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<html> <head> <title>MayaChemTools:Code:Matrix.pm</title> <meta http-equiv="content-type" content="text/html;charset=utf-8"> <link rel="stylesheet" type="text/css" href="../../../css/MayaChemToolsCode.css"> </head> <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10"> <br/> <center> <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a> </center> <br/> <pre> <a name="package-Matrix-"></a> 1 <span class="k">package </span><span class="i">Matrix</span><span class="sc">;</span> 2 <span class="c">#</span> 3 <span class="c"># $RCSfile: Matrix.pm,v $</span> 4 <span class="c"># $Date: 2015/02/28 20:47:17 $</span> 5 <span class="c"># $Revision: 1.16 $</span> 6 <span class="c">#</span> 7 <span class="c"># Author: Manish Sud <msud@san.rr.com></span> 8 <span class="c">#</span> 9 <span class="c"># Copyright (C) 2015 Manish Sud. All rights reserved.</span> 10 <span class="c">#</span> 11 <span class="c"># This file is part of MayaChemTools.</span> 12 <span class="c">#</span> 13 <span class="c"># MayaChemTools is free software; you can redistribute it and/or modify it under</span> 14 <span class="c"># the terms of the GNU Lesser General Public License as published by the Free</span> 15 <span class="c"># Software Foundation; either version 3 of the License, or (at your option) any</span> 16 <span class="c"># later version.</span> 17 <span class="c">#</span> 18 <span class="c"># MayaChemTools is distributed in the hope that it will be useful, but without</span> 19 <span class="c"># any warranty; without even the implied warranty of merchantability of fitness</span> 20 <span class="c"># for a particular purpose. See the GNU Lesser General Public License for more</span> 21 <span class="c"># details.</span> 22 <span class="c">#</span> 23 <span class="c"># You should have received a copy of the GNU Lesser General Public License</span> 24 <span class="c"># along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or</span> 25 <span class="c"># write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,</span> 26 <span class="c"># Boston, MA, 02111-1307, USA.</span> 27 <span class="c">#</span> 28 29 <span class="k">use</span> <span class="w">strict</span><span class="sc">;</span> 30 <span class="k">use</span> <span class="w">Carp</span><span class="sc">;</span> 31 <span class="k">use</span> <span class="w">Exporter</span><span class="sc">;</span> 32 <span class="k">use</span> <span class="w">Scalar::Util</span> <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 33 <span class="k">use</span> <span class="w">Vector</span><span class="sc">;</span> 34 35 <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> 36 37 <span class="i">@ISA</span> = <span class="q">qw(Exporter)</span><span class="sc">;</span> 38 <span class="i">@EXPORT</span> = <span class="q">qw(IsMatrix IdentityMatrix NewFromRows NewFromColumns NewFromDiagonal UnitMatrix ZeroMatrix)</span><span class="sc">;</span> 39 <span class="i">@EXPORT_OK</span> = <span class="q">qw(SetValuePrintFormat)</span><span class="sc">;</span> 40 41 <span class="i">%EXPORT_TAGS</span> = <span class="s">(</span> 42 <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> 43 <span class="s">)</span><span class="sc">;</span> 44 45 <span class="c"># Setup class variables...</span> 46 <span class="k">my</span><span class="s">(</span><span class="i">$ClassName</span><span class="cm">,</span> <span class="i">$ValueFormat</span><span class="cm">,</span> <span class="i">$MatrixPrintStyle</span><span class="s">)</span><span class="sc">;</span> 47 <span class="i">_InitializeClass</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 48 49 <span class="c">#</span> 50 <span class="c"># Using the following explicity overloaded operators, Perl automatically generates methods</span> 51 <span class="c"># for operations with no explicitly defined methods. Autogenerated methods are possible for</span> 52 <span class="c"># these operators:</span> 53 <span class="c">#</span> 54 <span class="c"># o Arithmetic operators: += -= *= /= **= %= ++ -- x= .=</span> 55 <span class="c"># o Increment and decrement: ++ --</span> 56 <span class="c">#</span> 57 <span class="c"># 'fallback' is set to 'false' to raise exception for all other operators.</span> 58 <span class="c">#</span> 59 <span class="k">use</span> <span class="w">overload</span> <span class="q">'""'</span> <span class="cm">=></span> <span class="q">'StringifyMatrix'</span><span class="cm">,</span> 60 61 <span class="q">'@{}'</span> <span class="cm">=></span> <span class="q">'_MatrixToArrayOperator'</span><span class="cm">,</span> 62 63 <span class="q">'+'</span> <span class="cm">=></span> <span class="q">'_MatrixAdditionOperator'</span><span class="cm">,</span> 64 <span class="q">'-'</span> <span class="cm">=></span> <span class="q">'_MatrixSubtractionOperator'</span><span class="cm">,</span> 65 <span class="q">'*'</span> <span class="cm">=></span> <span class="q">'_MatrixMultiplicationOperator'</span><span class="cm">,</span> 66 <span class="q">'/'</span> <span class="cm">=></span> <span class="q">'_MatrixDivisionOperator'</span><span class="cm">,</span> 67 <span class="q">'**'</span> <span class="cm">=></span> <span class="q">'_MatrixExponentiationOperator'</span><span class="cm">,</span> 68 <span class="q">'%'</span> <span class="cm">=></span> <span class="q">'_MatrixModulusOperator'</span><span class="cm">,</span> 69 70 <span class="q">'bool'</span> <span class="cm">=></span> <span class="q">'_MatrixBooleanOperator'</span><span class="cm">,</span> 71 <span class="q">'!'</span> <span class="cm">=></span> <span class="q">'_MatrixNotBooleanOperator'</span><span class="cm">,</span> 72 73 <span class="q">'=='</span> <span class="cm">=></span> <span class="q">'_MatrixEqualOperator'</span><span class="cm">,</span> 74 <span class="q">'!='</span> <span class="cm">=></span> <span class="q">'_MatrixNotEqualOperator'</span><span class="cm">,</span> 75 <span class="q">'<'</span> <span class="cm">=></span> <span class="q">'_MatrixLessThanOperator'</span><span class="cm">,</span> 76 <span class="q">'<='</span> <span class="cm">=></span> <span class="q">'_MatrixLessThanEqualOperator'</span><span class="cm">,</span> 77 <span class="q">'>'</span> <span class="cm">=></span> <span class="q">'_MatrixGreatarThanOperator'</span><span class="cm">,</span> 78 <span class="q">'>='</span> <span class="cm">=></span> <span class="q">'_MatrixGreatarThanEqualOperator'</span><span class="cm">,</span> 79 80 <span class="q">'neg'</span> <span class="cm">=></span> <span class="q">'_MatrixNegativeValueOperator'</span><span class="cm">,</span> 81 82 <span class="q">'abs'</span> <span class="cm">=></span> <span class="q">'_MatrixAbsoluteValueOperator'</span><span class="cm">,</span> 83 <span class="q">'exp'</span> <span class="cm">=></span> <span class="q">'_MatrixExpNaturalBaseOperator'</span><span class="cm">,</span> 84 <span class="q">'log'</span> <span class="cm">=></span> <span class="q">'_MatrixLogNaturalBaseOperator'</span><span class="cm">,</span> 85 <span class="q">'sqrt'</span> <span class="cm">=></span> <span class="q">'_MatrixSquareRootOperator'</span><span class="cm">,</span> 86 <span class="q">'cos'</span> <span class="cm">=></span> <span class="q">'_MatrixCosineOperator'</span><span class="cm">,</span> 87 <span class="q">'sin'</span> <span class="cm">=></span> <span class="q">'_MatrixSineOperator'</span><span class="cm">,</span> 88 89 <span class="q">'fallback'</span> <span class="cm">=></span> <span class="k">undef</span><span class="sc">;</span> 90 91 <span class="c"># Class constructor...</span> <a name="new-"></a> 92 <span class="k">sub </span><span class="m">new</span> <span class="s">{</span> 93 <span class="k">my</span><span class="s">(</span><span class="i">$Class</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 94 95 <span class="c"># Initialize object...</span> 96 <span class="k">my</span> <span class="i">$This</span> = <span class="s">{</span><span class="s">}</span><span class="sc">;</span> 97 <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">$Class</span><span class="sc">;</span> 98 <span class="i">$This</span><span class="i">->_InitializeMatrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 99 100 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 101 <span class="s">}</span> 102 103 <span class="c"># Initialize object data...</span> 104 <span class="c">#</span> <a name="_InitializeMatrix-"></a> 105 <span class="k">sub </span><span class="m">_InitializeMatrix</span> <span class="s">{</span> 106 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 107 108 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="s">)</span> && <span class="k">defined</span><span class="s">(</span><span class="i">$NumOfCols</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 109 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->_InitializeMatrix: NumOfRows and NumOfCols must be specified..."</span><span class="sc">;</span> 110 <span class="s">}</span> 111 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="s">(</span><span class="i">$NumOfRows</span> > <span class="n">0</span><span class="s">)</span> && <span class="s">(</span><span class="i">$NumOfRows</span> > <span class="n">0</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 112 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->_InitializeMatrix: NumOfRows and NumOfCols must be a positive number..."</span><span class="sc">;</span> 113 <span class="s">}</span> 114 <span class="c"># Initialize matrix elements to zero...</span> 115 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">Values</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 116 117 <span class="k">my</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">@EmptyRow</span><span class="s">)</span><span class="sc">;</span> 118 119 <span class="i">@EmptyRow</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 120 <span class="i">@EmptyRow</span> = <span class="s">(</span><span class="q">'0'</span><span class="s">)</span> x <span class="i">$NumOfCols</span><span class="sc">;</span> 121 122 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 123 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>]} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 124 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>]} = <span class="i">@EmptyRow</span><span class="sc">;</span> 125 <span class="s">}</span> 126 <span class="s">}</span> 127 128 <span class="c"># Initialize class ...</span> <a name="_InitializeClass-"></a> 129 <span class="k">sub </span><span class="m">_InitializeClass</span> <span class="s">{</span> 130 <span class="c">#Class name...</span> 131 <span class="i">$ClassName</span> = <span class="w">__PACKAGE__</span><span class="sc">;</span> 132 133 <span class="c"># Print style for matrix rows during StringifyMatrix operation.</span> 134 <span class="c"># Possible values: AllRowsInOneLine, OneRowPerLine</span> 135 <span class="c">#</span> 136 <span class="i">$MatrixPrintStyle</span> = <span class="q">"AllRowsInOneLine"</span><span class="sc">;</span> 137 138 <span class="c"># Print format for matrix values...</span> 139 <span class="i">$ValueFormat</span> = <span class="q">"%g"</span><span class="sc">;</span> 140 <span class="s">}</span> 141 142 <span class="c"># Get matrix size...</span> 143 <span class="c">#</span> <a name="GetSize-"></a> 144 <span class="k">sub </span><span class="m">GetSize</span> <span class="s">{</span> 145 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 146 147 <span class="k">return</span> <span class="s">(</span><span class="i">$This</span><span class="i">->GetNumOfRows</span><span class="s">(</span><span class="s">)</span><span class="cm">,</span> <span class="i">$This</span><span class="i">->GetNumOfColumns</span><span class="s">(</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span> 148 <span class="s">}</span> 149 150 <span class="c"># Get matrix dimensions...</span> 151 <span class="c">#</span> <a name="GetDimension-"></a> 152 <span class="k">sub </span><span class="m">GetDimension</span> <span class="s">{</span> 153 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 154 155 <span class="k">return</span> <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 156 <span class="s">}</span> 157 158 <span class="c"># Get number of rows in matrix</span> 159 <span class="c">#</span> <a name="GetNumOfRows-"></a> 160 <span class="k">sub </span><span class="m">GetNumOfRows</span> <span class="s">{</span> 161 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 162 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="s">)</span><span class="sc">;</span> 163 164 <span class="c"># Size of row array...</span> 165 <span class="i">$NumOfRows</span> = <span class="i">$#</span>{<span class="i">$This</span>->{<span class="w">Values</span>}} + <span class="n">1</span><span class="sc">;</span> 166 167 <span class="k">return</span> <span class="i">$NumOfRows</span><span class="sc">;</span> 168 <span class="s">}</span> 169 170 <span class="c"># Get number of columns in matrix</span> 171 <span class="c">#</span> <a name="GetNumOfColumns-"></a> 172 <span class="k">sub </span><span class="m">GetNumOfColumns</span> <span class="s">{</span> 173 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 174 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 175 176 <span class="c"># Size of column array for first row assuming sizes of columns are same...</span> 177 <span class="i">$NumOfCols</span> = <span class="i">$#</span>{<span class="i">$This</span>->{<span class="w">Values</span>}[<span class="n">0</span>]} + <span class="n">1</span><span class="sc">;</span> 178 179 <span class="k">return</span> <span class="i">$NumOfCols</span><span class="sc">;</span> 180 <span class="s">}</span> 181 182 <span class="c"># Get reference to array holding matrix values in order to directly manipulate these values...</span> 183 <span class="c">#</span> <a name="GetMatrixValuesReference-"></a> 184 <span class="k">sub </span><span class="m">GetMatrixValuesReference</span> <span class="s">{</span> 185 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 186 187 <span class="k">return</span> \<span class="i">@</span>{<span class="i">$This</span>->{<span class="w">Values</span>}}<span class="sc">;</span> 188 <span class="s">}</span> 189 190 <span class="c"># Copy matrix...</span> 191 <span class="c">#</span> <a name="Copy-"></a> 192 <span class="k">sub </span><span class="m">Copy</span> <span class="s">{</span> 193 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 194 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Matrix</span><span class="s">)</span><span class="sc">;</span> 195 196 <span class="c"># Create a new matrix...</span> 197 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 198 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 199 200 <span class="c"># Set matrix values...</span> 201 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> -<span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 202 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> -<span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 203 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 204 <span class="s">}</span> 205 <span class="s">}</span> 206 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 207 <span class="s">}</span> 208 209 <span class="c"># Create a new matrix using rows specified in one of the following formats:</span> 210 <span class="c"># o List of vector objects</span> 211 <span class="c"># o References to list of values</span> 212 <span class="c"># o List of strings containing row values delimited by space</span> 213 <span class="c">#</span> 214 <span class="c"># Each row must contain the same number of values.</span> 215 <span class="c">#</span> 216 <span class="c"># This functionality can be either invoked as a class function or an</span> 217 <span class="c"># object method.</span> 218 <span class="c">#</span> <a name="NewFromRows-"></a> 219 <span class="k">sub </span><span class="m">NewFromRows</span> <span class="s">{</span> 220 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">@OtherParamaters</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 221 222 <span class="k">if</span> <span class="s">(</span><span class="i">IsMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 223 <span class="k">return</span> <span class="i">_NewFromRowsOrColumns</span><span class="s">(</span><span class="q">'FromRows'</span><span class="cm">,</span> <span class="i">@OtherParamaters</span><span class="s">)</span><span class="sc">;</span> 224 <span class="s">}</span> 225 <span class="k">else</span> <span class="s">{</span> 226 <span class="k">return</span> <span class="i">_NewFromRowsOrColumns</span><span class="s">(</span><span class="q">'FromRows'</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 227 <span class="s">}</span> 228 <span class="s">}</span> 229 230 <span class="c"># Create a new matrix using columns specified in one of the following formats:</span> 231 <span class="c"># o List of vector objects</span> 232 <span class="c"># o References to list of values</span> 233 <span class="c"># o List of strings containing columns values delimited by space</span> 234 <span class="c">#</span> 235 <span class="c"># Each columns must contain the same number of values.</span> 236 <span class="c">#</span> 237 <span class="c"># This functionality can be either invoked as a class function or an</span> 238 <span class="c"># object method.</span> 239 <span class="c">#</span> <a name="NewFromColumns-"></a> 240 <span class="k">sub </span><span class="m">NewFromColumns</span> <span class="s">{</span> 241 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">@OtherParamaters</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 242 243 <span class="k">if</span> <span class="s">(</span><span class="i">IsMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 244 <span class="k">return</span> <span class="i">_NewFromRowsOrColumns</span><span class="s">(</span><span class="q">'FromColumns'</span><span class="cm">,</span> <span class="i">@OtherParamaters</span><span class="s">)</span><span class="sc">;</span> 245 <span class="s">}</span> 246 <span class="k">else</span> <span class="s">{</span> 247 <span class="k">return</span> <span class="i">_NewFromRowsOrColumns</span><span class="s">(</span><span class="q">'FromColumns'</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 248 <span class="s">}</span> 249 <span class="s">}</span> 250 251 <span class="c"># Create a new matrix using diagonal values specified in one of the following formats:</span> 252 <span class="c"># o A vector object</span> 253 <span class="c"># o Reference to list of values</span> 254 <span class="c"># o Strings containing diagonal values delimited by space</span> 255 <span class="c">#</span> 256 <span class="c"># This functionality can be either invoked as a class function or an</span> 257 <span class="c"># object method.</span> 258 <span class="c">#</span> <a name="NewFromDiagonal-"></a> 259 <span class="k">sub </span><span class="m">NewFromDiagonal</span> <span class="s">{</span> 260 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">@OtherParamaters</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 261 262 <span class="k">if</span> <span class="s">(</span><span class="i">IsMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 263 <span class="k">return</span> <span class="i">_NewFromDiagonal</span><span class="s">(</span><span class="i">@OtherParamaters</span><span class="s">)</span><span class="sc">;</span> 264 <span class="s">}</span> 265 <span class="k">else</span> <span class="s">{</span> 266 <span class="k">return</span> <span class="i">_NewFromDiagonal</span><span class="s">(</span><span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 267 <span class="s">}</span> 268 <span class="s">}</span> 269 270 <span class="c"># Create a new matrix using diagonal values specified in one of the following formats:</span> 271 <span class="c"># o A vector object</span> 272 <span class="c"># o Reference to list of values</span> 273 <span class="c"># o Strings containing diagonal values delimited by space</span> 274 <span class="c">#</span> <a name="_NewFromDiagonal-"></a> 275 <span class="k">sub </span><span class="m">_NewFromDiagonal</span> <span class="s">{</span> 276 <span class="k">my</span><span class="s">(</span><span class="i">@SpecifiedDiagonalValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 277 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">$ValuesRefs</span><span class="cm">,</span> <span class="i">$DiagonalValuesRef</span><span class="s">)</span><span class="sc">;</span> 278 279 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}::_NewFromDiagonal"</span><span class="sc">;</span> 280 <span class="k">if</span> <span class="s">(</span>!<span class="i">@SpecifiedDiagonalValues</span><span class="s">)</span> <span class="s">{</span> 281 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: No diagonal values specified..."</span><span class="sc">;</span> 282 <span class="s">}</span> 283 284 <span class="c"># Collect specified diagonal values...</span> 285 <span class="i">$CheckSizes</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$CombineValues</span> = <span class="n">1</span><span class="sc">;</span> 286 <span class="i">$ValuesRefs</span> = <span class="i">_ProcessSpecifiedMatrixValues</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">@SpecifiedDiagonalValues</span><span class="s">)</span><span class="sc">;</span> 287 <span class="i">$DiagonalValuesRef</span> = <span class="i">$ValuesRefs</span>->[<span class="n">0</span>]<span class="sc">;</span> 288 289 <span class="c"># Create a new matrix...