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Tempus_DIRK_ASA.cpp
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2 // ****************************************************************************
3 // Tempus: Copyright (2017) Sandia Corporation
4 //
5 // Distributed under BSD 3-clause license (See accompanying file Copyright.txt)
6 // ****************************************************************************
7 // @HEADER
8 
9 #include "Teuchos_UnitTestHarness.hpp"
10 #include "Teuchos_XMLParameterListHelpers.hpp"
11 #include "Teuchos_TimeMonitor.hpp"
12 #include "Teuchos_DefaultComm.hpp"
13 
14 #include "Thyra_VectorStdOps.hpp"
15 #include "Thyra_MultiVectorStdOps.hpp"
16 
17 #include "Tempus_IntegratorBasic.hpp"
18 #include "Tempus_IntegratorAdjointSensitivity.hpp"
19 
20 #include "Thyra_DefaultMultiVectorProductVector.hpp"
21 #include "Thyra_DefaultProductVector.hpp"
22 
23 #include "../TestModels/SinCosModel.hpp"
24 #include "../TestUtils/Tempus_ConvergenceTestUtils.hpp"
25 
26 #include <fstream>
27 #include <vector>
28 
29 namespace Tempus_Test {
30 
31 using Teuchos::RCP;
32 using Teuchos::ParameterList;
33 using Teuchos::sublist;
34 using Teuchos::getParametersFromXmlFile;
35 
36 using Tempus::IntegratorBasic;
37 using Tempus::SolutionHistory;
38 using Tempus::SolutionState;
39 
40 // ************************************************************
41 // ************************************************************
42 TEUCHOS_UNIT_TEST(DIRK, SinCos_ASA)
43 {
44  std::vector<std::string> RKMethods;
45  RKMethods.push_back("General DIRK");
46  RKMethods.push_back("RK Backward Euler");
47  RKMethods.push_back("DIRK 1 Stage Theta Method");
48  RKMethods.push_back("RK Implicit 1 Stage 1st order Radau IA");
49  RKMethods.push_back("SDIRK 2 Stage 2nd order");
50  RKMethods.push_back("RK Implicit 2 Stage 2nd order Lobatto IIIB");
51  RKMethods.push_back("SDIRK 2 Stage 3rd order");
52  RKMethods.push_back("EDIRK 2 Stage 3rd order");
53  RKMethods.push_back("EDIRK 2 Stage Theta Method");
54  RKMethods.push_back("SDIRK 3 Stage 4th order");
55  RKMethods.push_back("SDIRK 5 Stage 4th order");
56  RKMethods.push_back("SDIRK 5 Stage 5th order");
57 
58  std::vector<double> RKMethodErrors;
59  RKMethodErrors.push_back(8.48235e-05);
60  RKMethodErrors.push_back(0.0383339);
61  RKMethodErrors.push_back(0.000221028);
62  RKMethodErrors.push_back(0.0428449);
63  RKMethodErrors.push_back(8.48235e-05);
64  RKMethodErrors.push_back(0.000297933);
65  RKMethodErrors.push_back(4.87848e-06);
66  RKMethodErrors.push_back(7.30827e-07);
67  RKMethodErrors.push_back(0.000272997);
68  RKMethodErrors.push_back(3.10132e-07);
69  RKMethodErrors.push_back(7.56838e-10);
70  RKMethodErrors.push_back(1.32374e-10);
71 
72  Teuchos::RCP<const Teuchos::Comm<int> > comm =
73  Teuchos::DefaultComm<int>::getComm();
74  Teuchos::RCP<Teuchos::FancyOStream> my_out =
75  Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
76  my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
77  my_out->setOutputToRootOnly(0);
78 
79  for(std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {
80 
81  std::string RKMethod_ = RKMethods[m];
82  std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
83  std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
84  std::vector<double> StepSize;
85  std::vector<double> ErrorNorm;
86  const int nTimeStepSizes = 3; // 7 for error plots
87  double dt = 0.05;
88  double order = 0.0;
89  for (int n=0; n<nTimeStepSizes; n++) {
90 
91  // Read params from .xml file
92  RCP<ParameterList> pList =
93  getParametersFromXmlFile("Tempus_DIRK_SinCos.xml");
94 
95  // Setup the SinCosModel
96  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
97  RCP<SinCosModel<double> > model =
98  Teuchos::rcp(new SinCosModel<double>(scm_pl));
99 
100  // Set the Stepper
101  RCP<ParameterList> pl = sublist(pList, "Tempus", true);
102  pl->sublist("Default Stepper").set("Stepper Type", RKMethods[m]);
103  if (RKMethods[m] == "DIRK 1 Stage Theta Method" ||
104  RKMethods[m] == "EDIRK 2 Stage Theta Method") {
105  pl->sublist("Default Stepper").set<double>("theta", 0.5);
106  } else if (RKMethods[m] == "SDIRK 2 Stage 2nd order") {
107  pl->sublist("Default Stepper").set("gamma", 0.2928932188134524);
108  } else if (RKMethods[m] == "SDIRK 2 Stage 3rd order") {
109  pl->sublist("Default Stepper")
110  .set<std::string>("Gamma Type", "3rd Order A-stable");
111  }
112 
113  dt /= 2;
114 
115  // Setup sensitivities
116  ParameterList& sens_pl = pl->sublist("Sensitivities");
117  sens_pl.set("Mass Matrix Is Identity", true); // Necessary for explicit
118  ParameterList& interp_pl =
119  pl->sublist("Default Integrator").sublist("Solution History").sublist("Interpolator");
120  interp_pl.set("Interpolator Type", "Lagrange");
121  interp_pl.set("Order", 4); // All RK methods here are at most 5th order
122 
123  // Setup the Integrator and reset initial time step
124  pl->sublist("Default Integrator")
125  .sublist("Time Step Control").set("Initial Time Step", dt);
126  RCP<Tempus::IntegratorAdjointSensitivity<double> > integrator =
127  Tempus::integratorAdjointSensitivity<double>(pl, model);
128  order = integrator->getStepper()->getOrder();
129 
130  // Initial Conditions
131  // During the Integrator construction, the initial SolutionState
132  // is set by default to model->getNominalVales().get_x(). However,
133  // the application can set it also by 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, Teuchos::null,
143  DxDp0, Teuchos::null, Teuchos::null);
144 
145  // Integrate to timeMax
146  bool integratorStatus = integrator->advanceTime();
147  TEST_ASSERT(integratorStatus)
148 
149  // Test if at 'Final Time'
150  double time = integrator->getTime();
151  double timeFinal = pl->sublist("Default Integrator")
152  .sublist("Time Step Control").get<double>("Final Time");
153  double tol = 100.0 * std::numeric_limits<double>::epsilon();
154  TEST_FLOATING_EQUALITY(time, timeFinal, tol);
155 
156  // Time-integrated solution and the exact solution along with
157  // sensitivities (relying on response g(x) = x). Note we must transpose
158  // dg/dp since the integrator returns it in gradient form.
