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exp_mod_normal_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_LOG_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_log(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_log");
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_log(0.0);
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_log;
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::log;
62  using std::log;
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.to_var(stan::math::negative_infinity(),
75  y, mu, sigma, lambda);
76  else
77  return operands_and_partials.to_var(0.0, y, mu, sigma, lambda);
78  }
79 
80  const T_partials_return y_dbl = value_of(y_vec[n]);
81  const T_partials_return mu_dbl = value_of(mu_vec[n]);
82  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
83  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
84  const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
85  const T_partials_return v = lambda_dbl * sigma_dbl;
86  const T_partials_return v_sq = v * v;
87  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
88  / (SQRT_2 * sigma_dbl);
89  const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
90  const T_partials_return erf_calc1 = 0.5 * (1 + erf(u / (v * SQRT_2)));
91  const T_partials_return erf_calc2 = 0.5 * (1 + erf(u / (v * SQRT_2) - v
92  / SQRT_2));
93  const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
94  * erf_calc2;
95  const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
96  * exp(0.5 * v_sq - (-scaled_diff + (v / SQRT_2))
97  * (-scaled_diff + (v / SQRT_2)) - u) / sigma_dbl;
98  const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
99  * exp(-scaled_diff_sq) / sigma_dbl;
100 
101  const T_partials_return denom = erf_calc1 - erf_calc2
102  * exp(0.5 * v_sq - u);
103  const T_partials_return cdf_ = erf_calc1 - exp(-u + v_sq * 0.5)
104  * (erf_calc2);
105 
106  cdf_log += log(cdf_);
107 
109  operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
110  / denom;
112  operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
113  / denom;
115  operands_and_partials.d_x3[n]
116  += (-deriv_1 * v - deriv_3 * scaled_diff
117  * SQRT_2 - deriv_2 * sigma_dbl * SQRT_2
118  * (-SQRT_2 * 0.5 * (-lambda_dbl + scaled_diff * SQRT_2
119  / sigma_dbl)
120  - SQRT_2 * lambda_dbl))
121  / denom;
123  operands_and_partials.d_x4[n]
124  += exp(0.5 * v_sq - u)
125  * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
126  * exp(-(v / SQRT_2 - scaled_diff)
127  * (v / SQRT_2 - scaled_diff))
128  - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc2)
129  / denom;
130  }
131 
132  return operands_and_partials.to_var(cdf_log, y, mu, sigma, lambda);
133  }
134  }
135 }
136 #endif
137 
138 
139 
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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...
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_cdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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.
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132

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