Help to improve runtime of 3 dimensional matrix

hello everyone I wrote this code to read the indices of 3 dimensional matrix in a three column array. For n<100 (i.e. 100x100x100 matrix), MATLAB runs it in few hours. However, my final matrix is a 640x640x640 one for which MATLAB takes ages to finish. Could someone please help improve the code to run it faster. Any help is greatly appreciated.

clear all close all clc

n=640;

A = zeros(n,n,n);

Y = [0 0 0];

for i = 1:size(A(:, 1))

    i
        for j = 1:size(A(:, 2))

        for k = 1:size(A(:, 3))

            Y = [Y;i,j,k];  

        end

        end

end

[KL]

This looks like a poorly formed example of your original problem. Instead of the dummy operation you do with Y, explain your operation. Without knowing that it's hard to help you.

[Pervez Ahmed]

Sorry, It is not a dummmy operation. This is my original problem. Once i locate the indices of all the voxels in the 3D matrix i then have to calculate the distance of every voxel from the centre of the matrix.

Answer 1

[Stephen23]

Your code is hugely inefficient because you expand the output array on each iteration. Read this to know more about why that is so inefficient, and how to avoid this penalty:

https://www.mathworks.com/help/matlab/matlab_prog/preallocating-arrays.html

While you could solve this using array preallocation, loops, and indexing, a simpler and much more efficient solution is to use ndgrid (and avoid loops altogether):

>> [X,Y,Z] = ndgrid(1:n);
>> out = [Z(:),Y(:),X(:)];

Note that this will create a matrix out with 3*n^3 elements.

[Pervez Ahmed]

This worked. Thank you soo much stephen. I grately appreciate your help.

Answer 2

[Image Analyst]

Use meshgrid() to get a list of all coordinates, then use sqrt() to get distance to the middle. Untested code:

[X, Y, Z] = meshgrid(1:n, 1:n, 1:n);
distances = sqrt((X(:)-n/2).^2 + (Y(:)-n/2).^2 + (Z(:)-n/2).^2);
distances = reshape(distances, n, n, n);

and so on...

[Pervez Ahmed]

Thank you so much Image Analyst.