SinCosModel_impl.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_TEST_SINCOS_MODEL_IMPL_HPP
#define TEMPUS_TEST_SINCOS_MODEL_IMPL_HPP
 
#include "Teuchos_StandardParameterEntryValidators.hpp"
 
#include "Thyra_DefaultSpmdVectorSpace.hpp"
#include "Thyra_DetachedVectorView.hpp"
#include "Thyra_DetachedMultiVectorView.hpp"
#include "Thyra_DefaultSerialDenseLinearOpWithSolveFactory.hpp"
#include "Thyra_DefaultMultiVectorLinearOpWithSolve.hpp"
#include "Thyra_DefaultLinearOpSource.hpp"
#include "Thyra_VectorStdOps.hpp"
#include "Thyra_MultiVectorStdOps.hpp"
#include "Thyra_DefaultMultiVectorProductVector.hpp"
 
#include <iostream>
 
namespace Tempus_Test {
 
template <class Scalar>
SinCosModel<Scalar>::SinCosModel(Teuchos::RCP<Teuchos::ParameterList> pList_)
{
  isInitialized_     = false;
  dim_               = 2;
  Np_                = 3;     // Number of parameter vectors (p, dx/dp, dx_dot/dp)
  np_                = 3;     // Number of parameters in this vector (3)
  Ng_                = 1;     // Number of observation functions (1)
  ng_                = dim_;  // Number of elements in this observation function ( == x )
  acceptModelParams_ = false;
  useDfDpAsTangent_  = false;
  haveIC_            = true;
  a_                 = 0.0;
  f_                 = 1.0;
  L_                 = 1.0;
  x0_ic_             = 0.0;
  x1_ic_             = 1.0;
  t0_ic_             = 0.0;
 
  // Create x_space and f_space
  x_space_ = Thyra::defaultSpmdVectorSpace<Scalar>(dim_);
  f_space_ = Thyra::defaultSpmdVectorSpace<Scalar>(dim_);
  // Create p_space and g_space
  p_space_ = Thyra::defaultSpmdVectorSpace<Scalar>(np_);
  g_space_ = Thyra::defaultSpmdVectorSpace<Scalar>(ng_);
 
  setParameterList(pList_);
 
  // Create DxDp product space
  DxDp_space_ = Thyra::multiVectorProductVectorSpace(x_space_, np_);
}
 
template <class Scalar>
Thyra::ModelEvaluatorBase::InArgs<Scalar> SinCosModel<Scalar>::getExactSolution(
    double t) const
{
  TEUCHOS_TEST_FOR_EXCEPTION(!isInitialized_, std::logic_error,
                             "Error, setupInOutArgs_ must be called first!\n");
  Thyra::ModelEvaluatorBase::InArgs<Scalar> inArgs = inArgs_;
  double exact_t                                   = t;
  inArgs.set_t(exact_t);
  Teuchos::RCP<Thyra::VectorBase<Scalar> > exact_x = createMember(x_space_);
  {  // scope to delete DetachedVectorView
    Thyra::DetachedVectorView<Scalar> exact_x_view(*exact_x);
    exact_x_view[0] = a_ + b_ * sin((f_ / L_) * t + phi_);
    exact_x_view[1] = b_ * (f_ / L_) * cos((f_ / L_) * t + phi_);
  }
  inArgs.set_x(exact_x);
  Teuchos::RCP<Thyra::VectorBase<Scalar> > exact_x_dot = createMember(x_space_);
  {  // scope to delete DetachedVectorView
    Thyra::DetachedVectorView<Scalar> exact_x_dot_view(*exact_x_dot);
    exact_x_dot_view[0] = b_ * (f_ / L_) * cos((f_ / L_) * t + phi_);
    exact_x_dot_view[1] =
        -b_ * (f_ / L_) * (f_ / L_) * sin((f_ / L_) * t + phi_);
  }
  inArgs.set_x_dot(exact_x_dot);
  return (inArgs);
}
 
