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      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 (at) 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         /* Local variables */
     67         Scalar h;
     68         int nfev=0;
     69         const typename InputType::Index n = _x.size();
     70         const Scalar eps = internal::sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
     71         ValueType val1, val2;
     72         InputType x = _x;
     73         // TODO : we should do this only if the size is not already known
     74         val1.resize(Functor::values());
     75         val2.resize(Functor::values());
     76 
     77         // initialization
     78         switch(mode) {
     79             case Forward:
     80                 // compute f(x)
     81                 Functor::operator()(x, val1); nfev++;
     82                 break;
     83             case Central:
     84                 // do nothing
     85                 break;
     86             default:
     87                 assert(false);
     88         };
     89 
     90         // Function Body
     91         for (int j = 0; j < n; ++j) {
     92             h = eps * internal::abs(x[j]);
     93             if (h == 0.) {
     94                 h = eps;
     95             }
     96             switch(mode) {
     97                 case Forward:
     98                     x[j] += h;
     99                     Functor::operator()(x, val2);
    100                     nfev++;
    101                     x[j] = _x[j];
    102                     jac.col(j) = (val2-val1)/h;
    103                     break;
    104                 case Central:
    105                     x[j] += h;
    106                     Functor::operator()(x, val2); nfev++;
    107                     x[j] -= 2*h;
    108                     Functor::operator()(x, val1); nfev++;
    109                     x[j] = _x[j];
    110                     jac.col(j) = (val2-val1)/(2*h);
    111                     break;
    112                 default:
    113                     assert(false);
    114             };
    115         }
    116         return nfev;
    117     }
    118 private:
    119     Scalar epsfcn;
    120 
    121     NumericalDiff& operator=(const NumericalDiff&);
    122 };
    123 
    124 } // end namespace Eigen
    125 
    126 //vim: ai ts=4 sts=4 et sw=4
    127 #endif // EIGEN_NUMERICAL_DIFF_H
    128 
    129