Stan Math Library  2.12.0
reverse mode automatic differentiation
exp_mod_normal_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP
3 
15 #include <boost/random/normal_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20  namespace math {
21 
22  template <typename T_y, typename T_loc, typename T_scale,
23  typename T_inv_scale>
24  typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
25  exp_mod_normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
26  const T_inv_scale& lambda) {
27  static const char* function("exp_mod_normal_cdf");
28  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
29  T_inv_scale>::type
30  T_partials_return;
31 
32  T_partials_return cdf(1.0);
33  if (!(stan::length(y)
34  && stan::length(mu)
35  && stan::length(sigma)
36  && stan::length(lambda)))
37  return cdf;
38 
39  check_not_nan(function, "Random variable", y);
40  check_finite(function, "Location parameter", mu);
41  check_not_nan(function, "Scale parameter", sigma);
42  check_positive_finite(function, "Scale parameter", sigma);
43  check_positive_finite(function, "Inv_scale parameter", lambda);
44  check_not_nan(function, "Inv_scale parameter", lambda);
45  check_consistent_sizes(function,
46  "Random variable", y,
47  "Location parameter", mu,
48  "Scale parameter", sigma,
49  "Inv_scale paramter", lambda);
50 
52  operands_and_partials(y, mu, sigma, lambda);
53 
54  using std::exp;
55 
56  VectorView<const T_y> y_vec(y);
57  VectorView<const T_loc> mu_vec(mu);
58  VectorView<const T_scale> sigma_vec(sigma);
59  VectorView<const T_inv_scale> lambda_vec(lambda);
60  size_t N = max_size(y, mu, sigma, lambda);
61  const double sqrt_pi = std::sqrt(pi());
62  for (size_t n = 0; n < N; n++) {
63  if (is_inf(y_vec[n])) {
64  if (y_vec[n] < 0.0)
65  return operands_and_partials.value(0.0);
66  }
67 
68  const T_partials_return y_dbl = value_of(y_vec[n]);
69  const T_partials_return mu_dbl = value_of(mu_vec[n]);
70  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
71  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
72  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
73  const T_partials_return v = lambda_dbl * sigma_dbl;
74  const T_partials_return v_sq = v * v;
75  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (SQRT_2
76  * sigma_dbl);
77  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
78  const T_partials_return erf_calc = 0.5 * (1 + erf(-v / SQRT_2
79  + scaled_diff));
80  const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
81  * erf_calc;
82  const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
83  * exp(0.5 * v_sq - (scaled_diff - (v / SQRT_2))
84  * (scaled_diff - (v / SQRT_2)) - u) / sigma_dbl;
85  const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
86  * exp(-scaled_diff_sq) / sigma_dbl;
87 
88  const T_partials_return cdf_ = 0.5 * (1 + erf(u / (v * SQRT_2)))
89  - exp(-u + v_sq * 0.5) * (erf_calc);
90 
91  cdf *= cdf_;
92 
94  operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
95  / cdf_;
97  operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
98  / cdf_;
100  operands_and_partials.d_x3[n] += (-deriv_1 * v - deriv_3
101  * scaled_diff * SQRT_2 - deriv_2
102  * sigma_dbl * SQRT_2
103  * (-SQRT_2 * 0.5
104  * (-lambda_dbl + scaled_diff
105  * SQRT_2 / sigma_dbl) - SQRT_2
106  * lambda_dbl)) / cdf_;
108  operands_and_partials.d_x4[n] += exp(0.5 * v_sq - u)
109  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
110  * exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
111  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
112  }
113 
115  for (size_t n = 0; n < stan::length(y); ++n)
116  operands_and_partials.d_x1[n] *= cdf;
117  }
119  for (size_t n = 0; n < stan::length(mu); ++n)
120  operands_and_partials.d_x2[n] *= cdf;
121  }
123  for (size_t n = 0; n < stan::length(sigma); ++n)
124  operands_and_partials.d_x3[n] *= cdf;
125  }
127  for (size_t n = 0; n < stan::length(lambda); ++n)
128  operands_and_partials.d_x4[n] *= cdf;
129  }
130  return operands_and_partials.value(cdf);
131  }
132 
133  }
134 }
135 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
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.
Definition: value_of.hpp:16
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)
Definition: length.hpp:10
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)
Definition: erf.hpp:14
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, .
Definition: constants.hpp:20
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
int is_inf(const fvar< T > &x)
Returns 1 if the input's value is infinite and 0 otherwise.
Definition: is_inf.hpp:21
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.
double pi()
Return the value of pi.
Definition: constants.hpp:85
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4

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