NeuroBook/Include/about_ai/activation/activations.mqh

<EFBFBD><EFBFBD>//+------------------------------------------------------------------+

//|                                                  activations.mqh |

//|                                  Copyright 2021, MetaQuotes Ltd. |

//|                                             https://www.mql5.com |

//+------------------------------------------------------------------+

#property copyright "Copyright 2021, MetaQuotes Ltd."

#property link      "https://www.mql5.com"

//---

const double theta = 0;

const double a = 1.0;

const double b = 0.0;

//+------------------------------------------------------------------+

/// Threshold activation function

/// Constant 'theta' determines neuron activation function.

/// Parameter 'x' receives weighted sum of raw data.

//+------------------------------------------------------------------+

double ActStep(double x)

  {

   return (x >= theta ? 1 : 0);

  }

//+------------------------------------------------------------------+

/// Linear activation function

/// Constant 'a' defines the angle of inclination of line

/// Constant 'b' defines line offset from the origin

/// Parameter 'x' receives weighted sum of raw data.

//+------------------------------------------------------------------+

double ActLinear(double x)

  {

   return (a * x + b);

  }

//+------------------------------------------------------------------+

/// Derivative of linear activation function

/// Constant 'a' defines the angle of inclination of line

/// Parameter 'y' last state of the activation function (result of the feed-forward)

/// Here the parameter is added to unify the function form with similar ones for other activation functions.

//+------------------------------------------------------------------+

double ActLinearDerivative(double y)

  {

   return a;

  }

//+------------------------------------------------------------------+

/// Logistic activation function (Sigmoid)

/// Constant 'a' defines the range of function values from '0' to 'a'

/// Constant 'b' defines line offset from the origin

/// Parameter 'x' receives weighted sum of raw data.

//+------------------------------------------------------------------+

double ActSigmoid(double x)

  {

   return (a / (1 + exp(-x)) - b);

  }

//+------------------------------------------------------------------+

/// Derivative of logistic function

/// Constant 'a' defines the range of function values from '0' to 'a'

/// Constant 'b' defines line offset from the origin

/// Parameter 'y' last state of the activation function (result of the feed-forward)

//+------------------------------------------------------------------+

double ActSigmoidDerivative(double y)

  {

   y = MathMax(MathMin(y + b, a), 0.0);

   return (y * (1 - y / a));

  }

//+------------------------------------------------------------------+

/// Hyperbolic tangent

/// Parameter 'x' receives weighted sum of raw data.

//+------------------------------------------------------------------+

double ActTanh(double x)

  {

   return tanh(x);

  }

//+------------------------------------------------------------------+

/// Derivative of the hyperbolic tangent

/// Parameter 'y' last state of the activation function (result of the feed-forward)

//+------------------------------------------------------------------+

double ActTanhDerivative(double y)

  {

   y = MathMax(MathMin(y, 1.0), -1.0);

   return (1 - pow(y, 2));

  }

//+------------------------------------------------------------------+