Stan Math Library  2.20.0
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 
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  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";
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 cdf(1.0);
28  if (size_zero(y, mu, sigma, lambda))
29  return cdf;
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 
46  scalar_seq_view<T_y> y_vec(y);
47  scalar_seq_view<T_loc> mu_vec(mu);
48  scalar_seq_view<T_scale> sigma_vec(sigma);
49  scalar_seq_view<T_inv_scale> lambda_vec(lambda);
50  size_t N = max_size(y, mu, sigma, lambda);
51  const double sqrt_pi = std::sqrt(pi());
52  for (size_t n = 0; n < N; n++) {
53  if (is_inf(y_vec[n])) {
54  if (y_vec[n] < 0.0)
55  return ops_partials.build(0.0);
56  }
57 
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
73  = SQRT_2 / sqrt_pi * 0.5
74  * exp(0.5 * v_sq
75  - (scaled_diff - (v / SQRT_2)) * (scaled_diff - (v / SQRT_2))
76  - u)
77  / sigma_dbl;
78  const T_partials_return deriv_3
79  = SQRT_2 / sqrt_pi * 0.5 * exp(-scaled_diff_sq) / sigma_dbl;
80 
81  const T_partials_return cdf_
82  = 0.5 * (1 + erf(u / (v * SQRT_2))) - exp(-u + v_sq * 0.5) * (erf_calc);
83 
84  cdf *= cdf_;
85 
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
94  * (-SQRT_2 * 0.5
95  * (-lambda_dbl + scaled_diff * SQRT_2 / sigma_dbl)
96  - SQRT_2 * lambda_dbl))
97  / cdf_;
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)
105  / cdf_;
106  }
107 
109  for (size_t n = 0; n < stan::length(y); ++n)
110  ops_partials.edge1_.partials_[n] *= cdf;
111  }
113  for (size_t n = 0; n < stan::length(mu); ++n)
114  ops_partials.edge2_.partials_[n] *= cdf;
115  }
117  for (size_t n = 0; n < stan::length(sigma); ++n)
118  ops_partials.edge3_.partials_[n] *= cdf;
119  }
121  for (size_t n = 0; n < stan::length(lambda); ++n)
122  ops_partials.edge4_.partials_[n] *= cdf;
123  }
124  return ops_partials.build(cdf);
125 }
126 
127 } // namespace math
128 } // namespace stan
129 #endif
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
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.
Definition: length.hpp:16
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: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_

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