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mul_level.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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type='text/javascript' language='JavaScript' src='_mul_level_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="jac_lu_det.cpp.xml" target="_top">Prev</a> </td><td><a href="mul_level.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>General</option> <option>mul_level</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>General-></option> <option>ad_fun.cpp</option> <option>ad_in_c.cpp</option> <option>conj_grad.cpp</option> <option>cppad_eigen.hpp</option> <option>hes_minor_det.cpp</option> <option>hes_lu_det.cpp</option> <option>interface2c.cpp</option> <option>jac_minor_det.cpp</option> <option>jac_lu_det.cpp</option> <option>mul_level</option> <option>ode_stiff.cpp</option> <option>mul_level_ode.cpp</option> <option>mul_level_adolc_ode.cpp</option> <option>ode_taylor.cpp</option> <option>stack_machine.cpp</option> </select> </td> <td> <select onchange='choose_down0(this)'> <option>mul_level-></option> <option>mul_level.cpp</option> <option>change_const.cpp</option> </select> </td> <td> <select onchange='choose_current0(this)'> <option>Headings-></option> <option>Background</option> <option>Motivation</option> <option>General Solution</option> <option>General Procedure</option> <option>---..Start ADBaseTape</option> <option>---..Start ADDBaseTape</option> <option>---..Inner Function Calculations</option> <option>---..Derivative of Inner Function</option> <option>---..Outer Function</option> <option>---..Derivative of Outer Function</option> <option>Example</option> </select> </td> </tr></table><br/> <center><b><big><big>Using Multiple Levels of AD</big></big></b></center> <br/> <b><big><a name="Background" id="Background">Background</a></big></b> <br/> If <code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code> is an <code><font color="blue"><span style='white-space: nowrap'>ADFun<</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>></span></font></code> object, the vectors returned by <a href="forward.xml" target="_top"><span style='white-space: nowrap'>f.Forward</span></a> , and <a href="reverse.xml" target="_top"><span style='white-space: nowrap'>f.Reverse</span></a> , have values in the base type ( <code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code> ) and not <code><font color="blue"><span style='white-space: nowrap'>AD<</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>></span></font></code> . This reflects the fact that operations used to calculate these function values are not recorded by the tape corresponding to <code><font color="blue"><span style='white-space: nowrap'>AD<</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>></span></font></code> operations. <br/> <br/> <b><big><a name="Motivation" id="Motivation">Motivation</a></big></b> <br/> Suppose that you uses derivatives of one or more inner functions as part of the operations needed to compute an outer function. For example, the derivatives returned by <code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.Forward</span></font></code> might be used as part of Taylor's method for solving ordinary differential equations. In addition, we might want to differentiate the solution of a differential equation with respect to parameters in the equation. This can be accomplished in the following way: <ol type="1"><li> The operations during the calculations of the function defining the differential equation could be preformed using the a class of the form <code><font color="blue"><span style='white-space: nowrap'> AD< AD<double> ></span></font></code> . </li><li> The operations during the calculation of Taylor's method could be preformed using the <code><font color="blue"><span style='white-space: nowrap'> AD<double></span></font></code> class. </li><li> The results of the solution of the differential equation could then be preformed using the <code><font color="blue">double</font></code> class. </li></ol> <br/> <br/> <b><big><a name="General Solution" id="General Solution">General Solution</a></big></b> <br/> Provided that we are currently recording <code><font color="blue"><span style='white-space: nowrap'> AD<double></span></font></code> operations, and <code><i><font color="black"><span style='white-space: nowrap'>fin</span></font></i></code> is an <code><font color="blue"><span style='white-space: nowrap'>ADFun< AD<double> ></span></font></code> object, the operations used to compute the vectors returned by <code><i><font color="black"><span style='white-space: nowrap'>fin</span></font></i><font color="blue"><span style='white-space: nowrap'>.Forward</span></font></code> , <code><i><font color="black"><span style='white-space: nowrap'>fin</span></font></i><font color="blue"><span style='white-space: