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3 <title>MayaChemTools:Code:Graph::GraphMatrix.pm</title>
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13 <pre>
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14 <a name="package-Graph::GraphMatrix-"></a> 1 <span class="k">package </span><span class="i">Graph::GraphMatrix</span><span class="sc">;</span>
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15 2 <span class="c">#</span>
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16 3 <span class="c"># $RCSfile: GraphMatrix.pm,v $</span>
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17 4 <span class="c"># $Date: 2015/02/28 20:49:06 $</span>
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18 5 <span class="c"># $Revision: 1.17 $</span>
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19 6 <span class="c">#</span>
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20 7 <span class="c"># Author: Manish Sud <msud@san.rr.com></span>
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21 8 <span class="c">#</span>
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22 9 <span class="c"># Copyright (C) 2015 Manish Sud. All rights reserved.</span>
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23 10 <span class="c">#</span>
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24 11 <span class="c"># This file is part of MayaChemTools.</span>
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25 12 <span class="c">#</span>
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26 13 <span class="c"># MayaChemTools is free software; you can redistribute it and/or modify it under</span>
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27 14 <span class="c"># the terms of the GNU Lesser General Public License as published by the Free</span>
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28 15 <span class="c"># Software Foundation; either version 3 of the License, or (at your option) any</span>
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29 16 <span class="c"># later version.</span>
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30 17 <span class="c">#</span>
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31 18 <span class="c"># MayaChemTools is distributed in the hope that it will be useful, but without</span>
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32 19 <span class="c"># any warranty; without even the implied warranty of merchantability of fitness</span>
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33 20 <span class="c"># for a particular purpose. See the GNU Lesser General Public License for more</span>
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34 21 <span class="c"># details.</span>
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35 22 <span class="c">#</span>
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36 23 <span class="c"># You should have received a copy of the GNU Lesser General Public License</span>
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37 24 <span class="c"># along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or</span>
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38 25 <span class="c"># write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,</span>
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39 26 <span class="c"># Boston, MA, 02111-1307, USA.</span>
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40 27 <span class="c">#</span>
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41 28
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42 29 <span class="k">use</span> <span class="w">strict</span><span class="sc">;</span>
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43 30 <span class="k">use</span> <span class="w">Carp</span><span class="sc">;</span>
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44 31 <span class="k">use</span> <span class="w">Exporter</span><span class="sc">;</span>
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45 32 <span class="k">use</span> <span class="w">Graph</span><span class="sc">;</span>
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46 33 <span class="k">use</span> <span class="w">Matrix</span><span class="sc">;</span>
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47 34 <span class="k">use</span> <span class="w">Constants</span><span class="sc">;</span>
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48 35
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49 36 <span class="k">use</span> <span class="w">vars</span> <span class="q">qw(@ISA @EXPORT @EXPORT_OK %EXPORT_TAGS)</span><span class="sc">;</span>
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50 37
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51 38 <span class="i">@ISA</span> = <span class="q">qw(Exporter)</span><span class="sc">;</span>
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52 39 <span class="i">@EXPORT</span> = <span class="q">qw()</span><span class="sc">;</span>
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53 40 <span class="i">@EXPORT_OK</span> = <span class="q">qw()</span><span class="sc">;</span>
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54 41
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55 42 <span class="i">%EXPORT_TAGS</span> = <span class="s">(</span><span class="w">all</span> <span class="cm">=></span> <span class="s">[</span><span class="i">@EXPORT</span><span class="cm">,</span> <span class="i">@EXPORT_OK</span><span class="s">]</span><span class="s">)</span><span class="sc">;</span>
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56 43
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57 44 <span class="c"># Setup class variables...</span>
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58 45 <span class="k">my</span><span class="s">(</span><span class="i">$ClassName</span><span class="s">)</span><span class="sc">;</span>
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59 46 <span class="i">_InitializeClass</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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60 47
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61 48 <span class="c"># Overload Perl functions...</span>
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62 49 <span class="k">use</span> <span class="w">overload</span> <span class="q">'""'</span> <span class="cm">=></span> <span class="q">'StringifyGraphMatrix'</span><span class="sc">;</span>
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63 50
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64 51 <span class="c"># Class constructor...</span>
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65 <a name="new-"></a> 52 <span class="k">sub </span><span class="m">new</span> <span class="s">{</span>
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66 53 <span class="k">my</span><span class="s">(</span><span class="i">$Class</span><span class="cm">,</span> <span class="i">$Graph</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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67 54
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68 55 <span class="c"># Initialize object...</span>
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69 56 <span class="k">my</span> <span class="i">$This</span> = <span class="s">{</span><span class="s">}</span><span class="sc">;</span>
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70 57 <span class="k">bless</span> <span class="i">$This</span><span class="cm">,</span> <span class="k">ref</span><span class="s">(</span><span class="i">$Class</span><span class="s">)</span> || <span class="i">$Class</span><span class="sc">;</span>
