Stan Math Library
2.15.0
reverse mode automatic differentiation
stan
math
fwd
scal
fun
falling_factorial.hpp
Go to the documentation of this file.
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#ifndef STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
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#define STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
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#include <
stan/math/fwd/core.hpp
>
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#include <
stan/math/prim/scal/fun/falling_factorial.hpp
>
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#include <boost/math/special_functions/digamma.hpp>
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namespace
stan
{
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namespace
math {
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template
<
typename
T>
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inline
fvar<T>
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falling_factorial
(
const
fvar<T>
& x,
const
fvar<T>
& n) {
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using
boost::math::digamma
;
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T falling_fact(
falling_factorial
(x.
val_
, n.
val_
));
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return
fvar<T>
(falling_fact,
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falling_fact
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* (
digamma
(x.
val_
+ 1) -
digamma
(x.
val_
- n.
val_
+ 1))
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* x.
d_
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+ falling_fact
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*
digamma
(x.
val_
- n.
val_
+ 1) * n.
d_
);
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}
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template
<
typename
T>
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inline
fvar<T>
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falling_factorial
(
const
fvar<T>
& x,
double
n) {
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using
boost::math::digamma
;
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T falling_fact(
falling_factorial
(x.
val_
, n));
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return
fvar<T>
(falling_fact,
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falling_fact
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* (
digamma
(x.
val_
+ 1) -
digamma
(x.
val_
- n + 1))
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* x.
d_
);
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}
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template
<
typename
T>
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inline
fvar<T>
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falling_factorial
(
double
x,
const
fvar<T>
& n) {
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using
boost::math::digamma
;
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T falling_fact(
falling_factorial
(x, n.
val_
));
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return
fvar<T>
(falling_fact,
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falling_fact
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*
digamma
(x - n.
val_
+ 1) * n.
d_
);
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}
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}
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}
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#endif
falling_factorial.hpp
core.hpp
stan::math::fvar::d_
T d_
Definition:
fvar.hpp:16
stan
Definition:
log_sum_exp.hpp:8
stan::math::fvar::val_
T val_
Definition:
fvar.hpp:15
stan::math::falling_factorial
fvar< T > falling_factorial(const fvar< T > &x, const fvar< T > &n)
Definition:
falling_factorial.hpp:14
stan::math::fvar
Definition:
fvar.hpp:14
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition:
digamma.hpp:22
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