Stan Math Library  2.20.0
reverse mode automatic differentiation
exp_mod_normal_lccdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LCCDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
18 template <typename T_y, typename T_loc, typename T_scale, typename T_inv_scale>
20 exp_mod_normal_lccdf(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_lccdf";
23  typedef
24  typename stan::partials_return_type<T_y, T_loc, T_scale,
25  T_inv_scale>::type T_partials_return;
26 
27  T_partials_return ccdf_log(0.0);
28  if (size_zero(y, mu, sigma, lambda))
29  return ccdf_log;
30 
31  check_not_nan(function, "Random variable", y);
32  check_finite(function, "Location parameter", mu);
33  check_not_nan(function, "Scale parameter", sigma);
34  check_positive_finite(function, "Scale parameter", sigma);
35  check_positive_finite(function, "Inv_scale parameter", lambda);
36  check_not_nan(function, "Inv_scale parameter", lambda);
37  check_consistent_sizes(function, "Random variable", y, "Location parameter",
38  mu, "Scale parameter", sigma, "Inv_scale paramter",
39  lambda);
40 
42  y, mu, sigma, lambda);
43 
44  using std::exp;
45  using std::log;
46 
47  scalar_seq_view<T_y> y_vec(y);
48  scalar_seq_view<T_loc> mu_vec(mu);
49  scalar_seq_view<T_scale> sigma_vec(sigma);
50  scalar_seq_view<T_inv_scale> lambda_vec(lambda);
51  size_t N = max_size(y, mu, sigma, lambda);
52  const double sqrt_pi = std::sqrt(pi());
53  for (size_t n = 0; n < N; n++) {
54  if (is_inf(y_vec[n])) {
55  if (y_vec[n] > 0.0)
56  return ops_partials.build(negative_infinity());
57  else
58  return ops_partials.build(0.0);
59  }
60 
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 lambda_dbl = value_of(lambda_vec[n]);
65  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
66  const T_partials_return v = lambda_dbl * sigma_dbl;
67  const T_partials_return v_sq = v * v;
68  const T_partials_return scaled_diff
69  = (y_dbl - mu_dbl) / (SQRT_2 * sigma_dbl);
70  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
71  const T_partials_return erf_calc1 = 0.5 * (1 + erf(u / (v * SQRT_2)));
72  const T_partials_return erf_calc2
73  = 0.5 * (1 + erf(u / (v * SQRT_2) - v / SQRT_2));
74 
75  const T_partials_return deriv_1
76  = lambda_dbl * exp(0.5 * v_sq - u) * erf_calc2;
77  const T_partials_return deriv_2
78  = SQRT_2 / sqrt_pi * 0.5
79  * exp(0.5 * v_sq
80  - (-scaled_diff + (v / SQRT_2)) * (-scaled_diff + (v / SQRT_2))
81  - u)
82  / sigma_dbl;
83  const T_partials_return deriv_3
84  = SQRT_2 / sqrt_pi * 0.5 * exp(-scaled_diff_sq) / sigma_dbl;
85 
86  const T_partials_return ccdf_
87  = 1.0 - erf_calc1 + exp(-u + v_sq * 0.5) * (erf_calc2);
88 
89  ccdf_log += log(ccdf_);
90 
92  ops_partials.edge1_.partials_[n] -= (deriv_1 - deriv_2 + deriv_3) / ccdf_;
94  ops_partials.edge2_.partials_[n]
95  -= (-deriv_1 + deriv_2 - deriv_3) / ccdf_;
97  ops_partials.edge3_.partials_[n]
98  -= (-deriv_1 * v - deriv_3 * scaled_diff * SQRT_2
99  - deriv_2 * sigma_dbl * SQRT_2
100  * (-SQRT_2 * 0.5
101  * (-lambda_dbl + scaled_diff * SQRT_2 / sigma_dbl)
102  - SQRT_2 * lambda_dbl))
103  / ccdf_;
105  ops_partials.edge4_.partials_[n]
106  -= exp(0.5 * v_sq - u)
107  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
108  * exp(-(v / SQRT_2 - scaled_diff)
109  * (v / SQRT_2 - scaled_diff))
110  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc2)
111  / ccdf_;
112  }
113  return ops_partials.build(ccdf_log);
114 }
115 
116 } // namespace math
117 } // namespace stan
118 #endif
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lccdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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:13
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
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.
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:15
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:25
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
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
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)
Definition: max_size.hpp:9
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&#39;s value is infinite and 0 otherwise.
Definition: is_inf.hpp:20
internal::ops_partials_edge< double, Op2 > edge2_
double pi()
Return the value of pi.
Definition: constants.hpp:80
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_
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:115

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