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chsysdiss.cpp
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chsysdiss.cpp
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// Compilation options
// g++ -std=c++0x chsysdiss.cpp -lconfig++ -I /home/xavier/Notes/NonVanDissCH/ -I /home/xavier/boost-trunk/ -I /home/xavier/odeint-v2/
// g++ -std=c++0x chsysdiss.cpp -lconfig++ -I /home/xavier/Notes/CMA/NonVanDissCH/ -I /home/xavier/lib/boost-trunk/ -I /home/xavier/lib/odeint-v2/
#include <libconfig.h++>
#include <boost/numeric/odeint.hpp>
#include <cmath>
#include <vector>
#include <chsysdiss.hpp>
#include <fstream>
#include <sstream>
#include <algorithm>
namespace {
double interpolate(double y1, double y2, double u1, double u2, double xi) {
double a = (y2 - xi)/(y2 - y1);
return a*u1 + (1 - a)*u2;
};
double generateXi(double xi_left, double xi_right, int N,
std::vector<double>& xi) {
double dxi = (xi_right - xi_left)/N;
for (int i = 0; i < N + 1; ++i) {
xi[i] = xi_left + i*dxi;
}
return dxi;
}
void computeDerivative(const double* y,
const double* U,
const double* H,
const double* q,
const double* w,
const double* h,
const double* r,
const std::vector<bool>& diss,
const std::vector<double>& P,
const std::vector<double>& Q,
std::vector<double>& dZdt,
const int N) {
for (int i = 0; i < N + 1; ++i) {
dZdt[i + (N+1)*0] = U[i];
dZdt[i + (N+1)*1] = -Q[i];
dZdt[i + (N+1)*2] = std::pow(U[i],3)-2*P[i]*U[i];
if (diss[i] == false) {
dZdt[i + (N+1)*3] = w[i];
dZdt[i + (N+1)*4] = 0.5*h[i]+(0.5*U[i]*U[i]-P[i])*q[i];
dZdt[i + (N+1)*5] = -2*Q[i]*U[i]*q[i]+(3*U[i]*U[i]-2*P[i])*w[i];
} else {
dZdt[i + (N+1)*3] = 0.0;
dZdt[i + (N+1)*4] = 0.0;
dZdt[i + (N+1)*5] = 0.0;
}
dZdt[i + (N+1)*6] = 0.0;
}
}
void computePandQ(const double* y,
const double* U,
const double* H,
const double* q,
const double* w,
const double* h,
const double* r,
const std::vector<bool>& diss,
std::vector<double>& P,
std::vector<double>& Q,
const double dxi,
const int N) {
for (int j = 0; j < N + 1; ++j) {
P[j] = 0.0;
Q[j] = 0.0;
for (int i = 0; i < j; ++i) {
if (diss[i] == false) {
double coef = exp(-(y[j] - y[i]))/4.0 *(h[i] + U[i]*U[i]*q[i])*dxi;
P[j] += coef;
Q[j] -= coef;
}
}
for (int i = j; i < N + 1; ++i) {
if (diss[i] == false) {
double coef = exp((y[j] - y[i]))/4.0*(h[i] + U[i]*U[i]*q[i])*dxi;
P[j] += coef;
Q[j] += coef;
}
}
}
}
// double gFunction(double y, double U, double H,
// double q, double w, double h,
// double r) {
// double g2 = q + h + r*r;
// if (r == 0) {
// if ( w < 0 ) {
// double g1 = -w + 2*(1 + U*U)*q;
// if (g1 < g2) {
// return g1;
// } else {
// return g2;
// }
// } else {
// return g2;
// }
// } else {
// return g2;
// }
// }
// double yPlusHXi(double y, double U, double H,
// double q, double w, double h,
// double r) {
// return q + h;
// }
void writeVectorToFile(const std::string file_name, const std::vector<double>& vector) {
std::ofstream file(file_name);
for (std::vector<double>::const_iterator vec = vector.begin(); vec < vector.end(); ++vec) {
file << *vec << ",";
}
file.close();
}
double divide(double x1, double x2) {
if (fabs(x2) < 1e-16) {
return 0.;
} else {
return x1/x2;
}
};
void interpolateVector(std::vector<double>::const_iterator xi_begin,
std::vector<double>::const_iterator xi_end,
const double * u,
std::vector<double>::const_iterator phi_begin,
std::vector<double>::const_iterator phi_end,
double* u_phi,
bool is_u_derivative,
bool is_u_equal_y = false) {
if (phi_begin < phi_end) {
if (*phi_begin < *xi_begin) {
// We are outside the scope of phi.
if (is_u_equal_y) {
// extrapolate with line of slope one.
