| Stan Math Library 2.11.0 reverse mode automatic differentiation

- Main Page
- Modules
- Namespaces
- Classes
- Files

- File List
- File Members

grad_inc_beta.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_REV_SCAL_FUN_GRAD_INC_BETA_HPP
2 #define STAN_MATH_REV_SCAL_FUN_GRAD_INC_BETA_HPP
3
4 #include <stan/math/prim/scal/fun/grad_2F1.hpp>
5 #include <stan/math/rev/core.hpp>
6 #include <stan/math/rev/scal/fun/exp.hpp>
7 #include <stan/math/rev/scal/fun/fabs.hpp>
8 #include <stan/math/prim/scal/fun/lbeta.hpp>
9 #include <stan/math/rev/scal/fun/lgamma.hpp>
10 #include <stan/math/rev/scal/fun/log.hpp>
11 #include <stan/math/rev/scal/fun/log1m.hpp>
12 #include <stan/math/rev/scal/fun/value_of.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/rev/scal/fun/inc_beta.hpp>
15 #include <cmath>
16
17 namespace stan {
18 namespace math {
19
20 // Gradient of the incomplete beta function beta(a, b, z)
21 // with respect to the first two arguments, using the
22 // equivalence to a hypergeometric function.
23 // See http://dlmf.nist.gov/8.17#ii
24 inline void grad_inc_beta(var& g1, var& g2,
25 const var& a, const var& b, const var& z) {
26 var c1 = log(z);
27 var c2 = log1m(z);
28 var c3 = exp(lbeta(a, b)) * inc_beta(a, b, z);
29 var C = exp(a * c1 + b * c2) / a;
30 var dF1 = 0;
31 var dF2 = 0;
32 if (value_of(value_of(C)))
33 grad_2F1(dF1, dF2, a + b, var(1.0), a + 1, z);
34 g1 = (c1 - 1.0 / a) * c3 + C * (dF1 + dF2);
35 g2 = c2 * c3 + C * dF1;
36 }
37
38 }
39 }
40 #endif
core.hpp
exp.hpp
stan
Definition: log_sum_exp.hpp:8
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::lbeta
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::math::var
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:31
stan::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
inc_beta.hpp
stan::math::grad_inc_beta
void grad_inc_beta(stan::math::fvar< T > &g1, stan::math::fvar< T > &g2, stan::math::fvar< T > a, stan::math::fvar< T > b, stan::math::fvar< T > z)
Definition: grad_inc_beta.hpp:24
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
log.hpp
lgamma.hpp
grad_2F1.hpp
log1m.hpp
fabs.hpp
lbeta.hpp
value_of.hpp
value_of.hpp
stan::math::log1m
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16
stan::math::grad_2F1
void grad_2F1(T &gradA, T &gradC, T a, T b, T c, T z, T precision=1e-6)
Definition: grad_2F1.hpp:13

[ Stan Home Page ] © 2011–2016, Stan Development Team.