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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 <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/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 <boost/random/lognormal_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19
20 namespace stan {
21 namespace math {
22
23 template <typename T_y, typename T_loc, typename T_scale>
24 typename return_type<T_y, T_loc, T_scale>::type
25 lognormal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
26 static const char* function("lognormal_cdf");
27
28 typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
29 T_partials_return;
30
31 T_partials_return cdf = 1.0;
32
33 using boost::math::tools::promote_args;
34 using std::exp;
35 using std::log;
36
37 if (!(stan::length(y)
38 && stan::length(mu)
39 && stan::length(sigma)))
40 return cdf;
41
42 check_not_nan(function, "Random variable", y);
43 check_nonnegative(function, "Random variable", y);
44 check_finite(function, "Location parameter", mu);
45 check_positive_finite(function, "Scale parameter", sigma);
46
47 OperandsAndPartials<T_y, T_loc, T_scale>
48 operands_and_partials(y, mu, sigma);
49
50 VectorView<const T_y> y_vec(y);
51 VectorView<const T_loc> mu_vec(mu);
52 VectorView<const T_scale> sigma_vec(sigma);
53 size_t N = max_size(y, mu, sigma);
54
55 const double sqrt_pi = std::sqrt(pi());
56
57 for (size_t i = 0; i < stan::length(y); i++) {
58 if (value_of(y_vec[i]) == 0.0)
59 return operands_and_partials.value(0.0);
60 }
61
62 for (size_t n = 0; n < N; n++) {
63 const T_partials_return y_dbl = value_of(y_vec[n]);
64 const T_partials_return mu_dbl = value_of(mu_vec[n]);
65 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
66 const T_partials_return scaled_diff = (log(y_dbl) - mu_dbl)
67 / (sigma_dbl * SQRT_2);
68 const T_partials_return rep_deriv = SQRT_2 * 0.5 / sqrt_pi
69 * exp(-scaled_diff * scaled_diff) / sigma_dbl;
70
71 const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff);
72 cdf *= cdf_;
73
74 if (!is_constant_struct<T_y>::value)
75 operands_and_partials.d_x1[n] += rep_deriv / cdf_ / y_dbl;
76 if (!is_constant_struct<T_loc>::value)
77 operands_and_partials.d_x2[n] -= rep_deriv / cdf_;
78 if (!is_constant_struct<T_scale>::value)
79 operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2
80 / cdf_;
81 }
82
83 if (!is_constant_struct<T_y>::value) {
84 for (size_t n = 0; n < stan::length(y); ++n)
85 operands_and_partials.d_x1[n] *= cdf;
86 }
87 if (!is_constant_struct<T_loc>::value) {
88 for (size_t n = 0; n < stan::length(mu); ++n)
89 operands_and_partials.d_x2[n] *= cdf;
90 }
91 if (!is_constant_struct<T_scale>::value) {
92 for (size_t n = 0; n < stan::length(sigma); ++n)
93 operands_and_partials.d_x3[n] *= cdf;
94 }
95 return operands_and_partials.value(cdf);
96 }
97
98 }
99 }
100 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
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:60
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::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
square.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
include_summand.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::math::SQRT_2
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:20
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
partials_return_type.hpp
OperandsAndPartials.hpp
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:60
constants.hpp
check_finite.hpp
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:85
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
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:25
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::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
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38

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