1 /**
2  * @file methods/ann/activation_functions/inverse_quadratic_function.hpp
3  * @author Himanshu Pathak
4  *
5  * Definition and implementation of Inverse Quadratic function.
6  *
7  * mlpack is free software; you may redistribute it and/or modify it under the
8  * terms of the 3-clause BSD license.  You should have received a copy of the
9  * 3-clause BSD license along with mlpack.  If not, see
10  * http://www.opensource.org/licenses/BSD-3-Clause for more information.
11  */
12 #ifndef MLPACK_METHODS_ANN_ACTIVATION_FUNCTIONS_INVERSE_QUAD_FUNCTION_HPP
13 #define MLPACK_METHODS_ANN_ACTIVATION_FUNCTIONS_INVERSE_QUAD_FUNCTION_HPP
14 
15 #include <mlpack/prereqs.hpp>
16 
17 namespace mlpack {
18 namespace ann /** Artificial Neural Network. */ {
19 
20 /**
21  * The Inverse Quadratic function, defined by
22  *
23  * @f{eqnarray*}{
24  * f(x) = 1 / (1 + x^2) \\
25  * f'(x) = -2 * x / (1 + x^2)^2 \\
26  * @f}
27  */
28 class InvQuadFunction
29 {
30  public:
31   /**
32    * Computes the Inverse Quadratic function.
33    *
34    * @param x Input data.
35    * @return f(x).
36    */
Fn(const double x)37   static double Fn(const double x)
38   {
39     return 1 / ( 1 + x * x);
40   }
41 
42   /**
43    * Computes the Inverse Quadratic function.
44    *
45    * @param x Input data.
46    * @param y The resulting output activation.
47    */
48   template<typename InputVecType, typename OutputVecType>
Fn(const InputVecType & x,OutputVecType & y)49   static void Fn(const InputVecType& x, OutputVecType& y)
50   {
51     y = 1 / (1 + arma::pow(x, 2));
52   }
53 
54   /**
55    * Computes the first derivative of the Inverse Quadratic function.
56    *
57    * @param y Input data.
58    * @return f'(x)
59    */
Deriv(const double y)60   static double Deriv(const double y)
61   {
62     return  - 2 * y / std::pow(1 + std::pow(y, 2), 2);
63   }
64 
65   /**
66    * Computes the first derivatives of the Inverse Quadratic function.
67    *
68    * @param y Input data.
69    * @param x The resulting derivatives.
70    */
71   template<typename InputVecType, typename OutputVecType>
Deriv(const InputVecType & x,OutputVecType & y)72   static void Deriv(const InputVecType& x, OutputVecType& y)
73   {
74     y = - 2 * x / arma::pow(1 + arma::pow(x, 2), 2);
75   }
76 }; // class InvQuadFunction
77 
78 } // namespace ann
79 } // namespace mlpack
80 
81 #endif
82