Chaste Commit::ca8ccdedf819b6e02855bc0e8e6f50bdecbc5208
RungeKuttaFehlbergIvpOdeSolver.cpp
1/*
2
3Copyright (c) 2005-2024, University of Oxford.
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34*/
35
36#include "RungeKuttaFehlbergIvpOdeSolver.hpp"
37#include <cmath>
38#include <cfloat>
39#include <iostream>
40#include "Exception.hpp"
41
42/*
43 * PROTECTED FUNCTIONS =========================================================
44 */
45
47 AbstractOdeSystem* pOdeSystem,
48 std::vector<double>& rYValues,
49 std::vector<double>& rWorkingMemory,
50 double startTime,
51 double endTime,
52 double maxTimeStep,
53 double minTimeStep,
54 double tolerance,
55 bool outputSolution)
56{
57 const unsigned number_of_variables = pOdeSystem->GetNumberOfStateVariables();
58 mError.resize(number_of_variables);
59 mk1.resize(number_of_variables);
60 mk2.resize(number_of_variables);
61 mk3.resize(number_of_variables);
62 mk4.resize(number_of_variables);
63 mk5.resize(number_of_variables);
64 mk6.resize(number_of_variables);
65 myk2.resize(number_of_variables);
66 myk3.resize(number_of_variables);
67 myk4.resize(number_of_variables);
68 myk5.resize(number_of_variables);
69 myk6.resize(number_of_variables);
70
71 double current_time = startTime;
72 double time_step = maxTimeStep;
73 bool got_to_end = false;
74 bool accurate_enough = false;
75 unsigned number_of_time_steps = 0;
76
77 if (outputSolution)
78 { // Write out ICs
79 rSolution.rGetTimes().push_back(current_time);
80 rSolution.rGetSolutions().push_back(rYValues);
81 }
82
83 // should never get here if this bool has been set to true;
85 while (!got_to_end)
86 {
87 //std::cout << "New timestep\n" << std::flush;
88 while (!accurate_enough)
89 {
90 accurate_enough = true; // assume it is OK until we check and find otherwise
91
92 // Function that calls the appropriate one-step solver
93 CalculateNextYValue(pOdeSystem,
94 time_step,
95 current_time,
96 rYValues,
97 rWorkingMemory);
98
99 // Find the maximum error in this vector
100 double max_error = -DBL_MAX;
101 for (unsigned i=0; i<number_of_variables; i++)
102 {
103 if (mError[i] > max_error)
104 {
105 max_error = mError[i];
106 }
107 }
108
109 if (max_error > tolerance)
110 {// Reject the step-size and do it again.
111 accurate_enough = false;
112 //std::cout << "Approximation rejected\n" << std::flush;
113 }
114 else
115 {
116 // step forward the time since step has now been made
117 current_time = current_time + time_step;
118 //std::cout << "Approximation accepted with time step = "<< time_step << "\n" << std::flush;
119 //std::cout << "max_error = " << max_error << " tolerance = " << tolerance << "\n" << std::flush;
120 if (outputSolution)
121 { // Write out ICs
122 //std::cout << "In solver Time = " << current_time << " y = " << rWorkingMemory[0] << "\n" << std::flush;
123 rSolution.rGetTimes().push_back(current_time);
124 rSolution.rGetSolutions().push_back(rWorkingMemory);
125 number_of_time_steps++;
126 }
127 }
128
129 // Set a new step size based on the accuracy here
130 AdjustStepSize(time_step, max_error, tolerance, maxTimeStep, minTimeStep);
131 }
132
133 // For the next timestep check the step doesn't go past the end...
134 if (current_time + time_step > endTime)
135 { // Allow a smaller timestep for the final step.
136 time_step = endTime - current_time;
137 }
138
139 if (pOdeSystem->CalculateStoppingEvent(current_time,
140 rWorkingMemory) == true)
141 {
142 mStoppingTime = current_time;
144 }
145
146 if (mStoppingEventOccurred || current_time>=endTime)
147 {
148 got_to_end = true;
149 }
150
151 // Approximation accepted - put it in rYValues
152 rYValues.assign(rWorkingMemory.begin(), rWorkingMemory.end());
153 accurate_enough = false; // for next loop.
