lab8.cpp

#include "lab8.h"
#include <cmath>
#include <iostream>
#include <ctime>

// Ðåøåíèå óð-ÿ f(x) = 0 ìåòîäîì êàñàòåëüíûõ ñ òî÷íîñòüþ eps
double Newton(double x, func f, double eps)
{
	double temp{x};
	do
	{
		temp = x;
		x = temp - (f(temp)/deriveFunc(temp, f, eps,true));
	} while(!(std::abs(temp - x) < eps));

	return x;
}

// ×èñëåííîå èíòåãðèðîâàíèå f(x) â çàäàííîì èíòåðâàëå [a, b]
// ñ òî÷íîñòüþ â n òî÷åê ìåòîäîì Ìîíòå Êàðëî
// (áîëüøå òî÷åê - áîëüøå òî÷íîñòü)
double MonteCarloIntegration(func f, double a, double b, long n)
{
    double fs, u, r, x;
    srand(time(NULL));

    fs = 0.0;

    for(int i = 1; i <= n; ++i)
    {
        u = (double)rand()/(RAND_MAX+1);
        x = a + (b - a)*u;
        fs += f(x);
    }
    r = fs*(b-a)/n;
    return r;
}

// Ïðîèçâîäíàÿ ôóíêöèè (ëåâàÿ è ïðàâàÿ)
double deriveFunc(double x,func f,double eps,bool isRight){
	auto h{ (x!=0)? x/10 : 1};
	h = (isRight)? h : -h; // Èä¸ì ê íóëþ ëèáî ñïðàâà ëèáî ñëåâà
	auto F{(f(x+h) - f(x))/h};
	auto F1{0.0};
	bool fin{false};
	do
	{
		h/=10;
		F1 = (f(x+h) - f(x))/h;
		fin = std::abs(F1-F) <= eps;
		F = F1;

	} while(!fin);

	return F;
}

// Êîðíè êâàäðàòíîãî òð¸õ÷ëåíà
sqrTrinResult sqrTrinSolution(func f){
	double C = f(0);
	double B = deriveFunc(0,f,0.000001f,true);
	double A = f(1) - B - C;

	double Discrim { (B*B) - 4*A*C };
	double sqrtDiscrim{std::sqrt(Discrim)};

	sqrTrinResult result;
	result.X1 = (-B + sqrtDiscrim) / 2*A;
	result.X2 = (-B - sqrtDiscrim) / 2*A;

	return result;
}