</span> 290 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 291 292 <span class="i">$NumOfRows</span> = <span class="i">@</span>{<span class="i">$DiagonalValuesRef</span>}<span class="sc">;</span> 293 <span class="i">$NumOfCols</span> = <span class="i">$NumOfRows</span><span class="sc">;</span> 294 295 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 296 297 <span class="c"># Set diagonal values...</span> 298 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 299 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$RowIndex</span>] = <span class="i">$DiagonalValuesRef</span>->[<span class="i">$RowIndex</span>]<span class="sc">;</span> 300 <span class="s">}</span> 301 302 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 303 <span class="s">}</span> 304 305 <span class="c"># Create a new matrix using rows or columns specified in one of the following formats:</span> 306 <span class="c"># o List of vector objects</span> 307 <span class="c"># o References to list of values</span> 308 <span class="c"># o List of strings containing row values delimited by space</span> 309 <span class="c">#</span> 310 <span class="c"># Each row or column must contain the same number of values.</span> 311 <span class="c">#</span> <a name="_NewFromRowsOrColumns-"></a> 312 <span class="k">sub </span><span class="m">_NewFromRowsOrColumns</span> <span class="s">{</span> 313 <span class="k">my</span><span class="s">(</span><span class="i">$Mode</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 314 315 <span class="k">if</span> <span class="s">(</span><span class="i">$Mode</span> !~ <span class="q">/^(FromRows|FromColumns)$/i</span><span class="s">)</span> <span class="s">{</span> 316 <span class="w">croak</span> <span class="q">"Error: ${ClassName}::_NewFromRowsOrColumns: Unknown mode: $Mode..."</span><span class="sc">;</span> 317 <span class="s">}</span> 318 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">$ValuesRefs</span><span class="s">)</span><span class="sc">;</span> 319 320 <span class="c"># Retrieve information about specified values and make sure similar number of values</span> 321 <span class="c"># are specified for each row or column...</span> 322 <span class="k">if</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^FromRows$/i</span><span class="s">)</span> <span class="s">{</span> 323 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}::_NewFromRows"</span><span class="sc">;</span> 324 <span class="s">}</span> 325 <span class="k">else</span> <span class="s">{</span> 326 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}::_NewFromColumns"</span><span class="sc">;</span> 327 <span class="s">}</span> 328 <span class="i">$CheckSizes</span> = <span class="n">1</span><span class="sc">;</span> <span class="i">$CombineValues</span> = <span class="n">0</span><span class="sc">;</span> 329 <span class="i">$ValuesRefs</span> = <span class="i">_ProcessSpecifiedMatrixValues</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span><span class="sc">;</span> 330 331 <span class="c"># Create a new matrix...</span> 332 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</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">$RowMode</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 333 334 <span class="k">if</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^FromRows$/i</span><span class="s">)</span> <span class="s">{</span> 335 <span class="i">$NumOfRows</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$ValuesRefs</span>}<span class="sc">;</span> 336 <span class="i">$NumOfCols</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$ValuesRefs</span>->[<span class="n">0</span>]}<span class="sc">;</span> 337 <span class="i">$RowMode</span> = <span class="n">1</span><span class="sc">;</span> 338 <span class="s">}</span> 339 <span class="k">elsif</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^FromColumns$/i</span><span class="s">)</span> <span class="s">{</span> 340 <span class="i">$NumOfRows</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$ValuesRefs</span>->[<span class="n">0</span>]}<span class="sc">;</span> 341 <span class="i">$NumOfCols</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$ValuesRefs</span>}<span class="sc">;</span> 342 <span class="i">$RowMode</span> = <span class="n">0</span><span class="sc">;</span> 343 <span class="s">}</span> 344 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 345 346 <span class="c"># Setup matrix values...</span> 347 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 348 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 349 <span class="i">$Value</span> = <span class="i">$RowMode</span> ? <span class="i">$ValuesRefs</span>->[<span class="i">$RowIndex</span>]->[<span class="i">$ColIndex</span>]<span class="co">:</span> <span class="i">$ValuesRefs</span>->[<span class="i">$ColIndex</span>]->[<span class="i">$RowIndex</span>]<span class="sc">;</span> 350 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$Value</span><span class="sc">;</span> 351 <span class="s">}</span> 352 <span class="s">}</span> 353 354 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 355 <span class="s">}</span> 356 357 <span class="c"># Process specified matrix values in any of the following supported formats:</span> 358 <span class="c">#</span> 359 <span class="c"># o List of vector objects</span> 360 <span class="c"># o References to list of values</span> 361 <span class="c"># o List of strings containing row values delimited by space</span> 362 <span class="c">#</span> 363 <span class="c"># And return a reference to an array containing references to arrays with specified values.</span> 364 <span class="c">#</span> 365 <span class="c"># Value of CombineValuesStatus determines whether all the values specified are combined</span> 366 <span class="c"># into one array and return its reference as the only entry in the array being returned.</span> 367 <span class="c">#</span> <a name="_ProcessSpecifiedMatrixValues-"></a> 368 <span class="k">sub </span><span class="m">_ProcessSpecifiedMatrixValues</span> <span class="s">{</span> 369 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizesStatus</span><span class="cm">,</span> <span class="i">$CombineValuesStatus</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 370 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="cm">,</span> <span class="i">$TypeOfValue</span><span class="cm">,</span> <span class="i">@ValuesRefs</span><span class="s">)</span><span class="sc">;</span> 371 372 <span class="i">@ValuesRefs</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 373 <span class="k">if</span> <span class="s">(</span>!<span class="i">@SpecifiedValues</span><span class="s">)</span> <span class="s">{</span> 374 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: No values specified..."</span><span class="sc">;</span> 375 <span class="s">}</span> 376 377 <span class="c"># Collect values...</span> 378 <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@SpecifiedValues</span><span class="s">)</span> <span class="s">{</span> 379 <span class="i">$TypeOfValue</span> = <span class="k">ref</span> <span class="i">$Value</span><span class="sc">;</span> 380 381 <span class="k">if</span> <span class="s">(</span><span class="i">Vector::IsVector</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 382 <span class="c"># Feference to vector object...</span> 383 <span class="k">my</span><span class="s">(</span><span class="i">$ValuesRef</span><span class="s">)</span><span class="sc">;</span> 384 <span class="i">$ValuesRef</span> = <span class="i">$Value</span><span class="i">->GetValues</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 385 <span class="k">if</span> <span class="s">(</span>!<span class="i">@</span>{<span class="i">$ValuesRef</span>}<span class="s">)</span> <span class="s">{</span> 386 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Specified vector object must contain some values..."</span><span class="sc">;</span> 387 <span class="s">}</span> 388 <span class="k">push</span> <span class="i">@ValuesRefs</span><span class="cm">,</span> <span class="i">$ValuesRef</span><span class="sc">;</span> 389 <span class="s">}</span> 390 <span class="k">elsif</span> <span class="s">(</span><span class="i">$TypeOfValue</span> =~ <span class="q">/^ARRAY/</span><span class="s">)</span> <span class="s">{</span> 391 <span class="c"># Refernece to an array...</span> 392 <span class="k">if</span> <span class="s">(</span>!<span class="i">@</span>{<span class="i">$Value</span>}<span class="s">)</span> <span class="s">{</span> 393 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Specified array reference must contain some values..."</span><span class="sc">;</span> 394 <span class="s">}</span> 395 <span class="k">push</span> <span class="i">@ValuesRefs</span><span class="cm">,</span> <span class="i">$Value</span><span class="sc">;</span> 396 <span class="s">}</span> 397 <span class="k">elsif</span> <span class="s">(</span><span class="i">$TypeOfValue</span> <span class="k">eq</span> <span class="q">''</span><span class="s">)</span> <span class="s">{</span> 398 <span class="c"># String value...</span> 399 <span class="k">my</span><span class="s">(</span><span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 400 <span class="i">@Values</span> = <span class="k">split</span><span class="s">(</span><span class="q">' '</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 401 <span class="k">if</span> <span class="s">(</span>!<span class="i">@Values</span><span class="s">)</span> <span class="s">{</span> 402 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Specified string must contain some values..."</span><span class="sc">;</span> 403 <span class="s">}</span> 404 <span class="k">push</span> <span class="i">@ValuesRefs</span><span class="cm">,</span> \<span class="i">@Values</span><span class="sc">;</span> 405 <span class="s">}</span> 406 <span class="k">else</span> <span class="s">{</span> 407 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Value format, $TypeOfValue, of a specified value to be added to matrix object is not supported..."</span><span class="sc">;</span> 408 <span class="s">}</span> 409 <span class="s">}</span> 410 411 <span class="c"># Combine all specified values into one array...</span> 412 <span class="k">if</span> <span class="s">(</span><span class="i">$CombineValuesStatus</span><span class="s">)</span> <span class="s">{</span> 413 <span class="k">my</span><span class="s">(</span><span class="i">$ValuesRef</span><span class="cm">,</span> <span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 414 415 <span class="i">@Values</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 416 <span class="k">for</span> <span class="i">$ValuesRef</span> <span class="s">(</span><span class="i">@ValuesRefs</span><span class="s">)</span> <span class="s">{</span> 417 <span class="k">push</span> <span class="i">@Values</span><span class="cm">,</span> <span class="i">@</span>{<span class="i">$ValuesRef</span>}<span class="sc">;</span> 418 <span class="s">}</span> 419 <span class="i">@ValuesRefs</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 420 <span class="k">push</span> <span class="i">@ValuesRefs</span><span class="cm">,</span> \<span class="i">@Values</span><span class="sc">;</span> 421 <span class="s">}</span> 422 423 <span class="c"># Make sure reference to all specified value arrays contain the same number of values...</span> 424 <span class="k">if</span> <span class="s">(</span><span class="i">$CheckSizesStatus</span><span class="s">)</span> <span class="s">{</span> 425 <span class="k">my</span><span class="s">(</span><span class="i">$Index</span><span class="cm">,</span> <span class="i">$FirstValueSize</span><span class="s">)</span><span class="sc">;</span> 426 <span class="i">$FirstValueSize</span> = <span class="i">$#</span>{<span class="i">$ValuesRefs</span>[<span class="n">0</span>]}<span class="sc">;</span> 427 <span class="k">for</span> <span class="i">$Index</span> <span class="s">(</span><span class="n">1</span> .. <span class="i">$#ValuesRefs</span><span class="s">)</span> <span class="s">{</span> 428 <span class="k">if</span> <span class="s">(</span><span class="i">$FirstValueSize</span> != <span class="i">$#</span>{<span class="i">$ValuesRefs</span>[<span class="i">$Index</span>]}<span class="s">)</span> <span class="s">{</span> 429 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Number of values in each specified value type to be added to matrix object must be same..."</span><span class="sc">;</span> 430 <span class="s">}</span> 431 <span class="s">}</span> 432 <span class="s">}</span> 433 434 <span class="k">return</span> \<span class="i">@ValuesRefs</span><span class="sc">;</span> 435 <span class="s">}</span> 436 437 <span class="c"># Create a new zero matrix of specified size or default size of 3 x 3.</span> 438 <span class="c">#</span> 439 <span class="c"># This functionality can be either invoked as a class function or an</span> 440 <span class="c"># object method.</span> 441 <span class="c">#</span> <a name="ZeroMatrix-"></a> 442 <span class="k">sub </span><span class="m">ZeroMatrix (;$$$)</span> <span class="s">{</span> 443 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="cm">,</span> <span class="i">$ThirdParameter</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 444 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$Matrix</span><span class="s">)</span><span class="sc">;</span> 445 446 <span class="i">$This</span> = <span class="k">undef</span><span class="sc">;</span> 447 <span class="k">if</span> <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span> && <span class="i">IsMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 448 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="cm">,</span> <span class="i">$ThirdParameter</span><span class="s">)</span><span class="sc">;</span> 449 <span class="s">}</span> 450 <span class="k">else</span> <span class="s">{</span> 451 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="s">(</span><span class="k">undef</span><span class="cm">,</span> <span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="s">)</span><span class="sc">;</span> 452 <span class="s">}</span> 453 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="s">)</span> && <span class="k">defined</span><span class="s">(</span><span class="i">$NumOfCols</span><span class="s">)</span><span class="s">)</span> ? <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> <span class="co">:</span> <span class="s">(</span><span class="n">3</span><span class="cm">,</span> <span class="n">3</span><span class="s">)</span><span class="sc">;</span> 454 455 <span class="c"># Set up a new zero matrix</span> 456 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 457 458 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 459 <span class="s">}</span> 460 461 <span class="c"># Create a new unit matrix of specified size or default size of 3 x 3.</span> 462 <span class="c">#</span> 463 <span class="c"># This functionality can be either invoked as a class function or an</span> 464 <span class="c"># object method.</span> 465 <span class="c">#</span> <a name="UnitMatrix-"></a> 466 <span class="k">sub </span><span class="m">UnitMatrix (;$$$)</span> <span class="s">{</span> 467 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="cm">,</span> <span class="i">$ThirdParameter</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 468 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 469 470 <span class="i">$This</span> = <span class="k">undef</span><span class="sc">;</span> 471 <span class="k">if</span> <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span> && <span class="i">IsMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 472 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="cm">,</span> <span class="i">$ThirdParameter</span><span class="s">)</span><span class="sc">;</span> 473 <span class="s">}</span> 474 <span class="k">else</span> <span class="s">{</span> 475 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="s">(</span><span class="k">undef</span><span class="cm">,</span> <span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="s">)</span><span class="sc">;</span> 476 <span class="s">}</span> 477 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="s">)</span> && <span class="k">defined</span><span class="s">(</span><span class="i">$NumOfCols</span><span class="s">)</span><span class="s">)</span> ? <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> <span class="co">:</span> <span class="s">(</span><span class="n">3</span><span class="cm">,</span> <span class="n">3</span><span class="s">)</span><span class="sc">;</span> 478 479 <span class="c"># Set up a new zero matrix</span> 480 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 481 482 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfRows</span> != <span class="i">$NumOfCols</span><span class="s">)</span> <span class="s">{</span> 483 <span class="w">carp</span> <span class="q">"Warning: ${ClassName}::UnitMatrix: Specified matrix, $NumOfRows x $NumOfCols, is not a square matrix..."</span><span class="sc">;</span> 484 <span class="s">}</span> 485 486 <span class="c"># Initialize diagonal elements to 1...</span> 487 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 488 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$RowIndex</span>] = <span class="n">1.0</span><span class="sc">;</span> 489 <span class="s">}</span> 490 491 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 492 <span class="s">}</span> 493 494 <span class="c"># Identity matrix of specified size or size 3 x 3...</span> 495 <span class="c">#</span> <a name="IdentityMatrix-"></a> 496 <span class="k">sub </span><span class="m">IdentityMatrix (;$$$)</span> <span class="s">{</span> 497 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="cm">,</span> <span class="i">$ThirdParameter</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 498 499 <span class="k">return</span> <span class="i">UnitMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="cm">,</span> <span class="i">$ThirdParameter</span><span class="s">)</span><span class="sc">;</span> 500 <span class="s">}</span> 501 502 <span class="c"># Set all matrix values to 0s...</span> 503 <span class="c">#</span> <a name="Zero-"></a> 504 <span class="k">sub </span><span class="m">Zero</span> <span class="s">{</span> 505 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 506 507 <span class="k">return</span> <span class="i">$This</span><span class="i">->SetAllValues</span><span class="s">(</span><span class="n">0.0</span><span class="s">)</span><span class="sc">;</span> 508 <span class="s">}</span> 509 510 <span class="c"># Set all matrix values to 1s...</span> 511 <span class="c">#</span> <a name="One-"></a> 512 <span class="k">sub </span><span class="m">One</span> <span class="s">{</span> 513 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 514 515 <span class="k">return</span> <span class="i">$This</span><span class="i">->SetAllValues</span><span class="s">(</span><span class="n">1.0</span><span class="s">)</span><span class="sc">;</span> 516 <span class="s">}</span> 517 518 <span class="c"># Get a matrix value with row and column indicies starting from 0...</span> 519 <span class="c">#</span> <a name="GetValue-"></a> 520 <span class="k">sub </span><span class="m">GetValue</span> <span class="s">{</span> 521 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 522 523 <span class="k">if</span> <span class="s">(</span><span class="i">$SkipIndexCheck</span><span class="s">)</span> <span class="s">{</span> 524 <span class="i">$This</span><span class="i">->_GetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 525 <span class="s">}</span> 526 527 <span class="i">$This</span><span class="i">->_ValidateRowAndColumnIndicies</span><span class="s">(</span><span class="q">"Error: ${ClassName}::GetValue"</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 528 529 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 530 <span class="s">}</span> 531 532 <span class="c"># Get a matrix value...</span> 533 <span class="c">#</span> <a name="_GetValue-"></a> 534 <span class="k">sub </span><span class="m">_GetValue</span> <span class="s">{</span> 535 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 536 537 <span class="k">return</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 538 <span class="s">}</span> 539 540 <span class="c"># Set a matrix value with row and column indicies starting from 0...</span> 541 <span class="c">#</span> <a name="SetValue-"></a> 542 <span class="k">sub </span><span class="m">SetValue</span> <span class="s">{</span> 543 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SkipIndexCheck</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 544 545 <span class="k">if</span> <span class="s">(</span><span class="i">$SkipIndexCheck</span><span class="s">)</span> <span class="s">{</span> 546 <span class="i">$This</span><span class="i">->_SetValue</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 547 <span class="s">}</span> 548 549 <span class="i">$This</span><span class="i">->_ValidateRowAndColumnIndicies</span><span class="s">(</span><span class="q">"Error: ${ClassName}::SetValue"</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 550 551 <span class="k">return</span> <span class="i">$This</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">$Value</span><span class="s">)</span><span class="sc">;</span> 552 <span class="s">}</span> 553 554 <span class="c"># Set a matrix value...</span> 555 <span class="c">#</span> <a name="_SetValue-"></a> 556 <span class="k">sub </span><span class="m">_SetValue</span> <span class="s">{</span> 557 <span class="k">my</span><span class="s">(</span><span class="i">$This</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">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 558 559 <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$Value</span><span class="sc">;</span> 560 561 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 562 <span class="s">}</span> 563 564 <span class="c"># Set all matrix values to a specified value...