Algorithms for programmers. Ideas and source code - download pdf or read online

By Arndt J.

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E. the way array data is stored in the C language, as opposed to the Fortran language convention. Further let α ≥ 2 be the number of times the data set exceeds the RAM size. 5 one reads from disk (row by row, involving R seeks) the number of colums that just fit into RAM, does the (many, short) column-FFTs3 , writes back (again R seeks) and proceeds to the next block; this happens for α of these blocks, giving a total of 4 α R seeks for steps 1 and 3. In step 2 one has to read (α times) blocks of one or more rows, which lie in contiguous portions of the disk, perform the FFT on the rows and write back to disk, leading to a total of 2 α seeks.

Km ), ki ∈ 0, 1, 2, . . k ... x1 =0 x2 =0 where z = e± 2 π i/n , n = S1 S2 . . k where S = (S1 − 1, S2 − 1, . . 79) x=0 The inverse transform is again the one with the minus in the exponent of z. 80) x=0 which shows that the 2-dimensional FT can be accomplished by using 1-dimensional FTs to transform first the rows and then the columns8 . 13 (row column FFT) Compute the two dimensional FT of a[][] using the row column method procedure rowcol_ft(a[][], R, C) { complex a[R][C] // R (length-C) rows, C (length-R) columns for r:=0 to R-1 // FFT rows { fft(a[r][], C, is) } complex t[R] // scratch array for columns for c:=0 to C-1 // FFT columns { 7 Imagine 8 or a R × C matrix of R rows (of length C) and C columns (of length R).

Here is a clumsy attempt to find h(0) alone: Use the weighted transform with the weight sequence vx = V x where V n is very small. Then h(1) will in the result be multiplied with a small number and we hope to make it almost disappear. 000}. At least for integer sequences one could choose V n (more than two times) bigger than biggest possible value in h(1) and use rounding to nearest integer to isolate h(0) . Alas, even for modest sized arrays numerical overflow and underflow gives spurious results.

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Algorithms for programmers. Ideas and source code by Arndt J.


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