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Tempus_DIRK_ASA.cpp
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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_IntegratorAdjointSensitivity.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 TEUCHOS_UNIT_TEST(DIRK, SinCos_ASA)
44 {
45  std::vector<std::string> RKMethods;
46  RKMethods.push_back("General DIRK");
47  RKMethods.push_back("RK Backward Euler");
48  RKMethods.push_back("DIRK 1 Stage Theta Method");
49  RKMethods.push_back("RK Implicit 1 Stage 1st order Radau IA");
50  RKMethods.push_back("SDIRK 2 Stage 2nd order");
51  RKMethods.push_back("RK Implicit 2 Stage 2nd order Lobatto IIIB");
52  RKMethods.push_back("SDIRK 2 Stage 3rd order");
53  RKMethods.push_back("EDIRK 2 Stage 3rd order");
54  RKMethods.push_back("EDIRK 2 Stage Theta Method");
55  RKMethods.push_back("SDIRK 3 Stage 4th order");
56  RKMethods.push_back("SDIRK 5 Stage 4th order");
57  RKMethods.push_back("SDIRK 5 Stage 5th order");
58 
59  std::vector<double> RKMethodErrors;
60  RKMethodErrors.push_back(8.48235e-05);
61  RKMethodErrors.push_back(0.0383339);
62  RKMethodErrors.push_back(0.000221028);
63  RKMethodErrors.push_back(0.0428449);
64  RKMethodErrors.push_back(8.48235e-05);
65  RKMethodErrors.push_back(0.000297933);
66  RKMethodErrors.push_back(4.87848e-06);
67  RKMethodErrors.push_back(7.30827e-07);
68  RKMethodErrors.push_back(0.000272997);
69  RKMethodErrors.push_back(3.10132e-07);
70  RKMethodErrors.push_back(7.56838e-10);
71  RKMethodErrors.push_back(1.32374e-10);
72 
73  Teuchos::RCP<const Teuchos::Comm<int> > comm =
74  Teuchos::DefaultComm<int>::getComm();
75 
76  for (std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {
77  std::string RKMethod_ = RKMethods[m];
78  std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
79  std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
80  std::vector<double> StepSize;
81  std::vector<double> ErrorNorm;
82  const int nTimeStepSizes = 2; // 7 for error plots
83  double dt = 0.05;
84  double order = 0.0;
85  for (int n = 0; n < nTimeStepSizes; n++) {
86  // Read params from .xml file
87  RCP<ParameterList> pList =
88  getParametersFromXmlFile("Tempus_DIRK_SinCos.xml");
89 
90  // Setup the SinCosModel
91  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
92  RCP<SinCosModel<double> > model =
93  Teuchos::rcp(new SinCosModel<double>(scm_pl));
94 
95  // Set the Stepper
96  RCP<ParameterList> pl = sublist(pList, "Tempus", true);
97  pl->sublist("Default Stepper").set("Stepper Type", RKMethods[m]);
98  if (RKMethods[m] == "DIRK 1 Stage Theta Method" ||
99  RKMethods[m] == "EDIRK 2 Stage Theta Method") {
100  pl->sublist("Default Stepper").set<double>("theta", 0.5);
101  }
102  else if (RKMethods[m] == "SDIRK 2 Stage 2nd order") {
103  pl->sublist("Default Stepper").set("gamma", 0.2928932188134524);
104  }
105  else if (RKMethods[m] == "SDIRK 2 Stage 3rd order") {
106  pl->sublist("Default Stepper")
107  .set<std::string>("Gamma Type", "3rd Order A-stable");
108  }
109 
110  dt /= 2;
111 
112  // Setup sensitivities
113  ParameterList& sens_pl = pl->sublist("Sensitivities");
114  sens_pl.set("Mass Matrix Is Identity", true); // Necessary for explicit
115  ParameterList& interp_pl = pl->sublist("Default Integrator")
116  .sublist("Solution History")
117  .sublist("Interpolator");
118  interp_pl.set("Interpolator Type", "Lagrange");
119  interp_pl.set("Order", 4); // All RK methods here are at most 5th order
120 
121  // Setup the Integrator and reset initial time step
122  pl->sublist("Default Integrator")
123  .sublist("Time Step Control")
124  .set("Initial Time Step", dt);
125  RCP<Tempus::IntegratorAdjointSensitivity<double> > integrator =
126  Tempus::createIntegratorAdjointSensitivity<double>(pl, model);
127  order = integrator->getStepper()->getOrder();
128 
129  // Initial Conditions
130  // During the Integrator construction, the initial SolutionState
131  // is set by default to model->getNominalVales().get_x(). However,
132  // the application can set it also by
133  // integrator->initializeSolutionHistory.
