Tempus_UnitTest_RK_Utils.hpp

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//@HEADER
// *****************************************************************************
//          Tempus: Time Integration and Sensitivity Analysis Package
//
// Copyright 2017 NTESS and the Tempus contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
//@HEADER
 
#ifndef Tempus_UnitTest_RK_Utils_hpp
#define Tempus_UnitTest_RK_Utils_hpp
 
#include "Tempus_UnitTest_Utils.hpp"
 
#include "Tempus_StepperRKButcherTableau.hpp"
 
#include "Tempus_StepperIMEX_RK.hpp"
#include "Tempus_StepperIMEX_RK_Partition.hpp"
 
#include "Tempus_StepperRKModifierBase.hpp"
#include "Tempus_StepperRKModifierXBase.hpp"
#include "Tempus_StepperRKObserverBase.hpp"
#include "Tempus_StepperRKModifierDefault.hpp"
#include "Tempus_StepperRKModifierXDefault.hpp"
#include "Tempus_StepperRKObserverDefault.hpp"
#include "Tempus_StepperRKAppActionComposite.hpp"
 
namespace Tempus_Unit_Test {
 
using Teuchos::ParameterList;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::rcp_const_cast;
using Teuchos::rcp_dynamic_cast;
 
using Tempus::StepperFactory;
 
void testExplicitRKAccessorsFullConstruction(
    const RCP<Tempus::StepperExplicitRK<double>>& stepper)
{
  auto model = rcp(new Tempus_Test::SinCosModel<double>());
  stepper->setModel(model);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
 
  // Default values for construction.
  auto modifier             = rcp(new Tempus::StepperRKModifierDefault<double>());
  auto modifierX            = rcp(new Tempus::StepperRKModifierXDefault<double>());
  auto observer             = rcp(new Tempus::StepperRKObserverDefault<double>());
  bool useFSAL              = stepper->getUseFSAL();
  std::string ICConsistency = stepper->getICConsistency();
  bool ICConsistencyCheck   = stepper->getICConsistencyCheck();
  bool useEmbedded          = stepper->getUseEmbedded();
 
  // Test the set functions.
  stepper->setAppAction(modifier);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setAppAction(modifierX);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setAppAction(observer);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setUseFSAL(useFSAL);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setICConsistency(ICConsistency);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setICConsistencyCheck(ICConsistencyCheck);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setUseEmbedded(useEmbedded);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
 
  std::string stepperType = stepper->getStepperType();
  // Full argument list construction.
  if (stepperType == "RK Explicit 3 Stage 3rd order") {
    auto s = rcp(new Tempus::StepperERK_3Stage3rdOrder<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Explicit 3 Stage 3rd order by Heun") {
    auto s = rcp(new Tempus::StepperERK_3Stage3rdOrderHeun<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Explicit 3 Stage 3rd order TVD") {
    auto s = rcp(new Tempus::StepperERK_3Stage3rdOrderTVD<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Explicit 3/8 Rule") {
    auto s = rcp(new Tempus::StepperERK_3_8Rule<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Explicit 4 Stage 3rd order by Runge") {
    auto s = rcp(new Tempus::StepperERK_4Stage3rdOrderRunge<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Explicit 4 Stage") {
    auto s = rcp(new Tempus::StepperERK_4Stage4thOrder<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType ==
           "RK Explicit 5 Stage 3rd order by Kinnmark and Gray") {
    auto s = rcp(new Tempus::StepperERK_5Stage3rdOrderKandG<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "Bogacki-Shampine 3(2) Pair") {
    auto s = rcp(new Tempus::StepperERK_BogackiShampine32<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Forward Euler") {
    auto s = rcp(new Tempus::StepperERK_ForwardEuler<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "Merson 4(5) Pair") {
    auto s = rcp(new Tempus::StepperERK_Merson45<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Explicit Midpoint") {
    auto s = rcp(new Tempus::StepperERK_Midpoint<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Explicit Trapezoidal") {
    auto s = rcp(new Tempus::StepperERK_Trapezoidal<double>(
        model, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else
    TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
                               "Error - unknown stepperType = " + stepperType);
}
 
void testDIRKAccessorsFullConstruction(
    const RCP<Tempus::StepperDIRK<double>>& stepper)
{
  auto model = rcp(new Tempus_Test::SinCosModel<double>());
  stepper->setModel(model);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
 
