1 #ifndef STAN_MATH_PRIM_SCAL_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
4 #include <boost/random/uniform_01.hpp>
5 #include <boost/random/variate_generator.hpp>
36 template <
typename T_y,
typename T_loc,
typename T_scale>
37 typename return_type<T_y, T_loc, T_scale>::type
39 const T_loc& mu,
const T_scale& sigma) {
40 static const char*
function(
"stan::math::double_exponential_cdf");
53 using boost::math::tools::promote_args;
56 T_partials_return cdf(1.0);
63 operands_and_partials(y, mu, sigma);
71 for (
size_t n = 0; n < N; n++) {
72 const T_partials_return y_dbl =
value_of(y_vec[n]);
73 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
74 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
75 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (sigma_dbl);
76 const T_partials_return exp_scaled_diff =
exp(scaled_diff);
79 cdf *= exp_scaled_diff * 0.5;
81 cdf *= 1.0 - 0.5 / exp_scaled_diff;
85 for (
size_t n = 0; n < N; n++) {
86 const T_partials_return y_dbl =
value_of(y_vec[n]);
87 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
88 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
89 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / sigma_dbl;
90 const T_partials_return exp_scaled_diff =
exp(scaled_diff);
91 const T_partials_return inv_sigma = 1.0 / sigma_dbl;
95 operands_and_partials.
d_x1[n] += inv_sigma * cdf;
97 operands_and_partials.
d_x2[n] -= inv_sigma * cdf;
99 operands_and_partials.
d_x3[n] -= scaled_diff * inv_sigma * cdf;
101 const T_partials_return rep_deriv = cdf * inv_sigma
102 / (2.0 * exp_scaled_diff - 1.0);
104 operands_and_partials.
d_x1[n] += rep_deriv;
106 operands_and_partials.
d_x2[n] -= rep_deriv;
108 operands_and_partials.
d_x3[n] -= rep_deriv * scaled_diff;
111 return operands_and_partials.
to_var(cdf, y, mu, sigma);
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
size_t length(const std::vector< T > &x)
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)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
return_type< T_y, T_loc, T_scale >::type double_exponential_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the double exponential cumulative density function.
fvar< T > exp(const fvar< T > &x)
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.