TEUCHOS_UNIT_TEST( Rythmos_GlobalErrorEstimator, SinCos ) {
typedef Teuchos::ScalarTraits<double> ST;
// Forward Solve, storing data in linear interpolation buffer
int storageLimit = 100;
double finalTime = 0.1;
double dt = 0.1;
RCP<IntegratorBuilder<double> > ib = integratorBuilder<double>();
{
RCP<ParameterList> ibPL = Teuchos::parameterList();
ibPL->sublist("Integrator Settings").sublist("Integrator Selection").set("Integrator Type","Default Integrator");
ibPL->sublist("Integrator Settings").set("Final Time",finalTime);
ibPL->sublist("Integration Control Strategy Selection").set("Integration Control Strategy Type","Simple Integration Control Strategy");
ibPL->sublist("Integration Control Strategy Selection").sublist("Simple Integration Control Strategy").set("Take Variable Steps",false);
ibPL->sublist("Integration Control Strategy Selection").sublist("Simple Integration Control Strategy").set("Fixed dt",dt);
ibPL->sublist("Stepper Settings").sublist("Stepper Selection").set("Stepper Type","Backward Euler");
//ibPL->sublist("Stepper Settings").sublist("Stepper Selection").set("Stepper Type","Implicit RK");
//ibPL->sublist("Stepper Settings").sublist("Runge Kutta Butcher Tableau Selection").set("Runge Kutta Butcher Tableau Type","Backward Euler");
ibPL->sublist("Interpolation Buffer Settings").sublist("Trailing Interpolation Buffer Selection").set("Interpolation Buffer Type","Interpolation Buffer");
ibPL->sublist("Interpolation Buffer Settings").sublist("Trailing Interpolation Buffer Selection").sublist("Interpolation Buffer").set("StorageLimit",storageLimit);
ibPL->sublist("Interpolation Buffer Settings").sublist("Interpolator Selection").set("Interpolator Type","Linear Interpolator");
ib->setParameterList(ibPL);
}
RCP<SinCosModel> fwdModel = sinCosModel(true); // implicit formulation
Thyra::ModelEvaluatorBase::InArgs<double> fwdIC = fwdModel->getNominalValues();
RCP<Thyra::NonlinearSolverBase<double> > fwdNLSolver = timeStepNonlinearSolver<double>();
RCP<IntegratorBase<double> > fwdIntegrator = ib->create(fwdModel,fwdIC,fwdNLSolver);
RCP<const VectorBase<double> > x_final;
{
Array<double> time_vec;
time_vec.push_back(finalTime);
Array<RCP<const Thyra::VectorBase<double> > > x_final_array;
fwdIntegrator->getFwdPoints(time_vec,&x_final_array,NULL,NULL);
x_final = x_final_array[0];
}
// Verify x_final is correct
{
// Defaults from SinCos Model:
double f = 1.0;
double L = 1.0;
double a = 0.0;
double x_ic_0 = 0.0;
double x_ic_1 = 1.0;
double x_0 = dt/(1.0+std::pow(dt*f/L,2))*(x_ic_0/dt+x_ic_1+dt*std::pow(f/L,2)*a);
double x_1 = dt/(1.0+std::pow(dt*f/L,2))*(-std::pow(f/L,2)*x_ic_0+x_ic_1/dt+std::pow(f/L,2)*a);
double tol = 1.0e-10;
Thyra::ConstDetachedVectorView<double> x_final_view( *x_final );
TEST_FLOATING_EQUALITY( x_final_view[0], x_0, tol );
TEST_FLOATING_EQUALITY( x_final_view[1], x_1, tol );
}
// Copy InterpolationBuffer data into Cubic Spline interpolation buffer for use in Adjoint Solve
TimeRange<double> fwdTimeRange;
RCP<InterpolationBufferBase<double> > fwdCubicSplineInterpBuffer;
{
