How to replace fftn and ifftn with parallel statements

I basically understand that fftn can be replaced by the following code, but how is ifftn implemented?

psi=rand(10,10,10);
% costly way
fftpsi=fftn(psi);
% This might save you some RAM, to be tested
[m,n,p] = size(psi);
for k=1:p
    psi(:,:,k) = fftn(psi(:,:,k)); 
end
psi = reshape(psi,[m*n p]);
for i=1:m*n % you might work on bigger row-block to increase speed
    psi(i,:) = fft(psi(i,:));
end
psi = reshape(psi,[m n p]);

Answer 1

[Sanju]

Hi 耀 王,

The “ifftn” function in MATLAB is implemented using a similar approach as the code you provided for “fftn” It performs the inverse Fourier transform on each slice of the input array along the specified dimensions.

Here's an example of how you can implement “ifftn” ,

psi = rand(10, 10, 10);
ifftpsi = ifftn(psi);

[m, n, p] = size(psi);
for k = 1:p
    psi(:,:,k) = ifftn(psi(:,:,k)); 
end

psi = reshape(psi, [m*n p]);
for i = 1:m*n 
    psi(i,:) = ifft(psi(i,:));
end
psi = reshape(psi, [m n p]);

This code applies the inverse Fourier transform to each slice of “fftpsi” along the third dimension.

You can also refer to the below documentation link if required,

https://www.mathworks.com/help/matlab/ref/ifftn.html

Hope this Helps!