1<?xml version="1.0" standalone="yes"?> 2<library-reference id="odeint_reference"><title>odeint Reference</title><header name="boost/numeric/odeint/integrate/check_adapter.hpp"> 3<namespace name="boost"> 4<namespace name="numeric"> 5<namespace name="odeint"> 6<class name="checked_observer"><template> 7 <template-type-parameter name="Observer"/> 8 <template-type-parameter name="Checker"/> 9 </template><purpose>Adapter to combine observer and checker. </purpose><typedef name="observer_type"><type>Observer</type></typedef> 10<typedef name="checker_type"><type>Checker</type></typedef> 11<method-group name="public member functions"> 12<method name="operator()" cv="const"><type>void</type><template> 13 <template-type-parameter name="State"/> 14 <template-type-parameter name="Time"/> 15 </template><parameter name="state"><paramtype>const State &</paramtype></parameter><parameter name="t"><paramtype>Time</paramtype></parameter></method> 16</method-group> 17<constructor><parameter name="observer"><paramtype>observer_type &</paramtype></parameter><parameter name="checker"><paramtype>checker_type &</paramtype></parameter></constructor> 18</class><class name="checked_stepper"><template> 19 <template-type-parameter name="Stepper"/> 20 <template-type-parameter name="Checker"/> 21 <template-type-parameter name="StepperCategory"><default>typename base_tag<typename Stepper::stepper_category>::type</default></template-type-parameter> 22 </template></class><class-specialization name="checked_stepper"><template> 23 <template-type-parameter name="ControlledStepper"/> 24 <template-type-parameter name="Checker"/> 25 </template><specialization><template-arg>ControlledStepper</template-arg><template-arg>Checker</template-arg><template-arg>controlled_stepper_tag</template-arg></specialization><purpose>Adapter to combine controlled stepper and checker. </purpose><typedef name="stepper_type"><type>ControlledStepper</type></typedef> 26<typedef name="checker_type"><type>Checker</type></typedef> 27<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 28<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 29<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 30<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 31<method-group name="public member functions"> 32<method name="try_step"><type>controlled_step_result</type><template> 33 <template-type-parameter name="System"/> 34 <template-type-parameter name="StateInOut"/> 35 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="state"><paramtype>StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter><purpose>forward of the do_step method </purpose></method> 36</method-group> 37<constructor><parameter name="stepper"><paramtype>stepper_type &</paramtype></parameter><parameter name="checker"><paramtype>checker_type &</paramtype></parameter><purpose>Construct the checked_stepper. </purpose></constructor> 38</class-specialization><class-specialization name="checked_stepper"><template> 39 <template-type-parameter name="DenseOutStepper"/> 40 <template-type-parameter name="Checker"/> 41 </template><specialization><template-arg>DenseOutStepper</template-arg><template-arg>Checker</template-arg><template-arg>dense_output_stepper_tag</template-arg></specialization><purpose>Adapter to combine dense out stepper and checker. </purpose><typedef name="stepper_type"><type>DenseOutStepper</type></typedef> 42<typedef name="checker_type"><type>Checker</type></typedef> 43<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 44<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 45<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 46<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 47<method-group name="public member functions"> 48<method name="do_step"><type>std::pair< time_type, time_type ></type><template> 49 <template-type-parameter name="System"/> 50 </template><parameter name="system"><paramtype>System</paramtype></parameter></method> 51<method name="initialize"><type>void</type><template> 52 <template-type-parameter name="StateType"/> 53 </template><parameter name="x0"><paramtype>const StateType &</paramtype></parameter><parameter name="t0"><paramtype>time_type</paramtype></parameter><parameter name="dt0"><paramtype>time_type</paramtype></parameter></method> 54<method name="calc_state" cv="const"><type>void</type><template> 55 <template-type-parameter name="StateOut"/> 56 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>StateOut &</paramtype></parameter></method> 57<method name="calc_state" cv="const"><type>void</type><template> 58 <template-type-parameter name="StateOut"/> 59 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>const StateOut &</paramtype></parameter></method> 60<method name="current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 61<method name="current_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 62<method name="previous_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 63<method name="previous_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 64<method name="current_time_step" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 65</method-group> 66<constructor><parameter name="stepper"><paramtype>stepper_type &</paramtype></parameter><parameter name="checker"><paramtype>checker_type &</paramtype></parameter><purpose>Construct the checked_stepper. </purpose></constructor> 67</class-specialization><class-specialization name="checked_stepper"><template> 68 <template-type-parameter name="Stepper"/> 69 <template-type-parameter name="Checker"/> 70 </template><specialization><template-arg>Stepper</template-arg><template-arg>Checker</template-arg><template-arg>stepper_tag</template-arg></specialization><purpose>Adapter to combine basic stepper and checker. </purpose><typedef name="stepper_type"><type>Stepper</type></typedef> 71<typedef name="checker_type"><type>Checker</type></typedef> 72<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 73<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 74<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 75<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 76<method-group name="public member functions"> 77<method name="do_step"><type>void</type><template> 78 <template-type-parameter name="System"/> 79 <template-type-parameter name="StateInOut"/> 80 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="state"><paramtype>StateInOut &</paramtype></parameter><parameter name="t"><paramtype>const time_type</paramtype></parameter><parameter name="dt"><paramtype>const time_type</paramtype></parameter><purpose>forward of the do_step method </purpose></method> 81</method-group> 82<constructor><parameter name="stepper"><paramtype>stepper_type &</paramtype></parameter><parameter name="checker"><paramtype>checker_type &</paramtype></parameter><purpose>Construct the checked_stepper. </purpose></constructor> 83</class-specialization> 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</namespace> 136</namespace> 137</namespace> 138</header> 139<header name="boost/numeric/odeint/integrate/integrate.hpp"> 140<namespace name="boost"> 141<namespace name="numeric"> 142<namespace name="odeint"> 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<function name="integrate"><type>boost::enable_if< typename has_value_type< State >::type, size_t >::type</type><template> 168 <template-type-parameter name="System"/> 169 <template-type-parameter name="State"/> 170 <template-type-parameter name="Time"/> 171 <template-type-parameter name="Observer"/> 172 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. </para></description></parameter><parameter name="start_state"><paramtype>State &</paramtype><description><para>The initial state. </para></description></parameter><parameter name="start_time"><paramtype>Time</paramtype><description><para>Start time of the integration. </para></description></parameter><parameter name="end_time"><paramtype>Time</paramtype><description><para>End time of the integration. </para></description></parameter><parameter name="dt"><paramtype>Time</paramtype><description><para>Initial step size, will be adjusted during the integration. </para></description></parameter><parameter name="observer"><paramtype>Observer</paramtype><description><para>Observer that will be called after each time step. </para></description></parameter><purpose>Integrates the ODE. </purpose><description><para>Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. After each step, the observer is called.</para><para><note><para>A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt , obs );</para> 173</note> 174 175 176</para></description><returns><para>The number of steps performed. </para> 177</returns></function> 178<function name="integrate"><type>size_t</type><template> 179 <template-type-parameter name="Value"/> 180 <template-type-parameter name="System"/> 181 <template-type-parameter name="State"/> 182 <template-type-parameter name="Time"/> 183 <template-type-parameter name="Observer"/> 184 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter></function> 185<function name="integrate"><type>size_t</type><template> 186 <template-type-parameter name="System"/> 187 <template-type-parameter name="State"/> 188 <template-type-parameter name="Time"/> 189 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. </para></description></parameter><parameter name="start_state"><paramtype>State &</paramtype><description><para>The initial state. </para></description></parameter><parameter name="start_time"><paramtype>Time</paramtype><description><para>Start time of the integration. </para></description></parameter><parameter name="end_time"><paramtype>Time</paramtype><description><para>End time of the integration. </para></description></parameter><parameter name="dt"><paramtype>Time</paramtype><description><para>Initial step size, will be adjusted during the integration. </para></description></parameter><purpose>Integrates the ODE without observer calls. </purpose><description><para>Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. No observer is called.</para><para><note><para>A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt );</para> 190</note> 191 192 193</para></description><returns><para>The number of steps performed. </para> 194</returns></function> 195<function name="integrate"><type>size_t</type><template> 196 <template-type-parameter name="Value"/> 197 <template-type-parameter name="System"/> 198 <template-type-parameter name="State"/> 199 <template-type-parameter name="Time"/> 200 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter></function> 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</namespace> 226</namespace> 227</namespace> 228</header> 229<header name="boost/numeric/odeint/integrate/integrate_adaptive.hpp"> 230<namespace name="boost"> 231<namespace name="numeric"> 232<namespace name="odeint"> 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253<function name="integrate_adaptive"><type>size_t</type><template> 254 <template-type-parameter name="Stepper"/> 255 <template-type-parameter name="System"/> 256 <template-type-parameter name="State"/> 257 <template-type-parameter name="Time"/> 258 <template-type-parameter name="Observer"/> 259 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to be used for numerical integration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>Function/Functor defining the rhs of the ODE. </para></description></parameter><parameter name="start_state"><paramtype>State &</paramtype><description><para>The initial condition x0. </para></description></parameter><parameter name="start_time"><paramtype>Time</paramtype><description><para>The initial time t0. </para></description></parameter><parameter name="end_time"><paramtype>Time</paramtype><description><para>The final integration time tend. </para></description></parameter><parameter name="dt"><paramtype>Time</paramtype><description><para>The time step between observer calls, <emphasis>not</emphasis> necessarily the time step of the integration. </para></description></parameter><parameter name="observer"><paramtype>Observer</paramtype><description><para>Function/Functor called at equidistant time intervals. </para></description></parameter><purpose>Integrates the ODE with adaptive step size. </purpose><description><para>This function integrates the ODE given by system with the given stepper. The observer is called after each step. If the stepper has no error control, the step size remains constant and the observer is called at equidistant time points t0+n*dt. If the stepper is a ControlledStepper, the step size is adjusted and the observer is called in non-equidistant intervals.</para><para> 260 261</para></description><returns><para>The number of steps performed. </para> 262</returns></function> 263<function name="integrate_adaptive"><type>size_t</type><template> 264 <template-type-parameter name="Stepper"/> 265 <template-type-parameter name="System"/> 266 <template-type-parameter name="State"/> 267 <template-type-parameter name="Time"/> 268 <template-type-parameter name="Observer"/> 269 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 270<function name="integrate_adaptive"><type>size_t</type><template> 271 <template-type-parameter name="Stepper"/> 272 <template-type-parameter name="System"/> 273 <template-type-parameter name="State"/> 274 <template-type-parameter name="Time"/> 275 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><purpose>integrate_adaptive without an observer. </purpose></function> 276<function name="integrate_adaptive"><type>size_t</type><template> 277 <template-type-parameter name="Stepper"/> 278 <template-type-parameter name="System"/> 279 <template-type-parameter name="State"/> 280 <template-type-parameter name="Time"/> 281 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310</namespace> 311</namespace> 312</namespace> 313</header> 314<header name="boost/numeric/odeint/integrate/integrate_const.hpp"> 315<namespace name="boost"> 316<namespace name="numeric"> 317<namespace name="odeint"> 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332<function name="integrate_const"><type>size_t</type><template> 333 <template-type-parameter name="Stepper"/> 334 <template-type-parameter name="System"/> 335 <template-type-parameter name="State"/> 336 <template-type-parameter name="Time"/> 337 <template-type-parameter name="Observer"/> 338 <template-type-parameter name="StepOverflowChecker"/> 339 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to be used for numerical integration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>Function/Functor defining the rhs of the ODE. </para></description></parameter><parameter name="start_state"><paramtype>State &</paramtype><description><para>The initial condition x0. </para></description></parameter><parameter name="start_time"><paramtype>Time</paramtype><description><para>The initial time t0. </para></description></parameter><parameter name="end_time"><paramtype>Time</paramtype><description><para>The final integration time tend. </para></description></parameter><parameter name="dt"><paramtype>Time</paramtype><description><para>The time step between observer calls, <emphasis>not</emphasis> necessarily the time step of the integration. </para></description></parameter><parameter name="observer"><paramtype>Observer</paramtype><description><para>[optional] Function/Functor called at equidistant time intervals. </para></description></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype><description><para>[optional] Functor to check for step count overflows, if no checker is provided, no exception is thrown. </para></description></parameter><purpose>Integrates the ODE with constant step size. </purpose><description><para>Integrates the ODE defined by system using the given stepper. This method ensures that the observer is called at constant intervals dt. If the Stepper is a normal stepper without step size control, dt is also used for the numerical scheme. If a ControlledStepper is provided, the algorithm might reduce the step size to meet the error bounds, but it is ensured that the observer is always called at equidistant time points t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary and the dense output is used to call the observer at equidistant time points. If a <classname alt="boost::numeric::odeint::max_step_checker">max_step_checker</classname> is provided as StepOverflowChecker, a no_progress_error is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed.</para><para> 340 341</para></description><returns><para>The number of steps performed. </para> 342</returns></function> 343<function name="integrate_const"><type>size_t</type><template> 344 <template-type-parameter name="Stepper"/> 345 <template-type-parameter name="System"/> 346 <template-type-parameter name="State"/> 347 <template-type-parameter name="Time"/> 348 <template-type-parameter name="Observer"/> 349 <template-type-parameter name="StepOverflowChecker"/> 350 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 351<function name="integrate_const"><type>size_t</type><template> 352 <template-type-parameter name="Stepper"/> 353 <template-type-parameter name="System"/> 354 <template-type-parameter name="State"/> 355 <template-type-parameter name="Time"/> 356 <template-type-parameter name="Observer"/> 357 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><purpose>integrate_const without step overflow checker </purpose></function> 358<function name="integrate_const"><type>size_t</type><template> 359 <template-type-parameter name="Stepper"/> 360 <template-type-parameter name="System"/> 361 <template-type-parameter name="State"/> 362 <template-type-parameter name="Time"/> 363 <template-type-parameter name="Observer"/> 364 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 365<function name="integrate_const"><type>size_t</type><template> 366 <template-type-parameter name="Stepper"/> 367 <template-type-parameter name="System"/> 368 <template-type-parameter name="State"/> 369 <template-type-parameter name="Time"/> 370 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><purpose>integrate_const without observer calls </purpose></function> 371<function name="integrate_const"><type>size_t</type><template> 372 <template-type-parameter name="Stepper"/> 373 <template-type-parameter name="System"/> 374 <template-type-parameter name="State"/> 375 <template-type-parameter name="Time"/> 376 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="end_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409</namespace> 410</namespace> 411</namespace> 412</header> 413<header name="boost/numeric/odeint/integrate/integrate_n_steps.hpp"> 414<namespace name="boost"> 415<namespace name="numeric"> 416<namespace name="odeint"> 417 418 419 420 421 422 423 424 425<function name="integrate_n_steps"><type>Time</type><template> 426 <template-type-parameter name="Stepper"/> 427 <template-type-parameter name="System"/> 428 <template-type-parameter name="State"/> 429 <template-type-parameter name="Time"/> 430 <template-type-parameter name="Observer"/> 431 <template-type-parameter name="StepOverflowChecker"/> 432 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype></parameter></function> 433<function name="integrate_n_steps"><type>Time</type><template> 434 <template-type-parameter name="Stepper"/> 435 <template-type-parameter name="System"/> 436 <template-type-parameter name="State"/> 437 <template-type-parameter name="Time"/> 438 <template-type-parameter name="Observer"/> 439 <template-type-parameter name="StepOverflowChecker"/> 440 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype></parameter><purpose>Solves the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 441<function name="integrate_n_steps"><type>Time</type><template> 442 <template-type-parameter name="Stepper"/> 443 <template-type-parameter name="System"/> 444 <template-type-parameter name="State"/> 445 <template-type-parameter name="Time"/> 446 <template-type-parameter name="Observer"/> 447 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to be used for numerical integration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>Function/Functor defining the rhs of the ODE. </para></description></parameter><parameter name="start_state"><paramtype>State &</paramtype><description><para>The initial condition x0. </para></description></parameter><parameter name="start_time"><paramtype>Time</paramtype><description><para>The initial time t0. </para></description></parameter><parameter name="dt"><paramtype>Time</paramtype><description><para>The time step between observer calls, <emphasis>not</emphasis> necessarily the time step of the integration. </para></description></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype><description><para>Number of steps to be performed </para></description></parameter><parameter name="observer"><paramtype>Observer</paramtype><description><para>Function/Functor called at equidistant time intervals. </para></description></parameter><purpose>The same function as above, but without checker. </purpose><description><para>Integrates the ODE with constant step size.</para><para>This function is similar to integrate_const. The observer is called at equidistant time intervals t0 + n*dt. If the Stepper is a normal stepper without step size control, dt is also used for the numerical scheme. If a ControlledStepper is provided, the algorithm might reduce the step size to meet the error bounds, but it is ensured that the observer is always called at equidistant time points t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary and the dense output is used to call the observer at equidistant time points. The final integration time is always t0 + num_of_steps*dt. If a <classname alt="boost::numeric::odeint::max_step_checker">max_step_checker</classname> is provided as StepOverflowChecker, a no_progress_errror is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed.</para><para> 448 449</para></description><returns><para>The number of steps performed. </para> 450</returns></function> 451<function name="integrate_n_steps"><type>Time</type><template> 452 <template-type-parameter name="Stepper"/> 453 <template-type-parameter name="System"/> 454 <template-type-parameter name="State"/> 455 <template-type-parameter name="Time"/> 456 <template-type-parameter name="Observer"/> 457 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><purpose>Solves the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 458<function name="integrate_n_steps"><type>Time</type><template> 459 <template-type-parameter name="Stepper"/> 460 <template-type-parameter name="System"/> 461 <template-type-parameter name="State"/> 462 <template-type-parameter name="Time"/> 463 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype></parameter><purpose>The same function as above, but without observer calls. </purpose></function> 464<function name="integrate_n_steps"><type>Time</type><template> 465 <template-type-parameter name="Stepper"/> 466 <template-type-parameter name="System"/> 467 <template-type-parameter name="State"/> 468 <template-type-parameter name="Time"/> 469 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="start_time"><paramtype>Time</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype></parameter><purpose>Solves the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508</namespace> 509</namespace> 510</namespace> 511</header> 512<header name="boost/numeric/odeint/integrate/integrate_times.hpp"> 513<namespace name="boost"> 514<namespace name="numeric"> 515<namespace name="odeint"> 516<function name="integrate_times"><type>size_t</type><template> 517 <template-type-parameter name="Stepper"/> 518 <template-type-parameter name="System"/> 519 <template-type-parameter name="State"/> 520 <template-type-parameter name="TimeIterator"/> 521 <template-type-parameter name="Time"/> 522 <template-type-parameter name="Observer"/> 523 <template-type-parameter name="StepOverflowChecker"/> 524 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="times_start"><paramtype>TimeIterator</paramtype></parameter><parameter name="times_end"><paramtype>TimeIterator</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype></parameter></function> 525<function name="integrate_times"><type>size_t</type><template> 526 <template-type-parameter name="Stepper"/> 527 <template-type-parameter name="System"/> 528 <template-type-parameter name="State"/> 529 <template-type-parameter name="TimeIterator"/> 530 <template-type-parameter name="Time"/> 531 <template-type-parameter name="Observer"/> 532 <template-type-parameter name="StepOverflowChecker"/> 533 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="times_start"><paramtype>TimeIterator</paramtype></parameter><parameter name="times_end"><paramtype>TimeIterator</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype></parameter><purpose>Solves the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 534<function name="integrate_times"><type>size_t</type><template> 535 <template-type-parameter name="Stepper"/> 536 <template-type-parameter name="System"/> 537 <template-type-parameter name="State"/> 538 <template-type-parameter name="TimeRange"/> 539 <template-type-parameter name="Time"/> 540 <template-type-parameter name="Observer"/> 541 <template-type-parameter name="StepOverflowChecker"/> 542 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="times"><paramtype>const TimeRange &</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype></parameter><purpose>The same function as above, but with the observation times given as range. </purpose></function> 543<function name="integrate_times"><type>size_t</type><template> 544 <template-type-parameter name="Stepper"/> 545 <template-type-parameter name="System"/> 546 <template-type-parameter name="State"/> 547 <template-type-parameter name="TimeRange"/> 548 <template-type-parameter name="Time"/> 549 <template-type-parameter name="Observer"/> 550 <template-type-parameter name="StepOverflowChecker"/> 551 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="times"><paramtype>const TimeRange &</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><parameter name="checker"><paramtype>StepOverflowChecker</paramtype></parameter><purpose>Solves the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 552<function name="integrate_times"><type>size_t</type><template> 553 <template-type-parameter name="Stepper"/> 554 <template-type-parameter name="System"/> 555 <template-type-parameter name="State"/> 556 <template-type-parameter name="TimeIterator"/> 557 <template-type-parameter name="Time"/> 558 <template-type-parameter name="Observer"/> 559 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to be used for numerical integration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>Function/Functor defining the rhs of the ODE. </para></description></parameter><parameter name="start_state"><paramtype>State &</paramtype><description><para>The initial condition x0. </para></description></parameter><parameter name="times_start"><paramtype>TimeIterator</paramtype><description><para>Iterator to the start time </para></description></parameter><parameter name="times_end"><paramtype>TimeIterator</paramtype><description><para>Iterator to the end time </para></description></parameter><parameter name="dt"><paramtype>Time</paramtype><description><para>The time step between observer calls, <emphasis>not</emphasis> necessarily the time step of the integration. </para></description></parameter><parameter name="observer"><paramtype>Observer</paramtype><description><para>Function/Functor called at equidistant time intervals. </para></description></parameter><purpose>Integrates the ODE with observer calls at given time points. </purpose><description><para>Integrates the ODE given by system using the given stepper. This function does observer calls at the subsequent time points given by the range times_start, times_end. If the stepper has not step size control, the step size might be reduced occasionally to ensure observer calls exactly at the time points from the given sequence. If the stepper is a ControlledStepper, the step size is adjusted to meet the error bounds, but also might be reduced occasionally to ensure correct observer calls. If a DenseOutputStepper is provided, the dense output functionality is used to call the observer at the given times. The end time of the integration is always *(end_time-1). If a <classname alt="boost::numeric::odeint::max_step_checker">max_step_checker</classname> is provided as StepOverflowChecker, a no_progress_error is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed.