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Tempus_ExplicitRK_FSA.hpp
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1 //@HEADER
2 // *****************************************************************************
3 // Tempus: Time Integration and Sensitivity Analysis Package
4 //
5 // Copyright 2017 NTESS and the Tempus contributors.
6 // SPDX-License-Identifier: BSD-3-Clause
7 // *****************************************************************************
8 //@HEADER
9 
10 #include "Teuchos_UnitTestHarness.hpp"
11 #include "Teuchos_XMLParameterListHelpers.hpp"
12 #include "Teuchos_TimeMonitor.hpp"
13 #include "Teuchos_DefaultComm.hpp"
14 
15 #include "Thyra_VectorStdOps.hpp"
16 #include "Thyra_MultiVectorStdOps.hpp"
17 
18 #include "Tempus_IntegratorBasic.hpp"
19 #include "Tempus_IntegratorForwardSensitivity.hpp"
20 
21 #include "Thyra_DefaultMultiVectorProductVector.hpp"
22 #include "Thyra_DefaultProductVector.hpp"
23 
24 #include "../TestModels/SinCosModel.hpp"
25 #include "../TestUtils/Tempus_ConvergenceTestUtils.hpp"
26 
27 #include <fstream>
28 #include <vector>
29 
30 namespace Tempus_Test {
31 
32 using Teuchos::getParametersFromXmlFile;
33 using Teuchos::ParameterList;
34 using Teuchos::RCP;
35 using Teuchos::sublist;
36 
37 using Tempus::IntegratorBasic;
38 using Tempus::SolutionHistory;
39 using Tempus::SolutionState;
40 
41 // ************************************************************
42 // ************************************************************
43 void test_sincos_fsa(const std::string& method_name,
44  const bool use_combined_method,
45  const bool use_dfdp_as_tangent, Teuchos::FancyOStream& out,
46  bool& success)
47 {
48  std::vector<std::string> RKMethods;
49  RKMethods.push_back("RK Forward Euler");
50  RKMethods.push_back("RK Explicit 4 Stage");
51  RKMethods.push_back("RK Explicit 3/8 Rule");
52  RKMethods.push_back("RK Explicit 4 Stage 3rd order by Runge");
53  RKMethods.push_back("RK Explicit 5 Stage 3rd order by Kinnmark and Gray");
54  RKMethods.push_back("RK Explicit 3 Stage 3rd order");
55  RKMethods.push_back("RK Explicit 3 Stage 3rd order TVD");
56  RKMethods.push_back("RK Explicit 3 Stage 3rd order by Heun");
57  RKMethods.push_back("RK Explicit Midpoint");
58  RKMethods.push_back("RK Explicit Trapezoidal");
59  RKMethods.push_back("Heuns Method");
60  RKMethods.push_back("General ERK");
61 
62  // Check that method_name is valid
63  if (method_name != "") {
64  auto it = std::find(RKMethods.begin(), RKMethods.end(), method_name);
65  TEUCHOS_TEST_FOR_EXCEPTION(
66  it == RKMethods.end(), std::logic_error,
67  "Invalid RK method name '" << method_name << "'");
68  }
69 
70  std::vector<double> RKMethodErrors;
71  if (use_combined_method) {
72  RKMethodErrors.push_back(0.183799);
73  RKMethodErrors.push_back(6.88637e-06);
74  RKMethodErrors.push_back(6.88637e-06);
75  RKMethodErrors.push_back(0.000264154);
76  RKMethodErrors.push_back(5.22798e-05);
77  RKMethodErrors.push_back(0.000261896);
78  RKMethodErrors.push_back(0.000261896);
79  RKMethodErrors.push_back(0.000261896);
80  RKMethodErrors.push_back(0.00934377);
81  RKMethodErrors.push_back(0.00934377);
82  RKMethodErrors.push_back(0.00934377);
83  RKMethodErrors.push_back(6.88637e-06);
84  }
85  else {
86  RKMethodErrors.push_back(0.183799);
87  RKMethodErrors.push_back(2.1915e-05);
88  RKMethodErrors.push_back(2.23367e-05);
89  RKMethodErrors.push_back(0.000205051);
90  RKMethodErrors.push_back(2.85141e-05);
91  RKMethodErrors.push_back(0.000126478);
92  RKMethodErrors.push_back(9.64964e-05);
93  RKMethodErrors.push_back(0.000144616);
94  RKMethodErrors.push_back(0.00826159);
95  RKMethodErrors.push_back(0.00710492);
96  RKMethodErrors.push_back(0.00710492);
97  RKMethodErrors.push_back(2.1915e-05);
98  }
99  Teuchos::RCP<const Teuchos::Comm<int> > comm =
100  Teuchos::DefaultComm<int>::getComm();
101 