//
// 06/24/09 tscoffe:
// These are the exact sensitivities for the problem assuming the initial
// conditions are specified as:
//    s(0) = [1;0]    s(1) = [0;b/L]                 s(2) = [0;-b*f/(L*L)]
// sdot(0) = [0;0] sdot(1) = [0;-3*f*f*b/(L*L*L)] sdot(2) =
// [0;3*f*f*f*b/(L*L*L*L)]
//
template <class Scalar>
Thyra::ModelEvaluatorBase::InArgs<Scalar>
SinCosModel<Scalar>::getExactSensSolution(int j, double t) const
{
  TEUCHOS_TEST_FOR_EXCEPTION(!isInitialized_, std::logic_error,
                             "Error, setupInOutArgs_ must be called first!\n");
  Thyra::ModelEvaluatorBase::InArgs<Scalar> inArgs = inArgs_;
  if (!acceptModelParams_) {
    return inArgs;
  }
  TEUCHOS_ASSERT_IN_RANGE_UPPER_EXCLUSIVE(j, 0, np_);
  double exact_t = t;
  Scalar b       = b_;
  Scalar f       = f_;
  Scalar L       = L_;
  Scalar phi     = phi_;
  inArgs.set_t(exact_t);
  Teuchos::RCP<Thyra::VectorBase<Scalar> > exact_s = createMember(x_space_);
  {  // scope to delete DetachedVectorView
    Thyra::DetachedVectorView<Scalar> exact_s_view(*exact_s);
    if (j == 0) {  // dx/da
      exact_s_view[0] = 1.0;
      exact_s_view[1] = 0.0;
    }
    else if (j == 1) {  // dx/df
      exact_s_view[0] = (b / L) * t * cos((f / L) * t + phi);
      exact_s_view[1] = (b / L) * cos((f / L) * t + phi) -
                        (b * f * t / (L * L)) * sin((f / L) * t + phi);
    }
    else {  // dx/dL
      exact_s_view[0] = -(b * f * t / (L * L)) * cos((f / L) * t + phi);
      exact_s_view[1] = -(b * f / (L * L)) * cos((f / L) * t + phi) +
                        (b * f * f * t / (L * L * L)) * sin((f / L) * t + phi);
    }
  }
  inArgs.set_x(exact_s);
  Teuchos::RCP<Thyra::VectorBase<Scalar> > exact_s_dot = createMember(x_space_);
  {  // scope to delete DetachedVectorView
    Thyra::DetachedVectorView<Scalar> exact_s_dot_view(*exact_s_dot);
    if (j == 0) {  // dxdot/da
      exact_s_dot_view[0] = 0.0;
      exact_s_dot_view[1] = 0.0;
    }
    else if (j == 1) {  // dxdot/df
      exact_s_dot_view[0] = (b / L) * cos((f / L) * t + phi) -
                            (b * f * t / (L * L)) * sin((f / L) * t + phi);
      exact_s_dot_view[1] =
          -(2.0 * b * f / (L * L)) * sin((f / L) * t + phi) -
          (b * f * f * t / (L * L * L)) * cos((f / L) * t + phi);
    }
    else {  // dxdot/dL
      exact_s_dot_view[0] =
          -(b * f / (L * L)) * cos((f / L) * t + phi) +
          (b * f * f * t / (L * L * L)) * sin((f / L) * t + phi);
      exact_s_dot_view[1] =
          (2.0 * b * f * f / (L * L * L)) * sin((f / L) * t + phi) +
          (b * f * f * f * t / (L * L * L * L)) * cos((f / L) * t + phi);
    }
  }
  inArgs.set_x_dot(exact_s_dot);
  return (inArgs);
}
 
template <class Scalar>
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> >
SinCosModel<Scalar>::get_x_space() const
{
  return x_space_;
}
 
template <class Scalar>
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> >
SinCosModel<Scalar>::get_f_space() const
{
  return f_space_;
}
 
template <class Scalar>
Thyra::ModelEvaluatorBase::InArgs<Scalar>
SinCosModel<Scalar>::getNominalValues() const
{
  TEUCHOS_TEST_FOR_EXCEPTION(!isInitialized_, std::logic_error,
                             "Error, setupInOutArgs_ must be called first!\n");
  return nominalValues_;
}
 
template <class Scalar>
Teuchos::RCP<Thyra::LinearOpWithSolveBase<Scalar> >
SinCosModel<Scalar>::create_W() const
{
  using Teuchos::RCP;
  RCP<const Thyra::LinearOpWithSolveFactoryBase<Scalar> > W_factory =
      this->get_W_factory();
  RCP<Thyra::LinearOpBase<Scalar> > matrix = this->create_W_op();
  {
    // 01/20/09 tscoffe:  This is a total hack to provide a full rank matrix to
    // linearOpWithSolve because it ends up factoring the matrix during
    // initialization, which it really shouldn't do, or I'm doing something
    // wrong here.   The net effect is that I get exceptions thrown in
    // optimized mode due to the matrix being rank deficient unless I do this.
    RCP<Thyra::MultiVectorBase<Scalar> > multivec =
        Teuchos::rcp_dynamic_cast<Thyra::MultiVectorBase<Scalar> >(matrix,
                                                                   true);
    {
      RCP<Thyra::VectorBase<Scalar> > vec = Thyra::createMember(x_space_);
      {
        Thyra::DetachedVectorView<Scalar> vec_view(*vec);
        vec_view[0] = 0.0;
        vec_view[1] = 1.0;
      }
      V_V(multivec->col(0).ptr(), *vec);
      {
        Thyra::DetachedVectorView<Scalar> vec_view(*vec);
        vec_view[0] = 1.0;
        vec_view[1] = 0.0;
      }
      V_V(multivec->col(1).ptr(), *vec);
    }
  }
  RCP<Thyra::LinearOpWithSolveBase<Scalar> > W =
      Thyra::linearOpWithSolve<Scalar>(*W_factory, matrix);
  return W;
}
// Teuchos::RCP<Thyra::LinearOpWithSolveBase<Scalar> >
// SinCosModel<Scalar>::
// create_W() const
//{
//   return Thyra::multiVectorLinearOpWithSolve<Scalar>();
// }
 
