// Args:
// probs: A vector of probabilities to be evaluated. If no
// derivatives are desired then probs can either match the
// dimension of nu(), in which case it must sum to 1, or its
// dimension must be one less, in which case its sum must be
// non-negative but can't exceed 1. Element 0 is assumed to be
// the function of the other elements, so that probs0 = 1 -
// sum(probs). If derivatives are desired then probs.size()
// must be nu().size() - 1.
// gradient: The derivative of the unconstrained elements of
// probs. This is only accessed if nderivs > 0. It will be
// resized if needed, so that its dimension is one less than the
// dimension of nu().
// Hessian: Second derivative of logp with respect to the free
// elements of probs (i.e. not the first one). This matrix is
// only accessed if nderiv > 1, in which case it will be resized.
// nderiv: The number of derivatives desired.
double DirichletModel::Logp(const Vector &probs, Vector &gradient,
Matrix &Hessian, uint nderiv) const {
// Because sum(p)=1, there are only p.size()-1 free elements in p.
// The constraint is enforced by expressing the first element of p
// as a function of the other variables. The corresponding elements
// in g and h are zeroed.
if (probs.size() == nu().size() && nderiv == 0) {
return ddirichlet(probs, nu(), true);
} else if (probs.size() + 1 != nu().size()) {
report_error(
"probs is the wrong size in DirichletModel::Logp. "
"Its dimension should be one less than nu().size()");
}
const Vector &n(nu());
double p0 = 1 - sum(probs);
Vector full_probs(probs.size() + 1);
full_probs[0] = p0;
VectorView(full_probs, 1) = probs;
double ans = ddirichlet(full_probs, n, true);
if (nderiv > 0) {
gradient.resize(probs.size());
for (int i = 0; i < probs.size(); ++i) {
gradient[i] = (n[i + 1] - 1) / probs[i] - (n[0] - 1) / p0;
if (nderiv > 1) {
Hessian.resize(probs.size(), probs.size());
for (int j = 0; j < probs.size(); ++j) {
Hessian(i, j) =
-(n[0] - 1) / square(p0) -
(i == j ? (1.0 - n[i + 1]) / square(probs[i]) : 0.0);
}
}
}
}
return ans;
}
double MCS::logpri()const{
const Mat &Nu(this->Nu());
const Mat &Q(mod_->Q());
assert(Nu.same_dim(Q));
uint S = Nu.nrow();
double ans = 0;
for(uint s=0; s<S; ++s){
ans += ddirichlet(Q.row(s), Nu.row(s), true);
}
if(mod_->pi0_fixed()) return ans;
check_pi0();
ans += ddirichlet(mod_->pi0(), this->nu(), true);
return ans;
}
double PDM::pdf(const Matrix &Pi, bool logscale) const {
double ans(0);
for (uint i = 0; i < Pi.nrow(); ++i) {
ans += ddirichlet(Pi.row(i), Nu().row(1), true);
}
return logscale ? ans : exp(ans);
}
double DM::pdf(const Vector &pi, bool logscale) const {
return ddirichlet(pi, nu(), logscale);
}