134  RCP<Thyra::VectorBase<double> > x0 =
135  model->getNominalValues().get_x()->clone_v();
136  const int num_param = model->get_p_space(0)->dim();
137  RCP<Thyra::MultiVectorBase<double> > DxDp0 =
138  Thyra::createMembers(model->get_x_space(), num_param);
139  for (int i = 0; i < num_param; ++i)
140  Thyra::assign(DxDp0->col(i).ptr(),
141  *(model->getExactSensSolution(i, 0.0).get_x()));
142  integrator->initializeSolutionHistory(0.0, x0, Teuchos::null,
143  Teuchos::null, DxDp0, Teuchos::null,
144  Teuchos::null);
145 
146  // Integrate to timeMax
147  bool integratorStatus = integrator->advanceTime();
148  TEST_ASSERT(integratorStatus)
149 
150  // Test if at 'Final Time'
151  double time = integrator->getTime();
152  double timeFinal = pl->sublist("Default Integrator")
153  .sublist("Time Step Control")
154  .get<double>("Final Time");
155  double tol = 100.0 * std::numeric_limits<double>::epsilon();
156  TEST_FLOATING_EQUALITY(time, timeFinal, tol);
157 
158  // Time-integrated solution and the exact solution along with
159  // sensitivities (relying on response g(x) = x). Note we must transpose
160  // dg/dp since the integrator returns it in gradient form.
161  RCP<const Thyra::VectorBase<double> > x = integrator->getX();
162  RCP<const Thyra::MultiVectorBase<double> > DgDp = integrator->getDgDp();
163  RCP<Thyra::MultiVectorBase<double> > DxDp =
164  Thyra::createMembers(model->get_x_space(), num_param);
165  {
166  Thyra::ConstDetachedMultiVectorView<double> dgdp_view(*DgDp);
167  Thyra::DetachedMultiVectorView<double> dxdp_view(*DxDp);
168  const int num_g = DgDp->domain()->dim();
169  for (int i = 0; i < num_g; ++i)
170  for (int j = 0; j < num_param; ++j) dxdp_view(i, j) = dgdp_view(j, i);
171  }
172  RCP<const Thyra::VectorBase<double> > x_exact =
173  model->getExactSolution(time).get_x();
174  RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
175  Thyra::createMembers(model->get_x_space(), num_param);
176  for (int i = 0; i < num_param; ++i)
177  Thyra::assign(DxDp_exact->col(i).ptr(),
178  *(model->getExactSensSolution(i, time).get_x()));
179 
180  // Plot sample solution and exact solution
181  if (comm->getRank() == 0 && n == nTimeStepSizes - 1) {
182  typedef Thyra::DefaultProductVector<double> DPV;
183  typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
184 
185  std::ofstream ftmp("Tempus_" + RKMethod_ + "_SinCos_AdjSens.dat");
186  RCP<const SolutionHistory<double> > solutionHistory =
187  integrator->getSolutionHistory();
188  for (int i = 0; i < solutionHistory->getNumStates(); i++) {
189  RCP<const SolutionState<double> > solutionState =
190  (*solutionHistory)[i];
191  const double time_i = solutionState->getTime();
192  RCP<const DPV> x_prod_plot =
193  Teuchos::rcp_dynamic_cast<const DPV>(solutionState->getX());
194  RCP<const Thyra::VectorBase<double> > x_plot =
195  x_prod_plot->getVectorBlock(0);
196  RCP<const DMVPV> adjoint_prod_plot =
197  Teuchos::rcp_dynamic_cast<const DMVPV>(