</para><para> 560 561</para></description><returns><para>The number of steps performed. </para> 562</returns></function> 563<function name="integrate_times"><type>size_t</type><template> 564 <template-type-parameter name="Stepper"/> 565 <template-type-parameter name="System"/> 566 <template-type-parameter name="State"/> 567 <template-type-parameter name="TimeIterator"/> 568 <template-type-parameter name="Time"/> 569 <template-type-parameter name="Observer"/> 570 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="times_start"><paramtype>TimeIterator</paramtype></parameter><parameter name="times_end"><paramtype>TimeIterator</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><purpose>Solves the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 571<function name="integrate_times"><type>size_t</type><template> 572 <template-type-parameter name="Stepper"/> 573 <template-type-parameter name="System"/> 574 <template-type-parameter name="State"/> 575 <template-type-parameter name="TimeRange"/> 576 <template-type-parameter name="Time"/> 577 <template-type-parameter name="Observer"/> 578 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>State &</paramtype></parameter><parameter name="times"><paramtype>const TimeRange &</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><purpose>The same function as above, but with the observation times given as range. </purpose></function> 579<function name="integrate_times"><type>size_t</type><template> 580 <template-type-parameter name="Stepper"/> 581 <template-type-parameter name="System"/> 582 <template-type-parameter name="State"/> 583 <template-type-parameter name="TimeRange"/> 584 <template-type-parameter name="Time"/> 585 <template-type-parameter name="Observer"/> 586 </template><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="start_state"><paramtype>const State &</paramtype></parameter><parameter name="times"><paramtype>const TimeRange &</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter><parameter name="observer"><paramtype>Observer</paramtype></parameter><purpose>Solves the forwarding problem, can be called with Boost.Range as start_state. </purpose></function> 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631</namespace> 632</namespace> 633</namespace> 634</header> 635<header name="boost/numeric/odeint/integrate/max_step_checker.hpp"> 636<namespace name="boost"> 637<namespace name="numeric"> 638<namespace name="odeint"> 639<class name="failed_step_checker"><inherit access="public">boost::numeric::odeint::max_step_checker</inherit><purpose>A class for performing overflow checks on the failed step count in step size adjustments. </purpose><description><para>Used internally within the dense output stepper and integrate routines. </para></description><method-group name="public member functions"> 640<method name="operator()"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Increases the counter and performs the iteration check. </purpose></method> 641<method name="reset"><type>void</type><purpose>Resets the <classname alt="boost::numeric::odeint::max_step_checker">max_step_checker</classname> by setting the internal counter to 0. </purpose></method> 642</method-group> 643<constructor><parameter name="max_steps"><paramtype>const int</paramtype><default>500</default></parameter><purpose>Construct the <classname alt="boost::numeric::odeint::failed_step_checker">failed_step_checker</classname>. max_steps is the maximal number of iterations allowed before runtime_error is thrown. </purpose></constructor> 644</class><class name="max_step_checker"><purpose>A class for performing overflow checks on the step count in integrate functions. </purpose><description><para>Provide an instance of this class to integrate functions if you want to throw a runtime error if too many steps are performed without progress during the integrate routine. </para></description><method-group name="public member functions"> 645<method name="reset"><type>void</type><purpose>Resets the <classname alt="boost::numeric::odeint::max_step_checker">max_step_checker</classname> by setting the internal counter to 0. </purpose></method> 646<method name="operator()"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Increases the counter and performs the iteration check. </purpose></method> 647</method-group> 648<constructor><parameter name="max_steps"><paramtype>const int</paramtype><default>500</default></parameter><purpose>Construct the <classname alt="boost::numeric::odeint::max_step_checker">max_step_checker</classname>. max_steps is the maximal number of iterations allowed before runtime_error is thrown. </purpose></constructor> 649</class> 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701</namespace> 702</namespace> 703</namespace> 704</header> 705<header name="boost/numeric/odeint/iterator/adaptive_iterator.hpp"> 706<namespace name="boost"> 707<namespace name="numeric"> 708<namespace name="odeint"> 709<class name="adaptive_iterator"><template> 710 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 711 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 712 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 713 </template><purpose>ODE Iterator with adaptive step size. The value type of this iterator is the state type of the stepper. </purpose><description><para>Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with an adaptive step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt where dt is controlled by the stepper. This iterator can be used with ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_adaptive routine.</para><para><classname alt="boost::numeric::odeint::adaptive_iterator">adaptive_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.</para><para> 714</para></description><method-group name="public member functions"> 715</method-group> 716<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t_start"><paramtype>time_type</paramtype></parameter><parameter name="t_end"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></constructor> 717<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 718</class> 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767<function name="make_adaptive_iterator_begin"><type><classname>adaptive_iterator</classname>< Stepper, System, State ></type><template> 768 <template-type-parameter name="Stepper"/> 769 <template-type-parameter name="System"/> 770 <template-type-parameter name="State"/> 771 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::adaptive_iterator">adaptive_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 772 773</para></description><returns><para>The adaptive iterator. </para> 774</returns></function> 775<function name="make_adaptive_iterator_end"><type><classname>adaptive_iterator</classname>< Stepper, System, State ></type><template> 776 <template-type-parameter name="Stepper"/> 777 <template-type-parameter name="System"/> 778 <template-type-parameter name="State"/> 779 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::adaptive_iterator">adaptive_iterator</classname>. Constructs a end iterator. </purpose><description><para> 780 781</para></description><returns><para>The adaptive iterator. </para> 782</returns></function> 783<function name="make_adaptive_range"><type>std::pair< <classname>adaptive_iterator</classname>< Stepper, System, State >, <classname>adaptive_iterator</classname>< Stepper, System, State > ></type><template> 784 <template-type-parameter name="Stepper"/> 785 <template-type-parameter name="System"/> 786 <template-type-parameter name="State"/> 787 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function to construct a single pass range of adaptive iterators. A range is here a pair of <classname alt="boost::numeric::odeint::adaptive_iterator">adaptive_iterator</classname>. </purpose><description><para> 788 789</para></description><returns><para>The adaptive range. </para> 790</returns></function> 791</namespace> 792</namespace> 793</namespace> 794</header> 795<header name="boost/numeric/odeint/iterator/adaptive_time_iterator.hpp"> 796<namespace name="boost"> 797<namespace name="numeric"> 798<namespace name="odeint"> 799<class name="adaptive_time_iterator"><template> 800 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 801 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 802 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 803 </template><purpose>ODE Iterator with adaptive step size. The value type of this iterator is a std::pair containing state and time. </purpose><description><para>Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with an adaptive step size dt. After each iteration the iterator dereferences to a pair containing state and time at the next time point t+dt where dt is controlled by the stepper. This iterator can be used with ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_adaptive routine.</para><para><classname alt="boost::numeric::odeint::adaptive_iterator">adaptive_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is a std::pair of state and time of the stepper.</para><para> 804</para></description><method-group name="public member functions"> 805</method-group> 806<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t_start"><paramtype>time_type</paramtype></parameter><parameter name="t_end"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></constructor> 807<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 808</class> 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854<function name="make_adaptive_time_iterator_begin"><type><classname>adaptive_time_iterator</classname>< Stepper, System, State ></type><template> 855 <template-type-parameter name="Stepper"/> 856 <template-type-parameter name="System"/> 857 <template-type-parameter name="State"/> 858 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::adaptive_time_iterator">adaptive_time_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::adaptive_time_iterator">adaptive_time_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 859 860</para></description><returns><para>The adaptive time iterator. </para> 861</returns></function> 862<function name="make_adaptive_time_iterator_end"><type><classname>adaptive_time_iterator</classname>< Stepper, System, State ></type><template> 863 <template-type-parameter name="Stepper"/> 864 <template-type-parameter name="System"/> 865 <template-type-parameter name="State"/> 866 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::adaptive_time_iterator">adaptive_time_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::adaptive_time_iterator">adaptive_time_iterator</classname>. Constructs a end iterator. </purpose><description><para> 867 868</para></description><returns><para>The adaptive time iterator. </para> 869</returns></function> 870<function name="make_adaptive_time_range"><type>std::pair< <classname>adaptive_time_iterator</classname>< Stepper, System, State >, <classname>adaptive_time_iterator</classname>< Stepper, System, State > ></type><template> 871 <template-type-parameter name="Stepper"/> 872 <template-type-parameter name="System"/> 873 <template-type-parameter name="State"/> 874 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::adaptive_time_iterator">adaptive_time_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function to construct a single pass range of adaptive time iterators. A range is here a pair of adaptive_time_iterators. </purpose><description><para> 875 876</para></description><returns><para>The adaptive time range. </para> 877</returns></function> 878 879 880 881</namespace> 882</namespace> 883</namespace> 884</header> 885<header name="boost/numeric/odeint/iterator/const_step_iterator.hpp"> 886<namespace name="boost"> 887<namespace name="numeric"> 888<namespace name="odeint"> 889<class name="const_step_iterator"><template> 890 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 891 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 892 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 893 </template><purpose>ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper. </purpose><description><para>Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with constant step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_const routine.</para><para><classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.</para><para> 894</para></description><method-group name="public member functions"> 895</method-group> 896<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t_start"><paramtype>time_type</paramtype></parameter><parameter name="t_end"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></constructor> 897<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 898</class> 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941<function name="make_const_step_iterator_begin"><type><classname>const_step_iterator</classname>< Stepper, System, State ></type><template> 942 <template-type-parameter name="Stepper"/> 943 <template-type-parameter name="System"/> 944 <template-type-parameter name="State"/> 945 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 946 947</para></description><returns><para>The const step iterator. </para> 948</returns></function> 949<function name="make_const_step_iterator_end"><type><classname>const_step_iterator</classname>< Stepper, System, State ></type><template> 950 <template-type-parameter name="Stepper"/> 951 <template-type-parameter name="System"/> 952 <template-type-parameter name="State"/> 953 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname>. Constructs a end iterator. </purpose><description><para> 954 955</para></description><returns><para>The <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname>. </para> 956</returns></function> 957<function name="make_const_step_range"><type>std::pair< <classname>const_step_iterator</classname>< Stepper, System, State >, <classname>const_step_iterator</classname>< Stepper, System, State > ></type><template> 958 <template-type-parameter name="Stepper"/> 959 <template-type-parameter name="System"/> 960 <template-type-parameter name="State"/> 961 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> store a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function to construct a single pass range of const step iterators. A range is here a pair of <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname>. </purpose><description><para> 962 963</para></description><returns><para>The const step range. </para> 964</returns></function> 965 966 967 968 969 970 971</namespace> 972</namespace> 973</namespace> 974</header> 975<header name="boost/numeric/odeint/iterator/const_step_time_iterator.hpp"> 976<namespace name="boost"> 977<namespace name="numeric"> 978<namespace name="odeint"> 979<class name="const_step_time_iterator"><template> 980 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 981 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 982 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 983 </template><purpose>ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time. </purpose><description><para>Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with constant step size dt. After each iteration the iterator dereferences to a pair containing state and time at the next time point t+dt.. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_const routine.</para><para><classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is a pair with the state type and time type of the stepper.</para><para> 984</para></description><method-group name="public member functions"> 985</method-group> 986<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t_start"><paramtype>time_type</paramtype></parameter><parameter name="t_end"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></constructor> 987<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 988</class> 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028<function name="make_const_step_time_iterator_begin"><type><classname>const_step_time_iterator</classname>< Stepper, System, State ></type><template> 1029 <template-type-parameter name="Stepper"/> 1030 <template-type-parameter name="System"/> 1031 <template-type-parameter name="State"/> 1032 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 1033 1034</para></description><returns><para>The const step time iterator. </para> 1035</returns></function> 1036<function name="make_const_step_time_iterator_end"><type><classname>const_step_time_iterator</classname>< Stepper, System, State ></type><template> 1037 <template-type-parameter name="Stepper"/> 1038 <template-type-parameter name="System"/> 1039 <template-type-parameter name="State"/> 1040 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname> store a reference of s and changes its value during the iteration. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname>. Constructs a end iterator. </purpose><description><para> 1041 1042</para></description><returns><para>The const step time iterator. </para> 1043</returns></function> 1044<function name="make_const_step_time_range"><type>std::pair< <classname>const_step_time_iterator</classname>< Stepper, System, State >, <classname>const_step_time_iterator</classname>< Stepper, System, State > ></type><template> 1045 <template-type-parameter name="Stepper"/> 1046 <template-type-parameter name="System"/> 1047 <template-type-parameter name="State"/> 1048 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>typename traits::time_type< Stepper >::type</paramtype></parameter><parameter name="t_end"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The end time, at which the iteration should stop. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function to construct a single pass range of <classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname>. A range is here a pair of <classname alt="boost::numeric::odeint::const_step_time_iterator">const_step_time_iterator</classname>. </purpose><description><para> 1049 1050</para></description><returns><para>The const step time range. </para> 1051</returns></function> 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061</namespace> 1062</namespace> 1063</namespace> 1064</header> 1065<header name="boost/numeric/odeint/iterator/n_step_iterator.hpp"> 1066<namespace name="boost"> 1067<namespace name="numeric"> 1068<namespace name="odeint"> 1069<class name="n_step_iterator"><template> 1070 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 1071 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 1072 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 1073 </template><purpose>ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper. </purpose><description><para>Implements an iterator representing the solution of an ODE starting from t with n steps and a constant step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_n_steps routine.</para><para><classname alt="boost::numeric::odeint::n_step_iterator">n_step_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.</para><para> 1074</para></description><method-group name="public member functions"> 1075</method-group> 1076<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype></parameter></constructor> 1077<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 1078</class> 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115<function name="make_n_step_iterator_begin"><type><classname>n_step_iterator</classname>< Stepper, System, State ></type><template> 1116 <template-type-parameter name="Stepper"/> 1117 <template-type-parameter name="System"/> 1118 <template-type-parameter name="State"/> 1119 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype><description><para>The number of steps to be executed. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::n_step_iterator">n_step_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 1120 1121</para></description><returns><para>The n-step iterator. </para> 1122</returns></function> 1123<function name="make_n_step_iterator_end"><type><classname>n_step_iterator</classname>< Stepper, System, State ></type><template> 1124 <template-type-parameter name="Stepper"/> 1125 <template-type-parameter name="System"/> 1126 <template-type-parameter name="State"/> 1127 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::n_step_iterator">n_step_iterator</classname>. Constructs an end iterator. </purpose><description><para> 1128 1129</para></description><returns><para>The <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname>. </para> 1130</returns></function> 1131<function name="make_n_step_range"><type>std::pair< <classname>n_step_iterator</classname>< Stepper, System, State >, <classname>n_step_iterator</classname>< Stepper, System, State > ></type><template> 1132 <template-type-parameter name="Stepper"/> 1133 <template-type-parameter name="System"/> 1134 <template-type-parameter name="State"/> 1135 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> store a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype><description><para>The number of steps to be executed. </para></description></parameter><purpose>Factory function to construct a single pass range of n-step iterators. A range is here a pair of <classname alt="boost::numeric::odeint::n_step_iterator">n_step_iterator</classname>. </purpose><description><para> 1136 1137</para></description><returns><para>The n-step range. </para> 1138</returns></function> 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151</namespace> 1152</namespace> 1153</namespace> 1154</header> 1155<header name="boost/numeric/odeint/iterator/n_step_time_iterator.hpp"> 1156<namespace name="boost"> 1157<namespace name="numeric"> 1158<namespace name="odeint"> 1159<class name="n_step_time_iterator"><template> 1160 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 1161 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 1162 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 1163 </template><purpose>ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time. </purpose><description><para>Implements an iterator representing the solution of an ODE starting from t with n steps and a constant step size dt. After each iteration the iterator dereferences to a pair of state and time at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_n_steps routine.</para><para><classname alt="boost::numeric::odeint::n_step_time_iterator">n_step_time_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is pair of state and time.</para><para> 1164</para></description><method-group name="public member functions"> 1165</method-group> 1166<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype></parameter></constructor> 1167<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 1168</class> 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202<function name="make_n_step_time_iterator_begin"><type><classname>n_step_time_iterator</classname>< Stepper, System, State ></type><template> 1203 <template-type-parameter name="Stepper"/> 1204 <template-type-parameter name="System"/> 1205 <template-type-parameter name="State"/> 1206 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype><description><para>The number of steps to be executed. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::n_step_time_iterator">n_step_time_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 1207 1208</para></description><returns><para>The n-step iterator. </para> 1209</returns></function> 1210<function name="make_n_step_time_iterator_end"><type><classname>n_step_time_iterator</classname>< Stepper, System, State ></type><template> 1211 <template-type-parameter name="Stepper"/> 1212 <template-type-parameter name="System"/> 1213 <template-type-parameter name="State"/> 1214 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::n_step_time_iterator">n_step_time_iterator</classname>. Constructs an end iterator. </purpose><description><para> 1215 1216</para></description><returns><para>The <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname>. </para> 1217</returns></function> 1218<function name="make_n_step_time_range"><type>std::pair< <classname>n_step_time_iterator</classname>< Stepper, System, State >, <classname>n_step_time_iterator</classname>< Stepper, System, State > ></type><template> 1219 <template-type-parameter name="Stepper"/> 1220 <template-type-parameter name="System"/> 1221 <template-type-parameter name="State"/> 1222 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> store a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><parameter name="num_of_steps"><paramtype>size_t</paramtype><description><para>The number of steps to be executed. </para></description></parameter><purpose>Factory function to construct a single pass range of n-step iterators. A range is here a pair of <classname alt="boost::numeric::odeint::n_step_time_iterator">n_step_time_iterator</classname>. </purpose><description><para> 1223 1224</para></description><returns><para>The n-step range. </para> 1225</returns></function> 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241</namespace> 1242</namespace> 1243</namespace> 1244</header> 1245<header name="boost/numeric/odeint/iterator/times_iterator.hpp"> 1246<namespace name="boost"> 1247<namespace name="numeric"> 1248<namespace name="odeint"> 1249<class name="times_iterator"><template> 1250 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 1251 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 1252 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 1253 <template-type-parameter name="TimeIterator"><purpose><para>The iterator type for the sequence of time points. </para></purpose></template-type-parameter> 1254 </template><purpose>ODE Iterator with given evaluation points. The value type of this iterator is the state type of the stepper. </purpose><description><para>Implements an iterator representing the solution of an ODE from *t_start to *t_end evaluated at time points given by the sequence t_start to t_end. t_start and t_end are iterators representing a sequence of time points where the solution of the ODE should be evaluated. After each iteration the iterator dereferences to the state x at the next time *t_start++ until t_end is reached. This iterator can be used with Steppers, ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_times routine.</para><para><classname alt="boost::numeric::odeint::times_iterator">times_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.</para><para> 1255</para></description><method-group name="public member functions"> 1256</method-group> 1257<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t_start"><paramtype>TimeIterator</paramtype></parameter><parameter name="t_end"><paramtype>TimeIterator</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></constructor> 1258<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 1259</class> 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290<function name="make_times_iterator_begin"><type><classname>times_iterator</classname>< Stepper, System, State, TimeIterator ></type><template> 1291 <template-type-parameter name="Stepper"/> 1292 <template-type-parameter name="System"/> 1293 <template-type-parameter name="State"/> 1294 <template-type-parameter name="TimeIterator"/> 1295 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>TimeIterator</paramtype><description><para>Begin iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="t_end"><paramtype>TimeIterator</paramtype><description><para>End iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::times_iterator">times_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 1296 1297</para></description><returns><para>The times iterator. </para> 1298</returns></function> 1299<function name="make_times_iterator_end"><type><classname>times_iterator</classname>< Stepper, System, State, TimeIterator ></type><template> 1300 <template-type-parameter name="TimeIterator"/> 1301 <template-type-parameter name="Stepper"/> 1302 <template-type-parameter name="System"/> 1303 <template-type-parameter name="State"/> 1304 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::times_iterator">times_iterator</classname>. Constructs an end iterator. </purpose><description><para> 1305 1306 1307This function needs the TimeIterator type specifically defined as a template parameter. </para></description><returns><para>The times iterator.</para> 1308</returns></function> 1309<function name="make_times_range"><type>std::pair< <classname>times_iterator</classname>< Stepper, System, State, TimeIterator >, <classname>times_iterator</classname>< Stepper, System, State, TimeIterator > ></type><template> 1310 <template-type-parameter name="Stepper"/> 1311 <template-type-parameter name="System"/> 1312 <template-type-parameter name="State"/> 1313 <template-type-parameter name="TimeIterator"/> 1314 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> store a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>TimeIterator</paramtype><description><para>Begin iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="t_end"><paramtype>TimeIterator</paramtype><description><para>End iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function to construct a single pass range of times iterators. A range is here a pair of <classname alt="boost::numeric::odeint::times_iterator">times_iterator</classname>. </purpose><description><para> 1315 1316</para></description><returns><para>The times iterator range. </para> 1317</returns></function> 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336</namespace> 1337</namespace> 1338</namespace> 1339</header> 1340<header name="boost/numeric/odeint/iterator/times_time_iterator.hpp"> 1341<namespace name="boost"> 1342<namespace name="numeric"> 1343<namespace name="odeint"> 1344<class name="times_time_iterator"><template> 1345 <template-type-parameter name="Stepper"><purpose><para>The stepper type which should be used during the iteration. </para></purpose></template-type-parameter> 1346 <template-type-parameter name="System"><purpose><para>The type of the system function (ODE) which should be solved. </para></purpose></template-type-parameter> 1347 <template-type-parameter name="State"><purpose><para>The state type of the ODE. </para></purpose></template-type-parameter> 1348 <template-type-parameter name="TimeIterator"><purpose><para>The iterator type for the sequence of time points. </para></purpose></template-type-parameter> 1349 </template><purpose>ODE Iterator with given evaluation points. The value type of this iterator is a std::pair containing state and time. </purpose><description><para>Implements an iterator representing the solution of an ODE from *t_start to *t_end evaluated at time points given by the sequence t_start to t_end. t_start and t_end are iterators representing a sequence of time points where the solution of the ODE should be evaluated. After each iteration the iterator dereferences to a pair with the state and the time at the next evaluation point *t_start++ until t_end is reached. This iterator can be used with Steppers, ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_times routine.</para><para><classname alt="boost::numeric::odeint::times_time_iterator">times_time_iterator</classname> is a model of single-pass iterator.</para><para>The value type of this iterator is a pair of state and time type.</para><para> 1350</para></description><method-group name="public member functions"> 1351</method-group> 1352<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter><parameter name="t_start"><paramtype>TimeIterator</paramtype></parameter><parameter name="t_end"><paramtype>TimeIterator</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></constructor> 1353<constructor><parameter name="stepper"><paramtype>Stepper</paramtype></parameter><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="s"><paramtype>State &</paramtype></parameter></constructor> 1354</class> 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382<function name="make_times_time_iterator_begin"><type><classname>times_time_iterator</classname>< Stepper, System, State, TimeIterator ></type><template> 1383 <template-type-parameter name="Stepper"/> 1384 <template-type-parameter name="System"/> 1385 <template-type-parameter name="State"/> 1386 <template-type-parameter name="TimeIterator"/> 1387 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>TimeIterator</paramtype><description><para>Begin iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="t_end"><paramtype>TimeIterator</paramtype><description><para>End iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::times_time_iterator">times_time_iterator</classname>. Constructs a begin iterator. </purpose><description><para> 1388 1389</para></description><returns><para>The times_time iterator. </para> 1390</returns></function> 1391<function name="make_times_time_iterator_end"><type><classname>times_time_iterator</classname>< Stepper, System, State, TimeIterator ></type><template> 1392 <template-type-parameter name="TimeIterator"/> 1393 <template-type-parameter name="Stepper"/> 1394 <template-type-parameter name="System"/> 1395 <template-type-parameter name="State"/> 1396 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> stores a reference of s and changes its value during the iteration. </para></description></parameter><purpose>Factory function for <classname alt="boost::numeric::odeint::times_time_iterator">times_time_iterator</classname>. Constructs an end iterator. </purpose><description><para> 1397 1398 1399This function needs the TimeIterator type specifically defined as a template parameter. </para></description><returns><para>The times_time iterator.