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neg_binomial_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LOG_HPP
3
4 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
5 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
6 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
7 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
8 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
9 #include <stan/math/prim/scal/fun/constants.hpp>
10 #include <stan/math/prim/scal/fun/value_of.hpp>
11 #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
12 #include <stan/math/prim/scal/fun/multiply_log.hpp>
13 #include <stan/math/prim/scal/fun/digamma.hpp>
14 #include <stan/math/prim/scal/fun/lgamma.hpp>
15 #include <stan/math/prim/scal/fun/lbeta.hpp>
16 #include <stan/math/prim/scal/meta/length.hpp>
17 #include <stan/math/prim/scal/meta/VectorView.hpp>
18 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
19 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
20 #include <stan/math/prim/scal/meta/return_type.hpp>
21 #include <stan/math/prim/scal/meta/include_summand.hpp>
22 #include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
23 #include <stan/math/prim/scal/fun/inc_beta.hpp>
24 #include <stan/math/prim/scal/meta/max_size.hpp>
25 #include <boost/math/special_functions/digamma.hpp>
26 #include <boost/random/negative_binomial_distribution.hpp>
27 #include <boost/random/variate_generator.hpp>
28 #include <cmath>
29
30 namespace stan {
31 namespace math {
32
33 // NegBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
34 template <bool propto,
35 typename T_n,
36 typename T_shape, typename T_inv_scale>
37 typename return_type<T_shape, T_inv_scale>::type
38 neg_binomial_log(const T_n& n,
39 const T_shape& alpha,
40 const T_inv_scale& beta) {
41 typedef typename stan::partials_return_type<T_n, T_shape,
42 T_inv_scale>::type
43 T_partials_return;
44
45 static const char* function("neg_binomial_log");
46
47 if (!(stan::length(n)
48 && stan::length(alpha)
49 && stan::length(beta)))
50 return 0.0;
51
52 T_partials_return logp(0.0);
53 check_nonnegative(function, "Failures variable", n);
54 check_positive_finite(function, "Shape parameter", alpha);
55 check_positive_finite(function, "Inverse scale parameter", beta);
56 check_consistent_sizes(function,
57 "Failures variable", n,
58 "Shape parameter", alpha,
59 "Inverse scale parameter", beta);
60
61 if (!include_summand<propto, T_shape, T_inv_scale>::value)
62 return 0.0;
63
64 using std::log;
65 using std::log;
66
67 VectorView<const T_n> n_vec(n);
68 VectorView<const T_shape> alpha_vec(alpha);
69 VectorView<const T_inv_scale> beta_vec(beta);
70 size_t size = max_size(n, alpha, beta);
71
72 OperandsAndPartials<T_shape, T_inv_scale>
73 operands_and_partials(alpha, beta);
74
75 size_t len_ab = max_size(alpha, beta);
76 VectorBuilder<true, T_partials_return, T_shape, T_inv_scale>
77 lambda(len_ab);
78 for (size_t i = 0; i < len_ab; ++i)
79 lambda[i] = value_of(alpha_vec[i]) / value_of(beta_vec[i]);
80
81 VectorBuilder<true, T_partials_return, T_inv_scale>
82 log1p_beta(length(beta));
83 for (size_t i = 0; i < length(beta); ++i)
84 log1p_beta[i] = log1p(value_of(beta_vec[i]));
85
86 VectorBuilder<true, T_partials_return, T_inv_scale>
87 log_beta_m_log1p_beta(length(beta));
88 for (size_t i = 0; i < length(beta); ++i)
89 log_beta_m_log1p_beta[i] = log(value_of(beta_vec[i])) - log1p_beta[i];
90
91 VectorBuilder<true, T_partials_return, T_inv_scale, T_shape>
92 alpha_times_log_beta_over_1p_beta(len_ab);
93 for (size_t i = 0; i < len_ab; ++i)
94 alpha_times_log_beta_over_1p_beta[i]
95 = value_of(alpha_vec[i])
96 * log(value_of(beta_vec[i])
97 / (1.0 + value_of(beta_vec[i])));
98
99 VectorBuilder<!is_constant_struct<T_shape>::value,
