Stan Math Library  2.14.0
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  namespace math {
9 
10  template <typename F>
11  double
13  const Eigen::Matrix<double, Eigen::Dynamic, 1>& x,
14  int lambda,
15  double epsilon = 1e-03) {
16  using Eigen::Matrix;
17  using Eigen::Dynamic;
18 
19  Matrix<double, Dynamic, 1> x_temp(x);
20 
21  double grad = 0.0;
22  x_temp(lambda) = x(lambda) + 2.0 * epsilon;
23  grad = -f(x_temp);
24 
25  x_temp(lambda) = x(lambda) + -2.0 * epsilon;
26  grad += f(x_temp);
27 
28  x_temp(lambda) = x(lambda) + epsilon;
29  grad += 8.0 * f(x_temp);
30 
31  x_temp(lambda) = x(lambda) + -epsilon;
32  grad -= 8.0 * f(x_temp);
33 
34  return grad;
35  }
36 
64  template <typename F>
65  void
66  finite_diff_hessian(const F& f,
67  const Eigen::Matrix<double, -1, 1>& x,
68  double& fx,
69  Eigen::Matrix<double, -1, 1>& grad_fx,
70  Eigen::Matrix<double, -1, -1>& hess_fx,
71  double epsilon = 1e-03) {
72  using Eigen::Matrix;
73  using Eigen::Dynamic;
74 
75  int d = x.size();
76 
77  Matrix<double, Dynamic, 1> x_temp(x);
78  hess_fx.resize(d, d);
79 
80  finite_diff_gradient(f, x, fx, grad_fx);
81  double f_diff(0.0);
82  for (int i = 0; i < d; ++i) {
83  for (int j = i; j < d; ++j) {
84  x_temp(i) += 2.0 * epsilon;
85  if (i != j) {
86  f_diff = -finite_diff_hess_helper(f, x_temp, j);
87  x_temp(i) = x(i) + -2.0 * epsilon;
88  f_diff += finite_diff_hess_helper(f, x_temp, j);
89  x_temp(i) = x(i) + epsilon;
90  f_diff += 8.0 * finite_diff_hess_helper(f, x_temp, j);
91  x_temp(i) = x(i) + -epsilon;
92  f_diff -= 8.0 * finite_diff_hess_helper(f, x_temp, j);
93  f_diff /= 12.0 * epsilon * 12.0 * epsilon;
94  } else {
95  f_diff = -f(x_temp);
96  f_diff -= 30 * fx;
97  x_temp(i) = x(i) + -2.0 * epsilon;
98  f_diff -= f(x_temp);
99  x_temp(i) = x(i) + epsilon;
100  f_diff += 16.0 * f(x_temp);
101  x_temp(i) = x(i) - epsilon;
102  f_diff += 16.0 * f(x_temp);
103  f_diff /= 12 * epsilon * epsilon;
104  }
105 
106  x_temp(i) = x(i);
107 
108  hess_fx(j, i) = f_diff;
109  hess_fx(i, j) = hess_fx(j, i);
110  }
111  }
112  }
113  }
114 }
115 #endif
static void grad(vari *vi)
Compute the gradient for all variables starting from the specified root variable implementation.
Definition: grad.hpp:30
double finite_diff_hess_helper(const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, int lambda, double epsilon=1e-03)
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, double epsilon=1e-03)
Calculate the value and the Hessian of the specified function at the specified argument using second-...
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:94
void finite_diff_gradient(const F &f, const Eigen::Matrix< double, -1, 1 > &x, double &fx, Eigen::Matrix< double, -1, 1 > &grad_fx, double epsilon=1e-03)
Calculate the value and the gradient of the specified function at the specified argument using finite...

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