  // Default values for construction.
  auto modifier  = rcp(new Tempus::StepperRKModifierDefault<double>());
  auto modifierX = rcp(new Tempus::StepperRKModifierXDefault<double>());
  auto observer  = rcp(new Tempus::StepperRKObserverDefault<double>());
  auto solver    = rcp(new Thyra::NOXNonlinearSolver());
  solver->setParameterList(Tempus::defaultSolverParameters());
 
  bool useFSAL              = stepper->getUseFSAL();
  std::string ICConsistency = stepper->getICConsistency();
  bool ICConsistencyCheck   = stepper->getICConsistencyCheck();
  bool useEmbedded          = stepper->getUseEmbedded();
  bool zeroInitialGuess     = stepper->getZeroInitialGuess();
 
  // Test the set functions.
  stepper->setAppAction(modifierX);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setAppAction(observer);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setSolver(solver);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setUseFSAL(useFSAL);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setICConsistency(ICConsistency);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setICConsistencyCheck(ICConsistencyCheck);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setUseEmbedded(useEmbedded);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
  stepper->setZeroInitialGuess(zeroInitialGuess);
  stepper->initialize();
  TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
 
  std::string stepperType = stepper->getStepperType();
  // Full argument list construction.
  if (stepperType == "RK Backward Euler") {
    auto s = rcp(new Tempus::StepperDIRK_BackwardEuler<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SDIRK 2 Stage 2nd order") {
    double gamma = 0.2928932188134524;
    auto s       = rcp(new Tempus::StepperSDIRK_2Stage2ndOrder<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier, gamma));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SDIRK 3 Stage 2nd order") {
    auto s = rcp(new Tempus::StepperSDIRK_3Stage2ndOrder<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SDIRK 2 Stage 3rd order") {
    std::string gammaType = "3rd Order A-stable";
    double gamma          = 0.7886751345948128;
    auto s                = rcp(new Tempus::StepperSDIRK_2Stage3rdOrder<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier, gammaType, gamma));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "EDIRK 2 Stage 3rd order") {
    auto s = rcp(new Tempus::StepperEDIRK_2Stage3rdOrder<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "DIRK 1 Stage Theta Method") {
    double theta = 0.5;
    auto s       = rcp(new Tempus::StepperDIRK_1StageTheta<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier, theta));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "EDIRK 2 Stage Theta Method") {
    double theta = 0.5;
    auto s       = rcp(new Tempus::StepperEDIRK_2StageTheta<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier, theta));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
    s->setTheta(theta);
    s->initialize();
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Trapezoidal Rule") {
    auto s = rcp(new Tempus::StepperEDIRK_TrapezoidalRule<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Implicit Midpoint") {
    auto s = rcp(new Tempus::StepperSDIRK_ImplicitMidpoint<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SSPDIRK22") {
    auto s = rcp(new Tempus::StepperSDIRK_SSPDIRK22<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SSPDIRK32") {
    auto s = rcp(new Tempus::StepperSDIRK_SSPDIRK32<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SSPDIRK23") {
    auto s = rcp(new Tempus::StepperSDIRK_SSPDIRK23<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SSPDIRK33") {
    auto s = rcp(new Tempus::StepperSDIRK_SSPDIRK33<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Implicit 1 Stage 1st order Radau IA") {
    auto s = rcp(new Tempus::StepperDIRK_1Stage1stOrderRadauIA<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "RK Implicit 2 Stage 2nd order Lobatto IIIB") {
    auto s = rcp(new Tempus::StepperDIRK_2Stage2ndOrderLobattoIIIB<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SDIRK 5 Stage 4th order") {
    auto s = rcp(new Tempus::StepperSDIRK_5Stage4thOrder<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SDIRK 3 Stage 4th order") {
    auto s = rcp(new Tempus::StepperSDIRK_3Stage4thOrder<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SDIRK 5 Stage 5th order") {
    auto s = rcp(new Tempus::StepperSDIRK_5Stage5thOrder<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else if (stepperType == "SDIRK 2(1) Pair") {
    auto s = rcp(new Tempus::StepperSDIRK_21Pair<double>(
        model, solver, useFSAL, ICConsistency, ICConsistencyCheck, useEmbedded,
        zeroInitialGuess, modifier));
    TEUCHOS_TEST_FOR_EXCEPT(!s->isInitialized());
  }
  else
    TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
                               "Error - unknown stepperType = " + stepperType);
}
 
