public void AccuracyPerformanceTest_dim1()
{
//Create an ODE initial value problem
ODEInitialValueProblem ivp = new ODEInitialValueProblem(1, 0.015625, 0);
ExpressionParser parser = new ExpressionParser();
//1 dimensional first order nonlinear, nonhomogeneous, autonomous
ivp.F.funcs[0] = parser.EvaluateExpression("-(y+1)*(y+3)").ToDelegate("t", "y");
ivp.SetState(new VectorND(-2.0), 0);
//Solve the problem
ivp.SolveTo(20);
//Assess the error
double error = 0;
Func <double, double> actualSolution = (double tt) =>
{
return(-3 + 2 * Math.Pow((1 + Math.Exp(-2 * tt)), -1));
};
double a = 1; //test error on [a,b]
double b = 20;
double htest = 1; //test at every this
for (double t = a; t <= b; t += htest)
{
//Debug.Log("Estimated solution at t = " + t + ":" + ivp.SolutionData(0, t)
//+ " ; versus Actual solution at t = " + t + ":" + actualSolution(t)
//+ " ; Error = " + (ivp.SolutionData(0, t) - actualSolution(t)));
error += Math.Abs(ivp.SolutionData(0, t) - actualSolution(t));
}
//Test error against required total precision over the interval
Assert.LessOrEqual(error, solution_total_error_benchmark * 20);
}
public void SolutionData_OutOfBoundsNegative()
{
//Create an ODE initial value problem
ODEInitialValueProblem ivp = new ODEInitialValueProblem(3, 0.2, 0);
ExpressionParser parser = new ExpressionParser();
//Define a system in which the solution will be (3,4,5) at all times
ivp.F.funcs[0] = parser.EvaluateExpression("0").ToDelegate("t");
ivp.F.funcs[1] = parser.EvaluateExpression("0").ToDelegate("t");
ivp.F.funcs[2] = parser.EvaluateExpression("0").ToDelegate("t");
ivp.SetState(new VectorND(3, 4, 5), 0);
//Solve the problem
ivp.SolveTo(3);
//Check the solution data at t=25 where there is no data
Assert.IsNaN(ivp.SolutionData(0, -1));
Assert.IsNaN(ivp.SolutionData(1, -1));
Assert.IsNaN(ivp.SolutionData(2, -1));
}
public void SolutionData_atUpperBound()
{
//Create an ODE initial value problem
ODEInitialValueProblem ivp = new ODEInitialValueProblem(3, 0.2, 0);
ExpressionParser parser = new ExpressionParser();
//Define a system in which the solution will be (3,4,5) at all times
ivp.F.funcs[0] = parser.EvaluateExpression("0").ToDelegate("t");
ivp.F.funcs[1] = parser.EvaluateExpression("0").ToDelegate("t");
ivp.F.funcs[2] = parser.EvaluateExpression("0").ToDelegate("t");
ivp.SetState(new VectorND(3, 4, 5), 0);
//Solve the problem
ivp.SolveTo(3);
//Check the solution data at t=3
Assert.AreEqual(3, ivp.SolutionData(0, 3), general_purpose_required_accuracy);
Assert.AreEqual(4, ivp.SolutionData(1, 3), general_purpose_required_accuracy);
Assert.AreEqual(5, ivp.SolutionData(2, 3), general_purpose_required_accuracy);
}
public void AccuracyPerformanceTest_dim3()
{
//Create an ODE initial value problem
ODEInitialValueProblem ivp = new ODEInitialValueProblem(3, 0.0001, 0);
ExpressionParser parser = new ExpressionParser();
//3 dimensional first order linear non-homogenous non-autonomous
ivp.F.funcs[0] = parser.EvaluateExpression("u1+2*u2-2*u3+e^(-t)").ToDelegate("t", "u1", "u2", "u3");
ivp.F.funcs[1] = parser.EvaluateExpression("u2+u3-2*e^(-t)").ToDelegate("t", "u1", "u2", "u3");
ivp.F.funcs[2] = parser.EvaluateExpression("u1+2*u2+e^(-t)").ToDelegate("t", "u1", "u2", "u3");
ivp.SetState(new VectorND(3, -1, 1), 0);
//Solve the problem
ivp.SolveTo(20);
//Assess the error
double error = 0;
Func <double, VectorND> actualSolution = (double tt) =>
{
VectorND r = new VectorND(3);
r[0] = -3 * Math.Exp(-tt) - 3 * Math.Sin(tt) + 6 * Math.Cos(tt);
r[1] = 1.5 * Math.Exp(-tt) + 0.3 * Math.Sin(tt) - 2.1 * Math.Cos(tt) - 0.4 * Math.Exp(2 * tt);
r[2] = -Math.Exp(-tt) + 2.4 * Math.Cos(tt) + 1.8 * Math.Sin(tt) - 0.4 * Math.Exp(2 * tt);
return(r);
};
double a = 0; //test error on [a,b]
double b = 1;
double htest = 0.1; //test at every this
for (double t = a; t <= b; t += htest)
{
error += Math.Abs(ivp.SolutionData(0, t) - actualSolution(t)[0]);
error += Math.Abs(ivp.SolutionData(1, t) - actualSolution(t)[1]);
error += Math.Abs(ivp.SolutionData(2, t) - actualSolution(t)[2]);
}
//Test error against required total precision over the interval
Assert.LessOrEqual(error, solution_total_error_benchmark * 30); //3D * 10 points = 30 values
}
//Updates the object's position
public void UpdateObjectPosition()
{
//Some error checking, just in case. If error, simulation retains previous position.
if ((currentTime < ivp.GetDataLowerBound()) || (currentTime > ivp.GetDataUpperBound()))
{
//if (!(paused))
Debug.Log("Data out of bounds error at time = " + currentTime
+ "; Available data is on [" + ivp.GetDataLowerBound()
+ ", " + ivp.GetDataUpperBound() + "]");
}
else
{
if (!float.IsNaN((float)ivp.SolutionData(xIndex, currentTime)) && !float.IsNaN((float)ivp.SolutionData(yIndex, currentTime)) && !float.IsNaN((float)ivp.SolutionData(zIndex, currentTime)) &&
!float.IsInfinity((float)ivp.SolutionData(xIndex, currentTime)) && !float.IsInfinity((float)ivp.SolutionData(yIndex, currentTime)) && !float.IsInfinity((float)ivp.SolutionData(zIndex, currentTime)))
{
gameObject.transform.position = new Vector3(
(float)ivp.SolutionData(xIndex, currentTime),
(float)ivp.SolutionData(yIndex, currentTime),
(float)ivp.SolutionData(zIndex, currentTime));
}
}
}