Package ffx.numerics.switching

Class LinearDerivativeSwitch

java.lang.Object

ffx.numerics.switching.LinearDerivativeSwitch

All Implemented Interfaces:

UnivariateDiffFunction, UnivariateSwitchingFunction

public class LinearDerivativeSwitch
extends Object
implements UnivariateSwitchingFunction

A LinearDerivativeSwitch interpolates between 0 and 1 vi f(x) = 2*x - x^2.

The derivative is then linear in x: f'(x) = 2 - 2*x

Limiting behavior is given by: f(0) = 0, f(1) = 1, f'(0) = 2, f'(1) = 0.

Author:

Michael J. Schnieders

Constructor Summary

Constructors

Constructor	Description
LinearDerivativeSwitch()	Constructor for the LinearDerivativeSwitch.

Method Summary

Modifier and Type	Method	Description
boolean	constantOutsideBounds()	Remains 0 below the lower bound, and 1 above the upper bound (i.e.
double	firstDerivative(double x)	First derivative at a point.
int	getHighestOrderZeroDerivative()	The highest-order derivative that is zero at the bounds.
double	getOneBound()	Gets the one bound, where f(x) becomes one.
double	getZeroBound()	Gets the zero bound, where f(x) becomes zero.
double	nthDerivative(double x, int order)	N'th order derivative at a point.
double	secondDerivative(double x)	Second derivative at a point.
boolean	symmetricToUnity()	True if f(lb + delta) + f(ub - delta) = 1 for all delta between 0 and (ub - lb).
String	toString()
boolean	validOutsideBounds()	Remains in the range 0-1 outside the bounds.
double	valueAt(double x)	Value at a point

Methods inherited from class java.lang.Object

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

Methods inherited from interface ffx.numerics.switching.UnivariateSwitchingFunction

highestOrderZeroDerivativeAtZeroBound

Constructor Details

LinearDerivativeSwitch

public LinearDerivativeSwitch()

Constructor for the LinearDerivativeSwitch.

Method Details

constantOutsideBounds

public boolean constantOutsideBounds()

Remains 0 below the lower bound, and 1 above the upper bound (i.e. a multiplicative switch).

Specified by:

constantOutsideBounds in interface UnivariateSwitchingFunction

Returns:

df(x)/dx is zero outside range lb-ub.

firstDerivative

public double firstDerivative(double x)
                       throws IllegalArgumentException

First derivative at a point.

Specified by:

firstDerivative in interface UnivariateDiffFunction

Parameters:

x - a double.

Returns:

f'(x)

Throws:

IllegalArgumentException - If f'(x) is undefined at x.

getHighestOrderZeroDerivative

public int getHighestOrderZeroDerivative()

The highest-order derivative that is zero at the bounds.

Specified by:

getHighestOrderZeroDerivative in interface UnivariateSwitchingFunction

Returns:

Maximum order zero derivative at bounds.

getOneBound

public double getOneBound()

Gets the one bound, where f(x) becomes one.

Specified by:

getOneBound in interface UnivariateSwitchingFunction

Returns:

One bound

getZeroBound

public double getZeroBound()

Gets the zero bound, where f(x) becomes zero.

Specified by:

getZeroBound in interface UnivariateSwitchingFunction

Returns:

Zero bound

nthDerivative

public double nthDerivative(double x,
 int order)
                     throws IllegalArgumentException

N'th order derivative at a point. Should be relatively optional for any order above 2.

Specified by:

nthDerivative in interface UnivariateDiffFunction

Parameters:

x - a double.

order - Derivative order (>= 1)

Returns:

d^nf(x)/dx^n

Throws:

IllegalArgumentException - If derivative undefined at x.

secondDerivative

public double secondDerivative(double x)
                        throws IllegalArgumentException

Second derivative at a point.

Specified by:

secondDerivative in interface UnivariateDiffFunction

Parameters:

x - a double.

Returns:

f''(x)

Throws:

IllegalArgumentException - If f''(x) is undefined at x.

symmetricToUnity

public boolean symmetricToUnity()

True if f(lb + delta) + f(ub - delta) = 1 for all delta between 0 and (ub - lb). For example, a power switch with beta 1 is symmetric to unity, as f(l) + f(1-l) = 1, but beta 2 produces a non-unity result, where f(0.5) + f(0.5) = 0.5.

Specified by:

symmetricToUnity in interface UnivariateSwitchingFunction

Returns:

If symmetry produces unity result.

toString

public String toString()

Overrides:

toString in class Object

validOutsideBounds

public boolean validOutsideBounds()

Remains in the range 0-1 outside the bounds. Implied to be true if constantOutsideBounds is true.

Specified by:

validOutsideBounds in interface UnivariateSwitchingFunction

Returns:

min(f ( x)) = 0 and max(f(x)) = 1.

valueAt

public double valueAt(double x)
               throws IllegalArgumentException

Value at a point

Specified by:

valueAt in interface UnivariateDiffFunction

Parameters:

x - a double.

Returns:

f(x)

Throws:

IllegalArgumentException - If f(x) is undefined at x.