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A fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier transform (DFT) and its inverse. Fourier analysis converts time (or space) to frequency and vice versa; an FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, fast Fourier transforms are widely used for many applications in engineering, science, and mathematics.
There are several packages dealing with the fast fourier transform (FFT) problem. We will discuss the fastest one, which uses many threads and the multicore computer architecture. It is based on the PrallelColt as implemented by Piotr Wendykier.
In this example we will use DComplexFactory2D
factory to create a random
dense matrix (DenseDComplexMatrix2D
) and perform FCC.
1: #compute 2D Discrete Fourier Transform (DFT) of a random complex matrix: 2: 3: from cern.colt.matrix.tdcomplex import DComplexFactory2D 4: from edu.emory.mathcs.utils import ConcurrencyUtils 5: from edu.emory.mathcs.jtransforms.fft import * 6: 7: ConcurrencyUtils.setNumberOfThreads(2) # use 2 cores 8: M = DComplexFactory2D.dense.random(100,100) # random matrix 9: print type(M) 10: M.fft2() # compute 2D DFT in-place 11: # print M.toString()
This example is based on the real DenseDoubleMatrix2D
matrix.
You can also use 3D matrix methods, see DenseDoubleMatrix3D
This is 1D DFT transform of a complex matrix 1000×1000 using several processing cores:
Read the book "Scientific data analysis using Jython scripting and Java for more details. — Sergei Chekanov 2011/03/31 10:47