1 #ifndef STAN_MATH_PRIM_SCAL_FUN_GRAD_REG_INC_GAMMA_HPP 2 #define STAN_MATH_PRIM_SCAL_FUN_GRAD_REG_INC_GAMMA_HPP 48 template <
typename T1,
typename T2>
50 double precision = 1
e-6,
51 int max_steps = 1e5) {
58 return std::numeric_limits<TP>::quiet_NaN();
61 if (z >= a && z >= 8) {
64 T1 a_minus_one_minus_k = a - 1;
65 T1 fac = a_minus_one_minus_k;
68 TP delta = dfac / zpow;
70 for (
int k = 1; k < 10; ++k) {
71 a_minus_one_minus_k -= 1;
76 dfac = a_minus_one_minus_k * dfac + fac;
77 fac *= a_minus_one_minus_k;
81 domain_error(
"grad_reg_inc_gamma",
"is not converging",
"",
"");
84 return gamma_q(a, z) * (l - dig) +
exp(-z + (a - 1) * l) * S / g;
92 for (
int k = 1; k <= max_steps; ++k) {
93 S += s_sign >= 0.0 ?
exp(log_delta) : -
exp(log_delta);
94 log_s += log_z -
log(k);
98 domain_error(
"grad_reg_inc_gamma",
"is not converging",
"",
"");
99 if (log_delta <=
log(precision))
100 return gamma_p(a, z) * (dig - l) +
exp(a * l) * S / g;
102 domain_error(
"grad_reg_inc_gamma",
"k (internal counter)", max_steps,
104 " iterations, gamma function gradient did not converge.");
fvar< T > fabs(const fvar< T > &x)
fvar< T > log(const fvar< T > &x)
bool is_any_nan(const T &x)
Returns true if the input is NaN and false otherwise.
return_type< T1, T2 >::type grad_reg_inc_gamma(T1 a, T2 z, T1 g, T1 dig, double precision=1e-6, int max_steps=1e5)
Gradient of the regularized incomplete gamma functions igamma(a, z)
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
fvar< T > exp(const fvar< T > &x)
void domain_error(const char *function, const char *name, const T &y, const char *msg1, const char *msg2)
Throw a domain error with a consistently formatted message.
int is_inf(const fvar< T > &x)
Returns 1 if the input's value is infinite and 0 otherwise.
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
double e()
Return the base of the natural logarithm.
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
const double INFTY
Positive infinity.
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)