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neg_binomial_2_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_CDF_HPP
3
4 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
5 #include <stan/math/prim/scal/meta/include_summand.hpp>
6 #include <stan/math/prim/scal/fun/constants.hpp>
7 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
8
9 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
10 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
11 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
12 #include <stan/math/prim/scal/err/check_not_nan.hpp>
13
14 #include <stan/math/prim/scal/fun/value_of.hpp>
15 #include <stan/math/prim/scal/prob/beta_cdf.hpp>
16 #include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
17
18 #include <stan/math/prim/scal/fun/digamma.hpp>
19 #include <stan/math/prim/scal/fun/inc_beta.hpp>
20 #include <stan/math/prim/scal/fun/inc_beta_dda.hpp>
21 #include <stan/math/prim/scal/fun/inc_beta_ddb.hpp>
22 #include <stan/math/prim/scal/fun/inc_beta_ddz.hpp>
23
24 #include <boost/math/special_functions/digamma.hpp>
25 #include <boost/random/negative_binomial_distribution.hpp>
26 #include <boost/random/variate_generator.hpp>
27
28 #include <limits>
29 #include <vector>
30
31 namespace stan {
32 namespace math {
33
34 template <typename T_n, typename T_location,
35 typename T_precision>
36 typename return_type<T_location, T_precision>::type
37 neg_binomial_2_cdf(const T_n& n,
38 const T_location& mu,
39 const T_precision& phi) {
40 static const char* function("stan::prob::neg_binomial_2_cdf");
41 typedef typename stan::partials_return_type<T_n, T_location,
42 T_precision>::type
43 T_partials_return;
44
45 using stan::math::check_positive_finite;
46 using stan::math::check_nonnegative;
47 using stan::math::check_not_nan;
48 using stan::math::check_consistent_sizes;
49
50 // Ensure non-zero arugment lengths
51 if (!(stan::length(n) && stan::length(mu) && stan::length(phi)))
52 return 1.0;
53
54 T_partials_return P(1.0);
55
56 // Validate arguments
57 check_positive_finite(function, "Location parameter", mu);
58 check_positive_finite(function, "Precision parameter", phi);
59 check_not_nan(function, "Random variable", n);
60 check_consistent_sizes(function,
61 "Random variable", n,
62 "Location parameter", mu,
63 "Precision Parameter", phi);
64
65 // Wrap arguments in vector views
66 VectorView<const T_n> n_vec(n);
67 VectorView<const T_location> mu_vec(mu);
68 VectorView<const T_precision> phi_vec(phi);
69 size_t size = max_size(n, mu, phi);
70
71 // Compute vectorized CDF and gradient
72 using stan::math::value_of;
73 using stan::math::inc_beta;
74 using stan::math::inc_beta_ddz;
75 using stan::math::inc_beta_dda;
76 using stan::math::digamma;
77
78 OperandsAndPartials<T_location, T_precision>
79 operands_and_partials(mu, phi);
80
81 // Explicit return for extreme values
82 // The gradients are technically ill-defined, but treated as zero
83 for (size_t i = 0; i < stan::length(n); i++) {
84 if (value_of(n_vec[i]) < 0)
85 return operands_and_partials.to_var(0.0, mu, phi);
86 }
87
88 // Cache a few expensive function calls if phi is a parameter
89 VectorBuilder<!is_constant_struct<T_precision>::value,
90 T_partials_return, T_precision>
91 digamma_phi_vec(stan::length(phi));
92
93 VectorBuilder<!is_constant_struct<T_precision>::value,
94 T_partials_return, T_precision>
95 digamma_sum_vec(stan::length(phi));
96
97 if (!is_constant_struct<T_precision>::value) {
98 for (size_t i = 0; i < stan::length(phi); i++) {
99 const T_partials_return n_dbl = value_of(n_vec[i]);
100 const T_partials_return phi_dbl = value_of(phi_vec[i]);
101
102 digamma_phi_vec[i] = digamma(phi_dbl);
103 digamma_sum_vec[i] = digamma(n_dbl + phi_dbl + 1);
104 }
105 }
106
107 for (size_t i = 0; i < size; i++) {
108 // Explicit results for extreme values
109 // The gradients are technically ill-defined, but treated as zero
110 if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
111 return operands_and_partials.to_var(1.0, mu, phi);
112
113 const T_partials_return n_dbl = value_of(n_vec[i]);
114 const T_partials_return mu_dbl = value_of(mu_vec[i]);
115 const T_partials_return phi_dbl = value_of(phi_vec[i]);
116
117 const T_partials_return p_dbl = phi_dbl / (mu_dbl + phi_dbl);
118 const T_partials_return d_dbl = 1.0 / ((mu_dbl + phi_dbl)
119 * (mu_dbl + phi_dbl));
120
121 const T_partials_return P_i =
122 inc_beta(phi_dbl, n_dbl + 1.0, p_dbl);
123
124 P *= P_i;
125
126 if (!is_constant_struct<T_location>::value)
127 operands_and_partials.d_x1[i] +=
128 - inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl) * phi_dbl * d_dbl / P_i;
129
130 if (!is_constant_struct<T_precision>::value) {
131 operands_and_partials.d_x2[i]
132 += inc_beta_dda(phi_dbl, n_dbl + 1, p_dbl,
133 digamma_phi_vec[i],
134 digamma_sum_vec[i]) / P_i
135 + inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl)
136 * mu_dbl * d_dbl / P_i;
137 }
138 }
139
140 if (!is_constant_struct<T_location>::value) {
141 for (size_t i = 0; i < stan::length(mu); ++i)
142 operands_and_partials.d_x1[i] *= P;
143 }
144
145 if (!is_constant_struct<T_precision>::value) {
146 for (size_t i = 0; i < stan::length(phi); ++i)
147 operands_and_partials.d_x2[i] *= P;
148 }
149
150 return operands_and_partials.to_var(P, mu, phi);
151 }
152
153 } // math
154 } // stan
155 #endif
check_not_nan.hpp
stan::math::neg_binomial_2_cdf
return_type< T_location, T_precision >::type neg_binomial_2_cdf(const T_n &n, const T_location &mu, const T_precision &phi)
Definition: neg_binomial_2_cdf.hpp:37
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
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
inc_beta_ddz.hpp
digamma.hpp
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::inc_beta_ddz
T inc_beta_ddz(T a, T b, T z)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z.
Definition: inc_beta_ddz.hpp:27
inc_beta_ddb.hpp
include_summand.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::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
beta_cdf.hpp
stan::partials_return_type
Definition: partials_return_type.hpp:16
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
stan::math::max
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:21
grad_reg_inc_beta.hpp
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Definition: size.hpp:11
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
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:66
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::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16
inc_beta_dda.hpp

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