public void Apply_Expectation_has_base_point_as_in_base_process_and_fiber_point_as_original_fiber_point_plus_time_times_average_velocity()
{
var baseProcess = new RotatingWienerProcess(diffusionCoefficient: 0.577, angularVelocity: new Vector3(-0.8, 0.4, 1.3));
var integralProcess = CreateIntegralProcess(baseProcess);
var result = integralProcess.Apply(_point, _time).Expectation;
var baseResult = (OVector)ExtensionStochasticProcess.GetBaseState(result);
var fiberResult = (OVector)ExtensionStochasticProcess.GetFiberState(result);
var expectedBaseResult = (OVector)baseProcess.Apply(_basePoint, _time).Expectation;
Expect((baseResult - expectedBaseResult).Norm(), Is.LessThan(_tolerance));
var exepectedFiberResult = ExpectedFiberResult(baseResult);
Expect((fiberResult - exepectedFiberResult).Norm(), Is.LessThan(_tolerance));
}
public void Apply_Covariance_results_from_base_covariance_by_conjugating_with_numeric_differential()
{
const double eps = 1e-5;
const double tolerance = 1e-7;
var diffusionMatrix = new SymmetricMatrix(new double[][]
{
new double [] { +0.3, },
new double [] { -0.1, +0.4, },
new double [] { +0.1, +0.2, +0.4 }
});
var baseProcess = new WienerProcess(diffusionMatrix);
var integralProcess = CreateIntegralProcess(baseProcess);
var evolution = integralProcess.Apply(_point, _time);
var baseResult = (OVector)ExtensionStochasticProcess.GetBaseState(evolution.Expectation);
var baseDim = baseProcess.StateSpace.Dimension;
var differential = new Matrix(integralProcess.StateSpace.Dimension, baseDim);
differential.SetSubmatrix(integralProcess.BaseCoordinateIndex(), 0, Matrix.Id(baseDim));
for (int j = 0; j < baseDim; j++)
{
var delta = eps * Vector.Basis(j, baseDim);
var retarted = baseResult - delta;
var advanced = baseResult + delta;
var gradient = (ExpectedFiberResult(advanced) - ExpectedFiberResult(retarted)) / (2 * eps);
differential.SetSubmatrix(integralProcess.FiberCoordinateIndex(), j, gradient.AsColumn());
}
var expectedCovariance = baseProcess.Apply(_basePoint, _time).Covariance.Conjugate(differential);
Expect((evolution.Covariance - expectedCovariance).FrobeniusNorm(), Is.LessThan(tolerance));
}
public void SetUp()
{
_point = ExtensionStochasticProcess.CreateState(_basePoint, _fiberPoint);
}