159  RCP<const Thyra::VectorBase<double> > x = integrator->getX();
160  RCP<const Thyra::MultiVectorBase<double> > DgDp = integrator->getDgDp();
161  RCP<Thyra::MultiVectorBase<double> > DxDp =
162  Thyra::createMembers(model->get_x_space(), num_param);
163  {
164  Thyra::ConstDetachedMultiVectorView<double> dgdp_view(*DgDp);
165  Thyra::DetachedMultiVectorView<double> dxdp_view(*DxDp);
166  const int num_g = DgDp->domain()->dim();
167  for (int i=0; i<num_g; ++i)
168  for (int j=0; j<num_param; ++j)
169  dxdp_view(i,j) = dgdp_view(j,i);
170  }
171  RCP<const Thyra::VectorBase<double> > x_exact =
172  model->getExactSolution(time).get_x();
173  RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
174  Thyra::createMembers(model->get_x_space(), num_param);
175  for (int i=0; i<num_param; ++i)
176  Thyra::assign(DxDp_exact->col(i).ptr(),
177  *(model->getExactSensSolution(i, time).get_x()));
178 
179  // Plot sample solution and exact solution
180  if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
181  typedef Thyra::DefaultProductVector<double> DPV;
182  typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
183 
184  std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_AdjSens.dat");
185  RCP<const SolutionHistory<double> > solutionHistory =
186  integrator->getSolutionHistory();
187  for (int i=0; i<solutionHistory->getNumStates(); i++) {
188  RCP<const SolutionState<double> > solutionState =
189  (*solutionHistory)[i];
190  const double time_i = solutionState->getTime();
191  RCP<const DPV> x_prod_plot =
192  Teuchos::rcp_dynamic_cast<const DPV>(solutionState->getX());
193  RCP<const Thyra::VectorBase<double> > x_plot =
194  x_prod_plot->getVectorBlock(0);
195  RCP<const DMVPV > adjoint_prod_plot =
196  Teuchos::rcp_dynamic_cast<const DMVPV>(x_prod_plot->getVectorBlock(1));
197  RCP<const Thyra::MultiVectorBase<double> > adjoint_plot =
198  adjoint_prod_plot->getMultiVector();
199  RCP<const Thyra::VectorBase<double> > x_exact_plot =
200  model->getExactSolution(time_i).get_x();
201  ftmp << std::fixed << std::setprecision(7)
202  << time_i
203  << std::setw(11) << get_ele(*(x_plot), 0)
204  << std::setw(11) << get_ele(*(x_plot), 1)
205  << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 0)
206  << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 1)
207  << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 0)
208  << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 1)
209  << std::setw(11) << get_ele(*(x_exact_plot), 0)
210  << std::setw(11) << get_ele(*(x_exact_plot), 1)
211  << 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  //*my_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  *my_out << " Stepper = " << RKMethods[m] << std::endl;
256  *my_out << " =========================" << std::endl;
257  *my_out << " Expected order: " << order << std::endl;
258  *my_out << " Observed order: " << slope << std::endl;
259  *my_out << " =========================" << std::endl;
260  TEST_FLOATING_EQUALITY( slope, order, 0.03 );
261  TEST_FLOATING_EQUALITY( ErrorNorm[0], RKMethodErrors[m], 5.0e-4 );
262 
263  }
264  Teuchos::TimeMonitor::summarize();
265 }
266 
267 } // namespace Tempus_Test
Tempus_Test::SinCosModel
Sine-Cosine model problem from Rythmos. This is a canonical Sine-Cosine differential equation with a...
Definition: SinCosModel_decl.hpp:91
Tempus_Test::TEUCHOS_UNIT_TEST
TEUCHOS_UNIT_TEST(BackwardEuler, SinCos_ASA)
Definition: Tempus_BackwardEuler_ASA.cpp:47
Tempus::SolutionHistory
SolutionHistory is basically a container of SolutionStates. SolutionHistory maintains a collection of...
Definition: Tempus_Integrator.hpp:25
Tempus::SolutionState
Solution state for integrators and steppers. SolutionState contains the metadata for solutions and th...
Definition: Tempus_SolutionState_decl.hpp:56