RCP<PointwiseInterpolationBufferAppender<double> > piba = pointwiseInterpolationBufferAppender<double>();
RCP<InterpolationBuffer<double> > sinkInterpBuffer = interpolationBuffer<double>();
sinkInterpBuffer->setStorage(storageLimit);
RCP<CubicSplineInterpolator<double> > csi = cubicSplineInterpolator<double>();
sinkInterpBuffer->setInterpolator(csi);
RCP<const InterpolationBufferBase<double> > sourceInterpBuffer;
{
RCP<TrailingInterpolationBufferAcceptingIntegratorBase<double> > tibaib =
Teuchos::rcp_dynamic_cast<TrailingInterpolationBufferAcceptingIntegratorBase<double> >(fwdIntegrator,true);
sourceInterpBuffer = tibaib->getTrailingInterpolationBuffer();
}
fwdTimeRange = sourceInterpBuffer->getTimeRange();
piba->append(*sourceInterpBuffer, fwdTimeRange, Teuchos::outArg(*sinkInterpBuffer));
fwdCubicSplineInterpBuffer = sinkInterpBuffer;
TimeRange<double> sourceRange = sourceInterpBuffer->getTimeRange();
TimeRange<double> sinkRange = sinkInterpBuffer->getTimeRange();
TEST_EQUALITY( sourceRange.lower(), sinkRange.lower() );
TEST_EQUALITY( sourceRange.upper(), sinkRange.upper() );
}
// Adjoint Solve, reading forward solve data from Cubic Spline interpolation buffer
{
RCP<ParameterList> ibPL = Teuchos::parameterList();
ibPL->sublist("Integrator Settings").sublist("Integrator Selection").set("Integrator Type","Default Integrator");
ibPL->sublist("Integrator Settings").set("Final Time",finalTime);
ibPL->sublist("Integration Control Strategy Selection").set("Integration Control Strategy Type","Simple Integration Control Strategy");
ibPL->sublist("Integration Control Strategy Selection").sublist("Simple Integration Control Strategy").set("Take Variable Steps",false);
ibPL->sublist("Integration Control Strategy Selection").sublist("Simple Integration Control Strategy").set("Fixed dt",dt);
ibPL->sublist("Stepper Settings").sublist("Stepper Selection").set("Stepper Type","Backward Euler");
//ibPL->sublist("Stepper Settings").sublist("Stepper Selection").set("Stepper Type","Implicit RK");
//ibPL->sublist("Stepper Settings").sublist("Runge Kutta Butcher Tableau Selection").set("Runge Kutta Butcher Tableau Type","Implicit 1 Stage 2nd order Gauss");
ibPL->sublist("Interpolation Buffer Settings").sublist("Trailing Interpolation Buffer Selection").set("Interpolation Buffer Type","Interpolation Buffer");
ibPL->sublist("Interpolation Buffer Settings").sublist("Trailing Interpolation Buffer Selection").sublist("Interpolation Buffer").set("StorageLimit",storageLimit);
ibPL->sublist("Interpolation Buffer Settings").sublist("Interpolator Selection").set("Interpolator Type","Linear Interpolator");
ib->setParameterList(ibPL);
}
RCP<Thyra::ModelEvaluator<double> > adjModel;
{
RCP<Rythmos::AdjointModelEvaluator<double> > model =
Rythmos::adjointModelEvaluator<double>(
fwdModel, fwdTimeRange
);
//model->setFwdStateSolutionBuffer(fwdCubicSplineInterpBuffer);
adjModel = model;
}
Thyra::ModelEvaluatorBase::InArgs<double> adjIC = adjModel->getNominalValues();
double phi_ic_0 = 2.0;
double phi_ic_1 = 3.0;
{
// Initial conditions for adjoint:
