1 | // -*- coding: utf-8
|
---|
2 | // vim: set fileencoding=utf-8
|
---|
3 |
|
---|
4 | // This file is part of Eigen, a lightweight C++ template library
|
---|
5 | // for linear algebra.
|
---|
6 | //
|
---|
7 | // Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
|
---|
8 | //
|
---|
9 | // This Source Code Form is subject to the terms of the Mozilla
|
---|
10 | // Public License v. 2.0. If a copy of the MPL was not distributed
|
---|
11 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
---|
12 |
|
---|
13 | #ifndef EIGEN_NUMERICAL_DIFF_H
|
---|
14 | #define EIGEN_NUMERICAL_DIFF_H
|
---|
15 |
|
---|
16 | namespace Eigen {
|
---|
17 |
|
---|
18 | enum NumericalDiffMode {
|
---|
19 | Forward,
|
---|
20 | Central
|
---|
21 | };
|
---|
22 |
|
---|
23 |
|
---|
24 | /**
|
---|
25 | * This class allows you to add a method df() to your functor, which will
|
---|
26 | * use numerical differentiation to compute an approximate of the
|
---|
27 | * derivative for the functor. Of course, if you have an analytical form
|
---|
28 | * for the derivative, you should rather implement df() by yourself.
|
---|
29 | *
|
---|
30 | * More information on
|
---|
31 | * http://en.wikipedia.org/wiki/Numerical_differentiation
|
---|
32 | *
|
---|
33 | * Currently only "Forward" and "Central" scheme are implemented.
|
---|
34 | */
|
---|
35 | template<typename _Functor, NumericalDiffMode mode=Forward>
|
---|
36 | class NumericalDiff : public _Functor
|
---|
37 | {
|
---|
38 | public:
|
---|
39 | typedef _Functor Functor;
|
---|
40 | typedef typename Functor::Scalar Scalar;
|
---|
41 | typedef typename Functor::InputType InputType;
|
---|
42 | typedef typename Functor::ValueType ValueType;
|
---|
43 | typedef typename Functor::JacobianType JacobianType;
|
---|
44 |
|
---|
45 | NumericalDiff(Scalar _epsfcn=0.) : Functor(), epsfcn(_epsfcn) {}
|
---|
46 | NumericalDiff(const Functor& f, Scalar _epsfcn=0.) : Functor(f), epsfcn(_epsfcn) {}
|
---|
47 |
|
---|
48 | // forward constructors
|
---|
49 | template<typename T0>
|
---|
50 | NumericalDiff(const T0& a0) : Functor(a0), epsfcn(0) {}
|
---|
51 | template<typename T0, typename T1>
|
---|
52 | NumericalDiff(const T0& a0, const T1& a1) : Functor(a0, a1), epsfcn(0) {}
|
---|
53 | template<typename T0, typename T1, typename T2>
|
---|
54 | NumericalDiff(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2), epsfcn(0) {}
|
---|
55 |
|
---|
56 | enum {
|
---|
57 | InputsAtCompileTime = Functor::InputsAtCompileTime,
|
---|
58 | ValuesAtCompileTime = Functor::ValuesAtCompileTime
|
---|
59 | };
|
---|
60 |
|
---|
61 | /**
|
---|
62 | * return the number of evaluation of functor
|
---|
63 | */
|
---|
64 | int df(const InputType& _x, JacobianType &jac) const
|
---|
65 | {
|
---|
66 | using std::sqrt;
|
---|
67 | using std::abs;
|
---|
68 | /* Local variables */
|
---|
69 | Scalar h;
|
---|
70 | int nfev=0;
|
---|
71 | const typename InputType::Index n = _x.size();
|
---|
72 | const Scalar eps = sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
|
---|
73 | ValueType val1, val2;
|
---|
74 | InputType x = _x;
|
---|
75 | // TODO : we should do this only if the size is not already known
|
---|
76 | val1.resize(Functor::values());
|
---|
77 | val2.resize(Functor::values());
|
---|
78 |
|
---|
79 | // initialization
|
---|
80 | switch(mode) {
|
---|
81 | case Forward:
|
---|
82 | // compute f(x)
|
---|
83 | Functor::operator()(x, val1); nfev++;
|
---|
84 | break;
|
---|
85 | case Central:
|
---|
86 | // do nothing
|
---|
87 | break;
|
---|
88 | default:
|
---|
89 | eigen_assert(false);
|
---|
90 | };
|
---|
91 |
|
---|
92 | // Function Body
|
---|
93 | for (int j = 0; j < n; ++j) {
|
---|
94 | h = eps * abs(x[j]);
|
---|
95 | if (h == 0.) {
|
---|
96 | h = eps;
|
---|
97 | }
|
---|
98 | switch(mode) {
|
---|
99 | case Forward:
|
---|
100 | x[j] += h;
|
---|
101 | Functor::operator()(x, val2);
|
---|
102 | nfev++;
|
---|
103 | x[j] = _x[j];
|
---|
104 | jac.col(j) = (val2-val1)/h;
|
---|
105 | break;
|
---|
106 | case Central:
|
---|
107 | x[j] += h;
|
---|
108 | Functor::operator()(x, val2); nfev++;
|
---|
109 | x[j] -= 2*h;
|
---|
110 | Functor::operator()(x, val1); nfev++;
|
---|
111 | x[j] = _x[j];
|
---|
112 | jac.col(j) = (val2-val1)/(2*h);
|
---|
113 | break;
|
---|
114 | default:
|
---|
115 | eigen_assert(false);
|
---|
116 | };
|
---|
117 | }
|
---|
118 | return nfev;
|
---|
119 | }
|
---|
120 | private:
|
---|
121 | Scalar epsfcn;
|
---|
122 |
|
---|
123 | NumericalDiff& operator=(const NumericalDiff&);
|
---|
124 | };
|
---|
125 |
|
---|
126 | } // end namespace Eigen
|
---|
127 |
|
---|
128 | //vim: ai ts=4 sts=4 et sw=4
|
---|
129 | #endif // EIGEN_NUMERICAL_DIFF_H
|
---|
130 |
|
---|