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71 58 <span class="i">$This</span><span class="i">->_InitializeGraphMatrix</span><span class="s">(</span><span class="i">$Graph</span><span class="s">)</span><span class="sc">;</span>
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72 59
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73 60 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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74 61 <span class="s">}</span>
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75 62
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76 63 <span class="c"># Initialize object data...</span>
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77 <a name="_InitializeGraphMatrix-"></a> 64 <span class="k">sub </span><span class="m">_InitializeGraphMatrix</span> <span class="s">{</span>
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78 65 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Graph</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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79 66
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80 67 <span class="c"># Specified graph object...</span>
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81 68 <span class="i">$This</span>->{<span class="w">Graph</span>} = <span class="i">$Graph</span><span class="sc">;</span>
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82 69
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83 70 <span class="c"># Generated matrix...</span>
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84 71 <span class="i">$This</span>->{<span class="w">Matrix</span>} = <span class="k">undef</span><span class="sc">;</span>
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85 72 <span class="i">$This</span>->{<span class="w">MatrixType</span>} = <span class="k">undef</span><span class="sc">;</span>
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86 73
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87 74 <span class="c"># Row and columns IDs...</span>
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88 75 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">RowIDs</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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89 76 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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90 77
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91 78 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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92 79 <span class="s">}</span>
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93 80
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94 81 <span class="c"># Initialize class ...</span>
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95 <a name="_InitializeClass-"></a> 82 <span class="k">sub </span><span class="m">_InitializeClass</span> <span class="s">{</span>
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96 83 <span class="c">#Class name...</span>
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97 84 <span class="i">$ClassName</span> = <span class="w">__PACKAGE__</span><span class="sc">;</span>
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98 85 <span class="s">}</span>
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99 86
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100 87 <span class="c"># Generate the adjacency matrix for a simple graph.</span>
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101 88 <span class="c">#</span>
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102 89 <span class="c"># For a simple graph G with n vertices, the adjacency matrix for G is a n x n square matrix and</span>
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103 90 <span class="c"># its elements Mij are:</span>
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104 91 <span class="c">#</span>
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105 92 <span class="c"># . 0 if i == j</span>
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106 93 <span class="c"># . 1 if i != j and vertex Vi is adjacent to vertex Vj</span>
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107 94 <span class="c"># . 0 if i != j and vertex Vi is not adjacent to vertex Vj</span>
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108 95 <span class="c">#</span>
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109 <a name="GenerateAdjacencyMatrix-"></a> 96 <span class="k">sub </span><span class="m">GenerateAdjacencyMatrix</span> <span class="s">{</span>
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110 97 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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111 98 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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112 99
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113 100 <span class="c"># Get graph vertices...</span>
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114 101 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span>
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115 102 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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116 103 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span>
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117 104
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118 105 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfVertices</span> == <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
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119 106 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateAdjacencyMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span>
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120 107 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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121 108 <span class="s">}</span>
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122 109
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123 110 <span class="c"># Create adjacency matrix...</span>
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124 111 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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125 112
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126 113 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="s">)</span><span class="sc">;</span>
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127 114 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span>
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128 115
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129 116 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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130 117 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span>
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131 118 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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132 119 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span>
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133 120 <span class="i">$Value</span> = <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> ? <span class="n">0</span> <span class="co">:</span> <span class="s">(</span><span class="i">$Graph</span><span class="i">->HasEdge</span><span class="s">(</span><span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="s">)</span><span class="sc">;</span>
