# Vectorization over different array sizes

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Cyrill Slezak 2022-3-10

I'm trying to linearize (i.e. speed up) the following looped version of my code
for x=-range:1:range
for y=-range:1:range
for z=-range:1:range
canvas(index(1)+x,index(2)+y,index(3)+z)+=const*exp(-sum(((delta *[x,y,z]*RotationMatix)./[a,a,b]).^2));
end for
end for
end for
The element vise evaluation within the sum works well but I'm trying to also vectorize the remaining loops. I would appreciate any help and if you could point out why my aproach (below) fails I'd appreciate it!
[x y z] = ndgrid(-range:1:range,-range:1:range, -range:1:range);
canvas(index(1)-range:index(1)+range,index(2)-range:index(2)+range,index(3)-range:index(3)+range)+= ...
const*exp(-sum(((delta*[x(:) y(:) z(:)]*RotationMatix)./[a,a,b]).^2));
Thank you!

### 回答（1 个）

Suman Sahu 2023-2-13
The issue with your approach is that you are trying to use matrix addition between two arrays with different shapes. The first loop results in a 3D matrix of size (2 * range + 1)^3, whereas the second approach results in a 1D vector of size (2 * range + 1). You cannot add these two arrays together because they have different shapes.
To solve this problem, you can try to reshape the 1D vector into a 3D matrix of the same size as the output of the first loop before adding it to the canvas matrix. The following code should work:
[x, y, z] = ndgrid(-range:1:range, -range:1:range, -range:1:range);
result = const * exp(-sum(((delta * [x(:), y(:), z(:)] * RotationMatix) ./ [a, a, b]).^2));
%reshape so the result can be added to the canvas
result = reshape(result, size(x));
canvas(index(1)-range:index(1)+range, index(2)-range:index(2)+range, index(3)-range:index(3)+range) += result;

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