*u_phi = *u + (*phi_begin - *xi_begin);
} else {
// extrapolate with horizontal line.
*u_phi = *u;
}
interpolateVector(xi_begin, xi_end, u, phi_begin + 1, phi_end, u_phi + 1, is_u_derivative, is_u_equal_y);
} else {
while ((xi_begin + 1 < xi_end) && (*phi_begin >= *(xi_begin + 1))) {
++xi_begin;
++u;
}
if (xi_begin + 1 < xi_end ) {
if (is_u_derivative) {
*u_phi = *u;
} else {
*u_phi = interpolate(*xi_begin, *(xi_begin + 1),
*u, *(u + 1),
*phi_begin);
}
interpolateVector(xi_begin, xi_end, u, phi_begin + 1, phi_end, u_phi + 1, is_u_derivative, is_u_equal_y);
} else {
// We are outside the scope of phi. We extrapolate as above.
if (is_u_equal_y) {
*u_phi = *u + (*phi_begin - *xi_begin);
} else {
*u_phi = *u;
}
interpolateVector(xi_begin, xi_end, u, phi_begin + 1, phi_end, u_phi + 1, is_u_derivative, is_u_equal_y);
}
}
} else {
return;
}
};
void relabelingAndCopy(const std::vector<double>& xi,
double* u,
const std::vector<double>& g_inv,
std::vector<double>& new_u, const bool is_u_equal_y = false)
{
interpolateVector(xi.begin(), xi.end(),
u,
g_inv.begin(), g_inv.end(),
&new_u[0],
false, is_u_equal_y);
std::copy(new_u.begin(), new_u.end(), u);
};
void relabelingAndCopyDer(const std::vector<double>& xi,
double* q,
const std::vector<double>& g_inv,
const std::vector<double>& g_xi,
std::vector<double>& new_q)
{
const int N = xi.size();
std::transform(q, q + N, g_xi.begin(), new_q.begin(), divide);
interpolateVector(xi.begin(), xi.end(),
&new_q[0],
g_inv.begin(), g_inv.end(),
q,
true, false);
};
void integrateDer(double* y,
const double* y_xi,
const double dxi,
const int ind0,
const double y0,
const int N)
{
double* y_p = y + ind0;
double* y_n = y + ind0;
const double* y_xi_p = y_xi + ind0;
const double* y_xi_n = y_xi + ind0;
y_p[0] = y0;
while(y_p < y + N) {
++y_p;
++y_xi_p;
y_p[0] = y_p[-1] + y_xi_p[-1]*dxi;
}
while(y_n > y) {
--y_n;
--y_xi_n;
y_n[0] = y_n[1] - y_xi_n[0]*dxi;
}
}
} // anonymous namespace.
