double beta_logp(const T& x, const U& alpha, const V& beta) {
if(!arma::all(x > 0) || !arma::all(x < 1) ||
!arma::all(alpha > 0) || !arma::all(beta > 0))
return -std::numeric_limits<double>::infinity();
return arma::accu(lgamma(alpha+beta) - lgamma(alpha) - lgamma(beta)
+ schur_product(alpha - 1.0f, log_approx(x))
+ schur_product(beta - 1.0f, log_approx(1.0f - x)));
}
double gamma_logp(const T& x, const U& alpha, const V& beta) {
if(!arma::all(x > 0))
return -std::numeric_limits<double>::infinity();
return
arma::accu(schur_product((alpha - 1.0f),log_approx(x))
- schur_product(beta,x) - lgamma(alpha)
+ schur_product(alpha,log_approx(beta)));
}
// sigma denotes cov matrix rather than precision matrix
double multivariate_normal_sigma_logp(const arma::vec& x, const arma::vec& mu, const arma::mat& sigma) {
const double log_2pi = log(2 * arma::math::pi());
arma::mat R(arma::zeros<arma::mat>(sigma.n_cols,sigma.n_cols));
// non-positive definite test via chol
if(chol(R,sigma) == false) { return -std::numeric_limits<double>::infinity(); }
// otherwise calc logp
return -(x.n_elem * log_2pi + log_approx(arma::det(sigma)) + mahalanobis(x,mu,sigma))/2;
}
inline double calc() const {
return arma::accu(arma::schur(delta_, log_approx(lambda_)) - arma::schur(lambda_, x_));
}
double bernoulli_logp(const T& x, const U& p) {
if(!arma::all(x >= 0) || !arma::all(x <= 1))
return -std::numeric_limits<double>::infinity();
return arma::accu(schur_product(x,log_approx(p))
+ schur_product((1-x), log_approx(1-p)));
}
double binom_logp(const T& x, const U& n, const V& p) {
if(!arma::all(x >= 0) || !arma::all(x <= n))
return -std::numeric_limits<double>::infinity();
return arma::accu(schur_product(x,log_approx(p))
+ schur_product((n-x),log_approx(1-p)) + arma::factln(n) - arma::factln(x) - arma::factln(n-x));
}
double uniform_logp(const T& x, const U& lower, const V& upper) {
if(!arma::all(x > lower) || !arma::all(x < upper))
return -std::numeric_limits<double>::infinity();
return -arma::accu(log_approx(upper - lower));
}
double normal_logp(const T& x, const U& mu, const V& tau) {
return arma::accu(0.5f*log_approx(0.5f*tau/arma::math::pi())
- 0.5f * schur_product(tau, square(x - mu)));
}