public void NoRoot()
{
Func <double, double> f1 = x => x * x + 4;
Func <double, double> df1 = x => 2 * x;
Assert.That(() => NewtonRaphson.FindRoot(f1, df1, -5, 5, 1e-14, 50), Throws.TypeOf <NonConvergenceException>());
}
private static bool Solve(float x1, float y1, float x2, float y2, float L, out double a, out double v, out double b)
{
a = 0;
v = 0;
b = 0;
double d = x2 - x1;
double h = y2 - y1;
NewtonRaphson.Function f = delegate(double a0)
{
return(2.0 * a0 * Math.Sinh(d / (2.0 * a0)) - Math.Sqrt((L * L) - (h * h)));
};
NewtonRaphson.Function df = delegate(double a0)
{
return(2.0 * Math.Sinh(d / (2.0 * a0)) - d * Math.Cosh(d / (2.0 * a0)) / a0);
};
double newA = NewtonRaphson.FindRoot(0.01 * d, 0.00001, 100, f, df);
if (double.IsNaN(newA) || double.IsInfinity(newA))
{
return(false);
}
else
{
a = newA;
double k = 0.5 * (a * Math.Log((L + h) / (L - h)) - d);
v = k - x1;
b = y1 - a * Math.Cosh(k / a);
return(true);
}
}
public void LocalMinima()
{
Func <double, double> f1 = x => x * x * x - 2 * x + 2;
Func <double, double> df1 = x => 3 * x * x - 2;
Assert.AreEqual(0, f1(NewtonRaphson.FindRoot(f1, df1, -5, 6, 1e-14)));
//Assert.AreEqual(0, f1(NewtonRaphson.FindRoot(f1, df1, 1, -2, 4, 1e-14, 100)));
}
public void Cubic()
{
// with complex roots (looking for the real root only): 3x^3 + 4x^2 + 5x + 6, derivative 9x^2 + 8x + 5
Func <double, double> f1 = x => Polynomial.Evaluate(x, 6, 5, 4, 3);
Func <double, double> df1 = x => Polynomial.Evaluate(x, 5, 8, 9);
Assert.AreEqual(-1.265328088928, NewtonRaphson.FindRoot(f1, df1, -2, -1, 1e-10), 1e-6);
Assert.AreEqual(-1.265328088928, NewtonRaphson.FindRoot(f1, df1, -5, 5, 1e-10), 1e-6);
// real roots only: 2x^3 + 4x^2 - 50x + 6, derivative 6x^2 + 8x - 50
Func <double, double> f2 = x => Polynomial.Evaluate(x, 6, -50, 4, 2);
Func <double, double> df2 = x => Polynomial.Evaluate(x, -50, 8, 6);
Assert.AreEqual(-6.1466562197069, NewtonRaphson.FindRoot(f2, df2, -8, -5, 1e-10), 1e-6);
Assert.AreEqual(0.12124737195841, NewtonRaphson.FindRoot(f2, df2, -1, 1, 1e-10), 1e-6);
Assert.AreEqual(4.0254088477485, NewtonRaphson.FindRoot(f2, df2, 3, 5, 1e-10), 1e-6);
}
public void MultipleRoots()
{
// Roots at -2, 2
Func <double, double> f1 = x => x * x - 4;
Func <double, double> df1 = x => 2 * x;
Assert.AreEqual(0, f1(NewtonRaphson.FindRoot(f1, df1, -5, 6, 1e-14)));
Assert.AreEqual(-2, NewtonRaphson.FindRoot(f1, df1, -5, -1, 1e-14));
Assert.AreEqual(2, NewtonRaphson.FindRoot(f1, df1, 1, 4, 1e-14));
Assert.AreEqual(0, f1(NewtonRaphson.FindRoot(x => - f1(x), x => - df1(x), -5, 6, 1e-14)));
Assert.AreEqual(-2, NewtonRaphson.FindRoot(x => - f1(x), x => - df1(x), -5, -1, 1e-14));
Assert.AreEqual(2, NewtonRaphson.FindRoot(x => - f1(x), x => - df1(x), 1, 4, 1e-14));
// Roots at 3, 4
Func <double, double> f2 = x => (x - 3) * (x - 4);
Func <double, double> df2 = x => 2 * x - 7;
Assert.AreEqual(0, f2(NewtonRaphson.FindRoot(f2, df2, -5, 6, 1e-14)));
Assert.AreEqual(3, NewtonRaphson.FindRoot(f2, df2, -5, 3.5, 1e-14));
Assert.AreEqual(4, NewtonRaphson.FindRoot(f2, df2, 3.2, 5, 1e-14));
Assert.AreEqual(3, NewtonRaphson.FindRoot(f2, df2, 2.1, 3.9, 0.001, 50), 0.001);
Assert.AreEqual(3, NewtonRaphson.FindRoot(f2, df2, 2.1, 3.4, 0.001, 50), 0.001);
}