void testEigenMap()
{
Vector_t theta;
theta.setZero(4 * 5);
for (int i = 0; i < theta.size(); ++i)
theta(i) = i;
std::cout << theta << std::endl;
Eigen::Map<Matrix_t> Theta(theta.data(), 4, 5); // reshape
std::cout << Theta << std::endl;
Vector_t theta2(Eigen::Map<Vector_t>(Theta.data(), 5 * 4));
std::cout << theta2 << std::endl;
}
void forwardMap(double q[2], double qdot[2], double t, double x[2], double v[2]) {
// maps from (q, qdot) -> (x(t), v(t)) (forward in time)
// to go backward, let t -> -t
// first step: find auxiliary variables
// eta0 is between 0 and pi but extends to between 0 and 2pi based on the sign of the initial r-velocity
double eta0 = etaZero(q,qdot);
if (qdot[0]<0.0) {
eta0 = 2.0 * M_PI - eta0;
}
// etabase is between 0 and pi
double etabase = eta(q,qdot,t, eta0);
double omega3 = Omega3(q,qdot);
double omega2 = Omega2(q,qdot);
double J2 = Lmag(q,qdot);
double ham = H(q,qdot);
double e = eccentricity(q, qdot);
double c = c_aux(q, qdot);
// compute number of pis to add for correct branch (theta2 and theta3 must increase continuously)
double Tr = 2.0 * M_PI / omega3;
double tperi = (theta3(0.0, q, qdot) - theta3(eta0,q, qdot))/omega3;
double tapo = (theta3(M_PI, q, qdot) - theta3(eta0,q, qdot))/omega3;
// both these should be larger than 0 (time of *next* pericenter and apocenter)
while (tperi<0) {
tperi += Tr;
}
while (tapo<0) {
tapo += Tr;
}
// calculate number of half-periods (no. of peri- or apocenter passages)
int nstar = ((int) floor((t - GSL_MIN(tapo, tperi))/(Tr/2.0))) + 1;
// get r
double base = (1.0 + c/B_ISO * (1.0 - e * cos(etabase)));
x[0] = B_ISO * sqrt(base * base - 1.0);
// get phi
double tan1 = atan(sqrt((1.0 + e)/(1.0 - e)) * tan(etabase/2.0)) + M_PI * floor((etabase+M_PI)/(2.0 * M_PI));
double tan2 = (atan(sqrt((1.0 + e + 2.0 * B_ISO / c)/(1.0 - e + 2.0 * B_ISO / c)) * tan(etabase/2.0)) + M_PI * floor((etabase+M_PI)/(2.0 * M_PI)))/sqrt(1 + 4.0 * M_PI * B_ISO / (J2 * J2));
double th20 = theta2(eta0, q[1], q, qdot);
double th3 = theta3(etabase, q, qdot);
// fprintf(stdout, "%lg %lg %lg %lg\n", t, tan1, tan2,th3);
x[1] = th20 + omega2 * t - omega2/omega3 * th3 + tan1 + tan2;
// conservation of angular momentum gives phidot
v[1] = J2 / (x[0] * x[0]);
// conservation of energy gives magnitude of rdot
v[0] = M_SQRT2 * sqrt(ham - J2 * J2 / (2.0 * x[0] * x[0]) - Phi(x[0]));
// figure out the sign - if it started heading toward pericenter
// and has gone thru an even number of half-periods since then, vr<0
// likewise if it started heading toward apo and has gone thru an odd nm
// of half-periods, vr<0
if((GSL_IS_EVEN(nstar) && (tperi<tapo)) || (GSL_IS_ODD(nstar) && (tapo<tperi)))
v[0] *= -1.0;
}