</span> 565 <span class="c">#</span> <a name="SetAllValues-"></a> 566 <span class="k">sub </span><span class="m">SetAllValues</span> <span class="s">{</span> 567 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 568 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 569 570 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 571 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 572 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 573 <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$Value</span><span class="sc">;</span> 574 <span class="s">}</span> 575 <span class="s">}</span> 576 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 577 <span class="s">}</span> 578 579 <span class="c"># Set values of a row in a matrix value with row index starting from 0...</span> 580 <span class="c">#</span> <a name="SetRowValues-"></a> 581 <span class="k">sub </span><span class="m">SetRowValues</span> <span class="s">{</span> 582 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 583 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">$ValuesRefs</span><span class="cm">,</span> <span class="i">$RowValuesRef</span><span class="cm">,</span> <span class="i">$NumOfRowValues</span><span class="s">)</span><span class="sc">;</span> 584 585 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}->SetRowValues"</span><span class="sc">;</span> 586 587 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 588 <span class="i">$This</span><span class="i">->_ValidateRowIndex</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 589 590 <span class="c"># Collect specified row values...</span> 591 <span class="i">$CheckSizes</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$CombineValues</span> = <span class="n">1</span><span class="sc">;</span> 592 <span class="i">$ValuesRefs</span> = <span class="i">_ProcessSpecifiedMatrixValues</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span><span class="sc">;</span> 593 <span class="i">$RowValuesRef</span> = <span class="i">$ValuesRefs</span>->[<span class="n">0</span>]<span class="sc">;</span> 594 595 <span class="c"># Check number of specified row values...</span> 596 <span class="i">$NumOfRowValues</span> = <span class="i">@</span>{<span class="i">$RowValuesRef</span>}<span class="sc">;</span> 597 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfRowValues</span> != <span class="i">$NumOfCols</span><span class="s">)</span> <span class="s">{</span> 598 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Number of specified row values, $NumOfRowValues, must be equal to number of row values, $NumOfCols, in matrix..."</span><span class="sc">;</span> 599 <span class="s">}</span> 600 601 <span class="c"># Set row values...</span> 602 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRowValues</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 603 <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$RowValuesRef</span>->[<span class="i">$ColIndex</span>]<span class="sc">;</span> 604 <span class="s">}</span> 605 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 606 <span class="s">}</span> 607 608 <span class="c"># Add new row values to a matrix...</span> 609 <span class="c">#</span> <a name="AddRowValues-"></a> 610 <span class="k">sub </span><span class="m">AddRowValues</span> <span class="s">{</span> 611 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 612 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">$RowValueRef</span><span class="cm">,</span> <span class="i">$RowValuesRefs</span><span class="cm">,</span> <span class="i">$NumOfNewRows</span><span class="cm">,</span> <span class="i">$NumOfNewCols</span><span class="s">)</span><span class="sc">;</span> 613 614 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}->AddRowValues"</span><span class="sc">;</span> 615 616 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 617 618 <span class="c"># Collect specified row values...</span> 619 <span class="i">$CheckSizes</span> = <span class="n">1</span><span class="sc">;</span> <span class="i">$CombineValues</span> = <span class="n">0</span><span class="sc">;</span> 620 <span class="i">$RowValuesRefs</span> = <span class="i">_ProcessSpecifiedMatrixValues</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span><span class="sc">;</span> 621 622 <span class="c"># Check number of specified row values...</span> 623 <span class="i">$NumOfNewRows</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$RowValuesRefs</span>}<span class="sc">;</span> 624 <span class="i">$NumOfNewCols</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$RowValuesRefs</span>->[<span class="n">0</span>]}<span class="sc">;</span> 625 626 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfNewCols</span> != <span class="i">$NumOfCols</span><span class="s">)</span> <span class="s">{</span> 627 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Number of values in each specified row, $NumOfNewCols, must be equal to number of row values, $NumOfCols, in matrix..."</span><span class="sc">;</span> 628 <span class="s">}</span> 629 630 <span class="c"># Add each row to the matrix...</span> 631 <span class="i">$RowIndex</span> = <span class="i">$NumOfRows</span> - <span class="n">1</span><span class="sc">;</span> 632 <span class="k">for</span> <span class="i">$RowValueRef</span> <span class="s">(</span><span class="i">@</span>{<span class="i">$RowValuesRefs</span>}<span class="s">)</span> <span class="s">{</span> 633 <span class="i">$RowIndex</span>++<span class="sc">;</span> 634 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>]} = <span class="i">@</span>{<span class="i">$RowValueRef</span>}<span class="sc">;</span> 635 <span class="s">}</span> 636 637 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 638 <span class="s">}</span> 639 640 <span class="c"># Get values of a row in matrix as an array. In scalar context, number of row</span> 641 <span class="c"># values is returned...</span> 642 <span class="c">#</span> <a name="GetRowValues-"></a> 643 <span class="k">sub </span><span class="m">GetRowValues</span> <span class="s">{</span> 644 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 645 646 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsArray'</span><span class="cm">,</span> <span class="q">'FromRow'</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 647 <span class="s">}</span> 648 649 <span class="c"># Get values of a row in matrix as a vector object...</span> 650 <span class="c">#</span> <a name="GetRowValuesAsVector-"></a> 651 <span class="k">sub </span><span class="m">GetRowValuesAsVector</span> <span class="s">{</span> 652 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 653 654 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsVector'</span><span class="cm">,</span> <span class="q">'FromRow'</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 655 <span class="s">}</span> 656 657 <span class="c"># Get values of a row as row matrix object...</span> 658 <span class="c">#</span> <a name="GetRowValuesAsRowMatrix-"></a> 659 <span class="k">sub </span><span class="m">GetRowValuesAsRowMatrix</span> <span class="s">{</span> 660 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 661 662 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsRowMatrix'</span><span class="cm">,</span> <span class="q">'FromRow'</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 663 <span class="s">}</span> 664 665 <span class="c"># Get values of a row as column matrix object...</span> 666 <span class="c">#</span> <a name="GetRowValuesAsColumnMatrix-"></a> 667 <span class="k">sub </span><span class="m">GetRowValuesAsColumnMatrix</span> <span class="s">{</span> 668 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 669 670 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsColumnMatrix'</span><span class="cm">,</span> <span class="q">'FromRow'</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 671 <span class="s">}</span> 672 673 <span class="c"># Get values of a row in matrix as a space delimited string...</span> 674 <span class="c">#</span> <a name="GetRowValuesAsString-"></a> 675 <span class="k">sub </span><span class="m">GetRowValuesAsString</span> <span class="s">{</span> 676 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 677 678 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsString'</span><span class="cm">,</span> <span class="q">'FromRow'</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 679 <span class="s">}</span> 680 681 <span class="c"># Set values of a column in a matrix value with row index starting from 0...</span> 682 <span class="c">#</span> <a name="SetColumnValues-"></a> 683 <span class="k">sub </span><span class="m">SetColumnValues</span> <span class="s">{</span> 684 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 685 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">$ValuesRefs</span><span class="cm">,</span> <span class="i">$ColValuesRef</span><span class="cm">,</span> <span class="i">$NumOfColValues</span><span class="s">)</span><span class="sc">;</span> 686 687 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}->SetColumnValues"</span><span class="sc">;</span> 688 689 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 690 <span class="i">$This</span><span class="i">->_ValidateColumnIndex</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 691 692 <span class="c"># Collect specified row values...</span> 693 <span class="i">$CheckSizes</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$CombineValues</span> = <span class="n">1</span><span class="sc">;</span> 694 <span class="i">$ValuesRefs</span> = <span class="i">_ProcessSpecifiedMatrixValues</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span><span class="sc">;</span> 695 <span class="i">$ColValuesRef</span> = <span class="i">$ValuesRefs</span>->[<span class="n">0</span>]<span class="sc">;</span> 696 697 <span class="c"># Check number of specified col values...</span> 698 <span class="i">$NumOfColValues</span> = <span class="i">@</span>{<span class="i">$ColValuesRef</span>}<span class="sc">;</span> 699 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfColValues</span> != <span class="i">$NumOfRows</span><span class="s">)</span> <span class="s">{</span> 700 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Number of specified col values, $NumOfColValues, must be equal to number of column values, $NumOfRows, in matrix..."</span><span class="sc">;</span> 701 <span class="s">}</span> 702 703 <span class="c"># Set col values...</span> 704 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfColValues</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 705 <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$ColValuesRef</span>->[<span class="i">$RowIndex</span>]<span class="sc">;</span> 706 <span class="s">}</span> 707 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 708 <span class="s">}</span> 709 710 <span class="c"># Add new column values to a matrix...</span> 711 <span class="c">#</span> <a name="AddColumnValues-"></a> 712 <span class="k">sub </span><span class="m">AddColumnValues</span> <span class="s">{</span> 713 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 714 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</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">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">$ColValueRef</span><span class="cm">,</span> <span class="i">$ColValuesRefs</span><span class="cm">,</span> <span class="i">$NumOfNewRows</span><span class="cm">,</span> <span class="i">$NumOfNewCols</span><span class="s">)</span><span class="sc">;</span> 715 716 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}->AddColumnValues"</span><span class="sc">;</span> 717 718 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 719 720 <span class="c"># Collect specified column values...</span> 721 <span class="i">$CheckSizes</span> = <span class="n">1</span><span class="sc">;</span> <span class="i">$CombineValues</span> = <span class="n">0</span><span class="sc">;</span> 722 <span class="i">$ColValuesRefs</span> = <span class="i">_ProcessSpecifiedMatrixValues</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">@SpecifiedValues</span><span class="s">)</span><span class="sc">;</span> 723 724 <span class="c"># Check number of specified column values...</span> 725 <span class="i">$NumOfNewCols</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$ColValuesRefs</span>}<span class="sc">;</span> 726 <span class="i">$NumOfNewRows</span> = <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$ColValuesRefs</span>->[<span class="n">0</span>]}<span class="sc">;</span> 727 728 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfNewRows</span> != <span class="i">$NumOfRows</span><span class="s">)</span> <span class="s">{</span> 729 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: Number of values in each specified column, $NumOfNewRows, must be equal to number of column values, $NumOfRows, in matrix..."</span><span class="sc">;</span> 730 <span class="s">}</span> 731 732 <span class="c"># Add each column to the matrix...</span> 733 <span class="i">$ColIndex</span> = <span class="i">$NumOfCols</span> - <span class="n">1</span><span class="sc">;</span> 734 <span class="k">for</span> <span class="i">$ColValueRef</span> <span class="s">(</span><span class="i">@</span>{<span class="i">$ColValuesRefs</span>}<span class="s">)</span> <span class="s">{</span> 735 <span class="i">$ColIndex</span>++<span class="sc">;</span> 736 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 737 <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$ColValueRef</span>->[<span class="i">$RowIndex</span>]<span class="sc">;</span> 738 <span class="s">}</span> 739 <span class="s">}</span> 740 741 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 742 <span class="s">}</span> 743 744 <span class="c"># Get values of a column in matrix as an array. In scalar context, number of column</span> 745 <span class="c"># values is returned...</span> 746 <span class="c">#</span> <a name="GetColumnValues-"></a> 747 <span class="k">sub </span><span class="m">GetColumnValues</span> <span class="s">{</span> 748 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 749 750 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsArray'</span><span class="cm">,</span> <span class="q">'FromColumn'</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 751 <span class="s">}</span> 752 753 <span class="c"># Get values of a column in matrix as a vector object...</span> 754 <span class="c">#</span> <a name="GetColumnValuesAsVector-"></a> 755 <span class="k">sub </span><span class="m">GetColumnValuesAsVector</span> <span class="s">{</span> 756 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 757 758 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsVector'</span><span class="cm">,</span> <span class="q">'FromColumn'</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 759 <span class="s">}</span> 760 761 <span class="c"># Get values of a column as row matrix object...</span> 762 <span class="c">#</span> <a name="GetColumnValuesAsRowMatrix-"></a> 763 <span class="k">sub </span><span class="m">GetColumnValuesAsRowMatrix</span> <span class="s">{</span> 764 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 765 766 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsRowMatrix'</span><span class="cm">,</span> <span class="q">'FromColumn'</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 767 <span class="s">}</span> 768 769 <span class="c"># Get values of a column as column matrix object...</span> 770 <span class="c">#</span> <a name="GetColumnValuesAsColumnMatrix-"></a> 771 <span class="k">sub </span><span class="m">GetColumnValuesAsColumnMatrix</span> <span class="s">{</span> 772 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 773 774 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsColumnMatrix'</span><span class="cm">,</span> <span class="q">'FromColumn'</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 775 <span class="s">}</span> 776 777 <span class="c"># Get values of a column in matrix as a space delimited string...</span> 778 <span class="c">#</span> <a name="GetColumnValuesAsString-"></a> 779 <span class="k">sub </span><span class="m">GetColumnValuesAsString</span> <span class="s">{</span> 780 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 781 782 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetRowOrColumnValues</span><span class="s">(</span><span class="q">'AsString'</span><span class="cm">,</span> <span class="q">'FromColumn'</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 783 <span class="s">}</span> 784 785 <span class="c"># Get row or column values...</span> 786 <span class="c">#</span> <a name="_GetRowOrColumnValues-"></a> 787 <span class="k">sub </span><span class="m">_GetRowOrColumnValues</span> <span class="s">{</span> 788 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Mode</span><span class="cm">,</span> <span class="i">$ValueMode</span><span class="cm">,</span> <span class="i">$ValueModeIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 789 790 <span class="k">if</span> <span class="s">(</span><span class="i">$Mode</span> !~ <span class="q">/^(AsArray|AsVector|AsRowMatrix|AsColumnMatrix|AsString)$/i</span><span class="s">)</span> <span class="s">{</span> 791 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->_GetRowOrColumnValues: Unknown mode, $Mode, specified..."</span><span class="sc">;</span> 792 <span class="s">}</span> 793 <span class="k">if</span> <span class="s">(</span><span class="i">$ValueMode</span> !~ <span class="q">/^(FromRow|FromColumn)$/i</span><span class="s">)</span> <span class="s">{</span> 794 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->_GetRowOrColumnValues: Unknown value mode, $ValueMode, specified..."</span><span class="sc">;</span> 795 <span class="s">}</span> 796 797 <span class="c"># Setup error message prefix...</span> 798 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="s">)</span><span class="sc">;</span> 799 800 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"${ClassName}->_GetRowOrColumnValues"</span><span class="sc">;</span> 801 <span class="k">if</span> <span class="s">(</span><span class="i">$ValueMode</span> =~ <span class="q">/^FromRow$/i</span><span class="s">)</span> <span class="s">{</span> 802 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}->GetRowValues${Mode}"</span><span class="sc">;</span> 803 <span class="s">}</span> 804 <span class="k">elsif</span> <span class="s">(</span><span class="i">$ValueMode</span> =~ <span class="q">/^FromColumn$/i</span><span class="s">)</span> <span class="s">{</span> 805 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}->GetColumnValues${Mode}"</span><span class="sc">;</span> 806 <span class="s">}</span> 807 808 <span class="c"># Validate specified index and collect values...</span> 809 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</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">@Values</span><span class="s">)</span><span class="sc">;</span> 810 811 <span class="i">@Values</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 812 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 813 814 <span class="k">if</span> <span class="s">(</span><span class="i">$ValueMode</span> =~ <span class="q">/^FromRow$/i</span><span class="s">)</span> <span class="s">{</span> 815 <span class="i">$RowIndex</span> = <span class="i">$ValueModeIndex</span><span class="sc">;</span> 816 <span class="i">$This</span><span class="i">->_ValidateRowIndex</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 817 818 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 819 <span class="k">push</span> <span class="i">@Values</span><span class="cm">,</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 820 <span class="s">}</span> 821 <span class="s">}</span> 822 <span class="k">elsif</span> <span class="s">(</span><span class="i">$ValueMode</span> =~ <span class="q">/^FromColumn$/i</span><span class="s">)</span> <span class="s">{</span> 823 <span class="i">$ColIndex</span> = <span class="i">$ValueModeIndex</span><span class="sc">;</span> 824 <span class="i">$This</span><span class="i">->_ValidateColumnIndex</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 825 826 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 827 <span class="k">push</span> <span class="i">@Values</span><span class="cm">,</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 828 <span class="s">}</span> 829 <span class="s">}</span> 830 831 <span class="c"># Return values...</span> 832 <span class="k">if</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsRowMatrix$/i</span><span class="s">)</span> <span class="s">{</span> 833 <span class="k">return</span> <span class="i">NewFromRows</span><span class="s">(</span>\<span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 834 <span class="s">}</span> 835 <span class="k">elsif</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsColumnMatrix$/i</span><span class="s">)</span> <span class="s">{</span> 836 <span class="k">return</span> <span class="i">NewFromColumns</span><span class="s">(</span>\<span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 837 <span class="s">}</span> 838 <span class="k">elsif</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsVector$/i</span><span class="s">)</span> <span class="s">{</span> 839 <span class="k">return</span> <span class="i">new</span> <span class="i">Vector</span><span class="s">(</span><span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 840 <span class="s">}</span> 841 <span class="k">elsif</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsString$/i</span><span class="s">)</span> <span class="s">{</span> 842 <span class="k">return</span> <span class="k">join</span><span class="s">(</span><span class="q">' '</span><span class="cm">,</span> <span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 843 <span class="s">}</span> 844 <span class="k">else</span> <span class="s">{</span> 845 <span class="k">return</span> <span class="k">wantarray</span> ? <span class="i">@Values</span> <span class="co">:</span> <span class="k">scalar</span> <span class="i">@Values</span><span class="sc">;</span> 846 <span class="s">}</span> 847 <span class="s">}</span> 848 849 <span class="c"># Set values of the diagonal in a square matrix...