bool Simulation::checkIfInCollisionRegion(double y1, double U1, double H1, double q1, double w1, double h1, double r1) {
// if ((r1 == 0) && (w1 <= 0) && (-w1 + 2*(1 + U1*U1)*q1 <= q1 + h1) && (q1 >= 0)) {
if ((r1 == 0) && (w1 <= 0) && (-w1 + 2*(1 + U1*U1)*q1 <= q1 + h1) && (q1 >= 0)) {
return true;
} else {
return false;
}
}
bool Simulation::checkIfCollided(double y1, double U1, double H1, double q1, double w1, double h1, double r1) {
double radius = (q1 + h1)/(2*(U1*U1 + 1));
if ((r1 == 0) && ((q1 <=0) || ( (q1 >=0) && (w1 >= 0) && (w1 <= collision_limiter*(radius - q1)/radius) ))){
return true;
} else {
return false;
}
}
Simulation::Simulation() {
libconfig::Config cfg;
cfg.readFile("param_input.txt");
R = cfg.lookup("R");
N = cfg.lookup("N");
time_end = cfg.lookup("time_end");
dt = cfg.lookup("dt");
libconfig::Setting& time_setting = cfg.lookup("time");
int size_time = time_setting.getLength();
time.resize(size_time);
for (int i = 0; i < size_time; ++i) {
time[i] = time_setting[i];
}
dxi = 2*R/N;
xi.resize(N + 1);
for (int i = 0; i < N+1; ++i) {
xi[i] = -R + i*dxi;
}
new_xi.resize(N + 1);
track.resize(N + 1);
old_track.resize(N + 1);
g.resize(N + 1);
g_inv.resize(N + 1);
g_xi.resize(N + 1);
diss.resize(N + 1);
P.resize(N + 1);
Q.resize(N + 1);
local_var1.resize(N + 1);
Z.resize(7*(N + 1));
resetPointers(Z);
}
void Simulation::initPeakon() {
resetPointers(Z);
libconfig::Config cfg;
cfg.readFile("param_input.txt");
const double rho0 = cfg.lookup("rho0");
const double c = cfg.lookup("c");
double q1 = 0.0;
for (int i = 0; i < N + 1; ++i) {
y[i] = xi[i];
U[i] = c*exp(-c*fabs(xi[i]));
w[i] = -c*sign(xi[i])*exp(-c*fabs(xi[i]));
q[i] = 1.;
r[i] = rho0;
h[i] = U[i]*U[i] + w[i]*w[i] + r[i]*r[i];
}
int ind0 = ceil((N - 1)/2);
integrateDer(H, h, dxi, ind0, 0, N);
}
void Simulation::initCubic() {
resetPointers(Z);
// u = alpha*exp(-x^2)*x*(x-x0)*(x+x0)
libconfig::Config cfg;
cfg.readFile("param_input.txt");
const double rho0 = cfg.lookup("rho0");
const double rho0_x = cfg.lookup("rho0_x");
const double x0 = cfg.lookup("x0");
const double umax = cfg.lookup("umax");
const double xmax = 1/sqrt(3)*x0; // Point where u' vanishes
const double alpha = umax/(2*pow(xmax, 3));
const double beta = 1.0;
for (int i = 0; i < N + 1; ++i) {
y[i] = xi[i];
U[i] = alpha*exp(-beta*xi[i]*xi[i])*xi[i]*(xi[i] - x0)*(xi[i] + x0);
w[i] = alpha*exp(-beta*xi[i]*xi[i])*(3*xi[i]*xi[i] - x0*x0)-2*beta*xi[i]*U[i];
q[i] = 1.;
if (fabs(xi[i]) <= rho0_x) {
r[i] = rho0;
}
h[i] = U[i]*U[i] + w[i]*w[i] + r[i]*r[i];
}
int ind0 = ceil((N - 1)/2);
integrateDer(H, h, dxi, ind0, 0, N);
}
void Simulation::initCubic2() {
resetPointers(Z);
// u = alpha*exp(-x^2)*x*(x-x0)*(x+x0)
libconfig::Config cfg;
cfg.readFile("param_input.txt");
const double rho0 = cfg.lookup("rho0");
const double gamma = cfg.lookup("gamma");
const double x0 = cfg.lookup("x0");
const double umax = cfg.lookup("umax");
const double xmax = 1/sqrt(3)*x0; // Point where u' vanishes
const double alpha = umax/(2*pow(xmax, 3));
