/// <summary>
/// Создание квадратурной формулы
/// </summary>
/// <param name="n">Количество точек</param>
/// <param name="a">Левая граница</param>
/// <param name="b">Правая граница</param>
/// <param name="function">Функция</param>
/// <param name="weights">Функция, возвращающая k-ый момент весовой функции</param>
/// <param name="method">Ньютон-Котес (равноотстоящие узлы) или Гаусс</param>
/// <param name="type">Простая либо составная квадратурная формула</param>
/// <param name="parts">Количество участков разбиения составной квадратурной формулы</param>
public QuadratureFormulas(int n, double a, double b, Function function, WeightFunction weights, QFMethod method, QFType type, int parts = 10)
{
this.left = a;
this.right = b;
this.weights = weights;
this.N = n;
this.function = function;
this.type = type;
this.method = method;
this.parts = parts;
SetPolynomialSolver((x, left, right) => Poly.RootsFinding(x, left, right, 1000, 1E-15));
SetSystemSolver(Infrastructure.GaussSolve);
}
public static double NewtonRaphsonMethod(double[] polynomial, double a, double b, double epsilon, int maxIteration)
{
int i = 0;
var derivative = Derivative(polynomial);
double f0 = Poly.Evaluate(polynomial, a);
double x = a;
while (Math.Abs(Poly.Evaluate(polynomial, x)) > epsilon)
{
x -= f0 / Poly.Evaluate(derivative, x);
f0 = Poly.Evaluate(polynomial, x);
i++;
if (i >= maxIteration)
{
return(double.NaN);
}
}
return(x);
}
public static double BisectionMethod(double[] polynomial, double a, double b, double epsilon)
{
double x1 = a;
double x2 = b;
double fb = Poly.Evaluate(polynomial, b);
while (Math.Abs(x2 - x1) > epsilon)
{
double midpt = 0.5 * (x1 + x2);
if (fb * Poly.Evaluate(polynomial, midpt) > 0)
{
x2 = midpt;
}
else
{
x1 = midpt;
}
}
return(x2 - (x2 - x1) * Poly.Evaluate(polynomial, x2) / (Poly.Evaluate(polynomial, x2) - Poly.Evaluate(polynomial, x1)));
}
