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neg_binomial_2_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_HPP
3
4 #include <boost/math/special_functions/digamma.hpp>
5 #include <boost/random/negative_binomial_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
7 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
8 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
9 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
10 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
11 #include <stan/math/prim/scal/err/check_less.hpp>
12 #include <stan/math/prim/scal/fun/constants.hpp>
13 #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
14 #include <stan/math/prim/scal/fun/multiply_log.hpp>
15 #include <stan/math/prim/scal/fun/digamma.hpp>
16 #include <stan/math/prim/scal/fun/lgamma.hpp>
17 #include <stan/math/prim/scal/fun/value_of.hpp>
18 #include <stan/math/prim/scal/meta/length.hpp>
19 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
20 #include <stan/math/prim/scal/meta/VectorView.hpp>
21 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
22 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
23 #include <stan/math/prim/scal/meta/return_type.hpp>
24 #include <stan/math/prim/scal/meta/include_summand.hpp>
25 #include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
26 #include <cmath>
27
28 namespace stan {
29
30 namespace math {
31
32 // NegBinomial(n|mu, phi) [mu >= 0; phi > 0; n >= 0]
33 template <bool propto,
34 typename T_n,
35 typename T_location, typename T_precision>
36 typename return_type<T_location, T_precision>::type
37 neg_binomial_2_log(const T_n& n,
38 const T_location& mu,
39 const T_precision& phi) {
40 typedef typename stan::partials_return_type<T_n, T_location,
41 T_precision>::type
42 T_partials_return;
43
44 static const char* function("stan::math::neg_binomial_2_log");
45
46 using stan::math::check_positive_finite;
47 using stan::math::check_nonnegative;
48 using stan::math::value_of;
49 using stan::math::check_consistent_sizes;
50 using stan::math::include_summand;
51
52 // check if any vectors are zero length
53 if (!(stan::length(n)
54 && stan::length(mu)
55 && stan::length(phi)))
56 return 0.0;
57
58 T_partials_return logp(0.0);
59 check_nonnegative(function, "Failures variable", n);
60 check_positive_finite(function, "Location parameter", mu);
61 check_positive_finite(function, "Precision parameter", phi);
62 check_consistent_sizes(function,
63 "Failures variable", n,
64 "Location parameter", mu,
65 "Precision parameter", phi);
66
67 // check if no variables are involved and prop-to
68 if (!include_summand<propto, T_location, T_precision>::value)
69 return 0.0;
70
71 using stan::math::multiply_log;
72 using stan::math::digamma;
73 using stan::math::lgamma;
74 using std::log;
75 using std::log;
76
77 // set up template expressions wrapping scalars into vector views
78 VectorView<const T_n> n_vec(n);
79 VectorView<const T_location> mu_vec(mu);
80 VectorView<const T_precision> phi_vec(phi);
81 size_t size = max_size(n, mu, phi);
82
83 OperandsAndPartials<T_location, T_precision>
84 operands_and_partials(mu, phi);
85
86 size_t len_ep = max_size(mu, phi);
87 size_t len_np = max_size(n, phi);
88
89 VectorBuilder<true, T_partials_return, T_location> mu__(length(mu));
90 for (size_t i = 0, size = length(mu); i < size; ++i)
91 mu__[i] = value_of(mu_vec[i]);
92
93 VectorBuilder<true, T_partials_return, T_precision> phi__(length(phi));
94 for (size_t i = 0, size = length(phi); i < size; ++i)
95 phi__[i] = value_of(phi_vec[i]);
96
97 VectorBuilder<true, T_partials_return, T_precision> log_phi(length(phi));
98 for (size_t i = 0, size = length(phi); i < size; ++i)
99 log_phi[i] = log(phi__[i]);
100
101 VectorBuilder<true, T_partials_return, T_location, T_precision>
102 log_mu_plus_phi(len_ep);
103 for (size_t i = 0; i < len_ep; ++i)
104 log_mu_plus_phi[i] = log(mu__[i] + phi__[i]);
105
106 VectorBuilder<true, T_partials_return, T_n, T_precision>
107 n_plus_phi(len_np);
108 for (size_t i = 0; i < len_np; ++i)
109 n_plus_phi[i] = n_vec[i] + phi__[i];
110
111 for (size_t i = 0; i < size; i++) {
112 if (include_summand<propto>::value)
113 logp -= lgamma(n_vec[i] + 1.0);
114 if (include_summand<propto, T_precision>::value)
115 logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
116 if (include_summand<propto, T_location, T_precision>::value)
117 logp -= (n_plus_phi[i])*log_mu_plus_phi[i];
118 if (include_summand<propto, T_location>::value)
119 logp += multiply_log(n_vec[i], mu__[i]);
120 if (include_summand<propto, T_precision>::value)
121 logp += lgamma(n_plus_phi[i]);
122
123 if (!is_constant_struct<T_location>::value)
124 operands_and_partials.d_x1[i]
125 += n_vec[i]/mu__[i]
126 - (n_vec[i] + phi__[i])
127 / (mu__[i] + phi__[i]);
128 if (!is_constant_struct<T_precision>::value)
129 operands_and_partials.d_x2[i]
130 += 1.0 - n_plus_phi[i]/(mu__[i] + phi__[i])
131 + log_phi[i] - log_mu_plus_phi[i] - digamma(phi__[i])
132 + digamma(n_plus_phi[i]);
133 }
134 return operands_and_partials.value(logp);
135 }
136
137 template <typename T_n,
138 typename T_location, typename T_precision>
139 inline
140 typename return_type<T_location, T_precision>::type
141 neg_binomial_2_log(const T_n& n,
142 const T_location& mu,
143 const T_precision& phi) {
144 return neg_binomial_2_log<false>(n, mu, phi);
145 }
146 }
147 }
148 #endif
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:40
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
check_positive_finite.hpp
stan
Definition: log_sum_exp.hpp:8
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
digamma.hpp
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::math::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:68
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
binomial_coefficient_log.hpp
is_constant_struct.hpp
return_type.hpp
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:36
stan::return_type::type
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
include_summand.hpp
multiply_log.hpp
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:13
stan::partials_return_type
Definition: partials_return_type.hpp:16
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:38
VectorView.hpp
stan::math::neg_binomial_2_log
return_type< T_location, T_precision >::type neg_binomial_2_log(const T_n &n, const T_location &mu, const T_precision &phi)
Definition: neg_binomial_2_log.hpp:37
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
length.hpp
grad_reg_inc_beta.hpp
stan::math::multiply_log
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: multiply_log.hpp:15
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
stan::math::check_consistent_sizes
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
Definition: check_consistent_sizes.hpp:31
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
value_of.hpp
stan::VectorView
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
check_less.hpp
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:39
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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