AIActivationFunctionsSigmoid

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos

//@version=5

// @description Sigmoid activation function
library(title='AIActivationFunctionsSigmoid')

// reference:
//      https://github.com/andrewkirillov/AForge.NET/blob/master/Sources/Neuro/Activation%20Functions/SigmoidFunction.cs

//  The class represents sigmoid activation function with
//  the next expression:
//
//|                1
//| f(x) = ------------------
//|        1 + exp(-alpha * x)
//|
//|           alpha * exp(-alpha * x )
//| f'(x) = ---------------------------- = alpha * f(x) * (1 - f(x))
//|           (1 + exp(-alpha * x))^2
//
// - Function output range: (0, 1).
// - The alpha value determines steepness of the function. Increasing value of
// this property changes sigmoid to look more like a threshold function. Decreasing
// value of this property makes sigmoid to be very smooth (slowly growing from its
// minimum value to its maximum value).
//

// @function Function at value point.
// @param value float, value point.
// @param alpha float, default=2.0, sigmoid alpha value.
// @returns float
export function (float value, float alpha=2.0) => //{
    1.0 / (1.0 + math.exp( -alpha * value))
//{ usage:
//{ remarks:
//}}}

// @function Function derivate at value point.
// @param value float, value point.
// @param alpha float, default=2.0, sigmoid alpha value.
// @returns float
export derivate (float value, float alpha=2.0) => //{
    float _y = function(value)
    alpha * _y * (1.0 - _y)
//{ usage:
//{ remarks:
//}}}

// @function Function derivate at value point.
// @param value float, value point.
// @param alpha float, default=2.0, sigmoid alpha value.
// @returns float
export derivate2 (float value, float alpha=2.0) => //{
    alpha * value * (1.0 - value)
//{ usage:
//{ remarks:
//}}}