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Tempus_ExplicitRK_ASA.cpp
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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_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(ExplicitRK, SinCos_ASA)
43 {
44  std::vector<std::string> RKMethods;
45  RKMethods.push_back("RK Forward Euler");
46  RKMethods.push_back("RK Explicit 4 Stage");
47  RKMethods.push_back("RK Explicit 3/8 Rule");
48  RKMethods.push_back("RK Explicit 4 Stage 3rd order by Runge");
49  RKMethods.push_back("RK Explicit 5 Stage 3rd order by Kinnmark and Gray");
50  RKMethods.push_back("RK Explicit 3 Stage 3rd order");
51  RKMethods.push_back("RK Explicit 3 Stage 3rd order TVD");
52  RKMethods.push_back("RK Explicit 3 Stage 3rd order by Heun");
53  RKMethods.push_back("RK Explicit Midpoint");
54  RKMethods.push_back("RK Explicit Trapezoidal");
55  RKMethods.push_back("Heuns Method");
56  RKMethods.push_back("General ERK");
57 
58  std::vector<double> RKMethodErrors;
59  RKMethodErrors.push_back(0.154904);
60  RKMethodErrors.push_back(4.55982e-06);
61  RKMethodErrors.push_back(4.79132e-06);
62  RKMethodErrors.push_back(0.000113603);
63  RKMethodErrors.push_back(4.98796e-05);
64  RKMethodErrors.push_back(0.00014564);
65  RKMethodErrors.push_back(0.000121968);
66  RKMethodErrors.push_back(0.000109495);
67  RKMethodErrors.push_back(0.00559871);
68  RKMethodErrors.push_back(0.00710492);
69  RKMethodErrors.push_back(0.00710492);
70  RKMethodErrors.push_back(4.55982e-06);
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 = 7;
87  double dt = 0.2;
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_ExplicitRK_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  if (RKMethods[m] == "General ERK") {
103  pl->sublist("Demo Integrator").set("Stepper Name", "Demo Stepper 2");
104  pl->sublist("Demo Stepper 2").set("Initial Condition Consistency",
105  "None");
106  pl->sublist("Demo Stepper 2").set("Initial Condition Consistency Check",
107  false);
108  } else {
109  pl->sublist("Demo Stepper").set("Stepper Type", RKMethods[m]);
110  pl->sublist("Demo Stepper").set("Initial Condition Consistency",
111  "None");
112  pl->sublist("Demo Stepper").set("Initial Condition Consistency Check",
113  false);
114  }
115 
116 
117  dt /= 2;
118 
119  // Setup sensitivities
120  ParameterList& sens_pl = pl->sublist("Sensitivities");
121  sens_pl.set("Mass Matrix Is Identity", true); // Necessary for explicit
122  ParameterList& interp_pl =
123  pl->sublist("Demo Integrator").sublist("Solution History").sublist("Interpolator");
124  interp_pl.set("Interpolator Type", "Lagrange");
125  interp_pl.set("Order", 3); // All RK methods here are at most 4th order
126 
127  // Setup the Integrator and reset initial time step
128  pl->sublist("Demo Integrator")
129  .sublist("Time Step Control").set("Initial Time Step", dt);
130  RCP<Tempus::IntegratorAdjointSensitivity<double> > integrator =
131  Tempus::integratorAdjointSensitivity<double>(pl, model);
132  order = integrator->getStepper()->getOrder();
133 
134  // Initial Conditions
135  double t0 = pl->sublist("Demo Integrator")
136  .sublist("Time Step Control").get<double>("Initial Time");
137  // RCP<const Thyra::VectorBase<double> > x0 =
138  // model->getExactSolution(t0).get_x()->clone_v();
139  RCP<Thyra::VectorBase<double> > x0 =
140  model->getNominalValues().get_x()->clone_v();
141  const int num_param = model->get_p_space(0)->dim();
142  RCP<Thyra::MultiVectorBase<double> > DxDp0 =
143  Thyra::createMembers(model->get_x_space(), num_param);
144  for (int i=0; i<num_param; ++i)
145  Thyra::assign(DxDp0->col(i).ptr(),
146  *(model->getExactSensSolution(i, t0).get_x()));
147  integrator->initializeSolutionHistory(t0, x0, Teuchos::null, Teuchos::null,
148  DxDp0, Teuchos::null, Teuchos::null);
149 
150  // Integrate to timeMax
151  bool integratorStatus = integrator->advanceTime();
152  TEST_ASSERT(integratorStatus)
153 
154  // Test if at 'Final Time'
155  double time = integrator->getTime();
156  double timeFinal = pl->sublist("Demo Integrator")
157  .sublist("Time Step Control").get<double>("Final Time");
158  TEST_FLOATING_EQUALITY(time, timeFinal, 1.0e-14);
159 
160  // Time-integrated solution and the exact solution along with
161  // sensitivities (relying on response g(x) = x). Note we must transpose
162  // dg/dp since the integrator returns it in gradient form.