class StepperRKModifierTest
  : virtual public Tempus::StepperRKModifierBase<double> {
 public:
  StepperRKModifierTest()
    : testBEGIN_STEP(false),
      testBEGIN_STAGE(false),
      testBEFORE_SOLVE(false),
      testAFTER_SOLVE(false),
      testBEFORE_EXPLICIT_EVAL(false),
      testEND_STAGE(false),
      testEND_STEP(false),
      testCurrentValue(-0.99),
      testWorkingValue(-0.99),
      testDt(-1.5),
      testName("")
  {
  }
 
  virtual ~StepperRKModifierTest() {}
 
  virtual void modify(
      Teuchos::RCP<Tempus::SolutionHistory<double>> sh,
      Teuchos::RCP<Tempus::StepperRKBase<double>> stepper,
      const typename Tempus::StepperRKAppAction<double>::ACTION_LOCATION actLoc)
  {
    switch (actLoc) {
      case StepperRKAppAction<double>::BEGIN_STEP: {
        testBEGIN_STEP   = true;
        auto x           = sh->getCurrentState()->getX();
        testCurrentValue = get_ele(*(x), 0);
        testName         = stepper->getStepperType() + " - Modifier";
        stepper->setStepperName(testName);
        break;
      }
      case StepperRKAppAction<double>::BEGIN_STAGE: {
        testBEGIN_STAGE = true;
        break;
      }
      case StepperRKAppAction<double>::BEFORE_SOLVE: {
        testBEFORE_SOLVE = true;
        testDt           = sh->getWorkingState()->getTimeStep() / 10.0;
        break;
      }
      case StepperRKAppAction<double>::AFTER_SOLVE: {
        testAFTER_SOLVE = true;
        break;
      }
      case StepperRKAppAction<double>::BEFORE_EXPLICIT_EVAL: {
        testBEFORE_EXPLICIT_EVAL = true;
        break;
      }
      case StepperRKAppAction<double>::END_STAGE: {
        testEND_STAGE = true;
        break;
      }
      case StepperRKAppAction<double>::END_STEP: {
        testEND_STEP     = true;
        auto x           = sh->getWorkingState()->getX();
        testWorkingValue = get_ele(*(x), 0);
        break;
      }
      default:
        TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
                                   "Error - unknown action location.\n");
    }
  }
 
  bool testBEGIN_STEP;
  bool testBEGIN_STAGE;
  bool testBEFORE_SOLVE;
  bool testAFTER_SOLVE;
  bool testBEFORE_EXPLICIT_EVAL;
  bool testEND_STAGE;
  bool testEND_STEP;
  double testCurrentValue;
  double testWorkingValue;
  double testDt;
  std::string testName;
};
 
class StepperRKObserverTest
  : virtual public Tempus::StepperRKObserverBase<double> {
 public:
  StepperRKObserverTest()
    : testBEGIN_STEP(false),
      testBEGIN_STAGE(false),
      testBEFORE_SOLVE(false),
      testAFTER_SOLVE(false),
      testBEFORE_EXPLICIT_EVAL(false),
      testEND_STAGE(false),
      testEND_STEP(false),
      testCurrentValue(-0.99),
      testWorkingValue(-0.99),
      testDt(-1.5),
      testName("")
  {
  }
 
  virtual ~StepperRKObserverTest() {}
 
  virtual void observe(
      Teuchos::RCP<const Tempus::SolutionHistory<double>> sh,
      Teuchos::RCP<const Tempus::StepperRKBase<double>> stepper,
      const typename Tempus::StepperRKAppAction<double>::ACTION_LOCATION actLoc)
  {
    switch (actLoc) {
      case StepperRKAppAction<double>::BEGIN_STEP: {
        testBEGIN_STEP   = true;
        auto x           = sh->getCurrentState()->getX();
        testCurrentValue = get_ele(*(x), 0);
        break;
      }
      case StepperRKAppAction<double>::BEGIN_STAGE: {
        testBEGIN_STAGE = true;
        break;
      }
      case StepperRKAppAction<double>::BEFORE_SOLVE: {
        testBEFORE_SOLVE = true;
        testDt           = sh->getWorkingState()->getTimeStep() / 10.0;
        break;
      }
      case StepperRKAppAction<double>::AFTER_SOLVE: {
        testAFTER_SOLVE = true;
        testName        = stepper->getStepperType() + " - Observer";
        break;
      }
      case StepperRKAppAction<double>::BEFORE_EXPLICIT_EVAL: {
        testBEFORE_EXPLICIT_EVAL = true;
        break;
      }
      case StepperRKAppAction<double>::END_STAGE: {
        testEND_STAGE = true;
        break;
      }
      case StepperRKAppAction<double>::END_STEP: {
        testEND_STEP     = true;
        auto x           = sh->getWorkingState()->getX();
        testWorkingValue = get_ele(*(x), 0);
        break;
      }
      default:
        TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
                                   "Error - unknown action location.\n");
    }
  }
 
