Make a 3D matrix block diagonal

Hi all,

I have a 3-D matrix which I would like to make block-diagonal on its 2nd dimention. In my case I have:

clear ; clc

v = 1:3672 ;
Nc = 18 ;   % Rows
Nb = 4 ;    % Columns
nn = 51 ;   % Pages

M = reshape(v, Nc, Nb, nn) ; % 3D matrix which contains experimental data in my case

a small section of which looks like this:

>> M(:,1:3,1)

ans =

     1    19    37    55
     2    20    38    56
     3    21    39    57

and I would want to make it look like this:

>> M(:,1:3,1)

ans =

     1    19    37    55    0     0     0     0     0    0      0     0
     0     0    0     0     2    20    38    56     0    0      0     0
     0     0    0     0     0    0      0     0     3    21    39    57

And my attempt to make this happen is the following code:

clear ; clc

v = 1:3672 ;
Nc = 18 ;   % Rows
Nb = 4 ;    % Columns
nn = 51 ;   % Pages

M = reshape(v, Nc, Nb, nn) ;    % 3D matrix which contains experimental data in my case
Mn = zeros(Nc, Nc*Nb, nn) ;     % Preallocated new matrix with extended number of columns

% Convert subscripts to linear indices for the new matrix
ind = sub2ind(size(Mn), repmat(1:Nc, 1, Nb*nn), ...
                        repmat(reshape(reshape(1:(Nc*Nb), Nb, Nc)', Nb*Nc, 1), nn, 1)', ...
                        repelem(1:Nb, Nc*nn)) ;

% Allocate the old matrix M into the new Mn for the above calculated indices 
Mn(ind) = M ;

However, the above doesn't work as with a quick test even though the Mn matrix has the right shape, the allocation of the elements is not done in the appropriate places.

Preferably I would like to avoid blkdiag because I have to perform this for a very large number of other matrices and I have noticed from past experience that this function is fairly slow.

Thanks for your help in advance.

Answer 1

[Aman Banthia]

Hi Kostas,

It seems like you're trying to reshape a 3D matrix into a block-diagonal matrix on its 2nd dimension. The issue you're encountering is due to the incorrect calculation of linear indices for the new matrix.

You can try the following code which uses a loop over the third dimension of your matrix ‘M’. This code will create a block-diagonal structure where each block comes from the corresponding 2D slice of ‘M’. It's not using ‘blkdiag’ function, thus it should be faster.

clear ; clc

v = 1:3672 ;

Nc = 18 ;   % Rows

Nb = 4 ;    % Columns

nn = 51 ;   % Pages

M = reshape(v, Nc, Nb, nn) ;    % 3D matrix which contains experimental data in my case

Mn = zeros(Nc, Nc*Nb, nn) ;     % Preallocated new matrix with extended number of columns



for k = 1:nn
    
    for i = 1:Nc
        
        Mn(i, ((i-1)*Nb+1):i*Nb, k) = M(i,:,k);
        
    end
    
end

This code will create a new matrix ‘Mn’ where each row of each 2D slice of ‘M’ is placed on the diagonal of the corresponding 2D slice of ‘Mn’.

If you face performance issues with this code, you might need to consider using a sparse matrix representation or other optimization techniques.

Refer to the following MATLAB Documentation Link to know more about ‘blkdiag’ function:

https://in.mathworks.com/help/matlab/ref/blkdiag.html

Hope the above solution helps you.

Best Regards,

Aman Banthia