163  RCP<const Thyra::VectorBase<double> > x = integrator->getX();
164  RCP<const Thyra::MultiVectorBase<double> > DgDp = integrator->getDgDp();
165  RCP<Thyra::MultiVectorBase<double> > DxDp =
166  Thyra::createMembers(model->get_x_space(), num_param);
167  {
168  Thyra::ConstDetachedMultiVectorView<double> dgdp_view(*DgDp);
169  Thyra::DetachedMultiVectorView<double> dxdp_view(*DxDp);
170  const int num_g = DgDp->domain()->dim();
171  for (int i=0; i<num_g; ++i)
172  for (int j=0; j<num_param; ++j)
173  dxdp_view(i,j) = dgdp_view(j,i);
174  }
175  RCP<const Thyra::VectorBase<double> > x_exact =
176  model->getExactSolution(time).get_x();
177  RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
178  Thyra::createMembers(model->get_x_space(), num_param);
179  for (int i=0; i<num_param; ++i)
180  Thyra::assign(DxDp_exact->col(i).ptr(),
181  *(model->getExactSensSolution(i, time).get_x()));
182 
183  // Plot sample solution, exact solution, and adjoint solution
184  if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
185  typedef Thyra::DefaultProductVector<double> DPV;
186  typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
187 
188  std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_AdjSens.dat");
189  RCP<const SolutionHistory<double> > solutionHistory =
190  integrator->getSolutionHistory();
191  for (int i=0; i<solutionHistory->getNumStates(); i++) {
192  RCP<const SolutionState<double> > solutionState =
193  (*solutionHistory)[i];
194  const double time_i = solutionState->getTime();
195  RCP<const DPV> x_prod_plot =
196  Teuchos::rcp_dynamic_cast<const DPV>(solutionState->getX());
197  RCP<const Thyra::VectorBase<double> > x_plot =
198  x_prod_plot->getVectorBlock(0);
199  RCP<const DMVPV > adjoint_prod_plot =
200  Teuchos::rcp_dynamic_cast<const DMVPV>(x_prod_plot->getVectorBlock(1));
201  RCP<const Thyra::MultiVectorBase<double> > adjoint_plot =
202  adjoint_prod_plot->getMultiVector();
203  RCP<const Thyra::VectorBase<double> > x_exact_plot =
204  model->getExactSolution(time_i).get_x();
205  ftmp << std::fixed << std::setprecision(7)
206  << time_i
207  << std::setw(11) << get_ele(*(x_plot), 0)
208  << std::setw(11) << get_ele(*(x_plot), 1)
209  << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 0)
210  << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 1)
211  << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 0)
212  << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 1)
213  << std::setw(11) << get_ele(*(x_exact_plot), 0)
214  << std::setw(11) << get_ele(*(x_exact_plot), 1)
215  << std::endl;
216  }
217  ftmp.close();
218  }
219 
220  // Calculate the error
221  RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
222  RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
223  Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
224  Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
225  StepSize.push_back(dt);
226  double L2norm = Thyra::norm_2(*xdiff);
227  L2norm *= L2norm;
228  Teuchos::Array<double> L2norm_DxDp(num_param);
229  Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
230  for (int i=0; i<num_param; ++i)
231  L2norm += L2norm_DxDp[i]*L2norm_DxDp[i];
232  L2norm = std::sqrt(L2norm);
233  ErrorNorm.push_back(L2norm);
234 
235  //*my_out << " n = " << n << " dt = " << dt << " error = " << L2norm
236  // << std::endl;
237  }
238 
239  // Check the order and intercept
240  double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
241  *my_out << " Stepper = " << RKMethods[m] << std::endl;
242  *my_out << " =========================" << std::endl;
243  *my_out << " Expected order: " << order << std::endl;
244  *my_out << " Observed order: " << slope << std::endl;
245  *my_out << " =========================" << std::endl;
246  TEST_FLOATING_EQUALITY( slope, order, 0.015 );
247  TEST_FLOATING_EQUALITY( ErrorNorm[0], RKMethodErrors[m], 1.0e-4 );
248 
249  if (comm->getRank() == 0) {
250  std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_AdjSens-Error.dat");
251  double error0 = 0.8*ErrorNorm[0];
252  for (int n=0; n<nTimeStepSizes; n++) {
253  ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
254  << error0*(pow(StepSize[n]/StepSize[0],order)) << std::endl;
255  }
256  ftmp.close();
257  }
258  }
259 
260  Teuchos::TimeMonitor::summarize();
261 }
262 
263 } // 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