template <class Scalar>
Teuchos::RCP<Thyra::LinearOpBase<Scalar> > SinCosModel<Scalar>::create_W_op()
    const
{
  Teuchos::RCP<Thyra::MultiVectorBase<Scalar> > matrix =
      Thyra::createMembers(x_space_, dim_);
  return (matrix);
}
 
template <class Scalar>
Teuchos::RCP<const Thyra::LinearOpWithSolveFactoryBase<Scalar> >
SinCosModel<Scalar>::get_W_factory() const
{
  Teuchos::RCP<Thyra::LinearOpWithSolveFactoryBase<Scalar> > W_factory =
      Thyra::defaultSerialDenseLinearOpWithSolveFactory<Scalar>();
  return W_factory;
}
//  Teuchos::RCP<const Thyra::LinearOpBase<Scalar> > fwdOp =
//  this->create_W_op(); Teuchos::RCP<Thyra::LinearOpWithSolveBase<Scalar> > W =
//    Thyra::linearOpWithSolve<Scalar>(
//      *W_factory,
//      fwdOp
//      );
//  W_factory->initializeOp(
//      Thyra::defaultLinearOpSource<Scalar>(fwdOp),
//      &*W,
//      Thyra::SUPPORT_SOLVE_UNSPECIFIED
//      );
 
template <class Scalar>
Thyra::ModelEvaluatorBase::InArgs<Scalar> SinCosModel<Scalar>::createInArgs()
    const
{
  setupInOutArgs_();
  return inArgs_;
}
 
// Private functions overridden from ModelEvaluatorDefaultBase
 
template <class Scalar>
Thyra::ModelEvaluatorBase::OutArgs<Scalar>
SinCosModel<Scalar>::createOutArgsImpl() const
{
  setupInOutArgs_();
  return outArgs_;
}
 
template <class Scalar>
void SinCosModel<Scalar>::evalModelImpl(
    const Thyra::ModelEvaluatorBase::InArgs<Scalar> &inArgs,
    const Thyra::ModelEvaluatorBase::OutArgs<Scalar> &outArgs) const
{
  typedef Thyra::DefaultMultiVectorProductVector<Scalar> DMVPV;
  using Teuchos::RCP;
  using Teuchos::rcp_dynamic_cast;
  using Thyra::MultiVectorBase;
  using Thyra::VectorBase;
  TEUCHOS_TEST_FOR_EXCEPTION(!isInitialized_, std::logic_error,
                             "Error, setupInOutArgs_ must be called first!\n");
 
  const RCP<const VectorBase<Scalar> > x_in = inArgs.get_x().assert_not_null();
  Thyra::ConstDetachedVectorView<Scalar> x_in_view(*x_in);
 
  // double t = inArgs.get_t();
  Scalar a = a_;
  Scalar f = f_;
  Scalar L = L_;
  if (acceptModelParams_) {
    const RCP<const VectorBase<Scalar> > p_in =
        inArgs.get_p(0).assert_not_null();
    Thyra::ConstDetachedVectorView<Scalar> p_in_view(*p_in);
    a = p_in_view[0];
    f = p_in_view[1];
    L = p_in_view[2];
  }
 
  RCP<const MultiVectorBase<Scalar> > DxDp_in, DxdotDp_in;
  if (acceptModelParams_) {
    if (inArgs.get_p(1) != Teuchos::null)
      DxDp_in =
          rcp_dynamic_cast<const DMVPV>(inArgs.get_p(1))->getMultiVector();
    if (inArgs.get_p(2) != Teuchos::null)
      DxdotDp_in =
          rcp_dynamic_cast<const DMVPV>(inArgs.get_p(2))->getMultiVector();
  }
 
