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von_mises_rng.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_VON_MISES_RNG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_VON_MISES_RNG_HPP
3
4 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
5 #include <stan/math/prim/scal/err/check_finite.hpp>
6 #include <stan/math/prim/scal/err/check_greater.hpp>
7 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
8 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
9 #include <stan/math/prim/scal/fun/modified_bessel_first_kind.hpp>
10 #include <stan/math/prim/scal/fun/constants.hpp>
11 #include <stan/math/prim/scal/prob/uniform_rng.hpp>
12 #include <stan/math/prim/scal/meta/include_summand.hpp>
13 #include <cmath>
14
15 namespace stan {
16
17 namespace math {
18
19 // The algorithm used in von_mises_rng is a modified version of the
20 // algorithm in:
21 //
22 // Efficient Simulation of the von Mises Distribution
23 // D. J. Best and N. I. Fisher
24 // Journal of the Royal Statistical Society. Series C (Applied Statistics),
25 // Vol. 28, No. 2 (1979), pp. 152-157
26 //
27 // See licenses/stan-license.txt for Stan license.
28
29 template <class RNG>
30 inline double
31 von_mises_rng(const double mu,
32 const double kappa,
33 RNG& rng) {
34 using boost::variate_generator;
35 using stan::math::uniform_rng;
36 using std::fmod;
37 using std::log;
38 using std::pow;
39
40 static const char* function("stan::math::von_mises_rng");
41
42 stan::math::check_finite(function, "mean", mu);
43 stan::math::check_positive_finite(function, "inverse of variance", kappa);
44
45 double r = 1 + pow((1 + 4 * kappa * kappa), 0.5);
46 double rho = 0.5 * (r - pow(2 * r, 0.5)) / kappa;
47 double s = 0.5 * (1 + rho * rho) / rho;
48
49 bool done = 0;
50 double W;
51 while (!done) {
52 double Z = std::cos(stan::math::pi() * uniform_rng(0.0, 1.0, rng));
53 W = (1 + s * Z) / (s + Z);
54 double Y = kappa * (s - W);
55 double U2 = uniform_rng(0.0, 1.0, rng);
56 done = Y * (2 - Y) - U2 > 0;
57
58 if (!done)
59 done = log(Y / U2) + 1 - Y >= 0;
60 }
61
62 double U3 = uniform_rng(0.0, 1.0, rng) - 0.5;
63 double sign = ((U3 >= 0) - (U3 <= 0));
64
65 // it's really an fmod() with a positivity constraint
66 return sign * std::acos(W)
67 + fmod(fmod(mu, 2*stan::math::pi())+2*stan::math::pi(),
68 2*stan::math::pi());
69 }
70
71 }
72 }
73 #endif
stan::math::cos
fvar< T > cos(const fvar< T > &x)
Definition: cos.hpp:13
check_positive_finite.hpp
stan
Definition: log_sum_exp.hpp:8
stan::math::sign
int sign(const T &z)
Definition: sign.hpp:9
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
modified_bessel_first_kind.hpp
stan::math::fmod
fvar< T > fmod(const fvar< T > &x1, const fvar< T > &x2)
Definition: fmod.hpp:16
include_summand.hpp
check_greater.hpp
uniform_rng.hpp
check_nonnegative.hpp
stan::math::von_mises_rng
double von_mises_rng(const double mu, const double kappa, RNG &rng)
Definition: von_mises_rng.hpp:31
stan::math::uniform_rng
double uniform_rng(const double alpha, const double beta, RNG &rng)
Definition: uniform_rng.hpp:21
stan::math::acos
fvar< T > acos(const fvar< T > &x)
Definition: acos.hpp:14
stan::math::check_finite
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
Definition: check_finite.hpp:62
constants.hpp
check_finite.hpp
stan::math::pi
double pi()
Return the value of pi.
Definition: constants.hpp:86
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28

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