</para> 1400</returns></function> 1401<function name="make_times_time_range"><type>std::pair< <classname>times_time_iterator</classname>< Stepper, System, State, TimeIterator >, <classname>times_time_iterator</classname>< Stepper, System, State, TimeIterator > ></type><template> 1402 <template-type-parameter name="Stepper"/> 1403 <template-type-parameter name="System"/> 1404 <template-type-parameter name="State"/> 1405 <template-type-parameter name="TimeIterator"/> 1406 </template><parameter name="stepper"><paramtype>Stepper</paramtype><description><para>The stepper to use during the iteration. </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function (ODE) to solve. </para></description></parameter><parameter name="x"><paramtype>State &</paramtype><description><para>The initial state. <classname alt="boost::numeric::odeint::const_step_iterator">const_step_iterator</classname> store a reference of s and changes its value during the iteration. </para></description></parameter><parameter name="t_start"><paramtype>TimeIterator</paramtype><description><para>Begin iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="t_end"><paramtype>TimeIterator</paramtype><description><para>End iterator of the sequence of evaluation time points. </para></description></parameter><parameter name="dt"><paramtype>typename traits::time_type< Stepper >::type</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Factory function to construct a single pass range of times_time iterators. A range is here a pair of <classname alt="boost::numeric::odeint::times_iterator">times_iterator</classname>. </purpose><description><para> 1407 1408</para></description><returns><para>The times_time iterator range. </para> 1409</returns></function> 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431</namespace> 1432</namespace> 1433</namespace> 1434</header> 1435<header name="boost/numeric/odeint/stepper/adams_bashforth.hpp"> 1436<namespace name="boost"> 1437<namespace name="numeric"> 1438<namespace name="odeint"> 1439<class name="adams_bashforth"><template> 1440 <template-nontype-parameter name="Steps"><type>size_t</type><purpose><para>The number of steps (maximal 8). </para></purpose></template-nontype-parameter> 1441 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 1442 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 1443 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 1444 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 1445 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 1446 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 1447 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 1448 <template-type-parameter name="InitializingStepper"><default><classname alt="boost::numeric::odeint::extrapolation_stepper">extrapolation_stepper</classname>< order_helper<Steps>::value, State, Value, Deriv, Time, Algebra, Operations, Resizer ></default><purpose><para>The stepper for the first two steps. </para></purpose></template-type-parameter> 1449 </template><inherit access="public">algebra_stepper_base< Algebra, Operations ></inherit><purpose>The Adams-Bashforth multistep algorithm. </purpose><description><para>The Adams-Bashforth method is a multi-step algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also <ulink url="http://en.wikipedia.org/wiki/Linear_multistep_method">en.wikipedia.org/wiki/Linear_multistep_method</ulink>. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.</para><para>This class derives from algebra_base and inherits its interface via CRTP (current recurring template pattern). For more details see algebra_stepper_base.</para><para> 1450</para></description><typedef name="state_type"><type>State</type></typedef> 1451<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 1452<typedef name="value_type"><type>Value</type></typedef> 1453<typedef name="deriv_type"><type>Deriv</type></typedef> 1454<typedef name="wrapped_deriv_type"><type>state_wrapper< deriv_type ></type></typedef> 1455<typedef name="time_type"><type>Time</type></typedef> 1456<typedef name="resizer_type"><type>Resizer</type></typedef> 1457<typedef name="stepper_category"><type>stepper_tag</type></typedef> 1458<typedef name="initializing_stepper_type"><type>InitializingStepper</type></typedef> 1459<typedef name="algebra_stepper_base_type"><type>algebra_stepper_base< Algebra, Operations ></type></typedef> 1460<typedef name="algebra_type"><type>algebra_stepper_base_type::algebra_type</type></typedef> 1461<typedef name="operations_type"><type>algebra_stepper_base_type::operations_type</type></typedef> 1462<typedef name="order_type"><type>unsigned short</type></typedef> 1463<typedef name="step_storage_type"><type><emphasis>unspecified</emphasis></type></typedef> 1464<data-member name="steps" specifiers="static"><type>const size_t</type></data-member> 1465<data-member name="order_value" specifiers="static"><type>const order_type</type></data-member> 1466<method-group name="public member functions"> 1467<method name="order" cv="const"><type>order_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the order of the algorithm, which is equal to the number of steps. </purpose><description><para> 1468</para></description><returns><para>order of the method. </para> 1469</returns></method> 1470<method name="do_step"><type>void</type><template> 1471 <template-type-parameter name="System"/> 1472 <template-type-parameter name="StateInOut"/> 1473 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. After calling do_step the result is updated in x. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. It transforms the result in-place. </purpose><description><para> 1474</para></description></method> 1475<method name="do_step"><type>void</type><template> 1476 <template-type-parameter name="System"/> 1477 <template-type-parameter name="StateInOut"/> 1478 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>const StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut. </purpose></method> 1479<method name="do_step"><type>void</type><template> 1480 <template-type-parameter name="System"/> 1481 <template-type-parameter name="StateIn"/> 1482 <template-type-parameter name="StateOut"/> 1483 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. </purpose><description><para> 1484</para></description></method> 1485<method name="do_step"><type>void</type><template> 1486 <template-type-parameter name="System"/> 1487 <template-type-parameter name="StateIn"/> 1488 <template-type-parameter name="StateOut"/> 1489 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>const StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as StateOut. </purpose></method> 1490<method name="adjust_size"><type>void</type><template> 1491 <template-type-parameter name="StateType"/> 1492 </template><parameter name="x"><paramtype>const StateType &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 1493</para></description></method> 1494<method name="step_storage" cv="const"><type>const step_storage_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the storage of intermediate results. </purpose><description><para> 1495</para></description><returns><para>The storage of intermediate results. </para> 1496</returns></method> 1497<method name="step_storage"><type>step_storage_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the storage of intermediate results. </purpose><description><para> 1498</para></description><returns><para>The storage of intermediate results. </para> 1499</returns></method> 1500<method name="initialize"><type>void</type><template> 1501 <template-type-parameter name="ExplicitStepper"/> 1502 <template-type-parameter name="System"/> 1503 <template-type-parameter name="StateIn"/> 1504 </template><parameter name="explicit_stepper"><paramtype>ExplicitStepper</paramtype><description><para>the stepper used to fill the buffer of previous step results </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateIn &</paramtype><description><para>The state of the ODE which should be solved. After calling do_step the result is updated in x. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer. </purpose><description><para> 1505</para></description></method> 1506<method name="initialize"><type>void</type><template> 1507 <template-type-parameter name="System"/> 1508 <template-type-parameter name="StateIn"/> 1509 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateIn &</paramtype><description><para>The initial state of the ODE which should be solved, updated in this method. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The initial value of the time, updated in this method. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>Initialized the stepper. Does Steps-1 steps with an internal instance of InitializingStepper to fill the buffer. </purpose><description><para><note><para>The state x and time t are updated to the values after Steps-1 initial steps. </para> 1510</note> 1511 1512</para></description></method> 1513<method name="reset"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Resets the internal buffer of the stepper. </purpose></method> 1514<method name="is_initialized" cv="const"><type>bool</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns true if the stepper has been initialized. </purpose><description><para> 1515</para></description><returns><para>bool true if stepper is initialized, false otherwise </para> 1516</returns></method> 1517<method name="initializing_stepper" cv="const"><type>const initializing_stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the internal initializing stepper instance. </purpose><description><para> 1518</para></description><returns><para>initializing_stepper </para> 1519</returns></method> 1520<method name="initializing_stepper"><type>initializing_stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the internal initializing stepper instance. </purpose><description><para> 1521</para></description><returns><para>initializing_stepper </para> 1522</returns></method> 1523</method-group> 1524<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::adams_bashforth">adams_bashforth</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 1525</para></description></constructor> 1526<method-group name="private member functions"> 1527<method name="do_step_impl"><type>void</type><template> 1528 <template-type-parameter name="System"/> 1529 <template-type-parameter name="StateIn"/> 1530 <template-type-parameter name="StateOut"/> 1531 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 1532<method name="resize_impl"><type>bool</type><template> 1533 <template-type-parameter name="StateIn"/> 1534 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 1535</method-group> 1536</class><struct name="order_helper"><template> 1537 <template-nontype-parameter name="N"><type>int</type></template-nontype-parameter> 1538 </template><inherit access="public">boost::mpl::max::type< mpl::eval_if< mpl::equal_to< mpl::modulus< int_< N >, int_< 2 > >, int_< 0 > >, int_< N >, int_< N+1 > >::type, int_< 4 > ></inherit></struct> 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590</namespace> 1591</namespace> 1592</namespace> 1593</header> 1594<header name="boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp"> 1595<namespace name="boost"> 1596<namespace name="numeric"> 1597<namespace name="odeint"> 1598<class name="adams_bashforth_moulton"><template> 1599 <template-nontype-parameter name="Steps"><type>size_t</type><purpose><para>The number of steps (maximal 8). </para></purpose></template-nontype-parameter> 1600 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 1601 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 1602 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 1603 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 1604 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 1605 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 1606 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 1607 <template-type-parameter name="InitializingStepper"><default><classname alt="boost::numeric::odeint::runge_kutta4">runge_kutta4</classname>< State , Value , Deriv , Time , Algebra , Operations, Resizer ></default><purpose><para>The stepper for the first two steps. </para></purpose></template-type-parameter> 1608 </template><purpose>The Adams-Bashforth-Moulton multistep algorithm. </purpose><description><para>The Adams-Bashforth method is a multi-step predictor-corrector algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also <ulink url="http://en.wikipedia.org/wiki/Linear_multistep_method">en.wikipedia.org/wiki/Linear_multistep_method</ulink>. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.</para><para>This class derives from algebra_base and inherits its interface via CRTP (current recurring template pattern). For more details see algebra_stepper_base.</para><para> 1609</para></description><typedef name="state_type"><type>State</type></typedef> 1610<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 1611<typedef name="value_type"><type>Value</type></typedef> 1612<typedef name="deriv_type"><type>Deriv</type></typedef> 1613<typedef name="wrapped_deriv_type"><type>state_wrapper< deriv_type ></type></typedef> 1614<typedef name="time_type"><type>Time</type></typedef> 1615<typedef name="algebra_type"><type>Algebra</type></typedef> 1616<typedef name="operations_type"><type>Operations</type></typedef> 1617<typedef name="resizer_type"><type>Resizer</type></typedef> 1618<typedef name="stepper_category"><type>stepper_tag</type></typedef> 1619<typedef name="initializing_stepper_type"><type>InitializingStepper</type></typedef> 1620<typedef name="order_type"><type>unsigned short</type></typedef> 1621<data-member name="steps" specifiers="static"><type>const size_t</type></data-member> 1622<data-member name="order_value" specifiers="static"><type>const order_type</type></data-member> 1623<method-group name="public member functions"> 1624<method name="order" cv="const"><type>order_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the order of the algorithm, which is equal to the number of steps+1. </purpose><description><para> 1625</para></description><returns><para>order of the method. </para> 1626</returns></method> 1627<method name="do_step"><type>void</type><template> 1628 <template-type-parameter name="System"/> 1629 <template-type-parameter name="StateInOut"/> 1630 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. After calling do_step the result is updated in x. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. It transforms the result in-place. </purpose><description><para> 1631</para></description></method> 1632<method name="do_step"><type>void</type><template> 1633 <template-type-parameter name="System"/> 1634 <template-type-parameter name="StateInOut"/> 1635 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>const StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut. </purpose></method> 1636<method name="do_step"><type>void</type><template> 1637 <template-type-parameter name="System"/> 1638 <template-type-parameter name="StateIn"/> 1639 <template-type-parameter name="StateOut"/> 1640 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>const StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. </purpose><description><para> 1641</para></description></method> 1642<method name="do_step"><type>void</type><template> 1643 <template-type-parameter name="System"/> 1644 <template-type-parameter name="StateIn"/> 1645 <template-type-parameter name="StateOut"/> 1646 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be called with Boost.Range as StateOut. </purpose></method> 1647<method name="adjust_size"><type>void</type><template> 1648 <template-type-parameter name="StateType"/> 1649 </template><parameter name="x"><paramtype>const StateType &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 1650</para></description></method> 1651<method name="initialize"><type>void</type><template> 1652 <template-type-parameter name="ExplicitStepper"/> 1653 <template-type-parameter name="System"/> 1654 <template-type-parameter name="StateIn"/> 1655 </template><parameter name="explicit_stepper"><paramtype>ExplicitStepper</paramtype><description><para>the stepper used to fill the buffer of previous step results </para></description></parameter><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateIn &</paramtype><description><para>The initial state of the ODE which should be solved, updated after in this method. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The initial time, updated in this method. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer. </purpose><description><para><note><para>The state x and time t are updated to the values after Steps-1 initial steps. </para> 1656</note> 1657 1658</para></description></method> 1659<method name="initialize"><type>void</type><template> 1660 <template-type-parameter name="System"/> 1661 <template-type-parameter name="StateIn"/> 1662 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateIn &</paramtype><description><para>The state of the ODE which should be solved. After calling do_step the result is updated in x. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>Initialized the stepper. Does Steps-1 steps using the standard initializing stepper of the underlying <classname alt="boost::numeric::odeint::adams_bashforth">adams_bashforth</classname> stepper. </purpose><description><para> 1663</para></description></method> 1664<method name="reset"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Resets the internal buffers of the stepper. </purpose></method> 1665</method-group> 1666<constructor><parameter name=""><paramtype>void</paramtype></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::adams_bashforth">adams_bashforth</classname> class. </purpose></constructor> 1667<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><description><para>A copy of algebra is made and stored. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::adams_bashforth">adams_bashforth</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 1668</para></description></constructor> 1669<method-group name="private member functions"> 1670<method name="do_step_impl1"><type>void</type><template> 1671 <template-type-parameter name="System"/> 1672 <template-type-parameter name="StateInOut"/> 1673 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 1674<method name="do_step_impl2"><type>void</type><template> 1675 <template-type-parameter name="System"/> 1676 <template-type-parameter name="StateIn"/> 1677 <template-type-parameter name="StateInOut"/> 1678 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>StateIn const &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateInOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 1679<method name="resize_impl"><type>bool</type><template> 1680 <template-type-parameter name="StateIn"/> 1681 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 1682</method-group> 1683</class> 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735</namespace> 1736</namespace> 1737</namespace> 1738</header> 1739<header name="boost/numeric/odeint/stepper/adams_moulton.hpp"> 1740<namespace name="boost"> 1741<namespace name="numeric"> 1742<namespace name="odeint"> 1743<class name="adams_moulton"><template> 1744 <template-nontype-parameter name="Steps"><type>size_t</type></template-nontype-parameter> 1745 <template-type-parameter name="State"/> 1746 <template-type-parameter name="Value"><default>double</default></template-type-parameter> 1747 <template-type-parameter name="Deriv"><default>State</default></template-type-parameter> 1748 <template-type-parameter name="Time"><default>Value</default></template-type-parameter> 1749 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default></template-type-parameter> 1750 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default></template-type-parameter> 1751 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 1752 </template><typedef name="state_type"><type>State</type></typedef> 1753<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 1754<typedef name="value_type"><type>Value</type></typedef> 1755<typedef name="deriv_type"><type>Deriv</type></typedef> 1756<typedef name="wrapped_deriv_type"><type>state_wrapper< deriv_type ></type></typedef> 1757<typedef name="time_type"><type>Time</type></typedef> 1758<typedef name="algebra_type"><type>Algebra</type></typedef> 1759<typedef name="operations_type"><type>Operations</type></typedef> 1760<typedef name="resizer_type"><type>Resizer</type></typedef> 1761<typedef name="stepper_category"><type>stepper_tag</type></typedef> 1762<typedef name="stepper_type"><type>adams_moulton< Steps, State, Value, Deriv, Time, Algebra, Operations, Resizer ></type></typedef> 1763<typedef name="order_type"><type>unsigned short</type></typedef> 1764<typedef name="step_storage_type"><type><emphasis>unspecified</emphasis></type></typedef> 1765<data-member name="steps" specifiers="static"><type>const size_t</type></data-member> 1766<data-member name="order_value" specifiers="static"><type>const order_type</type></data-member> 1767<method-group name="public member functions"> 1768<method name="order" cv="const"><type>order_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 1769<method name="do_step"><type>void</type><template> 1770 <template-type-parameter name="System"/> 1771 <template-type-parameter name="StateInOut"/> 1772 <template-type-parameter name="StateIn"/> 1773 <template-type-parameter name="ABBuf"/> 1774 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>StateInOut &</paramtype></parameter><parameter name="pred"><paramtype>StateIn const &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="buf"><paramtype>const ABBuf &</paramtype></parameter></method> 1775<method name="do_step"><type>void</type><template> 1776 <template-type-parameter name="System"/> 1777 <template-type-parameter name="StateInOut"/> 1778 <template-type-parameter name="StateIn"/> 1779 <template-type-parameter name="ABBuf"/> 1780 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>const StateInOut &</paramtype></parameter><parameter name="pred"><paramtype>StateIn const &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="buf"><paramtype>const ABBuf &</paramtype></parameter></method> 1781<method name="do_step"><type>void</type><template> 1782 <template-type-parameter name="System"/> 1783 <template-type-parameter name="StateIn"/> 1784 <template-type-parameter name="PredIn"/> 1785 <template-type-parameter name="StateOut"/> 1786 <template-type-parameter name="ABBuf"/> 1787 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="pred"><paramtype>const PredIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="buf"><paramtype>const ABBuf &</paramtype></parameter></method> 1788<method name="do_step"><type>void</type><template> 1789 <template-type-parameter name="System"/> 1790 <template-type-parameter name="StateIn"/> 1791 <template-type-parameter name="PredIn"/> 1792 <template-type-parameter name="StateOut"/> 1793 <template-type-parameter name="ABBuf"/> 1794 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="pred"><paramtype>const PredIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>const StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="buf"><paramtype>const ABBuf &</paramtype></parameter></method> 1795<method name="adjust_size"><type>void</type><template> 1796 <template-type-parameter name="StateType"/> 1797 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 1798<method name="algebra"><type>algebra_type &</type></method> 1799<method name="algebra" cv="const"><type>const algebra_type &</type></method> 1800</method-group> 1801<constructor/> 1802<constructor><parameter name="algebra"><paramtype>algebra_type &</paramtype></parameter></constructor> 1803<copy-assignment><type>adams_moulton &</type><parameter name="stepper"><paramtype>const adams_moulton &</paramtype></parameter></copy-assignment> 1804<method-group name="private member functions"> 1805<method name="do_step_impl"><type>void</type><template> 1806 <template-type-parameter name="System"/> 1807 <template-type-parameter name="StateIn"/> 1808 <template-type-parameter name="PredIn"/> 1809 <template-type-parameter name="StateOut"/> 1810 <template-type-parameter name="ABBuf"/> 1811 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="pred"><paramtype>const PredIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="buf"><paramtype>const ABBuf &</paramtype></parameter></method> 1812<method name="resize_impl"><type>bool</type><template> 1813 <template-type-parameter name="StateIn"/> 1814 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 1815</method-group> 1816</class> 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868</namespace> 1869</namespace> 1870</namespace> 1871</header> 1872<header name="boost/numeric/odeint/stepper/adaptive_adams_bashforth_moulton.hpp"> 1873<namespace name="boost"> 1874<namespace name="numeric"> 1875<namespace name="odeint"> 1876<class name="adaptive_adams_bashforth_moulton"><template> 1877 <template-nontype-parameter name="Steps"><type>size_t</type></template-nontype-parameter> 1878 <template-type-parameter name="State"/> 1879 <template-type-parameter name="Value"><default>double</default></template-type-parameter> 1880 <template-type-parameter name="Deriv"><default>State</default></template-type-parameter> 1881 <template-type-parameter name="Time"><default>Value</default></template-type-parameter> 1882 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default></template-type-parameter> 1883 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default></template-type-parameter> 1884 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 1885 </template><inherit access="public">algebra_stepper_base< Algebra, Operations ></inherit><typedef name="order_type"><type>unsigned short</type></typedef> 1886<typedef name="state_type"><type>State</type></typedef> 1887<typedef name="value_type"><type>Value</type></typedef> 1888<typedef name="deriv_type"><type>Deriv</type></typedef> 1889<typedef name="time_type"><type>Time</type></typedef> 1890<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 1891<typedef name="wrapped_deriv_type"><type>state_wrapper< deriv_type ></type></typedef> 1892<typedef name="algebra_stepper_base_type"><type>algebra_stepper_base< Algebra, Operations ></type></typedef> 1893<typedef name="algebra_type"><type>algebra_stepper_base_type::algebra_type</type></typedef> 1894<typedef name="operations_type"><type>algebra_stepper_base_type::operations_type</type></typedef> 1895<typedef name="resizer_type"><type>Resizer</type></typedef> 1896<typedef name="stepper_category"><type>error_stepper_tag</type></typedef> 1897<typedef name="coeff_type"><type><emphasis>unspecified</emphasis></type></typedef> 1898<typedef name="stepper_type"><type>adaptive_adams_bashforth_moulton< Steps, State, Value, Deriv, Time, Algebra, Operations, Resizer ></type></typedef> 1899<data-member name="steps" specifiers="static"><type>const size_t</type></data-member> 1900<data-member name="order_value" specifiers="static"><type>const order_type</type></data-member> 1901<method-group name="public member functions"> 1902<method name="order" cv="const"><type>order_type</type></method> 1903<method name="stepper_order" cv="const"><type>order_type</type></method> 1904<method name="error_order" cv="const"><type>order_type</type></method> 1905<method name="do_step"><type>void</type><template> 1906 <template-type-parameter name="System"/> 1907 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 1908<method name="do_step"><type>void</type><template> 1909 <template-type-parameter name="System"/> 1910 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>state_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 1911<method name="do_step"><type>void</type><template> 1912 <template-type-parameter name="System"/> 1913 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="xerr"><paramtype>state_type &</paramtype></parameter></method> 1914<method name="do_step"><type>void</type><template> 1915 <template-type-parameter name="System"/> 1916 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>state_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="xerr"><paramtype>state_type &</paramtype></parameter></method> 1917<method name="initialize"><type>void</type><template> 1918 <template-type-parameter name="ExplicitStepper"/> 1919 <template-type-parameter name="System"/> 1920 </template><parameter name="stepper"><paramtype>ExplicitStepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 1921<method name="initialize"><type>void</type><template> 1922 <template-type-parameter name="System"/> 1923 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 1924<method name="do_step_impl"><type>void</type><template> 1925 <template-type-parameter name="System"/> 1926 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>state_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter><parameter name="xerr"><paramtype>state_type &</paramtype></parameter></method> 1927<method name="coeff" cv="const"><type>const coeff_type &</type></method> 1928<method name="coeff"><type>coeff_type &</type></method> 1929<method name="reset"><type>void</type></method> 1930<method name="dxdt" cv="const"><type>const deriv_type &</type></method> 1931</method-group> 1932<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default></parameter></constructor> 1933<method-group name="private member functions"> 1934<method name="resize_dxdt_impl"><type>bool</type><template> 1935 <template-type-parameter name="StateType"/> 1936 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 1937<method name="resize_xnew_impl"><type>bool</type><template> 1938 <template-type-parameter name="StateType"/> 1939 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 1940<method name="resize_xerr_impl"><type>bool</type><template> 1941 <template-type-parameter name="StateType"/> 1942 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 1943</method-group> 1944</class> 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996</namespace> 1997</namespace> 1998</namespace> 1999</header> 2000<header name="boost/numeric/odeint/stepper/bulirsch_stoer.hpp"> 2001<namespace name="boost"> 2002<namespace name="numeric"> 2003<namespace name="odeint"> 2004<class name="bulirsch_stoer"><template> 2005 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 2006 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 2007 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 2008 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 2009 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 2010 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 2011 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 2012 </template><purpose>The Bulirsch-Stoer algorithm. </purpose><description><para>The Bulirsch-Stoer is a controlled stepper that adjusts both step size and order of the method. The algorithm uses the modified midpoint and a polynomial extrapolation compute the solution.