My first thought here is, how is calling Function.value(x) different from calling Function.firstDerivative(x)? We don't really implement a "Evaluator" or "EvaluatorFactory" for returning a function's Function.value(x). We only provide Solvers and Solver factories for different ways of Numerically solving the Functions value(x) method for 0.
Will a Differentiator/Factory be solving for the derivative? In which case, as the algorithms used are really already implemented in the solvers, wouldn't we just expand them with methods that allow us to solve for the derivatives? For Example:
UnivariateRealSolver bs = new BisectionSolver(...);
double d = bs.solveFirstDerivative(min,max);
and
double d = bs.solveSecondDerivative(min,max);
-Mark
Matt Cliff wrote:
I have been scratching out an implementation of a numerical derivative to add to the commons-math and keep going back and forth between two approaches.
(all this would be in the o.a.c.math.analysis package)
(for brevity I have omitted the prefix UnivariateReal* )
--------------------------------------------------------------------
(1) a couple classes like Differentiator (interface) and DifferentiatorFactory (class), where we have a method like
"Differentiator DifferentiatorFactory.getDefaultDifferentiator( Function f )"
and another method like "double Differentiator.derivate( double x)" or "double Differentiator.value(double x)"
this keeps the same type of pattern as that of the *Solver
OR
(2) Add a class like DerivativeFactory which has a method like "Function DerivativeFactory.getDefaultDerivative( Function f )"
and use the existing "double Function.value( double x)" to obtain the numerical estimate.
I first implemented it using approach (1) but as the code and usage turned out, it seems that (2) was easier to use (and numerically has the same number or operations and function evaluations).
---------------------------------------------------------------------- using (2) the client code would look like
public myMethod() {
UnivariateRealFunction f = new SomeUserDefinedFunction();
UnivariateRealFunction fprime = DerivativeFactory.newInstance().getDefaultDerivative( f );
System.out.println( "f'(1.0) = "+ fprime.value(1.0) ); }
-------------------------------------------------------------------------
of course the Factory could allow for multiple types of Derivatives, the one I have currently implemented is a centered 5-point algorithm, which has an operational parameter of h (or a step-size), there may also be parameters to handle "infinite" derivative or jumps.
-- Mark Diggory Software Developer Harvard MIT Data Center http://osprey.hmdc.harvard.edu
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