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134 121 <span class="i">$Matrix</span><span class="i">->SetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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135 122 <span class="s">}</span>
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136 123 <span class="s">}</span>
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137 124 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"AdjacencyMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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138 125
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139 126 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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140 127 <span class="s">}</span>
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141 128
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142 129 <span class="c"># Generate the Siedel adjacency matrix for a simple graph.</span>
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143 130 <span class="c">#</span>
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144 131 <span class="c"># For a simple graph G with n vertices, the Siedal adjacency matrix for G is a n x n square matrix and</span>
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145 132 <span class="c"># its elements Mij are:</span>
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146 133 <span class="c">#</span>
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147 134 <span class="c"># . 0 if i == j</span>
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148 135 <span class="c"># . -1 if i != j and vertex Vi is adjacent to vertex Vj</span>
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149 136 <span class="c"># . 1 if i != j and vertex Vi is not adjacent to vertex Vj</span>
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150 137 <span class="c">#</span>
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151 <a name="GenerateSiedelAdjacencyMatrix-"></a> 138 <span class="k">sub </span><span class="m">GenerateSiedelAdjacencyMatrix</span> <span class="s">{</span>
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152 139 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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153 140 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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154 141
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155 142 <span class="c"># Get graph vertices...</span>
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156 143 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span>
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157 144 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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158 145 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span>
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159 146
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160 147 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfVertices</span> == <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
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161 148 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateSiedelAdjacencyMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span>
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162 149 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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163 150 <span class="s">}</span>
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164 151
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165 152 <span class="c"># Create Siedel adjacency matrix...</span>
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166 153 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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167 154
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168 155 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="s">)</span><span class="sc">;</span>
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169 156 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span>
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170 157
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171 158 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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172 159 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span>
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173 160 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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174 161 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span>
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175 162 <span class="i">$Value</span> = <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> ? <span class="n">0</span> <span class="co">:</span> <span class="s">(</span><span class="i">$Graph</span><span class="i">->HasEdge</span><span class="s">(</span><span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="s">)</span> ? <span class="n">-1</span> <span class="co">:</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
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176 163 <span class="i">$Matrix</span><span class="i">->SetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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177 164 <span class="s">}</span>
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178 165 <span class="s">}</span>
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179 166 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"SiedelAdjacencyMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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180 167
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181 168 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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182 169 <span class="s">}</span>
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183 170
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184 171 <span class="c"># Generate distance matrix for a simple graph using Floyd-Marshall algorithm [Ref 67].</span>
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185 172 <span class="c">#</span>
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186 173 <span class="c"># For a simple graph G with n vertices, the distance matrix for G is a n x n square matrix and</span>
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187 174 <span class="c"># its elements Mij are:</span>
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188 175 <span class="c">#</span>
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189 176 <span class="c"># . 0 if i == j</span>
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190 177 <span class="c"># . d if i != j and d is the shortest distance between vertex Vi and vertex Vj</span>
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191 178 <span class="c">#</span>
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192 179 <span class="c"># Note:</span>
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193 180 <span class="c"># . In the final matrix, BigNumber values correspond to vertices with no edges.</span>
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194 181 <span class="c">#</span>
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195 <a name="GenerateDistanceMatrix-"></a> 182 <span class="k">sub </span><span class="m">GenerateDistanceMatrix</span> <span class="s">{</span>
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196 183 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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197 184 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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198 185