102  for (std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {
103  // If we were given a method to run, skip this method if it doesn't match
104  if (method_name != "" && RKMethods[m] != method_name) continue;
105 
106  std::string RKMethod_ = RKMethods[m];
107  std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
108  std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
109  std::vector<double> StepSize;
110  std::vector<double> ErrorNorm;
111  const int nTimeStepSizes = 7;
112  double dt = 0.2;
113  double order = 0.0;
114  for (int n = 0; n < nTimeStepSizes; n++) {
115  // Read params from .xml file
116  RCP<ParameterList> pList =
117  getParametersFromXmlFile("Tempus_ExplicitRK_SinCos.xml");
118 
119  // Setup the SinCosModel
120  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
121  scm_pl->set("Use DfDp as Tangent", use_dfdp_as_tangent);
122  RCP<SinCosModel<double> > model =
123  Teuchos::rcp(new SinCosModel<double>(scm_pl));
124 
125  // Set the Stepper
126  RCP<ParameterList> pl = sublist(pList, "Tempus", true);
127  if (RKMethods[m] == "General ERK") {
128  pl->sublist("Demo Integrator").set("Stepper Name", "Demo Stepper 2");
129  }
130  else {
131  pl->sublist("Demo Stepper").set("Stepper Type", RKMethods[m]);
132  }
133 
134  dt /= 2;
135 
136  // Setup sensitivities
137  ParameterList& sens_pl = pl->sublist("Sensitivities");
138  if (use_combined_method)
139  sens_pl.set("Sensitivity Method", "Combined");
140  else
141  sens_pl.set("Sensitivity Method", "Staggered");
142  sens_pl.set("Use DfDp as Tangent", use_dfdp_as_tangent);
143  ParameterList& interp_pl = pl->sublist("Demo Integrator")
144  .sublist("Solution History")
145  .sublist("Interpolator");
146  interp_pl.set("Interpolator Type", "Lagrange");
147  interp_pl.set("Order", 3); // All RK methods here are at most 4th order
148 
149  // Setup the Integrator and reset initial time step
150  pl->sublist("Demo Integrator")
151  .sublist("Time Step Control")
152  .set("Initial Time Step", dt);
153  RCP<Tempus::IntegratorForwardSensitivity<double> > integrator =
154  Tempus::createIntegratorForwardSensitivity<double>(pl, model);
155  order = integrator->getStepper()->getOrder();
156 
157  // Initial Conditions
158  double t0 = pl->sublist("Demo Integrator")
159  .sublist("Time Step Control")
160  .get<double>("Initial Time");
161  // RCP<const Thyra::VectorBase<double> > x0 =
162  // model->getExactSolution(t0).get_x()->clone_v();
163  RCP<Thyra::VectorBase<double> > x0 =
164  model->getNominalValues().get_x()->clone_v();
165  const int num_param = model->get_p_space(0)->dim();
166  RCP<Thyra::MultiVectorBase<double> > DxDp0 =
167  Thyra::createMembers(model->get_x_space(), num_param);
168  for (int i = 0; i < num_param; ++i)
169  Thyra::assign(DxDp0->col(i).ptr(),
170  *(model->getExactSensSolution(i, t0).get_x()));
171  integrator->initializeSolutionHistory(t0, x0, Teuchos::null,
172  Teuchos::null, DxDp0, Teuchos::null,
173  Teuchos::null);
174 
175  // Integrate to timeMax
176  bool integratorStatus = integrator->advanceTime();
177  TEST_ASSERT(integratorStatus)
178 
179  // Test if at 'Final Time'
180  double time = integrator->getTime();
181  double timeFinal = pl->sublist("Demo Integrator")
182  .sublist("Time Step Control")
183  .get<double>("Final Time");
184  TEST_FLOATING_EQUALITY(time, timeFinal, 1.0e-14);
185 
186  // Time-integrated solution and the exact solution
187  RCP<const Thyra::VectorBase<double> > x = integrator->getX();
188  RCP<const Thyra::MultiVectorBase<double> > DxDp = integrator->getDxDp();
189  RCP<const Thyra::VectorBase<double> > x_exact =
190  model->getExactSolution(time).get_x();
191  RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
192  Thyra::createMembers(model->get_x_space(), num_param);
193  for (int i = 0; i < num_param; ++i)
194  Thyra::assign(DxDp_exact->col(i).ptr(),
195  *(model->getExactSensSolution(i, time).get_x()));
