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| date | Wed, 20 Jan 2016 09:23:18 -0500 |
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| 1 <html> | |
| 2 <head> | |
| 3 <title>MayaChemTools:Code:Graph::GraphMatrix.pm</title> | |
| 4 <meta http-equiv="content-type" content="text/html;charset=utf-8"> | |
| 5 <link rel="stylesheet" type="text/css" href="../../../css/MayaChemToolsCode.css"> | |
| 6 </head> | |
| 7 <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10"> | |
| 8 <br/> | |
| 9 <center> | |
| 10 <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a> | |
| 11 </center> | |
| 12 <br/> | |
| 13 <pre> | |
| 14 <a name="package-Graph::GraphMatrix-"></a> 1 <span class="k">package </span><span class="i">Graph::GraphMatrix</span><span class="sc">;</span> | |
| 15 2 <span class="c">#</span> | |
| 16 3 <span class="c"># $RCSfile: GraphMatrix.pm,v $</span> | |
| 17 4 <span class="c"># $Date: 2015/02/28 20:49:06 $</span> | |
| 18 5 <span class="c"># $Revision: 1.17 $</span> | |
| 19 6 <span class="c">#</span> | |
| 20 7 <span class="c"># Author: Manish Sud <msud@san.rr.com></span> | |
| 21 8 <span class="c">#</span> | |
| 22 9 <span class="c"># Copyright (C) 2015 Manish Sud. All rights reserved.</span> | |
| 23 10 <span class="c">#</span> | |
| 24 11 <span class="c"># This file is part of MayaChemTools.</span> | |
| 25 12 <span class="c">#</span> | |
| 26 13 <span class="c"># MayaChemTools is free software; you can redistribute it and/or modify it under</span> | |
| 27 14 <span class="c"># the terms of the GNU Lesser General Public License as published by the Free</span> | |
| 28 15 <span class="c"># Software Foundation; either version 3 of the License, or (at your option) any</span> | |
| 29 16 <span class="c"># later version.</span> | |
| 30 17 <span class="c">#</span> | |
| 31 18 <span class="c"># MayaChemTools is distributed in the hope that it will be useful, but without</span> | |
| 32 19 <span class="c"># any warranty; without even the implied warranty of merchantability of fitness</span> | |
| 33 20 <span class="c"># for a particular purpose. See the GNU Lesser General Public License for more</span> | |
| 34 21 <span class="c"># details.</span> | |
| 35 22 <span class="c">#</span> | |
| 36 23 <span class="c"># You should have received a copy of the GNU Lesser General Public License</span> | |
| 37 24 <span class="c"># along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or</span> | |
| 38 25 <span class="c"># write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,</span> | |
| 39 26 <span class="c"># Boston, MA, 02111-1307, USA.</span> | |
| 40 27 <span class="c">#</span> | |
| 41 28 | |
| 42 29 <span class="k">use</span> <span class="w">strict</span><span class="sc">;</span> | |
| 43 30 <span class="k">use</span> <span class="w">Carp</span><span class="sc">;</span> | |
| 44 31 <span class="k">use</span> <span class="w">Exporter</span><span class="sc">;</span> | |
| 45 32 <span class="k">use</span> <span class="w">Graph</span><span class="sc">;</span> | |
| 46 33 <span class="k">use</span> <span class="w">Matrix</span><span class="sc">;</span> | |
| 47 34 <span class="k">use</span> <span class="w">Constants</span><span class="sc">;</span> | |
| 48 35 | |
| 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> | |
| 50 37 | |
| 51 38 <span class="i">@ISA</span> = <span class="q">qw(Exporter)</span><span class="sc">;</span> | |
| 52 39 <span class="i">@EXPORT</span> = <span class="q">qw()</span><span class="sc">;</span> | |
| 53 40 <span class="i">@EXPORT_OK</span> = <span class="q">qw()</span><span class="sc">;</span> | |
| 54 41 | |
| 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> | |
| 56 43 | |
| 57 44 <span class="c"># Setup class variables...</span> | |
| 58 45 <span class="k">my</span><span class="s">(</span><span class="i">$ClassName</span><span class="s">)</span><span class="sc">;</span> | |
| 59 46 <span class="i">_InitializeClass</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 60 47 | |
| 61 48 <span class="c"># Overload Perl functions...</span> | |
| 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> | |
| 63 50 | |
| 64 51 <span class="c"># Class constructor...</span> | |
| 65 <a name="new-"></a> 52 <span class="k">sub </span><span class="m">new</span> <span class="s">{</span> | |
| 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> | |
| 67 54 | |
| 68 55 <span class="c"># Initialize object...</span> | |
| 69 56 <span class="k">my</span> <span class="i">$This</span> = <span class="s">{</span><span class="s">}</span><span class="sc">;</span> | |
