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Tempus_ExplicitRK_FSA.hpp
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3 // Tempus: Copyright (2017) Sandia Corporation
4 //
5 // Distributed under BSD 3-clause license (See accompanying file Copyright.txt)
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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_IntegratorForwardSensitivity.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 void test_sincos_fsa(const std::string& method_name,
43  const bool use_combined_method,
44  const bool use_dfdp_as_tangent,
45  Teuchos::FancyOStream &out, bool &success)
46 {
47  std::vector<std::string> RKMethods;
48  RKMethods.push_back("RK Forward Euler");
49  RKMethods.push_back("RK Explicit 4 Stage");
50  RKMethods.push_back("RK Explicit 3/8 Rule");
51  RKMethods.push_back("RK Explicit 4 Stage 3rd order by Runge");
52  RKMethods.push_back("RK Explicit 5 Stage 3rd order by Kinnmark and Gray");
53  RKMethods.push_back("RK Explicit 3 Stage 3rd order");
54  RKMethods.push_back("RK Explicit 3 Stage 3rd order TVD");
55  RKMethods.push_back("RK Explicit 3 Stage 3rd order by Heun");
56  RKMethods.push_back("RK Explicit Midpoint");
57  RKMethods.push_back("RK Explicit Trapezoidal");
58  RKMethods.push_back("Heuns Method");
59  RKMethods.push_back("General ERK");
60 
61  // Check that method_name is valid
62  if (method_name != "") {
63  auto it = std::find(RKMethods.begin(), RKMethods.end(), method_name);
64  TEUCHOS_TEST_FOR_EXCEPTION(it == RKMethods.end(), std::logic_error,
65  "Invalid RK method name '" << method_name << "'");
66  }
67 
68  std::vector<double> RKMethodErrors;
69  if (use_combined_method) {
70  RKMethodErrors.push_back(0.183799);
71  RKMethodErrors.push_back(6.88637e-06);
72  RKMethodErrors.push_back(6.88637e-06);
73  RKMethodErrors.push_back(0.000264154);
74  RKMethodErrors.push_back(5.22798e-05);
75  RKMethodErrors.push_back(0.000261896);
76  RKMethodErrors.push_back(0.000261896);
77  RKMethodErrors.push_back(0.000261896);
78  RKMethodErrors.push_back(0.00934377);
79  RKMethodErrors.push_back(0.00934377);
80  RKMethodErrors.push_back(0.00934377);
81  RKMethodErrors.push_back(6.88637e-06);
82  }
83  else {
84  RKMethodErrors.push_back(0.183799);
85  RKMethodErrors.push_back(2.1915e-05);
86  RKMethodErrors.push_back(2.23367e-05);
87  RKMethodErrors.push_back(0.000205051);
88  RKMethodErrors.push_back(2.85141e-05);
89  RKMethodErrors.push_back(0.000126478);
90  RKMethodErrors.push_back(9.64964e-05);
91  RKMethodErrors.push_back(0.000144616);
92  RKMethodErrors.push_back(0.00826159);
93  RKMethodErrors.push_back(0.00710492);
94  RKMethodErrors.push_back(0.00710492);
95  RKMethodErrors.push_back(2.1915e-05);
96  }
97  Teuchos::RCP<const Teuchos::Comm<int> > comm =
98  Teuchos::DefaultComm<int>::getComm();
99  Teuchos::RCP<Teuchos::FancyOStream> my_out =
100  Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
101  my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
102  my_out->setOutputToRootOnly(0);
103 
104  for(std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {
105 
106  // If we were given a method to run, skip this method if it doesn't match
107  if (method_name != "" && RKMethods[m] != method_name)
108  continue;
109 
110  std::string RKMethod_ = RKMethods[m];
111  std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
112  std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
113  std::vector<double> StepSize;
114  std::vector<double> ErrorNorm;
115  const int nTimeStepSizes = 7;
116  double dt = 0.2;
117  double order = 0.0;
118  for (int n=0; n<nTimeStepSizes; n++) {
119 
120  // Read params from .xml file
121  RCP<ParameterList> pList =
122  getParametersFromXmlFile("Tempus_ExplicitRK_SinCos.xml");
123 
124  // Setup the SinCosModel
125  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
