public void TestInterpolationMethod_NevillePolynomial()
{
double[] t = new double[] { 0.0, 1.0, 3.0, 4.0 };
double[] x = new double[] { 0.0, 3.0, 1.0, 3.0 };
IInterpolationMethod method = Interpolation.CreatePolynomial(t, x);
Assert.IsInstanceOfType(typeof(PolynomialInterpolation), method, "Type");
double dx, d2x;
for (int i = 0; i < t.Length; i++)
{
// verify the interpolated values exactly at the sample points.
Assert.AreEqual(x[i], method.Interpolate(t[i]), "A Exact Point " + i.ToString());
Assert.AreEqual(x[i], method.Differentiate(t[i], out dx, out d2x), "B Exact Point " + i.ToString());
}
// Maple: "with(CurveFitting);"
// Maple: "evalf(subs({x=0.1},PolynomialInterpolation([[0,0],[1,3],[3,1],[4,3]], x)),20);"
NumericAssert.AreAlmostEqual(.57225000000000000000, method.Interpolate(0.1), 1e-15, "A 0.1");
NumericAssert.AreAlmostEqual(.57225000000000000000, method.Differentiate(0.1, out dx, out d2x), 1e-15, "B 0.1");
NumericAssert.AreAlmostEqual(1.8840000000000000000, method.Interpolate(0.4), 1e-15, "A 0.4");
NumericAssert.AreAlmostEqual(1.8840000000000000000, method.Differentiate(0.4, out dx, out d2x), 1e-15, "B 0.4");
NumericAssert.AreAlmostEqual(3.0314166666666666667, method.Interpolate(1.1), 1e-15, "A 1.1");
NumericAssert.AreAlmostEqual(3.0314166666666666667, method.Differentiate(1.1, out dx, out d2x), 1e-15, "B 1.1");
NumericAssert.AreAlmostEqual(1.034666666666666667, method.Interpolate(3.2), 1e-15, "A 3.2");
NumericAssert.AreAlmostEqual(1.034666666666666667, method.Differentiate(3.2, out dx, out d2x), 1e-15, "B 3.2");
NumericAssert.AreAlmostEqual(6.281250000000000000, method.Interpolate(4.5), 1e-15, "A 4.5");
NumericAssert.AreAlmostEqual(6.281250000000000000, method.Differentiate(4.5, out dx, out d2x), 1e-15, "B 4.5");
NumericAssert.AreAlmostEqual(277.50000000000000000, method.Interpolate(10.0), 1e-15, "A 10.0");
NumericAssert.AreAlmostEqual(277.50000000000000000, method.Differentiate(10.0, out dx, out d2x), 1e-15, "B 10.0");
NumericAssert.AreAlmostEqual(-1010.8333333333333333, method.Interpolate(-10.0), 1e-15, "A -10.0");
NumericAssert.AreAlmostEqual(-1010.8333333333333333, method.Differentiate(-10.0, out dx, out d2x), 1e-15, "B -10.0");
}
public void TestInterpolationMethod_NevillePolynomial()
{
double[] t = new double[] { 0.0, 1.0, 3.0, 4.0 };
double[] x = new double[] { 0.0, 3.0, 1.0, 3.0 };
IInterpolationMethod method = Interpolation.CreatePolynomial(t, x);
Assert.That(method, Is.TypeOf(typeof(PolynomialInterpolation)), "Type");
double dx, d2x;
for (int i = 0; i < t.Length; i++)
{
// verify the interpolated values exactly at the sample points.
Assert.That(method.Interpolate(t[i]), Is.EqualTo(x[i]), "A Exact Point " + i.ToString());
Assert.That(method.Differentiate(t[i], out dx, out d2x), Is.EqualTo(x[i]), "B Exact Point " + i.ToString());
}
// Maple: "with(CurveFitting);"
// Maple: "evalf(subs({x=0.1},PolynomialInterpolation([[0,0],[1,3],[3,1],[4,3]], x)),20);"
Assert.That(method.Interpolate(0.1), NumericIs.AlmostEqualTo(.57225000000000000000, 1e-15), "A 0.1");
Assert.That(method.Differentiate(0.1, out dx, out d2x), NumericIs.AlmostEqualTo(.57225000000000000000, 1e-15), "B 0.1");
Assert.That(method.Interpolate(0.4), NumericIs.AlmostEqualTo(1.8840000000000000000, 1e-15), "A 0.4");
Assert.That(method.Differentiate(0.4, out dx, out d2x), NumericIs.AlmostEqualTo(1.8840000000000000000, 1e-15), "B 0.4");
Assert.That(method.Interpolate(1.1), NumericIs.AlmostEqualTo(3.0314166666666666667, 1e-15), "A 1.1");
Assert.That(method.Differentiate(1.1, out dx, out d2x), NumericIs.AlmostEqualTo(3.0314166666666666667, 1e-15), "B 1.1");
Assert.That(method.Interpolate(3.2), NumericIs.AlmostEqualTo(1.034666666666666667, 1e-15), "A 3.2");
Assert.That(method.Differentiate(3.2, out dx, out d2x), NumericIs.AlmostEqualTo(1.034666666666666667, 1e-15), "B 3.2");
Assert.That(method.Interpolate(4.5), NumericIs.AlmostEqualTo(6.281250000000000000, 1e-15), "A 4.5");
Assert.That(method.Differentiate(4.5, out dx, out d2x), NumericIs.AlmostEqualTo(6.281250000000000000, 1e-15), "B 4.5");
Assert.That(method.Interpolate(10.0), NumericIs.AlmostEqualTo(277.50000000000000000, 1e-15), "A 10.0");
Assert.That(method.Differentiate(10.0, out dx, out d2x), NumericIs.AlmostEqualTo(277.50000000000000000, 1e-15), "B 10.0");
Assert.That(method.Interpolate(-10.0), NumericIs.AlmostEqualTo(-1010.8333333333333333, 1e-15), "A -10.0");
Assert.That(method.Differentiate(-10.0, out dx, out d2x), NumericIs.AlmostEqualTo(-1010.8333333333333333, 1e-15), "B -10.0");
// Test Linear Case
for (int k = 2; k < 7; k++)
{
double[] linx, liny, linxtest, linytest;
BuildLinearCase(2, k, out linx, out liny, out linxtest, out linytest);
IInterpolationMethod linearMethod = Interpolation.CreatePolynomial(linx, liny);
for (int i = 0; i < linxtest.Length; i++)
{
Assert.That(linearMethod.Interpolate(linxtest[i]), NumericIs.AlmostEqualTo(linytest[i], 1e-12), String.Format("Linear k={0} i={1}", k, i));
}
}
}