| 70 57 <span class="k">bless</span> <span class="i">$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> | |
| 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> | |
| 72 59 | |
| 73 60 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 74 61 <span class="s">}</span> | |
| 75 62 | |
| 76 63 <span class="c"># Initialize object data...</span> | |
| 77 <a name="_InitializeGraphMatrix-"></a> 64 <span class="k">sub </span><span class="m">_InitializeGraphMatrix</span> <span class="s">{</span> | |
| 78 65 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Graph</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 79 66 | |
| 80 67 <span class="c"># Specified graph object...</span> | |
| 81 68 <span class="i">$This</span>->{<span class="w">Graph</span>} = <span class="i">$Graph</span><span class="sc">;</span> | |
| 82 69 | |
| 83 70 <span class="c"># Generated matrix...</span> | |
| 84 71 <span class="i">$This</span>->{<span class="w">Matrix</span>} = <span class="k">undef</span><span class="sc">;</span> | |
| 85 72 <span class="i">$This</span>->{<span class="w">MatrixType</span>} = <span class="k">undef</span><span class="sc">;</span> | |
| 86 73 | |
| 87 74 <span class="c"># Row and columns IDs...</span> | |
| 88 75 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">RowIDs</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 89 76 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 90 77 | |
| 91 78 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 92 79 <span class="s">}</span> | |
| 93 80 | |
| 94 81 <span class="c"># Initialize class ...</span> | |
| 95 <a name="_InitializeClass-"></a> 82 <span class="k">sub </span><span class="m">_InitializeClass</span> <span class="s">{</span> | |
| 96 83 <span class="c">#Class name...</span> | |
| 97 84 <span class="i">$ClassName</span> = <span class="w">__PACKAGE__</span><span class="sc">;</span> | |
| 98 85 <span class="s">}</span> | |
| 99 86 | |
| 100 87 <span class="c"># Generate the adjacency matrix for a simple graph.</span> | |
| 101 88 <span class="c">#</span> | |
| 102 89 <span class="c"># For a simple graph G with n vertices, the adjacency matrix for G is a n x n square matrix and</span> | |
| 103 90 <span class="c"># its elements Mij are:</span> | |
| 104 91 <span class="c">#</span> | |
| 105 92 <span class="c"># . 0 if i == j</span> | |
| 106 93 <span class="c"># . 1 if i != j and vertex Vi is adjacent to vertex Vj</span> | |
| 107 94 <span class="c"># . 0 if i != j and vertex Vi is not adjacent to vertex Vj</span> | |
| 108 95 <span class="c">#</span> | |
| 109 <a name="GenerateAdjacencyMatrix-"></a> 96 <span class="k">sub </span><span class="m">GenerateAdjacencyMatrix</span> <span class="s">{</span> | |
| 110 97 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 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> | |
| 112 99 | |
| 113 100 <span class="c"># Get graph vertices...</span> | |
| 114 101 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span> | |
| 115 102 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 116 103 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> | |
| 117 104 | |
| 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> | |
| 119 106 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateAdjacencyMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span> | |
| 120 107 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 121 108 <span class="s">}</span> | |
| 122 109 | |
| 123 110 <span class="c"># Create adjacency matrix...</span> | |
| 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">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span> | |
| 125 112 | |
| 126 113 <span class="i">$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> | |
| 127 114 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span> | |
| 128 115 | |
| 129 116 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> | |
| 130 117 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span> | |
| 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> | |
| 132 119 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span> | |
| 133 120 <span class="i">$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">$ColVertexID</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="s">)</span><span class="sc">;</span> | |
| 134 121 <span class="i">$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> | |
| 135 122 <span class="s">}</span> | |
| 136 123 <span class="s">}</span> | |
| 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> | |
| 138 125 | |
