FM / detail

/usr/include/boost/math/special_functions/detail/

/usr/include/boost/math/special_functions/detail

Name	Size	Mode	Actions
airy_ai_bi_zero.hpp	6294	0644	edit dl rm
bernoulli_details.hpp	26513	0644	edit dl rm
bessel_derivatives_linear.hpp	3378	0644	edit dl rm
bessel_i0.hpp	28135	0644	edit dl rm
bessel_i1.hpp	29933	0644	edit dl rm
bessel_ik.hpp	13917	0644	edit dl rm
bessel_j0.hpp	8585	0644	edit dl rm
bessel_j1.hpp	8951	0644	edit dl rm
bessel_jn.hpp	3909	0644	edit dl rm
bessel_jy.hpp	21868	0644	edit dl rm
bessel_jy_asym.hpp	6488	0644	edit dl rm
bessel_jy_derivatives_asym.hpp	4649	0644	edit dl rm
bessel_jy_derivatives_series.hpp	6944	0644	edit dl rm
bessel_jy_series.hpp	7241	0644	edit dl rm
bessel_jy_zero.hpp	24967	0644	edit dl rm
bessel_k0.hpp	22178	0644	edit dl rm
bessel_k1.hpp	25465	0644	edit dl rm
bessel_kn.hpp	2249	0644	edit dl rm
bessel_y0.hpp	10805	0644	edit dl rm
bessel_y1.hpp	9458	0644	edit dl rm
bessel_yn.hpp	3118	0644	edit dl rm
daubechies_scaling_integer_grid.hpp	233788	0644	edit dl rm
erf_inv.hpp	22738	0644	edit dl rm
fp_traits.hpp	17193	0644	edit dl rm
gamma_inva.hpp	7066	0644	edit dl rm
hypergeometric_0F1_bessel.hpp	1543	0644	edit dl rm
hypergeometric_1F1_addition_theorems_on_z.hpp	12980	0644	edit dl rm
hypergeometric_1F1_bessel.hpp	32781	0644	edit dl rm
hypergeometric_1F1_by_ratios.hpp	33540	0644	edit dl rm
hypergeometric_1F1_cf.hpp	1830	0644	edit dl rm
hypergeometric_1F1_large_a.hpp	1159	0644	edit dl rm
hypergeometric_1F1_large_abz.hpp	22101	0644	edit dl rm
hypergeometric_1F1_negative_b_regions.hpp	33376	0644	edit dl rm
hypergeometric_1F1_recurrence.hpp	17295	0644	edit dl rm
hypergeometric_1F1_scaled_series.hpp	2183	0644	edit dl rm
hypergeometric_1F1_small_a_negative_b_by_ratio.hpp	3893	0644	edit dl rm
hypergeometric_asym.hpp	5902	0644	edit dl rm
hypergeometric_cf.hpp	5826	0644	edit dl rm
hypergeometric_pade.hpp	3837	0644	edit dl rm
hypergeometric_pFq_checked_series.hpp	27943	0644	edit dl rm
hypergeometric_rational.hpp	5068	0644	edit dl rm
hypergeometric_separated_series.hpp	1449	0644	edit dl rm
hypergeometric_series.hpp	14422	0644	edit dl rm
ibeta_inverse.hpp	34072	0644	edit dl rm
ibeta_inv_ab.hpp	10363	0644	edit dl rm
iconv.hpp	1009	0644	edit dl rm
igamma_inverse.hpp	17414	0644	edit dl rm
igamma_large.hpp	39534	0644	edit dl rm
lambert_w_lookup_table.ipp	15601	0644	edit dl rm
lanczos_sse2.hpp	8916	0644	edit dl rm
lgamma_small.hpp	23295	0644	edit dl rm
polygamma.hpp	22596	0644	edit dl rm
round_fwd.hpp	2794	0644	edit dl rm
t_distribution_inv.hpp	17735	0644	edit dl rm
unchecked_bernoulli.hpp	76437	0644	edit dl rm
unchecked_factorial.hpp	46290	0644	edit dl rm

Edit: /usr/include/boost/math/special_functions/detail/hypergeometric_pade.hpp (3837B)

