Package org.apache.commons.math.optimization.fitting

Class ParametricGaussianFunction

  • All Implemented Interfaces:
    java.io.Serializable, ParametricRealFunction
    public class ParametricGaussianFunction
extends java.lang.Object
implements ParametricRealFunction, java.io.Serializable
    A Gaussian function. Specifically:

    f(x) = a + b*exp(-((x - c)^2 / (2*d^2)))

    The parameters have the following meaning:

    • a is a constant offset that shifts f(x) up or down
    • b is the height of the peak
    • c is the position of the center of the peak
    • d is related to the FWHM by FWHM = 2*sqrt(2*ln(2))*d
    Notation key:
    • x^n: x raised to the power of n
    • exp(x): e^x
    • sqrt(x): the square root of x
    • ln(x): the natural logarithm of x
    References:
    Since:
    2.2
    See Also:
    Serialized Form

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double[] gradient​(double x, double[] parameters)
      Computes the gradient vector for a four variable version of the function where the parameters, a, b, c, and d, are considered the variables, not x.
      double value​(double x, double[] parameters)
      Computes value of function f(x) for the specified x and parameters a, b, c, and d.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • ParametricGaussianFunction

        public ParametricGaussianFunction()
        Constructs an instance.

    • Method Detail

      • value

        public double value​(double x,
                    double[] parameters)
             throws ZeroException
        Computes value of function f(x) for the specified x and parameters a, b, c, and d.
        Specified by:
        value in interface ParametricRealFunction
        Parameters:
        x - x value
        parameters - values of a, b, c, and d
        Returns:
        value of f(x) evaluated at x with the specified parameters
        Throws:
        java.lang.IllegalArgumentException - if parameters is invalid as determined by validateParameters(double[])
        ZeroException - if parameters values are invalid as determined by validateParameters(double[])

      • gradient

        public double[] gradient​(double x,
                         double[] parameters)
                  throws ZeroException
        Computes the gradient vector for a four variable version of the function where the parameters, a, b, c, and d, are considered the variables, not x. That is, instead of computing the gradient vector for the function f(x) (which would just be the derivative of f(x) with respect to x since it's a one-dimensional function), computes the gradient vector for the function f(a, b, c, d) = a + b*exp(-((x - c)^2 / (2*d^2))) treating the specified x as a constant.

        The components of the computed gradient vector are the partial derivatives of f(a, b, c, d) with respect to each variable. That is, the partial derivative of f(a, b, c, d) with respect to a, the partial derivative of f(a, b, c, d) with respect to b, the partial derivative of f(a, b, c, d) with respect to c, and the partial derivative of f(a, b, c, d) with respect to d.

        Specified by:
        gradient in interface ParametricRealFunction
        Parameters:
        x - x value to be used as constant in f(a, b, c, d)
        parameters - values of a, b, c, and d for computation of gradient vector of f(a, b, c, d)
        Returns:
        gradient vector of f(a, b, c, d)
        Throws:
        java.lang.IllegalArgumentException - if parameters is invalid as determined by validateParameters(double[])
        ZeroException - if parameters values are invalid as determined by validateParameters(double[])