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Реализация метода Ньютона для вычисления вектора смещения

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ParkSuMin
2025-10-28 14:09:37 +03:00
parent 04b071f287
commit 8269990c3e
1 changed files with 57 additions and 4 deletions
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61
main.cpp
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@@ -46,12 +46,14 @@ double E1(double t) {
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
MatrixXd Y = MatrixXd::Zero(MATRIX_DIM, MATRIX_DIM);
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
VectorXd N = VectorXd::Zero(MATRIX_DIM);
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
VectorXd dX = VectorXd::Zero(MATRIX_DIM);
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
VectorXd X = VectorXd::Zero(MATRIX_DIM);
// <20><><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (<28><><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD>)
VectorXd X_backup = VectorXd::Zero(MATRIX_DIM);
void Jacobian(double dt) {
Y(0, 0) = 1, Y(0, 3) = -1. / dt;
@@ -95,10 +97,61 @@ void nevyzka(double dt, double cur_time) {
N(11) = E1(cur_time) - X(6);
N(12) = E2 - X(9);
// <20><><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD>
N = -1 * N;
}
int main() {
Jacobian(0.1);
double dt = T_Start; // <20><><EFBFBD> <20><> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
double dt_prev = dt; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD> <20><> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
double eps_max = ACR; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
double eps_min = 1e-10; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
int counter = 0; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD> <20><> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
double cur_time = 0; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD>
double eps_cur;
double eps;
double step_c = 0;
while (dt <= TK) {
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
int iteration = 0;
bool flag = true;
while (flag) {
Jacobian(dt);
nevyzka(dt, cur_time);
#ifdef _DEBUG
std::cout << Y << std::endl << N;
#endif
dX = Y.fullPivLu().solve(N);
#ifdef _DEBUG
std::cout << '\n' << dX;
#endif
X += dX;
iteration++;
double maximum = X.maxCoeff();
if (maximum <= ACR) {
flag = false;
}
else if (iteration == 7 && flag) {
iteration = 0;
dt /= 2.;
if (dt < SMN) {
std::cerr << "Sorry, but i can not solve this" << std::endl;
exit(-1);
}
X = X_backup;
}
}
// TODO: <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD> <20> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>,
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
}
// <20><><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/*Jacobian(0.1);
nevyzka(0.1, 0);
std::cout << Y << std::endl << N;
std::cout << Y << std::endl << N;*/
}