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gamma_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LOG_HPP
3
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
6 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
7 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
8 #include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
9 #include <stan/math/prim/scal/err/check_less_or_equal.hpp>
10 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
11 #include <stan/math/prim/scal/err/check_not_nan.hpp>
12 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
13 #include <stan/math/prim/scal/fun/constants.hpp>
14 #include <stan/math/prim/scal/fun/multiply_log.hpp>
15 #include <stan/math/prim/scal/fun/value_of.hpp>
16 #include <stan/math/prim/scal/fun/gamma_p.hpp>
17 #include <stan/math/prim/scal/fun/digamma.hpp>
18 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
19 #include <stan/math/prim/scal/meta/include_summand.hpp>
20 #include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
21 #include <cmath>
22
23 namespace stan {
24
25 namespace math {
26
49 template <bool propto,
50 typename T_y, typename T_shape, typename T_inv_scale>
51 typename return_type<T_y, T_shape, T_inv_scale>::type
52 gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
53 static const char* function("stan::math::gamma_log");
54 typedef typename stan::partials_return_type<T_y, T_shape,
55 T_inv_scale>::type
56 T_partials_return;
57
58 using stan::is_constant_struct;
59 using stan::math::check_not_nan;
60 using stan::math::check_positive_finite;
61 using stan::math::check_nonnegative;
62 using stan::math::check_consistent_sizes;
63 using stan::math::value_of;
64
65 // check if any vectors are zero length
66 if (!(stan::length(y)
67 && stan::length(alpha)
68 && stan::length(beta)))
69 return 0.0;
70
71 // set up return value accumulator
72 T_partials_return logp(0.0);
73
74 // validate args (here done over var, which should be OK)
75 check_not_nan(function, "Random variable", y);
76 check_positive_finite(function, "Shape parameter", alpha);
77 check_positive_finite(function, "Inverse scale parameter", beta);
78 check_consistent_sizes(function,
79 "Random variable", y,
80 "Shape parameter", alpha,
81 "Inverse scale parameter", beta);
82
83 // check if no variables are involved and prop-to
84 if (!include_summand<propto, T_y, T_shape, T_inv_scale>::value)
85 return 0.0;
86
87 // set up template expressions wrapping scalars into vector views
88 VectorView<const T_y> y_vec(y);
89 VectorView<const T_shape> alpha_vec(alpha);
90 VectorView<const T_inv_scale> beta_vec(beta);
91
92 for (size_t n = 0; n < length(y); n++) {
93 const T_partials_return y_dbl = value_of(y_vec[n]);
94 if (y_dbl < 0)
95 return LOG_ZERO;
96 }
97
98 size_t N = max_size(y, alpha, beta);
99 OperandsAndPartials<T_y, T_shape, T_inv_scale>
100 operands_and_partials(y, alpha, beta);
101
102 using boost::math::lgamma;
103 using stan::math::multiply_log;
104 using boost::math::digamma;
105 using std::log;
106
107 VectorBuilder<include_summand<propto, T_y, T_shape>::value,
108 T_partials_return, T_y> log_y(length(y));
109 if (include_summand<propto, T_y, T_shape>::value) {
110 for (size_t n = 0; n < length(y); n++) {
111 if (value_of(y_vec[n]) > 0)
112 log_y[n] = log(value_of(y_vec[n]));
113 }
114 }
115
116 VectorBuilder<include_summand<propto, T_shape>::value,
117 T_partials_return, T_shape> lgamma_alpha(length(alpha));
118 VectorBuilder<!is_constant_struct<T_shape>::value,
119 T_partials_return, T_shape> digamma_alpha(length(alpha));
120 for (size_t n = 0; n < length(alpha); n++) {
121 if (include_summand<propto, T_shape>::value)
122 lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
123 if (!is_constant_struct<T_shape>::value)
124 digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
125 }
126
127 VectorBuilder<include_summand<propto, T_shape, T_inv_scale>::value,
128 T_partials_return, T_inv_scale> log_beta(length(beta));
129 if (include_summand<propto, T_shape, T_inv_scale>::value) {
130 for (size_t n = 0; n < length(beta); n++)
131 log_beta[n] = log(value_of(beta_vec[n]));
132 }
133
134 for (size_t n = 0; n < N; n++) {
135 // pull out values of arguments
136 const T_partials_return y_dbl = value_of(y_vec[n]);
137 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
138 const T_partials_return beta_dbl = value_of(beta_vec[n]);
139
140 if (include_summand<propto, T_shape>::value)
141 logp -= lgamma_alpha[n];
142 if (include_summand<propto, T_shape, T_inv_scale>::value)
143 logp += alpha_dbl * log_beta[n];
144 if (include_summand<propto, T_y, T_shape>::value)
145 logp += (alpha_dbl-1.0) * log_y[n];
146 if (include_summand<propto, T_y, T_inv_scale>::value)
147 logp -= beta_dbl * y_dbl;
148
149 // gradients
150 if (!is_constant_struct<T_y>::value)
151 operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl - beta_dbl;
152 if (!is_constant_struct<T_shape>::value)
153 operands_and_partials.d_x2[n] += -digamma_alpha[n] + log_beta[n]
154 + log_y[n];
155 if (!is_constant_struct<T_inv_scale>::value)
156 operands_and_partials.d_x3[n] += alpha_dbl / beta_dbl - y_dbl;
157 }
158 return operands_and_partials.to_var(logp, y, alpha, beta);
159 }
160
161 template <typename T_y, typename T_shape, typename T_inv_scale>
162 inline
163 typename return_type<T_y, T_shape, T_inv_scale>::type
164 gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
165 return gamma_log<false>(y, alpha, beta);
166 }
167 }
168 }
169
170 #endif
check_not_nan.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
stan::math::check_not_nan
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
Definition: check_not_nan.hpp:63
check_positive_finite.hpp
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::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::OperandsAndPartials::to_var
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
Definition: OperandsAndPartials.hpp:322
stan::math::LOG_ZERO
const double LOG_ZERO
Definition: constants.hpp:175
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
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
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:16
stan::partials_return_type
Definition: partials_return_type.hpp:16
check_less_or_equal.hpp
stan::math::OperandsAndPartials::d_x3
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
Definition: OperandsAndPartials.hpp:259
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
gamma_p.hpp
stan::math::multiply_log
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: multiply_log.hpp:15
grad_reg_inc_gamma.hpp
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
constants.hpp
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::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
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
check_greater_or_equal.hpp
value_of.hpp
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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::gamma_log
return_type< T_y, T_shape, T_inv_scale >::type gamma_log(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
The log of a gamma density for y with the specified shape and inverse scale parameters.
Definition: gamma_log.hpp:52
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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