</span> 850 <span class="c">#</span> <a name="SetDiagonalValues-"></a> 851 <span class="k">sub </span><span class="m">SetDiagonalValues</span> <span class="s">{</span> 852 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">@SpecifiedDiagonalValues</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 853 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">$ValuesRefs</span><span class="cm">,</span> <span class="i">$NumOfDiagonalValues</span><span class="cm">,</span> <span class="i">$DiagonalValuesRef</span><span class="s">)</span><span class="sc">;</span> 854 855 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"Error: ${ClassName}->SetDiagonalValues"</span><span class="sc">;</span> 856 <span class="k">if</span> <span class="s">(</span>!<span class="i">@SpecifiedDiagonalValues</span><span class="s">)</span> <span class="s">{</span> 857 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: No diagonal values specified..."</span><span class="sc">;</span> 858 <span class="s">}</span> 859 860 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 861 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfRows</span> != <span class="i">$NumOfCols</span><span class="s">)</span> <span class="s">{</span> 862 <span class="w">croak</span> <span class="q">"Error: $ErrorMsgPrefix: Specified matrix, $NumOfRows x $NumOfCols, is not a square matrix..."</span><span class="sc">;</span> 863 <span class="s">}</span> 864 865 <span class="c"># Collect specified diagonal values...</span> 866 <span class="i">$CheckSizes</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$CombineValues</span> = <span class="n">1</span><span class="sc">;</span> 867 <span class="i">$ValuesRefs</span> = <span class="i">_ProcessSpecifiedMatrixValues</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="cm">,</span> <span class="i">$CombineValues</span><span class="cm">,</span> <span class="i">@SpecifiedDiagonalValues</span><span class="s">)</span><span class="sc">;</span> 868 <span class="i">$DiagonalValuesRef</span> = <span class="i">$ValuesRefs</span>->[<span class="n">0</span>]<span class="sc">;</span> 869 <span class="i">$NumOfDiagonalValues</span> = <span class="i">@</span>{<span class="i">$DiagonalValuesRef</span>}<span class="sc">;</span> 870 871 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfDiagonalValues</span> != <span class="i">$NumOfRows</span><span class="s">)</span> <span class="s">{</span> 872 <span class="w">croak</span> <span class="q">"Error: $ErrorMsgPrefix: Number of specified diagonal values, $NumOfDiagonalValues, must be equal to number of rows, $NumOfRows, in square matrix..."</span><span class="sc">;</span> 873 <span class="s">}</span> 874 875 <span class="c"># Set diagonal values...</span> 876 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 877 <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$RowIndex</span>] = <span class="i">$DiagonalValuesRef</span>->[<span class="i">$RowIndex</span>]<span class="sc">;</span> 878 <span class="s">}</span> 879 880 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 881 <span class="s">}</span> 882 883 <span class="c"># Get values of the diagonal in a square matrix as an array. In scalar context, number of</span> 884 <span class="c"># diagonal values is returned...</span> 885 <span class="c">#</span> <a name="GetDiagonalValues-"></a> 886 <span class="k">sub </span><span class="m">GetDiagonalValues</span> <span class="s">{</span> 887 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 888 889 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetDiagonalValues</span><span class="s">(</span><span class="q">'AsArray'</span><span class="s">)</span><span class="sc">;</span> 890 <span class="s">}</span> 891 892 <span class="c"># Get values of the diagonal in a square matrix as vector object...</span> 893 <span class="c">#</span> <a name="GetDiagonalValuesAsVector-"></a> 894 <span class="k">sub </span><span class="m">GetDiagonalValuesAsVector</span> <span class="s">{</span> 895 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 896 897 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetDiagonalValues</span><span class="s">(</span><span class="q">'AsVector'</span><span class="s">)</span><span class="sc">;</span> 898 <span class="s">}</span> 899 900 <span class="c"># Get values of the diagonal in a square matrix as row matrix object</span> 901 <span class="c">#</span> <a name="GetDiagonalValuesAsRowMatrix-"></a> 902 <span class="k">sub </span><span class="m">GetDiagonalValuesAsRowMatrix</span> <span class="s">{</span> 903 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 904 905 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetDiagonalValues</span><span class="s">(</span><span class="q">'AsRowMatrix'</span><span class="s">)</span><span class="sc">;</span> 906 <span class="s">}</span> 907 908 <span class="c"># Get values of the diagonal in a square matrix as column matrix object</span> 909 <span class="c">#</span> <a name="GetDiagonalValuesAsColumnMatrix-"></a> 910 <span class="k">sub </span><span class="m">GetDiagonalValuesAsColumnMatrix</span> <span class="s">{</span> 911 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 912 913 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetDiagonalValues</span><span class="s">(</span><span class="q">'AsColumnMatrix'</span><span class="s">)</span><span class="sc">;</span> 914 <span class="s">}</span> 915 916 <span class="c"># Get values of the diagonal in a square matrix as a space delimited string...</span> 917 <span class="c">#</span> <a name="GetDiagonalValuesAsString-"></a> 918 <span class="k">sub </span><span class="m">GetDiagonalValuesAsString</span> <span class="s">{</span> 919 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 920 921 <span class="k">return</span> <span class="i">$This</span><span class="i">->_GetDiagonalValues</span><span class="s">(</span><span class="q">'AsString'</span><span class="s">)</span><span class="sc">;</span> 922 <span class="s">}</span> 923 924 <span class="c"># Get diagonal values...</span> <a name="_GetDiagonalValues-"></a> 925 <span class="k">sub </span><span class="m">_GetDiagonalValues</span> <span class="s">{</span> 926 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Mode</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 927 928 <span class="k">if</span> <span class="s">(</span><span class="i">$Mode</span> !~ <span class="q">/^(AsArray|AsVector|AsRowMatrix|AsColumnMatrix|AsString)$/i</span><span class="s">)</span> <span class="s">{</span> 929 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->_GetDiagonalValues: Unknown mode, $Mode, specified..."</span><span class="sc">;</span> 930 <span class="s">}</span> 931 932 <span class="c"># Make sure it's a square matrix...</span> 933 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$ErrorMsgPrefix</span><span class="s">)</span><span class="sc">;</span> 934 935 <span class="i">$ErrorMsgPrefix</span> = <span class="q">"${ClassName}->_GetDiagonalValues${Mode}"</span><span class="sc">;</span> 936 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 937 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfRows</span> != <span class="i">$NumOfCols</span><span class="s">)</span> <span class="s">{</span> 938 <span class="w">croak</span> <span class="q">"Error: $ErrorMsgPrefix: Specified matrix, $NumOfRows x $NumOfCols, is not a square matrix..."</span><span class="sc">;</span> 939 <span class="s">}</span> 940 941 <span class="c"># Collect values...</span> 942 <span class="k">my</span><span class="s">(</span><span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 943 <span class="i">@Values</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 944 945 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 946 <span class="k">push</span> <span class="i">@Values</span><span class="cm">,</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$RowIndex</span>]<span class="sc">;</span> 947 <span class="s">}</span> 948 949 <span class="c"># Return values...</span> 950 <span class="k">if</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsRowMatrix$/i</span><span class="s">)</span> <span class="s">{</span> 951 <span class="k">return</span> <span class="i">NewFromRows</span><span class="s">(</span>\<span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 952 <span class="s">}</span> 953 <span class="k">elsif</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsColumnMatrix$/i</span><span class="s">)</span> <span class="s">{</span> 954 <span class="k">return</span> <span class="i">NewFromColumns</span><span class="s">(</span>\<span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 955 <span class="s">}</span> 956 <span class="k">elsif</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsVector$/i</span><span class="s">)</span> <span class="s">{</span> 957 <span class="k">return</span> <span class="i">new</span> <span class="i">Vector</span><span class="s">(</span><span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 958 <span class="s">}</span> 959 <span class="k">elsif</span> <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^AsString$/i</span><span class="s">)</span> <span class="s">{</span> 960 <span class="k">return</span> <span class="k">join</span><span class="s">(</span><span class="q">' '</span><span class="cm">,</span> <span class="i">@Values</span><span class="s">)</span><span class="sc">;</span> 961 <span class="s">}</span> 962 <span class="k">else</span> <span class="s">{</span> 963 <span class="k">return</span> <span class="k">wantarray</span> ? <span class="i">@Values</span> <span class="co">:</span> <span class="k">scalar</span> <span class="i">@Values</span><span class="sc">;</span> 964 <span class="s">}</span> 965 <span class="s">}</span> 966 967 <span class="c"># Is it a square matrix?</span> 968 <span class="c">#</span> <a name="IsSquare-"></a> 969 <span class="k">sub </span><span class="m">IsSquare</span> <span class="s">{</span> 970 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 971 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 972 973 <span class="k">return</span> <span class="s">(</span><span class="i">$NumOfRows</span> == <span class="i">$NumOfCols</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 974 <span class="s">}</span> 975 976 <span class="c"># Is it a unit matrix?</span> 977 <span class="c">#</span> 978 <span class="c"># A matrix is a unit matrix:</span> 979 <span class="c"># o It's a square matrix</span> 980 <span class="c"># o All its diagonal elements are ones and its off-diagonal elements are zeros</span> 981 <span class="c">#</span> <a name="IsUnit-"></a> 982 <span class="k">sub </span><span class="m">IsUnit</span> <span class="s">{</span> 983 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 984 985 <span class="c"># Is is a square matrix?</span> 986 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 987 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 988 <span class="s">}</span> 989 990 <span class="c"># Check matrix values...</span> 991 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$ExpectedValue</span><span class="s">)</span><span class="sc">;</span> 992 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 993 994 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 995 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 996 <span class="i">$ExpectedValue</span> = <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> ? <span class="n">1.0</span> <span class="co">:</span> <span class="n">0.0</span><span class="sc">;</span> 997 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="i">$ExpectedValue</span><span class="s">)</span> <span class="s">{</span> 998 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 999 <span class="s">}</span> 1000 <span class="s">}</span> 1001 <span class="s">}</span> 1002 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1003 <span class="s">}</span> 1004 1005 <span class="c"># Is it an identity matrix?</span> 1006 <span class="c">#</span> <a name="IsIdentity-"></a>1007 <span class="k">sub </span><span class="m">IsIdentity</span> <span class="s">{</span> 1008 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1009 1010 <span class="k">return</span> <span class="i">$This</span><span class="i">->IsUnit</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1011 <span class="s">}</span> 1012 1013 <span class="c"># Is it a diagonal matrix?</span> 1014 <span class="c">#</span> 1015 <span class="c"># A matrix is a diagonal matrix:</span> 1016 <span class="c"># o It's a square matrix</span> 1017 <span class="c"># o All its off-diagonal elements are zeros and its diagonal elements may or may not</span> 1018 <span class="c"># be zeros</span> 1019 <span class="c">#</span> 1020 <span class="c">#</span> <a name="IsDiagonal-"></a>1021 <span class="k">sub </span><span class="m">IsDiagonal</span> <span class="s">{</span> 1022 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1023 1024 <span class="c"># Is is a square matrix?</span> 1025 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1026 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1027 <span class="s">}</span> 1028 1029 <span class="c"># Check off-diagonal matrix values...</span> 1030 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1031 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1032 1033 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1034 <span class="j">COLINDEX:</span> <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1035 <span class="k">if</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1036 <span class="k">next</span> <span class="j">COLINDEX</span><span class="sc">;</span> 1037 <span class="s">}</span> 1038 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1039 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1040 <span class="s">}</span> 1041 <span class="s">}</span> 1042 <span class="s">}</span> 1043 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1044 <span class="s">}</span> 1045 1046 <span class="c"># Is it a lower bidiagonal matrix?</span> 1047 <span class="c">#</span> 1048 <span class="c"># A matrix is a lower bidiagonal matrix:</span> 1049 <span class="c"># o It's a square matrix</span> 1050 <span class="c"># o All its main diagonal and lower diagonal elements are non-zeros and all its</span> 1051 <span class="c"># other elements are zeros</span> 1052 <span class="c">#</span> <a name="IsLowerBiDiagonal-"></a>1053 <span class="k">sub </span><span class="m">IsLowerBiDiagonal</span> <span class="s">{</span> 1054 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1055 1056 <span class="c"># Is is a square matrix?</span> 1057 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1058 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1059 <span class="s">}</span> 1060 1061 <span class="c"># Check matrix values...</span> 1062 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</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">$Value</span><span class="s">)</span><span class="sc">;</span> 1063 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1064 1065 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1066 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1067 <span class="i">$Value</span> = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1068 <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> 1069 <span class="c"># Main diagonal...</span> 1070 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> == <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1071 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1072 <span class="s">}</span> 1073 <span class="s">}</span> 1074 <span class="k">elsif</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="s">(</span><span class="i">$ColIndex</span> + <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1075 <span class="c"># Lower diagonal...</span> 1076 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> == <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1077 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1078 <span class="s">}</span> 1079 <span class="s">}</span> 1080 <span class="k">else</span> <span class="s">{</span> 1081 <span class="c"># Other elements...</span> 1082 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1083 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1084 <span class="s">}</span> 1085 <span class="s">}</span> 1086 <span class="s">}</span> 1087 <span class="s">}</span> 1088 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1089 <span class="s">}</span> 1090 1091 <span class="c"># Is it an upper bidiagonal matrix?</span> 1092 <span class="c">#</span> 1093 <span class="c"># A matrix is an upper bidiagonal matrix:</span> 1094 <span class="c"># o It's a square matrix</span> 1095 <span class="c"># o All its main diagonal and upper diagonal elements are non-zeros and all its</span> 1096 <span class="c"># other elements are zeros</span> 1097 <span class="c">#</span> <a name="IsUpperBiDiagonal-"></a>1098 <span class="k">sub </span><span class="m">IsUpperBiDiagonal</span> <span class="s">{</span> 1099 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1100 1101 <span class="c"># Is is a square matrix?</span> 1102 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1103 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1104 <span class="s">}</span> 1105 <span class="c"># Check matrix values...</span> 1106 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 1107 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1108 1109 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1110 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1111 <span class="i">$Value</span> = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1112 <span class="k">if</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1113 <span class="c"># Main diagonal...</span> 1114 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> == <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1115 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1116 <span class="s">}</span> 1117 <span class="s">}</span> 1118 <span class="k">elsif</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="s">(</span><span class="i">$ColIndex</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1119 <span class="c"># Upper diagonal...</span> 1120 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> == <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1121 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1122 <span class="s">}</span> 1123 <span class="s">}</span> 1124 <span class="k">else</span> <span class="s">{</span> 1125 <span class="c"># Other elements...</span> 1126 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1127 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1128 <span class="s">}</span> 1129 <span class="s">}</span> 1130 <span class="s">}</span> 1131 <span class="s">}</span> 1132 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1133 <span class="s">}</span> 1134 1135 <span class="c"># Is it a bidiagonal matrix?</span> 1136 <span class="c">#</span> 1137 <span class="c"># A matrix is a bidiagonal matrix:</span> 1138 <span class="c">#</span> <a name="IsBiDiagonal-"></a>1139 <span class="k">sub </span><span class="m">IsBiDiagonal</span> <span class="s">{</span> 1140 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1141 1142 <span class="k">return</span> <span class="s">(</span><span class="i">$This</span><span class="i">->IsUpperBiDiagonal</span><span class="s">(</span><span class="s">)</span> || <span class="i">$This</span><span class="i">->IsLowerBiDiagonal</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 1143 <span class="s">}</span> 1144 1145 <span class="c"># Is it a tridiagonal matrix?</span> 1146 <span class="c">#</span> 1147 <span class="c"># A matrix is a tribidiagonal matrix:</span> 1148 <span class="c"># o It's a square matrix</span> 1149 <span class="c"># o All its main diagonal, upper diagonal, and lower diagonal elements are non-zeros and all its</span> 1150 <span class="c"># other elements are zeros</span> 1151 <span class="c">#</span> 1152 <span class="c">#</span> <a name="IsTriDiagonal-"></a>1153 <span class="k">sub </span><span class="m">IsTriDiagonal</span> <span class="s">{</span> 1154 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1155 1156 <span class="c"># Is is a square matrix?</span> 1157 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1158 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1159 <span class="s">}</span> 1160 1161 <span class="c"># Check matrix values...</span> 1162 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 1163 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1164 1165 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1166 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1167 <span class="i">$Value</span> = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1168 <span class="k">if</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1169 <span class="c"># Main diagonal...</span> 1170 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> == <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1171 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1172 <span class="s">}</span> 1173 <span class="s">}</span> 1174 <span class="k">elsif</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="s">(</span><span class="i">$ColIndex</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1175 <span class="c"># Upper diagonal...