  bool testBEGIN_STEP;
  bool testBEGIN_STAGE;
  bool testBEFORE_SOLVE;
  bool testAFTER_SOLVE;
  bool testBEFORE_EXPLICIT_EVAL;
  bool testEND_STAGE;
  bool testEND_STEP;
  double testCurrentValue;
  double testWorkingValue;
  double testDt;
  std::string testName;
};
 
class StepperRKModifierXTest
  : virtual public Tempus::StepperRKModifierXBase<double> {
 public:
  StepperRKModifierXTest()
    : testX_BEGIN_STEP(false),
      testX_BEGIN_STAGE(false),
      testX_BEFORE_SOLVE(false),
      testX_AFTER_SOLVE(false),
      testX_BEFORE_EXPLICIT_EVAL(false),
      testXDOT_END_STAGE(false),
      testX_END_STEP(false),
      testX(-0.99),
      testEndStageX(-0.99),
      testDt(-1.5),
      testTime(-1.5),
      testStageNumber(-1),
      testStageX(-0.99)
  {
  }
 
  virtual ~StepperRKModifierXTest() {}
 
  virtual void modify(
      Teuchos::RCP<Thyra::VectorBase<double>> x, const double time,
      const double dt, const int stageNumber,
      const typename Tempus::StepperRKModifierXBase<double>::MODIFIER_TYPE
          modType)
  {
    switch (modType) {
      case StepperRKModifierXBase<double>::X_BEGIN_STEP: {
        testX_BEGIN_STEP = true;
        testX            = get_ele(*(x), 0);
        break;
      }
      case StepperRKModifierXBase<double>::X_BEGIN_STAGE: {
        testX_BEGIN_STAGE = true;
        break;
      }
      case StepperRKModifierXBase<double>::X_BEFORE_SOLVE: {
        testX_BEFORE_SOLVE = true;
        testDt             = dt;
        break;
      }
      case StepperRKModifierXBase<double>::X_AFTER_SOLVE: {
        testX_AFTER_SOLVE = true;
        break;
      }
      case StepperRKModifierXBase<double>::X_BEFORE_EXPLICIT_EVAL: {
        testX_BEFORE_EXPLICIT_EVAL = true;
        testStageNumber            = stageNumber;
        testStageX                 = get_ele(*(x), 0);  // x should be the stage value.
        break;
      }
      case StepperRKModifierXBase<double>::X_END_STAGE: {
        testXDOT_END_STAGE = true;
        testEndStageX      = get_ele(*(x), 0);
        break;
      }
      case StepperRKModifierXBase<double>::X_END_STEP: {
        testX_END_STEP = true;
        testTime       = time;
        break;
      }
      default:
        TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
                                   "Error - unknown action location.\n");
    }
  }
 
  bool testX_BEGIN_STEP;
  bool testX_BEGIN_STAGE;
  bool testX_BEFORE_SOLVE;
  bool testX_AFTER_SOLVE;
  bool testX_BEFORE_EXPLICIT_EVAL;
  bool testXDOT_END_STAGE;
  bool testX_END_STEP;
  double testX;
  double testEndStageX;
  double testDt;
  double testTime;
  int testStageNumber;
  double testStageX;
};
 
void testRKAppAction(
    const Teuchos::RCP<Tempus::StepperRKBase<double>>& stepper,
    const Teuchos::RCP<const Thyra::ModelEvaluator<double>>& model,
    Teuchos::FancyOStream& out, bool& success)
{
  auto testNameOrig = stepper->getStepperType();
 
  // Test Modifier.
  {
    stepper->setModel(model);
    auto modifier = rcp(new StepperRKModifierTest());
    stepper->setAppAction(modifier);
    stepper->initialize();
    TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
    auto testName = testNameOrig + " - Modifier";
 
    // Create a SolutionHistory.
    auto solutionHistory = Tempus::createSolutionHistoryME(model);
 
    // Take one time step.
    stepper->setInitialConditions(solutionHistory);
    solutionHistory->initWorkingState();
    double dt = 0.1;
    solutionHistory->getWorkingState()->setTimeStep(dt);
    stepper->takeStep(solutionHistory);
 
