Cell entries as the third dimension of the cell2mat matrix.

I am using this code to initialize A and B:

for k=1:N
    for j=1:N
        A{k,j}=S(:,j).*D(k,:).';
        B(k,j,:)=A{k,j};
    end
end

Essentially, I want to create B directly from A without explicit loops as I found a vectorized way to create A.

[Rik]

You can probably use reshape and repmat to get implicit expansion to do this for you. What have you tried?

Also, you don't need A at all here to get B. Do you need A later?

[Anish Pradhan]

I do need A later. I have tried:

C = cellfun(@transpose,A,'un',0);

B2= reshape(cell2mat(C),[N,N,N])

But B and B2 are different in arrangement. For context, they both are part of an elaborate gradient calculation.

Answer 1

[Adam Danz]

Compute B outside of the loop

for k=1:N

for j=1:N

A{k,j}=S(:,j).*D(k,:).';

end

end

B = permute(reshape(horzcat(A{:}),size(A,1),size(A,2),[]),[2 3 1]);

Confirm that it's equal to the loop version of B

N = 3;  % Demo data
S = 100 * rand(N); 
D = 5 * rand(N);

for k=1:N
    for j=1:N
        A{k,j}=S(:,j).*D(k,:).';
        BLoop(k,j,:)=A{k,j};
    end
end
B = permute(reshape(horzcat(A{:}),size(A,1),size(A,2),[]),[2 3 1]); 

isequal(BLoop, B) % True means BLoop and B are equal

ans = logical
   1

Explanation

This is our goal

BLoop

BLoop = 
BLoop(:,:,1) =

  233.0973  127.4516  305.5177
  202.6588  110.8086  265.6223
   66.6101   36.4207   87.3051


BLoop(:,:,2) =

  188.3584   54.7575   69.7297
  325.8464   94.7265  120.6274
  235.6702   68.5114   87.2444


BLoop(:,:,3) =

  447.2431  180.8590   27.1600
  279.9638  113.2135   17.0015
  343.8104  139.0322   20.8788

First the columns of A are concatenated into a matrix

horzcat(A{:})

ans = 3×9

233.0973 202.6588 66.6101 127.4516 110.8086 36.4207 305.5177 265.6223 87.3051 188.3584 325.8464 235.6702 54.7575 94.7265 68.5114 69.7297 120.6274 87.2444 447.2431 279.9638 343.8104 180.8590 113.2135 139.0322 27.1600 17.0015 20.8788

Then the matrix is reshaped into a 3D array according to the shape of A. The shape looks like our goal but note that the order of the values do not match the goal.

reshape(horzcat(A{:}),size(A,1),size(A,2),[])

ans = 
ans(:,:,1) =

  233.0973  202.6588   66.6101
  188.3584  325.8464  235.6702
  447.2431  279.9638  343.8104


ans(:,:,2) =

  127.4516  110.8086   36.4207
   54.7575   94.7265   68.5114
  180.8590  113.2135  139.0322


ans(:,:,3) =

  305.5177  265.6223   87.3051
   69.7297  120.6274   87.2444
   27.1600   17.0015   20.8788

Finally, the dimensions of the 3D array are rearranged to move dim 1 to dim 3 per the instructions in "BLoop(k,j,:)"

B = permute(reshape(horzcat(A{:}),size(A,1),size(A,2),[]),[2 3 1])

B = 
B(:,:,1) =

  233.0973  127.4516  305.5177
  202.6588  110.8086  265.6223
   66.6101   36.4207   87.3051


B(:,:,2) =

  188.3584   54.7575   69.7297
  325.8464   94.7265  120.6274
  235.6702   68.5114   87.2444


B(:,:,3) =

  447.2431  180.8590   27.1600
  279.9638  113.2135   17.0015
  343.8104  139.0322   20.8788

Confirm that we have met the goal

isequal(B,BLoop)

ans = logical
   1

[Anish Pradhan]

Thank you so much Adam!