</span> 1176 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> == <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1177 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1178 <span class="s">}</span> 1179 <span class="s">}</span> 1180 <span class="k">elsif</span> <span class="s">(</span><span class="i">$RowIndex</span> == <span class="s">(</span><span class="i">$ColIndex</span> + <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1181 <span class="c"># Lower diagonal...</span> 1182 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> == <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1183 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1184 <span class="s">}</span> 1185 <span class="s">}</span> 1186 <span class="k">else</span> <span class="s">{</span> 1187 <span class="c"># Other elements...</span> 1188 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1189 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1190 <span class="s">}</span> 1191 <span class="s">}</span> 1192 <span class="s">}</span> 1193 <span class="s">}</span> 1194 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1195 <span class="s">}</span> 1196 1197 <span class="c"># Is it a lower triangular matrix?</span> 1198 <span class="c">#</span> 1199 <span class="c"># A matrix is a lower triangular matrix:</span> 1200 <span class="c"># o It's a square matrix</span> 1201 <span class="c"># o All its entries above the main diagonal are zero</span> 1202 <span class="c">#</span> <a name="IsLowerTriangular-"></a>1203 <span class="k">sub </span><span class="m">IsLowerTriangular</span> <span class="s">{</span> 1204 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1205 1206 <span class="k">return</span> <span class="i">$This</span><span class="i">->_IsLowerTriangularMatrix</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1207 <span class="s">}</span> 1208 1209 <span class="c"># Is it a left triangular matrix?</span> 1210 <span class="c">#</span> 1211 <span class="c"># A matrix is a left triangular matrix:</span> 1212 <span class="c"># o It's a square matrix</span> 1213 <span class="c"># o All its entries above the main diagonal are zero</span> 1214 <span class="c">#</span> <a name="IsLeftTriangular-"></a>1215 <span class="k">sub </span><span class="m">IsLeftTriangular</span> <span class="s">{</span> 1216 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1217 1218 <span class="k">return</span> <span class="i">$This</span><span class="i">->IsLowerTriangular</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1219 <span class="s">}</span> 1220 1221 <span class="c"># Is it a strictly lower triangular matrix?</span> 1222 <span class="c">#</span> 1223 <span class="c"># A matrix is a strictly lower triangular matrix:</span> 1224 <span class="c"># o It's a square matrix</span> 1225 <span class="c"># o All its entries on and above the main diagonal are zero</span> 1226 <span class="c">#</span> <a name="IsStrictlyLowerTriangular-"></a>1227 <span class="k">sub </span><span class="m">IsStrictlyLowerTriangular</span> <span class="s">{</span> 1228 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1229 <span class="k">my</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1230 1231 <span class="i">$DiagonalValue</span> = <span class="n">0</span><span class="sc">;</span> 1232 1233 <span class="k">return</span> <span class="i">$This</span><span class="i">->_IsLowerTriangularMatrix</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1234 <span class="s">}</span> 1235 1236 <span class="c"># Is it an unit lower triangular matrix?</span> 1237 <span class="c">#</span> 1238 <span class="c"># A matrix is an unit lower triangular matrix:</span> 1239 <span class="c"># o It's a square matrix</span> 1240 <span class="c"># o All its entries main diagonal are one</span> 1241 <span class="c"># o All its entries above the main diagonal are zero</span> 1242 <span class="c">#</span> <a name="IsUnitLowerTriangular-"></a>1243 <span class="k">sub </span><span class="m">IsUnitLowerTriangular</span> <span class="s">{</span> 1244 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1245 <span class="k">my</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1246 1247 <span class="i">$DiagonalValue</span> = <span class="n">1</span><span class="sc">;</span> 1248 1249 <span class="k">return</span> <span class="i">$This</span><span class="i">->_IsLowerTriangularMatrix</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1250 <span class="s">}</span> 1251 1252 <span class="c"># Is it a lower unitriangular matrix?</span> 1253 <span class="c">#</span> <a name="IsLowerUniTriangular-"></a>1254 <span class="k">sub </span><span class="m">IsLowerUniTriangular</span> <span class="s">{</span> 1255 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1256 1257 <span class="k">return</span> <span class="i">$This</span><span class="i">->IsUnitLowerTriangular</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1258 <span class="s">}</span> 1259 1260 <span class="c"># Is it a lower triangular, strictly lower triangular, or unit lower triangular matrix?</span> 1261 <span class="c">#</span> <a name="_IsLowerTriangularMatrix-"></a>1262 <span class="k">sub </span><span class="m">_IsLowerTriangularMatrix</span> <span class="s">{</span> 1263 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$DiagonalValue</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1264 1265 <span class="c"># Is is a square matrix?</span> 1266 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1267 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1268 <span class="s">}</span> 1269 <span class="c"># Check matrix values...</span> 1270 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</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">$CheckDiagonalValues</span><span class="s">)</span><span class="sc">;</span> 1271 1272 <span class="i">$CheckDiagonalValues</span> = <span class="k">defined</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 1273 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1274 1275 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1276 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1277 <span class="k">if</span> <span class="s">(</span><span class="i">$CheckDiagonalValues</span> && <span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1278 <span class="c"># Main diagonal...</span> 1279 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="i">$DiagonalValue</span><span class="s">)</span> <span class="s">{</span> 1280 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1281 <span class="s">}</span> 1282 <span class="s">}</span> 1283 <span class="k">elsif</span> <span class="s">(</span><span class="i">$RowIndex</span> < <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1284 <span class="c"># Elemens above the main diagonal...</span> 1285 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1286 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1287 <span class="s">}</span> 1288 <span class="s">}</span> 1289 <span class="s">}</span> 1290 <span class="s">}</span> 1291 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1292 <span class="s">}</span> 1293 1294 <span class="c"># Is it an upper triangular matrix?</span> 1295 <span class="c">#</span> 1296 <span class="c"># A matrix is an upper triangular matrix:</span> 1297 <span class="c"># o It's a square matrix</span> 1298 <span class="c"># o All its entries below the main diagonal are zero</span> 1299 <span class="c">#</span> <a name="IsUpperTriangular-"></a>1300 <span class="k">sub </span><span class="m">IsUpperTriangular</span> <span class="s">{</span> 1301 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1302 1303 <span class="k">return</span> <span class="i">$This</span><span class="i">->_IsUpperTriangularMatrix</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1304 <span class="s">}</span> 1305 1306 <span class="c"># Is it a right triangular matrix?</span> 1307 <span class="c">#</span> 1308 <span class="c"># A matrix is a right triangular matrix:</span> 1309 <span class="c"># o It's a square matrix</span> 1310 <span class="c"># o All its entries below the main diagonal are zero</span> 1311 <span class="c">#</span> <a name="IsRightTriangular-"></a>1312 <span class="k">sub </span><span class="m">IsRightTriangular</span> <span class="s">{</span> 1313 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1314 1315 <span class="k">return</span> <span class="i">$This</span><span class="i">->IsUpperTriangular</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1316 <span class="s">}</span> 1317 1318 <span class="c"># Is it a strictly upper triangular matrix?</span> 1319 <span class="c">#</span> 1320 <span class="c"># A matrix is a strictly upper triangular matrix:</span> 1321 <span class="c"># o It's a square matrix</span> 1322 <span class="c"># o All its entries on and below the main diagonal are zero</span> 1323 <span class="c">#</span> <a name="IsStrictlyUpperTriangular-"></a>1324 <span class="k">sub </span><span class="m">IsStrictlyUpperTriangular</span> <span class="s">{</span> 1325 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1326 <span class="k">my</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1327 1328 <span class="i">$DiagonalValue</span> = <span class="n">0</span><span class="sc">;</span> 1329 1330 <span class="k">return</span> <span class="i">$This</span><span class="i">->_IsUpperTriangularMatrix</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1331 <span class="s">}</span> 1332 1333 <span class="c"># Is it a unit upper triangular matrix?</span> 1334 <span class="c">#</span> 1335 <span class="c"># A matrix is an unit upper triangular matrix:</span> 1336 <span class="c"># o It's a square matrix</span> 1337 <span class="c"># o All its entries main diagonal are one</span> 1338 <span class="c"># o All its entries below the main diagonal are zero</span> 1339 <span class="c">#</span> <a name="IsUnitUpperTriangular-"></a>1340 <span class="k">sub </span><span class="m">IsUnitUpperTriangular</span> <span class="s">{</span> 1341 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1342 <span class="k">my</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1343 1344 <span class="i">$DiagonalValue</span> = <span class="n">1</span><span class="sc">;</span> 1345 1346 <span class="k">return</span> <span class="i">$This</span><span class="i">->_IsUpperTriangularMatrix</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span><span class="sc">;</span> 1347 <span class="s">}</span> 1348 1349 <span class="c"># Is it a upper unitriangular matrix?</span> 1350 <span class="c">#</span> <a name="IsUpperUniTriangular-"></a>1351 <span class="k">sub </span><span class="m">IsUpperUniTriangular</span> <span class="s">{</span> 1352 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1353 1354 <span class="k">return</span> <span class="i">$This</span><span class="i">->IsUnitUpperTriangular</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1355 <span class="s">}</span> 1356 1357 <span class="c"># Is it an upper triangular, strictly upper triangular, or unit upper triangular matrix?</span> 1358 <span class="c">#</span> <a name="_IsUpperTriangularMatrix-"></a>1359 <span class="k">sub </span><span class="m">_IsUpperTriangularMatrix</span> <span class="s">{</span> 1360 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$DiagonalValue</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1361 1362 <span class="c"># Is is a square matrix?</span> 1363 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1364 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1365 <span class="s">}</span> 1366 <span class="c"># Check matrix values...</span> 1367 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="cm">,</span> <span class="i">$CheckDiagonalValues</span><span class="s">)</span><span class="sc">;</span> 1368 1369 <span class="i">$CheckDiagonalValues</span> = <span class="k">defined</span><span class="s">(</span><span class="i">$DiagonalValue</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 1370 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1371 1372 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1373 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1374 <span class="k">if</span> <span class="s">(</span><span class="i">$CheckDiagonalValues</span> && <span class="i">$RowIndex</span> == <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1375 <span class="c"># Main diagonal...</span> 1376 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="i">$DiagonalValue</span><span class="s">)</span> <span class="s">{</span> 1377 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1378 <span class="s">}</span> 1379 <span class="s">}</span> 1380 <span class="k">elsif</span> <span class="s">(</span><span class="i">$RowIndex</span> > <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1381 <span class="c"># Elemens below the main diagonal...</span> 1382 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1383 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1384 <span class="s">}</span> 1385 <span class="s">}</span> 1386 <span class="s">}</span> 1387 <span class="s">}</span> 1388 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1389 <span class="s">}</span> 1390 1391 <span class="c"># Is it a symmetrix matrix?</span> 1392 <span class="c">#</span> 1393 <span class="c"># A matrix is a symmetric matrix:</span> 1394 <span class="c"># o It's a square matrix</span> 1395 <span class="c"># o Its elements are symmetric with respect to main diagonal. In other words,</span> 1396 <span class="c"># elements below the main diagonal are equal to the elements above the main</span> 1397 <span class="c"># diagonal.</span> 1398 <span class="c">#</span> 1399 <span class="c"># Transpose of a symmetric matrix equals the matrix itself.</span> 1400 <span class="c">#</span> <a name="IsSymmetric-"></a>1401 <span class="k">sub </span><span class="m">IsSymmetric</span> <span class="s">{</span> 1402 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1403 1404 <span class="c"># Is is a square matrix?</span> 1405 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1406 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1407 <span class="s">}</span> 1408 1409 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1410 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1411 1412 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1413 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$RowIndex</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1414 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$ColIndex</span>][<span class="i">$RowIndex</span>]<span class="s">)</span> <span class="s">{</span> 1415 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1416 <span class="s">}</span> 1417 <span class="s">}</span> 1418 <span class="s">}</span> 1419 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1420 <span class="s">}</span> 1421 1422 <span class="c"># Is it a anti symmetrix matrix?</span> 1423 <span class="c">#</span> 1424 <span class="c"># A matrix is an anti symmetric matrix:</span> 1425 <span class="c"># o It's a square matrix</span> 1426 <span class="c"># o Its elements are asymmetric with respect to main diagonal. In other words,</span> 1427 <span class="c"># elements below the main diagonal are equal to the negative of elements above</span> 1428 <span class="c"># the main diagonal.</span> 1429 <span class="c">#</span> 1430 <span class="c"># Transpose of a anti symmetric matrix equals the negative of the matrix.</span> 1431 <span class="c">#</span> <a name="IsAntiSymmetric-"></a>1432 <span class="k">sub </span><span class="m">IsAntiSymmetric</span> <span class="s">{</span> 1433 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1434 1435 <span class="c"># Is is a square matrix?</span> 1436 <span class="k">if</span> <span class="s">(</span>!<span class="i">$This</span><span class="i">->IsSquare</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1437 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1438 <span class="s">}</span> 1439 1440 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1441 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1442 1443 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1444 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$RowIndex</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1445 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != -<span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$ColIndex</span>][<span class="i">$RowIndex</span>]<span class="s">)</span> <span class="s">{</span> 1446 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1447 <span class="s">}</span> 1448 <span class="s">}</span> 1449 <span class="s">}</span> 1450 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1451 <span class="s">}</span> 1452 1453 <span class="c"># Is it a skew symmetrix matrix?</span> 1454 <span class="c">#</span> 1455 <span class="c"># It's another name for AnitSymmetricMatrix.</span> 1456 <span class="c">#</span> <a name="IsSkewSymmetric-"></a>1457 <span class="k">sub </span><span class="m">IsSkewSymmetric</span> <span class="s">{</span> 1458 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1459 1460 <span class="k">return</span> <span class="i">$This</span><span class="i">->IsAntiSymmetric</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1461 <span class="s">}</span> 1462 1463 <span class="c"># Is it a positive matrix with all its values >= zero?</span> 1464 <span class="c">#</span> <a name="IsPositive-"></a>1465 <span class="k">sub </span><span class="m">IsPositive</span> <span class="s">{</span> 1466 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1467 1468 <span class="c"># Check matrix values...</span> 1469 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1470 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1471 1472 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1473 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1474 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] < <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1475 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1476 <span class="s">}</span> 1477 <span class="s">}</span> 1478 <span class="s">}</span> 1479 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1480 <span class="s">}</span> 1481 1482 <span class="c"># Is it a positive matrix with all its values <= zero?</span> 1483 <span class="c">#</span> <a name="IsNegative-"></a>1484 <span class="k">sub </span><span class="m">IsNegative</span> <span class="s">{</span> 1485 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1486 1487 <span class="k">return</span> <span class="i">$This</span><span class="i">->IsPositive</span><span class="s">(</span><span class="s">)</span> ? <span class="n">0</span> <span class="co">:</span> <span class="n">1</span><span class="sc">;</span> 1488 <span class="s">}</span> 1489 1490 <span class="c"># Transpose the matrix by swaping rows with columns...</span> 1491 <span class="c">#</span> <a name="Transpose-"></a>1492 <span class="k">sub </span><span class="m">Transpose</span> <span class="s">{</span> 1493 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1494 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1495 1496 <span class="c"># Create the transpose matrix of size $NumOfCols x $NumOfRows</span> 1497 <span class="c">#</span> 1498 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1499 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="s">)</span><span class="sc">;</span> 1500 1501 <span class="c"># Swap rows and columns...</span> 1502 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1503 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1504 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$ColIndex</span>][<span class="i">$RowIndex</span>]<span class="sc">;</span> 1505 <span class="s">}</span> 1506 <span class="s">}</span> 1507 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 1508 <span class="s">}</span> 1509 1510 <span class="c"># Is it a matrix object?</span> <a name="IsMatrix-"></a>1511 <span class="k">sub </span><span class="m">IsMatrix ($)</span> <span class="s">{</span> 1512 <span class="k">my</span><span class="s">(</span><span class="i">$Object</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1513 1514 <span class="k">return</span> <span class="i">_IsMatrix</span><span class="s">(</span><span class="i">$Object</span><span class="s">)</span><span class="sc">;</span> 1515 <span class="s">}</span> 1516 1517 <span class="c"># Set value print format for an individual object or the whole class during StringifyMatrix operation...</span> <a name="SetValuePrintFormat-"></a>1518 <span class="k">sub </span><span class="m">SetValuePrintFormat ($;$)</span> <span class="s">{</span> 1519 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1520 1521 <span class="k">if</span> <span class="s">(</span><span class="s">(</span><span class="i">@_</span> == <span class="n">2</span><span class="s">)</span> && <span class="s">(</span><span class="i">_IsMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1522 <span class="c"># Set value print format for the specific object...</span> 1523 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ValuePrintFormat</span><span class="s">)</span> = <span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="s">)</span><span class="sc">;</span> 1524 1525 <span class="i">$This</span>->{<span class="w">ValueFormat</span>} = <span class="i">$ValuePrintFormat</span><span class="sc">;</span> 1526 <span class="s">}</span> 1527 <span class="k">else</span> <span class="s">{</span> 1528 <span class="c"># Set value print format for the class...