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det_by_lu.xml @upstream/2015.00.00.7 — raw · history · blame
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 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A:active { color : purple } </style> <script type='text/javascript' language='JavaScript' src='_det_by_lu_xml.js'> </script> </head> <body> <table><tr> <td> <a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a> </td> <td><a href="speed_utility.xml" target="_top">Prev</a> </td><td><a href="det_by_lu.cpp.xml" target="_top">Next</a> </td><td> <select onchange='choose_across0(this)'> <option>Index-></option> <option>contents</option> <option>reference</option> <option>index</option> <option>search</option> <option>external</option> </select> </td> <td> <select onchange='choose_up0(this)'> <option>Up-></option> <option>CppAD</option> <option>speed</option> <option>speed_utility</option> <option>det_by_lu</option> </select> </td> <td> <select onchange='choose_down3(this)'> <option>CppAD-></option> <option>Install</option> <option>Introduction</option> <option>AD</option> <option>ADFun</option> <option>preprocessor</option> <option>multi_thread</option> <option>library</option> <option>ipopt_solve</option> <option>Example</option> <option>speed</option> <option>Appendix</option> </select> </td> <td> <select onchange='choose_down2(this)'> <option>speed-></option> <option>speed_main</option> <option>speed_utility</option> <option>speed_double</option> <option>speed_adolc</option> <option>speed_cppad</option> <option>speed_fadbad</option> <option>speed_sacado</option> </select> </td> <td> <select onchange='choose_down1(this)'> <option>speed_utility-></option> <option>det_by_lu</option> <option>det_of_minor</option> <option>det_by_minor</option> <option>det_33</option> <option>det_grad_33</option> <option>mat_sum_sq</option> <option>ode_evaluate</option> <option>sparse_jac_fun</option> <option>sparse_hes_fun</option> <option>uniform_01</option> </select> </td> <td> <select onchange='choose_down0(this)'> <option>det_by_lu-></option> <option>det_by_lu.cpp</option> <option>det_by_lu.hpp</option> </select> </td> <td> <select onchange='choose_current0(this)'> <option>Headings-></option> <option>Syntax</option> <option>Inclusion</option> <option>Constructor</option> <option>Scalar</option> <option>n</option> <option>det</option> <option>---..a</option> <option>---..d</option> <option>Vector</option> <option>Example</option> <option>Source Code</option> </select> </td> </tr></table><br/> <center><b><big><big>Determinant Using Expansion by Lu Factorization</big></big></b></center> <br/> <b><big><a name="Syntax" id="Syntax">Syntax</a></big></b> <br/> <code><font color="blue"><span style='white-space: nowrap'># include <cppad/speed/det_by_lu.hpp><br/> </span></font></code> <code><font color="blue"><span style='white-space: nowrap'>det_by_lu<</span></font><i><font color="black"><span style='white-space: nowrap'>Scalar</span></font></i><font color="blue"><span style='white-space: nowrap'>> </span></font><i><font color="black"><span style='white-space: nowrap'>det</span></font></i><font color="blue"><span style='white-space: nowrap'>(</span></font><i><font color="black"><span style='white-space: nowrap'>n</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/> </span></font></code> <code><i><font color="black"><span style='white-space: nowrap'>d</span></font></i><font color="blue"><span style='white-space: nowrap'> = </span></font><i><font color="black"><span style='white-space: nowrap'>det</span></font></i><font color="blue"><span style='white-space: nowrap'>(</span></font><i><font color="black"><span style='white-space: nowrap'>a</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/> </span></font></code> <br/> <b><big><a name="Inclusion" id="Inclusion">Inclusion</a></big></b> <br/> The template class <code><font color="blue">det_by_lu</font></code> is defined in the <code><font color="blue">CppAD</font></code> namespace by including the file <code><font color="blue">cppad/speed/det_by_lu.hpp</font></code> (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by <a href="cppad.xml" target="_top"><span style='white-space: nowrap'>cppad.hpp</span></a> . <br/> <br/> <b><big><a name="Constructor" id="Constructor">Constructor</a></big></b> <br/> The syntax <code><font color="blue"><span style='white-space: nowrap'><br/>      det_by_lu<</span></font><i><font color="black"><span style='white-space: nowrap'>Scalar</span></font></i><font color="blue"><span style='white-space: nowrap'>> </span></font><i><font color="black"><span style='white-space: nowrap'>det</span></font></i><font color="blue"><span style='white-space: nowrap'>(</span></font><i><font color="black"><span style='white-space: nowrap'>n</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/> </span></font></code> constructs the object <code><i><font color="black"><span style='white-space: nowrap'>det</span></font></i></code> which can be used for evaluating the determinant of <code><i><font color="black"><span style='white-space: nowrap'>n</span></font></i></code> by <code><i><font color="black"><span style='white-space: nowrap'>n</span></font></i></code> matrices using LU factorization. <br/> <br/> <b><big><a name="Scalar" id="Scalar">Scalar</a></big></b> <br/> The type <code><i><font color="black"><span style='white-space: nowrap'>Scalar</span></font></i></code> can be any <a href="numerictype.xml" target="_top"><span style='white-space: nowrap'>NumericType</span></a> <br/> <br/> <b><big><a name="n" id="n">n</a></big></b> <br/> The