Stan Math Library  2.10.0
reverse mode automatic differentiation
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 
5 #include <stan/math/rev/core.hpp>
7 #include <vector>
8 
9 namespace stan {
10 
11  namespace math {
12 
41  template <typename F>
42  void
44  const Eigen::Matrix<double, -1, 1>& x,
45  double& fx,
46  Eigen::Matrix<double, -1, -1>& hess,
47  std::vector<Eigen::Matrix<double, -1, -1> >&
48  grad_hess_fx,
49  const double epsilon = 1e-04) {
50  using Eigen::Matrix;
51  using Eigen::Dynamic;
52 
53  int d = x.size();
54  double dummy_fx_eval;
55 
56  Matrix<double, Dynamic, 1> x_temp(x);
57  Matrix<double, Dynamic, 1> grad_auto(d);
58  Matrix<double, Dynamic, Dynamic> hess_auto(d, d);
59  Matrix<double, Dynamic, Dynamic> hess_diff(d, d);
60 
61  hessian(f, x, fx, grad_auto, hess);
62  for (int i = 0; i < d; ++i) {
63  hess_diff.setZero();
64 
65  x_temp(i) = x(i) + 2.0 * epsilon;
66  hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
67  hess_diff = -hess_auto;
68 
69  x_temp(i) = x(i) + -2.0 * epsilon;
70  hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
71  hess_diff += hess_auto;
72 
73  x_temp(i) = x(i) + epsilon;
74  hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
75  hess_diff += 8.0 * hess_auto;
76 
77  x_temp(i) = x(i) + -epsilon;
78  hessian(f, x_temp, dummy_fx_eval, grad_auto, hess_auto);
79  hess_diff -= 8.0 * hess_auto;
80 
81  x_temp(i) = x(i);
82  hess_diff /= 12.0 * epsilon;
83 
84  grad_hess_fx.push_back(hess_diff);
85  }
86  fx = f(x);
87  }
88 
89  }
90 }
91 #endif
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:45
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...
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:95

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