100 T_partials_return, T_shape>
101 digamma_alpha(length(alpha));
102 if (!is_constant_struct<T_shape>::value) {
103 for (size_t i = 0; i < length(alpha); ++i)
104 digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
105 }
106
107 VectorBuilder<!is_constant_struct<T_shape>::value,
108 T_partials_return, T_inv_scale> log_beta(length(beta));
109 if (!is_constant_struct<T_shape>::value) {
110 for (size_t i = 0; i < length(beta); ++i)
111 log_beta[i] = log(value_of(beta_vec[i]));
112 }
113
114 VectorBuilder<!is_constant_struct<T_inv_scale>::value,
115 T_partials_return, T_shape, T_inv_scale>
116 lambda_m_alpha_over_1p_beta(len_ab);
117 if (!is_constant_struct<T_inv_scale>::value) {
118 for (size_t i = 0; i < len_ab; ++i)
119 lambda_m_alpha_over_1p_beta[i] =
120 lambda[i]
121 - (value_of(alpha_vec[i])
122 / (1.0 + value_of(beta_vec[i])));
123 }
124
125 for (size_t i = 0; i < size; i++) {
126 if (alpha_vec[i] > 1e10) { // reduces numerically to Poisson
127 if (include_summand<propto>::value)
128 logp -= lgamma(n_vec[i] + 1.0);
129 if (include_summand<propto, T_shape, T_inv_scale>::value)
130 logp += multiply_log(n_vec[i], lambda[i]) - lambda[i];
131
132 if (!is_constant_struct<T_shape>::value)
133 operands_and_partials.d_x1[i]
134 += n_vec[i] / value_of(alpha_vec[i])
135 - 1.0 / value_of(beta_vec[i]);
136 if (!is_constant_struct<T_inv_scale>::value)
137 operands_and_partials.d_x2[i]
138 += (lambda[i] - n_vec[i]) / value_of(beta_vec[i]);
139 } else { // standard density definition
140 if (include_summand<propto, T_shape>::value)
141 if (n_vec[i] != 0)
142 logp += binomial_coefficient_log(n_vec[i]
143 + value_of(alpha_vec[i])
144 - 1.0,
145 n_vec[i]);
146 if (include_summand<propto, T_shape, T_inv_scale>::value)
147 logp +=
148 alpha_times_log_beta_over_1p_beta[i]
149 - n_vec[i] * log1p_beta[i];
150
151 if (!is_constant_struct<T_shape>::value)
152 operands_and_partials.d_x1[i]
153 += digamma(value_of(alpha_vec[i]) + n_vec[i])
154 - digamma_alpha[i]
155 + log_beta_m_log1p_beta[i];
156 if (!is_constant_struct<T_inv_scale>::value)
157 operands_and_partials.d_x2[i]
158 += lambda_m_alpha_over_1p_beta[i]
159 - n_vec[i] / (value_of(beta_vec[i]) + 1.0);
160 }
161 }
162 return operands_and_partials.value(logp);
163 }
164
165 template <typename T_n,
166 typename T_shape, typename T_inv_scale>
167 inline
168 typename return_type<T_shape, T_inv_scale>::type
169 neg_binomial_log(const T_n& n,
170 const T_shape& alpha,
171 const T_inv_scale& beta) {
172 return neg_binomial_log<false>(n, alpha, beta);
173 }
174
175 }
176 }
177 #endif
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
lgamma.hpp
stan::math::binomial_coefficient_log
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: binomial_coefficient_log.hpp:15
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
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:14
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:67
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:35
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:37
VectorView.hpp
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:14
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
lbeta.hpp
stan::math::log1p
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:15
inc_beta.hpp
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:64
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
stan::math::neg_binomial_log
return_type< T_shape, T_inv_scale >::type neg_binomial_log(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
Definition: neg_binomial_log.hpp:38
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:38
max_size.hpp
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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