  Scalar beta = inArgs.get_beta();
 
  const RCP<VectorBase<Scalar> > f_out          = outArgs.get_f();
  const RCP<Thyra::LinearOpBase<Scalar> > W_out = outArgs.get_W_op();
  RCP<Thyra::MultiVectorBase<Scalar> > DfDp_out;
  if (acceptModelParams_) {
    Thyra::ModelEvaluatorBase::Derivative<Scalar> DfDp = outArgs.get_DfDp(0);
    DfDp_out                                           = DfDp.getMultiVector();
  }
 
  if (inArgs.get_x_dot().is_null()) {
    // Evaluate the Explicit ODE f(x,t) [= 0]
    if (!is_null(f_out)) {
      Thyra::DetachedVectorView<Scalar> f_out_view(*f_out);
      f_out_view[0] = x_in_view[1];
      f_out_view[1] = (f / L) * (f / L) * (a - x_in_view[0]);
    }
    if (!is_null(W_out)) {
      RCP<Thyra::MultiVectorBase<Scalar> > matrix =
          Teuchos::rcp_dynamic_cast<Thyra::MultiVectorBase<Scalar> >(W_out,
                                                                     true);
      Thyra::DetachedMultiVectorView<Scalar> matrix_view(*matrix);
      matrix_view(0, 0) = 0.0;                        // d(f0)/d(x0_n)
      matrix_view(0, 1) = +beta;                      // d(f0)/d(x1_n)
      matrix_view(1, 0) = -beta * (f / L) * (f / L);  // d(f1)/d(x0_n)
      matrix_view(1, 1) = 0.0;                        // d(f1)/d(x1_n)
      // Note: alpha = d(xdot)/d(x_n) and beta = d(x)/d(x_n)
    }
    if (!is_null(DfDp_out)) {
      Thyra::DetachedMultiVectorView<Scalar> DfDp_out_view(*DfDp_out);
      DfDp_out_view(0, 0) = 0.0;
      DfDp_out_view(0, 1) = 0.0;
      DfDp_out_view(0, 2) = 0.0;
      DfDp_out_view(1, 0) = (f / L) * (f / L);
      DfDp_out_view(1, 1) = (2.0 * f / (L * L)) * (a - x_in_view[0]);
      DfDp_out_view(1, 2) = -(2.0 * f * f / (L * L * L)) * (a - x_in_view[0]);
 
      // Compute df/dp + (df/dx) * (dx/dp)
      if (useDfDpAsTangent_ && !is_null(DxDp_in)) {
        Thyra::ConstDetachedMultiVectorView<Scalar> DxDp(*DxDp_in);
        DfDp_out_view(0, 0) += DxDp(1, 0);
        DfDp_out_view(0, 1) += DxDp(1, 1);
        DfDp_out_view(0, 2) += DxDp(1, 2);
        DfDp_out_view(1, 0) += -(f / L) * (f / L) * DxDp(0, 0);
        DfDp_out_view(1, 1) += -(f / L) * (f / L) * DxDp(0, 1);
        DfDp_out_view(1, 2) += -(f / L) * (f / L) * DxDp(0, 2);
      }
    }
  }
  else {
    // Evaluate the implicit ODE f(xdot, x, t) [= 0]
    RCP<const VectorBase<Scalar> > x_dot_in;
    x_dot_in     = inArgs.get_x_dot().assert_not_null();
    Scalar alpha = inArgs.get_alpha();
    if (!is_null(f_out)) {
      Thyra::DetachedVectorView<Scalar> f_out_view(*f_out);
      Thyra::ConstDetachedVectorView<Scalar> x_dot_in_view(*x_dot_in);
      f_out_view[0] = x_dot_in_view[0] - x_in_view[1];
      f_out_view[1] = x_dot_in_view[1] - (f / L) * (f / L) * (a - x_in_view[0]);
    }
    if (!is_null(W_out)) {
      RCP<Thyra::MultiVectorBase<Scalar> > matrix =
          Teuchos::rcp_dynamic_cast<Thyra::MultiVectorBase<Scalar> >(W_out,
                                                                     true);
      Thyra::DetachedMultiVectorView<Scalar> matrix_view(*matrix);
      matrix_view(0, 0) = alpha;                      // d(f0)/d(x0_n)
      matrix_view(0, 1) = -beta;                      // d(f0)/d(x1_n)
      matrix_view(1, 0) = +beta * (f / L) * (f / L);  // d(f1)/d(x0_n)
      matrix_view(1, 1) = alpha;                      // d(f1)/d(x1_n)
      // Note: alpha = d(xdot)/d(x_n) and beta = d(x)/d(x_n)
    }
    if (!is_null(DfDp_out)) {
      Thyra::DetachedMultiVectorView<Scalar> DfDp_out_view(*DfDp_out);
      DfDp_out_view(0, 0) = 0.0;
      DfDp_out_view(0, 1) = 0.0;
      DfDp_out_view(0, 2) = 0.0;
      DfDp_out_view(1, 0) = -(f / L) * (f / L);
      DfDp_out_view(1, 1) = -(2.0 * f / (L * L)) * (a - x_in_view[0]);
      DfDp_out_view(1, 2) = +(2.0 * f * f / (L * L * L)) * (a - x_in_view[0]);
 
