Package org.hipparchus.analysis.polynomials

Class SmoothStepFactory.SmoothStepFunction

java.lang.Object

org.hipparchus.analysis.polynomials.PolynomialFunction

org.hipparchus.analysis.polynomials.SmoothStepFactory.SmoothStepFunction

All Implemented Interfaces:

Serializable, UnivariateDifferentiableFunction, FieldUnivariateFunction, UnivariateFunction

Direct Known Subclasses:

SmoothStepFactory.QuadraticSmoothStepFunction

Enclosing class:

SmoothStepFactory

public static class SmoothStepFactory.SmoothStepFunction
extends PolynomialFunction

Smoothstep function as defined here.

It is used to do a smooth transition between the "left edge" and the "right edge" with left edge assumed to be smaller than right edge.

By definition, for order n greater than 1 and input x, a smoothstep function respects at least the following properties :

• f(x <= leftEdge) = 0 and f(x >= rightEdge) = 1
• f'(leftEdge) = f'(rightEdge) = 0

If x is normalized between edges, we have at least :

• f(x <= 0) = 0 and f(x >= 1) = 1
• f'(0) = f'(1) = 0

Smoothstep functions of higher order n will have their higher time derivatives also equal to zero at edges...

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class org.hipparchus.analysis.polynomials.PolynomialFunction

PolynomialFunction.Parametric

Method Summary

Modifier and Type	Method	Description
protected void	checkInputEdges(double leftEdge, double rightEdge)	Check that left edge is lower than right edge.
protected double	clampInput(double leftEdge, double rightEdge, double x)	Clamp input between edges.
protected double	normalizeInput(double leftEdge, double rightEdge, double x)	Normalize input between left and right edges.
double	value(double xNormalized)	Compute the value of the smoothstep for the given argument normalized between edges.
double	value(double leftEdge, double rightEdge, double x)	Compute the value of the smoothstep function for the given edges and argument.

Methods inherited from class org.hipparchus.analysis.polynomials.PolynomialFunction

add, antiDerivative, degree, differentiate, equals, evaluate, getCoefficients, hashCode, integrate, multiply, negate, polynomialDerivative, subtract, toString, value

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.hipparchus.analysis.FieldUnivariateFunction

toCalculusFieldUnivariateFunction

Method Detail

value

public double value(double xNormalized)

Compute the value of the smoothstep for the given argument normalized between edges.

Specified by:

value in interface UnivariateFunction

Overrides:

value in class PolynomialFunction

Parameters:

xNormalized - Normalized argument for which the function value should be computed. It is expected to be between [0:1] and will throw an exception otherwise.

Returns:

the value of the polynomial at the given point.

See Also:

UnivariateFunction.value(double)

value

public double value(double leftEdge,
                    double rightEdge,
                    double x)
             throws MathIllegalArgumentException

Compute the value of the smoothstep function for the given edges and argument.

Note that right edge is expected to be greater than left edge. It will throw an exception otherwise.

Parameters:

leftEdge - left edge

rightEdge - right edge

x - Argument for which the function value should be computed

Returns:

the value of the polynomial at the given point

Throws:

MathIllegalArgumentException - if right edge is greater than left edge

See Also:

UnivariateFunction.value(double)

checkInputEdges

protected void checkInputEdges(double leftEdge,
                               double rightEdge)

Check that left edge is lower than right edge. Otherwise, throw an exception.

Parameters:

leftEdge - left edge

rightEdge - right edge

clampInput

protected double clampInput(double leftEdge,
                            double rightEdge,
                            double x)

Clamp input between edges.

Parameters:

leftEdge - left edge

rightEdge - right edge

x - input to clamp

Returns:

clamped input

normalizeInput

protected double normalizeInput(double leftEdge,
                                double rightEdge,
                                double x)

Normalize input between left and right edges.

Parameters:

leftEdge - left edge

rightEdge - right edge

x - input to normalize

Returns:

normalized input