    // Testing that each ACTION_LOCATION has been called.
    TEST_COMPARE(modifier->testBEGIN_STEP, ==, true);
    TEST_COMPARE(modifier->testBEGIN_STAGE, ==, true);
    TEST_COMPARE(modifier->testBEFORE_SOLVE, ==, true);
    TEST_COMPARE(modifier->testAFTER_SOLVE, ==, true);
    TEST_COMPARE(modifier->testBEFORE_EXPLICIT_EVAL, ==, true);
    TEST_COMPARE(modifier->testEND_STAGE, ==, true);
    TEST_COMPARE(modifier->testEND_STEP, ==, true);
 
    // Testing that values can be set through the modifier.
    auto x = solutionHistory->getCurrentState()->getX();
    TEST_FLOATING_EQUALITY(modifier->testCurrentValue, get_ele(*(x), 0),
                           1.0e-14);
    x = solutionHistory->getWorkingState()->getX();
    TEST_FLOATING_EQUALITY(modifier->testWorkingValue, get_ele(*(x), 0),
                           1.0e-14);
    auto Dt = solutionHistory->getWorkingState()->getTimeStep();
    TEST_FLOATING_EQUALITY(modifier->testDt, Dt / 10.0, 1.0e-14);
 
    TEST_COMPARE(modifier->testName, ==, testName);
  }
 
  // Test Observer.
  {
    stepper->setModel(model);
    auto observer = rcp(new StepperRKObserverTest());
    stepper->setAppAction(observer);
    stepper->setStepperName(testNameOrig);
    stepper->initialize();
    TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
 
    // Create a SolutionHistory.
    auto solutionHistory = Tempus::createSolutionHistoryME(model);
 
    // Take one time step.
    stepper->setInitialConditions(solutionHistory);
    solutionHistory->initWorkingState();
    double dt = 0.1;
    solutionHistory->getWorkingState()->setTimeStep(dt);
    stepper->takeStep(solutionHistory);
 
    // Testing that each ACTION_LOCATION has been called.
    TEST_COMPARE(observer->testBEGIN_STEP, ==, true);
    TEST_COMPARE(observer->testBEGIN_STAGE, ==, true);
    TEST_COMPARE(observer->testBEFORE_SOLVE, ==, true);
    TEST_COMPARE(observer->testAFTER_SOLVE, ==, true);
    TEST_COMPARE(observer->testBEFORE_EXPLICIT_EVAL, ==, true);
    TEST_COMPARE(observer->testEND_STAGE, ==, true);
    TEST_COMPARE(observer->testEND_STEP, ==, true);
 
    // Testing that values can be observed through the observer.
    auto x = solutionHistory->getCurrentState()->getX();
    TEST_FLOATING_EQUALITY(observer->testCurrentValue, get_ele(*(x), 0),
                           1.0e-14);
    x = solutionHistory->getWorkingState()->getX();
    TEST_FLOATING_EQUALITY(observer->testWorkingValue, get_ele(*(x), 0),
                           1.0e-14);
    auto Dt = solutionHistory->getWorkingState()->getTimeStep();
    TEST_FLOATING_EQUALITY(observer->testDt, Dt / 10.0, 1.0e-14);
 
    auto testName = testNameOrig + " - Observer";
    TEST_COMPARE(observer->testName, ==, testName);
  }
 
  // Test ModifierX.
  {
    stepper->setModel(model);
    auto modifierX = rcp(new StepperRKModifierXTest());
    stepper->setAppAction(modifierX);
    stepper->setStepperName(testNameOrig);
    stepper->initialize();
    TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
 
    // Create a SolutionHistory.
    auto solutionHistory = Tempus::createSolutionHistoryME(model);
 
    // Take one time step.
    stepper->setInitialConditions(solutionHistory);
    solutionHistory->initWorkingState();
    double dt = 0.1;
    solutionHistory->getWorkingState()->setTimeStep(dt);
    stepper->takeStep(solutionHistory);
 