</para><para> 2013</para></description><typedef name="state_type"><type>State</type></typedef> 2014<typedef name="value_type"><type>Value</type></typedef> 2015<typedef name="deriv_type"><type>Deriv</type></typedef> 2016<typedef name="time_type"><type>Time</type></typedef> 2017<typedef name="algebra_type"><type>Algebra</type></typedef> 2018<typedef name="operations_type"><type>Operations</type></typedef> 2019<typedef name="resizer_type"><type>Resizer</type></typedef> 2020<data-member name="m_k_max" specifiers="static"><type>const size_t</type></data-member> 2021<method-group name="public member functions"> 2022<method name="try_step"><type>controlled_step_result</type><template> 2023 <template-type-parameter name="System"/> 2024 <template-type-parameter name="StateInOut"/> 2025 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.</para><para> 2026 2027</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2028</returns></method> 2029<method name="try_step"><type>controlled_step_result</type><template> 2030 <template-type-parameter name="System"/> 2031 <template-type-parameter name="StateInOut"/> 2032 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>const StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter><purpose>Second version to solve the forwarding problem, can be used with Boost.Range as StateInOut. </purpose></method> 2033<method name="try_step"><type>controlled_step_result</type><template> 2034 <template-type-parameter name="System"/> 2035 <template-type-parameter name="StateInOut"/> 2036 <template-type-parameter name="DerivIn"/> 2037 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of state. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.</para><para> 2038 2039</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2040</returns></method> 2041<method name="try_step"><type>boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::type</type><template> 2042 <template-type-parameter name="System"/> 2043 <template-type-parameter name="StateIn"/> 2044 <template-type-parameter name="StateOut"/> 2045 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>Used to store the result of the step. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para><note><para>This method is disabled if state_type=time_type to avoid ambiguity.</para> 2046</note> 2047This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.</para><para> 2048 2049</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2050</returns></method> 2051<method name="try_step"><type>controlled_step_result</type><template> 2052 <template-type-parameter name="System"/> 2053 <template-type-parameter name="StateIn"/> 2054 <template-type-parameter name="DerivIn"/> 2055 <template-type-parameter name="StateOut"/> 2056 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of state. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>Used to store the result of the step. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.</para><para> 2057 2058</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2059</returns></method> 2060<method name="reset"><type>void</type><purpose>Resets the internal state of the stepper. </purpose></method> 2061<method name="adjust_size"><type>void</type><template> 2062 <template-type-parameter name="StateIn"/> 2063 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 2064</para></description></method> 2065</method-group> 2066<constructor><parameter name="eps_abs"><paramtype>value_type</paramtype><default>1E-6</default><description><para>Absolute tolerance level. </para></description></parameter><parameter name="eps_rel"><paramtype>value_type</paramtype><default>1E-6</default><description><para>Relative tolerance level. </para></description></parameter><parameter name="factor_x"><paramtype>value_type</paramtype><default>1.0</default><description><para>Factor for the weight of the state. </para></description></parameter><parameter name="factor_dxdt"><paramtype>value_type</paramtype><default>1.0</default><description><para>Factor for the weight of the derivative. </para></description></parameter><parameter name="max_dt"><paramtype>time_type</paramtype><default>static_cast< time_type >(0)</default></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::bulirsch_stoer">bulirsch_stoer</classname> class, including initialization of the error bounds. </purpose><description><para> 2067</para></description></constructor> 2068<method-group name="private member functions"> 2069<method name="resize_m_dxdt"><type>bool</type><template> 2070 <template-type-parameter name="StateIn"/> 2071 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2072<method name="resize_m_xnew"><type>bool</type><template> 2073 <template-type-parameter name="StateIn"/> 2074 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2075<method name="resize_impl"><type>bool</type><template> 2076 <template-type-parameter name="StateIn"/> 2077 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2078<method name="try_step_v1"><type>controlled_step_result</type><template> 2079 <template-type-parameter name="System"/> 2080 <template-type-parameter name="StateInOut"/> 2081 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 2082<method name="extrapolate"><type>void</type><template> 2083 <template-type-parameter name="StateInOut"/> 2084 </template><parameter name="k"><paramtype>size_t</paramtype></parameter><parameter name="table"><paramtype>state_table_type &</paramtype></parameter><parameter name="coeff"><paramtype>const value_matrix &</paramtype></parameter><parameter name="xest"><paramtype>StateInOut &</paramtype></parameter></method> 2085<method name="calc_h_opt" cv="const"><type>time_type</type><parameter name="h"><paramtype>time_type</paramtype></parameter><parameter name="error"><paramtype>value_type</paramtype></parameter><parameter name="k"><paramtype>size_t</paramtype></parameter></method> 2086<method name="set_k_opt"><type>controlled_step_result</type><parameter name="k"><paramtype>size_t</paramtype></parameter><parameter name="work"><paramtype>const inv_time_vector &</paramtype></parameter><parameter name="h_opt"><paramtype>const time_vector &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 2087<method name="in_convergence_window" cv="const"><type>bool</type><parameter name="k"><paramtype>size_t</paramtype></parameter></method> 2088<method name="should_reject" cv="const"><type>bool</type><parameter name="error"><paramtype>value_type</paramtype></parameter><parameter name="k"><paramtype>size_t</paramtype></parameter></method> 2089</method-group> 2090</class> 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142</namespace> 2143</namespace> 2144</namespace> 2145</header> 2146<header name="boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp"> 2147<namespace name="boost"> 2148<namespace name="numeric"> 2149<namespace name="odeint"> 2150<class name="bulirsch_stoer_dense_out"><template> 2151 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 2152 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 2153 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 2154 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 2155 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 2156 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 2157 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 2158 </template><purpose>The Bulirsch-Stoer algorithm. </purpose><description><para>The Bulirsch-Stoer is a controlled stepper that adjusts both step size and order of the method. The algorithm uses the modified midpoint and a polynomial extrapolation compute the solution. This class also provides dense output facility.</para><para> 2159</para></description><typedef name="state_type"><type>State</type></typedef> 2160<typedef name="value_type"><type>Value</type></typedef> 2161<typedef name="deriv_type"><type>Deriv</type></typedef> 2162<typedef name="time_type"><type>Time</type></typedef> 2163<typedef name="algebra_type"><type>Algebra</type></typedef> 2164<typedef name="operations_type"><type>Operations</type></typedef> 2165<typedef name="resizer_type"><type>Resizer</type></typedef> 2166<typedef name="stepper_category"><type>dense_output_stepper_tag</type></typedef> 2167<data-member name="m_k_max" specifiers="static"><type>const size_t</type></data-member> 2168<method-group name="public member functions"> 2169<method name="try_step"><type>controlled_step_result</type><template> 2170 <template-type-parameter name="System"/> 2171 <template-type-parameter name="StateIn"/> 2172 <template-type-parameter name="DerivIn"/> 2173 <template-type-parameter name="StateOut"/> 2174 <template-type-parameter name="DerivOut"/> 2175 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of state. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>Used to store the result of the step. </para></description></parameter><parameter name="dxdt_new"><paramtype>DerivOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.</para><para> 2176 2177</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2178</returns></method> 2179<method name="initialize"><type>void</type><template> 2180 <template-type-parameter name="StateType"/> 2181 </template><parameter name="x0"><paramtype>const StateType &</paramtype><description><para>The initial state. </para></description></parameter><parameter name="t0"><paramtype>const time_type &</paramtype><description><para>The initial time. </para></description></parameter><parameter name="dt0"><paramtype>const time_type &</paramtype><description><para>The initial time step. </para></description></parameter><purpose>Initializes the dense output stepper. </purpose><description><para> 2182</para></description></method> 2183<method name="do_step"><type>std::pair< time_type, time_type ></type><template> 2184 <template-type-parameter name="System"/> 2185 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><purpose>Does one time step. This is the main method that should be used to integrate an ODE with this stepper. </purpose><description><para><note><para>initialize has to be called before using this method to set the initial conditions x,t and the stepsize. </para> 2186</note> 2187 2188 2189</para></description><returns><para>Pair with start and end time of the integration step. </para> 2190</returns></method> 2191<method name="calc_state" cv="const"><type>void</type><template> 2192 <template-type-parameter name="StateOut"/> 2193 </template><parameter name="t"><paramtype>time_type</paramtype><description><para>The time at which the solution should be calculated, has to be in the current time interval. </para></description></parameter><parameter name="x"><paramtype>StateOut &</paramtype><description><para>The output variable where the result is written into. </para></description></parameter><purpose>Calculates the solution at an intermediate point within the last step. </purpose><description><para> 2194</para></description></method> 2195<method name="current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the current state of the solution. </purpose><description><para> 2196</para></description><returns><para>The current state of the solution x(t). </para> 2197</returns></method> 2198<method name="current_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the current time of the solution. </purpose><description><para> 2199</para></description><returns><para>The current time of the solution t. </para> 2200</returns></method> 2201<method name="previous_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the last state of the solution. </purpose><description><para> 2202</para></description><returns><para>The last state of the solution x(t-dt). </para> 2203</returns></method> 2204<method name="previous_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the last time of the solution. </purpose><description><para> 2205</para></description><returns><para>The last time of the solution t-dt. </para> 2206</returns></method> 2207<method name="current_time_step" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the current step size. </purpose><description><para> 2208</para></description><returns><para>The current step size. </para> 2209</returns></method> 2210<method name="reset"><type>void</type><purpose>Resets the internal state of the stepper. </purpose></method> 2211<method name="adjust_size"><type>void</type><template> 2212 <template-type-parameter name="StateIn"/> 2213 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 2214</para></description></method> 2215</method-group> 2216<constructor><parameter name="eps_abs"><paramtype>value_type</paramtype><default>1E-6</default><description><para>Absolute tolerance level. </para></description></parameter><parameter name="eps_rel"><paramtype>value_type</paramtype><default>1E-6</default><description><para>Relative tolerance level. </para></description></parameter><parameter name="factor_x"><paramtype>value_type</paramtype><default>1.0</default><description><para>Factor for the weight of the state. </para></description></parameter><parameter name="factor_dxdt"><paramtype>value_type</paramtype><default>1.0</default><description><para>Factor for the weight of the derivative. </para></description></parameter><parameter name="max_dt"><paramtype>time_type</paramtype><default>static_cast< time_type >(0)</default></parameter><parameter name="control_interpolation"><paramtype>bool</paramtype><default>false</default><description><para>Set true to additionally control the error of the interpolation. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::bulirsch_stoer">bulirsch_stoer</classname> class, including initialization of the error bounds. </purpose><description><para> 2217</para></description></constructor> 2218<method-group name="private member functions"> 2219<method name="extrapolate"><type>void</type><template> 2220 <template-type-parameter name="StateInOut"/> 2221 <template-type-parameter name="StateVector"/> 2222 </template><parameter name="k"><paramtype>size_t</paramtype></parameter><parameter name="table"><paramtype>StateVector &</paramtype></parameter><parameter name="coeff"><paramtype>const value_matrix &</paramtype></parameter><parameter name="xest"><paramtype>StateInOut &</paramtype></parameter><parameter name="order_start_index"><paramtype>size_t</paramtype><default>0</default></parameter></method> 2223<method name="extrapolate_dense_out"><type>void</type><template> 2224 <template-type-parameter name="StateVector"/> 2225 </template><parameter name="k"><paramtype>size_t</paramtype></parameter><parameter name="table"><paramtype>StateVector &</paramtype></parameter><parameter name="coeff"><paramtype>const value_matrix &</paramtype></parameter><parameter name="order_start_index"><paramtype>size_t</paramtype><default>0</default></parameter></method> 2226<method name="calc_h_opt" cv="const"><type>time_type</type><parameter name="h"><paramtype>time_type</paramtype></parameter><parameter name="error"><paramtype>value_type</paramtype></parameter><parameter name="k"><paramtype>size_t</paramtype></parameter></method> 2227<method name="in_convergence_window" cv="const"><type>bool</type><parameter name="k"><paramtype>size_t</paramtype></parameter></method> 2228<method name="should_reject" cv="const"><type>bool</type><parameter name="error"><paramtype>value_type</paramtype></parameter><parameter name="k"><paramtype>size_t</paramtype></parameter></method> 2229<method name="prepare_dense_output"><type>value_type</type><template> 2230 <template-type-parameter name="StateIn1"/> 2231 <template-type-parameter name="DerivIn1"/> 2232 <template-type-parameter name="StateIn2"/> 2233 <template-type-parameter name="DerivIn2"/> 2234 </template><parameter name="k"><paramtype>int</paramtype></parameter><parameter name="x_start"><paramtype>const StateIn1 &</paramtype></parameter><parameter name="dxdt_start"><paramtype>const DerivIn1 &</paramtype></parameter><parameter name=""><paramtype>const StateIn2 &</paramtype></parameter><parameter name=""><paramtype>const DerivIn2 &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 2235<method name="calculate_finite_difference"><type>void</type><template> 2236 <template-type-parameter name="DerivIn"/> 2237 </template><parameter name="j"><paramtype>size_t</paramtype></parameter><parameter name="kappa"><paramtype>size_t</paramtype></parameter><parameter name="fac"><paramtype>value_type</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter></method> 2238<method name="do_interpolation" cv="const"><type>void</type><template> 2239 <template-type-parameter name="StateOut"/> 2240 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter></method> 2241<method name="resize_impl"><type>bool</type><template> 2242 <template-type-parameter name="StateIn"/> 2243 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2244<method name="get_current_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2245<method name="get_current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2246<method name="get_old_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2247<method name="get_old_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2248<method name="get_current_deriv"><type>deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2249<method name="get_current_deriv" cv="const"><type>const deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2250<method name="get_old_deriv"><type>deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2251<method name="get_old_deriv" cv="const"><type>const deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2252<method name="toggle_current_state"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2253</method-group> 2254</class> 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306</namespace> 2307</namespace> 2308</namespace> 2309</header> 2310<header name="boost/numeric/odeint/stepper/controlled_adams_bashforth_moulton.hpp"> 2311<namespace name="boost"> 2312<namespace name="numeric"> 2313<namespace name="odeint"> 2314<class name="controlled_adams_bashforth_moulton"><template> 2315 <template-type-parameter name="ErrorStepper"/> 2316 <template-type-parameter name="StepAdjuster"><default>detail::pid_step_adjuster< typename ErrorStepper::state_type, typename ErrorStepper::value_type, typename ErrorStepper::deriv_type, typename ErrorStepper::time_type, typename ErrorStepper::algebra_type, typename ErrorStepper::operations_type, detail::H211PI ></default></template-type-parameter> 2317 <template-type-parameter name="OrderAdjuster"><default>default_order_adjuster< ErrorStepper::order_value, typename ErrorStepper::state_type, typename ErrorStepper::value_type, typename ErrorStepper::algebra_type ></default></template-type-parameter> 2318 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 2319 </template><typedef name="stepper_type"><type>ErrorStepper</type></typedef> 2320<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 2321<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 2322<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 2323<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 2324<typedef name="algebra_type"><type>stepper_type::algebra_type</type></typedef> 2325<typedef name="operations_type"><type>stepper_type::operations_type</type></typedef> 2326<typedef name="resizer_type"><type>Resizer</type></typedef> 2327<typedef name="step_adjuster_type"><type>StepAdjuster</type></typedef> 2328<typedef name="order_adjuster_type"><type>OrderAdjuster</type></typedef> 2329<typedef name="stepper_category"><type>controlled_stepper_tag</type></typedef> 2330<typedef name="wrapped_state_type"><type>stepper_type::wrapped_state_type</type></typedef> 2331<typedef name="wrapped_deriv_type"><type>stepper_type::wrapped_deriv_type</type></typedef> 2332<typedef name="error_storage_type"><type>boost::array< wrapped_state_type, 4 ></type></typedef> 2333<typedef name="coeff_type"><type>stepper_type::coeff_type</type></typedef> 2334<typedef name="controlled_stepper_type"><type>controlled_adams_bashforth_moulton< ErrorStepper, StepAdjuster, OrderAdjuster, Resizer ></type></typedef> 2335<data-member name="order_value" specifiers="static"><type>const stepper_type::order_type</type></data-member> 2336<method-group name="public member functions"> 2337<method name="initialize"><type>void</type><template> 2338 <template-type-parameter name="ExplicitStepper"/> 2339 <template-type-parameter name="System"/> 2340 </template><parameter name="stepper"><paramtype>ExplicitStepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 2341<method name="initialize"><type>void</type><template> 2342 <template-type-parameter name="System"/> 2343 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 2344<method name="initialize_controlled"><type>void</type><template> 2345 <template-type-parameter name="ExplicitStepper"/> 2346 <template-type-parameter name="System"/> 2347 </template><parameter name="stepper"><paramtype>ExplicitStepper</paramtype></parameter><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 2348<method name="try_step"><type>controlled_step_result</type><template> 2349 <template-type-parameter name="System"/> 2350 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inOut"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 2351<method name="try_step"><type>controlled_step_result</type><template> 2352 <template-type-parameter name="System"/> 2353 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="out"><paramtype>state_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 2354<method name="reset"><type>void</type></method> 2355</method-group> 2356<constructor><parameter name="step_adjuster"><paramtype>step_adjuster_type</paramtype><default>step_adjuster_type()</default></parameter></constructor> 2357<method-group name="private member functions"> 2358<method name="resize_dxdt_impl"><type>bool</type><template> 2359 <template-type-parameter name="StateType"/> 2360 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 2361<method name="resize_xerr_impl"><type>bool</type><template> 2362 <template-type-parameter name="StateType"/> 2363 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 2364<method name="resize_xnew_impl"><type>bool</type><template> 2365 <template-type-parameter name="StateType"/> 2366 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 2367</method-group> 2368</class><class name="default_order_adjuster"><template> 2369 <template-nontype-parameter name="MaxOrder"><type>size_t</type></template-nontype-parameter> 2370 <template-type-parameter name="State"/> 2371 <template-type-parameter name="Value"><default>double</default></template-type-parameter> 2372 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default></template-type-parameter> 2373 </template><typedef name="state_type"><type>State</type></typedef> 2374<typedef name="value_type"><type>Value</type></typedef> 2375<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 2376<typedef name="algebra_type"><type>Algebra</type></typedef> 2377<method-group name="public member functions"> 2378<method name="adjust_order"><type>size_t</type><parameter name="order"><paramtype>size_t</paramtype></parameter><parameter name="init"><paramtype>size_t</paramtype></parameter><parameter name="xerr"><paramtype>boost::array< wrapped_state_type, 4 > &</paramtype></parameter></method> 2379</method-group> 2380<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default></parameter></constructor> 2381</class> 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433</namespace> 2434</namespace> 2435</namespace> 2436</header> 2437<header name="boost/numeric/odeint/stepper/controlled_runge_kutta.hpp"> 2438<namespace name="boost"> 2439<namespace name="numeric"> 2440<namespace name="odeint"> 2441<class name="controlled_runge_kutta"><template> 2442 <template-type-parameter name="ErrorStepper"/> 2443 <template-type-parameter name="ErrorChecker"><default><classname alt="boost::numeric::odeint::default_error_checker">default_error_checker</classname>< typename ErrorStepper::value_type , typename ErrorStepper::algebra_type , typename ErrorStepper::operations_type ></default></template-type-parameter> 2444 <template-type-parameter name="StepAdjuster"><default>default_step_adjuster< typename ErrorStepper::value_type , typename ErrorStepper::time_type ></default></template-type-parameter> 2445 <template-type-parameter name="Resizer"><default>typename ErrorStepper::resizer_type</default></template-type-parameter> 2446 <template-type-parameter name="ErrorStepperCategory"><default>typename ErrorStepper::stepper_category</default></template-type-parameter> 2447 </template></class><class-specialization name="controlled_runge_kutta"><template> 2448 <template-type-parameter name="ErrorStepper"><purpose><para>The stepper type with error estimation, has to fulfill the ErrorStepper concept. </para></purpose></template-type-parameter> 2449 <template-type-parameter name="ErrorChecker"><purpose><para>The error checker </para></purpose></template-type-parameter> 2450 <template-type-parameter name="StepAdjuster"/> 2451 <template-type-parameter name="Resizer"><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 2452 </template><specialization><template-arg>ErrorStepper</template-arg><template-arg>ErrorChecker</template-arg><template-arg>StepAdjuster</template-arg><template-arg>Resizer</template-arg><template-arg>explicit_error_stepper_fsal_tag</template-arg></specialization><purpose>Implements step size control for Runge-Kutta FSAL steppers with error estimation. </purpose><description><para>This class implements the step size control for FSAL Runge-Kutta steppers with error estimation.</para><para> 2453</para></description><typedef name="stepper_type"><type>ErrorStepper</type></typedef> 2454<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 2455<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 2456<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 2457<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 2458<typedef name="algebra_type"><type>stepper_type::algebra_type</type></typedef> 2459<typedef name="operations_type"><type>stepper_type::operations_type</type></typedef> 2460<typedef name="resizer_type"><type>Resizer</type></typedef> 2461<typedef name="error_checker_type"><type>ErrorChecker</type></typedef> 2462<typedef name="step_adjuster_type"><type>StepAdjuster</type></typedef> 2463<typedef name="stepper_category"><type>explicit_controlled_stepper_fsal_tag</type></typedef> 2464<method-group name="public member functions"> 2465<method name="try_step"><type>controlled_step_result</type><template> 2466 <template-type-parameter name="System"/> 2467 <template-type-parameter name="StateInOut"/> 2468 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2469 2470</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2471</returns></method> 2472<method name="try_step"><type>controlled_step_result</type><template> 2473 <template-type-parameter name="System"/> 2474 <template-type-parameter name="StateInOut"/> 2475 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>const StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. Can be a boost range. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. Solves the forwarding problem and allows for using boost range as state_type. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2476 2477</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2478</returns></method> 2479<method name="try_step"><type>boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::type</type><template> 2480 <template-type-parameter name="System"/> 2481 <template-type-parameter name="StateIn"/> 2482 <template-type-parameter name="StateOut"/> 2483 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>Used to store the result of the step. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para><note><para>This method is disabled if state_type=time_type to avoid ambiguity.</para> 2484</note> 2485This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2486 2487</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2488</returns></method> 2489<method name="try_step"><type>controlled_step_result</type><template> 2490 <template-type-parameter name="System"/> 2491 <template-type-parameter name="StateInOut"/> 2492 <template-type-parameter name="DerivInOut"/> 2493 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. </para></description></parameter><parameter name="dxdt"><paramtype>DerivInOut &</paramtype><description><para>The derivative of state. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2494 2495</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2496</returns></method> 2497<method name="try_step"><type>controlled_step_result</type><template> 2498 <template-type-parameter name="System"/> 2499 <template-type-parameter name="StateIn"/> 2500 <template-type-parameter name="DerivIn"/> 2501 <template-type-parameter name="StateOut"/> 2502 <template-type-parameter name="DerivOut"/> 2503 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. </para></description></parameter><parameter name="dxdt_in"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>Used to store the result of the step. </para></description></parameter><parameter name="dxdt_out"><paramtype>DerivOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2504 2505</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2506</returns></method> 2507<method name="reset"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Resets the internal state of the underlying FSAL stepper. </purpose></method> 2508<method name="initialize"><type>void</type><template> 2509 <template-type-parameter name="DerivIn"/> 2510 </template><parameter name="deriv"><paramtype>const DerivIn &</paramtype><description><para>The initial derivative of the ODE. </para></description></parameter><purpose>Initializes the internal state storing an internal copy of the derivative. </purpose><description><para> 2511</para></description></method> 2512<method name="initialize"><type>void</type><template> 2513 <template-type-parameter name="System"/> 2514 <template-type-parameter name="StateIn"/> 2515 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>The initial state of the ODE which should be solved. