MNK

#include <iostream>
#include <cmath>
#include <iomanip>
#include <vector>

using namespace std;

typedef vector<double> DoubleVector;
typedef vector<vector<double>> DoubleMatrix;

#define N_table 9
#define xcp 0
#define ycp 1
#define tillday 2
#define form 3
#define a 0
#define b 1
#define x 0
#define y 1

double average(DoubleVector &arr) {
    double res = 0;
    for (int i = 0; i < arr.size(); i++) res += arr[i];

    return res / arr.size();
}

double geometric_mean(DoubleVector &arr) {
    double res = 1;
    for (int i = 0; i < arr.size(); i++) res *= arr[i];

    return pow(res, 1. / arr.size());
}

double harmonic_mean(DoubleVector &arr) {
    double res = 0;
    for (int i = 0; i < arr.size(); i++) res += 1 / arr[i];

    return arr.size() / res;
}

double calc_tilday(DoubleVector &X, DoubleVector &Y, double _xcp) {
    int tmp_i = 0;
    for (int i = 0; i < X.size(); i++) {
        if (_xcp == X[i]) return Y[i];
        else if (X[i] < _xcp) tmp_i = i;
    }

    return ((_xcp - X[tmp_i]) / (X[tmp_i + 1] - X[tmp_i])) * (Y[tmp_i + 1] - Y[tmp_i]) + Y[tmp_i];
}

void print_table(DoubleMatrix& tabl, int i_func) {
    cout << "Dependency selection table: " << endl;
    cout << "| # |    xcp    |    ycp    |    ~y    |    abs(ycp - ~y) / ~y" << endl;
    for (int i = 0; i < N_table; i++) {
        cout << "| " << i + 1 << ' ';
        for (int j = 0; j < 4; j++) cout << "| " << fixed << setprecision(3) << tabl[j][i] << "     ";
        if (i == i_func) cout << "+";
        cout << endl;
    }
}

void print_arr(DoubleVector &arr, char name_arr) {
    cout << name_arr << " = { " << arr[0];
    for (int i = 1; i < arr.size(); i++) cout << ", " << arr[i];
    cout << " }" << endl;
}

DoubleMatrix build_table(DoubleVector& X, DoubleVector& Y) {
    unsigned int size = X.size();
    DoubleMatrix res_tabl(4, vector<double> (N_table));

    DoubleVector tmp_res(3);
    tmp_res[0] = average(X);
    tmp_res[1] = geometric_mean(X);
    tmp_res[2] = harmonic_mean(X);
    for (int i = 0; i < 3; i++) for (int j = i; j < N_table; j += 3) res_tabl[xcp][j] = tmp_res[i];

    tmp_res[0] = average(Y);
    tmp_res[1] = geometric_mean(Y);
    tmp_res[2] = harmonic_mean(Y);
    for (int i = 0; i < size; i += 3) for (int j = i; j < N_table; j++) res_tabl[ycp][j] = tmp_res[i / 3];

    for (int i = 0; i < N_table; i++) {
        res_tabl[tillday][i] = calc_tilday(X, Y, res_tabl[xcp][i]);
        res_tabl[form][i] = fabs((res_tabl[ycp][i] - res_tabl[tillday][i]) / res_tabl[tillday][i]);
    }

    return res_tabl;
}

int min(DoubleVector &arr) {
    int min = 0;
    for (int i = 0; i < arr.size(); i++)
        if (arr[min] > arr[i]) min = i;

    return min;
}

DoubleMatrix func(DoubleVector &X, DoubleVector &Y, int i_func) {
    unsigned int size = X.size();
    DoubleMatrix res(2, vector<double> (size));
    if (i_func == 0)
        for (int i = 0; i < size; i++) {
            res[y][i] = Y[i];
            res[x][i] = X[i];
        }
    else if (i_func == 1)
        for (int i = 0; i < size; i++) {
            res[y][i] = Y[i];
            res[x][i] = 1. / X[i];
        }
    else if (i_func == 2)
        for (int i = 0; i < size; i++) {
            res[y][i] = Y[i];
            res[x][i] = log(X[i]);
        }
    else if (i_func == 3)
        for (int i = 0; i < size; i++) {
            res[y][i] = log(Y[i]);
            res[x][i] = X[i];
        }
    else if (i_func == 4)
        for (int i = 0; i < size; i++) {
            res[y][i] = log(Y[i]);
            res[x][i] = log(X[i]);
        }
    else if (i_func == 5)
        for (int i = 0; i < size; i++) {
            res[y][i] = log(Y[i]);
            res[x][i] = 1. / X[i];
        }
    else if (i_func == 6)
        for (int i = 0; i < size; i++) {
            res[y][i] = 1. / Y[i];
            res[x][i] = X[i];
        }
    else if (i_func == 7)
        for (int i = 0; i < size; i++) {
            res[y][i] = 1. / Y[i];
            res[x][i] = log(X[i]);
        }
    else if (i_func == 8)
        for (int i = 0; i < size; i++) {
            res[y][i] = 1. / Y[i];
            res[x][i] = 1. / X[i];
        }
    else cout << "ERROR: i_func = " << i_func;

