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| author | deepakjadmin |
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| date | Wed, 20 Jan 2016 11:55:01 -0500 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/mayachemtools/docs/modules/html/code/Matrix.html Wed Jan 20 11:55:01 2016 -0500 @@ -0,0 +1,2533 @@ +<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>