/**
* The normalized incomplete beta function of a, b, and x.
*
* Used to compute the cumulative density function for the beta
* distribution.
*
* @param a Shape parameter a <= 0; a and b can't both be 0
* @param b Shape parameter b <= 0
* @param x Random variate. 0 <= x <= 1
* @throws if constraints are violated or if any argument is NaN
*
* @return The normalized incomplete beta function.
*/
inline double ibeta(double a,
double b,
double x) {
check_not_nan("ibeta", "a", a);
check_not_nan("ibeta", "b", b);
check_not_nan("ibeta", "x", x);
return boost::math::ibeta(a, b, x);
}
inline void check_pos_definite(const char* function, const char* name,
const Eigen::Matrix<T_y, -1, -1>& y) {
check_symmetric(function, name, y);
check_positive_size(function, name, "rows", y.rows());
if (y.rows() == 1 && !(y(0, 0) > CONSTRAINT_TOLERANCE))
domain_error(function, name, "is not positive definite.", "");
Eigen::LDLT<Eigen::MatrixXd> cholesky = value_of_rec(y).ldlt();
if (cholesky.info() != Eigen::Success
|| !cholesky.isPositive()
|| (cholesky.vectorD().array() <= 0.0).any())
domain_error(function, name, "is not positive definite.", "");
check_not_nan(function, name, y);
}
inline std::vector<T> sort_desc(std::vector<T> xs) {
check_not_nan("sort_asc", "container argument", xs);
std::sort(xs.begin(), xs.end(), std::greater<T>());
return xs;
}
typename return_type<T_y, T_loc, T_covar>::type
multi_normal_cholesky_log(const T_y& y,
const T_loc& mu,
const T_covar& L) {
static const char* function("multi_normal_cholesky_log");
typedef typename scalar_type<T_covar>::type T_covar_elem;
typedef typename return_type<T_y, T_loc, T_covar>::type lp_type;
lp_type lp(0.0);
VectorViewMvt<const T_y> y_vec(y);
VectorViewMvt<const T_loc> mu_vec(mu);
size_t size_vec = max_size_mvt(y, mu);
int size_y = y_vec[0].size();
int size_mu = mu_vec[0].size();
if (size_vec > 1) {
int size_y_old = size_y;
int size_y_new;
for (size_t i = 1, size_ = length_mvt(y); i < size_; i++) {
int size_y_new = y_vec[i].size();
check_size_match(function,
"Size of one of the vectors of "
"the random variable", size_y_new,
"Size of another vector of the "
"random variable", size_y_old);
size_y_old = size_y_new;
}
int size_mu_old = size_mu;
int size_mu_new;
for (size_t i = 1, size_ = length_mvt(mu); i < size_; i++) {
int size_mu_new = mu_vec[i].size();
check_size_match(function,
"Size of one of the vectors of "
"the location variable", size_mu_new,
"Size of another vector of the "
"location variable", size_mu_old);
size_mu_old = size_mu_new;
}
(void) size_y_old;
(void) size_y_new;
(void) size_mu_old;
(void) size_mu_new;
}
check_size_match(function,
"Size of random variable", size_y,
"size of location parameter", size_mu);
check_size_match(function,
"Size of random variable", size_y,
"rows of covariance parameter", L.rows());
check_size_match(function,
"Size of random variable", size_y,
"columns of covariance parameter", L.cols());
for (size_t i = 0; i < size_vec; i++) {
check_finite(function, "Location parameter", mu_vec[i]);
check_not_nan(function, "Random variable", y_vec[i]);
}
if (size_y == 0)
return lp;
if (include_summand<propto>::value)
lp += NEG_LOG_SQRT_TWO_PI * size_y * size_vec;
if (include_summand<propto, T_covar_elem>::value)
lp -= L.diagonal().array().log().sum() * size_vec;
if (include_summand<propto, T_y, T_loc, T_covar_elem>::value) {
lp_type sum_lp_vec(0.0);
for (size_t i = 0; i < size_vec; i++) {
Eigen::Matrix<typename return_type<T_y, T_loc>::type,
Eigen::Dynamic, 1> y_minus_mu(size_y);
for (int j = 0; j < size_y; j++)
y_minus_mu(j) = y_vec[i](j)-mu_vec[i](j);
Eigen::Matrix<typename return_type<T_y, T_loc, T_covar>::type,
Eigen::Dynamic, 1>
half(mdivide_left_tri_low(L, y_minus_mu));
// FIXME: this code does not compile. revert after fixing subtract()
// Eigen::Matrix<typename
// boost::math::tools::promote_args<T_covar,
// typename value_type<T_loc>::type,
// typename value_type<T_y>::type>::type>::type,
// Eigen::Dynamic, 1>
// half(mdivide_left_tri_low(L, subtract(y, mu)));
sum_lp_vec += dot_self(half);
}
lp -= 0.5*sum_lp_vec;
}
return lp;
}
inline bool check_not_nan(const char* function,
const T_y& y,
const char* name,
T_result* result = 0) {
return check_not_nan(function,y,name,result,default_policy());
}
inline T2
modified_bessel_first_kind(int v, const T2 z) {
check_not_nan("modified_bessel_first_kind", "z", z);
return boost::math::cyl_bessel_i(v, z);
}