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The initial time. </para></description></parameter><purpose>Initializes the internal state storing an internal copy of the derivative. </purpose><description><para> 2516</para></description></method> 2517<method name="is_initialized" cv="const"><type>bool</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns true if the stepper has been initialized, false otherwise. </purpose><description><para> 2518</para></description><returns><para>true, if the stepper has been initialized, false otherwise. </para> 2519</returns></method> 2520<method name="adjust_size"><type>void</type><template> 2521 <template-type-parameter name="StateType"/> 2522 </template><parameter name="x"><paramtype>const StateType &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 2523</para></description></method> 2524<method name="stepper"><type>stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the instance of the underlying stepper. </purpose><description><para> 2525</para></description><returns><para>The instance of the underlying stepper. </para> 2526</returns></method> 2527<method name="stepper" cv="const"><type>const stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the instance of the underlying stepper. </purpose><description><para> 2528</para></description><returns><para>The instance of the underlying stepper. </para> 2529</returns></method> 2530</method-group> 2531<constructor><parameter name="error_checker"><paramtype>const error_checker_type &</paramtype><default>error_checker_type()</default><description><para>An instance of the error checker. </para></description></parameter><parameter name="step_adjuster"><paramtype>const step_adjuster_type &</paramtype><default>step_adjuster_type()</default></parameter><parameter name="stepper"><paramtype>const stepper_type &</paramtype><default>stepper_type()</default><description><para>An instance of the underlying stepper. </para></description></parameter><purpose>Constructs the controlled Runge-Kutta stepper. </purpose><description><para> 2532</para></description></constructor> 2533<method-group name="private member functions"> 2534<method name="resize_m_xerr_impl"><type>bool</type><template> 2535 <template-type-parameter name="StateIn"/> 2536 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2537<method name="resize_m_dxdt_impl"><type>bool</type><template> 2538 <template-type-parameter name="StateIn"/> 2539 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2540<method name="resize_m_dxdt_new_impl"><type>bool</type><template> 2541 <template-type-parameter name="StateIn"/> 2542 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2543<method name="resize_m_xnew_impl"><type>bool</type><template> 2544 <template-type-parameter name="StateIn"/> 2545 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2546<method name="try_step_v1"><type>controlled_step_result</type><template> 2547 <template-type-parameter name="System"/> 2548 <template-type-parameter name="StateInOut"/> 2549 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 2550</method-group> 2551</class-specialization><class-specialization name="controlled_runge_kutta"><template> 2552 <template-type-parameter name="ErrorStepper"><purpose><para>The stepper type with error estimation, has to fulfill the ErrorStepper concept. </para></purpose></template-type-parameter> 2553 <template-type-parameter name="ErrorChecker"><purpose><para>The error checker </para></purpose></template-type-parameter> 2554 <template-type-parameter name="StepAdjuster"/> 2555 <template-type-parameter name="Resizer"><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 2556 </template><specialization><template-arg>ErrorStepper</template-arg><template-arg>ErrorChecker</template-arg><template-arg>StepAdjuster</template-arg><template-arg>Resizer</template-arg><template-arg>explicit_error_stepper_tag</template-arg></specialization><purpose>Implements step size control for Runge-Kutta steppers with error estimation. </purpose><description><para>This class implements the step size control for standard Runge-Kutta steppers with error estimation.</para><para> 2557</para></description><typedef name="stepper_type"><type>ErrorStepper</type></typedef> 2558<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 2559<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 2560<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 2561<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 2562<typedef name="algebra_type"><type>stepper_type::algebra_type</type></typedef> 2563<typedef name="operations_type"><type>stepper_type::operations_type</type></typedef> 2564<typedef name="resizer_type"><type>Resizer</type></typedef> 2565<typedef name="error_checker_type"><type>ErrorChecker</type></typedef> 2566<typedef name="step_adjuster_type"><type>StepAdjuster</type></typedef> 2567<typedef name="stepper_category"><type>explicit_controlled_stepper_tag</type></typedef> 2568<method-group name="public member functions"> 2569<method name="try_step"><type>controlled_step_result</type><template> 2570 <template-type-parameter name="System"/> 2571 <template-type-parameter name="StateInOut"/> 2572 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2573 2574</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2575</returns></method> 2576<method name="try_step"><type>controlled_step_result</type><template> 2577 <template-type-parameter name="System"/> 2578 <template-type-parameter name="StateInOut"/> 2579 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>const StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. Can be a boost range. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. Solves the forwarding problem and allows for using boost range as state_type. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2580 2581</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2582</returns></method> 2583<method name="try_step"><type>controlled_step_result</type><template> 2584 <template-type-parameter name="System"/> 2585 <template-type-parameter name="StateInOut"/> 2586 <template-type-parameter name="DerivIn"/> 2587 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. Overwritten if the step is successful. </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of state. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2588 2589</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2590</returns></method> 2591<method name="try_step"><type>boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::type</type><template> 2592 <template-type-parameter name="System"/> 2593 <template-type-parameter name="StateIn"/> 2594 <template-type-parameter name="StateOut"/> 2595 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>Used to store the result of the step. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para><note><para>This method is disabled if state_type=time_type to avoid ambiguity.</para> 2596</note> 2597This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2598 2599</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2600</returns></method> 2601<method name="try_step"><type>controlled_step_result</type><template> 2602 <template-type-parameter name="System"/> 2603 <template-type-parameter name="StateIn"/> 2604 <template-type-parameter name="DerivIn"/> 2605 <template-type-parameter name="StateOut"/> 2606 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of state. </para></description></parameter><parameter name="t"><paramtype>time_type &</paramtype><description><para>The value of the time. Updated if the step is successful. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>Used to store the result of the step. </para></description></parameter><parameter name="dt"><paramtype>time_type &</paramtype><description><para>The step size. Updated. </para></description></parameter><purpose>Tries to perform one step. </purpose><description><para>This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.</para><para> 2607 2608</para></description><returns><para>success if the step was accepted, fail otherwise. </para> 2609</returns></method> 2610<method name="adjust_size"><type>void</type><template> 2611 <template-type-parameter name="StateType"/> 2612 </template><parameter name="x"><paramtype>const StateType &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 2613</para></description></method> 2614<method name="stepper"><type>stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the instance of the underlying stepper. </purpose><description><para> 2615</para></description><returns><para>The instance of the underlying stepper. </para> 2616</returns></method> 2617<method name="stepper" cv="const"><type>const stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the instance of the underlying stepper. </purpose><description><para> 2618</para></description><returns><para>The instance of the underlying stepper. </para> 2619</returns></method> 2620</method-group> 2621<constructor><parameter name="error_checker"><paramtype>const error_checker_type &</paramtype><default>error_checker_type()</default><description><para>An instance of the error checker. </para></description></parameter><parameter name="step_adjuster"><paramtype>const step_adjuster_type &</paramtype><default>step_adjuster_type()</default></parameter><parameter name="stepper"><paramtype>const stepper_type &</paramtype><default>stepper_type()</default><description><para>An instance of the underlying stepper. </para></description></parameter><purpose>Constructs the controlled Runge-Kutta stepper. </purpose><description><para> 2622</para></description></constructor> 2623<method-group name="private member functions"> 2624<method name="try_step_v1"><type>controlled_step_result</type><template> 2625 <template-type-parameter name="System"/> 2626 <template-type-parameter name="StateInOut"/> 2627 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 2628<method name="resize_m_xerr_impl"><type>bool</type><template> 2629 <template-type-parameter name="StateIn"/> 2630 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2631<method name="resize_m_dxdt_impl"><type>bool</type><template> 2632 <template-type-parameter name="StateIn"/> 2633 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2634<method name="resize_m_xnew_impl"><type>bool</type><template> 2635 <template-type-parameter name="StateIn"/> 2636 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2637</method-group> 2638</class-specialization><class name="default_error_checker"><template> 2639 <template-type-parameter name="Value"><purpose><para>The value type. </para></purpose></template-type-parameter> 2640 <template-type-parameter name="Algebra"><purpose><para>The algebra type. </para></purpose></template-type-parameter> 2641 <template-type-parameter name="Operations"><purpose><para>The operations type. </para></purpose></template-type-parameter> 2642 </template><purpose>The default error checker to be used with Runge-Kutta error steppers. </purpose><description><para>This class provides the default mechanism to compare the error estimates reported by Runge-Kutta error steppers with user defined error bounds. It is used by the controlled_runge_kutta steppers.</para><para> 2643</para></description><typedef name="value_type"><type>Value</type></typedef> 2644<typedef name="algebra_type"><type>Algebra</type></typedef> 2645<typedef name="operations_type"><type>Operations</type></typedef> 2646<method-group name="public member functions"> 2647<method name="error" cv="const"><type>value_type</type><template> 2648 <template-type-parameter name="State"/> 2649 <template-type-parameter name="Deriv"/> 2650 <template-type-parameter name="Err"/> 2651 <template-type-parameter name="Time"/> 2652 </template><parameter name="x_old"><paramtype>const State &</paramtype></parameter><parameter name="dxdt_old"><paramtype>const Deriv &</paramtype></parameter><parameter name="x_err"><paramtype>Err &</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter></method> 2653<method name="error" cv="const"><type>value_type</type><template> 2654 <template-type-parameter name="State"/> 2655 <template-type-parameter name="Deriv"/> 2656 <template-type-parameter name="Err"/> 2657 <template-type-parameter name="Time"/> 2658 </template><parameter name="algebra"><paramtype>algebra_type &</paramtype></parameter><parameter name="x_old"><paramtype>const State &</paramtype></parameter><parameter name="dxdt_old"><paramtype>const Deriv &</paramtype></parameter><parameter name="x_err"><paramtype>Err &</paramtype></parameter><parameter name="dt"><paramtype>Time</paramtype></parameter></method> 2659</method-group> 2660<constructor><parameter name="eps_abs"><paramtype>value_type</paramtype><default>static_cast< value_type >(1.0e-6)</default></parameter><parameter name="eps_rel"><paramtype>value_type</paramtype><default>static_cast< value_type >(1.0e-6)</default></parameter><parameter name="a_x"><paramtype>value_type</paramtype><default>static_cast< value_type >(1)</default></parameter><parameter name="a_dxdt"><paramtype>value_type</paramtype><default>static_cast< value_type >(1)</default></parameter></constructor> 2661</class><class name="default_step_adjuster"><template> 2662 <template-type-parameter name="Value"/> 2663 <template-type-parameter name="Time"/> 2664 </template><typedef name="time_type"><type>Time</type></typedef> 2665<typedef name="value_type"><type>Value</type></typedef> 2666<method-group name="public member functions"> 2667<method name="decrease_step" cv="const"><type>time_type</type><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="error"><paramtype>const value_type</paramtype></parameter><parameter name="error_order"><paramtype>const int</paramtype></parameter></method> 2668<method name="increase_step" cv="const"><type>time_type</type><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="error"><paramtype>value_type</paramtype></parameter><parameter name="stepper_order"><paramtype>const int</paramtype></parameter></method> 2669<method name="check_step_size_limit"><type>bool</type><parameter name="dt"><paramtype>const time_type</paramtype></parameter></method> 2670<method name="get_max_dt"><type>time_type</type></method> 2671</method-group> 2672<constructor><parameter name="max_dt"><paramtype>const time_type</paramtype><default>static_cast< time_type >(0)</default></parameter></constructor> 2673</class> 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725</namespace> 2726</namespace> 2727</namespace> 2728</header> 2729<header name="boost/numeric/odeint/stepper/controlled_step_result.hpp"> 2730<namespace name="boost"> 2731<namespace name="numeric"> 2732<namespace name="odeint"> 2733<enum name="controlled_step_result"><enumvalue name="success"><description><para>The trial step was successful, hence the state and the time have been advanced. </para></description></enumvalue><enumvalue name="fail"><description><para>The step was not successful and might possibly be repeated with a small step size. </para></description></enumvalue><purpose>Enum representing the return values of the controlled steppers. </purpose></enum> 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786</namespace> 2787</namespace> 2788</namespace> 2789</header> 2790<header name="boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp"> 2791<namespace name="boost"> 2792<namespace name="numeric"> 2793<namespace name="odeint"> 2794<class name="dense_output_runge_kutta"><template> 2795 <template-type-parameter name="Stepper"/> 2796 <template-type-parameter name="StepperCategory"><default>typename Stepper::stepper_category</default></template-type-parameter> 2797 </template></class><class-specialization name="dense_output_runge_kutta"><template> 2798 <template-type-parameter name="Stepper"><purpose><para>The stepper type of the underlying algorithm. </para></purpose></template-type-parameter> 2799 </template><specialization><template-arg>Stepper</template-arg><template-arg>explicit_controlled_stepper_fsal_tag</template-arg></specialization><purpose>The class representing dense-output Runge-Kutta steppers with FSAL property. </purpose><description><para>The interface is the same as for <classname alt="boost::numeric::odeint::dense_output_runge_kutta< Stepper, stepper_tag >">dense_output_runge_kutta< Stepper , stepper_tag ></classname>. This class provides dense output functionality based on methods with step size controlled</para><para> 2800</para></description><typedef name="controlled_stepper_type"><type>Stepper</type></typedef> 2801<typedef name="stepper_type"><type>controlled_stepper_type::stepper_type</type></typedef> 2802<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 2803<typedef name="wrapped_state_type"><type>stepper_type::wrapped_state_type</type></typedef> 2804<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 2805<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 2806<typedef name="wrapped_deriv_type"><type>stepper_type::wrapped_deriv_type</type></typedef> 2807<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 2808<typedef name="algebra_type"><type>stepper_type::algebra_type</type></typedef> 2809<typedef name="operations_type"><type>stepper_type::operations_type</type></typedef> 2810<typedef name="resizer_type"><type>stepper_type::resizer_type</type></typedef> 2811<typedef name="stepper_category"><type>dense_output_stepper_tag</type></typedef> 2812<typedef name="dense_output_stepper_type"><type>dense_output_runge_kutta< Stepper ></type></typedef> 2813<method-group name="public member functions"> 2814<method name="initialize"><type>void</type><template> 2815 <template-type-parameter name="StateType"/> 2816 </template><parameter name="x0"><paramtype>const StateType &</paramtype></parameter><parameter name="t0"><paramtype>time_type</paramtype></parameter><parameter name="dt0"><paramtype>time_type</paramtype></parameter></method> 2817<method name="do_step"><type>std::pair< time_type, time_type ></type><template> 2818 <template-type-parameter name="System"/> 2819 </template><parameter name="system"><paramtype>System</paramtype></parameter></method> 2820<method name="calc_state" cv="const"><type>void</type><template> 2821 <template-type-parameter name="StateOut"/> 2822 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>StateOut &</paramtype></parameter></method> 2823<method name="calc_state" cv="const"><type>void</type><template> 2824 <template-type-parameter name="StateOut"/> 2825 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>const StateOut &</paramtype></parameter></method> 2826<method name="resize"><type>bool</type><template> 2827 <template-type-parameter name="StateIn"/> 2828 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2829<method name="adjust_size"><type>void</type><template> 2830 <template-type-parameter name="StateType"/> 2831 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 2832<method name="current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2833<method name="current_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2834<method name="previous_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2835<method name="previous_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2836<method name="current_time_step" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2837</method-group> 2838<constructor><parameter name="stepper"><paramtype>const controlled_stepper_type &</paramtype><default>controlled_stepper_type()</default></parameter></constructor> 2839<method-group name="private member functions"> 2840<method name="get_current_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2841<method name="get_current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2842<method name="get_old_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2843<method name="get_old_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2844<method name="get_current_deriv"><type>deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2845<method name="get_current_deriv" cv="const"><type>const deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2846<method name="get_old_deriv"><type>deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2847<method name="get_old_deriv" cv="const"><type>const deriv_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2848<method name="toggle_current_state"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2849</method-group> 2850</class-specialization><class-specialization name="dense_output_runge_kutta"><template> 2851 <template-type-parameter name="Stepper"><purpose><para>The stepper type of the underlying algorithm. </para></purpose></template-type-parameter> 2852 </template><specialization><template-arg>Stepper</template-arg><template-arg>stepper_tag</template-arg></specialization><purpose>The class representing dense-output Runge-Kutta steppers. </purpose><description><para><note><para>In this stepper, the initialize method has to be called before using the do_step method.</para> 2853</note> 2854The dense-output functionality allows to interpolate the solution between subsequent integration points using intermediate results obtained during the computation. This version works based on a normal stepper without step-size control.</para><para> 2855</para></description><typedef name="stepper_type"><type>Stepper</type></typedef> 2856<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 2857<typedef name="wrapped_state_type"><type>stepper_type::wrapped_state_type</type></typedef> 2858<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 2859<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 2860<typedef name="wrapped_deriv_type"><type>stepper_type::wrapped_deriv_type</type></typedef> 2861<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 2862<typedef name="algebra_type"><type>stepper_type::algebra_type</type></typedef> 2863<typedef name="operations_type"><type>stepper_type::operations_type</type></typedef> 2864<typedef name="resizer_type"><type>stepper_type::resizer_type</type></typedef> 2865<typedef name="stepper_category"><type>dense_output_stepper_tag</type></typedef> 2866<typedef name="dense_output_stepper_type"><type>dense_output_runge_kutta< Stepper ></type></typedef> 2867<method-group name="public member functions"> 2868<method name="initialize"><type>void</type><template> 2869 <template-type-parameter name="StateType"/> 2870 </template><parameter name="x0"><paramtype>const StateType &</paramtype><description><para>The initial state of the ODE which should be solved. </para></description></parameter><parameter name="t0"><paramtype>time_type</paramtype><description><para>The initial time, at which the step should be performed. </para></description></parameter><parameter name="dt0"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>Initializes the stepper. Has to be called before do_step can be used to set the initial conditions and the step size. </purpose><description><para> 2871</para></description></method> 2872<method name="do_step"><type>std::pair< time_type, time_type ></type><template> 2873 <template-type-parameter name="System"/> 2874 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </para></description></parameter><purpose>Does one time step. </purpose><description><para><note><para>initialize has to be called before using this method to set the initial conditions x,t and the stepsize. </para> 2875</note> 2876 2877 2878</para></description><returns><para>Pair with start and end time of the integration step. </para> 2879</returns></method> 2880<method name="calc_state" cv="const"><type>void</type><template> 2881 <template-type-parameter name="StateOut"/> 2882 </template><parameter name="t"><paramtype>time_type</paramtype><description><para>The time at which the solution should be calculated, has to be in the current time interval. </para></description></parameter><parameter name="x"><paramtype>StateOut &</paramtype><description><para>The output variable where the result is written into. </para></description></parameter><purpose>Calculates the solution at an intermediate point. </purpose><description><para> 2883</para></description></method> 2884<method name="calc_state" cv="const"><type>void</type><template> 2885 <template-type-parameter name="StateOut"/> 2886 </template><parameter name="t"><paramtype>time_type</paramtype><description><para>The time at which the solution should be calculated, has to be in the current time interval. </para></description></parameter><parameter name="x"><paramtype>const StateOut &</paramtype><description><para>The output variable where the result is written into, can be a boost range. </para></description></parameter><purpose>Calculates the solution at an intermediate point. Solves the forwarding problem. </purpose><description><para> 2887</para></description></method> 2888<method name="adjust_size"><type>void</type><template> 2889 <template-type-parameter name="StateType"/> 2890 </template><parameter name="x"><paramtype>const StateType &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 2891</para></description></method> 2892<method name="current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the current state of the solution. </purpose><description><para> 2893</para></description><returns><para>The current state of the solution x(t). </para> 2894</returns></method> 2895<method name="current_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the current time of the solution. </purpose><description><para> 2896</para></description><returns><para>The current time of the solution t. </para> 2897</returns></method> 2898<method name="previous_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the last state of the solution. </purpose><description><para> 2899</para></description><returns><para>The last state of the solution x(t-dt). </para> 2900</returns></method> 2901<method name="previous_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the last time of the solution. </purpose><description><para> 2902</para></description><returns><para>The last time of the solution t-dt. </para> 2903</returns></method> 2904<method name="current_time_step" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Returns the current time step. </purpose><description><para> 2905</para></description><returns><para>dt. </para> 2906</returns></method> 2907</method-group> 2908<constructor><parameter name="stepper"><paramtype>const stepper_type &</paramtype><default>stepper_type()</default><description><para>An instance of the underlying stepper. </para></description></parameter><purpose>Constructs the dense_output_runge_kutta class. An instance of the underlying stepper can be provided. </purpose><description><para> 2909</para></description></constructor> 2910<method-group name="private member functions"> 2911<method name="get_current_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2912<method name="get_current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2913<method name="get_old_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2914<method name="get_old_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2915<method name="toggle_current_state"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter></method> 2916<method name="resize_impl"><type>bool</type><template> 2917 <template-type-parameter name="StateIn"/> 2918 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 2919</method-group> 2920</class-specialization> 2921 2922 2923 2924 2925 2926 2927 2928 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972</namespace> 2973</namespace> 2974</namespace> 2975</header> 2976<header name="boost/numeric/odeint/stepper/euler.hpp"> 2977<namespace name="boost"> 2978<namespace name="numeric"> 2979<namespace name="odeint"> 2980<class name="euler"><template> 2981 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 2982 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 2983 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 2984 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 2985 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 2986 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 2987 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 2988 </template><inherit access="public">explicit_stepper_base</inherit><purpose>An implementation of the Euler method. </purpose><description><para>The Euler method is a very simply solver for ordinary differential equations. This method should not be used for real applications. It is only useful for demonstration purposes. Step size control is not provided but trivial continuous output is available.</para><para>This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern), see explicit_stepper_base</para><para> 2989</para></description><typedef name="stepper_base_type"><type>explicit_stepper_base< <classname>euler</classname>< ... >,... ></type></typedef> 2990<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 2991<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 2992<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 2993<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 2994<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 2995<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 2996<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 2997<method-group name="public member functions"> 2998<method name="do_step_impl"><type>void</type><template> 2999 <template-type-parameter name="System"/> 3000 <template-type-parameter name="StateIn"/> 3001 <template-type-parameter name="DerivIn"/> 3002 <template-type-parameter name="StateOut"/> 3003 </template><parameter name=""><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name=""><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out of place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 3004</para></description></method> 3005<method name="calc_state" cv="const"><type>void</type><template> 3006 <template-type-parameter name="StateOut"/> 3007 <template-type-parameter name="StateIn1"/> 3008 <template-type-parameter name="StateIn2"/> 3009 </template><parameter name="x"><paramtype>StateOut &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="old_state"><paramtype>const StateIn1 &</paramtype></parameter><parameter name="t_old"><paramtype>time_type</paramtype></parameter><parameter name=""><paramtype>const StateIn2 &</paramtype></parameter><parameter name=""><paramtype>time_type</paramtype></parameter><purpose>This method is used for continuous output and it calculates the state <computeroutput>x</computeroutput> at a time <computeroutput>t</computeroutput> from the knowledge of two states <computeroutput>old_state</computeroutput> and <computeroutput>current_state</computeroutput> at time points <computeroutput>t_old</computeroutput> and <computeroutput>t_new</computeroutput>. </purpose></method> 3010<method name="adjust_size"><type>void</type><template> 3011 <template-type-parameter name="StateType"/> 3012 </template><parameter name="x"><paramtype>const StateType &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 3013</para></description></method> 3014</method-group> 3015<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the euler class. This constructor can be used as a default constructor of the algebra has a default constructor. </purpose><description><para> 3016</para></description></constructor> 3017</class> 3018 3019 3020 3021 3022 3023 3024 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069</namespace> 3070</namespace> 3071</namespace> 3072</header> 3073<header name="boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp"> 3074<namespace name="boost"> 3075<namespace name="numeric"> 3076<namespace name="odeint"> 3077<class name="explicit_error_generic_rk"><template> 3078 <template-nontype-parameter name="StageCount"><type>size_t</type><purpose><para>The number of stages of the Runge-Kutta algorithm. </para></purpose></template-nontype-parameter> 3079 <template-nontype-parameter name="Order"><type>size_t</type><purpose><para>The order of a stepper if the stepper is used without error estimation. </para></purpose></template-nontype-parameter> 3080 <template-nontype-parameter name="StepperOrder"><type>size_t</type><purpose><para>The order of a step if the stepper is used with error estimation. Usually Order and StepperOrder have the same value. </para></purpose></template-nontype-parameter> 3081 <template-nontype-parameter name="ErrorOrder"><type>size_t</type><purpose><para>The order of the error step if the stepper is used with error estimation. </para></purpose></template-nontype-parameter> 3082 <template-type-parameter name="State"><purpose><para>The type representing the state of the ODE. </para></purpose></template-type-parameter> 3083 <template-type-parameter name="Value"><default>double</default><purpose><para>The floating point type which is used in the computations. </para></purpose></template-type-parameter> 3084 <template-type-parameter name="Deriv"><default>State</default></template-type-parameter> 3085 <template-type-parameter name="Time"><default>Value</default><purpose><para>The type representing the independent variable - the time - of the ODE. </para></purpose></template-type-parameter> 3086 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 3087 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 3088 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 3089 </template><inherit access="public">explicit_error_stepper_base</inherit><purpose>A generic implementation of explicit Runge-Kutta algorithms with error estimation. This class is as a base class for all explicit Runge-Kutta steppers with error estimation. </purpose><description><para>This class implements the explicit Runge-Kutta algorithms with error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!