</span> 1529 <span class="k">my</span><span class="s">(</span><span class="i">$ValuePrintFormat</span><span class="s">)</span> = <span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="sc">;</span> 1530 1531 <span class="i">$ValueFormat</span> = <span class="i">$ValuePrintFormat</span><span class="sc">;</span> 1532 <span class="s">}</span> 1533 <span class="s">}</span> 1534 1535 <span class="c"># Set print style for matrix rows for an individual object or the whole class during StringifyMatrix</span> 1536 <span class="c"># operation.</span> 1537 <span class="c">#</span> 1538 <span class="c"># Possible values: AllRowsInOneLine, OneRowPerLine. Default: AllRowsInOneLine</span> 1539 <span class="c">#</span> <a name="SetMatrixPrintStyle-"></a>1540 <span class="k">sub </span><span class="m">SetMatrixPrintStyle ($;$)</span> <span class="s">{</span> 1541 <span class="k">my</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1542 1543 <span class="k">if</span> <span class="s">(</span><span class="s">(</span><span class="i">@_</span> == <span class="n">2</span><span class="s">)</span> && <span class="s">(</span><span class="i">_IsMatrix</span><span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1544 <span class="c"># Set value print format for the specific object...</span> 1545 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$MatrixPrintStyleValue</span><span class="s">)</span> = <span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="s">)</span><span class="sc">;</span> 1546 1547 <span class="k">if</span> <span class="s">(</span><span class="i">$MatrixPrintStyleValue</span> !~ <span class="q">/^(AllRowsInOneLine|OneRowPerLine)$/i</span><span class="s">)</span> <span class="s">{</span> 1548 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->SetMatrixPrintStyle: Specified MatrixPrintStyle, $MatrixPrintStyleValue, is not valid. Supported values: AllRowsInOneLine, OneRowPerLine..."</span><span class="sc">;</span> 1549 <span class="s">}</span> 1550 1551 <span class="i">$This</span>->{<span class="w">MatrixPrintStyle</span>} = <span class="i">$MatrixPrintStyleValue</span><span class="sc">;</span> 1552 <span class="s">}</span> 1553 <span class="k">else</span> <span class="s">{</span> 1554 <span class="c"># Set value print format for the class...</span> 1555 <span class="k">my</span><span class="s">(</span><span class="i">$MatrixPrintStyleValue</span><span class="s">)</span> = <span class="s">(</span><span class="i">$FirstParameter</span><span class="s">)</span><span class="sc">;</span> 1556 1557 <span class="k">if</span> <span class="s">(</span><span class="i">$MatrixPrintStyleValue</span> !~ <span class="q">/^(AllRowsInOneLine|OneRowPerLine)$/i</span><span class="s">)</span> <span class="s">{</span> 1558 <span class="w">croak</span> <span class="q">"Error: ${ClassName}::SetMatrixPrintStyle: Specified MatrixPrintStyle, $MatrixPrintStyleValue, is not valid. Supported values: AllRowsInOneLine, OneRowPerLine..."</span><span class="sc">;</span> 1559 <span class="s">}</span> 1560 1561 <span class="i">$MatrixPrintStyle</span> = <span class="i">$MatrixPrintStyleValue</span><span class="sc">;</span> 1562 <span class="s">}</span> 1563 <span class="s">}</span> 1564 1565 <span class="c"># Is it a matrix object?</span> 1566 <span class="c">#</span> <a name="_IsMatrix-"></a>1567 <span class="k">sub </span><span class="m">_IsMatrix</span> <span class="s">{</span> 1568 <span class="k">my</span><span class="s">(</span><span class="i">$Object</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1569 1570 <span class="k">return</span> <span class="s">(</span><span class="i">Scalar::Util::blessed</span><span class="s">(</span><span class="i">$Object</span><span class="s">)</span> && <span class="i">$Object</span><span class="i">->isa</span><span class="s">(</span><span class="i">$ClassName</span><span class="s">)</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 1571 <span class="s">}</span> 1572 1573 <span class="c"># Make sure it's a matrix reference...</span> 1574 <span class="c">#</span> <a name="_ValidateMatrix-"></a>1575 <span class="k">sub </span><span class="m">_ValidateMatrix</span> <span class="s">{</span> 1576 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">$Matrix</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1577 1578 <span class="k">if</span> <span class="s">(</span>!<span class="i">_IsMatrix</span><span class="s">(</span><span class="i">$Matrix</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1579 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: Object must be a matrix..."</span><span class="sc">;</span> 1580 <span class="s">}</span> 1581 <span class="s">}</span> 1582 1583 <span class="c"># Make sure both row and column indicies are valid...</span> 1584 <span class="c">#</span> <a name="_ValidateRowAndColumnIndicies-"></a>1585 <span class="k">sub </span><span class="m">_ValidateRowAndColumnIndicies</span> <span class="s">{</span> 1586 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColumnIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1587 1588 <span class="i">$This</span><span class="i">->_ValidateRowIndex</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span><span class="sc">;</span> 1589 <span class="i">$This</span><span class="i">->_ValidateColumnIndex</span><span class="s">(</span><span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$ColumnIndex</span><span class="s">)</span><span class="sc">;</span> 1590 1591 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 1592 <span class="s">}</span> 1593 1594 <span class="c"># Make sure it's a valid row index...</span> 1595 <span class="c">#</span> <a name="_ValidateRowIndex-"></a>1596 <span class="k">sub </span><span class="m">_ValidateRowIndex</span> <span class="s">{</span> 1597 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1598 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="s">)</span><span class="sc">;</span> 1599 1600 <span class="k">if</span> <span class="s">(</span>!<span class="k">defined</span> <span class="i">$RowIndex</span><span class="s">)</span> <span class="s">{</span> 1601 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: RowIndex must be defined..."</span><span class="sc">;</span> 1602 <span class="s">}</span> 1603 <span class="i">$NumOfRows</span> = <span class="i">$This</span><span class="i">->GetNumOfRows</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1604 <span class="k">if</span> <span class="s">(</span><span class="i">$RowIndex</span> < <span class="n">0</span> || <span class="i">$RowIndex</span> >= <span class="i">$NumOfRows</span><span class="s">)</span> <span class="s">{</span> 1605 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: RowIndex value $RowIndex must be >= 0 and < $NumOfRows, NumOfRows, in matrix..."</span><span class="sc">;</span> 1606 <span class="s">}</span> 1607 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 1608 <span class="s">}</span> 1609 1610 <span class="c"># Make sure it's a valid column index...</span> 1611 <span class="c">#</span> <a name="_ValidateColumnIndex-"></a>1612 <span class="k">sub </span><span class="m">_ValidateColumnIndex</span> <span class="s">{</span> 1613 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$ErrorMsgPrefix</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 1614 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 1615 1616 <span class="k">if</span> <span class="s">(</span>!<span class="k">defined</span> <span class="i">$ColIndex</span><span class="s">)</span> <span class="s">{</span> 1617 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: ColIndex must be defined..."</span><span class="sc">;</span> 1618 <span class="s">}</span> 1619 <span class="i">$NumOfCols</span> = <span class="i">$This</span><span class="i">->GetNumOfColumns</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1620 <span class="k">if</span> <span class="s">(</span><span class="i">$ColIndex</span> < <span class="n">0</span> || <span class="i">$ColIndex</span> >= <span class="i">$NumOfCols</span><span class="s">)</span> <span class="s">{</span> 1621 <span class="w">croak</span> <span class="q">"$ErrorMsgPrefix: ColIndex value $ColIndex must be >= 0 and < $NumOfCols, NumOfCols, in matrix..."</span><span class="sc">;</span> 1622 <span class="s">}</span> 1623 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 1624 <span class="s">}</span> 1625 1626 <span class="c">#</span> 1627 <span class="c"># Matrix addition operator supports two addition modes:</span> 1628 <span class="c"># . Addition of two matrices by adding corresponding matrix values</span> 1629 <span class="c"># . Addition of a scalar value to matrix values ($Matrix + 1)</span> 1630 <span class="c">#</span> 1631 <span class="c"># Caveats:</span> 1632 <span class="c"># . Addition of a matrix to scalar is not allowed (1 + $Matrix)</span> 1633 <span class="c">#</span> <a name="_MatrixAdditionOperator-"></a>1634 <span class="k">sub </span><span class="m">_MatrixAdditionOperator</span> <span class="s">{</span> 1635 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1636 1637 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixAdditionOperator: Matrix addition failed"</span><span class="sc">;</span> 1638 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 1639 1640 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1641 1642 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1643 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 1644 1645 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 1646 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 1647 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1648 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1649 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] + <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1650 <span class="s">}</span> 1651 <span class="s">}</span> 1652 <span class="s">}</span> 1653 <span class="k">else</span> <span class="s">{</span> 1654 <span class="c"># Scalar addition...</span> 1655 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 1656 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 1657 <span class="s">}</span> 1658 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1659 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1660 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] + <span class="i">$Other</span><span class="sc">;</span> 1661 <span class="s">}</span> 1662 <span class="s">}</span> 1663 <span class="s">}</span> 1664 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 1665 <span class="s">}</span> 1666 1667 <span class="c">#</span> 1668 <span class="c"># Matrix subtraction operator supports two subtraction modes:</span> 1669 <span class="c"># . Subtraction of two matrices by subtracting corresponding matrix values</span> 1670 <span class="c"># . Subtraction of a scalar value from matrix values ($Matrix - 1)</span> 1671 <span class="c">#</span> 1672 <span class="c"># Caveats:</span> 1673 <span class="c"># . Subtraction of a matrix from scalar is not allowed (1 - $Matrix)</span> 1674 <span class="c">#</span> <a name="_MatrixSubtractionOperator-"></a>1675 <span class="k">sub </span><span class="m">_MatrixSubtractionOperator</span> <span class="s">{</span> 1676 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1677 1678 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixSubtractionOperator: Matrix subtraction failed"</span><span class="sc">;</span> 1679 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 1680 1681 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1682 1683 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1684 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 1685 1686 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 1687 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 1688 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1689 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1690 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] - <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1691 <span class="s">}</span> 1692 <span class="s">}</span> 1693 <span class="s">}</span> 1694 <span class="k">else</span> <span class="s">{</span> 1695 <span class="c"># Scalar subtraction...</span> 1696 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 1697 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 1698 <span class="s">}</span> 1699 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1700 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1701 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] - <span class="i">$Other</span><span class="sc">;</span> 1702 <span class="s">}</span> 1703 <span class="s">}</span> 1704 <span class="s">}</span> 1705 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 1706 <span class="s">}</span> 1707 1708 <span class="c">#</span> 1709 <span class="c"># Matrix multiplication operator supports two multiplication modes:</span> 1710 <span class="c"># . Multiplication of two matrices</span> 1711 <span class="c"># . Multiplication of matrix values by a scalar ($Matrix * 1)</span> 1712 <span class="c">#</span> 1713 <span class="c"># Caveats:</span> 1714 <span class="c"># . Multiplication of a scalar by a is not allowed (1 * $Matrix)</span> 1715 <span class="c">#</span> <a name="_MatrixMultiplicationOperator-"></a>1716 <span class="k">sub </span><span class="m">_MatrixMultiplicationOperator</span> <span class="s">{</span> 1717 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="s">)</span><span class="sc">;</span> 1718 1719 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixMultiplicationOperator: Matrix multiplication failed"</span><span class="sc">;</span> 1720 <span class="i">$CheckSizes</span> = <span class="n">0</span><span class="sc">;</span> 1721 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="cm">,</span> <span class="i">$CheckSizes</span><span class="s">)</span><span class="sc">;</span> 1722 1723 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="s">)</span><span class="sc">;</span> 1724 1725 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 1726 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 1727 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows1</span><span class="cm">,</span> <span class="i">$NumOfCols1</span><span class="cm">,</span> <span class="i">$RowIndex1</span><span class="cm">,</span> <span class="i">$ColIndex1</span><span class="cm">,</span> <span class="i">$NumOfRows2</span><span class="cm">,</span> <span class="i">$NumOfCols2</span><span class="cm">,</span> <span class="i">$ColIndex2</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$RowColIndex</span><span class="s">)</span><span class="sc">;</span> 1728 1729 <span class="s">(</span><span class="i">$NumOfRows1</span><span class="cm">,</span> <span class="i">$NumOfCols1</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1730 <span class="s">(</span><span class="i">$NumOfRows2</span><span class="cm">,</span> <span class="i">$NumOfCols2</span><span class="s">)</span> = <span class="i">$Other</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1731 1732 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfCols1</span> != <span class="i">$NumOfRows2</span><span class="s">)</span> <span class="s">{</span> 1733 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: NumOfCols in first matrix of size $NumOfRows1 x $NumOfCols1 must be equal to NumOfRows in second matrix of size $NumOfRows2 x $NumOfCols2..."</span><span class="sc">;</span> 1734 <span class="s">}</span> 1735 1736 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows1</span><span class="cm">,</span> <span class="i">$NumOfCols2</span><span class="s">)</span><span class="sc">;</span> 1737 1738 <span class="k">for</span> <span class="i">$RowIndex1</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows1</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1739 <span class="k">for</span> <span class="i">$ColIndex2</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols2</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1740 <span class="i">$Value</span> = <span class="n">0</span><span class="sc">;</span> 1741 <span class="k">for</span> <span class="i">$RowColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols1</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1742 <span class="i">$Value</span> += <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex1</span>][<span class="i">$RowColIndex</span>] * <span class="i">$Other</span>->[<span class="i">$RowColIndex</span>][<span class="i">$ColIndex2</span>]<span class="sc">;</span> 1743 <span class="s">}</span> 1744 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex1</span>][<span class="i">$ColIndex2</span>] = <span class="i">$Value</span><span class="sc">;</span> 1745 <span class="s">}</span> 1746 <span class="s">}</span> 1747 <span class="s">}</span> 1748 <span class="k">else</span> <span class="s">{</span> 1749 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1750 1751 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1752 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 1753 <span class="c"># Scalar subtraction...</span> 1754 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 1755 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 1756 <span class="s">}</span> 1757 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1758 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1759 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] * <span class="i">$Other</span><span class="sc">;</span> 1760 <span class="s">}</span> 1761 <span class="s">}</span> 1762 <span class="s">}</span> 1763 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 1764 <span class="s">}</span> 1765 1766 <span class="c">#</span> 1767 <span class="c"># Matrix division operator supports two division modes:</span> 1768 <span class="c"># . Division of two matrices by dividing corresponding matrix values</span> 1769 <span class="c"># . Division matrix values by a scalar($Matrix/2)</span> 1770 <span class="c">#</span> 1771 <span class="c"># Caveats:</span> 1772 <span class="c"># . Division of scalar value by a matrix is not allowed (2/$Matrix)</span> 1773 <span class="c">#</span> <a name="_MatrixDivisionOperator-"></a>1774 <span class="k">sub </span><span class="m">_MatrixDivisionOperator</span> <span class="s">{</span> 1775 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1776 1777 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixDivisionOperator: Matrix division failed"</span><span class="sc">;</span> 1778 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 1779 1780 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1781 1782 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1783 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 1784 1785 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 1786 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 1787 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1788 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1789 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] / <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1790 <span class="s">}</span> 1791 <span class="s">}</span> 1792 <span class="s">}</span> 1793 <span class="k">else</span> <span class="s">{</span> 1794 <span class="c"># Scalar subtraction...</span> 1795 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 1796 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 1797 <span class="s">}</span> 1798 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1799 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1800 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] / <span class="i">$Other</span><span class="sc">;</span> 1801 <span class="s">}</span> 1802 <span class="s">}</span> 1803 <span class="s">}</span> 1804 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 1805 <span class="s">}</span> 1806 1807 <span class="c">#</span> 1808 <span class="c"># Matrix exponentiation operator supports two division modes:</span> 1809 <span class="c"># . Exponent of two matrices by exponentiation of corresponding matrix values</span> 1810 <span class="c"># . Exponentiation matrix values by a scalar ($Matrix ** 2)</span> 1811 <span class="c">#</span> 1812 <span class="c"># Caveats:</span> 1813 <span class="c"># . Exponentiation of scalar value by a matrix is not allowed (2 ** $Matrix)</span> 1814 <span class="c">#</span> <a name="_MatrixExponentiationOperator-"></a>1815 <span class="k">sub </span><span class="m">_MatrixExponentiationOperator</span> <span class="s">{</span> 1816 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1817 1818 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixExponentiationOperator: Matrix exponentiation failed"</span><span class="sc">;</span> 1819 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 1820 1821 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1822 1823 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1824 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 1825 1826 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 1827 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 1828 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1829 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1830 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] ** <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1831 <span class="s">}</span> 1832 <span class="s">}</span> 1833 <span class="s">}</span> 1834 <span class="k">else</span> <span class="s">{</span> 1835 <span class="c"># Scalar subtraction...