1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LPMF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LPMF_HPP 21 template <
bool propto,
typename T_n,
typename T_shape,
typename T_inv_scale>
23 const T_n& n,
const T_shape& alpha,
const T_inv_scale&
beta) {
27 static const char*
function =
"neg_binomial_lpmf";
32 T_partials_return logp(0.0);
37 alpha,
"Inverse scale parameter", beta);
51 size_t len_ab =
max_size(alpha, beta);
53 for (
size_t i = 0; i < len_ab; ++i)
57 for (
size_t i = 0; i <
length(beta); ++i)
62 for (
size_t i = 0; i <
length(beta); ++i)
63 log_beta_m_log1p_beta[i] =
log(
value_of(beta_vec[i])) - log1p_beta[i];
66 alpha_times_log_beta_over_1p_beta(len_ab);
67 for (
size_t i = 0; i < len_ab; ++i)
68 alpha_times_log_beta_over_1p_beta[i]
73 digamma_alpha(
length(alpha));
75 for (
size_t i = 0; i <
length(alpha); ++i)
83 for (
size_t i = 0; i <
length(beta); ++i)
89 lambda_m_alpha_over_1p_beta(len_ab);
91 for (
size_t i = 0; i < len_ab; ++i)
92 lambda_m_alpha_over_1p_beta[i]
97 for (
size_t i = 0; i <
size; i++) {
98 if (alpha_vec[i] > 1e10) {
100 logp -=
lgamma(n_vec[i] + 1.0);
105 ops_partials.
edge1_.partials_[i]
108 ops_partials.
edge2_.partials_[i]
109 += (lambda[i] - n_vec[i]) /
value_of(beta_vec[i]);
114 n_vec[i] +
value_of(alpha_vec[i]) - 1.0, n_vec[i]);
116 logp += alpha_times_log_beta_over_1p_beta[i] - n_vec[i] * log1p_beta[i];
119 ops_partials.
edge1_.partials_[i]
121 + log_beta_m_log1p_beta[i];
123 ops_partials.
edge2_.partials_[i]
124 += lambda_m_alpha_over_1p_beta[i]
125 - n_vec[i] / (
value_of(beta_vec[i]) + 1.0);
128 return ops_partials.
build(logp);
131 template <
typename T_n,
typename T_shape,
typename T_inv_scale>
133 const T_n& n,
const T_shape& alpha,
const T_inv_scale&
beta) {
134 return neg_binomial_lpmf<false>(n, alpha,
beta);
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
fvar< T > log(const fvar< T > &x)
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.
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
return_type< T_shape, T_inv_scale >::type neg_binomial_lpmf(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
size_t max_size(const T1 &x1, const T2 &x2)
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
fvar< T > log1p(const fvar< T > &x)
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, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.