</para><para>This class derives explicit_error_stepper_base which provides the stepper interface.</para><para> 3090</para></description><typedef name="stepper_base_type"><type>explicit_stepper_base< ... ></type></typedef> 3091<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 3092<typedef name="wrapped_state_type"><type>stepper_base_type::wrapped_state_type</type></typedef> 3093<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 3094<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 3095<typedef name="wrapped_deriv_type"><type>stepper_base_type::wrapped_deriv_type</type></typedef> 3096<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 3097<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 3098<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 3099<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 3100<typedef name="rk_algorithm_type"><type><emphasis>unspecified</emphasis></type></typedef> 3101<typedef name="coef_a_type"><type>rk_algorithm_type::coef_a_type</type></typedef> 3102<typedef name="coef_b_type"><type>rk_algorithm_type::coef_b_type</type></typedef> 3103<typedef name="coef_c_type"><type>rk_algorithm_type::coef_c_type</type></typedef> 3104<data-member name="stage_count" specifiers="static"><type>const size_t</type></data-member> 3105<method-group name="public member functions"> 3106<method name="do_step_impl"><type>void</type><template> 3107 <template-type-parameter name="System"/> 3108 <template-type-parameter name="StateIn"/> 3109 <template-type-parameter name="DerivIn"/> 3110 <template-type-parameter name="StateOut"/> 3111 <template-type-parameter name="Err"/> 3112 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><parameter name="xerr"><paramtype>Err &</paramtype><description><para>The result of the error estimation is written in xerr. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Futhermore, an estimation of the error is stored in <computeroutput>xerr</computeroutput>. <computeroutput>do_step_impl</computeroutput> is used by explicit_error_stepper_base. </purpose><description><para> 3113</para></description></method> 3114<method name="do_step_impl"><type>void</type><template> 3115 <template-type-parameter name="System"/> 3116 <template-type-parameter name="StateIn"/> 3117 <template-type-parameter name="DerivIn"/> 3118 <template-type-parameter name="StateOut"/> 3119 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 3120</para></description></method> 3121<method name="adjust_size"><type>void</type><template> 3122 <template-type-parameter name="StateIn"/> 3123 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 3124</para></description></method> 3125</method-group> 3126<constructor><parameter name="a"><paramtype>const coef_a_type &</paramtype><description><para>Triangular matrix of parameters b in the Butcher tableau. </para></description></parameter><parameter name="b"><paramtype>const coef_b_type &</paramtype><description><para>Last row of the butcher tableau. </para></description></parameter><parameter name="b2"><paramtype>const coef_b_type &</paramtype><description><para>Parameters for lower-order evaluation to estimate the error. </para></description></parameter><parameter name="c"><paramtype>const coef_c_type &</paramtype><description><para>Parameters to calculate the time points in the Butcher tableau. </para></description></parameter><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the explicit_error_generik_rk class with the given parameters a, b, b2 and c. See examples section for details on the coefficients. </purpose><description><para> 3127</para></description></constructor> 3128<method-group name="private member functions"> 3129<method name="resize_impl"><type>bool</type><template> 3130 <template-type-parameter name="StateIn"/> 3131 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3132</method-group> 3133</class> 3134 3135 3136 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 3185</namespace> 3186</namespace> 3187</namespace> 3188</header> 3189<header name="boost/numeric/odeint/stepper/explicit_generic_rk.hpp"> 3190<namespace name="boost"> 3191<namespace name="numeric"> 3192<namespace name="odeint"> 3193<class name="explicit_generic_rk"><template> 3194 <template-nontype-parameter name="StageCount"><type>size_t</type><purpose><para>The number of stages of the Runge-Kutta algorithm. </para></purpose></template-nontype-parameter> 3195 <template-nontype-parameter name="Order"><type>size_t</type><purpose><para>The order of the stepper. </para></purpose></template-nontype-parameter> 3196 <template-type-parameter name="State"><purpose><para>The type representing the state of the ODE. </para></purpose></template-type-parameter> 3197 <template-type-parameter name="Value"><purpose><para>The floating point type which is used in the computations. </para></purpose></template-type-parameter> 3198 <template-type-parameter name="Deriv"/> 3199 <template-type-parameter name="Time"><purpose><para>The type representing the independent variable - the time - of the ODE. </para></purpose></template-type-parameter> 3200 <template-type-parameter name="Algebra"><purpose><para>The algebra type. </para></purpose></template-type-parameter> 3201 <template-type-parameter name="Operations"><purpose><para>The operations type. </para></purpose></template-type-parameter> 3202 <template-type-parameter name="Resizer"><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 3203 </template><inherit access="public">explicit_stepper_base</inherit><purpose>A generic implementation of explicit Runge-Kutta algorithms. This class is as a base class for all explicit Runge-Kutta steppers. </purpose><description><para>This class implements the explicit Runge-Kutta algorithms without error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!</para><para>This class derives explicit_stepper_base which provides the stepper interface.</para><para> 3204</para></description><typedef name="stepper_base_type"><type>explicit_stepper_base< ... ></type></typedef> 3205<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 3206<typedef name="wrapped_state_type"><type>stepper_base_type::wrapped_state_type</type></typedef> 3207<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 3208<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 3209<typedef name="wrapped_deriv_type"><type>stepper_base_type::wrapped_deriv_type</type></typedef> 3210<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 3211<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 3212<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 3213<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 3214<typedef name="rk_algorithm_type"><type><emphasis>unspecified</emphasis></type></typedef> 3215<typedef name="coef_a_type"><type>rk_algorithm_type::coef_a_type</type></typedef> 3216<typedef name="coef_b_type"><type>rk_algorithm_type::coef_b_type</type></typedef> 3217<typedef name="coef_c_type"><type>rk_algorithm_type::coef_c_type</type></typedef> 3218<method-group name="public member functions"> 3219<method name="do_step_impl"><type>void</type><template> 3220 <template-type-parameter name="System"/> 3221 <template-type-parameter name="StateIn"/> 3222 <template-type-parameter name="DerivIn"/> 3223 <template-type-parameter name="StateOut"/> 3224 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out of place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 3225</para></description></method> 3226<method name="adjust_size"><type>void</type><template> 3227 <template-type-parameter name="StateIn"/> 3228 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 3229</para></description></method> 3230</method-group> 3231<constructor><parameter name="a"><paramtype>const coef_a_type &</paramtype><description><para>Triangular matrix of parameters b in the Butcher tableau. </para></description></parameter><parameter name="b"><paramtype>const coef_b_type &</paramtype><description><para>Last row of the butcher tableau. </para></description></parameter><parameter name="c"><paramtype>const coef_c_type &</paramtype><description><para>Parameters to calculate the time points in the Butcher tableau. </para></description></parameter><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::explicit_generic_rk">explicit_generic_rk</classname> class. See examples section for details on the coefficients. </purpose><description><para> 3232</para></description></constructor> 3233<method-group name="private member functions"> 3234<method name="resize_impl"><type>bool</type><template> 3235 <template-type-parameter name="StateIn"/> 3236 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3237</method-group> 3238</class> 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290</namespace> 3291</namespace> 3292</namespace> 3293</header> 3294<header name="boost/numeric/odeint/stepper/extrapolation_stepper.hpp"> 3295<namespace name="boost"> 3296<namespace name="numeric"> 3297<namespace name="odeint"> 3298<class name="extrapolation_stepper"><template> 3299 <template-nontype-parameter name="Order"><type>unsigned short</type></template-nontype-parameter> 3300 <template-type-parameter name="State"/> 3301 <template-type-parameter name="Value"><default>double</default></template-type-parameter> 3302 <template-type-parameter name="Deriv"><default>State</default></template-type-parameter> 3303 <template-type-parameter name="Time"><default>Value</default></template-type-parameter> 3304 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default></template-type-parameter> 3305 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default></template-type-parameter> 3306 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 3307 </template><inherit access="public">explicit_error_stepper_base</inherit><purpose>Extrapolation stepper with configurable order, and error estimation. </purpose><description><para>The extrapolation stepper is a stepper with error estimation and configurable order. The order is given as template parameter and needs to be an <emphasis>odd</emphasis> number. The stepper is based on several executions of the modified midpoint method and a Richardson extrapolation. This is essentially the same technique as for <classname alt="boost::numeric::odeint::bulirsch_stoer">bulirsch_stoer</classname>, but without the variable order.</para><para><note><para>The Order parameter has to be an even number greater 2. </para> 3308</note> 3309</para></description><typedef name="stepper_base_type"><type>explicit_error_stepper_base< <classname>extrapolation_stepper</classname>< ... >,... ></type></typedef> 3310<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 3311<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 3312<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 3313<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 3314<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 3315<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 3316<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 3317<typedef name="order_type"><type>unsigned short</type></typedef> 3318<data-member name="order_value" specifiers="static"><type>const order_type</type></data-member> 3319<data-member name="stepper_order_value" specifiers="static"><type>const order_type</type></data-member> 3320<data-member name="error_order_value" specifiers="static"><type>const order_type</type></data-member> 3321<data-member name="m_k_max" specifiers="static"><type>const size_t</type></data-member> 3322<method-group name="private member functions"> 3323<method name="BOOST_STATIC_ASSERT_MSG"><type/><parameter name=""><paramtype>((Order % 2)==0) &&(Order > 2)</paramtype></parameter><parameter name=""><paramtype>"extrapolation_stepper requires even Order larger than 2"</paramtype></parameter></method> 3324<method name="resize_impl"><type>bool</type><template> 3325 <template-type-parameter name="StateIn"/> 3326 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3327<method name="resize_m_xout"><type>bool</type><template> 3328 <template-type-parameter name="StateIn"/> 3329 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3330<method name="extrapolate"><type>void</type><template> 3331 <template-type-parameter name="StateInOut"/> 3332 </template><parameter name="k"><paramtype>size_t</paramtype></parameter><parameter name="table"><paramtype>state_table_type &</paramtype></parameter><parameter name="coeff"><paramtype>const value_matrix &</paramtype></parameter><parameter name="xest"><paramtype>StateInOut &</paramtype></parameter></method> 3333</method-group> 3334<method-group name="public member functions"> 3335<method name="do_step_impl"><type>void</type><template> 3336 <template-type-parameter name="System"/> 3337 <template-type-parameter name="StateIn"/> 3338 <template-type-parameter name="DerivIn"/> 3339 <template-type-parameter name="StateOut"/> 3340 <template-type-parameter name="Err"/> 3341 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="xerr"><paramtype>Err &</paramtype></parameter></method> 3342<method name="do_step_impl_io"><type>void</type><template> 3343 <template-type-parameter name="System"/> 3344 <template-type-parameter name="StateInOut"/> 3345 <template-type-parameter name="DerivIn"/> 3346 <template-type-parameter name="Err"/> 3347 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inout"><paramtype>StateInOut &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="xerr"><paramtype>Err &</paramtype></parameter></method> 3348<method name="do_step_impl"><type>void</type><template> 3349 <template-type-parameter name="System"/> 3350 <template-type-parameter name="StateIn"/> 3351 <template-type-parameter name="DerivIn"/> 3352 <template-type-parameter name="StateOut"/> 3353 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3354<method name="do_step_impl_io"><type>void</type><template> 3355 <template-type-parameter name="System"/> 3356 <template-type-parameter name="StateInOut"/> 3357 <template-type-parameter name="DerivIn"/> 3358 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="inout"><paramtype>StateInOut &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3359<method name="do_step_dxdt_impl"><type>void</type><template> 3360 <template-type-parameter name="System"/> 3361 <template-type-parameter name="StateInOut"/> 3362 <template-type-parameter name="DerivIn"/> 3363 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>StateInOut &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3364<method name="do_step_dxdt_impl"><type>void</type><template> 3365 <template-type-parameter name="System"/> 3366 <template-type-parameter name="StateIn"/> 3367 <template-type-parameter name="DerivIn"/> 3368 <template-type-parameter name="StateOut"/> 3369 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3370<method name="adjust_size"><type>void</type><template> 3371 <template-type-parameter name="StateIn"/> 3372 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3373</method-group> 3374<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default></parameter></constructor> 3375</class> 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427</namespace> 3428</namespace> 3429</namespace> 3430</header> 3431<header name="boost/numeric/odeint/stepper/generation.hpp"> 3432</header> 3433<header name="boost/numeric/odeint/stepper/implicit_euler.hpp"> 3434<namespace name="boost"> 3435<namespace name="numeric"> 3436<namespace name="odeint"> 3437<class name="implicit_euler"><template> 3438 <template-type-parameter name="ValueType"/> 3439 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 3440 </template><typedef name="value_type"><type>ValueType</type></typedef> 3441<typedef name="time_type"><type>value_type</type></typedef> 3442<typedef name="state_type"><type>boost::numeric::ublas::vector< value_type ></type></typedef> 3443<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 3444<typedef name="deriv_type"><type>state_type</type></typedef> 3445<typedef name="wrapped_deriv_type"><type>state_wrapper< deriv_type ></type></typedef> 3446<typedef name="matrix_type"><type>boost::numeric::ublas::matrix< value_type ></type></typedef> 3447<typedef name="wrapped_matrix_type"><type>state_wrapper< matrix_type ></type></typedef> 3448<typedef name="pmatrix_type"><type>boost::numeric::ublas::permutation_matrix< size_t ></type></typedef> 3449<typedef name="wrapped_pmatrix_type"><type>state_wrapper< pmatrix_type ></type></typedef> 3450<typedef name="resizer_type"><type>Resizer</type></typedef> 3451<typedef name="stepper_category"><type>stepper_tag</type></typedef> 3452<typedef name="stepper_type"><type>implicit_euler< ValueType, Resizer ></type></typedef> 3453<method-group name="public member functions"> 3454<method name="do_step"><type>void</type><template> 3455 <template-type-parameter name="System"/> 3456 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3457<method name="adjust_size"><type>void</type><template> 3458 <template-type-parameter name="StateType"/> 3459 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 3460</method-group> 3461<constructor><parameter name="epsilon"><paramtype>value_type</paramtype><default>1E-6</default></parameter></constructor> 3462<method-group name="private member functions"> 3463<method name="resize_impl"><type>bool</type><template> 3464 <template-type-parameter name="StateIn"/> 3465 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3466<method name="solve"><type>void</type><parameter name="x"><paramtype>state_type &</paramtype></parameter><parameter name="m"><paramtype>matrix_type &</paramtype></parameter></method> 3467</method-group> 3468</class> 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520</namespace> 3521</namespace> 3522</namespace> 3523</header> 3524<header name="boost/numeric/odeint/stepper/modified_midpoint.hpp"> 3525<namespace name="boost"> 3526<namespace name="numeric"> 3527<namespace name="odeint"> 3528<class name="modified_midpoint"><template> 3529 <template-type-parameter name="State"/> 3530 <template-type-parameter name="Value"><default>double</default></template-type-parameter> 3531 <template-type-parameter name="Deriv"><default>State</default></template-type-parameter> 3532 <template-type-parameter name="Time"><default>Value</default></template-type-parameter> 3533 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default></template-type-parameter> 3534 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default></template-type-parameter> 3535 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 3536 </template><inherit access="public">explicit_stepper_base</inherit><description><para>Implementation of the modified midpoint method with a configurable number of intermediate steps. This class is used by the Bulirsch-Stoer algorithm and is not meant for direct usage. </para></description><typedef name="stepper_base_type"><type>explicit_stepper_base< <classname>modified_midpoint</classname>< State, Value, Deriv, Time, Algebra, Operations, Resizer >, 2, State, Value, Deriv, Time, Algebra, Operations, Resizer ></type></typedef> 3537<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 3538<typedef name="wrapped_state_type"><type>stepper_base_type::wrapped_state_type</type></typedef> 3539<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 3540<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 3541<typedef name="wrapped_deriv_type"><type>stepper_base_type::wrapped_deriv_type</type></typedef> 3542<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 3543<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 3544<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 3545<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 3546<typedef name="stepper_type"><type>stepper_base_type::stepper_type</type></typedef> 3547<method-group name="public member functions"> 3548<method name="do_step_impl"><type>void</type><template> 3549 <template-type-parameter name="System"/> 3550 <template-type-parameter name="StateIn"/> 3551 <template-type-parameter name="DerivIn"/> 3552 <template-type-parameter name="StateOut"/> 3553 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3554<method name="set_steps"><type>void</type><parameter name="steps"><paramtype>unsigned short</paramtype></parameter></method> 3555<method name="steps" cv="const"><type>unsigned short</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3556<method name="adjust_size"><type>void</type><template> 3557 <template-type-parameter name="StateIn"/> 3558 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3559</method-group> 3560<constructor><parameter name="steps"><paramtype>unsigned short</paramtype><default>2</default></parameter><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default></parameter></constructor> 3561<method-group name="private member functions"> 3562<method name="resize_impl"><type>bool</type><template> 3563 <template-type-parameter name="StateIn"/> 3564 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3565</method-group> 3566</class><class name="modified_midpoint_dense_out"><template> 3567 <template-type-parameter name="State"/> 3568 <template-type-parameter name="Value"><default>double</default></template-type-parameter> 3569 <template-type-parameter name="Deriv"><default>State</default></template-type-parameter> 3570 <template-type-parameter name="Time"><default>Value</default></template-type-parameter> 3571 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default></template-type-parameter> 3572 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default></template-type-parameter> 3573 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 3574 </template><description><para>Implementation of the modified midpoint method with a configurable number of intermediate steps. This class is used by the dense output Bulirsch-Stoer algorithm and is not meant for direct usage. <note><para>This stepper is for internal use only and does not meet any stepper concept. </para> 3575</note> 3576</para></description><typedef name="state_type"><type>State</type></typedef> 3577<typedef name="value_type"><type>Value</type></typedef> 3578<typedef name="deriv_type"><type>Deriv</type></typedef> 3579<typedef name="time_type"><type>Time</type></typedef> 3580<typedef name="algebra_type"><type>Algebra</type></typedef> 3581<typedef name="operations_type"><type>Operations</type></typedef> 3582<typedef name="resizer_type"><type>Resizer</type></typedef> 3583<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 3584<typedef name="wrapped_deriv_type"><type>state_wrapper< deriv_type ></type></typedef> 3585<typedef name="stepper_type"><type><classname>modified_midpoint_dense_out</classname>< State, Value, Deriv, Time, Algebra, Operations, Resizer ></type></typedef> 3586<typedef name="deriv_table_type"><type>std::vector< wrapped_deriv_type ></type></typedef> 3587<method-group name="public member functions"> 3588<method name="do_step"><type>void</type><template> 3589 <template-type-parameter name="System"/> 3590 <template-type-parameter name="StateIn"/> 3591 <template-type-parameter name="DerivIn"/> 3592 <template-type-parameter name="StateOut"/> 3593 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="in"><paramtype>const StateIn &</paramtype></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="out"><paramtype>StateOut &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="x_mp"><paramtype>state_type &</paramtype></parameter><parameter name="derivs"><paramtype>deriv_table_type &</paramtype></parameter></method> 3594<method name="set_steps"><type>void</type><parameter name="steps"><paramtype>unsigned short</paramtype></parameter></method> 3595<method name="steps" cv="const"><type>unsigned short</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3596<method name="resize"><type>bool</type><template> 3597 <template-type-parameter name="StateIn"/> 3598 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3599<method name="adjust_size"><type>void</type><template> 3600 <template-type-parameter name="StateIn"/> 3601 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3602</method-group> 3603<constructor><parameter name="steps"><paramtype>unsigned short</paramtype><default>2</default></parameter><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default></parameter></constructor> 3604</class> 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617 3618 3619 3620 3621 3622 3623 3624 3625 3626 3627 3628 3629 3630 3631 3632 3633 3634 3635 3636 3637 3638 3639 3640 3641 3642 3643 3644 3645 3646 3647 3648 3649 3650 3651 3652 3653 3654 3655 3656</namespace> 3657</namespace> 3658</namespace> 3659</header> 3660<header name="boost/numeric/odeint/stepper/rosenbrock4.hpp"> 3661<namespace name="boost"> 3662<namespace name="numeric"> 3663<namespace name="odeint"> 3664<struct name="default_rosenbrock_coefficients"><template> 3665 <template-type-parameter name="Value"/> 3666 </template><typedef name="value_type"><type>Value</type></typedef> 3667<typedef name="order_type"><type>unsigned short</type></typedef> 3668<data-member name="gamma"><type>const value_type</type></data-member> 3669<data-member name="d1"><type>const value_type</type></data-member> 3670<data-member name="d2"><type>const value_type</type></data-member> 3671<data-member name="d3"><type>const value_type</type></data-member> 3672<data-member name="d4"><type>const value_type</type></data-member> 3673<data-member name="c2"><type>const value_type</type></data-member> 3674<data-member name="c3"><type>const value_type</type></data-member> 3675<data-member name="c4"><type>const value_type</type></data-member> 3676<data-member name="c21"><type>const value_type</type></data-member> 3677<data-member name="a21"><type>const value_type</type></data-member> 3678<data-member name="c31"><type>const value_type</type></data-member> 3679<data-member name="c32"><type>const value_type</type></data-member> 3680<data-member name="a31"><type>const value_type</type></data-member> 3681<data-member name="a32"><type>const value_type</type></data-member> 3682<data-member name="c41"><type>const value_type</type></data-member> 3683<data-member name="c42"><type>const value_type</type></data-member> 3684<data-member name="c43"><type>const value_type</type></data-member> 3685<data-member name="a41"><type>const value_type</type></data-member> 3686<data-member name="a42"><type>const value_type</type></data-member> 3687<data-member name="a43"><type>const value_type</type></data-member> 3688<data-member name="c51"><type>const value_type</type></data-member> 3689<data-member name="c52"><type>const value_type</type></data-member> 3690<data-member name="c53"><type>const value_type</type></data-member> 3691<data-member name="c54"><type>const value_type</type></data-member> 3692<data-member name="a51"><type>const value_type</type></data-member> 3693<data-member name="a52"><type>const value_type</type></data-member> 3694<data-member name="a53"><type>const value_type</type></data-member> 3695<data-member name="a54"><type>const value_type</type></data-member> 3696<data-member name="c61"><type>const value_type</type></data-member> 3697<data-member name="c62"><type>const value_type</type></data-member> 3698<data-member name="c63"><type>const value_type</type></data-member> 3699<data-member name="c64"><type>const value_type</type></data-member> 3700<data-member name="c65"><type>const value_type</type></data-member> 3701<data-member name="d21"><type>const value_type</type></data-member> 3702<data-member name="d22"><type>const value_type</type></data-member> 3703<data-member name="d23"><type>const value_type</type></data-member> 3704<data-member name="d24"><type>const value_type</type></data-member> 3705<data-member name="d25"><type>const value_type</type></data-member> 3706<data-member name="d31"><type>const value_type</type></data-member> 3707<data-member name="d32"><type>const value_type</type></data-member> 3708<data-member name="d33"><type>const value_type</type></data-member> 3709<data-member name="d34"><type>const value_type</type></data-member> 3710<data-member name="d35"><type>const value_type</type></data-member> 3711<data-member name="stepper_order" specifiers="static"><type>const order_type</type></data-member> 3712<data-member name="error_order" specifiers="static"><type>const order_type</type></data-member> 3713<method-group name="public member functions"> 3714</method-group> 3715<constructor><parameter name=""><paramtype>void</paramtype></parameter></constructor> 3716</struct><class name="rosenbrock4"><template> 3717 <template-type-parameter name="Value"/> 3718 <template-type-parameter name="Coefficients"><default>default_rosenbrock_coefficients< Value ></default></template-type-parameter> 3719 <template-type-parameter name="Resizer"><default>initially_resizer</default></template-type-parameter> 3720 </template><typedef name="value_type"><type>Value</type></typedef> 3721<typedef name="state_type"><type>boost::numeric::ublas::vector< value_type ></type></typedef> 3722<typedef name="deriv_type"><type>state_type</type></typedef> 3723<typedef name="time_type"><type>value_type</type></typedef> 3724<typedef name="matrix_type"><type>boost::numeric::ublas::matrix< value_type ></type></typedef> 3725<typedef name="pmatrix_type"><type>boost::numeric::ublas::permutation_matrix< size_t ></type></typedef> 3726<typedef name="resizer_type"><type>Resizer</type></typedef> 3727<typedef name="rosenbrock_coefficients"><type>Coefficients</type></typedef> 