</span> 1836 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 1837 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 1838 <span class="s">}</span> 1839 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1840 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1841 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] ** <span class="i">$Other</span><span class="sc">;</span> 1842 <span class="s">}</span> 1843 <span class="s">}</span> 1844 <span class="s">}</span> 1845 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 1846 <span class="s">}</span> 1847 1848 <span class="c">#</span> 1849 <span class="c"># Matrix modulus operator supports two division modes:</span> 1850 <span class="c"># . Modulus of two matrices by taking modulus between corresponding matrix values</span> 1851 <span class="c"># . Modulus of matrix values by a scalar ($Matrix % 2)</span> 1852 <span class="c">#</span> 1853 <span class="c"># Caveats:</span> 1854 <span class="c"># . Modulus of scalar value by a matrix is not allowed (2 % $Matrix)</span> 1855 <span class="c">#</span> <a name="_MatrixModulusOperator-"></a>1856 <span class="k">sub </span><span class="m">_MatrixModulusOperator</span> <span class="s">{</span> 1857 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1858 1859 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixModulusOperator: Matrix modulus failed"</span><span class="sc">;</span> 1860 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 1861 1862 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1863 1864 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1865 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 1866 1867 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 1868 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 1869 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1870 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1871 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] % <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 1872 <span class="s">}</span> 1873 <span class="s">}</span> 1874 <span class="s">}</span> 1875 <span class="k">else</span> <span class="s">{</span> 1876 <span class="c"># Scalar subtraction...</span> 1877 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 1878 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 1879 <span class="s">}</span> 1880 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1881 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1882 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] % <span class="i">$Other</span><span class="sc">;</span> 1883 <span class="s">}</span> 1884 <span class="s">}</span> 1885 <span class="s">}</span> 1886 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 1887 <span class="s">}</span> 1888 1889 <span class="c">#</span> 1890 <span class="c"># Matrix booelan operator checks whether a matrix contains at least one non-zero</span> 1891 <span class="c"># value...</span> 1892 <span class="c">#</span> <a name="_MatrixBooleanOperator-"></a>1893 <span class="k">sub </span><span class="m">_MatrixBooleanOperator</span> <span class="s">{</span> 1894 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1895 1896 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixBooleanOperator: Matrix boolean operation failed"</span><span class="sc">;</span> 1897 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 1898 1899 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1900 1901 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1902 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1903 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1904 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1905 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1906 <span class="s">}</span> 1907 <span class="s">}</span> 1908 <span class="s">}</span> 1909 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1910 <span class="s">}</span> 1911 1912 <span class="c">#</span> 1913 <span class="c"># Matrix not booelan operator checks whether a matrix contains only zero values...</span> 1914 <span class="c"># value...</span> 1915 <span class="c">#</span> <a name="_MatrixNotBooleanOperator-"></a>1916 <span class="k">sub </span><span class="m">_MatrixNotBooleanOperator</span> <span class="s">{</span> 1917 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1918 1919 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixNotBooleanOperator: Matrix not boolean operation failed"</span><span class="sc">;</span> 1920 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 1921 1922 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1923 1924 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1925 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1926 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1927 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="n">0.0</span><span class="s">)</span> <span class="s">{</span> 1928 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1929 <span class="s">}</span> 1930 <span class="s">}</span> 1931 <span class="s">}</span> 1932 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1933 <span class="s">}</span> 1934 1935 <span class="c">#</span> 1936 <span class="c"># Matrix equal operator supports two modes:</span> 1937 <span class="c"># . Comparison of corresponding values in two matrices</span> 1938 <span class="c"># . Comparing matrix values to a scalar ($Matrix == 2)</span> 1939 <span class="c">#</span> 1940 <span class="c"># Caveats:</span> 1941 <span class="c"># . Comparison of a scalar to matrix values is not allowed (2 == $Matrix)</span> 1942 <span class="c">#</span> <a name="_MatrixEqualOperator-"></a>1943 <span class="k">sub </span><span class="m">_MatrixEqualOperator</span> <span class="s">{</span> 1944 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1945 1946 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixEqualOperator: Matrix equal failed"</span><span class="sc">;</span> 1947 <span class="i">$CheckMatrixSizes</span> = <span class="n">0</span><span class="sc">;</span> 1948 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="s">)</span><span class="sc">;</span> 1949 1950 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 1951 1952 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1953 1954 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 1955 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 1956 <span class="k">my</span><span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="sc">;</span> 1957 1958 <span class="c"># Check sizes...</span> 1959 <span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span> = <span class="i">$Other</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 1960 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$NumOfRows</span> == <span class="i">$OtherNumOfRows</span> && <span class="i">$NumOfCols</span> == <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1961 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1962 <span class="s">}</span> 1963 1964 <span class="c"># Check values...</span> 1965 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1966 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1967 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="s">)</span> <span class="s">{</span> 1968 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1969 <span class="s">}</span> 1970 <span class="s">}</span> 1971 <span class="s">}</span> 1972 <span class="s">}</span> 1973 <span class="k">else</span> <span class="s">{</span> 1974 <span class="c"># Scalar comparison...</span> 1975 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 1976 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 1977 <span class="s">}</span> 1978 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1979 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 1980 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] != <span class="i">$Other</span><span class="s">)</span> <span class="s">{</span> 1981 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 1982 <span class="s">}</span> 1983 <span class="s">}</span> 1984 <span class="s">}</span> 1985 <span class="s">}</span> 1986 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 1987 <span class="s">}</span> 1988 1989 <span class="c">#</span> 1990 <span class="c"># Matrix not equal operator supports two modes:</span> 1991 <span class="c"># . Comparison of corresponding values in two matrices</span> 1992 <span class="c"># . Comparing matrix values to a scalar ($Matrix != 2)</span> 1993 <span class="c">#</span> 1994 <span class="c"># Caveats:</span> 1995 <span class="c"># . Comparison of a scalar to matrix values is not allowed (2 != $Matrix)</span> 1996 <span class="c">#</span> <a name="_MatrixNotEqualOperator-"></a>1997 <span class="k">sub </span><span class="m">_MatrixNotEqualOperator</span> <span class="s">{</span> 1998 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 1999 2000 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixNotEqualOperator: Matrix not equal failed"</span><span class="sc">;</span> 2001 <span class="i">$CheckMatrixSizes</span> = <span class="n">0</span><span class="sc">;</span> 2002 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="s">)</span><span class="sc">;</span> 2003 2004 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2005 2006 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2007 2008 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 2009 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 2010 <span class="k">my</span><span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="sc">;</span> 2011 2012 <span class="c"># Check sizes...</span> 2013 <span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span> = <span class="i">$Other</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2014 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$NumOfRows</span> == <span class="i">$OtherNumOfRows</span> && <span class="i">$NumOfCols</span> == <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2015 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 2016 <span class="s">}</span> 2017 2018 <span class="c"># Check values...</span> 2019 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2020 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2021 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] == <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="s">)</span> <span class="s">{</span> 2022 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2023 <span class="s">}</span> 2024 <span class="s">}</span> 2025 <span class="s">}</span> 2026 <span class="s">}</span> 2027 <span class="k">else</span> <span class="s">{</span> 2028 <span class="c"># Scalar comparison...</span> 2029 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 2030 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 2031 <span class="s">}</span> 2032 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2033 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2034 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] == <span class="i">$Other</span><span class="s">)</span> <span class="s">{</span> 2035 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2036 <span class="s">}</span> 2037 <span class="s">}</span> 2038 <span class="s">}</span> 2039 <span class="s">}</span> 2040 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 2041 <span class="s">}</span> 2042 2043 <span class="c">#</span> 2044 <span class="c"># Matrix less than operator supports two modes:</span> 2045 <span class="c"># . Comparison of corresponding values in two matrices</span> 2046 <span class="c"># . Comparing matrix values to a scalar ($Matrix < 2)</span> 2047 <span class="c">#</span> 2048 <span class="c"># Caveats:</span> 2049 <span class="c"># . Comparison of a scalar to matrix values is not allowed (2 < $Matrix)</span> 2050 <span class="c">#</span> <a name="_MatrixLessThanOperator-"></a>2051 <span class="k">sub </span><span class="m">_MatrixLessThanOperator</span> <span class="s">{</span> 2052 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2053 2054 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixLessThanOperator: Matrix less than failed"</span><span class="sc">;</span> 2055 <span class="i">$CheckMatrixSizes</span> = <span class="n">0</span><span class="sc">;</span> 2056 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="s">)</span><span class="sc">;</span> 2057 2058 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2059 2060 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2061 2062 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 2063 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 2064 <span class="k">my</span><span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="sc">;</span> 2065 2066 <span class="c"># Check sizes...</span> 2067 <span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span> = <span class="i">$Other</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2068 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$NumOfRows</span> == <span class="i">$OtherNumOfRows</span> && <span class="i">$NumOfCols</span> == <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2069 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2070 <span class="s">}</span> 2071 2072 <span class="c"># Check values...</span> 2073 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2074 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2075 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] >= <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="s">)</span> <span class="s">{</span> 2076 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2077 <span class="s">}</span> 2078 <span class="s">}</span> 2079 <span class="s">}</span> 2080 <span class="s">}</span> 2081 <span class="k">else</span> <span class="s">{</span> 2082 <span class="c"># Scalar comparison...</span> 2083 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 2084 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 2085 <span class="s">}</span> 2086 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2087 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2088 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] >= <span class="i">$Other</span><span class="s">)</span> <span class="s">{</span> 2089 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2090 <span class="s">}</span> 2091 <span class="s">}</span> 2092 <span class="s">}</span> 2093 <span class="s">}</span> 2094 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 2095 <span class="s">}</span> 2096 2097 <span class="c">#</span> 2098 <span class="c"># Matrix less than equal operator supports two modes:</span> 2099 <span class="c"># . Comparion of corresponding values in two matrices</span> 2100 <span class="c"># . Comparing matrix values to a scalar ($Matrix <= 2)</span> 2101 <span class="c">#</span> 2102 <span class="c"># Caveats:</span> 2103 <span class="c"># . Comparison of a scalar to matrix values is not allowed (2 <= $Matrix)</span> 2104 <span class="c">#</span> <a name="_MatrixLessThanEqualOperator-"></a>2105 <span class="k">sub </span><span class="m">_MatrixLessThanEqualOperator</span> <span class="s">{</span> 2106 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2107 2108 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixLessThanEqualOperator: Matrix less than equal failed"</span><span class="sc">;</span> 2109 <span class="i">$CheckMatrixSizes</span> = <span class="n">0</span><span class="sc">;</span> 2110 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="s">)</span><span class="sc">;</span> 2111 2112 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2113 2114 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2115 2116 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 2117 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 2118 <span class="k">my</span><span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="sc">;</span> 2119 2120 <span class="c"># Check sizes...</span> 2121 <span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span> = <span class="i">$Other</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2122 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$NumOfRows</span> == <span class="i">$OtherNumOfRows</span> && <span class="i">$NumOfCols</span> == <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2123 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2124 <span class="s">}</span> 2125 2126 <span class="c"># Check values...</span> 2127 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2128 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2129 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] > <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="s">)</span> <span class="s">{</span> 2130 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2131 <span class="s">}</span> 2132 <span class="s">}</span> 2133 <span class="s">}</span> 2134 <span class="s">}</span> 2135 <span class="k">else</span> <span class="s">{</span> 2136 <span class="c"># Scalar comparison...</span> 2137 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 2138 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 2139 <span class="s">}</span> 2140 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2141 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2142 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] > <span class="i">$Other</span><span class="s">)</span> <span class="s">{</span> 2143 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2144 <span class="s">}</span> 2145 <span class="s">}</span> 2146 <span class="s">}</span> 2147 <span class="s">}</span> 2148 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 2149 <span class="s">}</span> 2150 2151 <span class="c">#</span> 2152 <span class="c"># Matrix greatar than operator supports two modes:</span> 2153 <span class="c"># . Comparison of corresponding values in two matrices</span> 2154 <span class="c"># . Comparing matrix values to a scalar ($Matrix > 2)</span> 2155 <span class="c">#</span> 2156 <span class="c"># Caveats:</span> 2157 <span class="c"># . Comparison of a scalar to matrix values is not allowed (2 > $Matrix)</span> 2158 <span class="c">#</span> <a name="_MatrixGreatarThanOperator-"></a>2159 <span class="k">sub </span><span class="m">_MatrixGreatarThanOperator</span> <span class="s">{</span> 2160 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2161 2162 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixGreatarThanOperator: Matrix greatar than failed"</span><span class="sc">;</span> 2163 <span class="i">$CheckMatrixSizes</span> = <span class="n">0</span><span class="sc">;</span> 2164 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="s">)</span><span class="sc">;</span> 2165 2166 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2167 2168 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2169 2170 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 2171 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 2172 <span class="k">my</span><span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="sc">;</span> 2173 2174 <span class="c"># Check sizes...</span> 2175 <span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span> = <span class="i">$Other</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2176 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$NumOfRows</span> == <span class="i">$OtherNumOfRows</span> && <span class="i">$NumOfCols</span> == <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2177 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2178 <span class="s">}</span> 2179 2180 <span class="c"># Check values...</span> 2181 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2182 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2183 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] <= <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="s">)</span> <span class="s">{</span> 2184 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2185 <span class="s">}</span> 2186 <span class="s">}</span> 2187 <span class="s">}</span> 2188 <span class="s">}</span> 2189 <span class="k">else</span> <span class="s">{</span> 2190 <span class="c"># Scalar comparison...</span> 2191 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 2192 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 2193 <span class="s">}</span> 2194 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2195 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2196 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] <= <span class="i">$Other</span><span class="s">)</span> <span class="s">{</span> 2197 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2198 <span class="s">}</span> 2199 <span class="s">}</span> 2200 <span class="s">}</span> 2201 <span class="s">}</span> 2202 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 2203 <span class="s">}</span> 2204 2205 <span class="c">#</span> 2206 <span class="c"># Matrix greatar than equal operator supports two modes:</span> 2207 <span class="c"># . Comparison of corresponding values in two matrices</span> 2208 <span class="c"># . Comparing matrix values to a scalar ($Matrix >= 2)</span> 2209 <span class="c">#</span> 2210 <span class="c"># Caveats:</span> 2211 <span class="c"># . Comparison of a scalar to matrix values is not allowed (2 >= $Matrix)</span> 2212 <span class="c">#</span> <a name="_MatrixGreatarThanEqualOperator-"></a>2213 <span class="k">sub </span><span class="m">_MatrixGreatarThanEqualOperator</span> <span class="s">{</span> 2214 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2215 2216 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixGreatarThanEqualOperator: Matrix greatar than equal failed"</span><span class="sc">;</span> 2217 <span class="i">$CheckMatrixSizes</span> = <span class="n">0</span><span class="sc">;</span> 2218 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="s">)</span><span class="sc">;</span> 2219 2220 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2221 2222 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2223 2224 <span class="k">if</span> <span class="s">(</span><span class="i">$OtherIsMatrix</span><span class="s">)</span> <span class="s">{</span> 2225 <span class="c"># $OrderFlipped is set to false for two matrices...