| 139 126 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 140 127 <span class="s">}</span> | |
| 141 128 | |
| 142 129 <span class="c"># Generate the Siedel adjacency matrix for a simple graph.</span> | |
| 143 130 <span class="c">#</span> | |
| 144 131 <span class="c"># For a simple graph G with n vertices, the Siedal adjacency matrix for G is a n x n square matrix and</span> | |
| 145 132 <span class="c"># its elements Mij are:</span> | |
| 146 133 <span class="c">#</span> | |
| 147 134 <span class="c"># . 0 if i == j</span> | |
| 148 135 <span class="c"># . -1 if i != j and vertex Vi is adjacent to vertex Vj</span> | |
| 149 136 <span class="c"># . 1 if i != j and vertex Vi is not adjacent to vertex Vj</span> | |
| 150 137 <span class="c">#</span> | |
| 151 <a name="GenerateSiedelAdjacencyMatrix-"></a> 138 <span class="k">sub </span><span class="m">GenerateSiedelAdjacencyMatrix</span> <span class="s">{</span> | |
| 152 139 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 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> | |
| 154 141 | |
| 155 142 <span class="c"># Get graph vertices...</span> | |
| 156 143 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span> | |
| 157 144 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 158 145 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> | |
| 159 146 | |
| 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> | |
| 161 148 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateSiedelAdjacencyMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span> | |
| 162 149 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 163 150 <span class="s">}</span> | |
| 164 151 | |
| 165 152 <span class="c"># Create Siedel adjacency matrix...</span> | |
| 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">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span> | |
| 167 154 | |
| 168 155 <span class="i">$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> | |
| 169 156 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span> | |
| 170 157 | |
| 171 158 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> | |
| 172 159 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span> | |
| 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> | |
| 174 161 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span> | |
| 175 162 <span class="i">$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">$ColVertexID</span><span class="s">)</span> ? <span class="n">-1</span> <span class="co">:</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span> | |
| 176 163 <span class="i">$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> | |
| 177 164 <span class="s">}</span> | |
| 178 165 <span class="s">}</span> | |
| 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> | |
| 180 167 | |
| 181 168 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 182 169 <span class="s">}</span> | |
| 183 170 | |
| 184 171 <span class="c"># Generate distance matrix for a simple graph using Floyd-Marshall algorithm [Ref 67].</span> | |
| 185 172 <span class="c">#</span> | |
| 186 173 <span class="c"># For a simple graph G with n vertices, the distance matrix for G is a n x n square matrix and</span> | |
| 187 174 <span class="c"># its elements Mij are:</span> | |
| 188 175 <span class="c">#</span> | |
| 189 176 <span class="c"># . 0 if i == j</span> | |
| 190 177 <span class="c"># . d if i != j and d is the shortest distance between vertex Vi and vertex Vj</span> | |
| 191 178 <span class="c">#</span> | |
| 192 179 <span class="c"># Note:</span> | |
| 193 180 <span class="c"># . In the final matrix, BigNumber values correspond to vertices with no edges.</span> | |
| 194 181 <span class="c">#</span> | |
| 195 <a name="GenerateDistanceMatrix-"></a> 182 <span class="k">sub </span><span class="m">GenerateDistanceMatrix</span> <span class="s">{</span> | |
| 196 183 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 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> | |
| 198 185 | |
| 199 186 <span class="c"># Get graph vertices...</span> | |
| 200 187 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span> | |
| 201 188 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 202 189 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> | |
| 203 190 | |
| 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> | |
| 205 192 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateDistanceMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span> | |
| 206 193 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 207 194 <span class="s">}</span> | |