198  x_prod_plot->getVectorBlock(1));
199  RCP<const Thyra::MultiVectorBase<double> > adjoint_plot =
200  adjoint_prod_plot->getMultiVector();
201  RCP<const Thyra::VectorBase<double> > x_exact_plot =
202  model->getExactSolution(time_i).get_x();
203  ftmp << std::fixed << std::setprecision(7) << time_i << std::setw(11)
204  << get_ele(*(x_plot), 0) << std::setw(11)
205  << get_ele(*(x_plot), 1) << std::setw(11)
206  << get_ele(*(adjoint_plot->col(0)), 0) << std::setw(11)
207  << get_ele(*(adjoint_plot->col(0)), 1) << std::setw(11)
208  << get_ele(*(adjoint_plot->col(1)), 0) << std::setw(11)
209  << get_ele(*(adjoint_plot->col(1)), 1) << std::setw(11)
210  << get_ele(*(x_exact_plot), 0) << std::setw(11)
211  << get_ele(*(x_exact_plot), 1) << std::endl;
212  }
213  ftmp.close();
214  }
215 
216  // Calculate the error
217  RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
218  RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
219  Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
220  Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
221  StepSize.push_back(dt);
222  double L2norm = Thyra::norm_2(*xdiff);
223  L2norm *= L2norm;
224  Teuchos::Array<double> L2norm_DxDp(num_param);
225  Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
226  for (int i = 0; i < num_param; ++i)
227  L2norm += L2norm_DxDp[i] * L2norm_DxDp[i];
228  L2norm = std::sqrt(L2norm);
229  ErrorNorm.push_back(L2norm);
230 
231  // out << " n = " << n << " dt = " << dt << " error = " << L2norm
232  // << std::endl;
233  }
234 
235  if (comm->getRank() == 0) {
236  std::ofstream ftmp("Tempus_" + RKMethod_ + "_SinCos_AdjSens-Error.dat");
237  double error0 = 0.8 * ErrorNorm[0];
238  for (int n = 0; n < (int)StepSize.size(); n++) {
239  ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
240  << error0 * (pow(StepSize[n] / StepSize[0], order)) << std::endl;
241  }
242  ftmp.close();
243  }
244 
245  // if (RKMethods[m] == "SDIRK 5 Stage 4th order") {
246  // StepSize.pop_back(); StepSize.pop_back();
247  // ErrorNorm.pop_back(); ErrorNorm.pop_back();
248  // } else if (RKMethods[m] == "SDIRK 5 Stage 5th order") {
249  // StepSize.pop_back(); StepSize.pop_back(); StepSize.pop_back();
250  // ErrorNorm.pop_back(); ErrorNorm.pop_back(); ErrorNorm.pop_back();
251  // }
252 
253  // Check the order and intercept
254  double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
255  out << " Stepper = " << RKMethods[m] << std::endl;
256  out << " =========================" << std::endl;
257  out << " Expected order: " << order << std::endl;
258  out << " Observed order: " << slope << std::endl;
259  out << " =========================" << std::endl;
260  TEST_FLOATING_EQUALITY(slope, order, 0.03);
261  TEST_FLOATING_EQUALITY(ErrorNorm[0], RKMethodErrors[m], 5.0e-4);
262  }
263  Teuchos::TimeMonitor::summarize();
264 }
265 
266 } // namespace Tempus_Test
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