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Tempus_BackwardEuler_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 "Tempus_config.hpp"
15 #include "Tempus_IntegratorBasic.hpp"
16 #include "Tempus_IntegratorAdjointSensitivity.hpp"
17 
18 #include "Thyra_VectorStdOps.hpp"
19 #include "Thyra_MultiVectorStdOps.hpp"
20 
21 #include "../TestModels/SinCosModel.hpp"
22 #include "../TestUtils/Tempus_ConvergenceTestUtils.hpp"
23 
24 #include "Stratimikos_DefaultLinearSolverBuilder.hpp"
25 #include "Thyra_LinearOpWithSolveFactoryHelpers.hpp"
26 #include "Thyra_DefaultMultiVectorProductVector.hpp"
27 #include "Thyra_DefaultProductVector.hpp"
28 
29 #include <vector>
30 #include <fstream>
31 #include <sstream>
32 #include <limits>
33 
34 namespace Tempus_Test {
35 
36 using Teuchos::RCP;
37 using Teuchos::ParameterList;
38 using Teuchos::sublist;
39 using Teuchos::getParametersFromXmlFile;
40 
44 
45 // ************************************************************
46 // ************************************************************
47 TEUCHOS_UNIT_TEST(BackwardEuler, SinCos_ASA)
48 {
49  std::vector<double> StepSize;
50  std::vector<double> ErrorNorm;
51  const int nTimeStepSizes = 7;
52  double dt = 0.2;
53  double order = 0.0;
54  Teuchos::RCP<const Teuchos::Comm<int> > comm =
55  Teuchos::DefaultComm<int>::getComm();
56  Teuchos::RCP<Teuchos::FancyOStream> my_out =
57  Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
58  my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
59  my_out->setOutputToRootOnly(0);
60  for (int n=0; n<nTimeStepSizes; n++) {
61 
62  // Read params from .xml file
63  RCP<ParameterList> pList =
64  getParametersFromXmlFile("Tempus_BackwardEuler_SinCos.xml");
65 
66  // Setup the SinCosModel
67  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
68  RCP<SinCosModel<double> > model =
69  Teuchos::rcp(new SinCosModel<double>(scm_pl));
70 
71  dt /= 2;
72 
73  // Setup sensitivities
74  RCP<ParameterList> pl = sublist(pList, "Tempus", true);
75  ParameterList& sens_pl = pl->sublist("Sensitivities");
76  sens_pl.set("Mass Matrix Is Identity", false); // Just for testing
77  ParameterList& interp_pl =
78  pl->sublist("Default Integrator").sublist("Solution History").sublist("Interpolator");
79  interp_pl.set("Interpolator Type", "Lagrange");
80  interp_pl.set("Order", 0);
81 
82  // Set FSAL to false, because it is not currently setup for ASA.
83  pl->sublist("Default Stepper").set("Use FSAL", false);
84 
85  // Set IC consistency check to false, because it is not currently
86  // setup for ASA.
87  pl->sublist("Default Stepper")
88  .set("Initial Condition Consistency Check", false);
89 
90  // Setup the Integrator and reset initial time step
91  pl->sublist("Default Integrator")
92  .sublist("Time Step Control").set("Initial Time Step", dt);
93  RCP<Tempus::IntegratorAdjointSensitivity<double> > integrator =
94  Tempus::integratorAdjointSensitivity<double>(pl, model);
95  order = integrator->getStepper()->getOrder();
96 
97  // Initial Conditions
98  double t0 = pl->sublist("Default Integrator")
99  .sublist("Time Step Control").get<double>("Initial Time");
100  RCP<const Thyra::VectorBase<double> > x0 =
101  model->getExactSolution(t0).get_x();
102  const int num_param = model->get_p_space(0)->dim();
103  RCP<Thyra::MultiVectorBase<double> > DxDp0 =
104  Thyra::createMembers(model->get_x_space(), num_param);
105  for (int i=0; i<num_param; ++i)
106  Thyra::assign(DxDp0->col(i).ptr(),
107  *(model->getExactSensSolution(i, t0).get_x()));
108  integrator->initializeSolutionHistory(t0, x0, Teuchos::null, Teuchos::null,
109  DxDp0, Teuchos::null, Teuchos::null);
110 
111  // Integrate to timeMax
112  bool integratorStatus = integrator->advanceTime();
113  TEST_ASSERT(integratorStatus)
114 
115  // Test if at 'Final Time'
116  double time = integrator->getTime();
117  double timeFinal =pl->sublist("Default Integrator")
118  .sublist("Time Step Control").get<double>("Final Time");
119  TEST_FLOATING_EQUALITY(time, timeFinal, 1.0e-14);
120 
121  // Time-integrated solution and the exact solution along with
122  // sensitivities (relying on response g(x) = x). Note we must transpose
123  // dg/dp since the integrator returns it in gradient form.