| 208 195 | |
| 209 196 <span class="c"># Initialize matrix...</span> | |
| 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">$Value</span><span class="s">)</span><span class="sc">;</span> | |
| 211 198 | |
| 212 199 <span class="i">$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> | |
| 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> | |
| 214 201 | |
| 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> | |
| 216 203 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span> | |
| 217 204 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> | |
| 218 205 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span> | |
| 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> | |
| 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> | |
| 221 208 <span class="s">}</span> | |
| 222 209 <span class="s">}</span> | |
| 223 210 | |
| 224 211 <span class="c"># Create distance matrix...</span> | |
| 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> | |
| 226 213 | |
| 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> | |
| 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> | |
| 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> | |
| 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">$k</span>]<span class="sc">;</span> | |
| 231 218 <span class="k">if</span> <span class="s">(</span><span class="i">$Valuejk</span> < <span class="i">$MatrixValuesRef</span>->[<span class="i">$j</span>][<span class="i">$k</span>]<span class="s">)</span> <span class="s">{</span> | |
| 232 219 <span class="i">$MatrixValuesRef</span>->[<span class="i">$j</span>][<span class="i">$k</span>] = <span class="i">$Valuejk</span><span class="sc">;</span> | |
| 233 220 <span class="s">}</span> | |
| 234 221 <span class="s">}</span> | |
| 235 222 <span class="s">}</span> | |
| 236 223 <span class="s">}</span> | |
| 237 224 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"DistanceMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span> | |
| 238 225 | |
| 239 226 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 240 227 <span class="s">}</span> | |
| 241 228 | |
| 242 229 <span class="c"># Generate the incidence matrix for a simple graph.</span> | |
| 243 230 <span class="c">#</span> | |
| 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> | |
| 245 232 <span class="c"># its elements Mij are:</span> | |
| 246 233 <span class="c">#</span> | |
| 247 234 <span class="c"># . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related</span> | |
| 248 235 <span class="c"># . 0 otherwise</span> | |
| 249 236 <span class="c">#</span> | |
| 250 <a name="GenerateIncidenceMatrix-"></a> 237 <span class="k">sub </span><span class="m">GenerateIncidenceMatrix</span> <span class="s">{</span> | |
| 251 238 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 252 239 <span class="k">my</span><span class="s">(</span><span class="i">$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> | |
| 253 240 | |
| 254 241 <span class="c"># Get graph vertices and edges...</span> | |
| 255 242 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span> | |
| 256 243 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 257 244 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> | |
| 258 245 | |
| 259 246 <span class="i">@EdgeVertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetEdges</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 260 247 <span class="i">$NumOfEdges</span> = <span class="i">@EdgeVertexIDs</span>/<span class="n">2</span><span class="sc">;</span> | |
| 261 248 | |
| 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> | |
| 263 250 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateIncidenceMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span> | |
| 264 251 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 265 252 <span class="s">}</span> | |
| 266 253 | |
| 267 254 <span class="c"># Create incidence matrix...</span> | |
| 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">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span> | |
| 269 256 | |
| 270 257 <span class="i">$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> | |
| 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> | |
| 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">$NumOfEdges</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> | |
| 277 264 <span class="i">$EdgeVertexID1</span> = <span class="i">$EdgeVertexIDs</span>[<span class="i">$EdgeVertexIndex</span>]<span class="sc">;</span> <span class="i">$EdgeVertexIndex</span>++<span class="sc">;</span> | |
