/*
* File: HardSigmoidFunction.java
* Authors: Justin Basilico
* Project: Cognitive Foundry
*
* Copyright 2016 Cognitive Foundry. All rights reserved.
*/
package gov.sandia.cognition.learning.function.scalar;
import gov.sandia.cognition.math.AbstractDifferentiableUnivariateScalarFunction;
/**
* A hard sigmoid function, which is an approximation of a logistic sigmoid
* whose output is between 0 and 1. The function maps values between -2.5
* and 2.5 linearly between 0 and 1 and for values outside that range it is
* capped. Unlike the soft sigmoid it actually ends up producing values of 0
* and 1 for inputs outside of that range, where it is saturated.
*
* The functional form is: f(x) = min(1.0, max(0.0, 0.2 * x + 0.5))
*
* @author Justin Basilico
* @since 4.0.0
* @see SigmoidFunction
*/
public class HardSigmoidFunction
extends AbstractDifferentiableUnivariateScalarFunction
{
/**
* Creates a new {@link HardSigmoidFunction}.
*/
public HardSigmoidFunction()
{
super();
}
@Override
public HardSigmoidFunction clone()
{
return (HardSigmoidFunction) super.clone();
}
@Override
public double evaluate(
final double input)
{
return hardSigmoid(input);
}
@Override
public double differentiate(
final double input)
{
final double y = this.evaluate(input);
if (y == 0.0 || y == 1.0)
{
return 0.0;
}
else
{
return 0.2;
}
}
/**
* Computes the hard sigmoid function. The functional form is:
* f(x) = min(1.0, max(0.0, 0.2 * x + 0.5))
*
* @param input
* The input value to apply the hard sigmoid to.
* @return
* The output, which is between 0.0 and 1.0. If NaN is given, NaN will
* be returned.
*/
public static double hardSigmoid(
final double input)
{
double x = 0.2 * input + 0.5;
if (x <= 0.0)
{
x = 0.0;
}
else if (x >= 1.0)
{
x = 1.0;
}
return x;
}
}