MATLAB: How to average along all permutations of a 4D array

arrayssymmetry

I was looking for an efficient way of averaging along all permutations of a 4D array, in other words enforce super-symmetry. Given a 4D array ?, I want to compute ℬ such that:

where p is all the permutations of

For a 2D array

it is easy to enforce symmetry by setting

. Is there something similar for a 4D array?

Best Answer

Why not as follows?

assert( all(size(A)==size(A,1) )  & ndims(A)==4  , 'A must be NxNxNxN')
p=perms(1:4);
B=0;
for i=1:24
    
    B=B+permute(A,p(i,:));
    
end
B=B/24;

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MATLAB: Convert a 3D array to a 2D cell array

B=num2cell(A,3)

MATLAB: How to find duplicates in a structure

Numbered variables (or fields) is usually an indication that the thing would be much better stored as a matrix or cell array. In your case, just one 3D matrix or a vector cell array of 2D matrices would be easier to use:

BoundCoord = structfun(@(b) {b}, variable2)
%as a vector cell array of 2D matrices:
variable2.BoundCoord = BoundCoord;
%as a 3D matrix:
variable2.BoundCoord = cat(3, BoundCoord{:});

Note: rather than converting after the fact, you'd be better off fixing the structure creation to avoid these numbered fields in the first place.

This is now easier to manipulate. For example, to find which of the pages of the 3D matrix is repeated:

[~, ~, uid] = unique(reshape(variable2.BoundCoord, size(variable2.BoundCoord, 3), []), 'Rows')
samepages = accumarray((1:size(variable.BoundCoord, 3))', uid, [], @(p) {p})

Each cell of samepages contains the page index of identical 2D matrices. For this, I reshaped the matrices into rows and used unique with the 'rows' option to give them a unique id. Then used this id to build the cell array.

Best Answer

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MATLAB: Convert a 3D array to a 2D cell array

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