| 278 265 <span class="i">$EdgeVertexID2</span> = <span class="i">$EdgeVertexIDs</span>[<span class="i">$EdgeVertexIndex</span>]<span class="sc">;</span> <span class="i">$EdgeVertexIndex</span>++<span class="sc">;</span> | |
| 279 266 | |
| 280 267 <span class="i">$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> | |
| 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">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span> | |
| 282 269 <span class="s">}</span> | |
| 283 270 <span class="s">}</span> | |
| 284 271 <span class="i">$This</span><span class="i">->_SetMatrixAndAssociatedInformation</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="q">"IncidenceMatrix"</span><span class="cm">,</span> \<span class="i">@VertexIDs</span><span class="cm">,</span> \<span class="i">@EdgeVertexIDs</span><span class="s">)</span><span class="sc">;</span> | |
| 285 272 | |
| 286 273 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 287 274 <span class="s">}</span> | |
| 288 275 | |
| 289 276 <span class="c"># Generate the degree matrix for a simple graph.</span> | |
| 290 277 <span class="c">#</span> | |
| 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> | |
| 293 280 <span class="c">#</span> | |
| 294 281 <span class="c"># . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi</span> | |
| 295 282 <span class="c"># . 0 otherwise</span> | |
| 296 283 <span class="c">#</span> | |
| 297 <a name="GenerateDegreeMatrix-"></a> 284 <span class="k">sub </span><span class="m">GenerateDegreeMatrix</span> <span class="s">{</span> | |
| 298 285 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 299 286 <span class="k">my</span><span class="s">(</span><span class="i">$Graph</span><span class="cm">,</span> <span class="i">$NumOfVertices</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="s">)</span><span class="sc">;</span> | |
| 300 287 | |
| 301 288 <span class="c"># Get graph vertices...</span> | |
| 302 289 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span> | |
| 303 290 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 304 291 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> | |
| 305 292 | |
| 306 293 <span class="k">if</span> <span class="s">(</span><span class="i">$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">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span> | |
| 313 300 | |
| 314 301 <span class="i">$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> | |
| 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> | |
| 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> | |
| 341 328 | |
| 342 329 <span class="c"># Get graph vertices...</span> | |
| 343 330 <span class="i">$Graph</span> = <span class="i">$This</span>->{<span class="w">Graph</span>}<span class="sc">;</span> | |
| 344 331 <span class="i">@VertexIDs</span> = <span class="i">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 345 332 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> | |
| 346 333 | |
| 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> | |
| 348 335 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}->GenerateLaplacianMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span> | |
| 349 336 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 350 337 <span class="s">}</span> | |
| 351 338 | |
| 352 339 <span class="c"># Create adjacency matrix...</span> | |
| 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">$SkipIndexCheck</span><span class="s">)</span><span class="sc">;</span> | |
| 354 341 | |
| 355 342 <span class="i">$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> | |
| 356 343 <span class="i">$SkipIndexCheck</span> = <span class="n">1</span><span class="sc">;</span> | |
| 357 344 | |
| 358 345 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfVertices</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> | |
| 359 346 <span class="i">$RowVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$RowIndex</span>]<span class="sc">;</span> | |
| 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> | |
| 361 348 <span class="i">$ColVertexID</span> = <span class="i">$VertexIDs</span>[<span class="i">$ColIndex</span>]<span class="sc">;</span> | |
| 362 349 <span class="i">$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">$ColVertexID</span><span class="s">)</span> ? <span class="n">-1</span> <span class="co">:</span> <span class="n">0</span><span class="s">)</span><span class="sc">;</span> | |
| 363 350 <span class="i">$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> | |
