normal_cdf_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_LOG_HPP
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_finite.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/err/check_positive.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/meta/max_size.hpp>
#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
#include <limits>
namespace stan {
namespace math {
template <typename T_y, typename T_loc, typename T_scale>
typename return_type<T_y, T_loc, T_scale>::type
normal_cdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
static const char* function("normal_cdf_log");
typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
T_partials_return;
using std::log;
using std::exp;
T_partials_return cdf_log(0.0);
if (!(stan::length(y)
&& stan::length(mu)
&& stan::length(sigma)))
return cdf_log;
check_not_nan(function, "Random variable", y);
check_finite(function, "Location parameter", mu);
check_not_nan(function, "Scale parameter", sigma);
check_positive(function, "Scale parameter", sigma);
check_consistent_sizes(function,
"Random variable", y,
"Location parameter", mu,
"Scale parameter", sigma);
OperandsAndPartials<T_y, T_loc, T_scale>
operands_and_partials(y, mu, sigma);
VectorView<const T_y> y_vec(y);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
size_t N = max_size(y, mu, sigma);
const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return scaled_diff = (y_dbl - mu_dbl)
/ (sigma_dbl * SQRT_2);
T_partials_return one_p_erf;
if (scaled_diff < -37.5 * INV_SQRT_2)
one_p_erf = 0.0;
else if (scaled_diff < -5.0 * INV_SQRT_2)
one_p_erf = erfc(-scaled_diff);
else if (scaled_diff > 8.25 * INV_SQRT_2)
one_p_erf = 2.0;
else
one_p_erf = 1.0 + erf(scaled_diff);
cdf_log += LOG_HALF + log(one_p_erf);
if (contains_nonconstant_struct<T_y, T_loc, T_scale>::value) {
const T_partials_return rep_deriv_div_sigma
= scaled_diff < -37.5 * INV_SQRT_2
? std::numeric_limits<double>::infinity()
: SQRT_TWO_OVER_PI * exp(-scaled_diff * scaled_diff)
/ sigma_dbl / one_p_erf;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += rep_deriv_div_sigma;
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n] -= rep_deriv_div_sigma;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] -= rep_deriv_div_sigma
* scaled_diff * SQRT_2;
}
}
return operands_and_partials.value(cdf_log);
}
}
}
#endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
stan::math::LOG_HALF
const double LOG_HALF
Definition: constants.hpp:176
stan::math::check_finite
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
Definition: check_finite.hpp:57
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
check_positive.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
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::erf
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
is_constant_struct.hpp
stan::return_type::type
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
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::INV_SQRT_2
const double INV_SQRT_2
The value of 1 over the square root of 2, .
Definition: constants.hpp:26
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::check_not_nan
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
Definition: check_not_nan.hpp:57
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::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
constants.hpp
stan::math::normal_cdf_log
return_type< T_y, T_loc, T_scale >::type normal_cdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
Definition: normal_cdf_log.hpp:25
check_finite.hpp
stan::math::erfc
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
stan::math::check_positive
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
Definition: check_positive.hpp:63
stan::math::pi
double pi()
Return the value of pi.
Definition: constants.hpp:85
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::math::check_consistent_sizes
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
Definition: check_consistent_sizes.hpp:30
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::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
max_size.hpp

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