Stan Math Library  2.15.0
reverse mode automatic differentiation
exp_mod_normal_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LCDF_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_lcdf(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_lcdf");
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_log(0.0);
34  if (!(stan::length(y)
35  && stan::length(mu)
36  && stan::length(sigma)
37  && stan::length(lambda)))
38  return cdf_log;
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::log;
56  using std::log;
57  using std::exp;
58 
61  scalar_seq_view<const T_scale> sigma_vec(sigma);
62  scalar_seq_view<const T_inv_scale> lambda_vec(lambda);
63  size_t N = max_size(y, mu, sigma, lambda);
64  const double sqrt_pi = std::sqrt(pi());
65  for (size_t n = 0; n < N; n++) {
66  if (is_inf(y_vec[n])) {
67  if (y_vec[n] < 0.0)
68  return operands_and_partials.value(negative_infinity());
69  else
70  return operands_and_partials.value(0.0);
71  }
72 
73  const T_partials_return y_dbl = value_of(y_vec[n]);
74  const T_partials_return mu_dbl = value_of(mu_vec[n]);
75  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
76  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
77  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
78  const T_partials_return v = lambda_dbl * sigma_dbl;
79  const T_partials_return v_sq = v * v;
80  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
81  / (SQRT_2 * sigma_dbl);
82  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
83  const T_partials_return erf_calc1 = 0.5 * (1 + erf(u / (v * SQRT_2)));
84  const T_partials_return erf_calc2 = 0.5 * (1 + erf(u / (v * SQRT_2) - v
85  / SQRT_2));
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 - (-scaled_diff + (v / SQRT_2))
90  * (-scaled_diff + (v / SQRT_2)) - u) / sigma_dbl;
91  const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
92  * exp(-scaled_diff_sq) / sigma_dbl;
93 
94  const T_partials_return denom = erf_calc1 - erf_calc2
95  * exp(0.5 * v_sq - u);
96  const T_partials_return cdf_ = erf_calc1 - exp(-u + v_sq * 0.5)
97  * (erf_calc2);
98 
99  cdf_log += log(cdf_);
100 
102  operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
103  / denom;
105  operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
106  / denom;
108  operands_and_partials.d_x3[n]
109  += (-deriv_1 * v - deriv_3 * scaled_diff
110  * SQRT_2 - deriv_2 * sigma_dbl * SQRT_2
111  * (-SQRT_2 * 0.5 * (-lambda_dbl + scaled_diff * SQRT_2
112  / sigma_dbl)
113  - SQRT_2 * lambda_dbl))
114  / denom;
116  operands_and_partials.d_x4[n]
117  += exp(0.5 * v_sq - u)
118  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
119  * exp(-(v / SQRT_2 - scaled_diff)
120  * (v / SQRT_2 - scaled_diff))
121  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc2)
122  / denom;
123  }
124  return operands_and_partials.value(cdf_log);
125  }
126 
127  }
128 }
129 #endif
130 
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
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.
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
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
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lcdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
VectorView< T_return_type, false, true > d_x4

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