Stan Math Library  2.20.0
reverse mode automatic differentiation
von_mises_lpdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_VON_MISES_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_VON_MISES_LPDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
18 template <bool propto, typename T_y, typename T_loc, typename T_scale>
20  T_y const& y, T_loc const& mu, T_scale const& kappa) {
21  static char const* const function = "von_mises_lpdf";
23  T_partials_return;
24 
25  if (size_zero(y, mu, kappa))
26  return 0.0;
27 
28  using std::log;
29 
30  T_partials_return logp = 0.0;
31 
32  check_finite(function, "Random variable", y);
33  check_finite(function, "Location paramter", mu);
34  check_positive_finite(function, "Scale parameter", kappa);
35  check_consistent_sizes(function, "Random variable", y, "Location parameter",
36  mu, "Scale parameter", kappa);
37 
39  return logp;
40 
41  const bool y_const = is_constant_all<T_y>::value;
42  const bool mu_const = is_constant_all<T_loc>::value;
43  const bool kappa_const = is_constant_all<T_scale>::value;
44 
45  const bool compute_bessel0 = include_summand<propto, T_scale>::value;
46  const bool compute_bessel1 = !kappa_const;
47  const double TWO_PI = 2.0 * pi();
48 
49  scalar_seq_view<T_y> y_vec(y);
50  scalar_seq_view<T_loc> mu_vec(mu);
51  scalar_seq_view<T_scale> kappa_vec(kappa);
52 
55  T_scale>
56  log_bessel0(length(kappa));
57  for (size_t i = 0; i < length(kappa); i++) {
58  kappa_dbl[i] = value_of(kappa_vec[i]);
60  log_bessel0[i]
61  = log_modified_bessel_first_kind(0, value_of(kappa_vec[i]));
62  }
63 
64  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, kappa);
65 
66  size_t N = max_size(y, mu, kappa);
67 
68  for (size_t n = 0; n < N; n++) {
69  const T_partials_return y_ = value_of(y_vec[n]);
70  const T_partials_return y_dbl = y_ - floor(y_ / TWO_PI) * TWO_PI;
71  const T_partials_return mu_dbl = value_of(mu_vec[n]);
72 
73  T_partials_return bessel0 = 0;
74  if (compute_bessel0)
75  bessel0 = modified_bessel_first_kind(0, kappa_dbl[n]);
76  T_partials_return bessel1 = 0;
77  if (compute_bessel1)
78  bessel1 = modified_bessel_first_kind(-1, kappa_dbl[n]);
79  const T_partials_return kappa_sin = kappa_dbl[n] * sin(mu_dbl - y_dbl);
80  const T_partials_return kappa_cos = kappa_dbl[n] * cos(mu_dbl - y_dbl);
81 
83  logp -= LOG_TWO_PI;
85  logp -= log_bessel0[n];
87  logp += kappa_cos;
88 
89  if (!y_const)
90  ops_partials.edge1_.partials_[n] += kappa_sin;
91  if (!mu_const)
92  ops_partials.edge2_.partials_[n] -= kappa_sin;
93  if (!kappa_const)
94  ops_partials.edge3_.partials_[n]
95  += kappa_cos / kappa_dbl[n] - bessel1 / bessel0;
96  }
97  return ops_partials.build(logp);
98 }
99 
100 template <typename T_y, typename T_loc, typename T_scale>
102  T_y const& y, T_loc const& mu, T_scale const& kappa) {
103  return von_mises_lpdf<false>(y, mu, kappa);
104 }
105 
106 } // namespace math
107 } // namespace stan
108 #endif
fvar< T > cos(const fvar< T > &x)
Definition: cos.hpp:12
return_type< T_y, T_loc, T_scale >::type von_mises_lpdf(T_y const &y, T_loc const &mu, T_scale const &kappa)
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...
const double LOG_TWO_PI
Definition: constants.hpp:164
fvar< T > modified_bessel_first_kind(int v, const fvar< T > &z)
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > sin(const fvar< T > &x)
Definition: sin.hpp:11
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > floor(const fvar< T > &x)
Definition: floor.hpp:12
boost::math::tools::promote_args< T1, T2, double >::type log_modified_bessel_first_kind(const T1 v, const T2 z)
double pi()
Return the value of pi.
Definition: constants.hpp:80
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_

     [ Stan Home Page ] © 2011–2018, Stan Development Team.