public void TestIntegralOfGaussian(double a, double b, double expected)
{
Assert.AreEqual(
expected,
Integrate.DoubleExponential((x) => Math.Exp(-x * x / 2), a, b),
1e-10,
"DET Integral of e^(-x^2 /2) from {0} to {1}", a, b);
Assert.AreEqual(
expected,
Integrate.GaussKronrod((x) => Math.Exp(-x * x / 2), a, b),
1e-10,
"GK Integral of e^(-x^2 /2) from {0} to {1}", a, b);
Assert.AreEqual(
expected,
Integrate.GaussLegendre((x) => Math.Exp(-x * x / 2), a, b, order: 128),
1e-10,
"GL Integral of e^(-x^2 /2) from {0} to {1}", a, b);
}
public void TestIntegralOfSinc(double a, double b, double expected, double factor)
{
Assert.AreEqual(
expected,
factor * Integrate.DoubleExponential((x) => 1 / (1 + x * x), a, b),
1e-10,
"DET Integral of sin(pi*x)/(pi*x) from {0} to {1}", a, b);
Assert.AreEqual(
expected,
factor * Integrate.GaussKronrod((x) => 1 / (1 + x * x), a, b),
1e-10,
"GK Integral of sin(pi*x)/(pi*x) from {0} to {1}", a, b);
Assert.AreEqual(
expected,
factor * Integrate.GaussLegendre((x) => 1 / (1 + x * x), a, b, order: 128),
1e-10,
"GL Integral of sin(pi*x)/(pi*x) from {0} to {1}", a, b);
}
public void TestIntegrateFacade()
{
// TargetFunctionA
// integral_(0)^(10) exp(-x/5) (2 + sin(2 x)) dx = 9.1082
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA),
1e-5,
"Interval, Target 1e-08");
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA, 1e-10),
1e-10,
"Interval, Target 1e-10");
// TargetFunctionB
// integral_(0)^(1) integral_(0)^(10) exp(-x/5) (2 + sin(2 y)) dx dy = 11.7079
Assert.AreEqual(
Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB),
TargetAreaB,
1e-12,
"Rectangle, order 32");
Assert.AreEqual(
Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB, 22),
TargetAreaB,
1e-10,
"Rectangle, Order 22");
// TargetFunctionC
// integral_(-oo)^(oo) 1/(1 + x^2) dx = pi
Assert.AreEqual(
TargetAreaC,
Integrate.DoubleExponential(TargetFunctionC, StartC, StopC),
1e-5,
"DoubleExponential, 1/(1 + x^2)");
Assert.AreEqual(
TargetAreaC,
Integrate.DoubleExponential(TargetFunctionC, StartC, StopC, 1e-10),
1e-10,
"DoubleExponential, 1/(1 + x^2)");
// TargetFunctionD
// integral_(0)^(1) log(x) dx = -1
Assert.AreEqual(
TargetAreaD,
Integrate.DoubleExponential(TargetFunctionD, StartD, StopD),
1e-10,
"DoubleExponential, log(x)");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussLegendre(TargetFunctionD, StartD, StopD, order: 1024),
1e-10,
"GaussLegendre, log(x), order 1024");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 15),
1e-10,
"GaussKronrod, log(x), order 15");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 21),
1e-10,
"GaussKronrod, log(x), order 21");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 31),
1e-10,
"GaussKronrod, log(x), order 31");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 41),
1e-10,
"GaussKronrod, log(x), order 41");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 51),
1e-10,
"GaussKronrod, log(x), order 51");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 61),
1e-10,
"GaussKronrod, log(x), order 61");
double error, L1;
var Q = Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, out error, out L1, 1e-10, order: 15);
Assert.AreEqual(
Math.Abs(TargetAreaD),
Math.Abs(L1),
1e-10,
"GaussKronrod, L1");
// TargetFunctionE
// integral_(0)^(1) log^2(x) dx = 2
Assert.AreEqual(
TargetAreaE,
Integrate.DoubleExponential(TargetFunctionE, StartE, StopE),
1e-10,
"DoubleExponential, log^2(x)");
Assert.AreEqual(
TargetAreaE,
Integrate.GaussLegendre(TargetFunctionE, StartE, StopE, order: 128),
1e-5,
"GaussLegendre, log^2(x), order 128");
Assert.AreEqual(
TargetAreaE,
Integrate.GaussKronrod(TargetFunctionE, StartE, StopE, 1e-10, order: 15),
1e-10,
"GaussKronrod, log^2(x), order 15");
// TargetFunctionF
// integral_(0)^(oo) exp(-x) cos(x) dx = 1/2
Assert.AreEqual(
TargetAreaF,
Integrate.DoubleExponential(TargetFunctionF, StartF, StopF),
1e-10,
"DoubleExponential, e^(-x) cos(x)");
Assert.AreEqual(
TargetAreaF,
Integrate.GaussLegendre(TargetFunctionF, StartF, StopF, order: 128),
1e-10,
"GaussLegendre, e^(-x) cos(x), order 128");
Assert.AreEqual(
TargetAreaF,
Integrate.GaussKronrod(TargetFunctionF, StartF, StopF, 1e-10, order: 15),
1e-10,
"GaussKronrod, e^(-x) cos(x), order 15");
// TargetFunctionG
// integral_(0)^(1) sqrt(x)/sqrt(1 - x^2) dx = 1.19814
Assert.AreEqual(
TargetAreaG,
Integrate.DoubleExponential(TargetFunctionG, StartG, StopG),
1e-5,
"DoubleExponential, sqrt(x)/sqrt(1 - x^2)");
Assert.AreEqual(
TargetAreaG,
Integrate.GaussLegendre(TargetFunctionG, StartG, StopG, order: 128),
1e-10,
"GaussLegendre, sqrt(x)/sqrt(1 - x^2), order 128");
Assert.AreEqual(
TargetAreaG,
Integrate.GaussKronrod(TargetFunctionG, StartG, StopG, 1e-10, order: 15),
1e-10,
"GaussKronrod, sqrt(x)/sqrt(1 - x^2), order 15");
}