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lu_vec_ad.cpp.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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solve lu factor and with recorded pivoting syntax purpose storage convention n m matrix rhs result logdet example "/> <style type='text/css'> body { color : black } body { background-color : white } A:link { color : blue } A:visited { color : purple } A:active { color : purple } </style> <script type='text/javascript' language='JavaScript' src='_lu_vec_ad.cpp_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_example.cpp.xml" target="_top">Prev</a> </td><td><a href="lu_vec_ad_ok.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>Example</option> <option>ExampleUtility</option> <option>lu_vec_ad.cpp</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>Example-></option> <option>General</option> <option>ExampleUtility</option> <option>ListAllExamples</option> <option>testvector</option> </select> </td> <td> <select onchange='choose_down1(this)'> <option>ExampleUtility-></option> <option>example.cpp</option> <option>speed_example.cpp</option> <option>lu_vec_ad.cpp</option> </select> </td> <td> <select onchange='choose_down0(this)'> <option>lu_vec_ad.cpp-></option> <option>lu_vec_ad_ok.cpp</option> </select> </td> <td> <select onchange='choose_current0(this)'> <option>Headings-></option> <option>Syntax</option> <option>Purpose</option> <option>Storage Convention</option> <option>n</option> <option>m</option> <option>Matrix</option> <option>Rhs</option> <option>Result</option> <option>logdet</option> <option>Example</option> </select> </td> </tr></table><br/> <center><b><big><big>Lu Factor and Solve with Recorded Pivoting</big></big></b></center> <code><span style='white-space: nowrap'><br/> </span></code><b><big><a name="Syntax" id="Syntax">Syntax</a></big></b> <br/> <code><font color="blue"><span style='white-space: nowrap'>int LuVecAD(<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/>      size_t </span></font><i><font color="black"><span style='white-space: nowrap'>m</span></font></i><font color="blue"><span style='white-space: nowrap'>,<br/>      VecAD<</span></font><i><font color="black"><span style='white-space: nowrap'>double</span></font></i><font color="blue"><span style='white-space: nowrap'>> &</span></font><i><font color="black"><span style='white-space: nowrap'>Matrix</span></font></i><font color="blue"><span style='white-space: nowrap'>,<br/>      VecAD<</span></font><i><font color="black"><span style='white-space: nowrap'>double</span></font></i><font color="blue"><span style='white-space: nowrap'>> &</span></font><i><font color="black"><span style='white-space: nowrap'>Rhs</span></font></i><font color="blue"><span style='white-space: nowrap'>,<br/>      VecAD<</span></font><i><font color="black"><span style='white-space: nowrap'>double</span></font></i><font color="blue"><span style='white-space: nowrap'>> &</span></font><i><font color="black"><span style='white-space: nowrap'>Result</span></font></i><font color="blue"><span style='white-space: nowrap'>,<br/>      AD<</span></font><i><font color="black"><span style='white-space: nowrap'>double</span></font></i><font color="blue"><span style='white-space: nowrap'>> &</span></font><i><font color="black"><span style='white-space: nowrap'>logdet</span></font></i><font color="blue"><span style='white-space: nowrap'>)</span></font></code> <br/> <br/> <b><big><a name="Purpose" id="Purpose">Purpose</a></big></b> <br/> Solves the linear equation <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <mi mathvariant='italic'>Matrix</mi> <mo stretchy="false">*</mo> <mi mathvariant='italic'>Result</mi> <mo stretchy="false">=</mo> <mi mathvariant='italic'>Rhs</mi> </mrow></math> where <code><i><font color="black"><span style='white-space: nowrap'>Matrix</span></font></i></code> is an <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, <code><i><font color="black"><span style='white-space: nowrap'>Rhs</span></font></i></code> is an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mi mathvariant='italic'>x</mi> <mi mathvariant='italic'>m</mi> </mrow></math> matrix, and <code><i><font color="black"><span style='white-space: nowrap'>Result</span></font></i></code> is an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mi mathvariant='italic'>x</mi> <mi mathvariant='italic'>m</mi> </mrow></math> matrix. <code><span style='white-space: nowrap'><br/> <br/> </span></code>The routine <a href="lusolve.xml" target="_top"><span style='white-space: nowrap'>LuSolve</span></a> uses an arbitrary vector type, instead of <a href="vecad.xml" target="_top"><span style='white-space: nowrap'>VecAD</span></a> , to hold its elements. The pivoting operations for a <code><font color="blue">ADFun</font></code> object corresponding to an <code><font color="blue">LuVecAD</font></code> solution will change to be optimal for the matrix being factored. <code><span style='white-space: nowrap'><br/> <br/> </span></code>It is often the case that <code><font color="blue">LuSolve</font></code> is faster than <code><font color="blue">LuVecAD</font></code> when <code><font color="blue">LuSolve</font></code> uses a simple vector class with <a href="simplevector.xml#Elements of Specified Type" target="_top"><span style='white-space: nowrap'>elements of type