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neg_binomial_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
3
4 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
5 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
6 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
7 #include <stan/math/prim/scal/meta/include_summand.hpp>
8 #include <stan/math/prim/scal/fun/constants.hpp>
9 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
10 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
11 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
12 #include <stan/math/prim/scal/err/check_not_nan.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/prim/scal/fun/digamma.hpp>
15 #include <stan/math/prim/scal/fun/inc_beta.hpp>
16 #include <stan/math/prim/scal/fun/inc_beta_dda.hpp>
17 #include <stan/math/prim/scal/fun/inc_beta_ddb.hpp>
18 #include <stan/math/prim/scal/fun/inc_beta_ddz.hpp>
19 #include <cmath>
20 #include <limits>
21
22 namespace stan {
23 namespace math {
24
25 template <typename T_n, typename T_shape,
26 typename T_inv_scale>
27 typename return_type<T_shape, T_inv_scale>::type
28 neg_binomial_cdf(const T_n& n, const T_shape& alpha,
29 const T_inv_scale& beta) {
30 static const char* function("neg_binomial_cdf");
31 typedef typename stan::partials_return_type<T_n, T_shape,
32 T_inv_scale>::type
33 T_partials_return;
34
35 if (!(stan::length(n) && stan::length(alpha) && stan::length(beta)))
36 return 1.0;
37
38 T_partials_return P(1.0);
39
40 check_positive_finite(function, "Shape parameter", alpha);
41 check_positive_finite(function, "Inverse scale parameter", beta);
42 check_consistent_sizes(function,
43 "Failures variable", n,
44 "Shape parameter", alpha,
45 "Inverse scale parameter", beta);
46
47 VectorView<const T_n> n_vec(n);
48 VectorView<const T_shape> alpha_vec(alpha);
49 VectorView<const T_inv_scale> beta_vec(beta);
50 size_t size = max_size(n, alpha, beta);
51
52 OperandsAndPartials<T_shape, T_inv_scale>
53 operands_and_partials(alpha, beta);
54
55 // Explicit return for extreme values
56 // The gradients are technically ill-defined, but treated as zero
57 for (size_t i = 0; i < stan::length(n); i++) {
58 if (value_of(n_vec[i]) < 0)
59 return operands_and_partials.value(0.0);
60 }
61
62 VectorBuilder<!is_constant_struct<T_shape>::value,
63 T_partials_return, T_shape>
64 digamma_alpha_vec(stan::length(alpha));
65
66 VectorBuilder<!is_constant_struct<T_shape>::value,
67 T_partials_return, T_shape>
68 digamma_sum_vec(stan::length(alpha));
69
70 if (!is_constant_struct<T_shape>::value) {
71 for (size_t i = 0; i < stan::length(alpha); i++) {
72 const T_partials_return n_dbl = value_of(n_vec[i]);
73 const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
74
75 digamma_alpha_vec[i] = digamma(alpha_dbl);
76 digamma_sum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
77 }
78 }
79
80 for (size_t i = 0; i < size; i++) {
81 // Explicit results for extreme values
82 // The gradients are technically ill-defined, but treated as zero
83 if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
84 return operands_and_partials.value(1.0);
85
86 const T_partials_return n_dbl = value_of(n_vec[i]);
87 const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
88 const T_partials_return beta_dbl = value_of(beta_vec[i]);
89
90 const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
91 const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
92 * (1.0 + beta_dbl) );
93
94 const T_partials_return P_i =
95 inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
96
97 P *= P_i;
98
99 if (!is_constant_struct<T_shape>::value) {
100 operands_and_partials.d_x1[i]
101 += inc_beta_dda(alpha_dbl, n_dbl + 1, p_dbl,
102 digamma_alpha_vec[i],
103 digamma_sum_vec[i]) / P_i;
104 }
105
106 if (!is_constant_struct<T_inv_scale>::value)
107 operands_and_partials.d_x2[i] +=
108 inc_beta_ddz(alpha_dbl, n_dbl + 1.0, p_dbl) * d_dbl / P_i;
109 }
110
111 if (!is_constant_struct<T_shape>::value) {
112 for (size_t i = 0; i < stan::length(alpha); ++i)
113 operands_and_partials.d_x1[i] *= P;
114 }
115
116 if (!is_constant_struct<T_inv_scale>::value) {
117 for (size_t i = 0; i < stan::length(beta); ++i)
118 operands_and_partials.d_x2[i] *= P;
119 }
120
121 return operands_and_partials.value(P);
122 }
123
124 }
125 }
126 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
stan::math::neg_binomial_cdf
return_type< T_shape, T_inv_scale >::type neg_binomial_cdf(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
Definition: neg_binomial_cdf.hpp:28
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
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:39
inc_beta_ddz.hpp
digamma.hpp
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
is_constant_struct.hpp
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::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::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
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
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:22
partials_return_type.hpp
OperandsAndPartials.hpp
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
inc_beta.hpp
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_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
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15
inc_beta_dda.hpp

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