nowrap'>.Rev</span></font></code> , and <code><i><font color="black"><span style='white-space: nowrap'>fin</span></font></i><font color="blue"><span style='white-space: nowrap'>.RevTwo</span></font></code> , will be recorded on the tape corresponding to <code><font color="blue"><span style='white-space: nowrap'>AD<double></span></font></code> operations. <br/> <br/> <b><big><a name="General Procedure" id="General Procedure">General Procedure</a></big></b> <br/> <br/> <b><a name="General Procedure.Start ADBaseTape" id="General Procedure.Start ADBaseTape">Start ADBaseTape</a></b> <br/> The first step is to declare the independent variables using <code><font color="blue"><span style='white-space: nowrap'><br/>      Independent(</span></font><i><font color="black"><span style='white-space: nowrap'>x</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'>x</span></font></i></code> is a <a href="simplevector.xml" target="_top"><span style='white-space: nowrap'>SimpleVector</span></a> with elements of type <code><font color="blue"><span style='white-space: nowrap'>AD<double></span></font></code> . This will start recording a new tape of operations performed using <code><font color="blue"><span style='white-space: nowrap'>AD<double></span></font></code> class objects. <br/> <br/> <b><a name="General Procedure.Start ADDBaseTape" id="General Procedure.Start ADDBaseTape">Start ADDBaseTape</a></b> <br/> The next step is to declare the independent variables using <code><font color="blue"><span style='white-space: nowrap'><br/>      Independent(</span></font><i><font color="black"><span style='white-space: nowrap'>X</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'>X</span></font></i></code> is a <a href="simplevector.xml" target="_top"><span style='white-space: nowrap'>SimpleVector</span></a> with elements of type <code><font color="blue"><span style='white-space: nowrap'>AD< AD<double>) ></span></font></code> . This will start recording a new tape of operations performed using <code><font color="blue"><span style='white-space: nowrap'>AD< AD<double> ></span></font></code> class objects. <br/> <br/> <b><a name="General Procedure.Inner Function Calculations" id="General Procedure.Inner Function Calculations">Inner Function Calculations</a></b> <br/> The next step is to calculation the inner functions using <code><font color="blue"><span style='white-space: nowrap'>AD< AD<double> ></span></font></code> class objects. <br/> <br/> <b><a name="General Procedure.Derivative of Inner Function" id="General Procedure.Derivative of Inner Function">Derivative of Inner Function</a></b> <br/> The next step is to create the <code><font color="blue"><span style='white-space: nowrap'>ADFun< AD<double> ></span></font></code> function object <code><i><font color="black"><span style='white-space: nowrap'>fin</span></font></i></code> . This will also stop recording of operations performed using <code><font color="blue"><span style='white-space: nowrap'>AD< AD<double> ></span></font></code> class objects. The <code><i><font color="black"><span style='white-space: nowrap'>fin</span></font></i></code> object can then be used to calculate the derivatives needed to compute the outer function. <br/> <br/> <b><a name="General Procedure.Outer Function" id="General Procedure.Outer Function">Outer Function</a></b> <br/> The next step is to compute the outer function using <code><font color="blue"><span style='white-space: nowrap'>AD<double></span></font></code> class objects. <br/> <br/> <b><a name="General Procedure.Derivative of Outer Function" id="General Procedure.Derivative of Outer Function">Derivative of Outer Function</a></b> <br/> The next step is to create the <code><font color="blue"><span style='white-space: nowrap'>ADFun<double></span></font></code> function object <code><i><font color="black"><span style='white-space: nowrap'>fout</span></font></i></code> . This will also stop the recording of operations performed using <code><font color="blue"><span style='white-space: nowrap'>AD<double></span></font></code> class objects. The <code><i><font color="black"><span style='white-space: nowrap'>fout</span></font></i></code> object can then be used to calculate the derivatives of the outer function. <br/> <br/> <b><big><a name="Example" id="Example">Example</a></big></b> <br/> The files <a href="mul_level.cpp.xml" target="_top"><span style='white-space: nowrap'>mul_level.cpp</span></a> and <a href="change_const.cpp.xml" target="_top"><span style='white-space: nowrap'>change_const.cpp</span></a> contain an examples and tests of this procedure. They return true if they succeed and false otherwise. The file <a href="mul_level_ode.cpp.xml" target="_top"><span style='white-space: nowrap'>mul_level_ode.cpp</span></a> is a more complex example use of multiple tapes. <hr/>Input File: omh/mul_level.omh </body> </html> |