public void TestInterpolationMethod_Chebyshev2BarycentricPolynomial()
{
double[] x = new double[] { 0.0, 3.0, 2.5, 1.0, 3.0 };
IInterpolationMethod method = Interpolation.CreateOnChebyshevSecondKindPoints(0.0, 4.0, x);
Assert.That(method, Is.TypeOf(typeof(ChebyshevSecondKindPolynomialInterpolation)), "Type");
double[] t = Interpolation.GenerateChebyshevSecondKindSamplePoints(0.0, 4.0, 5);
for (int i = 0; i < 4; i++)
{
// verify the generated chebyshev2 points
double tt = 2.0 + (2.0 * Math.Cos(Math.PI * i * 0.25));
Assert.That(tt, NumericIs.AlmostEqualTo(t[i]), "Point " + i.ToString());
// verify the interpolated values exactly at the sample points.
Assert.That(method.Interpolate(tt), NumericIs.AlmostEqualTo(x[i]), "A Exact Point " + i.ToString());
}
// Maple: "with(CurveFitting);"
// Maple: "evalf(subs({x=0.1},PolynomialInterpolation(evalf([[2*cos(0*Pi/4)+2,0],[2*cos(1*Pi/4)+2,3],[2*cos(2*Pi/4)+2,2.5],[2*cos(3*Pi/4)+2,1],[2*cos(4*Pi/4)+2,3]]), x)),20);"
Assert.That(method.Interpolate(0.1), NumericIs.AlmostEqualTo(2.4826419375703841423, 1e-14), "A 0.1");
Assert.That(method.Interpolate(0.4), NumericIs.AlmostEqualTo(1.3814129880730972522, 1e-14), "A 0.4");
Assert.That(method.Interpolate(1.1), NumericIs.AlmostEqualTo(.8808232156067110292, 1e-15), "A 1.1");
Assert.That(method.Interpolate(3.2), NumericIs.AlmostEqualTo(3.478116015902536997, 1e-15), "A 3.2");
Assert.That(method.Interpolate(4.5), NumericIs.AlmostEqualTo(-5.035612822087164912, 1e-15), "A 4.5");
Assert.That(method.Interpolate(10.0), NumericIs.AlmostEqualTo(-369.20562748477140583, 1e-13), "A 10.0");
Assert.That(method.Interpolate(-10.0), NumericIs.AlmostEqualTo(1199.4696961966999204, 1e-12), "A -10.0");
}