124  RCP<const Thyra::VectorBase<double> > x = integrator->getX();
125  RCP<const Thyra::MultiVectorBase<double> > DgDp = integrator->getDgDp();
126  RCP<Thyra::MultiVectorBase<double> > DxDp =
127  Thyra::createMembers(model->get_x_space(), num_param);
128  {
129  Thyra::ConstDetachedMultiVectorView<double> dgdp_view(*DgDp);
130  Thyra::DetachedMultiVectorView<double> dxdp_view(*DxDp);
131  const int num_g = DgDp->domain()->dim();
132  for (int i=0; i<num_g; ++i)
133  for (int j=0; j<num_param; ++j)
134  dxdp_view(i,j) = dgdp_view(j,i);
135  }
136  RCP<const Thyra::VectorBase<double> > x_exact =
137  model->getExactSolution(time).get_x();
138  RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
139  Thyra::createMembers(model->get_x_space(), num_param);
140  for (int i=0; i<num_param; ++i)
141  Thyra::assign(DxDp_exact->col(i).ptr(),
142  *(model->getExactSensSolution(i, time).get_x()));
143 
144  // Plot sample solution, exact solution, and adjoint solution
145  if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
146  typedef Thyra::DefaultProductVector<double> DPV;
147  typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
148 
149  std::ofstream ftmp("Tempus_BackwardEuler_SinCos_AdjSens.dat");
150  RCP<const SolutionHistory<double> > solutionHistory =
151  integrator->getSolutionHistory();
152  for (int i=0; i<solutionHistory->getNumStates(); i++) {
153  RCP<const SolutionState<double> > solutionState = (*solutionHistory)[i];
154  const double time_i = solutionState->getTime();
155  RCP<const DPV> x_prod_plot =
156  Teuchos::rcp_dynamic_cast<const DPV>(solutionState->getX());
157  RCP<const Thyra::VectorBase<double> > x_plot =
158  x_prod_plot->getVectorBlock(0);
159  RCP<const DMVPV > adjoint_prod_plot =
160  Teuchos::rcp_dynamic_cast<const DMVPV>(x_prod_plot->getVectorBlock(1));
161  RCP<const Thyra::MultiVectorBase<double> > adjoint_plot =
162  adjoint_prod_plot->getMultiVector();
163  RCP<const Thyra::VectorBase<double> > x_exact_plot =
164  model->getExactSolution(time_i).get_x();
165  ftmp << std::fixed << std::setprecision(7)
166  << time_i
167  << std::setw(11) << get_ele(*(x_plot), 0)
168  << std::setw(11) << get_ele(*(x_plot), 1)
169  << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 0)
170  << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 1)
171  << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 0)
172  << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 1)
173  << std::setw(11) << get_ele(*(x_exact_plot), 0)
174  << std::setw(11) << get_ele(*(x_exact_plot), 1)
175  << std::endl;
176  }
177  ftmp.close();
178  }
179 
180  // Calculate the error
181  RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
182  RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
183  Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
184  Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
185  StepSize.push_back(dt);
186  double L2norm = Thyra::norm_2(*xdiff);
187  L2norm *= L2norm;
188  Teuchos::Array<double> L2norm_DxDp(num_param);
189  Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
190  for (int i=0; i<num_param; ++i)
191  L2norm += L2norm_DxDp[i]*L2norm_DxDp[i];
192  L2norm = std::sqrt(L2norm);
193  ErrorNorm.push_back(L2norm);
194 
195  *my_out << " n = " << n << " dt = " << dt << " error = " << L2norm
196  << std::endl;
197 
198  }
199 
200  // Check the order and intercept
201  double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
202  *my_out << " Stepper = BackwardEuler" << std::endl;
203  *my_out << " =========================" << std::endl;
204  *my_out << " Expected order: " << order << std::endl;
205  *my_out << " Observed order: " << slope << std::endl;
206  *my_out << " =========================" << std::endl;
207  TEST_FLOATING_EQUALITY( slope, order, 0.015 );
208  TEST_FLOATING_EQUALITY( ErrorNorm[0], 0.151746, 1.0e-4 );
209 
210  if (comm->getRank() == 0) {
211  std::ofstream ftmp("Tempus_BackwardEuler_SinCos_AdjSens-Error.dat");
212  double error0 = 0.8*ErrorNorm[0];
213  for (int n=0; n<nTimeStepSizes; n++) {
214  ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
215  << error0*(StepSize[n]/StepSize[0]) << std::endl;
216  }
217  ftmp.close();
218  }
219 
220 }
221 
222 } // namespace Tempus_Test
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TEUCHOS_UNIT_TEST(BackwardEuler, SinCos_ASA)
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