    return res;
}

DoubleVector calc_coef(DoubleVector &X, DoubleVector &Y, int i_func) {
    unsigned int size = X.size();
    DoubleVector coef(2);
    DoubleMatrix newXY = func(X, Y, i_func);

    double sumxy = 0,
        sumx = 0,
        sumy = 0,
        sumx2 = 0;
    for (int i = 0; i < size; i++) {
        sumxy += (newXY[x][i] * newXY[y][i]);
        sumx += newXY[x][i];
        sumy += newXY[y][i];
        sumx2 += (newXY[x][i] * newXY[x][i]);
    }

    coef[a] = (sumxy - (1. / size) * sumx * sumy) / (sumx2 - (1. / size) * sumx * sumx);
    coef[b] = (1. / size) * sumy - (coef[a] / size) * sumx;

    if (i_func == 3) {
        coef[a] = exp(coef[a]);
        coef[b] = exp(coef[b]);
    }
    else if (i_func == 4) coef[b] = exp(coef[b]);

    return coef;
}

void print_func(DoubleVector coef, int i_func) {
    cout << "Function MNK: " << endl;
    if (i_func == 0) cout << "y = " << coef[b] << " + " << coef[a] << " * x" << endl;
    else if (i_func == 1) cout << "y = " << coef[b] << " + " << coef[a] << " / x" << endl;
    else if (i_func == 2) cout << "y = " << coef[b] << " + " << coef[a] << " * ln(x)" << endl;
    else if (i_func == 3) cout << "y = " << coef[b] << " * " << coef[a] << "^x" << endl;
    else if (i_func == 4) cout << "y = " << coef[b] << " * x^" << coef[a] << endl;
    else if (i_func == 5) cout << "y = exp(" << coef[b] << " + " << coef[a] << " / x)" << endl;
    else if (i_func == 6) cout << "y = 1 / (" << coef[b] << " + " << coef[a] << " * x" << endl;
    else if (i_func == 7) cout << "y = 1 / (" << coef[b] << " + " << coef[a] << " * ln(x)" << endl;
    else if (i_func == 8) cout << "y = x(" << coef[b] << " + " << coef[a] << " * x)" << endl;
    else cout << "ERROR: i_func = " << i_func;
}

void go(DoubleVector& X, DoubleVector& Y) {

    if (X.size() != Y.size()) {
        cout << "ERROR: array sizes are not the same." << endl;
        cout << "size X = " << X.size() << "\tsize Y = " << Y.size() << endl;
        return;
    }

    DoubleMatrix table;
    table = build_table(X, Y);
    print_arr(X, 'X');
    print_arr(Y, 'Y');
    cout << endl;
    int i_func = min(table[3]);
    print_table(table, i_func);


    DoubleVector coef = calc_coef(X, Y, i_func);
    cout << endl;
    print_func(coef, i_func);

}

int main() {

    // площа зібрана, тис.га / harvested area, thsd.ha
    cout << "\n\tharvested area, thsd.ha\n";
    DoubleVector X1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
    DoubleVector Y1 = {165.5, 183.3, 179, 144.9, 137.4, 142.2, 94.7, 117.5, 155.6, 138.5, 133.3};
    go(X1, Y1);

    // обсяг виробництва, міл.ц / volume of production, mil.centner
    cout << "\n\tvolume of production, mil.centner\n";
    DoubleVector X2 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
    DoubleVector Y2 = {4.9621, 6.8285, 8.1169, 7.469, 6.1961, 6.0782, 4.7459, 6.0993, 7.9461, 7.5925, 6.5105};
    go(X2, Y2);

    // урожайність, ц з 1 га зібраної площі / yield, centner per ha of the harvested area
    cout << "\n\tyield, centner per ha of the harvested area\n";
    DoubleVector X3 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
    DoubleVector Y3 = {30, 37.2, 45.4, 51.5, 45.1, 42.7, 50.1, 51.9, 51.1, 54.8, 48.8};
    go(X3, Y3);

    return 0;
}