void LUdecomp(std::vector<std::vector<double> > A, std::vector<std::vector<double> > &L, std::vector<std::vector<double> > &U)
{
    int n = A.size();
    L.assign(n, std::vector<double>(n, 0));
    U.assign(n, std::vector<double>(n, 0));
    for (int i = 0; i < n; ++i)
        U[i][i] = 1;

    for (int i = 0; i < n; ++i)
    {
        for (int j = i; j < n; ++j)
        {
            L[j][i] = A[j][i];
            for (int k = 0; k < i; ++k)
                L[j][i] -= L[j][k] * U[k][i];
        }

        for (int j = i + 1; j < n; ++j)
        {
            U[i][j] = A[i][j];
            for (int k = 0; k < i; ++k)
                U[i][j] -= L[i][k] * U[k][j];
            U[i][j] /= L[i][i];
        }
    }
}

void inverseMatrix(std::vector<std::vector<double> > A, std::vector<std::vector<double> > &X)
{
    std::vector<std::vector<double> > L(A.size(), std::vector<double>(A.size(), 0));
    std::vector<std::vector<double> > U(A.size(), std::vector<double>(A.size(), 0));
    LUdecomp(A, L, U);
    int n = L.size();
    X.assign(n, std::vector<double>(n, 0));
    for (int i = n - 1; i >= 0; --i)
    {
        X[i][i] = 1;
        for (int k = i + 1; k < n; ++k)
            X[i][i] -= L[k][i] * X[i][k];
        X[i][i] /= L[i][i];

        for (int j = i - 1; j >= 0; --j)
        for (int k = j + 1; k < n; ++k)
            X[j][i] -= U[j][k] * X[k][i];

        for (int j = i - 1; j >= 0; --j){
            for (int k = j + 1; k < n; ++k)
                X[i][j] -= X[i][k] * L[k][j];
            X[i][j] /= L[j][j];
        }
    }
}
double f1(double x, double y, double z)
{
    return 2 * x - y - exp(-z);
}

double f2(double x, double y, double z)
{
    return -x + 2 * y*y - exp(-z);
}

double f3(double x, double y, double z)
{
    return exp(x) + y + z;
}

double f11(double x, double y, double z)
{
    return 2;
}

double f12(double x, double y, double z)
{
    return -1;
}

double f13(double x, double y, double z)
{
    return exp(-z);
}

double f21(double x, double y, double z)
{
    return -1;
}

double f22(double x, double y, double z)
{
    return 4 * y;
}

double f23(double x, double y, double z)
{
    return exp(-z);
}
double f31(double x, double y, double z)
{
    return exp(x);
}
double f32(double x, double y, double z)
{
    return 1;
}
double f33(double x, double y, double z)
{
    return 1;
}

void newton(std::vector<double> &x, std::vector<std::vector<double> > &iters)
{
    std::vector<double> xNext;
    std::vector<std::vector<double> > J(3, std::vector<double>(3, 0));
    double(*P[3][3])(double, double, double) = { { f11, f12, f13 }, { f21, f22, f23 }, {f31, f32, f33} };

    double norm = 0;
    do
    {
        for (int i = 0; i < 3; ++i)
        {
            for (int j = 0; j < 3; ++j)
            {
                J[i][j] = P[i][j](x[0], x[1], x[2]);
            }
        }
        std::vector<std::vector<double> > invJ;
        inverseMatrix(J, invJ);
        std::vector < std::vector<double>> F(3, std::vector<double>(1, 0));
        F[0][0] = f1(x[0], x[1], x[2]);
        F[1][0] = f2(x[0], x[1], x[2]);
        F[2][0] = f3(x[0], x[1], x[2]);

        std::vector < std::vector<double>> temp(3, std::vector<double>(1, 0));
        multiply(invJ, F, temp);
        xNext = { temp[0][0], temp[1][0], temp[2][0] };
        for (int i = 0; i < 3; ++i)
        {
            xNext[i] = x[i] - xNext[i];
        }
        norm = 0;
        for (int i = 0; i < 3; ++i)
        {
            norm = std::max(fabs(xNext[i] - x[i]), norm);
        }
        x = xNext;
        iters.push_back(x);
    } while (norm > eps);
}