///////////////////////////////////////////////////////////////////////////////
//  Copyright 2014 Anton Bikineev
//  Copyright 2014 Christopher Kormanyos
//  Copyright 2014 John Maddock
//  Copyright 2014 Paul Bristow
//  Distributed under the Boost
//  Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
//
#ifndef BOOST_MATH_HYPERGEOMETRIC_PADE_HPP
#define BOOST_MATH_HYPERGEOMETRIC_PADE_HPP

namespace boost{ namespace math{ namespace detail{

// Luke: C ---------- SUBROUTINE R1F1P(CP, Z, A, B, N) ----------
  // Luke: C ----- PADE APPROXIMATION OF 1F1( 1 ; CP ; -Z ) -------
  template <class T, class Policy>
  inline T hypergeometric_1F1_pade(const T& cp, const T& zp, const Policy& )
  {
    BOOST_MATH_STD_USING

static const T one = T(1);

// Luke: C ------------- INITIALIZATION -------------
    const T z = -zp;
    const T zz = z * z;
    T b0 = one;
    T a0 = one;
    T xi1 = one;
    T ct1 = cp + one;
    T cp1 = cp - one;

T b1 = one + (z / ct1);
    T a1 = b1 - (z / cp);

const unsigned max_iterations = boost::math::policies::get_max_series_iterations<Policy>();

T b2 = T(0), a2 = T(0);
    T result = T(0), prev_result;

for (unsigned k = 1; k < max_iterations; ++k)
    {
      // Luke: C ----- CALCULATION OF THE MULTIPLIERS -----
      // Luke: C ----------- FOR THE RECURSION ------------
      const T ct2 = ct1 * ct1;
      const T g1 = one + ((cp1 / (ct2 + ct1 + ct1)) * z);
      const T g2 = ((xi1 / (ct2 - one)) * ((xi1 + cp1) / ct2)) * zz;

// Luke: C ------- THE RECURRENCE RELATIONS ---------
      // Luke: C ------------ ARE AS FOLLOWS --------------
      b2 = (g1 * b1) + (g2 * b0);
      a2 = (g1 * a1) + (g2 * a0);

prev_result = result;
      result = a2 / b2;

// condition for interruption
      if ((fabs(result) * boost::math::tools::epsilon<T>()) > fabs(result - prev_result))
        break;

b0 = b1; b1 = b2;
      a0 = a1; a1 = a2;

ct1 += 2;
      xi1 += 1;
    }

return a2 / b2;
  }

// Luke: C -------- SUBROUTINE R2F1P(BP, CP, Z, A, B, N) --------
  // Luke: C ---- PADE APPROXIMATION OF 2F1( 1 , BP; CP ; -Z ) ----
  template <class T, class Policy>
  inline T hypergeometric_2F1_pade(const T& bp, const T& cp, const T& zp, const Policy& pol)
  {
    BOOST_MATH_STD_USING

static const T one = T(1);

// Luke: C ---------- INITIALIZATION -----------
    const T z = -zp;
    const T zz = z * z;
    T b0 = one;
    T a0 = one;
    T xi1 = one;
    T ct1 = cp;
    const T b1c1 = (cp - one) * (bp - one);

T b1 = one + ((z / (cp + one)) * (bp + one));
    T a1 = b1 - ((bp / cp) * z);

const unsigned max_iterations = boost::math::policies::get_max_series_iterations<Policy>();

T b2 = T(0), a2 = T(0);
    T result = T(0), prev_result = a1 / b1;

for (unsigned k = 1; k < max_iterations; ++k)
    {
      // Luke: C ----- CALCULATION OF THE MULTIPLIERS -----
      // Luke: C ----------- FOR THE RECURSION ------------
      const T ct2 = ct1 + xi1;
      const T ct3 = ct2 * ct2;
      const T g2 = (((((ct1 / ct3) * (bp - ct1)) / (ct3 - one)) * xi1) * (bp + xi1)) * zz;
      ++xi1;
      const T g1 = one + (((((xi1 + xi1) * ct1) + b1c1) / (ct3 + ct2 + ct2)) * z);

// Luke: C ------- THE RECURRENCE RELATIONS ---------
      // Luke: C ------------ ARE AS FOLLOWS --------------
      b2 = (g1 * b1) + (g2 * b0);
      a2 = (g1 * a1) + (g2 * a0);

prev_result = result;
      result = a2 / b2;

// condition for interruption
      if ((fabs(result) * boost::math::tools::epsilon<T>()) > fabs(result - prev_result))
        break;

b0 = b1; b1 = b2;
      a0 = a1; a1 = a2;

++ct1;
    }

return a2 / b2;
  }

} } } // namespaces

#endif // BOOST_MATH_HYPERGEOMETRIC_PADE_HPP

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