check_2F1_converges.hpp

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#ifndef STAN_MATH_PRIM_SCAL_ERR_CHECK_2F1_CONVERGES_HPP
#define STAN_MATH_PRIM_SCAL_ERR_CHECK_2F1_CONVERGES_HPP

#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/fun/is_nonpositive_integer.hpp>
#include <stan/math/prim/scal/fun/value_of_rec.hpp>
#include <cmath>
#include <limits>
#include <sstream>
#include <stdexcept>

namespace stan {
namespace math {

/**
 * Check if the hypergeometric function (2F1) called with
 * supplied arguments will converge, assuming arguments are
 * finite values.
 *
 * @tparam T_a1 Type of a1
 * @tparam T_a2 Type of a2
 * @tparam T_b1 Type of b1
 * @tparam T_z Type of z
 *
 * @param function Name of function ultimately relying on 2F1 (for error
 *   messages)
 * @param a1 Variable to check
 * @param a2 Variable to check
 * @param b1 Variable to check
 * @param z Variable to check
 *
 * @throw <code>domain_error</code> if 2F1(a1, a2, b1, z)
 *   does not meet convergence conditions, or if any coefficient is NaN.
 */
template <typename T_a1, typename T_a2, typename T_b1, typename T_z>
inline void check_2F1_converges(const char* function, const T_a1& a1,
                                const T_a2& a2, const T_b1& b1, const T_z& z) {
  using std::fabs;
  using std::floor;

  check_not_nan("check_3F2_converges", "a1", a1);
  check_not_nan("check_3F2_converges", "a2", a2);
  check_not_nan("check_3F2_converges", "b1", b1);
  check_not_nan("check_3F2_converges", "z", z);

  int num_terms = 0;
  bool is_polynomial = false;

  if (is_nonpositive_integer(a1) && fabs(a1) >= num_terms) {
    is_polynomial = true;
    num_terms = floor(fabs(value_of_rec(a1)));
  }
  if (is_nonpositive_integer(a2) && fabs(a2) >= num_terms) {
    is_polynomial = true;
    num_terms = floor(fabs(value_of_rec(a2)));
  }

  bool is_undefined = is_nonpositive_integer(b1) && fabs(b1) <= num_terms;

  if (!is_undefined
      && (is_polynomial || fabs(z) < 1 || (fabs(z) == 1 && b1 > a1 + a2)))
    return;

  std::stringstream msg;
  msg << "called from function '" << function << "', "
      << "hypergeometric function 2F1 does not meet convergence "
      << "conditions with given arguments. "
      << "a1: " << a1 << ", a2: " << a2 << ", "
      << "b1: " << b1 << ", z: " << z;
  throw std::domain_error(msg.str());
}

}  // namespace math
}  // namespace stan
#endif