const RCP<const Thyra::VectorSpaceBase<double> >
f_space = fwdModel->get_f_space();
const RCP<Thyra::VectorBase<double> > x_ic = createMember(f_space);
{
Thyra::DetachedVectorView<double> x_ic_view( *x_ic );
x_ic_view[0] = phi_ic_0;
x_ic_view[1] = phi_ic_1;
}
const RCP<Thyra::VectorBase<double> > xdot_ic = createMember(f_space);
V_S( Teuchos::outArg(*xdot_ic), ST::zero() );
adjIC.set_x(x_ic);
adjIC.set_x_dot(xdot_ic);
}
RCP<Thyra::LinearNonlinearSolver<double> > adjNLSolver = Thyra::linearNonlinearSolver<double>();
RCP<IntegratorBase<double> > adjIntegrator = ib->create(adjModel,adjIC,adjNLSolver);
RCP<const VectorBase<double> > phi_final;
{
Array<double> time_vec;
time_vec.push_back(finalTime);
Array<RCP<const Thyra::VectorBase<double> > > phi_final_array;
adjIntegrator->getFwdPoints(time_vec,&phi_final_array,NULL,NULL);
phi_final = phi_final_array[0];
}
// Verify phi_final is correct
{
// Defaults from SinCos Model:
double f = 1.0;
double L = 1.0;
double h = -dt;
double phi_0 = 1.0/(1.0+std::pow(f*h/L,2.0))*(phi_ic_0+std::pow(f/L,2.0)*h*phi_ic_1);
double phi_1 = 1.0/(1.0+std::pow(f*h/L,2.0))*(-h*phi_ic_0+phi_ic_1);
double tol = 1.0e-10;
Thyra::ConstDetachedVectorView<double> phi_final_view( *phi_final );
TEST_FLOATING_EQUALITY( phi_final_view[0], phi_0, tol );
TEST_FLOATING_EQUALITY( phi_final_view[1], phi_1, tol );
}
// Compute error estimate
//TEST_ASSERT( false );
}
void
Piro::MatrixFreeLinearOp<Scalar>::applyImpl(
const Thyra::EOpTransp M_trans,
const Thyra::MultiVectorBase<Scalar> &X,
const Teuchos::Ptr<Thyra::MultiVectorBase<Scalar> > &Y,
const Scalar alpha,
const Scalar beta) const
{
using Teuchos::RCP;
using Teuchos::Ptr;
TEUCHOS_TEST_FOR_EXCEPTION(
!this->opSupported(M_trans),
Thyra::Exceptions::OpNotSupported,
this->description() << " does not support operation " << Thyra::toString(M_trans));
TEUCHOS_TEST_FOR_EXCEPTION(
!X.range()->isCompatible(*this->domain()),
Thyra::Exceptions::IncompatibleVectorSpaces,
"Domain of " << this->description() << ": " << this->domain()->description() <<
" is not compatible with column space of " << X.description() << ": " << X.range()->description());
TEUCHOS_TEST_FOR_EXCEPTION(
!Y->range()->isCompatible(*this->range()),
Thyra::Exceptions::IncompatibleVectorSpaces,
"Range of " << this->description() << ": " << this->range()->description() <<
" is not compatible with column space of " << Y->description() << ": " << Y->range()->description());
TEUCHOS_TEST_FOR_EXCEPTION(
!Y->domain()->isCompatible(*X.domain()),
Thyra::Exceptions::IncompatibleVectorSpaces,
"Row space of " << Y->description() << ": " << Y->domain()->description() <<
" is not compatible with row space of " << X.description() << ": " << X.domain()->description());
TEUCHOS_TEST_FOR_EXCEPTION(
&X == Y.get(),
std::logic_error,
"X and Y arguments are both aliases of " << X.description());
if (alpha == Teuchos::ScalarTraits<Scalar>::zero()) {
// Y <- beta * Y
Thyra::Vt_S(Y, beta);
return;
}
typedef typename Teuchos::ScalarTraits<Scalar>::magnitudeType ScalarMagnitude;
RCP<const Thyra::VectorBase<Scalar> > x_dot_base;
