/// <summary>
/// Initializes a new instance of the <see cref="T:NewtonSolverMultiDim.NewtonMnimizer"/> class.
/// </summary>
/// <param name="tol">Tol.</param>
/// <param name="maxIt">Max it.</param>
public NewtonMnimizer(double tol, int maxIt)
{
solver = new NewtonSolver(tol, maxIt);
}
public static void Main(string[] args)
{
Func <double, double> normalDensity
= (x) => Math.Exp(-x * x / 2.0) / Math.Sqrt(2 * Math.PI);
CompositeIntegrator integrator = new CompositeIntegrator(4);
double integral = integrator.Integrate(normalDensity, -4, 4, 100);
Console.WriteLine("Integral is approximately {0}", integral);
NewtonSolver newtonSolver = new NewtonSolver(1e-16, 100);
// we want a function F(x,y)_1 = x^2 + y^2 - 2xy, F(x,y)_2 = x^2 - y^2
// you can check that F(x,x)_1 = 0 and F(x,x)_2 = 0 i.e. uncountably many solutions
Func <Vector <double>, Vector <double> > F = (x) => {
Vector <double> y = Vector <double> .Build.Dense(x.Count);
y[0] = x[0] * x[0] + x[1] * x[1] - 2 * x[0] * x[1];
y[1] = x[0] * x[0] - x[1] * x[1];
return(y);
};
Func <Vector <double>, Matrix <double> > J_F = (x) => {
int d = x.Count;
Matrix <double> J_F_vals = Matrix <double> .Build.Dense(d, d);
J_F_vals[0, 0] = 2 * x[0] - 2 * x[1]; J_F_vals[0, 1] = 2 * x[1] - 2 * x[0];
J_F_vals[1, 0] = 2 * x[0]; J_F_vals[1, 1] = -2 * x[1];
return(J_F_vals);
};
Vector <double> x0 = Vector <double> .Build.Dense(2);
x0[0] = 1; x0[1] = -1;
Vector <double> x1;
x1 = newtonSolver.Solve(F, J_F, x0);
Console.WriteLine(x1.ToString());
// we want a function F(x,y)_1 = x^2 + y^2 - 2xy - 1, F(x,y)_2 = x^2 - y^2 - 7
// you can check that [F(4,3), F(4,3)] = [0,0]
Func <Vector <double>, Vector <double> > F2 = (x) => {
Vector <double> y = Vector <double> .Build.Dense(x.Count);
y[0] = x[0] * x[0] + x[1] * x[1] - 2 * x[0] * x[1] - 1;
y[1] = x[0] * x[0] - x[1] * x[1] - 7;
return(y);
};
Func <Vector <double>, Matrix <double> > J_F2 = (x) => {
int d = x.Count;
Matrix <double> J_F_vals = Matrix <double> .Build.Dense(d, d);
J_F_vals[0, 0] = 2 * x[0] - 2 * x[1]; J_F_vals[0, 1] = 2 * x[1] - 2 * x[0];
J_F_vals[1, 0] = 2 * x[0]; J_F_vals[1, 1] = -2 * x[1];
return(J_F_vals);
};
x1 = newtonSolver.Solve(F2, J_F2, x0);
Console.WriteLine(x1.ToString());
NewtonMnimizer minimizer = new NewtonMnimizer(1e-5, 100);
Func <Vector <double>, double> f = (x) => x [0] * x [0] + x [1] * x [1];
Vector <double> startPt = Vector <double> .Build.Dense(2);
startPt[0] = 1; startPt[1] = -1;
Console.WriteLine("With approximate grad of f and hessian of f using f.d.");
Console.WriteLine(minimizer.Minimize(f, null, null, startPt));
Console.WriteLine("With exact grad_f and approximate hessian f using f.d.");
Func <Vector <double>, Vector <double> > grad_f = (x) => {
Vector <double> grad = Vector <double> .Build.Dense(x.Count);
grad[0] = 2 * x[0]; grad[1] = 2 * x[1];
return(grad);
};
Console.WriteLine(minimizer.Minimize(f, grad_f, null, startPt));
Console.WriteLine("With exact grad of f and hessian of f.");
Func <Vector <double>, Matrix <double> > hessian_f = (x) => {
Matrix <double> hessian = Matrix <double> .Build.Dense(x.Count, x.Count);
hessian[0, 0] = 2; hessian[0, 1] = 0;
hessian[1, 0] = 0; hessian[1, 1] = 2;
return(hessian);
};
Console.WriteLine(minimizer.Minimize(f, grad_f, hessian_f, startPt));
Console.ReadKey();
}