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function y = fftn(A, SIZE)
// Description:
// This function computes the N-dimensional discrete Fourier transform of A using a Fast Fourier Transform (FFT) algorithm.
// The optional vector argument SIZE may be used to specify the dimensions of the array to be used.
// If an element of SIZE is smaller than the corresponding dimension of A, then the dimension of A is truncated prior to performing the FFT.
// Otherwise, if an element of SIZE is larger than the corresponding dimension, then A is resized and padded with zeros.
// Calling sequence:
// Y = fftn(A)
// Y = fftn(A, SIZE)
// Parameters:
// A: Matrix, the input data for which the FFT is computed.
// SIZE: Optional vector specifying the dimensions of the output array. If provided, the dimensions of A are adjusted accordingly.
// Examples:
// fftn([6 9 7 ;2 9 9 ;0 3 1],[2 2])
// ans =
// 26. -10.
// 4. 4.
funcprot(0);
// Get the number of input arguments
rhs = argn(2);
// Check if the number of input arguments is valid
if rhs < 1 | rhs > 2 then
error("Wrong number of input arguments.");
end
// Perform action based on the number of input arguments
switch rhs
case 1 // If only A is provided
y = fft(A);
case 2 // If both A and SIZE are provided
// Check if A needs resizing
if size(A) == SIZE then
// No resizing needed
break;
elseif length(size(A)) ~= length(SIZE) then
error("Output size must have at least Ndims");
else
// Resize A using the resize_matrix function
A = resize_matrix(A, SIZE);
end
y = fft(A);
end
endfunction
/*
//test cases
i=%i;tol = 0.00001; pi = %pi ;
//test 1
Y = [41.0000 + 0*i ,-2.5000 + 2.5981*i ,-2.5000 - 2.5981*i ;2.0000 + 8.6603*i , 2.0000 + 3.4641*i , -8.5000 + 11.2583*i ;2.0000 - 8.6603*i , -8.5000 - 11.2583*i , 2.0000 - 3.4641*i]
assert_checkalmostequal(fftn([3 7 5;0 1 7;9 5 4]),Y,tol)
// test
assert_checkalmostequal(fftn([100 278;334 985]),[1697,-829;-941,473],tol)
assert_checkalmostequal(fftn([2:5;8 7 5 1;7 3 4 5;0 0 1 6],[2 2]),[20,0;-10,-2],tol)
assert_checkalmostequal(fftn([[i 2+3*i 2+pi;pi i+2 pi+i;1 5+2*5*i pi+10*i]],[2,2]),[7.1416 + 5.0000*i , -0.8584 - 3.0000*i; -3.1416 + 3.0000*i , -3.1416 - 1.0000*i],tol)
//error
fftn([2:5;8 7 5 1;7 3 4 5;0 0 1 6],[2]);
*/
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