openNN-v5.0.5【无需积分值】

// OpenNN: Open Neural Networks Library // www.opennn.net // // N U M E R I C A L D I F F E R E N T I A T I O N C L A S S H E A D E R // // Artificial Intelligence Techniques SL // artelnics@artelnics.com #ifndef NUMERICALDIFFERENTIATION_H #define NUMERICALDIFFERENTIATION_H // System includes #include<iostream> #include<vector> #include<vector> #include<limits> #include<cstddef> // OpenNN includes #include "config.h" using namespace std; using namespace Eigen; namespace OpenNN { /// This class contains methods for numerical differentiation of functions. /// In particular it implements the forward and central differences methods for derivatives, Jacobians, hessians or hessian forms. class NumericalDifferentiation { public: // Constructors explicit NumericalDifferentiation(); // Destructor virtual ~NumericalDifferentiation(); /// Enumeration of available methods for numerical differentiation. enum NumericalDifferentiationMethod{ForwardDifferences, CentralDifferences}; const NumericalDifferentiationMethod& get_numerical_differentiation_method() const; string write_numerical_differentiation_method() const; const Index& get_precision_digits() const; const bool& get_display() const; void set(const NumericalDifferentiation&); void set_numerical_differentiation_method(const NumericalDifferentiationMethod&); void set_numerical_differentiation_method(const string&); void set_precision_digits(const Index&); void set_display(const bool&); void set_default(); type calculate_eta() const; type calculate_h(const type&) const; Tensor<type, 1> calculate_h(const Tensor<type, 1>&) const; Tensor<type, 2> calculate_h(const Tensor<type, 2>&) const; Tensor<type, 4> calculate_h(const Tensor<type, 4>&) const; Tensor<type, 1> calculate_backward_differences_derivatives(const Tensor<type, 1>&, const Tensor<type, 1>&) const; // Serialization methods void from_XML(const tinyxml2::XMLDocument&); void write_XML(tinyxml2::XMLPrinter&) const; /// Returns the derivative of a function using the forward differences method. /// @param t Object constructor containing the member method to differentiate. /// @param f Pointer to the member method. /// @param x Differentiation point. template<class T> type calculate_forward_differences_derivatives(const T& t, type(T::*f)(const type&) const, const type& x) const { const type y = (t.*f)(x); const type h = calculate_h(x); const type y_forward = (t.*f)(x + h); const type d = (y_forward - y)/h; return d; } /// Returns the derivative of a function using the central differences method. /// @param t Object constructor containing the member method to differentiate. /// @param f Pointer to the member method. /// @param x Differentiation point. template<class T> type calculate_central_differences_derivatives(const T& t, type(T::*f)(const type&) const , const type& x) const { const type h = calculate_h(x); const type y_forward = (t.*f)(x+h); const type y_backward = (t.*f)(x-h); const type d = (y_forward - y_backward)/(static_cast<type>(2.0)*h); return d; } /// Returns the derivative of a function acording to the numerical differentiation method to be used. /// @param t Object constructor containing the member method to differentiate. /// @param f Pointer to the member method. /// @param x Differentiation point. template<class T> type calculate_derivatives(const T& t, type(T::*f)(const type&) const , const type& x) const { switch(numerical_differentiation_method) { case ForwardDifferences: { return calculate_forward_differences_derivatives(t, f, x); } case CentralDifferences: { return calculate_central_differences_derivatives(t, f, x); } } return 0.0; } /// Returns the derivatives of a vector function using the forward differences method. /// @param t Object constructor containing the member method to differentiate. /// @param f Pointer to the member method. /// @param x Input vector. template<class T> Tensor<type, 1> calculate_forward_differences_derivatives(const T& t, Tensor<type, 1>(T::*f)(const Tensor<type, 1>&) const, const Tensor<type, 1>& x) const { const Tensor<type, 1> h = calculate_h(x); const Tensor<type, 1> y = (t.*f)(x); const Tensor<type, 1> x_forward = x + h; const Tensor<type, 1> y_forward = (t.*f)(x_forward); const Tensor<type, 1> d = (y_forward - y)/h; return d; } template<class T> Tensor<type, 2> calculate_forward_differences_derivatives(const T& t, Tensor<type, 2>(T::*f)(const Tensor<type, 2>&) const, const Tensor<type, 2>& x) const { const Tensor<type, 2> h = calculate_h(x); const Tensor<type, 2> y = (t.*f)(x); const Tensor<type, 2> x_forward = x + h; const Tensor<type, 2> y_forward = (t.*f)(x_forward); const Tensor<type, 2> d = (y_forward - y)/h; return d; } /// Returns the derivatives of a vector function using the central differences method. /// @param t : Object constructor containing the member method to differentiate. /// @param f: Pointer to the member method. /// @param x: Input vector. template<class T> Tensor<type, 1> calculate_central_differences_derivatives(const T& t, Tensor<type, 1>(T::*f)(const Tensor<type, 1>&) const, const Tensor<type, 1>& x) const { const Tensor<type, 1> h = calculate_h(x); const Tensor<type, 1> x_forward = x + h; const Tensor<type, 1> x_backward = x - h; const Tensor<type, 1> y_forward = (t.*f)(x_forward); const Tensor<type, 1> y_backward = (t.*f)(x_backward); const Tensor<type, 1> y = (t.*f)(x); const Tensor<type, 1> d = (y_forward - y_backward)/(static_cast<type>(2.0)*h); return d; } template<class T> Tensor<type, 2> calculate_central_differences_derivatives(const T& t, Tensor<type, 2>(T::*f)(const Tensor<type, 2>&) const, const Tensor<type, 2>& x) const { const Tensor<type, 2> h = calculate_h(x); const Tensor<type, 2> x_forward = x + h; const Tensor<type, 2> x_backward = x - h; const Tensor<type, 2> y_forward = (t.*f)(x_forward); const Tensor<type, 2> y_backward = (t.*f)(x_backward); const Tensor<type, 2> y = (t.*f)(x); const Tensor<type, 2> d = (y_forward - y_backward)/(static_cast<type>(2.0)*h); return d; } template<class T> Tensor<type, 4> calculate_central_differences_derivatives(const T& t, Tensor<type, 4>(T::*f)(const Tensor<type, 4>&) const, const Tensor<type, 4>& x) const { const Tensor<type, 4> h = calculate_h(x); const Tensor<type, 4> x_forward = x + h; const Tensor<type, 4> x_backward = x - h; const Tensor<type, 4> y_forward = (t.*f)(x_forward); const Tensor<type, 4> y_backward = (t.*f)(x_backward); const Tensor<type, 4> y = (t.*f)(x); const Tensor<type, 4> d = (y_forward - y_backward)/(static_cast<type>(2.0)*h); return d; } /// Returns the derivatives of a vector function acording to the numerical differentiation method to be used. /// @param t : Object constructor containing the member method to differentiate. /// @param f: Pointer to the member method. /// @param x: Input vector. template<class T> Tensor<type, 1> calculate_derivatives(const T& t, Tensor<type, 1>(T::*f)(const Tensor<type, 1>&) const, const Tensor<type, 1>& x) const { switch(numerical_differentiation_method) { case ForwardDifferences: { return calculate_forward_differences_derivatives(t, f, x); } case CentralDifferences: { return calculate_central_di