if (basePoint_.supports(Thyra::ModelEvaluatorBase::IN_ARG_x_dot))
x_dot_base = basePoint_.get_x_dot();
RCP<const Thyra::VectorBase<Scalar> > x_base = basePoint_.get_x();
if (Teuchos::is_null(x_base)) {
x_base = model_->getNominalValues().get_x();
}
x_base.assert_not_null();
const ScalarMagnitude norm_x_base = Thyra::norm_2(*x_base);
// Number of columns common to both vectors X and Y
// (X and Y have compatible row spaces)
const Thyra::Ordinal colCount = X.domain()->dim();
for (Teuchos::Ordinal j = Teuchos::Ordinal(); j < colCount; ++j) {
const RCP<const Thyra::VectorBase<Scalar> > X_vec = X.col(j);
const RCP<Thyra::VectorBase<Scalar> > Y_vec = Y->col(j);
const ScalarMagnitude norm_dx = Thyra::norm_2(*X_vec);
if (norm_dx == Teuchos::ScalarTraits<ScalarMagnitude>::zero()) {
if (beta == Teuchos::ScalarTraits<Scalar>::zero()) {
// Y_vec <- 0
Thyra::put_scalar(Teuchos::ScalarTraits<ScalarMagnitude>::zero(), Y_vec.ptr());
} else {
// Y_vec <- beta * Y_vec
Thyra::scale(beta, Y_vec.ptr());
}
} else {
// Scalar perturbation
const ScalarMagnitude relative_pert_ratio = static_cast<ScalarMagnitude>(lambda_);
const ScalarMagnitude eta = (relative_pert_ratio * ((norm_x_base / norm_dx) + relative_pert_ratio));
// Compute perturbed residual
// Dynamic: f_pert <- f(x_dot_base + eta * (W_alpha * X), x_base + eta * (W_beta * X))
// Static: f_pert <- f(x_base + eta * X)
const RCP<Thyra::VectorBase<Scalar> > f_pert = Thyra::createMember(this->range());
{
Thyra::ModelEvaluatorBase::InArgs<Scalar> pertInArgs = model_->createInArgs();
{
pertInArgs.setArgs(basePoint_);
const bool isDynamic = Teuchos::nonnull(x_dot_base);
if (isDynamic) {
const RCP<Thyra::VectorBase<Scalar> > x_dot_pert = Thyra::createMember(this->domain());
const Scalar W_alpha = pertInArgs.get_alpha();
Thyra::V_VpStV<Scalar>(x_dot_pert.ptr(), *x_dot_base, W_alpha * eta, *X_vec);
pertInArgs.set_x_dot(x_dot_pert);
}
const RCP<Thyra::VectorBase<Scalar> > x_pert = Thyra::createMember(this->domain());
const Scalar W_beta = isDynamic ? pertInArgs.get_beta() : Teuchos::ScalarTraits<Scalar>::one();
Thyra::V_VpStV<Scalar>(x_pert.ptr(), *x_base, W_beta * eta, *X_vec);
pertInArgs.set_x(x_pert);
}
Thyra::ModelEvaluatorBase::OutArgs<Scalar> pertOutArgs = model_->createOutArgs();
{
pertOutArgs.set_f(f_pert);
}
model_->evalModel(pertInArgs, pertOutArgs);
}
// Y <- alpha * (1/eta) * (f_pert - f_base) + beta * Y
const Scalar alpha_over_eta = alpha / eta;
if (beta == Teuchos::ScalarTraits<Scalar>::zero()) {
// Y <- alpha * (1/eta) * (f_pert - f_base)
Thyra::V_StVpStV<Scalar>(Y_vec.ptr(), alpha_over_eta, *f_pert, -alpha_over_eta, *f_base_);
} else {
// Aliasing f_pert and alpha_op_X (f_pert == alpha_op_X)
const RCP<Thyra::VectorBase<Scalar> > alpha_op_X = f_pert;
// alpha_op_X <- alpha * (1/eta) * (f_pert - f_base)
Thyra::Vp_StV(alpha_op_X.ptr(), -Teuchos::ScalarTraits<Scalar>::one(), *f_base_);
const Scalar alpha_over_eta = alpha / eta;
Thyra::Vt_S(alpha_op_X.ptr(), alpha_over_eta);
// Y <- alpha_op_X + beta * Y
Thyra::Vp_V<Scalar>(Y_vec.ptr(), *alpha_op_X, beta);
}
}
}
}