double</span></a> , but the corresponding <a href="adfun.xml" target="_top"><span style='white-space: nowrap'>ADFun</span></a> objects have a fixed set of pivoting operations. <br/> <br/> <b><big><a name="Storage Convention" id="Storage Convention">Storage Convention</a></big></b> <br/> The matrices stored in row major order. To be specific, if <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>A</mi> </mrow></math> contains the vector storage for an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mi mathvariant='italic'>x</mi> <mi mathvariant='italic'>m</mi> </mrow></math> matrix, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>i</mi> </mrow></math> is between zero and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <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> </mrow></math> is between zero and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>m</mi> <mn>-1</mn> </mrow></math> , <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> (The length of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>A</mi> </mrow></math> must be equal to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">*</mo> <mi mathvariant='italic'>m</mi> </mrow></math> .) <br/> <br/> <b><big><a name="n" id="n">n</a></big></b> <br/> is the number of rows in <code><i><font color="black"><span style='white-space: nowrap'>Matrix</span></font></i></code> , <code><i><font color="black"><span style='white-space: nowrap'>Rhs</span></font></i></code> , and <code><i><font color="black"><span style='white-space: nowrap'>Result</span></font></i></code> . <br/> <br/> <b><big><a name="m" id="m">m</a></big></b> <br/> is the number of columns in <code><i><font color="black"><span style='white-space: nowrap'>Rhs</span></font></i></code> and <code><i><font color="black"><span style='white-space: nowrap'>Result</span></font></i></code> . It is ok for <code><i><font color="black"><span style='white-space: nowrap'>m</span></font></i></code> to be zero which is reasonable when you are only interested in the determinant of <code><i><font color="black"><span style='white-space: nowrap'>Matrix</span></font></i></code> . <br/> <br/> <b><big><a name="Matrix" id="Matrix">Matrix</a></big></b> <br/> On input, this is an <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 containing the variable coefficients for the equation we wish to solve. On output, the elements of <code><i><font color="black"><span style='white-space: nowrap'>Matrix</span></font></i></code> have been overwritten and are not specified. <br/> <br/> <b><big><a name="Rhs" id="Rhs">Rhs</a></big></b> <br/> On input, this is an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">×</mo> <mi mathvariant='italic'>m</mi> </mrow></math> matrix containing the right hand side for the equation we wish to solve. On output, the elements of <code><i><font color="black"><span style='white-space: nowrap'>Rhs</span></font></i></code> have been overwritten and are not specified. If <code><i><font color="black"><span style='white-space: nowrap'>m</span></font></i></code> is zero, <code><i><font color="black"><span style='white-space: nowrap'>Rhs</span></font></i></code> is not used. <br/> <br/> <b><big><a name="Result" id="Result">Result</a></big></b> <br/> On input, this is an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">×</mo> <mi mathvariant='italic'>m</mi> </mrow></math> matrix and the value of its elements do not matter. On output, the elements of <code><i><font color="black"><span style='white-space: nowrap'>Rhs</span></font></i></code> contain the solution of the equation we wish to solve (unless the value returned by <code><font color="blue">LuVecAD</font></code> is equal to zero). If <code><i><font color="black"><span style='white-space: nowrap'>m</span></font></i></code> is zero, <code><i><font color="black"><span style='white-space: nowrap'>Result</span></font></i></code> is not used. <br/> <br/> <b><big><a name="logdet" id="logdet">logdet</a></big></b> <br/> On input, the value of <code><i><font color="black"><span style='white-space: nowrap'>logdet</span></font></i></code> does not matter. On output, it has been set to the log of the determinant of <code><i><font color="black"><span style='white-space: nowrap'>Matrix</span></font></i></code> (but not quite). To be more specific, if <code><i><font color="black"><span style='white-space: nowrap'>signdet</span></font></i></code> is the value returned by <code><font color="blue">LuVecAD</font></code>, the determinant of <code><i><font color="black"><span style='white-space: nowrap'>Matrix</span></font></i></code> is given by the formula <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <mi mathvariant='italic'>det</mi> <mo stretchy="false">=</mo> <mi mathvariant='italic'>signdet</mi> <mi>exp</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>logdet</mi> <mo stretchy="false">)</mo> </mrow></math> This enables <code><font color="blue">LuVecAD</font></code> to use logs of absolute values. <br/> <br/> <b><big><a name="Example" id="Example">Example</a></big></b> <br/> The file <a href="lu_vec_ad_ok.cpp.xml" target="_top"><span style='white-space: nowrap'>lu_vec_ad_ok.cpp</span></a> contains an example and test of <code><font color="blue">LuVecAD</font></code>. It returns true if it succeeds and false otherwise. <hr/>Input File: example/lu_vec_ad.cpp </body> </html> |