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hessian.hpp
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1 #ifndef STAN_MATH_MIX_MAT_FUNCTOR_HESSIAN_HPP
2 #define STAN_MATH_MIX_MAT_FUNCTOR_HESSIAN_HPP
3 
4 #include <stan/math/fwd/core.hpp>
6 #include <stan/math/rev/core.hpp>
7 #include <vector>
8 
9 namespace stan {
10 
11  namespace math {
12 
13  using Eigen::Dynamic;
14 
44  template <typename F>
45  void
46  hessian(const F& f,
47  const Eigen::Matrix<double, Dynamic, 1>& x,
48  double& fx,
49  Eigen::Matrix<double, Dynamic, 1>& grad,
50  Eigen::Matrix<double, Dynamic, Dynamic>& H) {
51  H.resize(x.size(), x.size());
52  grad.resize(x.size());
53  try {
54  for (int i = 0; i < x.size(); ++i) {
55  start_nested();
56  Eigen::Matrix<fvar<var>, Dynamic, 1> x_fvar(x.size());
57  for (int j = 0; j < x.size(); ++j)
58  x_fvar(j) = fvar<var>(x(j), i == j);
59  fvar<var> fx_fvar = f(x_fvar);
60  grad(i) = fx_fvar.d_.val();
61  if (i == 0) fx = fx_fvar.val_.val();
62  stan::math::grad(fx_fvar.d_.vi_);
63  for (int j = 0; j < x.size(); ++j)
64  H(i, j) = x_fvar(j).val_.adj();
66  }
67  } catch (const std::exception& e) {
69  throw;
70  }
71  }
72  // time O(N^3); space O(N^2)
73  template <typename T, typename F>
74  void
75  hessian(const F& f,
76  const Eigen::Matrix<T, Dynamic, 1>& x,
77  T& fx,
78  Eigen::Matrix<T, Dynamic, 1>& grad,
79  Eigen::Matrix<T, Dynamic, Dynamic>& H) {
80  H.resize(x.size(), x.size());
81  grad.resize(x.size());
82  Eigen::Matrix<fvar<fvar<T> >, Dynamic, 1> x_fvar(x.size());
83  for (int i = 0; i < x.size(); ++i) {
84  for (int j = i; j < x.size(); ++j) {
85  for (int k = 0; k < x.size(); ++k)
86  x_fvar(k) = fvar<fvar<T> >(fvar<T>(x(k), j == k),
87  fvar<T>(i == k, 0));
88  fvar<fvar<T> > fx_fvar = f(x_fvar);
89  if (j == 0)
90  fx = fx_fvar.val_.val_;
91  if (i == j)
92  grad(i) = fx_fvar.d_.val_;
93  H(i, j) = fx_fvar.d_.d_;
94  H(j, i) = H(i, j);
95  }
96  }
97  }
98 
99  } // namespace math
100 } // namespace stan
101 #endif
static void grad(chainable *vi)
Compute the gradient for all variables starting from the specified root variable implementation.
Definition: grad.hpp:30
vari * vi_
Pointer to the implementation of this variable.
Definition: var.hpp:44
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:95
void hessian(const F &f, const Eigen::Matrix< double, Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Dynamic, 1 > &grad, Eigen::Matrix< double, Dynamic, Dynamic > &H)
Calculate the value, the gradient, and the Hessian, of the specified function at the specified argume...
Definition: hessian.hpp:46
static void recover_memory_nested()
Recover only the memory used for the top nested call.
double val() const
Return the value of this variable.
Definition: var.hpp:234
static void start_nested()
Record the current position so that recover_memory_nested() can find it.

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