154 //std::cout << "Finished Time Step\n" << std::flush;
155 }
156 rSolution.SetNumberOfTimeSteps(number_of_time_steps);
157}
158
160 double timeStep,
161 double time,
162 std::vector<double>& rCurrentYValues,
163 std::vector<double>& rNextYValues)
164{
165 const unsigned num_equations = pAbstractOdeSystem->GetNumberOfStateVariables();
166
167
168 std::vector<double>& dy = rNextYValues; // re-use memory (not that it makes much difference here!)
169
170 pAbstractOdeSystem->EvaluateYDerivatives(time, rCurrentYValues, dy);
171
172 for (unsigned i=0; i<num_equations; i++)
173 {
174 mk1[i] = timeStep*dy[i];
175 myk2[i] = rCurrentYValues[i] + 0.25*mk1[i];
176 }
177
178 pAbstractOdeSystem->EvaluateYDerivatives(time + 0.25*timeStep, myk2, dy);
179 for (unsigned i=0; i<num_equations; i++)
180 {
181 mk2[i] = timeStep*dy[i];
182 myk3[i] = rCurrentYValues[i] + 0.09375*mk1[i] + 0.28125*mk2[i];
183 }
184
185 pAbstractOdeSystem->EvaluateYDerivatives(time + 0.375*timeStep, myk3, dy);
186 for (unsigned i=0; i<num_equations; i++)
187 {
188 mk3[i] = timeStep*dy[i];
189 myk4[i] = rCurrentYValues[i] + m1932o2197*mk1[i] - m7200o2197*mk2[i]
190 + m7296o2197*mk3[i];
191 }
192
193 pAbstractOdeSystem->EvaluateYDerivatives(time+m12o13*timeStep, myk4, dy);
194 for (unsigned i=0; i<num_equations; i++)
195 {
196 mk4[i] = timeStep*dy[i];
197 myk5[i] = rCurrentYValues[i] + m439o216*mk1[i] - 8*mk2[i]
198 + m3680o513*mk3[i]- m845o4104*mk4[i];
199 }
200
201 pAbstractOdeSystem->EvaluateYDerivatives(time+timeStep, myk5, dy);
202 for (unsigned i=0; i<num_equations; i++)
203 {
204 mk5[i] = timeStep*dy[i];
205 myk6[i] = rCurrentYValues[i] - m8o27*mk1[i] + 2*mk2[i] - m3544o2565*mk3[i]
206 + m1859o4104*mk4[i] - 0.275*mk5[i];
207 }
208
209 pAbstractOdeSystem->EvaluateYDerivatives(time+0.5*timeStep, myk6, dy);
210 for (unsigned i=0; i<num_equations; i++)
211 {
212 mk6[i] = timeStep*dy[i];
213 mError[i] = (1/timeStep)*fabs(m1o360*mk1[i] - m128o4275*mk3[i]
214 - m2197o75240*mk4[i] + 0.02*mk5[i]+ m2o55*mk6[i]);
215 rNextYValues[i] = rCurrentYValues[i] + m25o216*mk1[i] + m1408o2565*mk3[i]
216 + m2197o4104*mk4[i] - 0.2*mk5[i];
217 }
218}
219
221 const double& rError,
222 const double& rTolerance,
223 const double& rMaxTimeStep,
224 const double& rMinTimeStep)
225{
226 // Work out scaling factor delta for the step size
227 double delta = pow(rTolerance/(2.0*rError), 0.25);
228
229 // Maximum adjustment is *0.1 or *4
230 if (delta <= 0.1)
231 {
232 rCurrentStepSize *= 0.1;
233 }
234 else if (delta >= 4.0)
235 {
236 rCurrentStepSize *= 4.0;
237 }
238 else
239 {
240 rCurrentStepSize *= delta;
241 }
242
243 if (rCurrentStepSize > rMaxTimeStep)
244 {
245 rCurrentStepSize = rMaxTimeStep;
246 }
247
248 if (rCurrentStepSize < rMinTimeStep)
249 {
250 std::cout << "rCurrentStepSize = " << rCurrentStepSize << "\n" << std::flush;
251 std::cout << "rMinTimeStep = " << rMinTimeStep << "\n" << std::flush;
252
253 EXCEPTION("RKF45 Solver: Ode needs a smaller timestep than the set minimum\n");
254 }
255
256}
257
258
259/*
260 * PUBLIC FUNCTIONS=============================================================
261 */
262
264 : m1932o2197(1932.0/2197.0), // you need the .0 s - caused me no end of trouble.
