Closing the loop in function objects
------------------------------------

                 Key: MATH-535
                 URL: https://issues.apache.org/jira/browse/MATH-535
             Project: Commons Math
          Issue Type: New Feature
            Reporter: Gilles
            Priority: Minor
             Fix For: 3.0


Some function classes (in package "analysis.function") now contains a 
"Parametric" inner class that provides a parametric version of the function 
represented by the enclosing class.

# We could enhance the "UnivariateRealFunction" interface to contain:
{noformat}
  public ParametricUnivariateRealFunction createParametricFunction();
{noformat}
which, e.g. for the "Gaussian" concrete class, would translate to:
{noformat}
  public Gaussian.Parametric createParametricFunction() {
    return new Gaussian.Parametric();
  }
{noformat}
# We could enhance the "ParametricUnivariateRealFunction" interface to contain:
{noformat}
  public UnivariateRealFunction createFunction(double[] param);
{noformat}
which, in "Gaussian.Parametric", would translate to:
{noformat}
  public Gaussian createFunction(double[] param) {
    validateParameters(param);
    return new Gaussian(param[0], param[1], param[2]);
  }
{noformat}

In both cases, it would allow programming against interfaces.

For the first case, not all current implementations of "UnivariateRealFunction" 
provide a "Parametric" version (and for most there are no parameters). So 
either we create a new "AbstractUnivariateRealFunction" that provides a default 
implementation of "createParametricFunction" (throwing an exception) and make 
all current function classes extends this one, or we create a new interface 
(something like "ParametricFactory") that declares the new 
"createParametricFunction()" and add the "implements ParametricFactory" clause 
to any class that provides a parametric version.
I think that the latter is the cleanest. Or is there still another possibility?


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