1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP 18 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_inv_scale>
20 const T_y& y,
const T_loc& mu,
const T_scale& sigma,
21 const T_inv_scale& lambda) {
22 static const char*
function =
"exp_mod_normal_cdf";
25 T_inv_scale>::type T_partials_return;
27 T_partials_return cdf(1.0);
38 mu,
"Scale parameter", sigma,
"Inv_scale paramter",
42 y, mu, sigma, lambda);
50 size_t N =
max_size(y, mu, sigma, lambda);
52 for (
size_t n = 0; n < N; n++) {
55 return ops_partials.
build(0.0);
58 const T_partials_return y_dbl =
value_of(y_vec[n]);
59 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
60 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
61 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
62 const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
63 const T_partials_return v = lambda_dbl * sigma_dbl;
64 const T_partials_return v_sq = v * v;
65 const T_partials_return scaled_diff
66 = (y_dbl - mu_dbl) / (
SQRT_2 * sigma_dbl);
67 const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
68 const T_partials_return erf_calc
69 = 0.5 * (1 +
erf(-v /
SQRT_2 + scaled_diff));
70 const T_partials_return deriv_1
71 = lambda_dbl *
exp(0.5 * v_sq - u) * erf_calc;
72 const T_partials_return deriv_2
75 - (scaled_diff - (v /
SQRT_2)) * (scaled_diff - (v /
SQRT_2))
78 const T_partials_return deriv_3
79 =
SQRT_2 / sqrt_pi * 0.5 *
exp(-scaled_diff_sq) / sigma_dbl;
81 const T_partials_return cdf_
82 = 0.5 * (1 +
erf(u / (v *
SQRT_2))) -
exp(-u + v_sq * 0.5) * (erf_calc);
87 ops_partials.
edge1_.partials_[n] += (deriv_1 - deriv_2 + deriv_3) / cdf_;
89 ops_partials.
edge2_.partials_[n] += (-deriv_1 + deriv_2 - deriv_3) / cdf_;
91 ops_partials.
edge3_.partials_[n]
92 += (-deriv_1 * v - deriv_3 * scaled_diff * SQRT_2
93 - deriv_2 * sigma_dbl * SQRT_2
95 * (-lambda_dbl + scaled_diff * SQRT_2 / sigma_dbl)
96 - SQRT_2 * lambda_dbl))
99 ops_partials.
edge4_.partials_[n]
100 +=
exp(0.5 * v_sq - u)
101 * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
102 *
exp(-(v / SQRT_2 - scaled_diff)
103 * (v / SQRT_2 - scaled_diff))
104 - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc)
110 ops_partials.
edge1_.partials_[n] *= cdf;
114 ops_partials.
edge2_.partials_[n] *= cdf;
118 ops_partials.
edge3_.partials_[n] *= cdf;
122 ops_partials.
edge4_.partials_[n] *= cdf;
124 return ops_partials.
build(cdf);
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
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...
internal::ops_partials_edge< double, Op4 > edge4_
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.
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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, .
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
Template metaprogram to calculate the partial derivative type resulting from promoting all the scalar...
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.
int is_inf(const fvar< T > &x)
Returns 1 if the input's value is infinite and 0 otherwise.
internal::ops_partials_edge< double, Op2 > edge2_
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_