      // Compute df/dp + (df/dx_dot) * (dx_dot/dp) + (df/dx) * (dx/dp)
      if (useDfDpAsTangent_ && !is_null(DxdotDp_in)) {
        Thyra::ConstDetachedMultiVectorView<Scalar> DxdotDp(*DxdotDp_in);
        DfDp_out_view(0, 0) += DxdotDp(0, 0);
        DfDp_out_view(0, 1) += DxdotDp(0, 1);
        DfDp_out_view(0, 2) += DxdotDp(0, 2);
        DfDp_out_view(1, 0) += DxdotDp(1, 0);
        DfDp_out_view(1, 1) += DxdotDp(1, 1);
        DfDp_out_view(1, 2) += DxdotDp(1, 2);
      }
      if (useDfDpAsTangent_ && !is_null(DxDp_in)) {
        Thyra::ConstDetachedMultiVectorView<Scalar> DxDp(*DxDp_in);
        DfDp_out_view(0, 0) += -DxDp(1, 0);
        DfDp_out_view(0, 1) += -DxDp(1, 1);
        DfDp_out_view(0, 2) += -DxDp(1, 2);
        DfDp_out_view(1, 0) += (f / L) * (f / L) * DxDp(0, 0);
        DfDp_out_view(1, 1) += (f / L) * (f / L) * DxDp(0, 1);
        DfDp_out_view(1, 2) += (f / L) * (f / L) * DxDp(0, 2);
      }
    }
  }
 
  // Responses:  g = x
  if (acceptModelParams_) {
    RCP<VectorBase<Scalar> > g_out = outArgs.get_g(0);
    if (g_out != Teuchos::null) Thyra::assign(g_out.ptr(), *x_in);
 
    RCP<Thyra::MultiVectorBase<Scalar> > DgDp_out =
        outArgs.get_DgDp(0, 0).getMultiVector();
    if (DgDp_out != Teuchos::null) Thyra::assign(DgDp_out.ptr(), Scalar(0.0));
 
    RCP<Thyra::MultiVectorBase<Scalar> > DgDx_out =
        outArgs.get_DgDx(0).getMultiVector();
    if (DgDx_out != Teuchos::null) {
      Thyra::DetachedMultiVectorView<Scalar> DgDx_out_view(*DgDx_out);
      DgDx_out_view(0, 0) = 1.0;
      DgDx_out_view(0, 1) = 0.0;
      DgDx_out_view(1, 0) = 0.0;
      DgDx_out_view(1, 1) = 1.0;
    }
  }
}
 
template <class Scalar>
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> >
SinCosModel<Scalar>::get_p_space(int l) const
{
  if (!acceptModelParams_) {
    return Teuchos::null;
  }
  TEUCHOS_ASSERT_IN_RANGE_UPPER_EXCLUSIVE(l, 0, Np_);
  if (l == 0)
    return p_space_;
  else if (l == 1 || l == 2)
    return DxDp_space_;
  return Teuchos::null;
}
 
template <class Scalar>
Teuchos::RCP<const Teuchos::Array<std::string> >
SinCosModel<Scalar>::get_p_names(int l) const
{
  if (!acceptModelParams_) {
    return Teuchos::null;
  }
  TEUCHOS_ASSERT_IN_RANGE_UPPER_EXCLUSIVE(l, 0, Np_);
  Teuchos::RCP<Teuchos::Array<std::string> > p_strings =
      Teuchos::rcp(new Teuchos::Array<std::string>());
  if (l == 0) {
    p_strings->push_back("Model Coefficient:  a");
    p_strings->push_back("Model Coefficient:  f");
    p_strings->push_back("Model Coefficient:  L");
  }
  else if (l == 1)
    p_strings->push_back("DxDp");
  else if (l == 2)
    p_strings->push_back("Dx_dotDp");
  return p_strings;
}
 
template <class Scalar>
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> >
SinCosModel<Scalar>::get_g_space(int j) const
{
  TEUCHOS_ASSERT_IN_RANGE_UPPER_EXCLUSIVE(j, 0, Ng_);
  return g_space_;
}
 
