/// <summary>Initializes a new instance of the <see cref="Algorithm"/> class.
/// </summary>
/// <param name="gaussTschebyscheffConstantAbscissasIntegrator">The <see cref="GaussTschebyscheffConstAbscissaIntegrator"/> object which serves as factory for the current object.</param>
internal Algorithm(GaussTschebyscheffConstAbscissaIntegrator gaussTschebyscheffConstantAbscissasIntegrator)
{
m_IntegratorFactory = gaussTschebyscheffConstantAbscissasIntegrator;
WeightFunction = OneDimNumericalIntegrator.WeightFunction.Create(x => 1.0 / Math.Sqrt(1.0 - x * x));
m_EvaluationPoints = GaussianQuadrature.Tschebyscheff.GetValue(m_IntegratorFactory.Order, out m_Weight);
}
public void GetValue_OneOverWeightfunction_BenchmarkResult(
[Values(100, 125)]
int order)
{
var gaussTschebyscheffIntegrator = new GaussTschebyscheffConstAbscissaIntegrator(order);
var numericalIntegrator = gaussTschebyscheffIntegrator.Create();
double lowerBound = -1.0;
double upperBound = 1.0;
Assert.That(numericalIntegrator.TrySetBounds(lowerBound, upperBound) == true, String.Format("1-dimensional Integrator {0} does not support individual lower/upper bounds", numericalIntegrator.Factory.Name.String));
numericalIntegrator.FunctionToIntegrate = (x, k) => Math.Sqrt(1.0 - x * x); // for Tschebyscheff Integrator, the integrator is 1 in this case!
double expected = upperBound - lowerBound;
double actual = numericalIntegrator.GetValue();
Assert.That(actual, Is.EqualTo(expected).Within(1E-4), String.Format("1-dimensional integrator {0}.", numericalIntegrator.Factory.Name));
}
public void GetValue_OneOverWeightfunction_BenchmarkResult(
[Values(100, 150)]
int order,
[Values(-1.0, 2.5)]
double lowerBound,
[Values(1.0, 6.4)]
double upperBound)
{
var gaussTschebyscheffIntegrator = new GaussTschebyscheffConstAbscissaIntegrator(order);
var numericalIntegrator = gaussTschebyscheffIntegrator.Create();
Assert.That(numericalIntegrator.TrySetBounds(lowerBound, upperBound) == true, String.Format("1-dimensional Integrator {0} does not support individual lower/upper bounds", numericalIntegrator.Factory.Name.String));
numericalIntegrator.FunctionToIntegrate = (x, k) => 1.0 / numericalIntegrator.WeightFunction.GetValue(x);
double expected = upperBound - lowerBound;
double actual = numericalIntegrator.GetValue();
Assert.That(actual, Is.EqualTo(expected).Within(1E-3), String.Format("1-dimensional integrator {0}.", numericalIntegrator.Factory.Name));
}
public void GetValue_ThreeTimesXToThePowerOf3_BenchmarkResult(
[Values(80, 100, 125)]
int order)
{
var gaussTschebyscheffIntegrator = new GaussTschebyscheffConstAbscissaIntegrator(order);
var numericalIntegrator = gaussTschebyscheffIntegrator.Create();
double lowerBound = -1.0;
double upperBound = 1.0;
Assert.That(numericalIntegrator.TrySetBounds(lowerBound, upperBound) == true, String.Format("1-dimensional Integrator {0} does not support individual lower/upper bounds", numericalIntegrator.Factory.Name.String));
numericalIntegrator.FunctionToIntegrate = (x, k) => 3.0 * x * x * x;
double a = 1.0; // see §21.5.25 in "Taschenbuch der Mathematik", Bronstein, Semendjajew, Musiol, Mühlig, 1995
double expected = 3.0 / 5.0 * Math.Sqrt(Math.Pow(a * a - upperBound * upperBound, 5)) - a * a * Math.Sqrt(Math.Pow(a * a - upperBound * upperBound, 3)) - 3.0 / 5.0 * Math.Sqrt(Math.Pow(a * a - lowerBound * lowerBound, 5)) - a * a * Math.Sqrt(Math.Pow(a * a - lowerBound * lowerBound, 3));
double actual = numericalIntegrator.GetValue();
Assert.That(actual, Is.EqualTo(expected).Within(1E-6), String.Format("1-dimensional integrator {0}.", numericalIntegrator.Factory.Name));
}