| 364 351 <span class="s">}</span> | |
| 365 352 <span class="s">}</span> | |
| 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> | |
| 367 354 | |
| 368 355 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 369 356 <span class="s">}</span> | |
| 370 357 | |
| 371 358 <span class="c"># Generate the normalized Laplacian matrix for a simple graph.</span> | |
| 372 359 <span class="c">#</span> | |
| 373 360 <span class="c"># For a simple graph G with n vertices, the normalized Laplacian matrix L for G is a n x n square matrix and</span> | |
| 374 361 <span class="c"># its elements Lij are:</span> | |
| 375 362 <span class="c">#</span> | |
| 376 363 <span class="c"># . 1 if i == j and deg(Vi) != 0</span> | |
| 377 364 <span class="c"># . -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj</span> | |
| 378 365 <span class="c"># . 0 otherwise</span> | |
| 379 366 <span class="c">#</span> | |
| 380 367 <span class="c">#</span> | |
| 381 <a name="GenerateNormalizedLaplacianMatrix-"></a> 368 <span class="k">sub </span><span class="m">GenerateNormalizedLaplacianMatrix</span> <span class="s">{</span> | |
| 382 369 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 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> | |
| 384 371 | |
| 385 372 <span class="c"># Get graph vertices...</span> | |
| 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">$Graph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> | |
| 388 375 <span class="i">$NumOfVertices</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> | |
| 389 376 | |
| 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: ${ClassName}->GenerateNormalizedLaplacianMatrix: Specified graph doesn't contain any vertices: No matrix generated..."</span><span class="sc">;</span> | |
| 392 379 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 393 380 <span class="s">}</span> | |
| 394 381 | |
| 395 382 <span class="c"># Create adjacency matrix...</span> | |
| 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> | |
| 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> | |
| 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}-${EdgeVertexID1}"</span><span class="sc">;</span> | |
| 501 488 | |
| 502 489 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}}<span class="cm">,</span> <span class="i">$EdgeID</span><span class="sc">;</span> | |
| 503 490 <span class="s">}</span> | |
| 504 491 <span class="s">}</span> | |
| 505 492 <span class="k">else</span> <span class="s">{</span> | |
| 506 493 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">ColumnIDs</span>}}<span class="cm">,</span> <span class="i">@</span>{<span class="i">$VertexIDsRef</span>}<span class="sc">;</span> | |
| 507 494 <span class="s">}</span> | |
| 508 495 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> | |
| 509 496 <span class="s">}</span> | |
| 510 497 | |
| 511 498 <span class="c"># Return a string containg data for GraphMatrix object...</span> | |
| 512 <a name="StringifyGraphMatrix-"></a> 499 <span class="k">sub </span><span class="m">StringifyGraphMatrix</span> <span class="s">{</span> | |
| 513 500 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> | |
| 514 501 <span class="k">my</span><span class="s">(</span><span class="i">$GraphMatrixString</span><span class="cm">,</span> <span class="i">$RowIDs</span><span class="s">)</span><span class="sc">;</span> | |
| 515 502 | |
| 516 503 <span class="i">$GraphMatrixString</span> = <span class="q">"GraphMatrix:"</span><span class="sc">;</span> | |
| 517 504 | |
| 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: $This->{MatrixType}"</span> <span class="co">:</span> <span class="q">"MatrixType: <Undefined>"</span><span class="sc">;</span> | |
| 519 506 <span class="i">$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> | |
| 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: @{$This->{ColumnIDs}}"</span> <span class="co">:</span> <span class="q">"; ColumnIDs: <Undefined>"</span><span class="sc">;</span> | |
| 521 508 | |
| 522 509 <span class="i">$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: $This->{Matrix}"</span> <span class="co">:</span> <span class="q">"; Matrix: <Undefined>"</span><span class="sc">;</span> | |
| 523 510 | |
| 524 511 <span class="k">return</span> <span class="i">$GraphMatrixString</span><span class="sc">;</span> | |
| 525 512 <span class="s">}</span> | |
| 526 513 | |
| 527 <a name="EOF-"></a></pre> | |
| 528 <p> </p> | |
| 529 <br /> | |
| 530 <center> | |
| 531 <img src="../../../images/h2o2.png"> | |
| 532 </center> | |
| 533 </body> | |
| 534 </html> |