const double beta = 1.0;
for (int i = 0; i < N + 1; ++i) {
y[i] = xi[i];
U[i] = alpha*exp(-beta*xi[i]*xi[i])*xi[i]*(xi[i] - x0)*(xi[i] + x0);
w[i] = alpha*exp(-beta*xi[i]*xi[i])*(3*xi[i]*xi[i] - x0*x0)-2*beta*xi[i]*U[i];
q[i] = 1.;
r[i] = rho0*exp(-gamma*xi[i]*xi[i]);
h[i] = U[i]*U[i] + w[i]*w[i] + r[i]*r[i];
}
int ind0 = ceil((N - 1)/2);
integrateDer(H, h, dxi, ind0, 0, N);
}
void Simulation::initAntipeakon() {
resetPointers(Z);
for (int i = 0; i < N + 1; ++i) {
y[i] = xi[i];
}
libconfig::Config cfg;
cfg.readFile("param_input.txt");
const double p1 = cfg.lookup("p1");
const double p2 = cfg.lookup("p2");
const double q1 = cfg.lookup("q1");
const double q2 = cfg.lookup("q2");
const double rho0 = cfg.lookup("rho0");
const double rho0_x = cfg.lookup("rho0_x");
for (int i = 0; i < N + 1; ++i) {
U[i] = p1*exp(-fabs(y[i] - q1)) + p2*exp(-fabs(y[i] - q2));
w[i] = -sign(y[i]-q1)*p1*exp(-fabs(y[i]-q1))
-sign(y[i]-q2)*p2*exp(-fabs(y[i]-q2));
r[i] = rho0*exp(-10*std::pow(xi[i]/R, 2.));
if (fabs(xi[i]) <= rho0_x) {
r[i] = rho0;
}
q[i] = 1.0;
h[i] = U[i]*U[i] + w[i]*w[i] + r[i]*r[i];
}
int ind0 = ceil((N - 1)/2);
integrateDer(H, h, dxi, ind0, 0, N);
}
void Simulation::relabelingAndCopyAll(){
resetPointers(Z);
computeG();
double new_dxi = generateXi(g[0], g[N], N, new_xi);
interpolateVector(g.begin(), g.end(),
&xi[0],
new_xi.begin(), new_xi.end(),
&g_inv[0],
false, true);
relabelingAndCopy(xi, y, g_inv, local_var1, true);
relabelingAndCopy(xi, U, g_inv, local_var1, false);
relabelingAndCopy(xi, H, g_inv, local_var1, true);
relabelingAndCopyDer(xi, q, g_inv, g_xi, local_var1);
relabelingAndCopyDer(xi, w, g_inv, g_xi, local_var1);
relabelingAndCopyDer(xi, h, g_inv, g_xi, local_var1);
std::copy(new_xi.begin(), new_xi.end(), xi.begin());
dxi = new_dxi;
setTrack();
setDiss();
}
void Simulation::solve() {
typedef boost::numeric::odeint::runge_kutta_dopri5< state_type > stepper_type;
stepper_type stepper = boost::numeric::odeint::runge_kutta_dopri5< state_type >();
double t = 0;
solution.push_back(Z);
solution_diss.push_back(diss);
solution_time.push_back(0.0);
for (std::vector<double>::const_iterator time_it = time.begin(); time_it < time.end() - 1; ++time_it) {
while (t <= time_it[1]) {
resetPointers(Z);
integrate_const(stepper, *this, Z, t, t + dt, dt);
removeEnergy();
t += dt;
}
resetPointers(Z);
// fixYandH();
if (is_relabeling) {
relabelingAndCopyAll();
}
solution.push_back(Z);
solution_diss.push_back(diss);
solution_time.push_back(*time_it);
}
}
void Simulation::operator() (const state_type& ZZ, state_type& dZdt, const double /* t */ ) {
std::vector<double> PP(N + 1);
std::vector<double> QQ(N + 1);
const double* yy = &ZZ[0*(N + 1)];
const double* UU = &ZZ[1*(N + 1)];
const double* HH = &ZZ[2*(N + 1)];
const double* qq = &ZZ[3*(N + 1)];
const double* ww = &ZZ[4*(N + 1)];
const double* hh = &ZZ[5*(N + 1)];
const double* rr = &ZZ[6*(N + 1)];
::computePandQ(yy, UU, HH,
qq, ww, hh, rr,
diss,
PP, QQ, dxi, N);
::computeDerivative(yy, UU, HH,
qq, ww, hh, rr,
diss,
