public void TestDifferentiate()
{
MathFunction f = Math.Exp;
MathFunction Df = Math.Exp;
Assert.Equal(Df(-5), NumericalTools.Differentiate(f)(-5), 2);
Assert.Equal(Df(-1), NumericalTools.Differentiate(f)(-1), 2);
Assert.Equal(Df(0), NumericalTools.Differentiate(f)(0), 2);
Assert.Equal(Df(1), NumericalTools.Differentiate(f)(1), 2);
Assert.Equal(Df(5), NumericalTools.Differentiate(f)(5), 2);
f = Math.Sin;
Df = Math.Cos;
Assert.Equal(Df(-5), NumericalTools.Differentiate(f)(-5), 2);
Assert.Equal(Df(-1), NumericalTools.Differentiate(f)(-1), 2);
Assert.Equal(Df(0), NumericalTools.Differentiate(f)(0), 2);
Assert.Equal(Df(1), NumericalTools.Differentiate(f)(1), 2);
Assert.Equal(Df(5), NumericalTools.Differentiate(f)(5), 2);
f = x => Math.Pow(x, 3);
Df = x => 3 * Math.Pow(x, 2);
Assert.Equal(Df(-5), NumericalTools.Differentiate(f)(-5), 2);
Assert.Equal(Df(-1), NumericalTools.Differentiate(f)(-1), 2);
Assert.Equal(Df(0), NumericalTools.Differentiate(f)(0), 2);
Assert.Equal(Df(1), NumericalTools.Differentiate(f)(1), 2);
Assert.Equal(Df(5), NumericalTools.Differentiate(f)(5), 2);
}
public void TestInverse()
{
MathFunction f = Math.Exp;
Assert.Equal(0, NumericalTools.Inverse(f, -10, 10)(1), 2);
Assert.Equal(1, NumericalTools.Inverse(f, -10, 10)(Math.E), 2);
f = x => 2 * x;
Assert.Equal(2, NumericalTools.Inverse(f, -10, 10)(4), 2);
Assert.Equal(-1, NumericalTools.Inverse(f, -10, 10)(-2), 2);
}
public void TestFindRoot()
{
MathFunction f = x => Math.Exp(x) - 1;
Assert.Equal(0, NumericalTools.FindRoot(f, -1, 5), 2);
f = x => Math.Pow(x, 3) - 1;
Assert.Equal(1, NumericalTools.FindRoot(f, -1, 5), 2);
f = x => Math.Sin(x);
Assert.Equal(Math.PI, NumericalTools.FindRoot(f, Math.PI / 2, 3 * Math.PI / 2), 2);
}
public void TestIntegrate()
{
// Values found with WolframAlpha
double a = -4;
double b = 5;
MathFunction f = Math.Exp;
Assert.Equal(148.39, NumericalTools.Integrate(f, a, b), 2);
a = 1;
b = 2;
f = x => 1 / x;
Assert.Equal(0.69315, NumericalTools.Integrate(f, a, b), 2);
}
