How can I compute rms of 3D cubes from 3D meshgrid array in vectorized fashion?

I have a 3D array of magnitude values across x,y,z space - dim: (400,400,300). I want to calculate the rms of the magnitude across all (10,10,10) cubes. My loop solution to this looks as follows:

for iz = 1:30

for iy = 1:40

for ix = 1:40

[idx,idy,idz] = meshgrid([((ix-1)*10)+1:ix*10],[((iy-1)*10)+1:iy*10],[((iz-1)*10)+1:iz*10]);

li = sub2ind(size(magfield),idx,idy,idz);

cmag(ix,iy,iz) = rms(magfield(li),"all");

end

end

end

How could I compute cmag in a vectorized way not using any loops? Thanks!

Answer 1

[Aman Banthia]

Hi Lucas,

I understand that you want to use vectorized method instead of a ‘for’ loop to calculate the rms of the magnitude across all (10,10,10) cubes.

To compute ‘cmag’ in a vectorized way without using any loops, you can utilize the “reshape” and “permute” functions in MATLAB. Here is an example of how you can modify your code:

% Reshape the magnitude array into a 2D array of (10, 10, 10) cubes
  
reshaped_mag = reshape(magfield, [10, 10, 10, 40, 40, 30]);
  
% Permute the dimensions to group the cubes together
  
permuted_mag = permute(reshaped_mag, [1, 4, 2, 5, 3, 6]);
  
% Compute the RMS along the first three dimensions
  
cmag = rms(permuted_mag, [1, 2, 3]);

In this vectorized approach, we first reshape the ‘magfield’ array into a 6D array where each cube is represented by the first three dimensions (10, 10, 10). Then, we permute the dimensions to group the cubes together. Finally, we compute the RMS along the first three dimensions using the rms function.

By using this vectorized approach, you can avoid the nested loops and calculate ‘cmag’ efficiently without sacrificing performance.

Please refer to the following MATLAB documentation for more details:

1. https://in.mathworks.com/help/matlab/ref/rms.html
2. https://in.mathworks.com/help/matlab/ref/permute.html
3. https://in.mathworks.com/help/matlab/ref/reshape.html

Hope the above solution helps you.

Best Regards,

Aman Banthia