Stan Math Library  2.15.0
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 
16 #include <boost/random/normal_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21  namespace math {
22 
23  template <typename T_y, typename T_loc, typename T_scale,
24  typename T_inv_scale>
26  exp_mod_normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
27  const T_inv_scale& lambda) {
28  static const char* function("exp_mod_normal_cdf");
29  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
30  T_inv_scale>::type
31  T_partials_return;
32 
33  T_partials_return cdf(1.0);
34  if (!(stan::length(y)
35  && stan::length(mu)
36  && stan::length(sigma)
37  && stan::length(lambda)))
38  return cdf;
39 
40  check_not_nan(function, "Random variable", y);
41  check_finite(function, "Location parameter", mu);
42  check_not_nan(function, "Scale parameter", sigma);
43  check_positive_finite(function, "Scale parameter", sigma);
44  check_positive_finite(function, "Inv_scale parameter", lambda);
45  check_not_nan(function, "Inv_scale parameter", lambda);
46  check_consistent_sizes(function,
47  "Random variable", y,
48  "Location parameter", mu,
49  "Scale parameter", sigma,
50  "Inv_scale paramter", lambda);
51 
53  operands_and_partials(y, mu, sigma, lambda);
54 
55  using std::exp;
56 
59  scalar_seq_view<const T_scale> sigma_vec(sigma);
60  scalar_seq_view<const T_inv_scale> lambda_vec(lambda);
61  size_t N = max_size(y, mu, sigma, lambda);
62  const double sqrt_pi = std::sqrt(pi());
63  for (size_t n = 0; n < N; n++) {
64  if (is_inf(y_vec[n])) {
65  if (y_vec[n] < 0.0)
66  return operands_and_partials.value(0.0);
67  }
68 
69  const T_partials_return y_dbl = value_of(y_vec[n]);
70  const T_partials_return mu_dbl = value_of(mu_vec[n]);
71  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
72  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
73  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
74  const T_partials_return v = lambda_dbl * sigma_dbl;
75  const T_partials_return v_sq = v * v;
76  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (SQRT_2
77  * sigma_dbl);
78  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
79  const T_partials_return erf_calc = 0.5 * (1 + erf(-v / SQRT_2
80  + scaled_diff));
81  const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
82  * erf_calc;
83  const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
84  * exp(0.5 * v_sq - (scaled_diff - (v / SQRT_2))
85  * (scaled_diff - (v / SQRT_2)) - u) / sigma_dbl;
86  const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
87  * exp(-scaled_diff_sq) / sigma_dbl;
88 
89  const T_partials_return cdf_ = 0.5 * (1 + erf(u / (v * SQRT_2)))
90  - exp(-u + v_sq * 0.5) * (erf_calc);
91 
92  cdf *= cdf_;
93 
95  operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
96  / cdf_;
98  operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
99  / cdf_;
101  operands_and_partials.d_x3[n] += (-deriv_1 * v - deriv_3
102  * scaled_diff * SQRT_2 - deriv_2
103  * sigma_dbl * SQRT_2
104  * (-SQRT_2 * 0.5
105  * (-lambda_dbl + scaled_diff
106  * SQRT_2 / sigma_dbl) - SQRT_2
107  * lambda_dbl)) / cdf_;
109  operands_and_partials.d_x4[n] += exp(0.5 * v_sq - u)
110  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
111  * exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
112  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
113  }
114 
116  for (size_t n = 0; n < stan::length(y); ++n)
117  operands_and_partials.d_x1[n] *= cdf;
118  }
120  for (size_t n = 0; n < stan::length(mu); ++n)
121  operands_and_partials.d_x2[n] *= cdf;
122  }
124  for (size_t n = 0; n < stan::length(sigma); ++n)
125  operands_and_partials.d_x3[n] *= cdf;
126  }
128  for (size_t n = 0; n < stan::length(lambda); ++n)
129  operands_and_partials.d_x4[n] *= cdf;
130  }
131  return operands_and_partials.value(cdf);
132  }
133 
134  }
135 }
136 #endif
VectorView< T_return_type, false, true > d_x2
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)
Definition: sqrt.hpp:14
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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
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
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
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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&#39;s value is infinite and 0 otherwise.
Definition: is_inf.hpp:21
double pi()
Return the value of pi.
Definition: constants.hpp:85
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.
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4

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