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finite_diff_grad_hessian.hpp
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1 #ifndef STAN_MATH_MIX_MAT_FUNCTOR_FINITE_DIFF_GRAD_HESSIAN_HPP
2 #define STAN_MATH_MIX_MAT_FUNCTOR_FINITE_DIFF_GRAD_HESSIAN_HPP
3
4 #include <stan/math/prim/mat/fun/Eigen.hpp>
5 #include <stan/math/rev/core.hpp>
6 #include <stan/math/mix/mat/functor/hessian.hpp>
7 #include <vector>
8
9 namespace stan {
10 namespace math {
11
40 template <typename F>
41 void
42 finite_diff_grad_hessian(const F& f,
43 const Eigen::Matrix<double, -1, 1>& x,
44 double& fx,
45 Eigen::Matrix<double, -1, -1>& hess,
46 std::vector<Eigen::Matrix<double, -1, -1> >&
47 grad_hess_fx,
48 const double epsilon = 1e-04) {
49 using Eigen::Matrix;
50 using Eigen::Dynamic;
51
52 int d = x.size();
53 double dummy_fx_eval;
54
55 Matrix<double, Dynamic, 1> x_temp(x);
56 Matrix<double, Dynamic, 1> grad_auto(d);
57 Matrix<double, Dynamic, Dynamic> hess_auto(d, d);
58 Matrix<double, Dynamic, Dynamic> hess_diff(d, d);
59
60 hessian(f, x, fx, grad_auto, hess);
61 for (int i = 0; i < d; ++i) {
62 hess_diff.setZero();
63
64 x_temp(i) = x(i) + 2.0 * epsilon;
65 hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
66 hess_diff = -hess_auto;
67
68 x_temp(i) = x(i) + -2.0 * epsilon;
69 hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
70 hess_diff += hess_auto;
71
72 x_temp(i) = x(i) + epsilon;
73 hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
74 hess_diff += 8.0 * hess_auto;
75
76 x_temp(i) = x(i) + -epsilon;
77 hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
78 hess_diff -= 8.0 * hess_auto;
79
80 x_temp(i) = x(i);
81 hess_diff /= 12.0 * epsilon;
82
83 grad_hess_fx.push_back(hess_diff);
84 }
85 fx = f(x);
86 }
87
88 }
89 }
90 #endif
stan::math::hessian
void hessian(const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Eigen::Dynamic, 1 > &grad, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &H)
Calculate the value, the gradient, and the Hessian, of the specified function at the specified argume...
Definition: hessian.hpp:44
core.hpp
stan
Definition: log_sum_exp.hpp:8
stan::math::finite_diff_grad_hessian
void finite_diff_grad_hessian(const F &f, const Eigen::Matrix< double,-1, 1 > &x, double &fx, Eigen::Matrix< double,-1,-1 > &hess, std::vector< Eigen::Matrix< double,-1,-1 > > &grad_hess_fx, const double epsilon=1e-04)
Calculate the value and the gradient of the hessian of the specified function at the specified argume...
Definition: finite_diff_grad_hessian.hpp:42
hessian.hpp
Eigen.hpp
stan::math::e
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:94

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