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199 186 <span class="c"># Get graph vertices...</span>
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200 187 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span>
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201 188 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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202 189 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span>
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203 190
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204 191 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfVertices</span> == <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
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205 192 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateDistanceMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span>
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206 193 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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207 194 <span class="s">}</span>
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208 195
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209 196 <span class="c"># Initialize matrix...</span>
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210 197 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$MatrixValuesRef</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
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211 198
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212 199 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="s">)</span><span class="sc">;</span>
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213 200 <span class="i">$MatrixValuesRef</span> = <span class="i">$Matrix</span><span class="i">->GetMatrixValuesReference</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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214 201
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215 202 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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216 203 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span>
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217 204 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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218 205 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span>
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219 206 <span class="i">$Value</span> = <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> ? <span class="n">0</span> <span class="co">:</span> <span class="s">(</span><span class="i">$Graph</span><span class="i">->HasEdge</span><span class="s">(</span><span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="w">BigNumber</span><span class="s">)</span><span class="sc">;</span>
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220 207 <span class="i">$MatrixValuesRef</span>->[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$Value</span><span class="sc">;</span>
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221 208 <span class="s">}</span>
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222 209 <span class="s">}</span>
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223 210
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224 211 <span class="c"># Create distance matrix...</span>
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225 212 <span class="k">my</span><span class="s">(</span><span class="i">$i</span><span class="cm">,</span> <span class="i">$j</span><span class="cm">,</span> <span class="i">$k</span><span class="cm">,</span> <span class="i">$Valuejk</span><span class="s">)</span><span class="sc">;</span>
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226 213
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227 214 <span class="k">for</span> <span class="i">$i</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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228 215 <span class="k">for</span> <span class="i">$j</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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229 216 <span class="k">for</span> <span class="i">$k</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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230 217 <span class="i">$Valuejk</span> = <span class="i">$MatrixValuesRef</span>->[<span class="i">$j</span>][<span class="i">$i</span>] + <span class="i">$MatrixValuesRef</span>->[<span class="i">$i</span>][<span class="i">$k</span>]<span class="sc">;</span>
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231 218 <span class="k">if</span> <span class="s">(</span><span class="i">$Valuejk</span> < <span class="i">$MatrixValuesRef</span>->[<span class="i">$j</span>][<span class="i">$k</span>]<span class="s">)</span> <span class="s">{</span>
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232 219 <span class="i">$MatrixValuesRef</span>->[<span class="i">$j</span>][<span class="i">$k</span>] = <span class="i">$Valuejk</span><span class="sc">;</span>
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233 220 <span class="s">}</span>
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234 221 <span class="s">}</span>
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|
235 222 <span class="s">}</span>
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|
236 223 <span class="s">}</span>
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237 224 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"DistanceMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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238 225
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239 226 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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240 227 <span class="s">}</span>
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241 228
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242 229 <span class="c"># Generate the incidence matrix for a simple graph.</span>
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243 230 <span class="c">#</span>
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244 231 <span class="c"># For a simple graph G with n vertices and e edges, the incidence matrix for G is a n x e matrix</span>
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|
245 232 <span class="c"># its elements Mij are:</span>
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246 233 <span class="c">#</span>
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|
247 234 <span class="c"># . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related</span>
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|
248 235 <span class="c"># . 0 otherwise</span>
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|
249 236 <span class="c">#</span>
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250 <a name="GenerateIncidenceMatrix-"></a> 237 <span class="k">sub </span><span class="m">GenerateIncidenceMatrix</span> <span class="s">{</span>
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251 238 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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|
252 239 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfEdges</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="cm">,</span> <span class="i">@EdgeVertexIDs</span><span class="s">)</span><span class="sc">;</span>
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253 240
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|
254 241 <span class="c"># Get graph vertices and edges...</span>
