Applying the Vector Radix Method to Multidimensional, Multiprocessor, Out-of-Core Fast Fourier Transforms

Date of Award

3-1-2001

Document Type

Thesis (Master's)

Department or Program

Department of Computer Science

First Advisor

Tom Cormen

Abstract

We describe an efficient algorithm for calculating Fast Fourier Transforms on matrices of arbitrarily high dimension using the vector-radix method when the problem size is out-of-core (i.e., when the size of the data set is larger than the total available memory of the system). The algorithm takes advantage of multiple processors when they are present, but it is also efficient on single-processor systems. Our work is an extension of work done by Lauren Baptist in [Bapt99], which applied the vector-radix method to 2-dimensional out-of-core matrices. To determine the effectiveness of the algorithm, we present empirical results as well as an analysis of the I/O, communication, and computational complexity. We perform the empirical tests on a DEC 2100 server and on a cluster of Pentium-based Linux workstations. We compare our results with the traditional dimensional method of calculating multidimensional FFTs, and show that as the number of dimensions increases, the vector-radix-based algorithm becomes increasingly effective relative to the dimensional method. In order to calculate the complexity of the algorithm, it was necessary to develop a method for analyzing the interprocessor communication costs of the BMMC data-permutation algorithm (presented in [CSW98]) used by our FFT algorithms. We present this analysis method and show how it was derived.

Comments

Originally posted in the Dartmouth College Computer Science Technical Report Series, number TR2001-388.

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