Stan Math Library  2.10.0
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 
14 #include <boost/random/normal_distribution.hpp>
15 #include <boost/math/special_functions/fpclassify.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20 
21  namespace math {
22 
23  template <typename T_y, typename T_loc, typename T_scale,
24  typename T_inv_scale>
25  typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
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("stan::math::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 
38 
39  T_partials_return cdf(1.0);
40  // check if any vectors are zero length
41  if (!(stan::length(y)
42  && stan::length(mu)
43  && stan::length(sigma)
44  && stan::length(lambda)))
45  return cdf;
46 
47  check_not_nan(function, "Random variable", y);
48  check_finite(function, "Location parameter", mu);
49  check_not_nan(function, "Scale parameter", sigma);
50  check_positive_finite(function, "Scale parameter", sigma);
51  check_positive_finite(function, "Inv_scale parameter", lambda);
52  check_not_nan(function, "Inv_scale parameter", lambda);
53  check_consistent_sizes(function,
54  "Random variable", y,
55  "Location parameter", mu,
56  "Scale parameter", sigma,
57  "Inv_scale paramter", lambda);
58 
60  operands_and_partials(y, mu, sigma, lambda);
61 
62  using stan::math::SQRT_2;
63  using std::exp;
64 
65  VectorView<const T_y> y_vec(y);
66  VectorView<const T_loc> mu_vec(mu);
67  VectorView<const T_scale> sigma_vec(sigma);
68  VectorView<const T_inv_scale> lambda_vec(lambda);
69  size_t N = max_size(y, mu, sigma, lambda);
70  const double sqrt_pi = std::sqrt(stan::math::pi());
71  for (size_t n = 0; n < N; n++) {
72  if (boost::math::isinf(y_vec[n])) {
73  if (y_vec[n] < 0.0)
74  return operands_and_partials.value(0.0);
75  }
76 
77  const T_partials_return y_dbl = value_of(y_vec[n]);
78  const T_partials_return mu_dbl = value_of(mu_vec[n]);
79  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
80  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
81  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
82  const T_partials_return v = lambda_dbl * sigma_dbl;
83  const T_partials_return v_sq = v * v;
84  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (SQRT_2
85  * sigma_dbl);
86  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
87  const T_partials_return erf_calc = 0.5 * (1 + erf(-v / SQRT_2
88  + scaled_diff));
89  const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
90  * erf_calc;
91  const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
92  * exp(0.5 * v_sq - (scaled_diff - (v / SQRT_2))
93  * (scaled_diff - (v / SQRT_2)) - u) / sigma_dbl;
94  const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
95  * exp(-scaled_diff_sq) / sigma_dbl;
96 
97  const T_partials_return cdf_ = 0.5 * (1 + erf(u / (v * SQRT_2)))
98  - exp(-u + v_sq * 0.5) * (erf_calc);
99 
100  cdf *= cdf_;
101 
103  operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
104  / cdf_;
106  operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
107  / cdf_;
109  operands_and_partials.d_x3[n] += (-deriv_1 * v - deriv_3
110  * scaled_diff * SQRT_2 - deriv_2
111  * sigma_dbl * SQRT_2
112  * (-SQRT_2 * 0.5
113  * (-lambda_dbl + scaled_diff
114  * SQRT_2 / sigma_dbl) - SQRT_2
115  * lambda_dbl)) / cdf_;
117  operands_and_partials.d_x4[n] += exp(0.5 * v_sq - u)
118  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
119  * exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
120  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
121  }
122 
124  for (size_t n = 0; n < stan::length(y); ++n)
125  operands_and_partials.d_x1[n] *= cdf;
126  }
128  for (size_t n = 0; n < stan::length(mu); ++n)
129  operands_and_partials.d_x2[n] *= cdf;
130  }
132  for (size_t n = 0; n < stan::length(sigma); ++n)
133  operands_and_partials.d_x3[n] *= cdf;
134  }
136  for (size_t n = 0; n < stan::length(lambda); ++n)
137  operands_and_partials.d_x4[n] *= cdf;
138  }
139 
140  return operands_and_partials.value(cdf);
141  }
142  }
143 }
144 #endif
145 
146 
147 
VectorView< T_return_type, false, true > d_x2
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
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
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
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
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:21
bool isinf(const stan::math::var &v)
Checks if the given number is infinite.
Definition: boost_isinf.hpp:22
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
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:86
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
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
VectorView< T_return_type, false, true > d_x4

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