Stan Math Library  2.20.0
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 
12 #include <cmath>
13 
14 namespace stan {
15 namespace math {
16 
36 template <bool propto, typename T_y, typename T_loc, typename T_scale>
38  const T_y& y, const T_loc& mu, const T_scale& sigma) {
39  static const char* function = "normal_lpdf";
41  T_partials_return;
42 
43  using std::log;
44 
45  if (size_zero(y, mu, sigma))
46  return 0.0;
47 
48  T_partials_return logp(0.0);
49 
50  check_not_nan(function, "Random variable", y);
51  check_finite(function, "Location parameter", mu);
52  check_positive(function, "Scale parameter", sigma);
53  check_consistent_sizes(function, "Random variable", y, "Location parameter",
54  mu, "Scale parameter", sigma);
56  return 0.0;
57 
58  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
59 
60  scalar_seq_view<T_y> y_vec(y);
61  scalar_seq_view<T_loc> mu_vec(mu);
62  scalar_seq_view<T_scale> sigma_vec(sigma);
63  size_t N = max_size(y, mu, sigma);
64 
67  T_scale>
68  log_sigma(length(sigma));
69  for (size_t i = 0; i < length(sigma); i++) {
70  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
72  log_sigma[i] = log(value_of(sigma_vec[i]));
73  }
74 
75  for (size_t n = 0; n < N; n++) {
76  const T_partials_return y_dbl = value_of(y_vec[n]);
77  const T_partials_return mu_dbl = value_of(mu_vec[n]);
78 
79  const T_partials_return y_minus_mu_over_sigma
80  = (y_dbl - mu_dbl) * inv_sigma[n];
81  const T_partials_return y_minus_mu_over_sigma_squared
82  = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
83 
84  static double NEGATIVE_HALF = -0.5;
85 
87  logp += NEG_LOG_SQRT_TWO_PI;
89  logp -= log_sigma[n];
91  logp += NEGATIVE_HALF * y_minus_mu_over_sigma_squared;
92 
93  T_partials_return scaled_diff = inv_sigma[n] * y_minus_mu_over_sigma;
95  ops_partials.edge1_.partials_[n] -= scaled_diff;
97  ops_partials.edge2_.partials_[n] += scaled_diff;
99  ops_partials.edge3_.partials_[n]
100  += -inv_sigma[n] + inv_sigma[n] * y_minus_mu_over_sigma_squared;
101  }
102  return ops_partials.build(logp);
103 }
104 
105 template <typename T_y, typename T_loc, typename T_scale>
107  const T_y& y, const T_loc& mu, const T_scale& sigma) {
108  return normal_lpdf<false>(y, mu, sigma);
109 }
110 
111 } // namespace math
112 } // namespace stan
113 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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:37
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
const double NEG_LOG_SQRT_TWO_PI
Definition: constants.hpp:156
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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