196 
197  // Plot sample solution and exact solution
198  if (comm->getRank() == 0 && n == nTimeStepSizes - 1) {
199  typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
200 
201  std::ofstream ftmp("Tempus_" + RKMethod_ + "_SinCos_Sens.dat");
202  RCP<const SolutionHistory<double> > solutionHistory =
203  integrator->getSolutionHistory();
204  RCP<Thyra::MultiVectorBase<double> > DxDp_exact_plot =
205  Thyra::createMembers(model->get_x_space(), num_param);
206  for (int i = 0; i < solutionHistory->getNumStates(); i++) {
207  RCP<const SolutionState<double> > solutionState =
208  (*solutionHistory)[i];
209  double time_i = solutionState->getTime();
210  RCP<const DMVPV> x_prod_plot =
211  Teuchos::rcp_dynamic_cast<const DMVPV>(solutionState->getX());
212  RCP<const Thyra::VectorBase<double> > x_plot =
213  x_prod_plot->getMultiVector()->col(0);
214  RCP<const Thyra::MultiVectorBase<double> > DxDp_plot =
215  x_prod_plot->getMultiVector()->subView(
216  Teuchos::Range1D(1, num_param));
217  RCP<const Thyra::VectorBase<double> > x_exact_plot =
218  model->getExactSolution(time_i).get_x();
219  for (int j = 0; j < num_param; ++j)
220  Thyra::assign(DxDp_exact_plot->col(j).ptr(),
221  *(model->getExactSensSolution(j, time_i).get_x()));
222  ftmp << std::fixed << std::setprecision(7) << time_i << std::setw(11)
223  << get_ele(*(x_plot), 0) << std::setw(11)
224  << get_ele(*(x_plot), 1);
225  for (int j = 0; j < num_param; ++j)
226  ftmp << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 0)
227  << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 1);
228  ftmp << std::setw(11) << get_ele(*(x_exact_plot), 0) << std::setw(11)
229  << get_ele(*(x_exact_plot), 1);
230  for (int j = 0; j < num_param; ++j)
231  ftmp << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 0)
232  << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 1);
233  ftmp << std::endl;
234  }
235  ftmp.close();
236  }
237 
238  // Calculate the error
239  RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
240  RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
241  Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
242  Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
243  StepSize.push_back(dt);
244  double L2norm = Thyra::norm_2(*xdiff);
245  L2norm *= L2norm;
246  Teuchos::Array<double> L2norm_DxDp(num_param);
247  Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
248  for (int i = 0; i < num_param; ++i)
249  L2norm += L2norm_DxDp[i] * L2norm_DxDp[i];
250  L2norm = std::sqrt(L2norm);
251  ErrorNorm.push_back(L2norm);
252 
253  out << " n = " << n << " dt = " << dt << " error = " << L2norm
254  << std::endl;
255  }
256 
257  // Check the order and intercept
258  double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
259  out << " Stepper = " << RKMethods[m] << std::endl;
260  out << " =========================" << std::endl;
261  out << " Expected order: " << order << std::endl;
262  out << " Observed order: " << slope << std::endl;
263  out << " =========================" << std::endl;
264  TEST_FLOATING_EQUALITY(slope, order, 0.04);
265  TEST_FLOATING_EQUALITY(ErrorNorm[0], RKMethodErrors[m], 1.0e-4);
266 
267  if (comm->getRank() == 0) {
268  std::ofstream ftmp("Tempus_" + RKMethod_ + "_SinCos_Sens-Error.dat");
269  double error0 = 0.8 * ErrorNorm[0];
270  for (int n = 0; n < nTimeStepSizes; n++) {
271  ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
272  << error0 * (pow(StepSize[n] / StepSize[0], order)) << std::endl;
273  }
274  ftmp.close();
275  }
276  }
277 
278  Teuchos::TimeMonitor::summarize();
279 }
280 
281 } // namespace Tempus_Test
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Tempus_Test::test_sincos_fsa
void test_sincos_fsa(const bool use_combined_method, const bool use_dfdp_as_tangent, Teuchos::FancyOStream &out, bool &success)
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