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log_mix.hpp
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#ifndef STAN_MATH_FWD_SCAL_FUN_LOG_MIX_HPP
#define STAN_MATH_FWD_SCAL_FUN_LOG_MIX_HPP
#include <stan/math/fwd/core.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/log_mix.hpp>
#include <boost/math/tools/promotion.hpp>
#include <cmath>
namespace stan {
namespace math {
using boost::math::tools::promote_args;
using boost::is_same;
/* Returns an array of size N with partials of log_mix wrt to its
* parameters instantiated as fvar<T>
*
* @tparam T_theta theta scalar type
* @tparam T_lambda1 lambda_1 scalar type
* @tparam T_lambda2 lambda_2 scalar type
*
* @param[in] N output array size
* @param[in] theta_d mixing proportion theta
* @param[in] lambda1_d log_density with mixing proportion theta
* @param[in] lambda2_d log_density with mixing proportion 1.0 - theta
* @param[out] partials_array array of partials derivatives
*/
template <typename T_theta, typename T_lambda1, typename T_lambda2, int N>
inline 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]) {
typedef typename promote_args<T_theta, T_lambda1, T_lambda2>::type
partial_return_type;
using std::exp;
typename promote_args<T_lambda1, T_lambda2>::type lam2_m_lam1
= lambda2 - lambda1;
typename promote_args<T_lambda1, T_lambda2>::type exp_lam2_m_lam1
= exp(lam2_m_lam1);
typename promote_args<T_lambda1, T_lambda2>::type one_m_exp_lam2_m_lam1
= 1.0 - exp_lam2_m_lam1;
typename promote_args<double, T_theta>::type one_m_t = 1.0 - theta;
partial_return_type one_m_t_prod_exp_lam2_m_lam1
= one_m_t * exp_lam2_m_lam1;
partial_return_type t_plus_one_m_t_prod_exp_lam2_m_lam1
= theta + one_m_t_prod_exp_lam2_m_lam1;
partial_return_type one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1
= 1.0 / t_plus_one_m_t_prod_exp_lam2_m_lam1;
unsigned int offset = 0;
if (is_same<T_theta, partial_return_type>::value) {
partials_array[offset]
= one_m_exp_lam2_m_lam1
* one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1;
++offset;
}
if (is_same<T_lambda1, partial_return_type>::value) {
partials_array[offset]
= theta * one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1;
++offset;
}
if (is_same<T_lambda2, partial_return_type>::value) {
partials_array[offset]
= one_m_t_prod_exp_lam2_m_lam1
* one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1;
}
}
template <typename T>
inline
fvar<T>
log_mix(const fvar<T>& theta, const fvar<T>& lambda1,
const fvar<T>& lambda2) {
using stan::math::log_mix;
using stan::math::value_of;
if (lambda1.val_ > lambda2.val_) {
fvar<T> partial_deriv_array[3];
log_mix_partial_helper(theta, lambda1, lambda2, partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1.val_, lambda2.val_),
theta.d_ * value_of(partial_deriv_array[0])
+ lambda1.d_ * value_of(partial_deriv_array[1])
+ lambda2.d_ * value_of(partial_deriv_array[2]));
} else {
fvar<T> partial_deriv_array[3];
log_mix_partial_helper(1.0 - theta, lambda2, lambda1,
partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1.val_, lambda2.val_),
-theta.d_ * value_of(partial_deriv_array[0])
+ lambda1.d_ * value_of(partial_deriv_array[2])
+ lambda2.d_ * value_of(partial_deriv_array[1]));
}
}
template <typename T>
inline
fvar<T>
log_mix(const fvar<T>& theta, const fvar<T>& lambda1,
const double lambda2) {
using stan::math::log_mix;
using stan::math::value_of;
if (lambda1.val_ > lambda2) {
fvar<T> partial_deriv_array[2];
log_mix_partial_helper(theta, lambda1, lambda2,
partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1.val_, lambda2),
theta.d_ * value_of(partial_deriv_array[0])
+ lambda1.d_ * value_of(partial_deriv_array[1]));
} else {
fvar<T> partial_deriv_array[2];
log_mix_partial_helper(1.0 - theta, lambda2, lambda1,
partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1.val_, lambda2),
-theta.d_ * value_of(partial_deriv_array[0])
