Stan Math Library  2.10.0
reverse mode automatic differentiation
finite_diff_hessian.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_FUNCTOR_FINITE_DIFF_HESSIAN_HPP
2 #define STAN_MATH_PRIM_MAT_FUNCTOR_FINITE_DIFF_HESSIAN_HPP
3 
6 
7 namespace stan {
8 
9  namespace math {
10 
11  template <typename F>
12  double
14  const Eigen::Matrix<double, Eigen::Dynamic, 1>& x,
15  const int lambda,
16  const double epsilon = 1e-03) {
17  using Eigen::Matrix;
18  using Eigen::Dynamic;
19 
20  Matrix<double, Dynamic, 1> x_temp(x);
21 
22  double grad = 0.0;
23  x_temp(lambda) = x(lambda) + 2.0 * epsilon;
24  grad = -f(x_temp);
25 
26  x_temp(lambda) = x(lambda) + -2.0 * epsilon;
27  grad += f(x_temp);
28 
29  x_temp(lambda) = x(lambda) + epsilon;
30  grad += 8.0 * f(x_temp);
31 
32  x_temp(lambda) = x(lambda) + -epsilon;
33  grad -= 8.0 * f(x_temp);
34 
35  return grad;
36  }
37 
65  template <typename F>
66  void
67  finite_diff_hessian(const F& f,
68  const Eigen::Matrix<double, -1, 1>& x,
69  double& fx,
70  Eigen::Matrix<double, -1, 1>& grad_fx,
71  Eigen::Matrix<double, -1, -1>& hess_fx,
72  const double epsilon = 1e-03) {
73  using Eigen::Matrix;
74  using Eigen::Dynamic;
75 
76  int d = x.size();
77 
78  Matrix<double, Dynamic, 1> x_temp(x);
79  hess_fx.resize(d, d);
80 
81  finite_diff_gradient(f, x, fx, grad_fx);
82  double f_diff(0.0);
83  for (int i = 0; i < d; ++i) {
84  for (int j = i; j < d; ++j) {
85  x_temp(i) += 2.0 * epsilon;
86  if (i != j) {
87  f_diff = -finite_diff_hess_helper(f, x_temp, j);
88  x_temp(i) = x(i) + -2.0 * epsilon;
89  f_diff += finite_diff_hess_helper(f, x_temp, j);
90  x_temp(i) = x(i) + epsilon;
91  f_diff += 8.0 * finite_diff_hess_helper(f, x_temp, j);
92  x_temp(i) = x(i) + -epsilon;
93  f_diff -= 8.0 * finite_diff_hess_helper(f, x_temp, j);
94  f_diff /= 12.0 * epsilon * 12.0 * epsilon;
95  } else {
96  f_diff = -f(x_temp);
97  f_diff -= 30 * fx;
98  x_temp(i) = x(i) + -2.0 * epsilon;
99  f_diff -= f(x_temp);
100  x_temp(i) = x(i) + epsilon;
101  f_diff += 16.0 * f(x_temp);
102  x_temp(i) = x(i) - epsilon;
103  f_diff += 16.0 * f(x_temp);
104  f_diff /= 12 * epsilon * epsilon;
105  }
106 
107  x_temp(i) = x(i);
108 
109  hess_fx(j, i) = f_diff;
110  hess_fx(i, j) = hess_fx(j, i);
111  }
112  }
113  }
114  }
115 }
116 #endif
static void grad(vari *vi)
Compute the gradient for all variables starting from the specified root variable implementation.
Definition: grad.hpp:30
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:95
void finite_diff_gradient(const F &f, const Eigen::Matrix< double,-1, 1 > &x, double &fx, Eigen::Matrix< double,-1, 1 > &grad_fx, const double epsilon=1e-03)
Calculate the value and the gradient of the specified function at the specified argument using finite...
void finite_diff_hessian(const F &f, const Eigen::Matrix< double,-1, 1 > &x, double &fx, Eigen::Matrix< double,-1, 1 > &grad_fx, Eigen::Matrix< double,-1,-1 > &hess_fx, const double epsilon=1e-03)
Calculate the value and the Hessian of the specified function at the specified argument using second-...
double finite_diff_hess_helper(const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, const int lambda, const double epsilon=1e-03)

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