poisson_binomial_log_probs.hpp

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#ifndef STAN_MATH_PRIM_FUN_POISSON_BINOMIAL_LOG_PROBS_HPP
#define STAN_MATH_PRIM_FUN_POISSON_BINOMIAL_LOG_PROBS_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/log1m.hpp>
#include <stan/math/prim/fun/log_sum_exp.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/vector_seq_view.hpp>
 
namespace stan {
namespace math {
 
template <typename T_theta, typename T_scalar = scalar_type_t<T_theta>,
          require_eigen_vector_t<T_theta>* = nullptr>
plain_type_t<T_theta> poisson_binomial_log_probs(int y, const T_theta& theta) {
  int size_theta = theta.size();
  plain_type_t<T_theta> log_theta = log(theta);
  plain_type_t<T_theta> log1m_theta = log1m(theta);
 
  Eigen::Matrix<T_scalar, Eigen::Dynamic, Eigen::Dynamic> alpha(size_theta + 1,
                                                                y + 1);
 
  // alpha[i, j] = log prob of j successes in first i trials
  alpha(0, 0) = 0.0;
  for (int i = 0; i < size_theta; ++i) {
    // no success in i trials
    alpha(i + 1, 0) = alpha(i, 0) + log1m_theta[i];
 
    // 0 < j < i successes in i trials
    for (int j = 0; j < std::min(y, i); ++j) {
      alpha(i + 1, j + 1) = log_sum_exp(alpha(i, j) + log_theta[i],
                                        alpha(i, j + 1) + log1m_theta[i]);
    }
 
    // i successes in i trials
    if (i < y) {
      alpha(i + 1, i + 1) = alpha(i, i) + log_theta(i);
    }
  }
 
  return alpha.row(size_theta);
}
 
template <typename T_y, typename T_theta, require_vt_integral<T_y>* = nullptr>
auto poisson_binomial_log_probs(const T_y& y, const T_theta& theta) {
  using T_scalar = scalar_type_t<T_theta>;
  size_t max_sizes = std::max(stan::math::size(y), size_mvt(theta));
  std::vector<Eigen::Matrix<T_scalar, Eigen::Dynamic, 1>> result(max_sizes);
  scalar_seq_view<T_y> y_vec(y);
  vector_seq_view<T_theta> theta_vec(theta);
 
  for (size_t i = 0; i < max_sizes; ++i) {
    result[i] = poisson_binomial_log_probs(y_vec[i], theta_vec[i]);
  }
 
  return result;
}
 
}  // namespace math
}  // namespace stan
#endif