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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 
4 #include <boost/random/normal_distribution.hpp>
5 #include <boost/math/special_functions/fpclassify.hpp>
6 #include <boost/random/variate_generator.hpp>
15 #include <cmath>
16 
17 namespace stan {
18 
19  namespace math {
20 
21  template <typename T_y, typename T_loc, typename T_scale,
22  typename T_inv_scale>
23  typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
24  exp_mod_normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
25  const T_inv_scale& lambda) {
26  static const char* function("stan::math::exp_mod_normal_cdf");
27  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
28  T_inv_scale>::type
29  T_partials_return;
30 
36 
37  T_partials_return cdf(1.0);
38  // check if any vectors are zero length
39  if (!(stan::length(y)
40  && stan::length(mu)
41  && stan::length(sigma)
42  && stan::length(lambda)))
43  return cdf;
44 
45  check_not_nan(function, "Random variable", y);
46  check_finite(function, "Location parameter", mu);
47  check_not_nan(function, "Scale parameter", sigma);
48  check_positive_finite(function, "Scale parameter", sigma);
49  check_positive_finite(function, "Inv_scale parameter", lambda);
50  check_not_nan(function, "Inv_scale parameter", lambda);
51  check_consistent_sizes(function,
52  "Random variable", y,
53  "Location parameter", mu,
54  "Scale parameter", sigma,
55  "Inv_scale paramter", lambda);
56 
58  operands_and_partials(y, mu, sigma, lambda);
59 
60  using stan::math::SQRT_2;
61  using std::exp;
62 
63  VectorView<const T_y> y_vec(y);
64  VectorView<const T_loc> mu_vec(mu);
65  VectorView<const T_scale> sigma_vec(sigma);
66  VectorView<const T_inv_scale> lambda_vec(lambda);
67  size_t N = max_size(y, mu, sigma, lambda);
68  const double sqrt_pi = std::sqrt(stan::math::pi());
69  for (size_t n = 0; n < N; n++) {
70  if (boost::math::isinf(y_vec[n])) {
71  if (y_vec[n] < 0.0)
72  return operands_and_partials.to_var(0.0, y, mu, sigma, lambda);
73  }
74 
75  const T_partials_return y_dbl = value_of(y_vec[n]);
76  const T_partials_return mu_dbl = value_of(mu_vec[n]);
77  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
78  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
79  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
80  const T_partials_return v = lambda_dbl * sigma_dbl;
81  const T_partials_return v_sq = v * v;
82  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (SQRT_2
83  * sigma_dbl);
84  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
85  const T_partials_return erf_calc = 0.5 * (1 + erf(-v / SQRT_2
86  + scaled_diff));
87  const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
88  * erf_calc;
89  const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
90  * exp(0.5 * v_sq - (scaled_diff - (v / SQRT_2))
91  * (scaled_diff - (v / SQRT_2)) - u) / sigma_dbl;
92  const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
93  * exp(-scaled_diff_sq) / sigma_dbl;
94 
95  const T_partials_return cdf_ = 0.5 * (1 + erf(u / (v * SQRT_2)))
96  - exp(-u + v_sq * 0.5) * (erf_calc);
97 
98  cdf *= cdf_;
99 
101  operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
102  / cdf_;
104  operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
105  / cdf_;
107  operands_and_partials.d_x3[n] += (-deriv_1 * v - deriv_3
108  * scaled_diff * SQRT_2 - deriv_2
109  * sigma_dbl * SQRT_2
110  * (-SQRT_2 * 0.5
111  * (-lambda_dbl + scaled_diff
112  * SQRT_2 / sigma_dbl) - SQRT_2
113  * lambda_dbl)) / cdf_;
115  operands_and_partials.d_x4[n] += exp(0.5 * v_sq - u)
116  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
117  * exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
118  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
119  }
120 
122  for (size_t n = 0; n < stan::length(y); ++n)
123  operands_and_partials.d_x1[n] *= cdf;
124  }
126  for (size_t n = 0; n < stan::length(mu); ++n)
127  operands_and_partials.d_x2[n] *= cdf;
128  }
130  for (size_t n = 0; n < stan::length(sigma); ++n)
131  operands_and_partials.d_x3[n] *= cdf;
132  }
134  for (size_t n = 0; n < stan::length(lambda); ++n)
135  operands_and_partials.d_x4[n] *= cdf;
136  }
137 
138  return operands_and_partials.to_var(cdf, y, mu, sigma, lambda);
139  }
140  }
141 }
142 #endif
143 
144 
145 
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
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
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
A variable implementation that stores operands and derivatives with respect to the variable...
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
double pi()
Return the value of pi.
Definition: constants.hpp:86
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.

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