126  scm_pl->set("Use DfDp as Tangent", use_dfdp_as_tangent);
127  RCP<SinCosModel<double> > model =
128  Teuchos::rcp(new SinCosModel<double>(scm_pl));
129 
130  // Set the Stepper
131  RCP<ParameterList> pl = sublist(pList, "Tempus", true);
132  if (RKMethods[m] == "General ERK") {
133  pl->sublist("Demo Integrator").set("Stepper Name", "Demo Stepper 2");
134  } else {
135  pl->sublist("Demo Stepper").set("Stepper Type", RKMethods[m]);
136  }
137 
138 
139  dt /= 2;
140 
141  // Setup sensitivities
142  ParameterList& sens_pl = pl->sublist("Sensitivities");
143  if (use_combined_method)
144  sens_pl.set("Sensitivity Method", "Combined");
145  else
146  sens_pl.set("Sensitivity Method", "Staggered");
147  sens_pl.set("Use DfDp as Tangent", use_dfdp_as_tangent);
148  ParameterList& interp_pl =
149  pl->sublist("Demo Integrator").sublist("Solution History").sublist("Interpolator");
150  interp_pl.set("Interpolator Type", "Lagrange");
151  interp_pl.set("Order", 3); // All RK methods here are at most 4th order
152 
153  // Setup the Integrator and reset initial time step
154  pl->sublist("Demo Integrator")
155  .sublist("Time Step Control").set("Initial Time Step", dt);
156  RCP<Tempus::IntegratorForwardSensitivity<double> > integrator =
157  Tempus::integratorForwardSensitivity<double>(pl, model);
158  order = integrator->getStepper()->getOrder();
159 
160  // Initial Conditions
161  double t0 = pl->sublist("Demo Integrator")
162  .sublist("Time Step Control").get<double>("Initial Time");
163  // RCP<const Thyra::VectorBase<double> > x0 =
164  // model->getExactSolution(t0).get_x()->clone_v();
165  RCP<Thyra::VectorBase<double> > x0 =
166  model->getNominalValues().get_x()->clone_v();
167  const int num_param = model->get_p_space(0)->dim();
168  RCP<Thyra::MultiVectorBase<double> > DxDp0 =
169  Thyra::createMembers(model->get_x_space(), num_param);
170  for (int i=0; i<num_param; ++i)
171  Thyra::assign(DxDp0->col(i).ptr(),
172  *(model->getExactSensSolution(i, t0).get_x()));
173  integrator->initializeSolutionHistory(t0, x0, Teuchos::null, Teuchos::null,
174  DxDp0, Teuchos::null, Teuchos::null);
175 
176  // Integrate to timeMax
177  bool integratorStatus = integrator->advanceTime();
178  TEST_ASSERT(integratorStatus)
179 
180  // Test if at 'Final Time'
181  double time = integrator->getTime();
182  double timeFinal = pl->sublist("Demo Integrator")
183  .sublist("Time Step Control").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(Teuchos::Range1D(1,num_param));
216  RCP<const Thyra::VectorBase<double> > x_exact_plot =
217  model->getExactSolution(time_i).get_x();
218  for (int j=0; j<num_param; ++j)
219  Thyra::assign(DxDp_exact_plot->col(j).ptr(),
220  *(model->getExactSensSolution(j, time_i).get_x()));
221  ftmp << std::fixed << std::setprecision(7)
222  << time_i
223  << std::setw(11) << get_ele(*(x_plot), 0)
224  << std::setw(11) << 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)
229  << std::setw(11) << 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  *my_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  *my_out << " Stepper = " << RKMethods[m] << std::endl;
260  *my_out << " =========================" << std::endl;
261  *my_out << " Expected order: " << order << std::endl;
262  *my_out << " Observed order: " << slope << std::endl;
263  *my_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
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)
Definition: Tempus_BackwardEuler_FSA.hpp:48
Tempus::SolutionHistory
SolutionHistory is basically a container of SolutionStates. SolutionHistory maintains a collection of...
Definition: Tempus_Integrator.hpp:25
method_name
std::string method_name
Definition: Tempus_DIRK_Combined_FSA.cpp:15
Tempus::SolutionState
Solution state for integrators and steppers. SolutionState contains the metadata for solutions and th...
Definition: Tempus_SolutionState_decl.hpp:56