    // Testing that each ACTION_LOCATION has been called.
    TEST_COMPARE(modifierX->testX_BEGIN_STEP, ==, true);
    TEST_COMPARE(modifierX->testX_BEGIN_STAGE, ==, true);
    TEST_COMPARE(modifierX->testX_BEFORE_SOLVE, ==, true);
    TEST_COMPARE(modifierX->testX_AFTER_SOLVE, ==, true);
    TEST_COMPARE(modifierX->testX_BEFORE_EXPLICIT_EVAL, ==, true);
    TEST_COMPARE(modifierX->testXDOT_END_STAGE, ==, true);
    TEST_COMPARE(modifierX->testX_END_STEP, ==, true);
 
    const double relTol = 1.0e-14;
    // Testing that values can be set through the modifierX.
    auto x = solutionHistory->getCurrentState()->getX();
    TEST_FLOATING_EQUALITY(modifierX->testX, get_ele(*(x), 0), relTol);
    auto Dt = solutionHistory->getWorkingState()->getTimeStep();
    TEST_FLOATING_EQUALITY(modifierX->testDt, Dt, relTol);
 
    auto time = solutionHistory->getWorkingState()->getTime();
    TEST_FLOATING_EQUALITY(modifierX->testTime, time, relTol);
 
    // Stage Number should be -1 outside stage loop.
    TEST_COMPARE(stepper->getStageNumber(), ==, -1);
    // The last stage number through X_BEFORE_EXPLICIT_EVAL should be
    // the number of stages minus one.
    TEST_COMPARE(modifierX->testStageNumber, ==,
                 stepper->getNumberOfStages() - 1);
 
    if (rcp_dynamic_cast<Tempus::StepperIMEX_RK<double>>(stepper) !=
            Teuchos::null ||
        rcp_dynamic_cast<Tempus::StepperIMEX_RK_Partition<double>>(stepper) !=
            Teuchos::null) {
      TEST_FLOATING_EQUALITY(modifierX->testStageX, 2.0, relTol);
      TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 2.0, relTol);
    }
    else if (stepper->isImplicit()) {
      // Stage values are overwritten and not available
      // outside takeStep, so direct comparisons are needed.
      if (rcp_dynamic_cast<Tempus::StepperDIRK_BackwardEuler<double>>(
              stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09900990099009901,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09900990099009901,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_2Stage2ndOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09979317463412091,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09979317463412091,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_3Stage2ndOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.049921670528461,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.049921670528461,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_2Stage3rdOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.02171123447937569,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.02171123447937569,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperEDIRK_2Stage3rdOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06659267480577136,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06659267480577136,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperDIRK_1StageTheta<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperEDIRK_2StageTheta<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperEDIRK_TrapezoidalRule<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_ImplicitMidpoint<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK22<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.0748907323303947,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.0748907323303947,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK32<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.08321767099874625,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.08321767099874625,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK23<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.07878078755122744,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.07878078755122744,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK33<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.08525184184135257,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.08525184184135257,
                               relTol);
      }
      else if (rcp_dynamic_cast<
                   Tempus::StepperDIRK_1Stage1stOrderRadauIA<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09900990099009901,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09900990099009901,
                               relTol);
      }
      else if (rcp_dynamic_cast<
                   Tempus::StepperDIRK_2Stage2ndOrderLobattoIIIB<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_5Stage4thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09983340822548158,
                               1.0e-14);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09983340822548158,
                               1.0e-14);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_3Stage4thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, -0.009988159068259408,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, -0.009988159068259408,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_5Stage5thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06446224812649308,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06446224812649308,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_21Pair<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.001960592098813843,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.001960592098813843,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperDIRK_General<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09979317463412091,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09979317463412091,
                               relTol);
      }
      else {
        TEUCHOS_TEST_FOR_EXCEPTION(
            true, std::logic_error,
            "Error - unknown stepperType = " + stepper->getStepperType());
      }
    }
    else {
      // Stage values are overwritten and not available
      // outside takeStep, so direct comparisons are needed.
      if (rcp_dynamic_cast<Tempus::StepperERK_3_8Rule<double>>(stepper) !=
          Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09966666666666668,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09966666666666668,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_3Stage3rdOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.1, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.1, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_3Stage3rdOrderHeun<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06666666666666667,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06666666666666667,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_3Stage3rdOrderTVD<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.05, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.05, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_4Stage3rdOrderRunge<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.0995, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.0995, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_4Stage4thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09975, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09975, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_5Stage3rdOrderKandG<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06662222222222222,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06662222222222222,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_BogackiShampine32<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09983333333333333,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09983333333333333,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_ForwardEuler<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.0, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.0, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_General<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09975, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09975, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_Merson45<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09983333333333332,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09983333333333332,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_Midpoint<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.05, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.05, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_Trapezoidal<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.1, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.1, relTol);
      }
      else {
        TEUCHOS_TEST_FOR_EXCEPTION(
            true, std::logic_error,
            "Error - unknown stepperType = " + stepper->getStepperType());
      }
    }
  }
 
