1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP
15 #include <boost/random/normal_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
38 template <
typename T_y,
typename T_loc,
typename T_scale>
39 typename return_type<T_y, T_loc, T_scale>::type
40 normal_cdf(
const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
41 static const char*
function(
"stan::math::normal_cdf");
53 T_partials_return cdf(1.0);
67 "Location parameter", mu,
68 "Scale parameter", sigma);
72 operands_and_partials(y, mu, sigma);
80 for (
size_t n = 0; n < N; n++) {
81 const T_partials_return y_dbl =
value_of(y_vec[n]);
82 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
83 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
84 const T_partials_return scaled_diff = (y_dbl - mu_dbl)
86 T_partials_return cdf_;
90 cdf_ = 0.5 *
erfc(-scaled_diff);
94 cdf_ = 0.5 * (1.0 +
erf(scaled_diff));
101 const T_partials_return rep_deriv
104 : SQRT_TWO_OVER_PI * 0.5
105 *
exp(-scaled_diff * scaled_diff) / cdf_ / sigma_dbl;
107 operands_and_partials.
d_x1[n] += rep_deriv;
109 operands_and_partials.
d_x2[n] -= rep_deriv;
111 operands_and_partials.
d_x3[n] -= rep_deriv * scaled_diff *
SQRT_2;
117 operands_and_partials.
d_x1[n] *= cdf;
121 operands_and_partials.
d_x2[n] *= cdf;
125 operands_and_partials.
d_x3[n] *= cdf;
128 return operands_and_partials.
value(cdf);
VectorView< T_return_type, false, true > d_x2
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.
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
fvar< T > erf(const fvar< T > &x)
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, .
const double INV_SQRT_2
The value of 1 over the square root of 2, .
fvar< T > exp(const fvar< T > &x)
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
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.
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.
fvar< T > erfc(const fvar< T > &x)
double pi()
Return the value of pi.
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[].
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
return_type< T_y, T_loc, T_scale >::type normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the normal cumulative distribution function for the given variate, location, and scale.
VectorView< T_return_type, false, true > d_x1