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|
|
255 242 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span>
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|
|
256 243 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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|
|
257 244 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span>
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|
258 245
|
|
|
259 246 <span class="i">@EdgeVertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetEdges</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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260 247 <span class="i">$NumOfEdges</span> = <span class="i">@EdgeVertexIDs</span>/<span class="n">2</span><span class="sc">;</span>
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|
261 248
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|
262 249 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfVertices</span> == <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
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|
263 250 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateIncidenceMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span>
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|
264 251 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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|
|
265 252 <span class="s">}</span>
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|
266 253
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|
267 254 <span class="c"># Create incidence matrix...</span>
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|
268 255 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$EdgeVertexIndex</span><span class="cm">,</span> <span class="i">$VertexID</span><span class="cm">,</span> <span class="i">$EdgeVertexID1</span><span class="cm">,</span> <span class="i">$EdgeVertexID2</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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|
|
269 256
|
|
|
270 257 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfEdges</span><span class="s">)</span><span class="sc">;</span>
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|
|
271 258
|
|
|
272 259 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span>
|
|
|
273 260 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
|
|
|
274 261 <span class="i">$VertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span>
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|
|
275 262 <span class="i">$EdgeVertexIndex</span> = <span class="n">0</span><span class="sc">;</span>
|
|
|
276 263 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfEdges</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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|
|
277 264 <span class="i">$EdgeVertexID1</span> = <span class="i">$EdgeVertexIDs</span>[<span class="i">$EdgeVertexIndex</span>]<span class="sc">;</span> <span class="i">$EdgeVertexIndex</span>++<span class="sc">;</span>
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|
278 265 <span class="i">$EdgeVertexID2</span> = <span class="i">$EdgeVertexIDs</span>[<span class="i">$EdgeVertexIndex</span>]<span class="sc">;</span> <span class="i">$EdgeVertexIndex</span>++<span class="sc">;</span>
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|
279 266
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|
|
280 267 <span class="i">$Value</span> = <span class="s">(</span><span class="i">$VertexID</span> == <span class="i">$EdgeVertexID1</span> || <span class="i">$VertexID</span> == <span class="i">$EdgeVertexID2</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span>
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|
281 268 <span class="i">$Matrix</span><span class="i">->SetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
|
|
|
282 269 <span class="s">}</span>
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|
|
283 270 <span class="s">}</span>
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|
|
284 271 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"IncidenceMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="cm">,</span> \<span class="i">@EdgeVertexIDs</span><span class="s">)</span><span class="sc">;</span>
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|
|
285 272
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|
|
286 273 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
|
|
|
287 274 <span class="s">}</span>
|
|
|
288 275
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|
|
289 276 <span class="c"># Generate the degree matrix for a simple graph.</span>
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|
290 277 <span class="c">#</span>
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|
|
291 278 <span class="c"># For a simple graph G with n vertices, the degree matrix for G is a n x n square matrix and</span>
|
|
|
292 279 <span class="c"># its elements Mij are:</span>
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|
|
293 280 <span class="c">#</span>
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|
|
294 281 <span class="c"># . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi</span>
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|
|
295 282 <span class="c"># . 0 otherwise</span>
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|
|
296 283 <span class="c">#</span>
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|
297 <a name="GenerateDegreeMatrix-"></a> 284 <span class="k">sub </span><span class="m">GenerateDegreeMatrix</span> <span class="s">{</span>
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|
298 285 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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|
299 286 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
|
|
|
300 287
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|
|
301 288 <span class="c"># Get graph vertices...</span>
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|
|
302 289 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span>
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|
|
303 290 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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|
|
304 291 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span>
|
|
|
305 292
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|
|
306 293 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfVertices</span> == <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
|
|
|
307 294 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateDegreeMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span>
|
|
|
308 295 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
|
|
|
309 296 <span class="s">}</span>
|
|
|
310 297
|
|
|
311 298 <span class="c"># Create degree matrix...</span>
|
|
|
312 299 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$Index</span><span class="cm">,</span> <span class="i">$VertexID</span><span class="cm">,</span> <span class="i">$Degree</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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|
|
313 300
|
|
|
314 301 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="s">)</span><span class="sc">;</span>
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|
|
315 302 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span>
|
|
|
316 303
|
|
|
317 304 <span class="k">for</span> <span class="i">$Index</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
|
|
|
318 305 <span class="i">$VertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$Index</span>]<span class="sc">;</span>
|