265 m7200o2197(7200.0/2197.0),
266 m7296o2197(7296.0/2197.0),
267 m12o13(12.0/13.0),
268 m439o216(439.0/216.0),
269 m3680o513(3680.0/513.0),
270 m845o4104(845.0/4104.0),
271 m8o27(8.0/27.0),
272 m3544o2565(3544.0/2565.0),
273 m1859o4104(1859.0/4104.0),
274 m1o360(1.0/360.0),
275 m128o4275(128.0/4275.0),
276 m2197o75240(2197.0/75240.0),
277 m2o55(2.0/55.0),
278 m25o216(25.0/216.0),
279 m1408o2565(1408.0/2565.0),
280 m2197o4104(2197.0/4104.0)
281{
282}
283
285 std::vector<double>& rYValues,
286 double startTime,
287 double endTime,
288 double timeStep,
289 double tolerance)
290{
291 assert(rYValues.size()==pOdeSystem->GetNumberOfStateVariables());
292 assert(endTime > startTime);
293 assert(timeStep > 0.0);
294
296 if (pOdeSystem->CalculateStoppingEvent(startTime, rYValues) == true)
297 {
298 EXCEPTION("(Solve with sampling) Stopping event is true for initial condition");
299 }
300 // Allocate working memory
301 std::vector<double> working_memory(rYValues.size());
302 // And solve...
303 OdeSolution solutions;
304 //solutions.SetNumberOfTimeSteps((unsigned)(10.0*(startTime-endTime)/timeStep));
305 bool return_solution = true;
306 InternalSolve(solutions, pOdeSystem, rYValues, working_memory, startTime, endTime, timeStep, 1e-5, tolerance, return_solution);
307 return solutions;
308}
309
311 std::vector<double>& rYValues,
312 double startTime,
313 double endTime,
314 double timeStep)
315{
316 assert(rYValues.size()==pOdeSystem->GetNumberOfStateVariables());
317 assert(endTime > startTime);
318 assert(timeStep > 0.0);
319
321 if (pOdeSystem->CalculateStoppingEvent(startTime, rYValues) == true)
322 {
323 EXCEPTION("(Solve without sampling) Stopping event is true for initial condition");
324 }
325 // Allocate working memory
326 std::vector<double> working_memory(rYValues.size());
327 // And solve...
328 OdeSolution not_required_solution;
329 bool return_solution = false;
330 InternalSolve(not_required_solution, pOdeSystem, rYValues, working_memory, startTime, endTime, timeStep, 1e-4, 1e-5, return_solution);
331}
332
333
334// Serialization for Boost >= 1.36
#define EXCEPTION(message)
#define CHASTE_CLASS_EXPORT(T)
virtual void EvaluateYDerivatives(double time, const std::vector< double > &rY, std::vector< double > &rDY)=0
virtual bool CalculateStoppingEvent(double time, const std::vector< double > &rY)
void SetNumberOfTimeSteps(unsigned numTimeSteps)
std::vector< std::vector< double > > & rGetSolutions()
std::vector< double > & rGetTimes()
void AdjustStepSize(double &rCurrentStepSize, const double &rError, const double &rTolerance, const double &rMaxTimeStep, const double &rMinTimeStep)
void InternalSolve(OdeSolution &rSolution, AbstractOdeSystem *pAbstractOdeSystem, std::vector< double > &rCurrentYValues, std::vector< double > &rWorkingMemory, double startTime, double endTime, double maxTimeStep, double minTimeStep, double tolerance, bool outputSolution)
OdeSolution Solve(AbstractOdeSystem *pAbstractOdeSystem, std::vector< double > &rYValues, double startTime, double endTime, double timeStep, double ignoredSamplingTime)
void CalculateNextYValue(AbstractOdeSystem *pAbstractOdeSystem, double timeStep, double time, std::vector< double > &rCurrentYValues, std::vector< double > &rNextYValues)