// private
 
template <class Scalar>
void SinCosModel<Scalar>::setupInOutArgs_() const
{
  if (isInitialized_) {
    return;
  }
 
  using Teuchos::RCP;
  typedef Thyra::ModelEvaluatorBase MEB;
  {
    // Set up prototypical InArgs
    MEB::InArgsSetup<Scalar> inArgs;
    inArgs.setModelEvalDescription(this->description());
    inArgs.setSupports(MEB::IN_ARG_t);
    inArgs.setSupports(MEB::IN_ARG_x);
    inArgs.setSupports(MEB::IN_ARG_beta);
    inArgs.setSupports(MEB::IN_ARG_x_dot);
    inArgs.setSupports(MEB::IN_ARG_alpha);
    if (acceptModelParams_) {
      inArgs.set_Np(Np_);
    }
    inArgs_ = inArgs;
  }
 
  {
    // Set up prototypical OutArgs
    MEB::OutArgsSetup<Scalar> outArgs;
    outArgs.setModelEvalDescription(this->description());
    outArgs.setSupports(MEB::OUT_ARG_f);
    outArgs.setSupports(MEB::OUT_ARG_W_op);
    if (acceptModelParams_) {
      outArgs.set_Np_Ng(Np_, Ng_);
      outArgs.setSupports(MEB::OUT_ARG_DfDp, 0, MEB::DERIV_MV_JACOBIAN_FORM);
      outArgs.setSupports(MEB::OUT_ARG_DgDp, 0, 0, MEB::DERIV_MV_JACOBIAN_FORM);
      outArgs.setSupports(MEB::OUT_ARG_DgDx, 0, MEB::DERIV_MV_GRADIENT_FORM);
    }
    outArgs_ = outArgs;
  }
 
  // Set up nominal values
  nominalValues_ = inArgs_;
  if (haveIC_) {
    nominalValues_.set_t(t0_ic_);
    const RCP<Thyra::VectorBase<Scalar> > x_ic = createMember(x_space_);
    {  // scope to delete DetachedVectorView
      Thyra::DetachedVectorView<Scalar> x_ic_view(*x_ic);
      x_ic_view[0] = a_ + b_ * sin((f_ / L_) * t0_ic_ + phi_);
      x_ic_view[1] = b_ * (f_ / L_) * cos((f_ / L_) * t0_ic_ + phi_);
    }
    nominalValues_.set_x(x_ic);
    if (acceptModelParams_) {
      const RCP<Thyra::VectorBase<Scalar> > p_ic = createMember(p_space_);
      {
        Thyra::DetachedVectorView<Scalar> p_ic_view(*p_ic);
        p_ic_view[0] = a_;
        p_ic_view[1] = f_;
        p_ic_view[2] = L_;
      }
      nominalValues_.set_p(0, p_ic);
    }
    const RCP<Thyra::VectorBase<Scalar> > x_dot_ic = createMember(x_space_);
    {  // scope to delete DetachedVectorView
      Thyra::DetachedVectorView<Scalar> x_dot_ic_view(*x_dot_ic);
      x_dot_ic_view[0] = b_ * (f_ / L_) * cos((f_ / L_) * t0_ic_ + phi_);
      x_dot_ic_view[1] =
          -b_ * (f_ / L_) * (f_ / L_) * sin((f_ / L_) * t0_ic_ + phi_);
    }
    nominalValues_.set_x_dot(x_dot_ic);
  }
 
  isInitialized_ = true;
}
 
template <class Scalar>
void SinCosModel<Scalar>::setParameterList(
    Teuchos::RCP<Teuchos::ParameterList> const &paramList)
{
  using Teuchos::get;
  using Teuchos::ParameterList;
  Teuchos::RCP<ParameterList> tmpPL =
      Teuchos::rcp(new ParameterList("SinCosModel"));
  if (paramList != Teuchos::null) tmpPL = paramList;
  tmpPL->validateParametersAndSetDefaults(*this->getValidParameters());
  this->setMyParamList(tmpPL);
  Teuchos::RCP<ParameterList> pl = this->getMyNonconstParamList();
  bool acceptModelParams         = get<bool>(*pl, "Accept model parameters");
  bool haveIC                    = get<bool>(*pl, "Provide nominal values");
  bool useDfDpAsTangent          = get<bool>(*pl, "Use DfDp as Tangent");
  if ((acceptModelParams != acceptModelParams_) || (haveIC != haveIC_)) {
    isInitialized_ = false;
  }
  acceptModelParams_ = acceptModelParams;
  haveIC_            = haveIC;
  useDfDpAsTangent_  = useDfDpAsTangent;
  a_                 = get<Scalar>(*pl, "Coeff a");
  f_                 = get<Scalar>(*pl, "Coeff f");
  L_                 = get<Scalar>(*pl, "Coeff L");
  x0_ic_             = get<Scalar>(*pl, "IC x0");
  x1_ic_             = get<Scalar>(*pl, "IC x1");
  t0_ic_             = get<Scalar>(*pl, "IC t0");
  calculateCoeffFromIC_();
  setupInOutArgs_();
}
 