|
|
319 306 <span class="i">$Degree</span> = <span class="i">$Graph</span><span class="i">->GetDegree</span><span class="s">(</span><span class="i">$VertexID</span><span class="s">)</span><span class="sc">;</span>
|
|
|
320 307 <span class="i">$Matrix</span><span class="i">->SetValue</span><span class="s">(</span><span class="i">$Index</span><span class="cm">,</span> <span class="i">$Index</span><span class="cm">,</span> <span class="i">$Degree</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
|
|
|
321 308 <span class="s">}</span>
|
|
|
322 309 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"DegreeMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
|
|
|
323 310
|
|
|
324 311 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
|
|
|
325 312 <span class="s">}</span>
|
|
|
326 313
|
|
|
327 314 <span class="c"># Generate the Laplacian matrix for a simple graph.</span>
|
|
|
328 315 <span class="c">#</span>
|
|
|
329 316 <span class="c"># For a simple graph G with n vertices, the Laplacian matrix for G is a n x n square matrix and</span>
|
|
|
330 317 <span class="c"># its elements Mij are:</span>
|
|
|
331 318 <span class="c">#</span>
|
|
|
332 319 <span class="c"># . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi</span>
|
|
|
333 320 <span class="c"># . -1 if i != j and vertex Vi is adjacent to vertex Vj</span>
|
|
|
334 321 <span class="c"># . 0 otherwise</span>
|
|
|
335 322 <span class="c">#</span>
|
|
|
336 323 <span class="c"># Note: The Laplacian matrix is the difference between the degree matrix and adjacency matrix.</span>
|
|
|
337 324 <span class="c">#</span>
|
|
|
338 <a name="GenerateLaplacianMatrix-"></a> 325 <span class="k">sub </span><span class="m">GenerateLaplacianMatrix</span> <span class="s">{</span>
|
|
|
339 326 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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340 327 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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341 328
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342 329 <span class="c"># Get graph vertices...</span>
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343 330 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span>
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344 331 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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|
345 332 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span>
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346 333
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347 334 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfVertices</span> == <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
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348 335 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateLaplacianMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span>
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349 336 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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350 337 <span class="s">}</span>
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351 338
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352 339 <span class="c"># Create adjacency matrix...</span>
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353 340 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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354 341
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355 342 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="s">)</span><span class="sc">;</span>
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356 343 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span>
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357 344
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358 345 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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359 346 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span>
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|
360 347 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
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|
|
361 348 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span>
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|
362 349 <span class="i">$Value</span> = <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> ? <span class="i">$Graph</span><span class="i">->GetDegree</span><span class="s">(</span><span class="i">$RowVertexID</span><span class="s">)</span> <span class="co">:</span> <span class="s">(</span><span class="i">$Graph</span><span class="i">->HasEdge</span><span class="s">(</span><span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="s">)</span> ? <span class="n">-1</span> <span class="co">:</span> <span class="n">0</span><span class="s">)</span><span class="sc">;</span>
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|
363 350 <span class="i">$Matrix</span><span class="i">->SetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
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|
364 351 <span class="s">}</span>
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|
365 352 <span class="s">}</span>
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366 353 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"LaplacianMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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367 354
|
|
|
368 355 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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|
|
369 356 <span class="s">}</span>
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370 357
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371 358 <span class="c"># Generate the normalized Laplacian matrix for a simple graph.</span>
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372 359 <span class="c">#</span>
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373 360 <span class="c"># For a simple graph G with n vertices, the normalized Laplacian matrix L for G is a n x n square matrix and</span>
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|
374 361 <span class="c"># its elements Lij are:</span>
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|
375 362 <span class="c">#</span>
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|
376 363 <span class="c"># . 1 if i == j and deg(Vi) != 0</span>
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|
|
377 364 <span class="c"># . -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj</span>
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|
378 365 <span class="c"># . 0 otherwise</span>
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|
|
379 366 <span class="c">#</span>
|
|
|
380 367 <span class="c">#</span>
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|
381 <a name="GenerateNormalizedLaplacianMatrix-"></a> 368 <span class="k">sub </span><span class="m">GenerateNormalizedLaplacianMatrix</span> <span class="s">{</span>
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382 369 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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383 370 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
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384 371
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|
385 372 <span class="c"># Get graph vertices...</span>
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|
386 373 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span>
|
|
|
387 374 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
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|
