[jira] Commented: (MATH-216) Faster and more computationally-efficient Fast Fourier Transform implementation

["Luc Maisonobe (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/MATH-216?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12656413#action_12656413 ] 

Luc Maisonobe commented on MATH-216:
------------------------------------

At first sight, the patch seemed good to me (apart from naming conventions, but this is detail we can take care of later).
However, when I apply it, the testSinFunction() unit test fails: result[1] is -0.1164 - 0.1764314556963682i instead of 0 - 0.5i.

> Faster and more computationally-efficient Fast Fourier Transform implementation
> -------------------------------------------------------------------------------
>
>                 Key: MATH-216
>                 URL: https://issues.apache.org/jira/browse/MATH-216
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 1.2
>            Reporter: Daniel Kuan
>            Priority: Minor
>             Fix For: 2.1
>
>         Attachments: RootsOfUnityOptimization-20081214.patch
>
>
> Here are some suggestions on improving the speed and computational-efficiency of FastFourierTransformer.
> 1. Store roots of unity as a double array of arrays instead of Complex array.
> No need for all the functionality that comes with class Complex when all that is required are the values of the roots of unity.
> 2. Keep track of the largest set of roots of unity calculated so far, and adopt Singleton pattern.
> Subsequent requests for smaller sets of roots of unity can be derived from the largest set -- no need to recalculate the roots of unity from scratch.
> 3. When computing the nth roots of unity, need only compute n/4 roots instead of all n roots.
> Since the roots of unity lie along a circle of unity radius, trigonometric relations can be leveraged to reduce the number of roots that need to be computed from n to n/4.
> 4. Execute transform algorithm on double primitives instead of on class Complex.
> New instances of Complex are instantiated each time a simple arithmetic operation is performed on the Complex variables. Much time is lost to object creation and initialisation.

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