Package org.hipparchus.analysis.polynomials

Class SmoothStepFactory.FieldSmoothStepFunction<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.analysis.polynomials.FieldPolynomialFunction<T>

org.hipparchus.analysis.polynomials.SmoothStepFactory.FieldSmoothStepFunction<T>

Type Parameters:

T - type of the field element

All Implemented Interfaces:

CalculusFieldUnivariateFunction<T>

Enclosing class:

SmoothStepFactory

public static class SmoothStepFactory.FieldSmoothStepFunction<T extends CalculusFieldElement<T>>
extends FieldPolynomialFunction<T>

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...

Method Summary

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

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

add, antiDerivative, degree, differentiate, evaluate, getCoefficients, getField, integrate, integrate, multiply, negate, polynomialDerivative, subtract

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

value

public T value(double xNormalized)

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

Overrides:

value in class FieldPolynomialFunction<T extends CalculusFieldElement<T>>

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 T value(T xNormalized)

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

Specified by:

value in interface CalculusFieldUnivariateFunction<T extends CalculusFieldElement<T>>

Overrides:

value in class FieldPolynomialFunction<T extends CalculusFieldElement<T>>

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 T value(double leftEdge,
               double rightEdge,
               T 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 T clampInput(double leftEdge,
                       double rightEdge,
                       T x)

Clamp input between edges.

Parameters:

leftEdge - left edge

rightEdge - right edge

x - input to clamp

Returns:

clamped input

normalizeInput

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

Normalize input between left and right edges.

Parameters:

leftEdge - left edge

rightEdge - right edge

x - input to normalize

Returns:

normalized input