public void MultipleTests_Examples()
{
// Let's say we would like to compute the definite
// integral of the function f(x) = cos(x) from -1 to 1
Func <double, double> f = (x) => Math.Cos(x);
double a = -1;
double b = +1;
double trapez = TrapezoidalRule.Integrate(f, a, b, steps: 1000); // 1.6829414
double romberg = RombergMethod.Integrate(f, a, b); // 1.6829419
double nagk = NonAdaptiveGaussKronrod.Integrate(f, a, b); // 1.6829419
// Now let's say we would like to compute an improper integral
// from -infinite to +infinite, such as the integral of a Gaussian
// PDF (which should evaluate to 1):
Func <double, double> g = (x) => (1 / Math.Sqrt(2 * Math.PI)) * Math.Exp(-(x * x) / 2);
double iagk = InfiniteAdaptiveGaussKronrod.Integrate(g,
Double.NegativeInfinity, Double.PositiveInfinity); // Output should be 0.99999...
Assert.AreEqual(1.6829414086350976, trapez); // 1.6829414086350976
Assert.AreEqual(1.682941969615797, romberg); // 1.682941969615797
Assert.AreEqual(1.6829419595739716, nagk); // 1.6829419595739716
Assert.AreEqual(0.99999999999999978, iagk); // 0.99999999999999978
}
public void InfiniteGaussKronrodTest()
{
for (int i = -10; i < 10; i++)
{
Func <double, double> pdf = (x) => Normal.Derivative(x - i);
Func <double, double> E = (x) => x *pdf(x);
UFunction UE = (x) => x *pdf(x);
double expected = Quadpack.Integrate(UE,
Double.NegativeInfinity, Double.PositiveInfinity);
double actual = InfiniteAdaptiveGaussKronrod.Integrate(E,
Double.NegativeInfinity, Double.PositiveInfinity);
Assert.AreEqual(expected, actual, 1e-3);
Assert.AreEqual(i, actual, 1e-3);
}
}
public void InfiniteGaussKronrodTest()
{
NormalDistribution norm;
for (int i = -10; i < 10; i++)
{
norm = new NormalDistribution(i, 1);
Func <double, double> E = (x) => x *norm.ProbabilityDensityFunction(x);
UFunction UE = (x) => x *norm.ProbabilityDensityFunction(x);
double expected = Quadpack.Integrate(UE,
Double.NegativeInfinity, Double.PositiveInfinity);
double actual = InfiniteAdaptiveGaussKronrod.Integrate(E,
Double.NegativeInfinity, Double.PositiveInfinity);
Assert.AreEqual(expected, actual, 1e-3);
Assert.AreEqual(norm.Mean, actual, 1e-3);
}
}