template <class Scalar>
Teuchos::RCP<const Teuchos::ParameterList>
SinCosModel<Scalar>::getValidParameters() const
{
  static Teuchos::RCP<const Teuchos::ParameterList> validPL;
  if (is_null(validPL)) {
    Teuchos::RCP<Teuchos::ParameterList> pl = Teuchos::parameterList();
    pl->set("Accept model parameters", false);
    pl->set("Provide nominal values", true);
    pl->set("Use DfDp as Tangent", false);
    pl->set<std::string>("Output File Name", "Tempus_BDF2_SinCos");
    Teuchos::setDoubleParameter("Coeff a", 0.0, "Coefficient a in model", &*pl);
    Teuchos::setDoubleParameter("Coeff f", 1.0, "Coefficient f in model", &*pl);
    Teuchos::setDoubleParameter("Coeff L", 1.0, "Coefficient L in model", &*pl);
    Teuchos::setDoubleParameter("IC x0", 0.0, "Initial Condition for x0", &*pl);
    Teuchos::setDoubleParameter("IC x1", 1.0, "Initial Condition for x1", &*pl);
    Teuchos::setDoubleParameter("IC t0", 0.0, "Initial time t0", &*pl);
    Teuchos::setIntParameter("Number of Time Step Sizes", 1,
                             "Number time step sizes for convergence study",
                             &*pl);
    validPL = pl;
  }
  return validPL;
}
 
template <class Scalar>
void SinCosModel<Scalar>::calculateCoeffFromIC_()
{
  phi_ = atan(((f_ / L_) / x1_ic_) * (x0_ic_ - a_)) - (f_ / L_) * t0_ic_;
  b_   = x1_ic_ / ((f_ / L_) * cos((f_ / L_) * t0_ic_ + phi_));
}
 
template <class Scalar>
Teuchos::RCP<Thyra::LinearOpWithSolveBase<Scalar> >
SinCosModelAdjoint<Scalar>::create_W() const
{
  using Teuchos::RCP;
  RCP<const Thyra::LinearOpWithSolveFactoryBase<Scalar> > W_factory =
      this->get_W_factory();
  RCP<Thyra::LinearOpBase<Scalar> > matrix = this->create_W_op();
  {
    // 01/20/09 tscoffe:  This is a total hack to provide a full rank matrix to
    // linearOpWithSolve because it ends up factoring the matrix during
    // initialization, which it really shouldn't do, or I'm doing something
    // wrong here.   The net effect is that I get exceptions thrown in
    // optimized mode due to the matrix being rank deficient unless I do this.
    RCP<Thyra::MultiVectorBase<Scalar> > multivec =
        Teuchos::rcp_dynamic_cast<Thyra::MultiVectorBase<Scalar> >(matrix,
                                                                   true);
    {
      RCP<Thyra::VectorBase<Scalar> > vec = Thyra::createMember(this->f_space_);
      {
        Thyra::DetachedVectorView<Scalar> vec_view(*vec);
        vec_view[0] = 0.0;
        vec_view[1] = 1.0;
      }
      V_V(multivec->col(0).ptr(), *vec);
      {
        Thyra::DetachedVectorView<Scalar> vec_view(*vec);
        vec_view[0] = 1.0;
        vec_view[1] = 0.0;
      }
      V_V(multivec->col(1).ptr(), *vec);
    }
  }
  RCP<Thyra::LinearOpWithSolveBase<Scalar> > W =
      Thyra::linearOpWithSolve<Scalar>(*W_factory, matrix);
  return W;
}
 
template <class Scalar>
Teuchos::RCP<Thyra::LinearOpBase<Scalar> >
SinCosModelAdjoint<Scalar>::create_W_op() const
{
  Teuchos::RCP<Thyra::MultiVectorBase<Scalar> > matrix =
      Thyra::createMembers(this->f_space_, this->dim_);
  return (matrix);
}
 
