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log_mix.hpp
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1 #ifndef STAN_MATH_REV_SCAL_FUN_LOG_MIX_HPP
2 #define STAN_MATH_REV_SCAL_FUN_LOG_MIX_HPP
3 
12 #include <cmath>
13 
14 namespace stan {
15 
16  namespace math {
17 
18  /* Computes shared terms in log_mix partial derivative calculations
19  *
20  * @param[in] theta_val value of mixing proportion theta.
21  * @param[in] lambda1_val value of log density multiplied by theta.
22  * @param[in] lambda2_val value of log density multiplied by 1 - theta.
23  * @param[out] one_m_exp_lam2_m_lam1 shared term in deriv calculation.
24  * @param[out] one_m_t_prod_exp_lam2_m_lam1 shared term in deriv calculation.
25  * @param[out] one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1 shared term in deriv calculation.
26  */
27  inline void
28  log_mix_partial_helper(const double& theta_val,
29  const double& lambda1_val,
30  const double& lambda2_val,
31  double& one_m_exp_lam2_m_lam1,
32  double& one_m_t_prod_exp_lam2_m_lam1,
33  double& one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1) {
34  using std::exp;
35  double lam2_m_lam1 = lambda2_val - lambda1_val;
36  double exp_lam2_m_lam1 = exp(lam2_m_lam1);
37  one_m_exp_lam2_m_lam1 = 1 - exp_lam2_m_lam1;
38  double one_m_t = 1 - theta_val;
39  one_m_t_prod_exp_lam2_m_lam1 = one_m_t * exp_lam2_m_lam1;
40  one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1
41  = 1 / (theta_val + one_m_t_prod_exp_lam2_m_lam1);
42  }
43 
83  template <typename T_theta,
84  typename T_lambda1,
85  typename T_lambda2>
86  inline
88  log_mix(const T_theta& theta,
89  const T_lambda1& lambda1,
90  const T_lambda2& lambda2) {
91  using std::log;
92  using stan::math::log_mix;
93  using stan::math::log1m;
95 
97  operands_and_partials(theta, lambda1, lambda2);
98 
99  double theta_double = value_of(theta);
100  const double lambda1_double = value_of(lambda1);
101  const double lambda2_double = value_of(lambda2);
102 
103  double log_mix_function_value
104  = log_mix(theta_double, lambda1_double, lambda2_double);
105 
106  double one_m_exp_lam2_m_lam1(0.0);
107  double one_m_t_prod_exp_lam2_m_lam1(0.0);
108  double one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1(0.0);
109 
110  if (lambda1 > lambda2) {
111  log_mix_partial_helper(theta_double,
112  lambda1_double,
113  lambda2_double,
114  one_m_exp_lam2_m_lam1,
115  one_m_t_prod_exp_lam2_m_lam1,
116  one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1);
117  } else {
118  log_mix_partial_helper(1.0 - theta_double,
119  lambda2_double,
120  lambda1_double,
121  one_m_exp_lam2_m_lam1,
122  one_m_t_prod_exp_lam2_m_lam1,
123  one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1);
124  one_m_exp_lam2_m_lam1 = -one_m_exp_lam2_m_lam1;
125  theta_double = one_m_t_prod_exp_lam2_m_lam1;
126  one_m_t_prod_exp_lam2_m_lam1 = 1.0 - value_of(theta);
127  }
128 
130  operands_and_partials.d_x1[0]
131  = one_m_exp_lam2_m_lam1
132  * one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1;
134  operands_and_partials.d_x2[0]
135  = theta_double
136  * one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1;
138  operands_and_partials.d_x3[0]
139  = one_m_t_prod_exp_lam2_m_lam1
140  * one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1;
141 
142  return operands_and_partials.to_var(log_mix_function_value);
143  }
144 
145  } // namespace math
146 
147 } // namespace stan
148 
149 #endif
void log_mix_partial_helper(const T_theta &theta, const T_lambda1 &lambda1, const T_lambda2 &lambda2, typename promote_args< T_theta, T_lambda1, T_lambda2 >::type(&partials_array)[N])
Definition: log_mix.hpp:31
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
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)
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
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...
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
A variable implementation that stores operands and derivatives with respect to the variable...
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > log_mix(const fvar< T > &theta, const fvar< T > &lambda1, const fvar< T > &lambda2)
Return the log mixture density with specified mixing proportion and log densities and its derivative ...
Definition: log_mix.hpp:116
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16

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