt or tol
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58 if (isnumeric (skewopt))
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59 tol = skewopt;
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60 skewopt = "nonskew";
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61 elseif (! ischar (skewopt))
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62 error ("issymmetric: second argument must be a non-negative scalar TOL, or one of the strings: 'skew' / 'nonskew'");
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63 endif
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64 endif
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65
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66 ## Validate inputs
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67 retval = (isnumeric (A) || islogical (A)) && issquare (A);
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68 if (! retval)
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69 return;
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70 endif
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71
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72 if (! (strcmp (skewopt, "skew") || strcmp (skewopt, "nonskew")))
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73 error ("issymmetric: SKEWOPT must be 'skew' or 'nonskew'");
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74 endif
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75
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76 if (! (isnumeric (tol) && isscalar (tol) && tol >= 0))
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77 error ("issymmetric: TOL must be a scalar >= 0");
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78 endif
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79
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80 ## Calculate symmetry
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81 if (strcmp (skewopt, "nonskew"))
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82 if (tol == 0)
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83 ## check for exact symmetry
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84 retval = ! any ((A != A.')(:));
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85 else
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86 norm_x = norm (A, Inf);
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87 retval = norm_x == 0 || norm (A - A.', Inf) / norm_x <= tol;
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88 endif
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89 else
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90 ## skew symmetry
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91 if (tol == 0)
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92 retval = ! any ((A != -A.')(:));
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93 else
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94 norm_x = norm (A, Inf);
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95 retval = norm_x == 0 || norm (A + A.', Inf) / norm_x <= tol;
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96 endif
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97 endif
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98
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99 endfunction
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100
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101
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102 %!assert (issymmetric (1))
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103 %!assert (! issymmetric ([1, 2]))
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104 %!assert (issymmetric ([]))
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105 %!assert (issymmetric ([1, 2; 2, 1]))
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106 %!assert (issymmetric ([1, 2.1; 2, 1.1], 0.2))
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107 %!assert (issymmetric ([1, 2i; 2i, 1]))
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108 %!assert (issymmetric (speye (100)))
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109 %!assert (issymmetric (logical (eye (2))))
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110 %!assert (issymmetric ([0, 2; -2, 0], "skew"))
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111 %!assert (! issymmetric ([0, 2; -2, eps], "skew"))
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112 %!assert (issymmetric ([0, 2; -2, eps], "skew", eps))
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113
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114 %!assert (! (issymmetric ("test")))
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115 %!assert (! (issymmetric ("t")))
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116 %!assert (! (issymmetric (["te"; "et"])))
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117 %!assert (! issymmetric ({1}))
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118 %!test
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119 %! s.a = 1;
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120 %! assert (! issymmetric (s));
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121
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122 ## Test input validation
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123 %!error issymmetric ()
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124 %!error issymmetric (1,2,3,4)
0f98040552de issymetric.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
diff changeset
125 %!error <second argument must be> issymmetric (1, {"skew"})
0f98040552de issymetric.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
diff changeset
126 %!error <SKEWOPT must be 'skew' or 'nonskew'> issymmetric (1, "foobar")
0f98040552de issymetric.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
diff changeset
127 %!error <SKEWOPT must be 'skew' or 'nonskew'> issymmetric (1, "foobar")
0f98040552de issymetric.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
diff changeset
128 %!error <TOL must be a scalar .= 0> issymmetric (1, "skew", {1})
0f98040552de issymetric.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
diff changeset
129 %!error <TOL must be a scalar .= 0> issymmetric (1, "skew", [1 1])
0f98040552de issymetric.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
diff changeset
130 %!error <TOL must be a scalar .= 0> issymmetric (1, -1)