answindow.cpp

#include "answindow.h"
#include "ui_answindow.h"
#include "math.h"
#include <QMessageBox>
#include <QDebug>
#include <ctime>

double x1, x2, x3;

const double eps = 0.001;
const double epsS = eps/3;
const double epsP = eps/10000;
const int pointsNum = 100000000;

double f1(double x, int d){
    if (d == 0){
        return exp(x)+2;
    } else {
        return exp(x);
    }
}
double f2(double x, int d){
    if (d == 1){
        return (1/(x*x));
    } else if (d == 2){
        return (-2/(x*x*x));
    }
    return (-1/x);
}
double f3(double x , int d){
    if (d == 1){
        return (-2.0/3);
    } else if (d == 2){
        return 0;
    }
    return ((-2.0/3)*x-2.0/3);
}

double AnsWindow::integral_simpson(double (*f)(double, int), double a, double b){
    double t1=epsS+1, t2=0;
    for (int i=2; (i<=4)||(abs(t2-t1)>epsS); i*=2)
    {
        double h, sum2=0, sum4=0, sum=0;
        h=(b-a)/(2*i);
        for (int j=1; j<=2*i-1; j+=2)
        {
            sum4+=f(a+h*j, 0);
            sum2+=f(a+h*(j+1), 0);
        }
        sum=f(a, 0)+4*sum4+2*sum2-f(b, 0);
        t1=t2;
        t2=(h/3)*sum;
    }
    return t2;
}

double root(double a, double b, double (*f1)(double, int), double (*f2)(double,int)){
    double d = 0,c = 0;
    int decisionC = 0;
    double middle = (b+a)/2;
    if ((f1(middle,1)-f2(middle,1)) *(f1(middle,2)-f2(middle,2)) >0){
        decisionC = 0;
        d = b - ((f1(b,0)-f2(b,0))/(f1(b,1)-f2(b,1)));
    } else {
        decisionC = 1;
        d = a - ((f1(a,0)-f2(a,0))/(f1(a,1)-f2(a,1)));
    }
    while (abs(d-c)>epsP){
        c = (a* (f1(b,0) - f2(b,0)) - b* (f1(a,0)-f2(a,0)) )/( (f1(b,0) - f2(b,0)) - (f1(a,0) - f2(a,0)));
        d = d - ((f1(d,0)-f2(d,0))/(f1(d,1)-f2(d,1)));
        if (decisionC){
            b = c;
        } else {
            a = c;
        }
    }
    return c<d?(2*c+epsP)/2:(2*d+epsP)/2;
}


double AnsWindow::integral_monte(double (*f)(double,int), double a, double b, double miny, double maxy){
    double s = (b-a) * (maxy-miny);
    qsrand((unsigned)time(0));
    double k = 0;
    double genX, genY;
    for (int i = 0; i < pointsNum; ++i){
        genX = a + ((double) qrand() / RAND_MAX * (b - a));
        genY = miny + ((double) qrand() / RAND_MAX * (maxy - miny));
        if (genY<=f(genX,0)) ++k;
    }
    return s*(k/pointsNum);
}


AnsWindow::AnsWindow(QWidget *parent) :
    QWidget(parent),
    ui(new Ui::AnsWindow)
{
    ui->setupUi(this);
    this->setFixedSize(900, 900);

    unsigned int start_time = clock();
    x1 = root(-5, -3, f1, f3);
    x2 = root(-2, -1, f2, f3);
    x3 = root(-1, -0.1, f1, f2);
    double sv1 = integral_simpson(f1, x1, x3), sv2 = integral_simpson(f3, x1, x2), sv3 = integral_simpson(f2, x2, x3);
    double mv1 = integral_monte(f1, x1, x3, 0, 3), mv2 = integral_monte(f3, x1, x2, 0, 3), mv3 = integral_monte(f2, x2, x3, 0, 3);
    double sS = sv1 - sv2 - sv3;
    double mS = mv1 - mv2 - mv3;
    unsigned int end_time = clock();

    QString text = "Loading progect Polynomials2...\n\nGraphics.....................OK\nCalculation..................OK\nLegend.......................OK\n\nOUTPUT:\n\n";
    text += "f1(x) = exp(2)+2\nf2(x) = -1/x\nf3(x) = -2(x+1)/3\n\n";
    text += "EPSILON = " + QString::number(eps) + "\n\n";
    text += "Epsilon for points (E1) = " + QString::number(epsP) + "\n\n";
    text += "f1(x) = f2(x); x = " + QString::number(x1) + "\n";
    text += "f2(x) = f3(x); x = " + QString::number(x2) + "\n";
    text += "f1(x) = f2(x); x = " + QString::number(x3) + "\n\n";

    text += "FORMULA\n";
    text += "S = integral(f1(x), x1, x3) - integral(f3(x), x1, x2) - integral(f2(x),x2,x3)\n\n";
    text += "Epsilon for area (E2) = " + QString::number(epsS) + "\n\n";
    text += "Simpson method\n";
    text += "S = " + QString::number(sv1) + " - " + QString::number(sv2) + " - " + QString::number(sv3) + "\n";
    text += "S = " + QString::number(sS) + "\n\n";
    text += "Monte Carlo method (N = "+QString::number(pointsNum)+")\n";
    text += "S = " + QString::number(mv1) + " - " + QString::number(mv2) + " - " + QString::number(mv3) + "\n";
    text += "S = " + QString::number(mS) +"\n\n";
    text += "ANSWER: S(s) = " + QString::number(sS)+"; S(m) = "+ QString::number(mS) + "\n\n";
    text += "Process returned 0 (0x0)\nExecution time : " + QString::number(1.0*(end_time-start_time)/1000);
    ui->label->setText(text);
}

AnsWindow::~AnsWindow()
{
    delete ui;
}