Package ffx.numerics.switching

Class MultiplicativeSwitch

java.lang.Object
ffx.numerics.switching.MultiplicativeSwitch
All Implemented Interfaces:
UnivariateDiffFunction, UnivariateSwitchingFunction
public class MultiplicativeSwitch extends Object implements UnivariateSwitchingFunction
The 6 coefficients of the multiplicative polynomial switch are unique given the distances "a" and "b". They are found by solving a system of 6 equations, which define the boundary conditions of the switch.
f(a) = 1
f'(a) = f"(a) = 0
f(b) = f'(b) = f"(b) = 0
Author:
Michael J. Schnieders

  • Constructor Details

    • MultiplicativeSwitch

      public MultiplicativeSwitch()
      Constructs a MultiplicativeSwitch that starts at f(0)=1 and ends at f(1)=0. The switch smoothly interpolates from 1 to 0 across that range, with zero first and second derivatives at off and cut.

    • MultiplicativeSwitch

      public MultiplicativeSwitch(double a, double b)
      Constructs a MultiplicativeSwitch that starts at f(a)=1 and ends at f(b)=0. The switch smoothly interpolates from 1 to 0 across that range, with zero first and second derivatives at off and cut.
      Parameters:
      a - f(a)=1
      b - f(b)=0

  • 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.

    • dtaper

      public double dtaper(double r, double r2, double r3, double r4)
      First derivative of the switching function at r.
      Parameters:
      r - r
      r2 - r^2
      r3 - r^3
      r4 - r^4
      Returns:
      First derivative of switch at r

    • dtaper

      public double dtaper(double r)
      First derivative of the switching function at r.
      Parameters:
      r - r
      Returns:
      First derivative of switch at r

    • firstDerivative

      public double firstDerivative(double x)
      First derivative at a point.
      Specified by:
      firstDerivative in interface UnivariateDiffFunction
      Parameters:
      x - a double.
      Returns:
      f'(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

    • getSwitchEnd

      public double getSwitchEnd()
      Get the value where the switch starts.
      Returns:
      Switch start.

    • getSwitchStart

      public double getSwitchStart()
      Get the value where the switch starts.
      Returns:
      Switch start.

    • 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)
      Second derivative at a point.
      Specified by:
      secondDerivative in interface UnivariateDiffFunction
      Parameters:
      x - a double.
      Returns:
      f''(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.

    • taper

      public double taper(double r, double r2, double r3, double r4, double r5)
      Value of the switching function at r.
      Parameters:
      r - r
      r2 - r^2
      r3 - r^3
      r4 - r^4
      r5 - r^5
      Returns:
      Value of switch at r

    • taper

      public double taper(double r)
      Value of the switching function at r.
      Parameters:
      r - r
      Returns:
      Value of switch at r

    • 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.