public static double[] Moments(double a, double b, int N, ComputationalWorkShop.Function.F w)
{
var moments = new double[2 * N];
for (int i = 0; i < 2 * N; i++)
{
moments[i] = Moment(a, b, i, w);
}
return(moments);
}
private static double MomentMiddle(
double a,
double b,
int m,
int k,
ComputationalWorkShop.Function.F w)
{
var h = (b - a) / m;
var sum = 0.0;
var alpha = a + (h / 2);
for (int i = 0; i < m; i++)
{
sum += w(alpha + (i * h)) * Math.Pow(alpha + (i * h), k);
}
return(h * sum);
}
public static double GaussType(
double a,
double b,
int N,
ComputationalWorkShop.Function.F w,
ComputationalWorkShop.Function.F f)
{
var moments = Moments(a, b, N, w);
var polynome = Lab6.FindPolynome(moments);
var x = Tools.Algebra.SolveSquare(polynome);
Array.Sort(x);
var matrix = new double[2, 2] {
{ 1, 1 }, { x[0], x[1] }
};
var vector = new double[2] {
moments[0], moments[1]
};
var A = Tools.Algebra.Cramer(matrix, vector);
return(A[0] * f(x[0]) + A[1] * f(x[1]));
}
public static double Gauss2NodesCompound(
double a,
double b,
int m,
ComputationalWorkShop.Function.F f)
{
var h = (b - a) / m;
var hh = h / 2;
var sum = 0.0;
var t1 = -Math.Sqrt(3) / 3;
var t2 = Math.Sqrt(3) / 3;
for (int i = 0; i < m; i++)
{
var temp = a + i * h;
var f1 = f(hh * t1 + temp + hh);
var f2 = f(hh * t2 + temp + hh);
sum += hh * (f1 + f2);
}
return(sum);
}
private static double Moment(double a, double b, int k, ComputationalWorkShop.Function.F w)
{
var h = (int)((b - a) / step);
return(MomentMiddle(a, b, h, k, w));
}
