interpolation.cpp

#include <iostream>
#include <tuple>
#include <vector>
#include "matplotlibcpp.h"

namespace plt = matplotlibcpp;

//global
std::vector<float> interpolated;

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

void runInterpolation(std::tuple<std::vector<float>, std::vector<float>, float> input)
{

    std::vector<float> xx = std::get<0>(input);
    std::vector<float> yy = std::get<1>(input);
    float interX = std::get<2>(input);
    int ijk{0};

    int ii{0};
    float w_interX{0};
    int size = xx.size();

    for (auto &fi : yy)
    {
        float factor{1};
        int jj{0};

        float xi = xx[ii];

        for (auto &xj : xx)
        {
            float factor_i{1};
            if (xj != xi)
            {
                factor_i = (interX - xj) / (xi - xj);
            }

            factor = factor * factor_i;
        }

        w_interX = w_interX + fi * factor;

        ii++;
    }

    std::cout << " :: " << w_interX << std::endl;

    interpolated.push_back(w_interX);
}

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

void plotNumericalApproach(std::vector<float> xx1, std::vector<float> yy1, std::vector<float> xx2, std::vector<float> yy2)
{
    plt::figure_size(1200, 780);
    plt::title("Interpolation");
    plt::plot(xx1, yy1);
    plt::plot(xx2, yy2, "r-");
    plt::show();
}

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

int main()
{

    //line----------------------------------------

    std::vector<float> xi{1, 2, 4, 8};
    std::vector<float> f_xi{1, 3, 7, 11};
    std::vector<float> interX{1.2, 3.0, 6.0, 7.0};

    //sin----------------------------------------

    // std::vector<float> xi{0.0, 0.52, 1.052, 1.578, 2.105, 2.631, 3.157, 3.684, 4.210, 4.736, 5.26, 5.78, 6.31, 6.84, 7.36, 7.89, 8.42, 8.94, 9.473, 10.0};
    // std::vector<float> f_xi{0.0, 0.50, 0.86, 0.9999, 0.86, 0.488, -0.016, -0.5163, -0.8766, -0.999, -0.852, -0.473, 0.032, 0.530, 0.884, 0.999, 0.843, 0.459, -0.048, -0.544};
    // std::vector<float> interX{0.001, 0.75, 1.0, 1.5, 2.0, 2.5, 2.7, 3.4, 3.8, 4.1, 4.8, 5.3, 5.9, 6.4, 6.9, 7.5, 8.0, 8.5, 8.9, 9.1};

    //quadratic---------------------------------

    // std::vector<float> xi{-5.0, -3.88, -2.778, -1.667, -0.556,  0.556, 1.667,  2.778,  3.88,  5.0};
    // std::vector<float> f_xi{25.0, 15.129,  7.738, 2.778,  0.308,  0.308, 2.778,  7.738, 15.129, 25.0};
    // std::vector<float> interX{-4.6, -3.8, -2.7,  -1.5, -0.4, 0.8, 2.1, 3.3, 3.9, 4.7};

    std::tuple<std::vector<float>, std::vector<float>, float> input;
    std::tuple<std::vector<float>, std::vector<float>> output;

    for (auto &interXi : interX)
    {

        input = std::make_tuple(xi, f_xi, interXi);

        runInterpolation(input);
    }
    plotNumericalApproach(xi, f_xi, interX, interpolated);
}