Faster and more computationally-efficient Fast Fourier Transform implementation
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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
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.
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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