static double [] Newton(Binary_Function equations, Binary_Function [,] jacobiMatrix, double [] initialValues, double eps)
{
int n = equations.GetInvocationList().Length;
double[,] intermediateMatrix = new double[n, n];
double[] z = new double[n];
do
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
intermediateMatrix[i, j] = jacobiMatrix[i, j](initialValues[0], initialValues[1]);
}
}
Delegate[] equationsList = equations.GetInvocationList();
double [] b = new double[initialValues.GetLength(0)];
int q = 0;
foreach (Delegate f in equationsList)
{
if (f is Binary_Function)
{
b[q++] = (f as Binary_Function)(initialValues[0], initialValues[1]);
}
}
z = Gauss(intermediateMatrix, b);
for (int i = 0; i < initialValues.GetLength(0); i++)
{
initialValues[i] = initialValues[i] - z[i];
}
} while (z[0] > eps);
return(initialValues);
}
static void Main(string[] args)
{
Console.WriteLine("Hello World!");
// For Trapezium
Console.WriteLine("Trapezium method for integral(3x^4 + x), x from 0 to 1.5");
Unary_Function f1 = (x) => 3 * x * x * x * x + x;
Console.WriteLine(String.Format("{0:f5}", Trapezium(f1, 0, 1.5, 81, 0.001)));
// For Power Iteration
double[,] powerIterationMatrix = { { 1.4, 0.5, 0.6 },
{ 0.5, 1.4, 0.3 },
{ 0.6, 0.3, 1.4 } };
Console.WriteLine("\nPower Iteration method\nThe max eigenvalue is:");
Console.WriteLine(String.Format("{0:f5}",
PowerIteration(powerIterationMatrix, new double[] { 1, 1, 1 }, 0.001)));
// For Newton
Binary_Function equationsSystem = (x, y) => Math.Tan(x * y + 0.1) - x * x;
equationsSystem += (x, y) => x * x + 2 * y * y - 1;
Binary_Function eq1dx = (x, y) => y * (1 / Math.Cos(x * y + 0.1) * Math.Cos(x * y + 0.1)) - 2 * x;
Binary_Function eq1dy = (x, y) => x * (1 / Math.Cos(x * y + 0.1) * Math.Cos(x * y + 0.1));
Binary_Function eq2dx = (x, y) => 2 * x;
Binary_Function eq2dy = (x, y) => 4 * y;
Binary_Function[,] jacobiMatrix = { { eq1dx, eq1dy },
{ eq2dx, eq2dy } };
double[] newtonResult = Newton(equationsSystem, jacobiMatrix, new double[] { 1.25, 0 }, 0.001);
Console.WriteLine("\nSolution by Newton ");
for (int i = 0; i < newtonResult.GetLength(0); i++)
{
Console.WriteLine($"x[{i}] = {String.Format("{0:f6}", newtonResult[i])}");
}
}
