Package ffx.numerics.switching

Class PowerSwitch

java.lang.Object
ffx.numerics.switching.PowerSwitch
All Implemented Interfaces:
UnivariateDiffFunction, UnivariateSwitchingFunction
public class PowerSwitch extends Object implements UnivariateSwitchingFunction
A PowerSwitch interpolates between 0 and 1 vi f(x) = (ax)^beta, where x must be between 0 and 1/a.
Author:
Jacob M. Litman, Michael J. Schnieders

  • Constructor Details

    • PowerSwitch

      public PowerSwitch()
      Default Constructor of the PowerSwitch: constructs a linear switch.

    • PowerSwitch

      public PowerSwitch(double a, double beta)
      Constructor of the PowerSwitch.
      Parameters:
      a - The upper bound of the switch is 1.0 / a.
      beta - The power of the function f(x) = (ax)^beta,

  • 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.

    • getExponent

      public double getExponent()
      Gets the value of beta in f(x) = (a*x)^beta
      Returns:
      Exponent of input

    • 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.

    • getMultiplier

      public double getMultiplier()
      Gets the value of a in f(x) = (a*x)^beta.
      Returns:
      Multiplier of input

    • 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

    • highestOrderZeroDerivativeAtZeroBound

      public int highestOrderZeroDerivativeAtZeroBound()
      Power switch derivatives can be zero at the zero bound if the exponent is greater than the derivative order.
      Specified by:
      highestOrderZeroDerivativeAtZeroBound in interface UnivariateSwitchingFunction
      Returns:
      the highest order zero derivative at 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.