integration.cpp

#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip> // std::setprecision
#include "matplotlibcpp.h"

namespace plt = matplotlibcpp;

//-----------------------------------------------------------

std::vector<int> generateLinspace(std::vector<double> vec)
{

    std::vector<int> linspace;

    int size = vec.size();

    for (int ii = 0; ii < size; ii++)
    {

        linspace.push_back(ii);
    }

    return linspace;
}

//-----------------------------------------------------------

double function(double xx)
{

    return std::sqrt(1 - xx * xx);
}

//-----------------------------------------------------------

std::vector<double> rectangleMethod(double (*function)(double), double aa, double bb, int n)
{

    std::vector<double> output;
    double sum{0};

    double h = (bb - aa) / n;

    for (int ii = 0; ii < n; ii++)
    {

        sum += function(aa + (ii + 0.5) * h);

        output.push_back(2 * sum * h);
    }

    return output;
}

//-----------------------------------------------------------

std::vector<double> trapezoidalMethod(double (*function)(double), double aa, double bb, int n)
{

    std::vector<double> output;
    double h = (bb - aa) / n;
    double aA = function(aa) * 0.5;
    double bB = function(bb) * 0.5;

    double sum{0};

    for (int ii = 1; ii < n; ii++)
    {

        sum += function(aa + ii * h);

        output.push_back(2 * h * (aA + bB + sum));
    }
    return output;
}

//-----------------------------------------------------------

void plot(std::vector<double> yy)
{

    plt::figure_size(1200, 780);

    std::vector<int> xx = generateLinspace(yy);

    plt::plot(xx, yy);
    plt::title("Numerical Integration");
    plt::named_plot("trapezoid method", xx, yy, "b-");
    plt::legend();
    plt::show();
}

//-----------------------------------------------------------

int main()
{

    std::vector<double> output1;
    std::vector<double> output2;

    output1 = rectangleMethod(function, -1, 1, 100000);
    output2 = trapezoidalMethod(function, -1, 1, 100000);

    //rectangle Method
    // for (auto &i : output1)
    // {

    //     std::cout << std::setprecision(10) << " ==> " << i << std::endl;
    // }

    // plot(output1);

    // trapezoidal Method

    for (auto &i : output2)
    {

        std::cout << std::setprecision(10) << " ==> " << i << std::endl;
    }
    plot(output2);
}