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From "Luc Maisonobe (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-1143) Helper methods to FiniteDifferencesDifferentiator
Date Thu, 30 Apr 2015 12:39:06 GMT

[ https://issues.apache.org/jira/browse/MATH-1143?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14521431#comment-14521431
]

Luc Maisonobe commented on MATH-1143:
-------------------------------------

{quote}
I am not sure I understand, how this constructor works. It seems that it defines derivatives
in the fixed point.
{quote}

Yes. A DerivativeStructure instance is just one set of values, just like a double which would
hold a value f(x). If you want to have f(x) for several x values, you create as many double
as you want, this is the same for DerivativeStructure, you create one instance for each x
value.

Your example to create a function is almost good. It just misses one point: you don't use
the derivatives of ds itself, only its value. This may be fine if you are sure ds is already
your canonical variable, but it would not work if your function is the last step of a composition.
The DerivativeStructure class has been created to handle the second case, which explains why
it seems overkill in simpler cases.

In fact, in your case you seem to already do separately the computation of the derivatives
with separate code, using your someDerivativeCalculationHere function. This is the kind of
things DerivativesStructure could do for you. In fact, as long as you have a way to implement
"someOperationHere" using only Java (i.e. with primitive operations, Math/FastMath/StrictMath
functions and even calls to intermediate functions, then you can reimplement it so it directly
computes the derivatives at the same time and most importantly at any order, without requiring
you to find the expression for the derivatives. This is the essence of automatic differentiation.
There is even the Apache Commons Nable project (unfortunately not fully functional) that could
do this for you, i.e. you give it a UnivariateFunction and it creates the corresponding UnivariateDifferentiableFunction
automatically.

What you seem to ask here is for something different: you already have the function and derivatives
available, but probably only at the order at which you did code them. Then if you want to
put the result in a DerivativeStructure instance, the class simply acts as a container for
the values, and serves no other purpose. Then of course it seems complicated for just doing
this.

> Helper methods to FiniteDifferencesDifferentiator
> -------------------------------------------------
>
>                 Key: MATH-1143
>                 URL: https://issues.apache.org/jira/browse/MATH-1143
>             Project: Commons Math
>          Issue Type: Improvement
>            Reporter: Alexander Nozik
>            Priority: Trivial
>
> A DerivativeStructure and UnivariateDifferentiableFunction are great tools if one needs
to investigate the whole function but are not convenient if one just needs derivative in a
given point.
> Perhaps you could add some helper methods to FiniteDifferencesDifferentiator or to utility
class like FunctionUtils. Also it would be good to have helper methods to get the derivatives
of UnivariateDifferentiableFunction or MultivariateDifferentiableFunction as simple Univariate
or Multivariate functions (or vector-functions).

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