Stan Math Library  2.12.0
reverse mode automatic differentiation
exp_mod_normal_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CCDF_LOG_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_ccdf_log(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_ccdf_log");
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 ccdf_log(0.0);
33  if (!(stan::length(y)
34  && stan::length(mu)
35  && stan::length(sigma)
36  && stan::length(lambda)))
37  return ccdf_log;
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::log;
55  using std::log;
56  using std::exp;
57 
58  VectorView<const T_y> y_vec(y);
59  VectorView<const T_loc> mu_vec(mu);
60  VectorView<const T_scale> sigma_vec(sigma);
61  VectorView<const T_inv_scale> lambda_vec(lambda);
62  size_t N = max_size(y, mu, sigma, lambda);
63  const double sqrt_pi = std::sqrt(pi());
64  for (size_t n = 0; n < N; n++) {
65  if (is_inf(y_vec[n])) {
66  if (y_vec[n] > 0.0)
67  return operands_and_partials.value(negative_infinity());
68  else
69  return operands_and_partials.value(0.0);
70  }
71 
72  const T_partials_return y_dbl = value_of(y_vec[n]);
73  const T_partials_return mu_dbl = value_of(mu_vec[n]);
74  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
75  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
76  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
77  const T_partials_return v = lambda_dbl * sigma_dbl;
78  const T_partials_return v_sq = v * v;
79  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
80  / (SQRT_2 * sigma_dbl);
81  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
82  const T_partials_return erf_calc1 = 0.5 * (1 + erf(u / (v * SQRT_2)));
83  const T_partials_return erf_calc2 = 0.5 * (1 + erf(u / (v * SQRT_2)
84  - v / SQRT_2));
85 
86  const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
87  * erf_calc2;
88  const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
89  * exp(0.5 * v_sq
90  - (-scaled_diff + (v / SQRT_2)) * (-scaled_diff
91  + (v / SQRT_2)) - u)
92  / sigma_dbl;
93  const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
94  * exp(-scaled_diff_sq) / sigma_dbl;
95 
96  const T_partials_return ccdf_ = 1.0 - erf_calc1 + exp(-u + v_sq * 0.5)
97  * (erf_calc2);
98 
99  ccdf_log += log(ccdf_);
100 
102  operands_and_partials.d_x1[n]
103  -= (deriv_1 - deriv_2 + deriv_3) / ccdf_;
105  operands_and_partials.d_x2[n]
106  -= (-deriv_1 + deriv_2 - deriv_3) / ccdf_;
108  operands_and_partials.d_x3[n]
109  -= (-deriv_1 * v - deriv_3 * scaled_diff * SQRT_2 - deriv_2
110  * sigma_dbl * SQRT_2
111  * (-SQRT_2 * 0.5 * (-lambda_dbl + scaled_diff * SQRT_2
112  / sigma_dbl)
113  - SQRT_2 * lambda_dbl))
114  / ccdf_;
116  operands_and_partials.d_x4[n] -= exp(0.5 * v_sq - u)
117  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
118  * exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
119  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc2)
120  / ccdf_;
121  }
122  return operands_and_partials.value(ccdf_log);
123  }
124 
125  }
126 }
127 #endif
128 
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
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
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
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_ccdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
VectorView< T_return_type, false, true > d_x4

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