  // Test Composite.
  {
    stepper->setModel(model);
 
    auto modifier  = rcp(new StepperRKModifierTest());
    auto observer  = rcp(new StepperRKObserverTest());
    auto modifierX = rcp(new StepperRKModifierXTest());
    auto composite = rcp(new Tempus::StepperRKAppActionComposite<double>());
 
    composite->addRKAppAction(modifier);
    composite->addRKAppAction(observer);
    composite->addRKAppAction(modifierX);
    stepper->setAppAction(composite);
 
    stepper->initialize();
    TEUCHOS_TEST_FOR_EXCEPT(!stepper->isInitialized());
 
    // Create a SolutionHistory.
    auto solutionHistory = Tempus::createSolutionHistoryME(model);
 
    // Take one time step.
    stepper->setInitialConditions(solutionHistory);
    solutionHistory->initWorkingState();
    double dt = 0.1;
    solutionHistory->getWorkingState()->setTimeStep(dt);
    stepper->takeStep(solutionHistory);
 
    auto xCS = solutionHistory->getCurrentState()->getX();
    auto xWS = solutionHistory->getWorkingState()->getX();
    auto Dt  = solutionHistory->getWorkingState()->getTimeStep();
 
    // Test Modifier.
    // Testing that each ACTION_LOCATION has been called.
    TEST_COMPARE(modifier->testBEGIN_STEP, ==, true);
    TEST_COMPARE(modifier->testBEGIN_STAGE, ==, true);
    TEST_COMPARE(modifier->testBEFORE_SOLVE, ==, true);
    TEST_COMPARE(modifier->testAFTER_SOLVE, ==, true);
    TEST_COMPARE(modifier->testBEFORE_EXPLICIT_EVAL, ==, true);
    TEST_COMPARE(modifier->testEND_STAGE, ==, true);
    TEST_COMPARE(modifier->testEND_STEP, ==, true);
 
    const double relTol = 1.0e-14;
    // Testing that values can be set through the modifier.
    TEST_FLOATING_EQUALITY(modifier->testCurrentValue, get_ele(*(xCS), 0),
                           relTol);
    TEST_FLOATING_EQUALITY(modifier->testWorkingValue, get_ele(*(xWS), 0),
                           relTol);
    TEST_FLOATING_EQUALITY(modifier->testDt, Dt / 10.0, relTol);
 
    auto testName = testNameOrig + " - Modifier";
    TEST_COMPARE(modifier->testName, ==, testName);
 
    // Test Observer.
    // Testing that each ACTION_LOCATION has been called.
    TEST_COMPARE(observer->testBEGIN_STEP, ==, true);
    TEST_COMPARE(observer->testBEGIN_STAGE, ==, true);
    TEST_COMPARE(observer->testBEFORE_SOLVE, ==, true);
    TEST_COMPARE(observer->testAFTER_SOLVE, ==, true);
    TEST_COMPARE(observer->testBEFORE_EXPLICIT_EVAL, ==, true);
    TEST_COMPARE(observer->testEND_STAGE, ==, true);
    TEST_COMPARE(observer->testEND_STEP, ==, true);
 
    // Testing that values can be observed through the observer.
    TEST_FLOATING_EQUALITY(observer->testCurrentValue, get_ele(*(xCS), 0),
                           relTol);
    TEST_FLOATING_EQUALITY(observer->testWorkingValue, get_ele(*(xWS), 0),
                           relTol);
    TEST_FLOATING_EQUALITY(observer->testDt, Dt / 10.0, relTol);
 
    testName = testNameOrig + " - Observer";
    TEST_COMPARE(observer->testName, ==, testName);
 
    // Test ModifierX.
    // Testing that each ACTION_LOCATION has been called.
    TEST_COMPARE(modifierX->testX_BEGIN_STEP, ==, true);
    TEST_COMPARE(modifierX->testX_BEGIN_STAGE, ==, true);
    TEST_COMPARE(modifierX->testX_BEFORE_SOLVE, ==, true);
    TEST_COMPARE(modifierX->testX_AFTER_SOLVE, ==, true);
    TEST_COMPARE(modifierX->testX_BEFORE_EXPLICIT_EVAL, ==, true);
    TEST_COMPARE(modifierX->testXDOT_END_STAGE, ==, true);
    TEST_COMPARE(modifierX->testX_END_STEP, ==, true);
 
    // Testing that values can be set through the modifierX.
    TEST_FLOATING_EQUALITY(modifierX->testX, get_ele(*(xCS), 0), relTol);
    TEST_FLOATING_EQUALITY(modifierX->testDt, Dt, relTol);
 
    auto time = solutionHistory->getWorkingState()->getTime();
    TEST_FLOATING_EQUALITY(modifierX->testTime, time, relTol);
 