+ lambda1.d_ * value_of(partial_deriv_array[1]));
}
}
template<typename T>
inline
fvar<T>
log_mix(const fvar<T>& theta, const double lambda1,
const fvar<T>& lambda2) {
using stan::math::log_mix;
using stan::math::value_of;
if (lambda1 > lambda2.val_) {
fvar<T> partial_deriv_array[2];
log_mix_partial_helper(theta, lambda1, lambda2,
partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1, lambda2.val_),
theta.d_ * value_of(partial_deriv_array[0])
+ lambda2.d_ * value_of(partial_deriv_array[1]));
} else {
fvar<T> partial_deriv_array[2];
log_mix_partial_helper(1.0 - theta, lambda2, lambda1,
partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1, lambda2.val_),
-theta.d_ * value_of(partial_deriv_array[0])
+ lambda2.d_ * value_of(partial_deriv_array[1]));
}
}
template<typename T>
inline
fvar<T>
log_mix(const double theta, const fvar<T>& lambda1,
const fvar<T>& lambda2) {
using stan::math::log_mix;
using stan::math::value_of;
if (lambda1.val_ > lambda2.val_) {
fvar<T> partial_deriv_array[2];
log_mix_partial_helper(theta, lambda1, lambda2, partial_deriv_array);
return fvar<T>(log_mix(theta, lambda1.val_, lambda2.val_),
lambda1.d_ * value_of(partial_deriv_array[0])
+ lambda2.d_ * value_of(partial_deriv_array[1]));
} else {
fvar<T> partial_deriv_array[2];
log_mix_partial_helper(1.0 - theta, lambda2, lambda1,
partial_deriv_array);
return fvar<T>(log_mix(theta, lambda1.val_, lambda2.val_),
lambda1.d_ * value_of(partial_deriv_array[1])
+ lambda2.d_ * value_of(partial_deriv_array[0]));
}
}
template<typename T>
inline
fvar<T>
log_mix(const fvar<T>& theta, const double lambda1, const double lambda2) {
using stan::math::log_mix;
using stan::math::value_of;
if (lambda1 > lambda2) {
fvar<T> partial_deriv_array[1];
log_mix_partial_helper(theta, lambda1, lambda2, partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1, lambda2),
theta.d_ * value_of(partial_deriv_array[0]));
} else {
fvar<T> partial_deriv_array[1];
log_mix_partial_helper(1.0 - theta, lambda2, lambda1,
partial_deriv_array);
return fvar<T>(log_mix(theta.val_, lambda1, lambda2),
-theta.d_ * value_of(partial_deriv_array[0]));
}
}
template<typename T>
inline
fvar<T>
log_mix(const double theta, const fvar<T>& lambda1, const double lambda2) {
using stan::math::log_mix;
using stan::math::value_of;
if (lambda1.val_ > lambda2) {
fvar<T> partial_deriv_array[1];
log_mix_partial_helper(theta, lambda1, lambda2, partial_deriv_array);
return fvar<T>(log_mix(theta, lambda1.val_, lambda2),
lambda1.d_ * value_of(partial_deriv_array[0]));
} else {
fvar<T> partial_deriv_array[1];
log_mix_partial_helper(1.0 - theta, lambda2, lambda1,
partial_deriv_array);
return fvar<T>(log_mix(theta, lambda1.val_, lambda2),
lambda1.d_ * value_of(partial_deriv_array[0]));
}
}
template<typename T>
inline
fvar<T>
log_mix(const double theta, const double lambda1, const fvar<T>& lambda2) {
using stan::math::log_mix;
using stan::math::value_of;
if (lambda1 > lambda2.val_) {
fvar<T> partial_deriv_array[1];
log_mix_partial_helper(theta, lambda1, lambda2, partial_deriv_array);
return fvar<T>(log_mix(theta, lambda1, lambda2.val_),
lambda2.d_ * value_of(partial_deriv_array[0]));
} else {
fvar<T> partial_deriv_array[1];
log_mix_partial_helper(1.0 - theta, lambda2, lambda1,
partial_deriv_array);
return fvar<T>(log_mix(theta, lambda1, lambda2.val_),
lambda2.d_ * value_of(partial_deriv_array[0]));
}
}
}
}
#endif
core.hpp
stan::math::fvar::d_
T d_
Definition: fvar.hpp:15
stan::math::log_mix_partial_helper
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
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::fvar::val_
T val_
Definition: fvar.hpp:14
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
log_mix.hpp
value_of.hpp
stan::math::log_mix
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
stan::math::fvar
Definition: fvar.hpp:13

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