const Key& CountDictionary<Key>::sample(){
//put that somewhere else...
if(!sampling_allowed){
std::vector<double> w(this->dict.size());
arg_vec.resize(this->dict.size());
int idx = 0;
for(typename std::unordered_map<Key,unsigned>::iterator it = this->dict.begin();it != this->dict.end();++it){
arg_vec[idx] = it->first;
w[idx] = it->second;
++idx;
}
std::discrete_distribution<int> dtmp(w.begin(),w.end());
distrib.param(dtmp.param());
/*
std::vector<double> p = distrib.probabilities();
for(int i = 0; i < p.size();++i){
std::cout << arg_vec[i] << p[i] << endl;
}
*/
sampling_allowed = true;
}
//distrib.reset() ?;
return arg_vec[distrib(rd_generator)];
}
/** Solves a cubic equation: ax^3 + bx^2 + cx + d = 0 using "Cardan's formula"
* (see: Bronstein, S.131f)
*/
double Action_Vector::solve_cubic_eq(double a, double b, double c, double d) {
const double one3 = 1.0 / 3.0;
const double one27 = 1.0 / 27.0;
double droot = 0;
double r, s, t;
double p, q, rho, phi;
double D, u, v;
std::vector<double> dtmp(3);
/* Coeff. for normal form x^3 + rx^2 + sx + t = 0 */
r = b / a;
s = c / a;
t = d / a;
/* Coeff. for red. eq. y^3 + py + q = 0 with y = x + r/3 bzw. (x = y - r/3) */
p = s - r * r * one3;
q = 2.0 * r * r * r * one27 - r * s * one3 + t;
/* Dummy variables */
rho = sqrt(-p * p * p * one27);
phi = acos(-q / (2.0 * rho));
/* Discriminante(?) */
D = pow((p * one3),3) + q * q * 0.25;
if(D > 0){ /* x real -> one real solution */
u = pow(-q * 0.5 + sqrt(D), one3);
v = -p / u * one3;
droot = (u + v) - r * one3;
} else if(D <= 0){
/* three real solutions (d < 0) | one real solution + one real double solution or
one real triple solution (d = 0) */
dtmp[0] = 2.0 * pow(rho, one3) * cos(phi * one3) - r * one3;
dtmp[1] = 2.0 * pow(rho, one3) * cos((phi + Constants::TWOPI ) * one3) - r * one3;
dtmp[2] = 2.0 * pow(rho, one3) * cos((phi + Constants::FOURPI) * one3) - r * one3;
sort(dtmp.begin(), dtmp.end());
//qsort((void *) dtmp, (size_t) 3, sizeof(double), cmpdouble);
droot = dtmp[0];
}
return droot;
}