    // Stage Number should be -1 outside stage loop.
    TEST_COMPARE(stepper->getStageNumber(), ==, -1);
    // The last stage number through X_BEFORE_EXPLICIT_EVAL should be
    // the number of stages minus one.
    TEST_COMPARE(modifierX->testStageNumber, ==,
                 stepper->getNumberOfStages() - 1);
 
    if (rcp_dynamic_cast<Tempus::StepperIMEX_RK<double>>(stepper) !=
            Teuchos::null ||
        rcp_dynamic_cast<Tempus::StepperIMEX_RK_Partition<double>>(stepper) !=
            Teuchos::null) {
      TEST_FLOATING_EQUALITY(modifierX->testStageX, 2.0, relTol);
      TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 2.0, relTol);
    }
    else if (stepper->isImplicit()) {
      // Stage values are overwritten and not available
      // outside takeStep, so direct comparisons are needed.
      if (rcp_dynamic_cast<Tempus::StepperDIRK_BackwardEuler<double>>(
              stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09900990099009901,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09900990099009901,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_2Stage2ndOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09979317463412091,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09979317463412091,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_3Stage2ndOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.049921670528461,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.049921670528461,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_2Stage3rdOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.02171123447937569,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.02171123447937569,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperEDIRK_2Stage3rdOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06659267480577136,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06659267480577136,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperDIRK_1StageTheta<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperEDIRK_2StageTheta<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperEDIRK_TrapezoidalRule<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_ImplicitMidpoint<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK22<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.0748907323303947,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.0748907323303947,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK32<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.08321767099874625,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.08321767099874625,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK23<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.07878078755122744,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.07878078755122744,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_SSPDIRK33<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.08525184184135257,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.08525184184135257,
                               relTol);
      }
      else if (rcp_dynamic_cast<
                   Tempus::StepperDIRK_1Stage1stOrderRadauIA<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09900990099009901,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09900990099009901,
                               relTol);
      }
      else if (rcp_dynamic_cast<
                   Tempus::StepperDIRK_2Stage2ndOrderLobattoIIIB<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.04987531172069826,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.04987531172069826,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_5Stage4thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09983340822548158,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09983340822548158,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_3Stage4thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, -0.009988159068259408,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, -0.009988159068259408,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_5Stage5thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06446224812649308,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06446224812649308,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperSDIRK_21Pair<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.001960592098813843,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.001960592098813843,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperDIRK_General<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09979317463412091,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09979317463412091,
                               relTol);
      }
      else {
        TEUCHOS_TEST_FOR_EXCEPTION(
            true, std::logic_error,
            "Error - unknown stepperType = " + stepper->getStepperType());
      }
    }
    else {
      // For explicit steppers, stageX is under written and not available
      // outside takeStep, so direct comparisons are needed.
      if (rcp_dynamic_cast<Tempus::StepperERK_3_8Rule<double>>(stepper) !=
          Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09966666666666668,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09966666666666668,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_3Stage3rdOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.1, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.1, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_3Stage3rdOrderHeun<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06666666666666667,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06666666666666667,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_3Stage3rdOrderTVD<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.05, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.05, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_4Stage3rdOrderRunge<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.0995, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.0995, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_4Stage4thOrder<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09975, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09975, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_5Stage3rdOrderKandG<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.06662222222222222,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.06662222222222222,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_BogackiShampine32<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09983333333333333,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09983333333333333,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_ForwardEuler<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.0, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.0, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_General<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09975, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09975, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_Merson45<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.09983333333333332,
                               relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.09983333333333332,
                               relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_Midpoint<double>>(stepper) !=
               Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.05, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.05, relTol);
      }
      else if (rcp_dynamic_cast<Tempus::StepperERK_Trapezoidal<double>>(
                   stepper) != Teuchos::null) {
        TEST_FLOATING_EQUALITY(modifierX->testStageX, 0.1, relTol);
        TEST_FLOATING_EQUALITY(modifierX->testEndStageX, 0.1, relTol);
      }
      else {
        TEUCHOS_TEST_FOR_EXCEPTION(
            true, std::logic_error,
            "Error - unknown stepperType = " + stepper->getStepperType());
      }
    }
  }
}
 
}  // namespace Tempus_Unit_Test
#endif  // Tempus_UnitTest_RK_Utils_hpp