/// <summary>
/// Create a rational (with poles; Bulirsch & Stoer) interpolation based on arbitrary points.
/// </summary>
/// <param name="points">The sample points t. Supports both lists and arrays.</param>
/// <param name="values">The sample point values x(t). Supports both lists and arrays.</param>
/// <returns>
/// An interpolation scheme optimized for the given sample points and values,
/// which can then be used to compute interpolations and extrapolations
/// on arbitrary points.
/// </returns>
public static IInterpolationMethod CreateRational(
IList<double> points,
IList<double> values
)
{
RationalInterpolation method = new RationalInterpolation();
method.Init(points, values);
return method;
}
public void TestInterpolationMethod_RationalWithPoles()
{
double[] t = new double[] { 0, 1, 3, 4, 5 };
double[] x = new double[] { 0, 3, 1000, -1000, 3 };
RationalInterpolation method = new RationalInterpolation();
method.Init(t, x);
for(int i = 0; i < t.Length; i++)
{
Assert.AreEqual(x[i], method.Interpolate(t[i]), "Exact Point " + i.ToString());
}
// Maple: "with(CurveFitting);"
// Maple: "evalf(subs({x=0.1},RationalInterpolation([[0,0],[1,3],[3,1000],[4,-1000], [5,3]], x)),20);"
NumericAssert.AreAlmostEqual(.19389203383553566255, method.Interpolate(0.1), 1e-14, "A 0.1");
NumericAssert.AreAlmostEqual(.88132900698869875369, method.Interpolate(0.4), 1e-14, "A 0.4");
NumericAssert.AreAlmostEqual(3.5057665681580626913, method.Interpolate(1.1), 1e-15, "A 1.1");
NumericAssert.AreAlmostEqual(1548.7666642693586902, method.Interpolate(3.01), 1e-13, "A 3.01");
NumericAssert.AreAlmostEqual(3362.2564334253633516, method.Interpolate(3.02), 1e-13, "A 3.02");
NumericAssert.AreAlmostEqual(-22332.603641443806014, method.Interpolate(3.03), 1e-12, "A 3.03");
NumericAssert.AreAlmostEqual(-440.30323769822443789, method.Interpolate(3.1), 1e-14, "A 3.1");
NumericAssert.AreAlmostEqual(-202.42421196280566349, method.Interpolate(3.2), 1e-14, "A 3.2");
NumericAssert.AreAlmostEqual(21.208249625210155439, method.Interpolate(4.5), 1e-14, "A 4.5");
NumericAssert.AreAlmostEqual(-4.8936986959784751517, method.Interpolate(10.0), 1e-13, "A 10.0");
NumericAssert.AreAlmostEqual(-3.6017584308603731307, method.Interpolate(-10.0), 1e-13, "A -10.0");
}
public void TestInterpolationMethod_RationalWithPoles()
{
double[] t = new double[] { 0, 1, 3, 4, 5 };
double[] x = new double[] { 0, 3, 1000, -1000, 3 };
RationalInterpolation method = new RationalInterpolation();
method.Init(t, x);
for(int i = 0; i < t.Length; i++)
{
Assert.That(method.Interpolate(t[i]), Is.EqualTo(x[i]), "Exact Point " + i.ToString());
}
// Maple: "with(CurveFitting);"
// Maple: "evalf(subs({x=0.1},RationalInterpolation([[0,0],[1,3],[3,1000],[4,-1000], [5,3]], x)),20);"
Assert.That(method.Interpolate(0.1), NumericIs.AlmostEqualTo(.19389203383553566255, 1e-14), "A 0.1");
Assert.That(method.Interpolate(0.4), NumericIs.AlmostEqualTo(.88132900698869875369, 1e-14), "A 0.4");
Assert.That(method.Interpolate(1.1), NumericIs.AlmostEqualTo(3.5057665681580626913, 1e-15), "A 1.1");
Assert.That(method.Interpolate(3.01), NumericIs.AlmostEqualTo(1548.7666642693586902, 1e-13), "A 3.01");
Assert.That(method.Interpolate(3.02), NumericIs.AlmostEqualTo(3362.2564334253633516, 1e-13), "A 3.02");
Assert.That(method.Interpolate(3.03), NumericIs.AlmostEqualTo(-22332.603641443806014, 1e-12), "A 3.03");
Assert.That(method.Interpolate(3.1), NumericIs.AlmostEqualTo(-440.30323769822443789, 1e-14), "A 3.1");
Assert.That(method.Interpolate(3.2), NumericIs.AlmostEqualTo(-202.42421196280566349, 1e-14), "A 3.2");
Assert.That(method.Interpolate(4.5), NumericIs.AlmostEqualTo(21.208249625210155439, 1e-14), "A 4.5");
Assert.That(method.Interpolate(10.0), NumericIs.AlmostEqualTo(-4.8936986959784751517, 1e-13), "A 10.0");
Assert.That(method.Interpolate(-10.0), NumericIs.AlmostEqualTo(-3.6017584308603731307, 1e-13), "A -10.0");
// Test Linear Case
for(int k = 2; k < 6; k++)
{
double[] linx, liny, linxtest, linytest;
BuildLinearCase(2, k, out linx, out liny, out linxtest, out linytest);
IInterpolationMethod linearMethod = Interpolation.CreateRational(linx, liny);
for(int i = 0; i < linxtest.Length; i++)
{
// very weak test, but rational with poles is incredibly bad in the linear case
Assert.That(linearMethod.Interpolate(linxtest[i]), Is.Not.NaN, String.Format("Linear k={0} i={1}", k, i));
}
}
}