|
388 375 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span>
|
|
|
389 376
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|
|
390 377 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfVertices</span> == <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
|
|
|
391 378 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateNormalizedLaplacianMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span>
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|
392 379 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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|
|
393 380 <span class="s">}</span>
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|
394 381
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|
395 382 <span class="c"># Create adjacency matrix...</span>
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|
396 383 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="cm">,</span> <span class="i">$RowVertexDegree</span><span class="cm">,</span> <span class="i">$ColVertexDegree</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
|
|
|
397 384
|
|
|
398 385 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="s">)</span><span class="sc">;</span>
|
|
|
399 386 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span>
|
|
|
400 387
|
|
|
401 388 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
|
|
|
402 389 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span>
|
|
|
403 390 <span class="i">$RowVertexDegree</span> = <span class="i">$Graph</span><span class="i">->GetDegree</span><span class="s">(</span><span class="i">$RowVertexID</span><span class="s">)</span><span class="sc">;</span>
|
|
|
404 391 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
|
|
|
405 392 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span>
|
|
|
406 393 <span class="i">$Value</span> = <span class="n">0</span><span class="sc">;</span>
|
|
|
407 394 <span class="k">if</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span>
|
|
|
408 395 <span class="i">$Value</span> = <span class="s">(</span><span class="i">$RowVertexDegree</span> == <span class="n">0</span><span class="s">)</span> ? <span class="n">0</span> <span class="co">:</span> <span class="n">1</span><span class="sc">;</span>
|
|
|
409 396 <span class="s">}</span>
|
|
|
410 397 <span class="k">else</span> <span class="s">{</span>
|
|
|
411 398 <span class="i">$ColVertexDegree</span> = <span class="i">$Graph</span><span class="i">->GetDegree</span><span class="s">(</span><span class="i">$ColVertexID</span><span class="s">)</span><span class="sc">;</span>
|
|
|
412 399 <span class="i">$Value</span> = <span class="i">$Graph</span><span class="i">->HasEdge</span><span class="s">(</span><span class="i">$RowVertexID</span><span class="cm">,</span> <span class="i">$ColVertexID</span><span class="s">)</span> ? <span class="s">(</span><span class="n">-1</span>/<span class="k">sqrt</span><span class="s">(</span><span class="i">$RowVertexDegree</span> * <span class="i">$ColVertexDegree</span><span class="s">)</span><span class="s">)</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span>
|
|
|
413 400 <span class="s">}</span>
|
|
|
414 401 <span class="i">$Matrix</span><span class="i">->SetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span>
|
|
|
415 402 <span class="s">}</span>
|
|
|
416 403 <span class="s">}</span>
|
|
|
417 404 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"NormalizedLaplacianMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span>
|
|
|
418 405
|
|
|
419 406 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
|
|
|
420 407 <span class="s">}</span>
|
|
|
421 408
|
|
|
422 409 <span class="c"># Generate the admittance matrix for a simple graph.</span>
|
|
|
423 410 <span class="c">#</span>
|
|
|
424 <a name="GenerateAdmittanceMatrix-"></a> 411 <span class="k">sub </span><span class="m">GenerateAdmittanceMatrix</span> <span class="s">{</span>
|
|
|
425 412 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
|
|
|
426 413
|
|
|
427 414 <span class="i">$This</span><span class="i">->GenerateLaplacianMatrix</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
|
|
|
428 415 <span class="i">$This</span>->{<span class="w">MatrixType</span>} = <span class="q">"AdmittanceMatrix"</span><span class="sc">;</span>
|
|
|
429 416
|
|
|
430 417 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
|
|
|
431 418 <span class="s">}</span>
|
|
|
432 419
|
|
|
433 420 <span class="c"># Generate the Kirchhoff matrix for a simple graph.</span>
|
|
|
434 421 <span class="c">#</span>
|
|
|
435 <a name="GenerateKirchhoffMatrix-"></a> 422 <span class="k">sub </span><span class="m">GenerateKirchhoffMatrix</span> <span class="s">{</span>
|
|
|
436 423 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
|
|
|
437 424
|
|
|
438 425 <span class="i">$This</span><span class="i">->GenerateLaplacianMatrix</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span>
|
|
|
439 426 <span class="i">$This</span>->{<span class="w">MatrixType</span>} = <span class="q">"KirchhoffMatrix"</span><span class="sc">;</span>
|
|
|
440 427
|
|
|
441 428 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
|
|
|
442 429 <span class="s">}</span>
|
|
|
443 430
|
|
|
444 431 <span class="c"># Get generated matrix...</span>
|
|
|
445 432 <span class="c">#</span>
|
|
|
446 <a name="GetMatrix-"></a> 433 <span class="k">sub </span><span class="m">GetMatrix</span> <span class="s">{</span>
|
|
|
447 434 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
|
|
|
448 435
|
|
|
449 436 <span class="k">return</span> <span class="i">$This</span>->{<span class="w">Matrix</span>}<span class="sc">;</span>
|
|
|
450 437 <span class="s">}</span>
|
|
|
451 438
|
|
|
452 439 <span class="c"># Get matrix type...</span>
|
|
|
453 440 <span class="c">#</span>
|
|
|
454 <a name="GetMatrixType-"></a> 441 <span class="k">sub </span><span class="m">GetMatrixType</span> <span class="s">{</span>
|
|
|
455 442 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
|
|
|
456 443
|
|
|
457 444 <span class="k">return</span> <span class="i">$This</span>->{<span class="w">MatrixType</span>}<span class="sc">;</span>
|
|
|
458 445 <span class="s">}</span>
|
|
|
459 446
|
|
|
460 447 <span class="c"># Get row IDs...</span>
|
|
|
461 448 <span class="c">#</span>
|
|
|
462 <a name="GetRowIDs-"></a> 449 <span class="k">sub </span><span class="m">GetRowIDs</span> <span class="s">{</span>
|
|
|
463 450 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
|
|
|
464 451
|
|
|
465 452 <span class="k">return</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">RowIDs</span>}}<span class="sc">;</span>
|
|
|
466 453 <span class="s">}</span>
|
|
|
467 454
|
|
|
468 455 <span class="c"># Get column IDs...</span>
|
|
|
469 456 <span class="c">#</span>
|
|
|
470 <a name="GetColumnIDs-"></a> 457 <span class="k">sub </span><span class="m">GetColumnIDs</span> <span class="s">{</span>
|
|
|
471 458 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
|
|
|
472 459
|
|
|
473 460 <span class="k">return</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}}<span class="sc">;</span>
|
|
|
474 461 <span class="s">}</span>
|
|
|
475 462
|
|
|
476 463
|
|
|
477 464 <span class="c"># Setup matrix and other associated information...</span>
|
|
|
478 465 <span class="c">#</span>
|
|
|
479 <a name="_SetMatrixAndAssociatedInformation-"></a> 466 <span class="k">sub </span><span class="m">_SetMatrixAndAssociatedInformation</span> <span class="s">{</span>
|
|
|
480 467 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$MatrixType</span><span class="cm">,</span> <span class="i">$VertexIDsRef</span><span class="cm">,</span> <span class="i">$EdgeVertexIDsRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