3728<typedef name="stepper_category"><type>stepper_tag</type></typedef> 3729<typedef name="order_type"><type>unsigned short</type></typedef> 3730<typedef name="wrapped_state_type"><type>state_wrapper< state_type ></type></typedef> 3731<typedef name="wrapped_deriv_type"><type>state_wrapper< deriv_type ></type></typedef> 3732<typedef name="wrapped_matrix_type"><type>state_wrapper< matrix_type ></type></typedef> 3733<typedef name="wrapped_pmatrix_type"><type>state_wrapper< pmatrix_type ></type></typedef> 3734<typedef name="stepper_type"><type>rosenbrock4< Value, Coefficients, Resizer ></type></typedef> 3735<data-member name="stepper_order" specifiers="static"><type>const order_type</type></data-member> 3736<data-member name="error_order" specifiers="static"><type>const order_type</type></data-member> 3737<method-group name="public member functions"> 3738<method name="order" cv="const"><type>order_type</type></method> 3739<method name="do_step"><type>void</type><template> 3740 <template-type-parameter name="System"/> 3741 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>const state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="xout"><paramtype>state_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="xerr"><paramtype>state_type &</paramtype></parameter></method> 3742<method name="do_step"><type>void</type><template> 3743 <template-type-parameter name="System"/> 3744 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter><parameter name="xerr"><paramtype>state_type &</paramtype></parameter></method> 3745<method name="do_step"><type>void</type><template> 3746 <template-type-parameter name="System"/> 3747 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>const state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="xout"><paramtype>state_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3748<method name="do_step"><type>void</type><template> 3749 <template-type-parameter name="System"/> 3750 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 3751<method name="prepare_dense_output"><type>void</type></method> 3752<method name="calc_state"><type>void</type><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>state_type &</paramtype></parameter><parameter name="x_old"><paramtype>const state_type &</paramtype></parameter><parameter name="t_old"><paramtype>time_type</paramtype></parameter><parameter name="x_new"><paramtype>const state_type &</paramtype></parameter><parameter name="t_new"><paramtype>time_type</paramtype></parameter></method> 3753<method name="adjust_size"><type>void</type><template> 3754 <template-type-parameter name="StateType"/> 3755 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 3756</method-group> 3757<constructor><parameter name=""><paramtype>void</paramtype></parameter></constructor> 3758<method-group name="protected member functions"> 3759<method name="resize_impl"><type>bool</type><template> 3760 <template-type-parameter name="StateIn"/> 3761 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3762<method name="resize_x_err"><type>bool</type><template> 3763 <template-type-parameter name="StateIn"/> 3764 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3765</method-group> 3766</class> 3767 3768 3769 3770 3771 3772 3773 3774 3775 3776 3777 3778 3779 3780 3781 3782 3783 3784 3785 3786 3787 3788 3789 3790 3791 3792 3793 3794 3795 3796 3797 3798 3799 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817 3818</namespace> 3819</namespace> 3820</namespace> 3821</header> 3822<header name="boost/numeric/odeint/stepper/rosenbrock4_controller.hpp"> 3823<namespace name="boost"> 3824<namespace name="numeric"> 3825<namespace name="odeint"> 3826<class name="rosenbrock4_controller"><template> 3827 <template-type-parameter name="Stepper"/> 3828 </template><typedef name="stepper_type"><type>Stepper</type></typedef> 3829<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 3830<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 3831<typedef name="wrapped_state_type"><type>stepper_type::wrapped_state_type</type></typedef> 3832<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 3833<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 3834<typedef name="wrapped_deriv_type"><type>stepper_type::wrapped_deriv_type</type></typedef> 3835<typedef name="resizer_type"><type>stepper_type::resizer_type</type></typedef> 3836<typedef name="stepper_category"><type>controlled_stepper_tag</type></typedef> 3837<typedef name="controller_type"><type>rosenbrock4_controller< Stepper ></type></typedef> 3838<method-group name="public member functions"> 3839<method name="error"><type>value_type</type><parameter name="x"><paramtype>const state_type &</paramtype></parameter><parameter name="xold"><paramtype>const state_type &</paramtype></parameter><parameter name="xerr"><paramtype>const state_type &</paramtype></parameter></method> 3840<method name="last_error" cv="const"><type>value_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3841<method name="try_step"><type>boost::numeric::odeint::controlled_step_result</type><template> 3842 <template-type-parameter name="System"/> 3843 </template><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 3844<method name="try_step"><type>boost::numeric::odeint::controlled_step_result</type><template> 3845 <template-type-parameter name="System"/> 3846 </template><parameter name="sys"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>const state_type &</paramtype></parameter><parameter name="t"><paramtype>time_type &</paramtype></parameter><parameter name="xout"><paramtype>state_type &</paramtype></parameter><parameter name="dt"><paramtype>time_type &</paramtype></parameter></method> 3847<method name="adjust_size"><type>void</type><template> 3848 <template-type-parameter name="StateType"/> 3849 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 3850<method name="stepper"><type>stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3851<method name="stepper" cv="const"><type>const stepper_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3852</method-group> 3853<constructor><parameter name="atol"><paramtype>value_type</paramtype><default>1.0e-6</default></parameter><parameter name="rtol"><paramtype>value_type</paramtype><default>1.0e-6</default></parameter><parameter name="stepper"><paramtype>const stepper_type &</paramtype><default>stepper_type()</default></parameter></constructor> 3854<constructor><parameter name="atol"><paramtype>value_type</paramtype></parameter><parameter name="rtol"><paramtype>value_type</paramtype></parameter><parameter name="max_dt"><paramtype>time_type</paramtype></parameter><parameter name="stepper"><paramtype>const stepper_type &</paramtype><default>stepper_type()</default></parameter></constructor> 3855<method-group name="protected member functions"> 3856<method name="resize_m_xerr"><type>bool</type><template> 3857 <template-type-parameter name="StateIn"/> 3858 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3859<method name="resize_m_xnew"><type>bool</type><template> 3860 <template-type-parameter name="StateIn"/> 3861 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3862</method-group> 3863</class> 3864 3865 3866 3867 3868 3869 3870 3871 3872 3873 3874 3875 3876 3877 3878 3879 3880 3881 3882 3883 3884 3885 3886 3887 3888 3889 3890 3891 3892 3893 3894 3895 3896 3897 3898 3899 3900 3901 3902 3903 3904 3905 3906 3907 3908 3909 3910 3911 3912 3913 3914 3915</namespace> 3916</namespace> 3917</namespace> 3918</header> 3919<header name="boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp"> 3920<namespace name="boost"> 3921<namespace name="numeric"> 3922<namespace name="odeint"> 3923<class name="rosenbrock4_dense_output"><template> 3924 <template-type-parameter name="ControlledStepper"/> 3925 </template><typedef name="controlled_stepper_type"><type>ControlledStepper</type></typedef> 3926<typedef name="unwrapped_controlled_stepper_type"><type>unwrap_reference< controlled_stepper_type >::type</type></typedef> 3927<typedef name="stepper_type"><type>unwrapped_controlled_stepper_type::stepper_type</type></typedef> 3928<typedef name="value_type"><type>stepper_type::value_type</type></typedef> 3929<typedef name="state_type"><type>stepper_type::state_type</type></typedef> 3930<typedef name="wrapped_state_type"><type>stepper_type::wrapped_state_type</type></typedef> 3931<typedef name="time_type"><type>stepper_type::time_type</type></typedef> 3932<typedef name="deriv_type"><type>stepper_type::deriv_type</type></typedef> 3933<typedef name="wrapped_deriv_type"><type>stepper_type::wrapped_deriv_type</type></typedef> 3934<typedef name="resizer_type"><type>stepper_type::resizer_type</type></typedef> 3935<typedef name="stepper_category"><type>dense_output_stepper_tag</type></typedef> 3936<typedef name="dense_output_stepper_type"><type>rosenbrock4_dense_output< ControlledStepper ></type></typedef> 3937<method-group name="public member functions"> 3938<method name="initialize"><type>void</type><template> 3939 <template-type-parameter name="StateType"/> 3940 </template><parameter name="x0"><paramtype>const StateType &</paramtype></parameter><parameter name="t0"><paramtype>time_type</paramtype></parameter><parameter name="dt0"><paramtype>time_type</paramtype></parameter></method> 3941<method name="do_step"><type>std::pair< time_type, time_type ></type><template> 3942 <template-type-parameter name="System"/> 3943 </template><parameter name="system"><paramtype>System</paramtype></parameter></method> 3944<method name="calc_state"><type>void</type><template> 3945 <template-type-parameter name="StateOut"/> 3946 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>StateOut &</paramtype></parameter></method> 3947<method name="calc_state"><type>void</type><template> 3948 <template-type-parameter name="StateOut"/> 3949 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>const StateOut &</paramtype></parameter></method> 3950<method name="adjust_size"><type>void</type><template> 3951 <template-type-parameter name="StateType"/> 3952 </template><parameter name="x"><paramtype>const StateType &</paramtype></parameter></method> 3953<method name="current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3954<method name="current_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3955<method name="previous_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3956<method name="previous_time" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3957<method name="current_time_step" cv="const"><type>time_type</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3958</method-group> 3959<constructor><parameter name="stepper"><paramtype>const controlled_stepper_type &</paramtype><default>controlled_stepper_type()</default></parameter></constructor> 3960<method-group name="private member functions"> 3961<method name="get_current_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3962<method name="get_current_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3963<method name="get_old_state"><type>state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3964<method name="get_old_state" cv="const"><type>const state_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3965<method name="toggle_current_state"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter></method> 3966<method name="resize_impl"><type>bool</type><template> 3967 <template-type-parameter name="StateIn"/> 3968 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 3969</method-group> 3970</class> 3971 3972 3973 3974 3975 3976 3977 3978 3979 3980 3981 3982 3983 3984 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 4001 4002 4003 4004 4005 4006 4007 4008 4009 4010 4011 4012 4013 4014 4015 4016 4017 4018 4019 4020 4021 4022</namespace> 4023</namespace> 4024</namespace> 4025</header> 4026<header name="boost/numeric/odeint/stepper/runge_kutta4.hpp"> 4027<namespace name="boost"> 4028<namespace name="numeric"> 4029<namespace name="odeint"> 4030<class name="runge_kutta4"><template> 4031 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 4032 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 4033 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 4034 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 4035 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 4036 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 4037 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 4038 </template><inherit access="public">boost::numeric::odeint::explicit_generic_rk< StageCount, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer ></inherit><purpose>The classical Runge-Kutta stepper of fourth order. </purpose><description><para>The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also <ulink url="http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">en.wikipedia.org/wiki/Runge-Kutta_methods</ulink> The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.</para><para>This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from <classname alt="boost::numeric::odeint::explicit_generic_rk">explicit_generic_rk</classname> which is a generic Runge-Kutta algorithm. For more details see explicit_stepper_base and <classname alt="boost::numeric::odeint::explicit_generic_rk">explicit_generic_rk</classname>.</para><para> 4039</para></description><typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 4040<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4041<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 4042<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 4043<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4044<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 4045<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 4046<method-group name="public member functions"> 4047<method name="do_step_impl"><type>void</type><template> 4048 <template-type-parameter name="System"/> 4049 <template-type-parameter name="StateIn"/> 4050 <template-type-parameter name="DerivIn"/> 4051 <template-type-parameter name="StateOut"/> 4052 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out of place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 4053</para></description></method> 4054<method name="adjust_size"><type>void</type><template> 4055 <template-type-parameter name="StateIn"/> 4056 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 4057</para></description></method> 4058</method-group> 4059<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::runge_kutta4">runge_kutta4</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4060</para></description></constructor> 4061</class> 4062 4063 4064 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 4079 4080 4081 4082 4083 4084 4085 4086 4087 4088 4089 4090 4091 4092 4093 4094 4095 4096 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 4110 4111 4112 4113</namespace> 4114</namespace> 4115</namespace> 4116</header> 4117<header name="boost/numeric/odeint/stepper/runge_kutta4_classic.hpp"> 4118<namespace name="boost"> 4119<namespace name="numeric"> 4120<namespace name="odeint"> 4121<class name="runge_kutta4_classic"><template> 4122 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 4123 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 4124 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 4125 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 4126 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 4127 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 4128 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 4129 </template><inherit access="public">explicit_stepper_base</inherit><purpose>The classical Runge-Kutta stepper of fourth order. </purpose><description><para>The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also <ulink url="http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">en.wikipedia.org/wiki/Runge-Kutta_methods</ulink> The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided. This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.</para><para>This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). For more details see explicit_stepper_base.</para><para> 4130</para></description><typedef name="stepper_base_type"><type>explicit_stepper_base< <classname>runge_kutta4_classic</classname>< ... >,... ></type></typedef> 4131<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 4132<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4133<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 4134<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 4135<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4136<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 4137<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 4138<method-group name="public member functions"> 4139<method name="do_step_impl"><type>void</type><template> 4140 <template-type-parameter name="System"/> 4141 <template-type-parameter name="StateIn"/> 4142 <template-type-parameter name="DerivIn"/> 4143 <template-type-parameter name="StateOut"/> 4144 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out of place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 4145</para></description></method> 4146<method name="adjust_size"><type>void</type><template> 4147 <template-type-parameter name="StateType"/> 4148 </template><parameter name="x"><paramtype>const StateType &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 4149</para></description></method> 4150</method-group> 4151<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::runge_kutta4_classic">runge_kutta4_classic</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4152</para></description></constructor> 4153<method-group name="private member functions"> 4154<method name="resize_impl"><type>bool</type><template> 4155 <template-type-parameter name="StateIn"/> 4156 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 4157</method-group> 4158</class> 4159 4160 4161 4162 4163 4164 4165 4166 4167 4168 4169 4170 4171 4172 4173 4174 4175 4176 4177 4178 4179 4180 4181 4182 4183 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209 4210</namespace> 4211</namespace> 4212</namespace> 4213</header> 4214<header name="boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp"> 4215<namespace name="boost"> 4216<namespace name="numeric"> 4217<namespace name="odeint"> 4218<class name="runge_kutta_cash_karp54"><template> 4219 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 4220 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 4221 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 4222 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 4223 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 4224 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 4225 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 4226 </template><inherit access="public">boost::numeric::odeint::explicit_error_generic_rk< StageCount, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer ></inherit><purpose>The Runge-Kutta Cash-Karp method. </purpose><description><para>The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see <ulink url="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_methods">en.wikipedia.org/wiki/Cash-Karp_methods</ulink>. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.</para><para>This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from <classname alt="boost::numeric::odeint::explicit_error_generic_rk">explicit_error_generic_rk</classname> which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and <classname alt="boost::numeric::odeint::explicit_error_generic_rk">explicit_error_generic_rk</classname>.</para><para> 4227</para></description><typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 4228<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4229<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 4230<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 4231<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4232<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 4233<typedef name="resizer_typ"><type>stepper_base_type::resizer_type</type></typedef> 4234<method-group name="public member functions"> 4235<method name="do_step_impl"><type>void</type><template> 4236 <template-type-parameter name="System"/> 4237 <template-type-parameter name="StateIn"/> 4238 <template-type-parameter name="DerivIn"/> 4239 <template-type-parameter name="StateOut"/> 4240 <template-type-parameter name="Err"/> 4241 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><parameter name="xerr"><paramtype>Err &</paramtype><description><para>The result of the error estimation is written in xerr. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Futhermore, an estimation of the error is stored in <computeroutput>xerr</computeroutput>. <computeroutput>do_step_impl</computeroutput> is used by explicit_error_stepper_base. </purpose><description><para> 4242</para></description></method> 4243<method name="do_step_impl"><type>void</type><template> 4244 <template-type-parameter name="System"/> 4245 <template-type-parameter name="StateIn"/> 4246 <template-type-parameter name="DerivIn"/> 4247 <template-type-parameter name="StateOut"/> 4248 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 4249</para></description></method> 4250<method name="adjust_size"><type>void</type><template> 4251 <template-type-parameter name="StateIn"/> 4252 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 4253</para></description></method> 4254</method-group> 4255<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::runge_kutta_cash_karp54">runge_kutta_cash_karp54</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4256</para></description></constructor> 4257</class> 4258 4259 4260 4261 4262 4263 4264 4265 4266 4267 4268 4269 4270 4271 4272 4273 4274 4275 4276 4277 4278 4279 4280 4281 4282 4283 4284 4285 4286 4287 4288 4289 4290 4291 4292 4293 4294 4295 4296 4297 4298 4299 4300 4301 4302 4303 4304 4305 4306 4307 4308 4309</namespace> 4310</namespace> 4311</namespace> 4312</header> 4313<header name="boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp"> 4314<namespace name="boost"> 4315<namespace name="numeric"> 4316<namespace name="odeint"> 4317<class name="runge_kutta_cash_karp54_classic"><template> 4318 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 4319 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 4320 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 4321 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 4322 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 4323 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 4324 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 4325 </template><inherit access="public">explicit_error_stepper_base</inherit><purpose>The Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm. </purpose><description><para>The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see <ulink url="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_method">en.wikipedia.org/wiki/Cash-Karp_method</ulink>. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.</para><para>This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.</para><para> 4326</para></description><typedef name="stepper_base_type"><type>explicit_error_stepper_base< <classname>runge_kutta_cash_karp54_classic</classname>< ... >,... ></type></typedef> 4327<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 4328<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4329<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 4330<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 4331<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4332<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 4333<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 4334<method-group name="public member functions"> 4335<method name="do_step_impl"><type>void</type><template> 4336 <template-type-parameter name="System"/> 4337 <template-type-parameter name="StateIn"/> 4338 <template-type-parameter name="DerivIn"/> 4339 <template-type-parameter name="StateOut"/> 4340 <template-type-parameter name="Err"/> 4341 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><parameter name="xerr"><paramtype>Err &</paramtype><description><para>The result of the error estimation is written in xerr. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. </purpose><description><para>The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Futhermore, an estimation of the error is stored in <computeroutput>xerr</computeroutput>. Access to this step functionality is provided by explicit_error_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly.</para><para> 4342</para></description></method> 4343<method name="do_step_impl"><type>void</type><template> 4344 <template-type-parameter name="System"/> 4345 <template-type-parameter name="StateIn"/> 4346 <template-type-parameter name="DerivIn"/> 4347 <template-type-parameter name="StateOut"/> 4348 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_error_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 4349</para></description></method> 4350<method name="adjust_size"><type>void</type><template> 4351 <template-type-parameter name="StateIn"/> 4352 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 4353</para></description></method> 4354</method-group> 4355<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::runge_kutta_cash_karp54_classic">runge_kutta_cash_karp54_classic</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4356</para></description></constructor> 4357<method-group name="private member functions"> 4358<method name="resize_impl"><type>bool</type><template> 4359 <template-type-parameter name="StateIn"/> 4360 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 4361</method-group> 4362</class> 4363 4364 4365 4366 4367 4368 4369 4370 4371 4372 4373 4374 4375 4376 4377 4378 4379 4380 4381 4382 4383 4384 4385 4386 4387 4388 4389 4390 4391 4392 4393 4394 4395 4396 4397 4398 4399 4400 4401 4402 4403 4404 4405 4406 4407 4408 4409 4410 4411 4412 4413 4414</namespace> 4415</namespace> 4416</namespace> 4417</header> 4418<header name="boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp"> 4419<namespace name="boost"> 4420<namespace name="numeric"> 4421<namespace name="odeint"> 4422<class name="runge_kutta_dopri5"><template> 4423 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 4424 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 4425 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 4426 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 4427 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 4428 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 4429 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 4430 </template><inherit access="public">explicit_error_stepper_fsal_base</inherit><purpose>The Runge-Kutta Dormand-Prince 5 method. </purpose><description><para>The Runge-Kutta Dormand-Prince 5 method is a very popular method for solving ODEs, see <ulink url=""/>. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is available which make this method favourable for many applications.</para><para>This class derives from explicit_error_stepper_fsal_base and inherits its interface via CRTP (current recurring template pattern). The method possesses the FSAL (first-same-as-last) property. See explicit_error_stepper_fsal_base for more details.</para><para> 4431</para></description><typedef name="stepper_base_type"><type>explicit_error_stepper_fsal_base< <classname>runge_kutta_dopri5</classname>< ... >,... ></type></typedef> 4432<typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 4433<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4434<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 4435<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 4436<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4437<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 4438<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 4439<method-group name="public member functions"> 4440<method name="do_step_impl"><type>void</type><template> 4441 <template-type-parameter name="System"/> 4442 <template-type-parameter name="StateIn"/> 4443 <template-type-parameter name="DerivIn"/> 4444 <template-type-parameter name="StateOut"/> 4445 <template-type-parameter name="DerivOut"/> 4446 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt_in"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. dxdt_in is not modified by this method </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dxdt_out"><paramtype>DerivOut &</paramtype><description><para>The result of the new derivative at time t+dt. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt_in</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Furthermore, the derivative is update out-of-place, hence the input is assumed to be in <computeroutput>dxdt_in</computeroutput> and the output in <computeroutput>dxdt_out</computeroutput>. Access to this step functionality is provided by explicit_error_stepper_fsal_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 4447</para></description></method> 4448<method name="do_step_impl"><type>void</type><template> 4449 <template-type-parameter name="System"/> 4450 <template-type-parameter name="StateIn"/> 4451 <template-type-parameter name="DerivIn"/> 4452 <template-type-parameter name="StateOut"/> 4453 <template-type-parameter name="DerivOut"/> 4454 <template-type-parameter name="Err"/> 4455 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt_in"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. dxdt_in is not modified by this method </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dxdt_out"><paramtype>DerivOut &</paramtype><description><para>The result of the new derivative at time t+dt. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><parameter name="xerr"><paramtype>Err &</paramtype><description><para>An estimation of the error. