diff_newton.cpp

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

namespace plt = matplotlibcpp;

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

std::vector<double> generateLinspaceDiff(std::vector<double> vec, double start, double stop)
{

    std::vector<double> linspace;

    int size = vec.size();

    double h = (stop - start) / size;

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

        linspace.push_back(start + h * ii);
    }

    std::cout << "size: " << size << std::endl;
    std::cout << "linspace: " << linspace.size() << std::endl;

    return linspace;
}

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

double function(double xx)
{

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

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

void plotDiff(std::vector<double> yy, double start, double stop)
{

    plt::figure_size(1200, 780);

    std::vector<double> xx = generateLinspaceDiff(yy, start, stop);

    plt::plot(xx, yy);
    plt::title("Numerical Differentiation");
    plt::named_plot("Newton method", xx, yy);
    plt::legend();
    plt::show();
}

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

double functionDiff(double xx)
{

    return xx * xx * xx;
}

std::vector<double> differentiationNewton(double (*functionDiff)(double), double aa, double bb, int n)
{

    double h = (bb - aa) / n;
    std::vector<double> output;

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

        double check = (functionDiff((bb * ii) / h + aa + h) - functionDiff((bb * ii) / h + aa)) / n;
        output.push_back((functionDiff((bb * ii) / h + aa + h) - functionDiff((bb * ii) / h + aa)) / n);
        std::cout << " => " << check << std::endl;
    }

    return output;
}

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

int main()
{

    std::vector<double> output3 = differentiationNewton(functionDiff, -2.0, 2.0, 10000);
    plotDiff(output3, -2.0, 2.0);
}