|
|
|
481 468
|
|
|
482 469 <span class="i">$This</span>->{<span class="w">Matrix</span>} = <span class="i">$Matrix</span><span class="sc">;</span>
|
|
|
483 470 <span class="i">$This</span>->{<span class="w">MatrixType</span>} = <span class="i">$MatrixType</span><span class="sc">;</span>
|
|
|
484 471
|
|
|
485 472 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">RowIDs</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
|
|
|
486 473 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
|
|
|
487 474
|
|
|
488 475 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">RowIDs</span>}} = <span class="i">@</span>{<span class="i">$VertexIDsRef</span>}<span class="sc">;</span>
|
|
|
489 476
|
|
|
490 477 <span class="k">if</span> <span class="s">(</span><span class="i">$MatrixType</span> =~ <span class="q">/^IncidenceMatrix$/i</span><span class="s">)</span> <span class="s">{</span>
|
|
|
491 478 <span class="c"># Setup column IDs using edge vertex IDs...</span>
|
|
|
492 479 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfEdges</span><span class="cm">,</span> <span class="i">$EdgeVertexIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$EdgeVertexID1</span><span class="cm">,</span> <span class="i">$EdgeVertexID2</span><span class="cm">,</span> <span class="i">$EdgeID</span><span class="s">)</span><span class="sc">;</span>
|
|
|
493 480
|
|
|
494 481 <span class="i">$NumOfEdges</span> = <span class="s">(</span><span class="k">scalar</span> <span class="i">@</span>{<span class="i">$EdgeVertexIDsRef</span>}<span class="s">)</span>/<span class="n">2</span><span class="sc">;</span>
|
|
|
495 482 <span class="i">$EdgeVertexIndex</span> = <span class="n">0</span><span class="sc">;</span>
|
|
|
496 483
|
|
|
497 484 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfEdges</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
|
|
|
498 485 <span class="i">$EdgeVertexID1</span> = <span class="i">$EdgeVertexIDsRef</span>->[<span class="i">$EdgeVertexIndex</span>]<span class="sc">;</span> <span class="i">$EdgeVertexIndex</span>++<span class="sc">;</span>
|
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499 486 <span class="i">$EdgeVertexID2</span> = <span class="i">$EdgeVertexIDsRef</span>->[<span class="i">$EdgeVertexIndex</span>]<span class="sc">;</span> <span class="i">$EdgeVertexIndex</span>++<span class="sc">;</span>
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500 487 <span class="i">$EdgeID</span> = <span class="s">(</span><span class="i">$EdgeVertexID1</span> < <span class="i">$EdgeVertexID2</span><span class="s">)</span> ? <span class="q">"${EdgeVertexID1}-${EdgeVertexID2}"</span> <span class="co">:</span> <span class="q">"${EdgeVertexID2}-${EdgeVertexID1}"</span><span class="sc">;</span>
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501 488
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502 489 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}}<span class="cm">,</span> <span class="i">$EdgeID</span><span class="sc">;</span>
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503 490 <span class="s">}</span>
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504 491 <span class="s">}</span>
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505 492 <span class="k">else</span> <span class="s">{</span>
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506 493 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}}<span class="cm">,</span> <span class="i">@</span>{<span class="i">$VertexIDsRef</span>}<span class="sc">;</span>
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507 494 <span class="s">}</span>
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508 495 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span>
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509 496 <span class="s">}</span>
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510 497
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511 498 <span class="c"># Return a string containg data for GraphMatrix object...</span>
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512 <a name="StringifyGraphMatrix-"></a> 499 <span class="k">sub </span><span class="m">StringifyGraphMatrix</span> <span class="s">{</span>
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513 500 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
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514 501 <span class="k">my</span><span class="s">(</span><span class="i">$GraphMatrixString</span><span class="cm">,</span> <span class="i">$RowIDs</span><span class="s">)</span><span class="sc">;</span>
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515 502
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516 503 <span class="i">$GraphMatrixString</span> = <span class="q">"GraphMatrix:"</span><span class="sc">;</span>
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517 504
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518 505 <span class="i">$GraphMatrixString</span> .= <span class="s">(</span><span class="k">defined</span> <span class="i">$This</span>->{<span class="w">MatrixType</span>}<span class="s">)</span> ? <span class="q">" MatrixType: $This->{MatrixType}"</span> <span class="co">:</span> <span class="q">"MatrixType: <Undefined>"</span><span class="sc">;</span>
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519 506 <span class="i">$GraphMatrixString</span> .= <span class="s">(</span><span class="k">scalar</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">RowIDs</span>}}<span class="s">)</span> ? <span class="q">"; RowIDs: @{$This->{RowIDs}}"</span> <span class="co">:</span> <span class="q">"; RowIDs: <Undefined>"</span><span class="sc">;</span>
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520 507 <span class="i">$GraphMatrixString</span> .= <span class="s">(</span><span class="k">scalar</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}}<span class="s">)</span> ? <span class="q">"; ColumnIDs: @{$This->{ColumnIDs}}"</span> <span class="co">:</span> <span class="q">"; ColumnIDs: <Undefined>"</span><span class="sc">;</span>
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521 508
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522 509 <span class="i">$GraphMatrixString</span> .= <span class="s">(</span><span class="k">defined</span> <span class="i">$This</span>->{<span class="w">Matrix</span>}<span class="s">)</span> ? <span class="q">"; Matrix: $This->{Matrix}"</span> <span class="co">:</span> <span class="q">"; Matrix: <Undefined>"</span><span class="sc">;</span>
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523 510
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524 511 <span class="k">return</span> <span class="i">$GraphMatrixString</span><span class="sc">;</span>
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525 512 <span class="s">}</span>
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526 513
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527 <a name="EOF-"></a></pre>
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528 <p> </p>
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529 <br />
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530 <center>
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531 <img src="../../../images/h2o2.png">
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532 </center>
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533 </body>
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534 </html>
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