#include "Header.h"
#include <Eigen/Dense>
using namespace Eigen;

Solver::Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u) {
    A = _A, B = _B, C = _C, D = _D, N = _N;
    upper = _u, lower = _l;
	L = upper - lower;
	dx = L / N;
}

void Solver::Execute_Linear(double val1, double val2) {

    MatrixXd local = MatrixXd::Zero(2, 2);
    VectorXd local_load(2);

    local(0, 0) = -A / dx - B / 2. + C * dx / 3.;
    local(0, 1) = A / dx + B / 2. + C * dx / 6.;
    local(1, 0) = A / dx - B / 2. + C * dx / 6.;
    local(1, 1) = -A / dx + B / 2. + C * dx / 3.;

    local_load(0) = -D * dx / 2.;
    local_load(1) = -D * dx / 2.;

    MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
    VectorXd global_load = VectorXd::Zero(N + 1);

    // Ансамблирование
    for (int elem = 0; elem < N; ++elem) {
        int node_i = elem;
        int node_j = elem + 1;

        ansamb(node_i, node_i) += local(0, 0);
        ansamb(node_i, node_j) += local(0, 1);
        ansamb(node_j, node_i) += local(1, 0);
        ansamb(node_j, node_j) += local(1, 1);

        global_load(node_i) += local_load(0);
        global_load(node_j) += local_load(1);
    }

#if DEBUG
    std::cout << std::endl << "Before:" << std::endl;
    std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
    std::cout << "Ansamb load vector:\n" << global_load << std::endl;
#endif

    double u_right = val2;

    // Clear first and last rows
    ansamb.row(0).setZero();
    ansamb.row(N).setZero();

    // u'(0) = u(0)
    ansamb(0, 0) = dx + 1;
    ansamb(0, 1) = -1;
    global_load(0) = 0;

    // u(10) = u_right = 5
    ansamb(N, N) = 1;
    global_load(N) = u_right;

#if DEBUG
    std::cout << "\nAfter:" << std::endl;
    std::cout << "Modified matrix:\n" << ansamb << std::endl;
    std::cout << "Modified load vector:\n" << global_load << std::endl;
#endif

    VectorXd solution = ansamb.fullPivLu().solve(global_load);
    std::cout << "\nSolution:" << std::endl;
    std::cout << solution << std::endl;

    std::ofstream file("matrix_linear.txt");
    for (int i = 0; i < N; i++) {
        file << solution(i) << ' ';
    }
    file << std::endl;
}

void Solver::Execute_Cubic(double val1, double val2) {

    int mat_dim = 1 + N * 3;
    Eigen::MatrixXd Amat(mat_dim, mat_dim);
    Eigen::VectorXd b(mat_dim);
    Amat.setZero();
    b.setZero();

    // Assemble matrix
    for (int i = 0; i < mat_dim - 3; i += 3) {
        Amat(i, i + 0) -= A * 37.0 / 10.0 / dx;
        Amat(i, i + 1) -= A * (-189.0) / 40.0 / dx;
        Amat(i, i + 2) -= A * 27.0 / 20.0 / dx;
        Amat(i, i + 3) -= A * (-13.0) / 40.0 / dx;
        Amat(i + 1, i + 0) -= A * (-189.0) / 40.0 / dx;
        Amat(i + 1, i + 1) -= A * 54.0 / 5.0 / dx;
        Amat(i + 1, i + 2) -= A * (-297.0) / 40.0 / dx;
        Amat(i + 1, i + 3) -= A * 27.0 / 20.0 / dx;
        Amat(i + 2, i + 0) -= A * 27.0 / 20.0 / dx;
        Amat(i + 2, i + 1) -= A * (-297.0) / 40.0 / dx;
        Amat(i + 2, i + 2) -= A * 54.0 / 5.0 / dx;
        Amat(i + 2, i + 3) -= A * (-189.0) / 40.0 / dx;
        Amat(i + 3, i + 0) -= A * (-13.0) / 40.0 / dx;
        Amat(i + 3, i + 1) -= A * 27.0 / 20.0 / dx;
        Amat(i + 3, i + 2) -= A * (-189.0) / 40.0 / dx;
        Amat(i + 3, i + 3) -= A * 37.0 / 10.0 / dx;

        Amat(i + 0, i + 0) += B * (-1.0) / 2.0;
        Amat(i + 0, i + 1) += B * 57.0 / 80.0;
        Amat(i + 0, i + 2) += B * (-3.0) / 10.0;
        Amat(i + 0, i + 3) += B * 7.0 / 80.0;
        Amat(i + 1, i + 0) += B * (-57.0) / 80.0;

        Amat(i + 1, i + 2) += B * 81.0 / 80.0;
        Amat(i + 1, i + 3) += B * (-3.0) / 10;
        Amat(i + 2, i + 0) += B * 3.0 / 10.0;
        Amat(i + 2, i + 1) += B * (-81.0) / 80.0;

        Amat(i + 2, i + 3) += B * 57.0 / 80.0;
        Amat(i + 3, i + 0) += B * (-7.0) / 80.0;
        Amat(i + 3, i + 1) += B * 3.0 / 10.0;
        Amat(i + 3, i + 2) += B * (-57.0) / 80.0;
        Amat(i + 3, i + 3) += B * 1.0 / 2.0;
    }

    // Assembdxe vector
    for (int i = 0; i < mat_dim - 3; i += 3) {
        b(i) -= D * dx / 8.0;
        b(i + 1) -= D * 3.0 * dx / 8.0;
        b(i + 2) -= D * 3.0 * dx / 8.0;
        b(i + 3) -= D * dx / 8.0;
    }


    Amat.row(0).setZero();
    Amat(0, 0) = dx / 3.0 + 1;
    Amat(0, 1) = -1;
    b(0) = 0;

    Amat.row(mat_dim - 1).setZero();
    Amat(mat_dim - 1, mat_dim - 1) = 1;
    b(mat_dim - 1) = val2;

    // Решение системы
    VectorXd solution = Amat.colPivHouseholderQr().solve(b);
    std::cout << "\nSolution:" << std::endl;
    std::cout << solution << std::endl;
    
    std::ofstream file("matrix_cubic.txt");
    for (int i = 0; i < solution.size(); i++) {
        file << solution(i) << ' ';
    }
    file << std::endl;
}