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt_in</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Furthermore, the derivative is update out-of-place, hence the input is assumed to be in <computeroutput>dxdt_in</computeroutput> and the output in <computeroutput>dxdt_out</computeroutput>. Access to this step functionality is provided by explicit_error_stepper_fsal_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. An estimation of the error is calculated. </purpose><description><para> 4456</para></description></method> 4457<method name="calc_state" cv="const"><type>void</type><template> 4458 <template-type-parameter name="StateOut"/> 4459 <template-type-parameter name="StateIn1"/> 4460 <template-type-parameter name="DerivIn1"/> 4461 <template-type-parameter name="StateIn2"/> 4462 <template-type-parameter name="DerivIn2"/> 4463 </template><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="x"><paramtype>StateOut &</paramtype></parameter><parameter name="x_old"><paramtype>const StateIn1 &</paramtype></parameter><parameter name="deriv_old"><paramtype>const DerivIn1 &</paramtype></parameter><parameter name="t_old"><paramtype>time_type</paramtype></parameter><parameter name=""><paramtype>const StateIn2 &</paramtype></parameter><parameter name="deriv_new"><paramtype>const DerivIn2 &</paramtype></parameter><parameter name="t_new"><paramtype>time_type</paramtype></parameter><purpose>This method is used for continuous output and it calculates the state <computeroutput>x</computeroutput> at a time <computeroutput>t</computeroutput> from the knowledge of two states <computeroutput>old_state</computeroutput> and <computeroutput>current_state</computeroutput> at time points <computeroutput>t_old</computeroutput> and <computeroutput>t_new</computeroutput>. It also uses internal variables to calculate the result. Hence this method must be called after two successful <computeroutput>do_step</computeroutput> calls. </purpose></method> 4464<method name="adjust_size"><type>void</type><template> 4465 <template-type-parameter name="StateIn"/> 4466 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 4467</para></description></method> 4468</method-group> 4469<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::runge_kutta_dopri5">runge_kutta_dopri5</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4470</para></description></constructor> 4471<method-group name="private member functions"> 4472<method name="resize_k_x_tmp_impl"><type>bool</type><template> 4473 <template-type-parameter name="StateIn"/> 4474 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 4475<method name="resize_dxdt_tmp_impl"><type>bool</type><template> 4476 <template-type-parameter name="StateIn"/> 4477 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 4478</method-group> 4479</class> 4480 4481 4482 4483 4484 4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 4497 4498 4499 4500 4501 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 4513 4514 4515 4516 4517 4518 4519 4520 4521 4522 4523 4524 4525 4526 4527 4528 4529 4530 4531</namespace> 4532</namespace> 4533</namespace> 4534</header> 4535<header name="boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp"> 4536<namespace name="boost"> 4537<namespace name="numeric"> 4538<namespace name="odeint"> 4539<class name="runge_kutta_fehlberg78"><template> 4540 <template-type-parameter name="State"><purpose><para>The state type. </para></purpose></template-type-parameter> 4541 <template-type-parameter name="Value"><default>double</default><purpose><para>The value type. </para></purpose></template-type-parameter> 4542 <template-type-parameter name="Deriv"><default>State</default><purpose><para>The type representing the time derivative of the state. </para></purpose></template-type-parameter> 4543 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 4544 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< State >::algebra_type</default><purpose><para>The algebra type. </para></purpose></template-type-parameter> 4545 <template-type-parameter name="Operations"><default>typename operations_dispatcher< State >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 4546 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 4547 </template><inherit access="public">boost::numeric::odeint::explicit_error_generic_rk< StageCount, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer ></inherit><purpose>The Runge-Kutta Fehlberg 78 method. </purpose><description><para>The Runge-Kutta Fehlberg 78 method is a standard method for high-precision applications. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.</para><para>This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from <classname alt="boost::numeric::odeint::explicit_error_generic_rk">explicit_error_generic_rk</classname> which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and <classname alt="boost::numeric::odeint::explicit_error_generic_rk">explicit_error_generic_rk</classname>.</para><para> 4548</para></description><typedef name="state_type"><type>stepper_base_type::state_type</type></typedef> 4549<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4550<typedef name="deriv_type"><type>stepper_base_type::deriv_type</type></typedef> 4551<typedef name="time_type"><type>stepper_base_type::time_type</type></typedef> 4552<typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4553<typedef name="operations_type"><type>stepper_base_type::operations_type</type></typedef> 4554<typedef name="resizer_type"><type>stepper_base_type::resizer_type</type></typedef> 4555<method-group name="public member functions"> 4556<method name="do_step_impl"><type>void</type><template> 4557 <template-type-parameter name="System"/> 4558 <template-type-parameter name="StateIn"/> 4559 <template-type-parameter name="DerivIn"/> 4560 <template-type-parameter name="StateOut"/> 4561 <template-type-parameter name="Err"/> 4562 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><parameter name="xerr"><paramtype>Err &</paramtype><description><para>The result of the error estimation is written in xerr. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Futhermore, an estimation of the error is stored in <computeroutput>xerr</computeroutput>. <computeroutput>do_step_impl</computeroutput> is used by explicit_error_stepper_base. </purpose><description><para> 4563</para></description></method> 4564<method name="do_step_impl"><type>void</type><template> 4565 <template-type-parameter name="System"/> 4566 <template-type-parameter name="StateIn"/> 4567 <template-type-parameter name="DerivIn"/> 4568 <template-type-parameter name="StateOut"/> 4569 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </para></description></parameter><parameter name="in"><paramtype>const StateIn &</paramtype><description><para>The state of the ODE which should be solved. in is not modified in this method </para></description></parameter><parameter name="dxdt"><paramtype>const DerivIn &</paramtype><description><para>The derivative of x at t. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="out"><paramtype>StateOut &</paramtype><description><para>The result of the step is written in out. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. The derivative <computeroutput>dxdt</computeroutput> of <computeroutput>in</computeroutput> at the time <computeroutput>t</computeroutput> is passed to the method. The result is updated out-of-place, hence the input is in <computeroutput>in</computeroutput> and the output in <computeroutput>out</computeroutput>. Access to this step functionality is provided by explicit_stepper_base and <computeroutput>do_step_impl</computeroutput> should not be called directly. </purpose><description><para> 4570</para></description></method> 4571<method name="adjust_size"><type>void</type><template> 4572 <template-type-parameter name="StateIn"/> 4573 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 4574</para></description></method> 4575</method-group> 4576<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the runge_kutta_cash_fehlberg78 class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4577</para></description></constructor> 4578</class> 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 4592 4593 4594 4595 4596 4597 4598 4599 4600 4601 4602 4603 4604 4605 4606 4607 4608 4609 4610 4611 4612 4613 4614 4615 4616 4617 4618 4619 4620 4621 4622 4623 4624 4625 4626 4627 4628 4629 4630</namespace> 4631</namespace> 4632</namespace> 4633</header> 4634<header name="boost/numeric/odeint/stepper/stepper_categories.hpp"> 4635<namespace name="boost"> 4636<namespace name="numeric"> 4637<namespace name="odeint"> 4638<struct name="base_tag"><template> 4639 <template-type-parameter name="tag"/> 4640 </template></struct><struct-specialization name="base_tag"><template> 4641 </template><specialization><template-arg>controlled_stepper_tag</template-arg></specialization><typedef name="type"><type>controlled_stepper_tag</type></typedef> 4642</struct-specialization><struct-specialization name="base_tag"><template> 4643 </template><specialization><template-arg>dense_output_stepper_tag</template-arg></specialization><typedef name="type"><type>dense_output_stepper_tag</type></typedef> 4644</struct-specialization><struct-specialization name="base_tag"><template> 4645 </template><specialization><template-arg>error_stepper_tag</template-arg></specialization><typedef name="type"><type>stepper_tag</type></typedef> 4646</struct-specialization><struct-specialization name="base_tag"><template> 4647 </template><specialization><template-arg>explicit_controlled_stepper_fsal_tag</template-arg></specialization><typedef name="type"><type>controlled_stepper_tag</type></typedef> 4648</struct-specialization><struct-specialization name="base_tag"><template> 4649 </template><specialization><template-arg>explicit_controlled_stepper_tag</template-arg></specialization><typedef name="type"><type>controlled_stepper_tag</type></typedef> 4650</struct-specialization><struct-specialization name="base_tag"><template> 4651 </template><specialization><template-arg>explicit_error_stepper_fsal_tag</template-arg></specialization><typedef name="type"><type>stepper_tag</type></typedef> 4652</struct-specialization><struct-specialization name="base_tag"><template> 4653 </template><specialization><template-arg>explicit_error_stepper_tag</template-arg></specialization><typedef name="type"><type>stepper_tag</type></typedef> 4654</struct-specialization><struct-specialization name="base_tag"><template> 4655 </template><specialization><template-arg>stepper_tag</template-arg></specialization><typedef name="type"><type>stepper_tag</type></typedef> 4656</struct-specialization><struct name="controlled_stepper_tag"/><struct name="dense_output_stepper_tag"/><struct name="error_stepper_tag"><inherit access="public">boost::numeric::odeint::stepper_tag</inherit></struct><struct name="explicit_controlled_stepper_fsal_tag"><inherit access="public">boost::numeric::odeint::controlled_stepper_tag</inherit></struct><struct name="explicit_controlled_stepper_tag"><inherit access="public">boost::numeric::odeint::controlled_stepper_tag</inherit></struct><struct name="explicit_error_stepper_fsal_tag"><inherit access="public">boost::numeric::odeint::error_stepper_tag</inherit></struct><struct name="explicit_error_stepper_tag"><inherit access="public">boost::numeric::odeint::error_stepper_tag</inherit></struct><struct name="stepper_tag"/> 4657 4658 4659 4660 4661 4662 4663 4664 4665 4666 4667 4668 4669 4670 4671 4672 4673 4674 4675 4676 4677 4678 4679 4680 4681 4682 4683 4684 4685 4686 4687 4688 4689 4690 4691 4692 4693 4694 4695 4696 4697 4698 4699 4700 4701 4702 4703 4704 4705 4706 4707 4708</namespace> 4709</namespace> 4710</namespace> 4711</header> 4712<header name="boost/numeric/odeint/stepper/symplectic_euler.hpp"> 4713<namespace name="boost"> 4714<namespace name="numeric"> 4715<namespace name="odeint"> 4716<class name="symplectic_euler"><template> 4717 <template-type-parameter name="Coor"><purpose><para>The type representing the coordinates q. </para></purpose></template-type-parameter> 4718 <template-type-parameter name="Momentum"><default>Coor</default><purpose><para>The type representing the coordinates p. </para></purpose></template-type-parameter> 4719 <template-type-parameter name="Value"><default>double</default><purpose><para>The basic value type. Should be something like float, double or a high-precision type. </para></purpose></template-type-parameter> 4720 <template-type-parameter name="CoorDeriv"><default>Coor</default><purpose><para>The type representing the time derivative of the coordinate dq/dt. </para></purpose></template-type-parameter> 4721 <template-type-parameter name="MomentumDeriv"><default>Coor</default></template-type-parameter> 4722 <template-type-parameter name="Time"><default>Value</default><purpose><para>The type representing the time t. </para></purpose></template-type-parameter> 4723 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< Coor >::algebra_type</default><purpose><para>The algebra. </para></purpose></template-type-parameter> 4724 <template-type-parameter name="Operations"><default>typename operations_dispatcher< Coor >::operations_type</default><purpose><para>The operations. </para></purpose></template-type-parameter> 4725 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy. </para></purpose></template-type-parameter> 4726 </template><inherit access="public">symplectic_nystroem_stepper_base</inherit><purpose>Implementation of the symplectic Euler method. </purpose><description><para>The method is of first order and has one stage. It is described HERE.</para><para> 4727</para></description><typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4728<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4729<method-group name="public member functions"> 4730</method-group> 4731<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::symplectic_euler">symplectic_euler</classname>. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4732</para></description></constructor> 4733</class> 4734 4735 4736 4737 4738 4739 4740 4741 4742 4743 4744 4745 4746 4747 4748 4749 4750 4751 4752 4753 4754 4755 4756 4757 4758 4759 4760 4761 4762 4763 4764 4765 4766 4767 4768 4769 4770 4771 4772 4773 4774 4775 4776 4777 4778 4779 4780 4781 4782 4783 4784 4785</namespace> 4786</namespace> 4787</namespace> 4788</header> 4789<header name="boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp"> 4790<namespace name="boost"> 4791<namespace name="numeric"> 4792<namespace name="odeint"> 4793<class name="symplectic_rkn_sb3a_m4_mclachlan"><template> 4794 <template-type-parameter name="Coor"><purpose><para>The type representing the coordinates q. </para></purpose></template-type-parameter> 4795 <template-type-parameter name="Momentum"><default>Coor</default><purpose><para>The type representing the coordinates p. </para></purpose></template-type-parameter> 4796 <template-type-parameter name="Value"><default>double</default><purpose><para>The basic value type. Should be something like float, double or a high-precision type. </para></purpose></template-type-parameter> 4797 <template-type-parameter name="CoorDeriv"><default>Coor</default><purpose><para>The type representing the time derivative of the coordinate dq/dt. </para></purpose></template-type-parameter> 4798 <template-type-parameter name="MomentumDeriv"><default>Coor</default></template-type-parameter> 4799 <template-type-parameter name="Time"><default>Value</default><purpose><para>The type representing the time t. </para></purpose></template-type-parameter> 4800 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< Coor >::algebra_type</default><purpose><para>The algebra. </para></purpose></template-type-parameter> 4801 <template-type-parameter name="Operations"><default>typename operations_dispatcher< Coor >::operations_type</default><purpose><para>The operations. </para></purpose></template-type-parameter> 4802 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy. </para></purpose></template-type-parameter> 4803 </template><inherit access="public">symplectic_nystroem_stepper_base</inherit><purpose>Implementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order. </purpose><description><para>The method is of fourth order and has five stages. It is described HERE. This method can be used with multiprecision types since the coefficients are defined analytically.</para><para>ToDo: add reference to paper.</para><para> 4804</para></description><typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4805<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4806<method-group name="public member functions"> 4807</method-group> 4808<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan">symplectic_rkn_sb3a_m4_mclachlan</classname>. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4809</para></description></constructor> 4810</class> 4811 4812 4813 4814 4815 4816 4817 4818 4819 4820 4821 4822 4823 4824 4825 4826 4827 4828 4829 4830 4831 4832 4833 4834 4835 4836 4837 4838 4839 4840 4841 4842 4843 4844 4845 4846 4847 4848 4849 4850 4851 4852 4853 4854 4855 4856 4857 4858 4859 4860 4861 4862</namespace> 4863</namespace> 4864</namespace> 4865</header> 4866<header name="boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp"> 4867<namespace name="boost"> 4868<namespace name="numeric"> 4869<namespace name="odeint"> 4870<class name="symplectic_rkn_sb3a_mclachlan"><template> 4871 <template-type-parameter name="Coor"><purpose><para>The type representing the coordinates q. </para></purpose></template-type-parameter> 4872 <template-type-parameter name="Momentum"><default>Coor</default><purpose><para>The type representing the coordinates p. </para></purpose></template-type-parameter> 4873 <template-type-parameter name="Value"><default>double</default><purpose><para>The basic value type. Should be something like float, double or a high-precision type. </para></purpose></template-type-parameter> 4874 <template-type-parameter name="CoorDeriv"><default>Coor</default><purpose><para>The type representing the time derivative of the coordinate dq/dt. </para></purpose></template-type-parameter> 4875 <template-type-parameter name="MomentumDeriv"><default>Coor</default></template-type-parameter> 4876 <template-type-parameter name="Time"><default>Value</default><purpose><para>The type representing the time t. </para></purpose></template-type-parameter> 4877 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< Coor >::algebra_type</default><purpose><para>The algebra. </para></purpose></template-type-parameter> 4878 <template-type-parameter name="Operations"><default>typename operations_dispatcher< Coor >::operations_type</default><purpose><para>The operations. </para></purpose></template-type-parameter> 4879 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy. </para></purpose></template-type-parameter> 4880 </template><inherit access="public">symplectic_nystroem_stepper_base</inherit><purpose>Implement of the symmetric B3A method of Runge-Kutta-Nystroem method of sixth order. </purpose><description><para>The method is of fourth order and has six stages. It is described HERE. This method cannot be used with multiprecision types since the coefficients are not defined analytically.</para><para>ToDo Add reference to the paper.</para><para> 4881</para></description><typedef name="algebra_type"><type>stepper_base_type::algebra_type</type></typedef> 4882<typedef name="value_type"><type>stepper_base_type::value_type</type></typedef> 4883<method-group name="public member functions"> 4884</method-group> 4885<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored inside explicit_stepper_base. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::symplectic_rkn_sb3a_mclachlan">symplectic_rkn_sb3a_mclachlan</classname>. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 4886</para></description></constructor> 4887</class> 4888 4889 4890 4891 4892 4893 4894 4895 4896 4897 4898 4899 4900 4901 4902 4903 4904 4905 4906 4907 4908 4909 4910 4911 4912 4913 4914 4915 4916 4917 4918 4919 4920 4921 4922 4923 4924 4925 4926 4927 4928 4929 4930 4931 4932 4933 4934 4935 4936 4937 4938 4939</namespace> 4940</namespace> 4941</namespace> 4942</header> 4943<header name="boost/numeric/odeint/stepper/velocity_verlet.hpp"> 4944<namespace name="boost"> 4945<namespace name="numeric"> 4946<namespace name="odeint"> 4947<class name="velocity_verlet"><template> 4948 <template-type-parameter name="Coor"><purpose><para>The type representing the coordinates. </para></purpose></template-type-parameter> 4949 <template-type-parameter name="Velocity"><default>Coor</default><purpose><para>The type representing the velocities. </para></purpose></template-type-parameter> 4950 <template-type-parameter name="Value"><default>double</default><purpose><para>The type value type. </para></purpose></template-type-parameter> 4951 <template-type-parameter name="Acceleration"><default>Coor</default><purpose><para>The type representing the acceleration. </para></purpose></template-type-parameter> 4952 <template-type-parameter name="Time"><default>Value</default><purpose><para>The time representing the independent variable - the time. </para></purpose></template-type-parameter> 4953 <template-type-parameter name="TimeSq"><default>Time</default><purpose><para>The time representing the square of the time. </para></purpose></template-type-parameter> 4954 <template-type-parameter name="Algebra"><default>typename algebra_dispatcher< Coor >::algebra_type</default><purpose><para>The algebra. </para></purpose></template-type-parameter> 4955 <template-type-parameter name="Operations"><default>typename operations_dispatcher< Coor >::operations_type</default><purpose><para>The operations type. </para></purpose></template-type-parameter> 4956 <template-type-parameter name="Resizer"><default>initially_resizer</default><purpose><para>The resizer policy type. </para></purpose></template-type-parameter> 4957 </template><inherit access="public">algebra_stepper_base< Algebra, Operations ></inherit><purpose>The Velocity-Verlet algorithm. </purpose><description><para><ulink url="http://en.wikipedia.org/wiki/Verlet_integration">The Velocity-Verlet algorithm</ulink> is a method for simulation of molecular dynamics systems. It solves the ODE a=f(r,v',t) where r are the coordinates, v are the velocities and a are the accelerations, hence v = dr/dt, a=dv/dt.</para><para> 4958</para></description><typedef name="algebra_stepper_base_type"><type>algebra_stepper_base< Algebra, Operations ></type></typedef> 4959<typedef name="algebra_type"><type>algebra_stepper_base_type::algebra_type</type></typedef> 4960<typedef name="operations_type"><type>algebra_stepper_base_type::operations_type</type></typedef> 4961<typedef name="coor_type"><type>Coor</type></typedef> 4962<typedef name="velocity_type"><type>Velocity</type></typedef> 4963<typedef name="acceleration_type"><type>Acceleration</type></typedef> 4964<typedef name="state_type"><type>std::pair< coor_type, velocity_type ></type></typedef> 4965<typedef name="deriv_type"><type>std::pair< velocity_type, acceleration_type ></type></typedef> 4966<typedef name="wrapped_acceleration_type"><type>state_wrapper< acceleration_type ></type></typedef> 4967<typedef name="value_type"><type>Value</type></typedef> 4968<typedef name="time_type"><type>Time</type></typedef> 4969<typedef name="time_square_type"><type>TimeSq</type></typedef> 4970<typedef name="resizer_type"><type>Resizer</type></typedef> 4971<typedef name="stepper_category"><type>stepper_tag</type></typedef> 4972<typedef name="order_type"><type>unsigned short</type></typedef> 4973<data-member name="order_value" specifiers="static"><type>const order_type</type></data-member> 4974<method-group name="public member functions"> 4975<method name="order" cv="const"><type>order_type</type><parameter name=""><paramtype>void</paramtype></parameter><description><para> 4976</para></description><returns><para>Returns the order of the stepper. </para> 4977</returns></method> 4978<method name="do_step"><type>void</type><template> 4979 <template-type-parameter name="System"/> 4980 <template-type-parameter name="StateInOut"/> 4981 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. </para></description></parameter><parameter name="x"><paramtype>StateInOut &</paramtype><description><para>The state of the ODE which should be solved. The state is pair of Coor and Velocity. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. It transforms the result in-place. </purpose><description><para>It can be used like <programlisting language="c++">pair< coordinates , velocities > state; 4982stepper.do_step( sys , x , t , dt ); 4983</programlisting></para><para> 4984</para></description></method> 4985<method name="do_step"><type>void</type><template> 4986 <template-type-parameter name="System"/> 4987 <template-type-parameter name="StateInOut"/> 4988 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. </para></description></parameter><parameter name="x"><paramtype>const StateInOut &</paramtype><description><para>The state of the ODE which should be solved. The state is pair of Coor and Velocity. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. It transforms the result in-place. </purpose><description><para>It can be used like <programlisting language="c++">pair< coordinates , velocities > state; 4989stepper.do_step( sys , x , t , dt ); 4990</programlisting></para><para> 4991</para></description></method> 4992<method name="do_step"><type>void</type><template> 4993 <template-type-parameter name="System"/> 4994 <template-type-parameter name="CoorIn"/> 4995 <template-type-parameter name="VelocityIn"/> 4996 <template-type-parameter name="AccelerationIn"/> 4997 <template-type-parameter name="CoorOut"/> 4998 <template-type-parameter name="VelocityOut"/> 4999 <template-type-parameter name="AccelerationOut"/> 5000 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. </para></description></parameter><parameter name="qin"><paramtype>CoorIn const &</paramtype></parameter><parameter name="pin"><paramtype>VelocityIn const &</paramtype></parameter><parameter name="ain"><paramtype>AccelerationIn const &</paramtype></parameter><parameter name="qout"><paramtype>CoorOut &</paramtype></parameter><parameter name="pout"><paramtype>VelocityOut &</paramtype></parameter><parameter name="aout"><paramtype>AccelerationOut &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The value of the time, at which the step should be performed. </para></description></parameter><parameter name="dt"><paramtype>time_type</paramtype><description><para>The step size. </para></description></parameter><purpose>This method performs one step. It transforms the result in-place. Additionally to the other methods the coordinates, velocities and accelerations are passed directly to do_step and they are transformed out-of-place. </purpose><description><para>It can be used like <programlisting language="c++">coordinates qin , qout; 5001velocities pin , pout; 5002accelerations ain, aout; 5003stepper.do_step( sys , qin , pin , ain , qout , pout , aout , t , dt ); 5004</programlisting></para><para> 5005</para></description></method> 5006<method name="adjust_size"><type>void</type><template> 5007 <template-type-parameter name="StateIn"/> 5008 </template><parameter name="x"><paramtype>const StateIn &</paramtype><description><para>A state from which the size of the temporaries to be resized is deduced. </para></description></parameter><purpose>Adjust the size of all temporaries in the stepper manually. </purpose><description><para> 5009</para></description></method> 5010<method name="reset"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter><purpose>Resets the internal state of this stepper. After calling this method it is safe to use all <computeroutput>do_step</computeroutput> method without explicitly initializing the stepper. </purpose></method> 5011<method name="initialize"><type>void</type><template> 5012 <template-type-parameter name="AccelerationIn"/> 5013 </template><parameter name="ain"><paramtype>const AccelerationIn &</paramtype></parameter><purpose>Initializes the internal state of the stepper. </purpose><description><para> 5014</para></description></method> 5015<method name="initialize"><type>void</type><template> 5016 <template-type-parameter name="System"/> 5017 <template-type-parameter name="CoorIn"/> 5018 <template-type-parameter name="VelocityIn"/> 5019 </template><parameter name="system"><paramtype>System</paramtype><description><para>The system function for the next calls of <computeroutput>do_step</computeroutput>. </para></description></parameter><parameter name="qin"><paramtype>const CoorIn &</paramtype><description><para>The current coordinates of the ODE. </para></description></parameter><parameter name="pin"><paramtype>const VelocityIn &</paramtype><description><para>The current velocities of the ODE. </para></description></parameter><parameter name="t"><paramtype>time_type</paramtype><description><para>The current time of the ODE. </para></description></parameter><purpose>Initializes the internal state of the stepper. </purpose><description><para>This method is equivalent to <programlisting language="c++">Acceleration a; 5020system( qin , pin , a , t ); 5021stepper.initialize( a ); 5022</programlisting></para><para> 5023</para></description></method> 5024<method name="is_initialized" cv="const"><type>bool</type><parameter name=""><paramtype>void</paramtype></parameter><description><para> 5025</para></description><returns><para>Returns if the stepper is initialized. </para> 5026</returns></method> 5027</method-group> 5028<constructor><parameter name="algebra"><paramtype>const algebra_type &</paramtype><default>algebra_type()</default><description><para>A copy of algebra is made and stored. </para></description></parameter><purpose>Constructs the <classname alt="boost::numeric::odeint::velocity_verlet">velocity_verlet</classname> class. This constructor can be used as a default constructor if the algebra has a default constructor. </purpose><description><para> 5029</para></description></constructor> 5030<method-group name="private member functions"> 5031<method name="initialize_acc"><type>void</type><template> 5032 <template-type-parameter name="System"/> 5033 <template-type-parameter name="CoorIn"/> 5034 <template-type-parameter name="VelocityIn"/> 5035 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="qin"><paramtype>const CoorIn &</paramtype></parameter><parameter name="pin"><paramtype>const VelocityIn &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter></method> 5036<method name="do_step_v1"><type>void</type><template> 5037 <template-type-parameter name="System"/> 5038 <template-type-parameter name="StateInOut"/> 5039 </template><parameter name="system"><paramtype>System</paramtype></parameter><parameter name="x"><paramtype>StateInOut &</paramtype></parameter><parameter name="t"><paramtype>time_type</paramtype></parameter><parameter name="dt"><paramtype>time_type</paramtype></parameter></method> 5040<method name="resize_impl"><type>bool</type><template> 5041 <template-type-parameter name="StateIn"/> 5042 </template><parameter name="x"><paramtype>const StateIn &</paramtype></parameter></method> 5043<method name="get_current_acc"><type>acceleration_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 5044<method name="get_current_acc" cv="const"><type>const acceleration_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 5045<method name="get_old_acc"><type>acceleration_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 5046<method name="get_old_acc" cv="const"><type>const acceleration_type &</type><parameter name=""><paramtype>void</paramtype></parameter></method> 5047<method name="toggle_current_acc"><type>void</type><parameter name=""><paramtype>void</paramtype></parameter></method> 5048</method-group> 5049</class> 5050 5051 5052 5053 5054 5055 5056 5057 5058 5059 5060 5061 5062 5063 5064 5065 5066 5067 5068 5069 5070 5071 5072 5073 5074 5075 5076 5077 5078 5079 5080 5081 5082 5083 5084 5085 5086 5087 5088 5089 5090 5091 5092 5093 5094 5095 5096 5097 5098 5099 5100 5101</namespace> 5102</namespace> 5103</namespace> 5104</header> 5105</library-reference>