</span> 2226 <span class="k">my</span><span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="sc">;</span> 2227 2228 <span class="c"># Check sizes...</span> 2229 <span class="s">(</span><span class="i">$OtherNumOfRows</span><span class="cm">,</span> <span class="i">$OtherNumOfCols</span><span class="s">)</span> = <span class="i">$Other</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2230 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$NumOfRows</span> == <span class="i">$OtherNumOfRows</span> && <span class="i">$NumOfCols</span> == <span class="i">$OtherNumOfCols</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2231 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2232 <span class="s">}</span> 2233 2234 <span class="c"># Check values...</span> 2235 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2236 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2237 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] < <span class="i">$Other</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="s">)</span> <span class="s">{</span> 2238 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2239 <span class="s">}</span> 2240 <span class="s">}</span> 2241 <span class="s">}</span> 2242 <span class="s">}</span> 2243 <span class="k">else</span> <span class="s">{</span> 2244 <span class="c"># Scalar comparison...</span> 2245 <span class="k">if</span> <span class="s">(</span><span class="i">$OrderFlipped</span><span class="s">)</span> <span class="s">{</span> 2246 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: First object must be a matrix..."</span><span class="sc">;</span> 2247 <span class="s">}</span> 2248 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2249 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2250 <span class="k">if</span> <span class="s">(</span><span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] < <span class="i">$Other</span><span class="s">)</span> <span class="s">{</span> 2251 <span class="k">return</span> <span class="n">0</span><span class="sc">;</span> 2252 <span class="s">}</span> 2253 <span class="s">}</span> 2254 <span class="s">}</span> 2255 <span class="s">}</span> 2256 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 2257 <span class="s">}</span> 2258 2259 <span class="c">#</span> 2260 <span class="c"># Matrix negative value operator returns a matrix with values corresponding to</span> 2261 <span class="c"># negative values of a matrix</span> 2262 <span class="c">#</span> <a name="_MatrixNegativeValueOperator-"></a>2263 <span class="k">sub </span><span class="m">_MatrixNegativeValueOperator</span> <span class="s">{</span> 2264 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2265 2266 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixNegativeValueOperator: Matrix negative value operation failed"</span><span class="sc">;</span> 2267 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 2268 2269 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2270 2271 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2272 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 2273 2274 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2275 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2276 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = - <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 2277 <span class="s">}</span> 2278 <span class="s">}</span> 2279 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 2280 <span class="s">}</span> 2281 2282 <span class="c">#</span> 2283 <span class="c"># Matrix absolute value operator returns a matrix with values corresponding to</span> 2284 <span class="c"># absolute values of a matrix</span> 2285 <span class="c">#</span> <a name="_MatrixAbsoluteValueOperator-"></a>2286 <span class="k">sub </span><span class="m">_MatrixAbsoluteValueOperator</span> <span class="s">{</span> 2287 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2288 2289 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixAbsoluteValueOperator: Matrix absolute value operation failed"</span><span class="sc">;</span> 2290 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 2291 2292 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2293 2294 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2295 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 2296 2297 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2298 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2299 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="k">abs</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 2300 <span class="s">}</span> 2301 <span class="s">}</span> 2302 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 2303 <span class="s">}</span> 2304 2305 <span class="c">#</span> 2306 <span class="c"># Matrix exp natural base operator returns a matrix with values corresponding to</span> 2307 <span class="c"># e raised to the power of values in a matrix</span> 2308 <span class="c">#</span> <a name="_MatrixExpNaturalBaseOperator-"></a>2309 <span class="k">sub </span><span class="m">_MatrixExpNaturalBaseOperator</span> <span class="s">{</span> 2310 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2311 2312 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixExpNaturalBaseOperator: Matrix exp operation failed"</span><span class="sc">;</span> 2313 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 2314 2315 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2316 2317 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2318 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 2319 2320 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2321 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2322 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="k">exp</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 2323 <span class="s">}</span> 2324 <span class="s">}</span> 2325 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 2326 <span class="s">}</span> 2327 2328 <span class="c">#</span> 2329 <span class="c"># Matrix log natural base operator returns a matrix with values corresponding to</span> 2330 <span class="c"># log of values in a matrix</span> 2331 <span class="c">#</span> <a name="_MatrixLogNaturalBaseOperator-"></a>2332 <span class="k">sub </span><span class="m">_MatrixLogNaturalBaseOperator</span> <span class="s">{</span> 2333 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2334 2335 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixLogNaturalBaseOperator: Matrix log operation failed"</span><span class="sc">;</span> 2336 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 2337 2338 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2339 2340 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2341 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 2342 2343 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2344 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2345 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="k">log</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 2346 <span class="s">}</span> 2347 <span class="s">}</span> 2348 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 2349 <span class="s">}</span> 2350 2351 <span class="c">#</span> 2352 <span class="c"># Matrix square root operator returns a matrix with values corresponding to</span> 2353 <span class="c"># sqrt of values in a matrix</span> 2354 <span class="c">#</span> <a name="_MatrixSquareRootOperator-"></a>2355 <span class="k">sub </span><span class="m">_MatrixSquareRootOperator</span> <span class="s">{</span> 2356 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2357 2358 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixSquareRootOperator: Matrix sqrt operation failed"</span><span class="sc">;</span> 2359 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 2360 2361 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2362 2363 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2364 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 2365 2366 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2367 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2368 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="k">sqrt</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 2369 <span class="s">}</span> 2370 <span class="s">}</span> 2371 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 2372 <span class="s">}</span> 2373 2374 <span class="c">#</span> 2375 <span class="c"># Matrix sine root operator returns a matrix with values corresponding to</span> 2376 <span class="c"># sin of values in a matrix</span> 2377 <span class="c">#</span> <a name="_MatrixSineOperator-"></a>2378 <span class="k">sub </span><span class="m">_MatrixSineOperator</span> <span class="s">{</span> 2379 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2380 2381 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixSineOperator: Matrix sin operation failed"</span><span class="sc">;</span> 2382 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 2383 2384 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2385 2386 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2387 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 2388 2389 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2390 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2391 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="k">sin</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 2392 <span class="s">}</span> 2393 <span class="s">}</span> 2394 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 2395 <span class="s">}</span> 2396 2397 <span class="c">#</span> 2398 <span class="c"># Matrix cosine root operator returns a matrix with values corresponding to</span> 2399 <span class="c"># cos of values in a matrix</span> 2400 <span class="c">#</span> <a name="_MatrixCosineOperator-"></a>2401 <span class="k">sub </span><span class="m">_MatrixCosineOperator</span> <span class="s">{</span> 2402 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$ErrorMsg</span><span class="s">)</span><span class="sc">;</span> 2403 2404 <span class="i">$ErrorMsg</span> = <span class="q">"_MatrixCosineOperator: Matrix cos operation failed"</span><span class="sc">;</span> 2405 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span> = <span class="i">_ProcessOverloadedOperatorParameters</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">@_</span><span class="s">)</span><span class="sc">;</span> 2406 2407 <span class="k">my</span><span class="s">(</span><span class="i">$Matrix</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$ColIndex</span><span class="s">)</span><span class="sc">;</span> 2408 2409 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2410 <span class="i">$Matrix</span> = <span class="i">new</span> <span class="i">Matrix</span><span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span><span class="sc">;</span> 2411 2412 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2413 <span class="k">for</span> <span class="i">$ColIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfCols</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2414 <span class="i">$Matrix</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>] = <span class="k">cos</span> <span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>][<span class="i">$ColIndex</span>]<span class="sc">;</span> 2415 <span class="s">}</span> 2416 <span class="s">}</span> 2417 <span class="k">return</span> <span class="i">$Matrix</span><span class="sc">;</span> 2418 <span class="s">}</span> 2419 2420 <span class="c"># Turn matrix into array for @{$Matrix} operation...</span> 2421 <span class="c">#</span> <a name="_MatrixToArrayOperator-"></a>2422 <span class="k">sub </span><span class="m">_MatrixToArrayOperator</span> <span class="s">{</span> 2423 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 2424 2425 <span class="k">return</span> \<span class="i">@</span>{<span class="i">$This</span>->{<span class="w">Values</span>}}<span class="sc">;</span> 2426 <span class="s">}</span> 2427 2428 <span class="c"># Always return true in boolean context...</span> 2429 <span class="c">#</span> <a name="_BoolifyMatrix-"></a>2430 <span class="k">sub </span><span class="m">_BoolifyMatrix</span> <span class="s">{</span> 2431 <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> 2432 2433 <span class="k">return</span> <span class="n">1</span><span class="sc">;</span> 2434 <span class="s">}</span> 2435 2436 <span class="c"># Process parameters passed to overloaded operators...</span> 2437 <span class="c">#</span> 2438 <span class="c"># For uninary operators, $SecondParameter is not defined.</span> <a name="_ProcessOverloadedOperatorParameters-"></a>2439 <span class="k">sub </span><span class="m">_ProcessOverloadedOperatorParameters</span> <span class="s">{</span> 2440 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="cm">,</span> <span class="i">$ParametersOrderStatus</span><span class="cm">,</span> <span class="i">$CheckMatrixSizesStatus</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 2441 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="cm">,</span> <span class="i">$CheckMatrixSizes</span><span class="s">)</span><span class="sc">;</span> 2442 2443 <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="s">)</span> = <span class="s">(</span><span class="i">$FirstParameter</span><span class="cm">,</span> <span class="i">$SecondParameter</span><span class="s">)</span><span class="sc">;</span> 2444 <span class="i">$OrderFlipped</span> = <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$ParametersOrderStatus</span><span class="s">)</span> && <span class="i">$ParametersOrderStatus</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 2445 <span class="i">$CheckMatrixSizes</span> = <span class="s">(</span><span class="k">defined</span> <span class="i">$CheckMatrixSizesStatus</span><span class="s">)</span> ? <span class="i">$CheckMatrixSizesStatus</span> <span class="co">:</span> <span class="n">1</span><span class="sc">;</span> 2446 2447 <span class="i">_ValidateMatrix</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">$This</span><span class="s">)</span><span class="sc">;</span> 2448 2449 <span class="i">$OtherIsMatrix</span> = <span class="n">0</span><span class="sc">;</span> 2450 <span class="k">if</span> <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$Other</span><span class="s">)</span> && <span class="s">(</span><span class="k">ref</span> <span class="i">$Other</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2451 <span class="c"># Make sure $Other is a matrix...</span> 2452 <span class="i">_ValidateMatrix</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">$Other</span><span class="s">)</span><span class="sc">;</span> 2453 <span class="k">if</span> <span class="s">(</span><span class="i">$CheckMatrixSizes</span><span class="s">)</span> <span class="s">{</span> 2454 <span class="i">_ValidateMatrixSizesAreEqual</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="s">)</span><span class="sc">;</span> 2455 <span class="s">}</span> 2456 <span class="i">$OtherIsMatrix</span> = <span class="n">1</span><span class="sc">;</span> 2457 <span class="s">}</span> 2458 <span class="k">return</span> <span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Other</span><span class="cm">,</span> <span class="i">$OrderFlipped</span><span class="cm">,</span> <span class="i">$OtherIsMatrix</span><span class="s">)</span><span class="sc">;</span> 2459 <span class="s">}</span> 2460 2461 <span class="c"># Make sure size of the two matrices contain the same number of values...</span> <a name="_ValidateMatrixSizesAreEqual-"></a>2462 <span class="k">sub </span><span class="m">_ValidateMatrixSizesAreEqual</span> <span class="s">{</span> 2463 <span class="k">my</span><span class="s">(</span><span class="i">$ErrorMsg</span><span class="cm">,</span> <span class="i">$Matrix1</span><span class="cm">,</span> <span class="i">$Matrix2</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 2464 <span class="k">my</span><span class="s">(</span><span class="i">$NumOfRows1</span><span class="cm">,</span> <span class="i">$NumOfCols1</span><span class="cm">,</span> <span class="i">$NumOfRows2</span><span class="cm">,</span> <span class="i">$NumOfCols2</span><span class="s">)</span><span class="sc">;</span> 2465 2466 <span class="s">(</span><span class="i">$NumOfRows1</span><span class="cm">,</span> <span class="i">$NumOfCols1</span><span class="s">)</span> = <span class="i">$Matrix1</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2467 <span class="s">(</span><span class="i">$NumOfRows2</span><span class="cm">,</span> <span class="i">$NumOfCols2</span><span class="s">)</span> = <span class="i">$Matrix2</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2468 2469 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$NumOfRows1</span> == <span class="i">$NumOfRows2</span> && <span class="i">$NumOfCols1</span> == <span class="i">$NumOfCols2</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2470 <span class="w">croak</span> <span class="q">"Error: ${ClassName}->${ErrorMsg}: Size of the matrices must be same..."</span><span class="sc">;</span> 2471 <span class="s">}</span> 2472 <span class="s">}</span> 2473 2474 <span class="c"># Return a string containing matrix values...</span> 2475 <span class="c">#</span> <a name="StringifyMatrix-"></a>2476 <span class="k">sub </span><span class="m">StringifyMatrix</span> <span class="s">{</span> 2477 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 2478 <span class="k">my</span><span class="s">(</span><span class="i">$MatrixString</span><span class="cm">,</span> <span class="i">$MatrixPrintStyleValue</span><span class="cm">,</span> <span class="i">$PrintFormat</span><span class="cm">,</span> <span class="i">$AllRowsInOneLine</span><span class="cm">,</span> <span class="i">$FormatString</span><span class="cm">,</span> <span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="cm">,</span> <span class="i">$RowIndex</span><span class="cm">,</span> <span class="i">$RowNum</span><span class="cm">,</span> <span class="i">$RowString</span><span class="cm">,</span> <span class="i">@ValuesFormat</span><span class="s">)</span><span class="sc">;</span> 2479 2480 <span class="s">(</span><span class="i">$NumOfRows</span><span class="cm">,</span> <span class="i">$NumOfCols</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->GetSize</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 2481 2482 <span class="i">$MatrixPrintStyleValue</span> = <span class="s">(</span><span class="k">exists</span> <span class="i">$This</span>->{<span class="w">MatrixPrintStyle</span>}<span class="s">)</span> ? <span class="i">$This</span>->{<span class="w">MatrixPrintStyle</span>} <span class="co">:</span> <span class="i">$MatrixPrintStyle</span><span class="sc">;</span> 2483 <span class="i">$AllRowsInOneLine</span> = <span class="s">(</span><span class="i">$MatrixPrintStyleValue</span> =~ <span class="q">/^AllRowsInOneLine$/i</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 2484 2485 <span class="i">$PrintFormat</span> = <span class="s">(</span><span class="k">exists</span> <span class="i">$This</span>->{<span class="w">ValueFormat</span>}<span class="s">)</span> ? <span class="i">$This</span>->{<span class="w">ValueFormat</span>} <span class="co">:</span> <span class="i">$ValueFormat</span><span class="sc">;</span> 2486 2487 <span class="i">@ValuesFormat</span> = <span class="s">(</span><span class="i">$PrintFormat</span><span class="s">)</span> x <span class="i">$NumOfCols</span><span class="sc">;</span> 2488 <span class="i">$FormatString</span> = <span class="k">join</span> <span class="q">' '</span><span class="cm">,</span> <span class="i">@ValuesFormat</span><span class="sc">;</span> 2489 2490 <span class="i">$MatrixString</span> = <span class="k">sprintf</span> <span class="q">"<Size: $NumOfRows x $NumOfCols;"</span><span class="sc">;</span> 2491 <span class="k">if</span> <span class="s">(</span><span class="i">$AllRowsInOneLine</span><span class="s">)</span> <span class="s">{</span> 2492 <span class="i">$MatrixString</span> .= <span class="k">sprintf</span> <span class="q">" Values:"</span><span class="sc">;</span> 2493 <span class="s">}</span> 2494 <span class="k">else</span> <span class="s">{</span> 2495 <span class="i">$MatrixString</span> .= <span class="k">sprintf</span> <span class="q">" Values:\n"</span><span class="sc">;</span> 2496 <span class="s">}</span> 2497 2498 <span class="i">$RowNum</span> = <span class="n">0</span><span class="sc">;</span> 2499 <span class="k">for</span> <span class="i">$RowIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$NumOfRows</span> -<span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 2500 <span class="i">$RowNum</span>++<span class="sc">;</span> 2501 <span class="i">$RowString</span> = <span class="k">sprintf</span> <span class="q">"Row${RowNum}:[$FormatString]"</span><span class="cm">,</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">Values</span>}[<span class="i">$RowIndex</span>]}<span class="sc">;</span> 2502 <span class="k">if</span> <span class="s">(</span><span class="i">$AllRowsInOneLine</span><span class="s">)</span> <span class="s">{</span> 2503 <span class="i">$MatrixString</span> .= <span class="q">" $RowString"</span><span class="sc">;</span> 2504 <span class="s">}</span> 2505 <span class="k">else</span> <span class="s">{</span> 2506 <span class="i">$MatrixString</span> .= <span class="q">"$RowString\n"</span><span class="sc">;</span> 2507 <span class="s">}</span> 2508 <span class="s">}</span> 2509 <span class="i">$MatrixString</span> .= <span class="q">">"</span><span class="sc">;</span> 2510 <span class="k">return</span> <span class="i">$MatrixString</span><span class="sc">;</span> 2511 <span class="s">}</span> 2512 <a name="EOF-"></a></pre> <p> </p> <br /> <center> <img src="../../../images/h2o2.png"> </center> </body> </html>