std::vector<double> CanonicalAverager::calculate_weights(const std::vector<double> &energies, const Binner &binner, const DArray &lnG, const BArray &lnG_support, double beta) {
// Assert the arrays got same shape and are one dimensional
assert(lnG.same_shape(lnG_support));
assert(lnG.get_shape().size()==1);
unsigned int nbins = lnG.get_shape(0);
// First make a histogram of the energies given as argument
UArray histogram(nbins);
for(std::vector<double>::const_iterator it=energies.begin(); it < energies.end(); it++) {
int bin = binner.calc_bin(*it);
if (0 <= bin && bin < static_cast<int>(nbins)) {
histogram(bin)++;
}
}
// Calculate the support for this histogram
BArray histogram_support = histogram > 0;
// Calculate the normalization constant for the canonical distribution,
// by summing over the area with both the histogram and the estimated
// entropy (lnG) has support. The normalization constant is given by
//
// lnZ_beta = log(Z_beta) = log[ sum_E exp( S(E) - beta*E ) ]
//
// To calculate this we use the log-sum-exp trick
BArray support = histogram_support && lnG_support;
DArray binning = binner.get_binning_centered();
DArray summands(nbins);
for (BArray::constwheretrueiterator it = support.get_constwheretrueiterator(); it(); ++it) {
summands(it) = lnG(it) - beta*binning(it);
}
double lnZ_beta = log_sum_exp(summands, support);
// Now calculate the probability for each bin according to the canonical ensemble
DArray P_beta(nbins);
for (BArray::constwheretrueiterator it = support.get_constwheretrueiterator(); it(); ++it) {
P_beta(it) = exp(-beta*binning(it) + lnG(it) - lnZ_beta);
}
// Calculate the weight for each energy in the energy vector
std::vector<double> weights;
for(std::vector<double>::const_iterator it=energies.begin(); it < energies.end(); it++) {
int bin = binner.calc_bin(*it);
if (0 <= bin && bin < static_cast<int>(nbins)) {
double weight = 1.0/static_cast<double>(histogram(bin)) * P_beta(bin);
weights.push_back(weight);
}
else {
weights.push_back(0);
}
}
return weights;
}