PP, QQ,
dZdt,
N);
}
void Simulation::computeG() {
std::transform(q, q + N + 1, h, g_xi.begin(), [](double a, double b) {
return a + b;
});
int ind0 = ceil((N - 1)/2);
integrateDer(&g[0], &g_xi[0], dxi, ind0, 0.0, N);
}
void Simulation::computePandQ() {
resetPointers(Z);
::computePandQ(y, U, H,
q, w, h, r, diss,
P, Q, dxi, N);
}
void Simulation::resetPointers(state_type& ZZ) {
y = &ZZ[0*(N + 1)];
U = &ZZ[1*(N + 1)];
H = &ZZ[2*(N + 1)];
q = &ZZ[3*(N + 1)];
w = &ZZ[4*(N + 1)];
h = &ZZ[5*(N + 1)];
r = &ZZ[6*(N + 1)];
}
void Simulation::writeToFile() {
std::ofstream param_file("param.txt");
std::ofstream xi_file("xi.txt");
std::ofstream t_file("t.txt");
std::ofstream y_file("y.txt");
std::ofstream U_file("U.txt");
std::ofstream H_file("H.txt");
std::ofstream q_file("q.txt");
std::ofstream w_file("w.txt");
std::ofstream M_file("M.txt");
std::ofstream h_file("h.txt");
std::ofstream r_file("r.txt");
double* diss_p;
param_file << R <<"," << N;
for (int i = 0; i < N + 1; ++i) {
xi_file << xi[i] << ",";
}
for (int j = 0; j < solution.size(); ++j) {
t_file << solution_time[j] << ",";
resetPointers(solution[j]);
const std::vector<bool>& diss_p = solution_diss[j];
// setDiss();
int M = N + 1;
for (int i = 0; i < N + 1; ++i) {
if (diss_p[i] == true) {
--M;
} else {
y_file << y[i] << ",";
U_file << U[i] << ",";
H_file << H[i] << ",";
q_file << q[i] << ",";
w_file << w[i] << ",";
h_file << h[i] << ",";
r_file << r[i] << ",";
}
}
M_file << M <<",";
}
xi_file.close();
t_file.close();
y_file.close();
U_file.close();
H_file.close();
q_file.close();
M_file.close();
w_file.close();
h_file.close();
r_file.close();
}
void Simulation::init() {
libconfig::Config cfg;
cfg.readFile("param_input.txt");
const std::string init_type = cfg.lookup("init");
is_relabeling = cfg.lookup("is_relabeling");
if (init_type == "peakon") {
initPeakon();
} else if (init_type == "antipeakon") {
initAntipeakon();
} else if (init_type == "cubic") {
initCubic();
} else if (init_type == "cubic2") {
initCubic2();
}
diss.assign(N + 1, false);
collision_limiter = 0.0;
if (is_relabeling) {
relabelingAndCopyAll();
} else {
setTrack();
}
}
void Simulation::setTrack() {
for (int i = 0; i < N + 1; ++i) {
track[i] = checkIfInCollisionRegion(y[i], U[i], H[i], q[i], w[i], h[i], r[i]);
}
}
void Simulation::setDiss() {
for (int i = 0; i < N + 1; ++i) {
diss[i] = checkIfCollided(y[i], U[i], H[i], q[i], w[i], h[i], r[i]);
}
}
void Simulation::removeEnergy() {
resetPointers(Z);
std::copy(track.begin(), track.end(), old_track.begin());
setTrack();
bool need_set_track = false;
for (int i = 0; i < N + 1; ++i) {
if (old_track[i] && not(track[i])) {
// if ((q[i] < (q[i] + h[i])/(2*(1 + U[i]*U[i]))) && (q[i] >= 0) && (w[i] >= 0)) {
if ((q[i] < (q[i] + h[i])/(2*(1 + U[i]*U[i])))) {
// collision_limiter = max(collision_limiter, 10*w[i]);
diss[i] = true;
q[i] = 0.0;
w[i] = 0.0;
need_set_track = true;
}
}
}
if (need_set_track) {
setTrack();
}
}
int main() {
Simulation sim;
sim.init();
sim.solve();
sim.writeToFile();
}