By J. Arndt
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Additional resources for Algorithms for Programmers - Ideas, Source Code
3 4 7 6 5 5 4 7 6 6 5 4 7 7 6 5 4 8 9 10 11 8 9 10 11 11 8 9 10 10 11 8 9 9 10 11 8 12 13 14 15 12 15 14 13 13 12 15 14 14 13 12 15 15 14 13 12 8 9 10 11 11 8 9 10 10 11 8 9 9 10 11 8 Mass storage convolution using the MFA The matrix Fourier algorithm is also an ideal candidate for a mass storage FFT , that is an FFT for a data set that does not fit into physical RAM. Algorithms on data sets that do not fit into physical RAM are sometimes called external : a mass storage FFT is an external FFT.
Apply a (length C) FFT on each row (of the transposed matrix). (memory access is without skips) 6. Multiply each matrix element (index r, c) by exp(−σ 2 π i r c/n). 7. Apply a (length R) FFT on each column (of the transposed matrix). (memory access with C-skips) Note that steps 3, 4 and 5 constitute a length-C convolution on each row. cc] The algorithm can be used for mass storage convolutions if care is taken to minimize the number of disk seeks. Minimization of the number of disk seeks The number of disk seeks has to be kept minimal because these are slow operations which, if occur too often, degrade performance unacceptably.
Memory access with C-skips) Note that steps 3, 4 and 5 constitute a length-C convolution on each row. cc] The algorithm can be used for mass storage convolutions if care is taken to minimize the number of disk seeks. Minimization of the number of disk seeks The number of disk seeks has to be kept minimal because these are slow operations which, if occur too often, degrade performance unacceptably. √ The crucial modification of the use of the MFA is not to choose R and C as close as possible to n as is usually done.