template <class Scalar>
Thyra::ModelEvaluatorBase::InArgs<Scalar>
SinCosModelAdjoint<Scalar>::createInArgs() const
{
  // This ME should use the same InArgs as the base SinCosModel.  However
  // we can't just use it's InArgs directly because the description won't
  // match (which is checked in debug builds).  Instead create a new InArgsSetup
  // initialized by SinCosModel::createInArgs() and set the description
  // appropriately.
  typedef Thyra::ModelEvaluatorBase MEB;
  MEB::InArgsSetup<Scalar> inArgs = SinCosModel<Scalar>::createInArgs();
  inArgs.setModelEvalDescription(this->description());
  return inArgs;
}
 
template <class Scalar>
Thyra::ModelEvaluatorBase::OutArgs<Scalar>
SinCosModelAdjoint<Scalar>::createOutArgsImpl() const
{
  typedef Thyra::ModelEvaluatorBase MEB;
  MEB::OutArgsSetup<Scalar> outArgs;
  outArgs.setModelEvalDescription(this->description());
  outArgs.setSupports(
      MEB::OUT_ARG_f);  // Apparently all models have to support f
  outArgs.setSupports(MEB::OUT_ARG_W_op);
  outArgs.set_Np_Ng(this->Np_, 0);
  return outArgs;
}
 
template <class Scalar>
void SinCosModelAdjoint<Scalar>::evalModelImpl(
    const Thyra::ModelEvaluatorBase::InArgs<Scalar> &inArgs,
    const Thyra::ModelEvaluatorBase::OutArgs<Scalar> &outArgs) const
{
  using Teuchos::RCP;
  using Teuchos::rcp_dynamic_cast;
  using Thyra::MultiVectorBase;
  using Thyra::VectorBase;
  TEUCHOS_TEST_FOR_EXCEPTION(!this->isInitialized_, std::logic_error,
                             "Error, setupInOutArgs_ must be called first!\n");
 
  const RCP<const VectorBase<Scalar> > x_in = inArgs.get_x().assert_not_null();
  Thyra::ConstDetachedVectorView<Scalar> x_in_view(*x_in);
 
  // double t = inArgs.get_t();
  // Scalar a = this->a_;
  Scalar f = this->f_;
  Scalar L = this->L_;
  if (this->acceptModelParams_) {
    const RCP<const VectorBase<Scalar> > p_in =
        inArgs.get_p(0).assert_not_null();
    Thyra::ConstDetachedVectorView<Scalar> p_in_view(*p_in);
    // a = p_in_view[0];
    f = p_in_view[1];
    L = p_in_view[2];
  }
 
  Scalar beta = inArgs.get_beta();
 
  const RCP<Thyra::LinearOpBase<Scalar> > W_out = outArgs.get_W_op();
  if (inArgs.get_x_dot().is_null()) {
    // Evaluate the Explicit ODE f(x,t) [= 0]
    if (!is_null(W_out)) {
      RCP<Thyra::MultiVectorBase<Scalar> > matrix =
          Teuchos::rcp_dynamic_cast<Thyra::MultiVectorBase<Scalar> >(W_out,
                                                                     true);
      Thyra::DetachedMultiVectorView<Scalar> matrix_view(*matrix);
      matrix_view(0, 0) = 0.0;                        // d(f0)/d(x0_n)
      matrix_view(1, 0) = +beta;                      // d(f0)/d(x1_n)
      matrix_view(0, 1) = -beta * (f / L) * (f / L);  // d(f1)/d(x0_n)
      matrix_view(1, 1) = 0.0;                        // d(f1)/d(x1_n)
      // Note: alpha = d(xdot)/d(x_n) and beta = d(x)/d(x_n)
    }
  }
  else {
    // Evaluate the implicit ODE f(xdot, x, t) [= 0]
    RCP<const VectorBase<Scalar> > x_dot_in;
    x_dot_in     = inArgs.get_x_dot().assert_not_null();
    Scalar alpha = inArgs.get_alpha();
    if (!is_null(W_out)) {
      RCP<Thyra::MultiVectorBase<Scalar> > matrix =
          Teuchos::rcp_dynamic_cast<Thyra::MultiVectorBase<Scalar> >(W_out,
                                                                     true);
      Thyra::DetachedMultiVectorView<Scalar> matrix_view(*matrix);
      matrix_view(0, 0) = alpha;                      // d(f0)/d(x0_n)
      matrix_view(1, 0) = -beta;                      // d(f0)/d(x1_n)
      matrix_view(0, 1) = +beta * (f / L) * (f / L);  // d(f1)/d(x0_n)
      matrix_view(1, 1) = alpha;                      // d(f1)/d(x1_n)
      // Note: alpha = d(xdot)/d(x_n) and beta = d(x)/d(x_n)
    }
  }
}
 
}  // namespace Tempus_Test
#endif  // TEMPUS_TEST_SINCOS_MODEL_IMPL_HPP