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From "Luc Maisonobe (JIRA)" <>
Subject [jira] Resolved: (MATH-216) Faster and more computationally-efficient Fast Fourier Transform implementation
Date Tue, 03 Feb 2009 20:02:05 GMT


Luc Maisonobe resolved MATH-216.

       Resolution: Fixed
    Fix Version/s:     (was: 2.1)

fixed in trunk as of r740400.
The patch has been applied with slight changes.
thanks for the patch

> Faster and more computationally-efficient Fast Fourier Transform implementation
> -------------------------------------------------------------------------------
>                 Key: MATH-216
>                 URL:
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 1.2
>            Reporter: Daniel Kuan
>            Priority: Minor
>             Fix For: 2.0
>         Attachments: RootsOfUnityOptimization-20081214.patch, RootsOfUnityOptimization-20090125.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
> 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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