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inc_beta_dda.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_FUN_INC_BETA_DDA_HPP
2 #define STAN_MATH_PRIM_SCAL_FUN_INC_BETA_DDA_HPP
3
4 #include <stan/math/prim/scal/fun/inc_beta.hpp>
5 #include <stan/math/prim/scal/fun/inc_beta_ddb.hpp>
6 #include <cmath>
7
8 namespace stan {
9 namespace math {
10
11 template <typename T>
12 T inc_beta_ddb(T a, T b, T z,
13 T digamma_b, T digamma_ab);
14
37 template <typename T>
38 T inc_beta_dda(T a, T b, T z,
39 T digamma_a, T digamma_ab) {
40 using std::log;
41
42 if (b > a)
43 if ((0.1 < z && z <= 0.75 && b > 500)
44 || (0.01 < z && z <= 0.1 && b > 2500)
45 || (0.001 < z && z <= 0.01 && b > 1e5))
46 return -inc_beta_ddb(b, a, 1 - z, digamma_a, digamma_ab);
47
48 if (z > 0.75 && a < 500)
49 return -inc_beta_ddb(b, a, 1 - z, digamma_a, digamma_ab);
50 if (z > 0.9 && a < 2500)
51 return -inc_beta_ddb(b, a, 1 - z, digamma_a, digamma_ab);
52 if (z > 0.99 && a < 1e5)
53 return -inc_beta_ddb(b, a, 1 - z, digamma_a, digamma_ab);
54 if (z > 0.999)
55 return -inc_beta_ddb(b, a, 1 - z, digamma_a, digamma_ab);
56
57 double threshold = 1e-10;
58
59 digamma_a += 1.0 / a; // Need digamma(a + 1), not digamma(a);
60
61 // Common prefactor to regularize numerator and denomentator
62 T prefactor = (a + 1) / (a + b);
63 prefactor = prefactor * prefactor * prefactor;
64
65 T sum_numer = (digamma_ab - digamma_a) * prefactor;
66 T sum_denom = prefactor;
67
68 T summand = prefactor * z * (a + b) / (a + 1);
69
70 T k = 1;
71 digamma_ab += 1.0 / (a + b);
72 digamma_a += 1.0 / (a + 1);
73
74 while (fabs(summand) > threshold) {
75 sum_numer += (digamma_ab - digamma_a) * summand;
76 sum_denom += summand;
77
78 summand *= (1 + (a + b) / k) * (1 + k) / (1 + (a + 1) / k);
79 digamma_ab += 1.0 / (a + b + k);
80 digamma_a += 1.0 / (a + 1 + k);
81 ++k;
82 summand *= z / k;
83
84 if (k > 1e5)
85 throw std::domain_error("stan::math::inc_beta_dda did "
86 "not converge within 100000 iterations");
87 }
88 return inc_beta(a, b, z) * (log(z) + sum_numer / sum_denom);
89 }
90
91 } // math
92 } // stan
93
94 #endif
stan::math::fabs
fvar< T > fabs(const fvar< T > &x)
Definition: fabs.hpp:14
stan::math::inc_beta_dda
T inc_beta_dda(T a, T b, T z, T digamma_a, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.
Definition: inc_beta_dda.hpp:38
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::math::inc_beta_ddb
T inc_beta_ddb(T a, T b, T z, T digamma_b, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b.
Definition: inc_beta_ddb.hpp:38
inc_beta_ddb.hpp
stan::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
stan::math::domain_error
void domain_error(const char *function, const char *name, const T &y, const char *msg1, const char *msg2)
Throw a domain error with a consistently formatted message.
Definition: domain_error.hpp:32
stan::math::e
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:95
inc_beta.hpp

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