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lognormal_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_HPP
3
4 #include <boost/random/lognormal_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_finite.hpp>
9 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
10 #include <stan/math/prim/scal/err/check_not_nan.hpp>
11 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
12 #include <stan/math/prim/scal/fun/constants.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/prim/scal/fun/square.hpp>
15 #include <stan/math/prim/scal/meta/include_summand.hpp>
16 #include <cmath>
17
18 namespace stan {
19 namespace math {
20
21 template <typename T_y, typename T_loc, typename T_scale>
22 typename return_type<T_y, T_loc, T_scale>::type
23 lognormal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
24 static const char* function("stan::math::lognormal_cdf");
25
26 typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
27 T_partials_return;
28
29 T_partials_return cdf = 1.0;
30
31 using stan::math::check_not_nan;
32 using stan::math::check_finite;
33 using stan::math::check_nonnegative;
34 using stan::math::check_positive_finite;
35 using boost::math::tools::promote_args;
36 using stan::math::value_of;
37 using std::exp;
38 using std::log;
39
40 // check if any vectors are zero length
41 if (!(stan::length(y)
42 && stan::length(mu)
43 && stan::length(sigma)))
44 return cdf;
45
46 check_not_nan(function, "Random variable", y);
47 check_nonnegative(function, "Random variable", y);
48 check_finite(function, "Location parameter", mu);
49 check_positive_finite(function, "Scale parameter", sigma);
50
51 OperandsAndPartials<T_y, T_loc, T_scale>
52 operands_and_partials(y, mu, sigma);
53
54 VectorView<const T_y> y_vec(y);
55 VectorView<const T_loc> mu_vec(mu);
56 VectorView<const T_scale> sigma_vec(sigma);
57 size_t N = max_size(y, mu, sigma);
58
59 const double sqrt_pi = std::sqrt(stan::math::pi());
60
61 for (size_t i = 0; i < stan::length(y); i++) {
62 if (value_of(y_vec[i]) == 0.0)
63 return operands_and_partials.to_var(0.0, y, mu, sigma);
64 }
65
66 for (size_t n = 0; n < N; n++) {
67 const T_partials_return y_dbl = value_of(y_vec[n]);
68 const T_partials_return mu_dbl = value_of(mu_vec[n]);
69 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
70 const T_partials_return scaled_diff = (log(y_dbl) - mu_dbl)
71 / (sigma_dbl * SQRT_2);
72 const T_partials_return rep_deriv = SQRT_2 * 0.5 / sqrt_pi
73 * exp(-scaled_diff * scaled_diff) / sigma_dbl;
74
75 // cdf
76 const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff);
77 cdf *= cdf_;
78
79 // gradients
80 if (!is_constant_struct<T_y>::value)
81 operands_and_partials.d_x1[n] += rep_deriv / cdf_ / y_dbl;
82 if (!is_constant_struct<T_loc>::value)
83 operands_and_partials.d_x2[n] -= rep_deriv / cdf_;
84 if (!is_constant_struct<T_scale>::value)
85 operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2
86 / cdf_;
87 }
88
89 if (!is_constant_struct<T_y>::value) {
90 for (size_t n = 0; n < stan::length(y); ++n)
91 operands_and_partials.d_x1[n] *= cdf;
92 }
93 if (!is_constant_struct<T_loc>::value) {
94 for (size_t n = 0; n < stan::length(mu); ++n)
95 operands_and_partials.d_x2[n] *= cdf;
96 }
97 if (!is_constant_struct<T_scale>::value) {
98 for (size_t n = 0; n < stan::length(sigma); ++n)
99 operands_and_partials.d_x3[n] *= cdf;
100 }
101
102 return operands_and_partials.to_var(cdf, y, mu, sigma);
103 }
104 }
105 }
106 #endif
check_not_nan.hpp
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.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
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
square.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
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::SQRT_2
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:21
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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
stan::math::check_finite
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
Definition: check_finite.hpp:62
constants.hpp
check_finite.hpp
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::erfc
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
stan::math::pi
double pi()
Return the value of pi.
Definition: constants.hpp:86
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
stan::math::lognormal_cdf
return_type< T_y, T_loc, T_scale >::type lognormal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Definition: lognormal_cdf.hpp:23
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
stan::partials_return_type::type
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
Definition: partials_return_type.hpp:26
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

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