Good method to store pyramid shaped cell array?

Hi all,

I need to store some matrices in a cell, say I have 4 matrices: e1, e2, e3, e4, I need to compute the product of the matrix transpose and the matrix itself like:

e1' * e1; e1' * e2;
e2' * e2; e2' * e3;
e3' * e3; e3' * e4;
e4' * e4;

So the matrix transpose product itself, and the matrix transpose multiply the next matrix. I can use a 4-by-2 cell to store these, but the last cell element would be void, any better ways? I'd like to keep the hierarchical structure. Cheers!

Edit: I'm sorry, I should have made the question clearer. I just generate a 4-by-2 cell array and store these in it, leaving the last cell element void. I think it is fine for now.

Answer 1

[Darshan Ramakant Bhat]

You can make use the of the linear indexing of MATLAB. Basically 2D matrix can be stored as a single dimension cell array. To access a particular row,column you can convert the subscript to linear index and then access it from the array. Example code can be like below:

MAT_cell = cell(1,7);
MAT_cell{1} = "e1'*e1";
MAT_cell{2} = "e2'*e2";
MAT_cell{3} = "e3'*e3";
MAT_cell{4} = "e4'*e4";
MAT_cell{5} = "e1'*e2";
MAT_cell{6} = "e2'*e3";
MAT_cell{7} = "e3'*e4";
matSize = [4 2];
% The index (3,2) can be accessed like below:
linIndex = sub2ind(matSize,3,2);
val = MAT_cell(linIndex)

I hope this will help you.

[Walter Roberson]

I do not understand why you used "" string objects in combination with cell arrays? If you were trying to create an array of string objects then use MAT_cell = strings(1,7) and use () indexing instead of {} indexing.

But it looks to me as if the poster is not interested in constructing strings and instead wants actual computation.

[Darshan Ramakant Bhat]

Hi Walter,

I just represented matrices as string, just for the understanding and simplicity purpose. The string should be replaced by the actual matrix in the original implementation.

Answer 2

[Jos (10584)]

If you have too many void cells in an array, you could consider a sparse encoding scheme, where you store the indices and the contents of your cell structure, similar to SPARSE. In your case however, having a single void cell, I would not take the trouble. Nonetheless, here is one approach:

C = {'one',[],[] ; [] 2 [] ; [] 3 4 ; [] [] [] ; 5 '6' []} % a cell array with many voids
  % encode into sparse format using a structure
  tf = ~cellfun(@isempty,C) ; % non-empty cells
  S.size = size(C) ;
  S.index = find(tf) ; % index
  S.values = C(tf) ;
  whos % encoding into sparse saves some memory ...

    % rebuild
    C2 = cell(S.size) ;
    [C2{S.index}] = deal(S.values{:})
    isequal(C, C2) % check ...