Stan Math Library  2.14.0
reverse mode automatic differentiation
normal_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_LPDF_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 
41  template <bool propto,
42  typename T_y, typename T_loc, typename T_scale>
44  normal_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
45  static const char* function("normal_lpdf");
47  T_partials_return;
48 
49  using std::log;
51  using std::log;
52 
53  if (!(stan::length(y)
54  && stan::length(mu)
55  && stan::length(sigma)))
56  return 0.0;
57 
58  T_partials_return logp(0.0);
59 
60  check_not_nan(function, "Random variable", y);
61  check_finite(function, "Location parameter", mu);
62  check_positive(function, "Scale parameter", sigma);
63  check_consistent_sizes(function,
64  "Random variable", y,
65  "Location parameter", mu,
66  "Scale parameter", sigma);
68  return 0.0;
69 
71  operands_and_partials(y, mu, sigma);
72 
73  VectorView<const T_y> y_vec(y);
74  VectorView<const T_loc> mu_vec(mu);
75  VectorView<const T_scale> sigma_vec(sigma);
76  size_t N = max_size(y, mu, sigma);
77 
80  T_partials_return, T_scale> log_sigma(length(sigma));
81  for (size_t i = 0; i < length(sigma); i++) {
82  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
84  log_sigma[i] = log(value_of(sigma_vec[i]));
85  }
86 
87  for (size_t n = 0; n < N; n++) {
88  const T_partials_return y_dbl = value_of(y_vec[n]);
89  const T_partials_return mu_dbl = value_of(mu_vec[n]);
90 
91  const T_partials_return y_minus_mu_over_sigma
92  = (y_dbl - mu_dbl) * inv_sigma[n];
93  const T_partials_return y_minus_mu_over_sigma_squared
94  = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
95 
96  static double NEGATIVE_HALF = - 0.5;
97 
99  logp += NEG_LOG_SQRT_TWO_PI;
101  logp -= log_sigma[n];
103  logp += NEGATIVE_HALF * y_minus_mu_over_sigma_squared;
104 
105  T_partials_return scaled_diff = inv_sigma[n] * y_minus_mu_over_sigma;
107  operands_and_partials.d_x1[n] -= scaled_diff;
109  operands_and_partials.d_x2[n] += scaled_diff;
111  operands_and_partials.d_x3[n]
112  += -inv_sigma[n] + inv_sigma[n] * y_minus_mu_over_sigma_squared;
113  }
114  return operands_and_partials.value(logp);
115  }
116 
117  template <typename T_y, typename T_loc, typename T_scale>
118  inline
120  normal_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
121  return normal_lpdf<false>(y, mu, sigma);
122  }
123 
124  }
125 }
126 #endif
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.
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.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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...
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
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
return_type< T_y, T_loc, T_scale >::type normal_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s...
Definition: normal_lpdf.hpp:44
const double NEG_LOG_SQRT_TWO_PI
Definition: constants.hpp:181
VectorBuilder allocates type T1 values to be used as intermediate values.
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
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
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.
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
VectorView< T_return_type, false, true > d_x1

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