1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP 31 template <
typename T_y,
typename T_loc,
typename T_scale>
33 const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
34 static const char*
function =
"normal_cdf";
40 T_partials_return cdf(1.0);
50 mu,
"Scale parameter", sigma);
58 const double SQRT_TWO_OVER_PI =
std::sqrt(2.0 /
pi());
60 for (
size_t n = 0; n < N; n++) {
61 const T_partials_return y_dbl =
value_of(y_vec[n]);
62 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
63 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
64 const T_partials_return scaled_diff
65 = (y_dbl - mu_dbl) / (sigma_dbl *
SQRT_2);
66 T_partials_return cdf_;
70 cdf_ = 0.5 *
erfc(-scaled_diff);
74 cdf_ = 0.5 * (1.0 +
erf(scaled_diff));
79 const T_partials_return rep_deriv
82 : SQRT_TWO_OVER_PI * 0.5 *
exp(-scaled_diff * scaled_diff)
85 ops_partials.
edge1_.partials_[n] += rep_deriv;
87 ops_partials.
edge2_.partials_[n] -= rep_deriv;
89 ops_partials.
edge3_.partials_[n] -= rep_deriv * scaled_diff *
SQRT_2;
95 ops_partials.
edge1_.partials_[n] *= cdf;
99 ops_partials.
edge2_.partials_[n] *= cdf;
103 ops_partials.
edge3_.partials_[n] *= cdf;
105 return ops_partials.
build(cdf);
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > sqrt(const fvar< T > &x)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
fvar< T > erf(const fvar< T > &x)
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
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, .
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
fvar< T > exp(const fvar< T > &x)
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > erfc(const fvar< T > &x)
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
double pi()
Return the value of pi.
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.
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_