public static void ValidateProcess(IStochasticProcess process, IManifoldPoint point, double time, double eps, double tolerance)
{
var trivialEvolution = process.Apply(point, time: 0);
Assert.That(process.StateSpace.GetTranslation(trivialEvolution.Expectation, point).Norm(), Is.LessThan(_tolerance));
Assert.That(trivialEvolution.Covariance.FrobeniusNorm(), Is.LessThan(_tolerance));
ValidateMappingDifferential(process.Apply(time), point, eps, tolerance);
}
public static StochasticManifoldPoint Apply(this IStochasticProcess process, StochasticManifoldPoint stochasticPoint, double time)
{
var diff = process.ExpectationDifferential(stochasticPoint.Expectation, time);
var prediction = process.Apply(stochasticPoint.Expectation, time);
return(new StochasticManifoldPoint(prediction.Expectation, stochasticPoint.Covariance.Conjugate(diff) + prediction.Covariance));
}
public StochasticManifoldPoint Apply(IManifoldPoint point, double time)
{
var state = new State(point);
var basePoint = _baseProcess.Apply(state.BasePoint, time);
var fiberPoint = FiberEvolution(state, basePoint, time);
var answerExpectation = new ProductManifold.Point(basePoint.Expectation, fiberPoint.Point.Expectation);
var answerCovariance = new SymmetricMatrix(_stateSpace.Dimension);
answerCovariance.SetSubmatrix(0, basePoint.Covariance);
answerCovariance.SetSubmatrix(_baseProcess.StateSpace.Dimension, fiberPoint.Point.Covariance);
answerCovariance.SetSubmatrix(_baseProcess.StateSpace.Dimension, 0, fiberPoint.MixedCovariance);
return(new StochasticManifoldPoint(answerExpectation, answerCovariance));
}
public void Predict(double time)
{
_estimate = _processModel.Apply(_estimate, time - _time);
_time = time;
}
public StochasticManifoldPoint Apply(IManifoldPoint point)
{
return(_process.Apply(point, _time));
}
