Package ffx.numerics.switching

Class CompositeSwitch

java.lang.Object

ffx.numerics.switching.CompositeSwitch

All Implemented Interfaces:

UnivariateDiffFunction, UnivariateSwitchingFunction

public class CompositeSwitch
extends Object
implements UnivariateSwitchingFunction

The CompositeSwitch uses a primary switch in the middle, and then two secondary switches at the ends of the path to smoothly switch to the primary switch. For example, one can smoothly interpolate from 0/0/0 value/derivative/second derivative to a linear switch by multiplying the linear switch by a MultiplicativeSwitch in the range 0-0.1.

At present, there is an assumption that x gets linearly scaled when passed to the switch; at the ends, s(x) = f(g(x))*h(x), where h(x) is the primary switch, g(x) = x / (switching range), and f(g(x)) is the secondary switch.

Author:

Jacob M. Litman, Michael J. Schnieders

Constructor Summary

Constructors

Constructor	Description
CompositeSwitch()	Builds a switch that uses MultiplicativeSwitches at the ends (0-0.1, 0.9-1.0) to smoothly interpolate a linear switch between 0 and 1 with smooth 2'nd and 3'rd derivatives.
CompositeSwitch(UnivariateSwitchingFunction primary)	Builds a switch that uses MultiplicativeSwitches at the ends (0-0.1, 0.9-1.0) to smoothly interpolate a provided switch between 0 and 1 with smooth 2'nd and 3'rd derivatives.
CompositeSwitch(UnivariateSwitchingFunction primary, UnivariateSwitchingFunction start, UnivariateSwitchingFunction end, double lbPrimary, double ubPrimary)	Builds a composite switch in .
CompositeSwitch(UnivariateSwitchingFunction primary, UnivariateSwitchingFunction start, UnivariateSwitchingFunction end, double lbPrimary, double ubPrimary, double lb, double ub)	Builds a composite switch in .

Method Summary

Modifier and Type	Method	Description
boolean	constantOutsideBounds()	Remains 0 below the lower bound, and 1 above the upper bound (i.e. a multiplicative switch).
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

CompositeSwitch

public CompositeSwitch()

Builds a switch that uses MultiplicativeSwitches at the ends (0-0.1, 0.9-1.0) to smoothly interpolate a linear switch between 0 and 1 with smooth 2'nd and 3'rd derivatives. Will not be quite linear from 0-0.1 and 0.9-1.0.

CompositeSwitch

public CompositeSwitch(UnivariateSwitchingFunction primary)

Builds a switch that uses MultiplicativeSwitches at the ends (0-0.1, 0.9-1.0) to smoothly interpolate a provided switch between 0 and 1 with smooth 2'nd and 3'rd derivatives.

Parameters:

primary - Primary switch to obey exactly from 0.1-0.9.

CompositeSwitch

public CompositeSwitch(UnivariateSwitchingFunction primary,
 UnivariateSwitchingFunction start,
 UnivariateSwitchingFunction end,
 double lbPrimary,
 double ubPrimary)

Builds a composite switch in .

Parameters:

primary - Primary switch to obey exactly from lbPrimary to ubPrimary.

start - Switch to interpolate from 0 to primary between 0 and lbPrimary; assumed to internally function from 0-1.

end - Switch to interpolate from primary to 1.0 between ubPrimary and 1; assumed to internally function from 0-1.

lbPrimary - Value at which primary should begin to be obeyed exactly.

ubPrimary - Value at which primary should stop being obeyed exactly.

CompositeSwitch

public CompositeSwitch(UnivariateSwitchingFunction primary,
 UnivariateSwitchingFunction start,
 UnivariateSwitchingFunction end,
 double lbPrimary,
 double ubPrimary,
 double lb,
 double ub)

Builds a composite switch in .

Parameters:

primary - Primary switch to obey exactly from lbPrimary to ubPrimary.

start - Switch to interpolate from 0 to primary between 0 and lbPrimary; assumed to internally function from 0-1.

end - Switch to interpolate from primary to 1.0 between ubPrimary and 1; assumed to internally function from 0-1.

lbPrimary - Value at which primary should begin to be obeyed exactly.

ubPrimary - Value at which primary should stop being obeyed exactly.

lb - Overall lower bound of the CompositeSwitch.

ub - Overall upper bound of the CompositeSwitch.

Method Details

constantOutsideBounds

public boolean constantOutsideBounds()

Description copied from interface: UnivariateSwitchingFunction

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

Description copied from interface: UnivariateDiffFunction

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()

Description copied from interface: UnivariateSwitchingFunction

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()

Description copied from interface: UnivariateSwitchingFunction

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

Specified by:

getOneBound in interface UnivariateSwitchingFunction

Returns:

One bound

getZeroBound

public double getZeroBound()

Description copied from interface: UnivariateSwitchingFunction

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

Description copied from interface: UnivariateDiffFunction

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

Description copied from interface: UnivariateDiffFunction

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()

Description copied from interface: UnivariateSwitchingFunction

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()

Description copied from interface: UnivariateSwitchingFunction

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

Description copied from interface: UnivariateDiffFunction

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.