[136] | 1 | // -*- coding: utf-8
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| 2 | // vim: set fileencoding=utf-8
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| 3 |
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| 4 | // This file is part of Eigen, a lightweight C++ template library
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| 5 | // for linear algebra.
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| 6 | //
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| 7 | // Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
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| 8 | //
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| 9 | // This Source Code Form is subject to the terms of the Mozilla
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| 10 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 11 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 12 |
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| 13 | #ifndef EIGEN_NUMERICAL_DIFF_H
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| 14 | #define EIGEN_NUMERICAL_DIFF_H
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| 15 |
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| 16 | namespace Eigen {
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| 17 |
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| 18 | enum NumericalDiffMode {
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| 19 | Forward,
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| 20 | Central
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| 21 | };
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| 22 |
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| 23 |
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| 24 | /**
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| 25 | * This class allows you to add a method df() to your functor, which will
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| 26 | * use numerical differentiation to compute an approximate of the
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| 27 | * derivative for the functor. Of course, if you have an analytical form
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| 28 | * for the derivative, you should rather implement df() by yourself.
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| 29 | *
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| 30 | * More information on
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| 31 | * http://en.wikipedia.org/wiki/Numerical_differentiation
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| 32 | *
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| 33 | * Currently only "Forward" and "Central" scheme are implemented.
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| 34 | */
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| 35 | template<typename _Functor, NumericalDiffMode mode=Forward>
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| 36 | class NumericalDiff : public _Functor
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| 37 | {
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| 38 | public:
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| 39 | typedef _Functor Functor;
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| 40 | typedef typename Functor::Scalar Scalar;
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| 41 | typedef typename Functor::InputType InputType;
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| 42 | typedef typename Functor::ValueType ValueType;
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| 43 | typedef typename Functor::JacobianType JacobianType;
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| 44 |
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| 45 | NumericalDiff(Scalar _epsfcn=0.) : Functor(), epsfcn(_epsfcn) {}
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| 46 | NumericalDiff(const Functor& f, Scalar _epsfcn=0.) : Functor(f), epsfcn(_epsfcn) {}
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| 47 |
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| 48 | // forward constructors
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| 49 | template<typename T0>
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| 50 | NumericalDiff(const T0& a0) : Functor(a0), epsfcn(0) {}
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| 51 | template<typename T0, typename T1>
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| 52 | NumericalDiff(const T0& a0, const T1& a1) : Functor(a0, a1), epsfcn(0) {}
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| 53 | template<typename T0, typename T1, typename T2>
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| 54 | NumericalDiff(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2), epsfcn(0) {}
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| 55 |
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| 56 | enum {
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| 57 | InputsAtCompileTime = Functor::InputsAtCompileTime,
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| 58 | ValuesAtCompileTime = Functor::ValuesAtCompileTime
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| 59 | };
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| 60 |
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| 61 | /**
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| 62 | * return the number of evaluation of functor
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| 63 | */
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| 64 | int df(const InputType& _x, JacobianType &jac) const
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| 65 | {
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| 66 | using std::sqrt;
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| 67 | using std::abs;
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| 68 | /* Local variables */
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| 69 | Scalar h;
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| 70 | int nfev=0;
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| 71 | const typename InputType::Index n = _x.size();
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| 72 | const Scalar eps = sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
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| 73 | ValueType val1, val2;
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| 74 | InputType x = _x;
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| 75 | // TODO : we should do this only if the size is not already known
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| 76 | val1.resize(Functor::values());
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| 77 | val2.resize(Functor::values());
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| 78 |
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| 79 | // initialization
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| 80 | switch(mode) {
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| 81 | case Forward:
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| 82 | // compute f(x)
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| 83 | Functor::operator()(x, val1); nfev++;
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| 84 | break;
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| 85 | case Central:
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| 86 | // do nothing
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| 87 | break;
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| 88 | default:
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| 89 | eigen_assert(false);
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| 90 | };
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| 91 |
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| 92 | // Function Body
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| 93 | for (int j = 0; j < n; ++j) {
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| 94 | h = eps * abs(x[j]);
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| 95 | if (h == 0.) {
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| 96 | h = eps;
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| 97 | }
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| 98 | switch(mode) {
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| 99 | case Forward:
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| 100 | x[j] += h;
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| 101 | Functor::operator()(x, val2);
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| 102 | nfev++;
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| 103 | x[j] = _x[j];
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| 104 | jac.col(j) = (val2-val1)/h;
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| 105 | break;
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| 106 | case Central:
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| 107 | x[j] += h;
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| 108 | Functor::operator()(x, val2); nfev++;
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| 109 | x[j] -= 2*h;
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| 110 | Functor::operator()(x, val1); nfev++;
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| 111 | x[j] = _x[j];
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| 112 | jac.col(j) = (val2-val1)/(2*h);
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| 113 | break;
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| 114 | default:
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| 115 | eigen_assert(false);
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| 116 | };
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| 117 | }
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| 118 | return nfev;
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| 119 | }
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| 120 | private:
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| 121 | Scalar epsfcn;
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| 122 |
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| 123 | NumericalDiff& operator=(const NumericalDiff&);
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| 124 | };
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| 125 |
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| 126 | } // end namespace Eigen
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| 127 |
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| 128 | //vim: ai ts=4 sts=4 et sw=4
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| 129 | #endif // EIGEN_NUMERICAL_DIFF_H
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| 130 |
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