argument <code><i><font color="black"><span style='white-space: nowrap'>n</span></font></i></code> has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      size_t </span></font><i><font color="black"><span style='white-space: nowrap'>n</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> <br/> <b><big><a name="det" id="det">det</a></big></b> <br/> The syntax <code><font color="blue"><span style='white-space: nowrap'><br/>      </span></font><i><font color="black"><span style='white-space: nowrap'>d</span></font></i><font color="blue"><span style='white-space: nowrap'> = </span></font><i><font color="black"><span style='white-space: nowrap'>det</span></font></i><font color="blue"><span style='white-space: nowrap'>(</span></font><i><font color="black"><span style='white-space: nowrap'>a</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/> </span></font></code> returns the determinant of the matrix <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>A</mi> </mrow></math> using LU factorization. <br/> <br/> <b><a name="det.a" id="det.a">a</a></b> <br/> The argument <code><i><font color="black"><span style='white-space: nowrap'>a</span></font></i></code> has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      const </span></font><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i><font color="blue"><span style='white-space: nowrap'> &</span></font><i><font color="black"><span style='white-space: nowrap'>a</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> It must be a <code><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i></code> with length <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">*</mo> <mi mathvariant='italic'>n</mi> </mrow></math> and with It must be a <code><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i></code> with length <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">*</mo> <mi mathvariant='italic'>n</mi> </mrow></math> and with elements of type <code><i><font color="black"><span style='white-space: nowrap'>Scalar</span></font></i></code> . The elements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">×</mo> <mi mathvariant='italic'>n</mi> </mrow></math> matrix <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>A</mi> </mrow></math> are defined, for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>i</mi> <mo stretchy="false">=</mo> <mn>0</mn> <mo stretchy="false">,</mo> <mo stretchy="false">…</mo> <mo stretchy="false">,</mo> <mi mathvariant='italic'>n</mi> <mn>-1</mn> </mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>j</mi> <mo stretchy="false">=</mo> <mn>0</mn> <mo stretchy="false">,</mo> <mo stretchy="false">…</mo> <mo stretchy="false">,</mo> <mi mathvariant='italic'>n</mi> <mn>-1</mn> </mrow></math> , by <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <msub><mi mathvariant='italic'>A</mi> <mrow><mi mathvariant='italic'>i</mi> <mo stretchy="false">,</mo> <mi mathvariant='italic'>j</mi> </mrow> </msub> <mo stretchy="false">=</mo> <mi mathvariant='italic'>a</mi> <mo stretchy="false">[</mo> <mi mathvariant='italic'>i</mi> <mo stretchy="false">*</mo> <mi mathvariant='italic'>m</mi> <mo stretchy="false">+</mo> <mi mathvariant='italic'>j</mi> <mo stretchy="false">]</mo> </mrow></math> <br/> <b><a name="det.d" id="det.d">d</a></b> <br/> The return value <code><i><font color="black"><span style='white-space: nowrap'>d</span></font></i></code> has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      </span></font><i><font color="black"><span style='white-space: nowrap'>Scalar</span></font></i><font color="blue"><span style='white-space: nowrap'> </span></font><i><font color="black"><span style='white-space: nowrap'>d</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> <br/> <b><big><a name="Vector" id="Vector">Vector</a></big></b> <br/> If <code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code> is a <code><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i></code> object, it must support the syntax <code><font color="blue"><span style='white-space: nowrap'><br/>      </span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>[</span></font><i><font color="black"><span style='white-space: nowrap'>i</span></font></i><font color="blue"><span style='white-space: nowrap'>]<br/> </span></font></code> where <code><i><font color="black"><span style='white-space: nowrap'>i</span></font></i></code> has type <code><font color="blue">size_t</font></code> with value less than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">*</mo> <mi mathvariant='italic'>n</mi> </mrow></math> . This must return a <code><i><font color="black"><span style='white-space: nowrap'>Scalar</span></font></i></code> value corresponding to the <code><i>i</i></code>-th element of the vector <code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code> . This is the only requirement of the type <code><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i></code> . <br/> <br/> <b><big><a name="Example" id="Example">Example</a></big></b> <br/> The file <a href="det_by_lu.cpp.xml" target="_top"><span style='white-space: nowrap'>det_by_lu.cpp</span></a> contains an example and test of <code><font color="blue">det_by_lu.hpp</font></code>. It returns true if it succeeds and false otherwise. <br/> <br/> <b><big><a name="Source Code" id="Source Code">Source Code</a></big></b> <br/> The file <a href="det_by_lu.hpp.xml" target="_top"><span style='white-space: nowrap'>det_by_lu.hpp</span></a> contains the source for this template function. <hr/>Input File: cppad/speed/det_by_lu.hpp </body> </html> |