99 lines
2.9 KiB
C++
99 lines
2.9 KiB
C++
#include "Header.h"
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#include <Eigen/Dense>
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using namespace Eigen;
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Solver::Solver(double _A, double _B, double _C, int _N, int _l, int _u) {
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A = _A, B = _B, C = _C, N = _N;
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upper = _u, lower = _l;
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L = upper - lower;
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dx = L / N;
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}
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void Solver::Execute_Linear() {
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MatrixXd local = MatrixXd::Zero(2, 2);
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local(0, 0) = A / dx - B / 2;
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local(0, 1) = -A / dx + B / 2;
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local(1, 0) = -A / dx - B / 2;
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local(1, 1) = A / dx + B / 2;
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std::cout << "Local matrix:\n" << local << std::endl;
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VectorXd local_load(2);
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local_load(0) = C * dx / 2;
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local_load(1) = C * dx / 2;
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// Àíñàìáëèðîâàííûå ìàòðèöà è âåêòîð
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MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
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VectorXd global_load = VectorXd::Zero(N + 1);
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// Àíñàìáëèðîâàíèå äëÿ êàæäîãî êîíå÷íîãî ýëåìåíòà
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for (int elem = 0; elem < N; ++elem) {
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int node_i = elem;
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int node_j = elem + 1;
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// Ìàòðèöà æåñòêîñòè
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ansamb(node_i, node_i) += local(0, 0);
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ansamb(node_i, node_j) += local(0, 1);
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ansamb(node_j, node_i) += local(1, 0);
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ansamb(node_j, node_j) += local(1, 1);
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// Âåêòîð íàãðóçêè
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global_load(node_i) += local_load(0);
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global_load(node_j) += local_load(1);
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}
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std::cout << "Before:" << std::endl;
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std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
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std::cout << "Ansamb load vector:\n" << global_load << std::endl;
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// ÃÓ 1-ãî ðîäà
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double u_left = 5.0; // u(1) = 5
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double u_right = 15.0; // u(6) = 15
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// 1. Ó÷¸ò óñëîâèÿ u(1)=5
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for (int i = 1; i < N + 1; ++i) {
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global_load(i) -= ansamb(i, 0) * u_left;
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}
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// Îáíóëÿåì ïåðâóþ ñòðîêó è ñòîëáåö ìàòðèöû, óñòàíàâëèâàåì äèàãîíàëü = 1
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ansamb.row(0).setZero();
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ansamb.col(0).setZero();
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ansamb(0, 0) = 1.0;
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global_load(0) = u_left;
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// 2. Ó÷¸ò óñëîâèÿ u(6)=15
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for (int i = 0; i < N; ++i) {
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global_load(i) -= ansamb(i, N) * u_right;
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}
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// Îáíóëÿåì ïîñëåäíþþ ñòðîêó è ñòîëáåö ìàòðèöû, óñòàíàâëèâàåì äèàãîíàëü = 1
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ansamb.row(N).setZero();
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ansamb.col(N).setZero();
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ansamb(N, N) = 1.0;
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global_load(N) = u_right;
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std::cout << "\nAfter:" << std::endl;
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std::cout << "Modified matrix:\n" << ansamb << std::endl;
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std::cout << "Modified load vector:\n" << global_load << std::endl;
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VectorXd solution = ansamb.fullPivLu().solve(global_load);
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std::cout << "\nSolution:" << std::endl;
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std::cout << solution << std::endl;
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std::ofstream file("matrix_2.txt");
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for (int i = 0; i < N + 1; i++) {
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file << solution(i) << ' ';
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}
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file << std::endl;
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}
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void Solver::Execute_Cubic() {
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MatrixXd local = MatrixXd::Zero(2, 2);
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local(0, 0) = A * 37/(10 * dx) + B / 2;
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local(0, 1) = -A / dx + B / 2;
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local(0, 1) = A;
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local(1, 0) = -A / dx - B / 2;
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local(1, 1) = A / dx + B / 2;
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std::cout << "Local matrix:\n" << local << std::endl;
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VectorXd local_load(2);
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local_load(0) = C * dx / 2;
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local_load(1) = C * dx / 2;
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} |