1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_HPP
4 #include <boost/random/lognormal_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
21 template <
typename T_y,
typename T_loc,
typename T_scale>
22 typename return_type<T_y, T_loc, T_scale>::type
24 static const char*
function(
"stan::math::lognormal_cdf");
29 T_partials_return cdf = 1.0;
35 using boost::math::tools::promote_args;
52 operands_and_partials(y, mu, sigma);
63 return operands_and_partials.
to_var(0.0, y, mu, sigma);
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)
72 const T_partials_return rep_deriv = SQRT_2 * 0.5 / sqrt_pi
73 *
exp(-scaled_diff * scaled_diff) / sigma_dbl;
76 const T_partials_return cdf_ = 0.5 *
erfc(-scaled_diff);
81 operands_and_partials.
d_x1[n] += rep_deriv / cdf_ / y_dbl;
83 operands_and_partials.
d_x2[n] -= rep_deriv / cdf_;
85 operands_and_partials.
d_x3[n] -= rep_deriv * scaled_diff * SQRT_2
91 operands_and_partials.
d_x1[n] *= cdf;
95 operands_and_partials.
d_x2[n] *= cdf;
99 operands_and_partials.
d_x3[n] *= cdf;
102 return operands_and_partials.
to_var(cdf, y, mu, sigma);
fvar< T > sqrt(const fvar< T > &x)
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.
fvar< T > log(const fvar< T > &x)
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...
const double SQRT_2
The value of the square root of 2, .
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
fvar< T > erfc(const fvar< T > &x)
double pi()
Return the value of pi.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
return_type< T_y, T_loc, T_scale >::type lognormal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
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.