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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 0d755097d73f
children c0fa4a9eef95
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1 ## Copyright (C) 1996-2019 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 {} {} ishermitian (@var{A})
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22 ## @deftypefnx {} {} ishermitian (@var{A}, @var{tol})
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23 ## @deftypefnx {} {} ishermitian (@var{A}, @qcode{"skew"})
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24 ## @deftypefnx {} {} ishermitian (@var{A}, @qcode{"skew"}, @var{tol})
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25 ## Return true if @var{A} is a Hermitian or skew-Hermitian 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 Hermitian or @qcode{"skew"} for
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32 ## skew-Hermitian.
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33 ##
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34 ## Background: A matrix is Hermitian if the complex conjugate transpose of the
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35 ## matrix is equal to the original matrix: @w{@tcode{@var{A} == @var{A}'}}. If
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36 ## a tolerance is given then the calculation is
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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-Hermitian if the complex conjugate transpose of the matrix
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40 ## is equal to the negative of the original matrix:
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41 ## @w{@tcode{@var{A} == -@var{A}'}}. If a
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42 ## tolerance is given then the calculation is
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43 ## @code{norm (@var{A} + @var{A}', Inf) / norm (@var{A}, Inf) < @var{tol}}.
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44 ## @seealso{issymmetric, isdefinite}
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45 ## @end deftypefn
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46
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47 ## Author: A. S. Hodel <scotte@eng.auburn.edu>
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48 ## Created: August 1993
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49 ## Adapted-By: jwe
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50
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51 function retval = ishermitian (A, skewopt = "nonskew", tol = 0)
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52
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53 if (nargin < 1 || nargin > 3)
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54 print_usage ();
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55 endif
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56
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57 if (nargin == 2)
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58 ## Decode whether second argument is skewopt or tol
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59 if (isnumeric (skewopt))
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60 tol = skewopt;
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61 skewopt = "nonskew";
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62 elseif (! ischar (skewopt))
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63 error ("ishermitian: second argument must be a non-negative scalar TOL, or one of the strings: 'skew' / 'nonskew'");
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64 endif
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65 endif
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66
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67 ## Validate inputs
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68 retval = (isnumeric (A) || islogical (A)) && issquare (A);
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69 if (! retval)
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70 return;
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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 ("ishermitian: 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 ("ishermitian: TOL must be a scalar >= 0");
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79 endif
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80
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81 ## Calculate Hermitian-ness
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82 if (strcmp (skewopt, "nonskew"))
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83 if (tol == 0)
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84 ## check for exact symmetry
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85 retval = ! any ((A != A')(:));
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86 else
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87 if (islogical (A))
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88 ## Hack to allow norm to work. Choose single to minimize memory.
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89 A = single (A);
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90 endif
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91 norm_x = norm (A, Inf);
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92 retval = norm_x == 0 || norm (A - A', Inf) / norm_x <= tol;
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93 endif
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94 else
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95 ## skew-Hermitian
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96 if (tol == 0)
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97 retval = ! any ((A != -A')(:));
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98 else
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99 if (islogical (A))
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100 ## Hack to allow norm to work. Choose single to minimize memory.
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101 A = single (A);
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102 endif
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103 norm_x = norm (A, Inf);
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104 retval = norm_x == 0 || norm (A + A', Inf) / norm_x <= tol;
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105 endif
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106 endif
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107
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108 endfunction
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109
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110
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111 %!assert (ishermitian (1))
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112 %!assert (! ishermitian ([1, 2]))
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113 %!assert (ishermitian ([]))
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114 %!assert (ishermitian ([1, 2; 2, 1]))
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115 %!assert (ishermitian ([1, 2.1; 2, 1.1], 0.2))
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116 %!assert (ishermitian ([1, -2i; 2i, 1]))
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117 %!assert (ishermitian (speye (100)))
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parents: 25054
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118 %!assert (ishermitian (logical (eye (2))))
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119 %!assert (! ishermitian (logical ([1 1; 0 1])))
0d755097d73f issymetric.m, ishermitian.m: Don't error on logical matrices (bug #42487).
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parents: 26043
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120 %!assert (ishermitian (logical ([1 1; 0 1]), 0.5))
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parents: 25054
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121 %!assert (ishermitian ([0, 2i; 2i, 0], "skew"))
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parents: 25054
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122 %!assert (! ishermitian ([0, 2; -2, eps], "skew"))
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
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parents: 25054
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123 %!assert (ishermitian ([0, 2; -2, eps], "skew", eps))
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ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
parents:
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124
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Rik <rik@octave.org>
parents: 25054
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125 %!assert (! (ishermitian ("test")))
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
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parents: 25054
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126 %!assert (! (ishermitian ("t")))
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
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parents: 25054
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127 %!assert (! (ishermitian (["te"; "et"])))
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
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parents: 25054
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128 %!assert (! ishermitian ({1}))
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ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
parents:
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129 %!test
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
parents:
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130 %! s.a = 1;
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5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14363
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131 %! assert (! ishermitian (s));
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f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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132
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Rik <rik@octave.org>
parents: 25054
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133 ## Test input validation
14363
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parents: 14138
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134 %!error ishermitian ()
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Rik <rik@octave.org>
parents: 25054
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135 %!error ishermitian (1,2,3,4)
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
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136 %!error <second argument must be> ishermitian (1, {"skew"})
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
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137 %!error <SKEWOPT must be 'skew' or 'nonskew'> ishermitian (1, "foobar")
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
diff changeset
138 %!error <SKEWOPT must be 'skew' or 'nonskew'> ishermitian (1, "foobar")
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
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139 %!error <TOL must be a scalar .= 0> ishermitian (1, "skew", {1})
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
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140 %!error <TOL must be a scalar .= 0> ishermitian (1, "skew", [1 1])
114ad8f22ee6 ishermitian.m; Overhaul function and expand to check skew-symmetry (bug #53556).
Rik <rik@octave.org>
parents: 25054
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141 %!error <TOL must be a scalar .= 0> ishermitian (1, -1)