concatenation of N^2 3x3 matrixes into a 3Nx3N matrix

Question

I have N^2 matrixes. Each one is a 3x3 matrix. One way to concatenation them to a 3Nx3N matrix is to write A(:,:,i)= # 3x3 matrix i=1:N^2

B=[A11 A12 ..A1N;A21 ...A2N;...] But When N is large is a tedious work. What do you offer?

Answer 1

Here's a really fast one-liner that only uses RESHAPE and PERMUTE:

B = reshape(permute(reshape(A,3,3*N,N),[2 1 3]),3*N,3*N).';

And a test:

>> N=2;
>> A = rand(3,3,N^2)
A(:,:,1) =
    0.5909    0.6571    0.8082
    0.7118    0.6090    0.7183
    0.4694    0.9588    0.5582
A(:,:,2) =
    0.1791    0.6844    0.6286
    0.4164    0.4140    0.5833
    0.1380    0.1099    0.8970
A(:,:,3) =
    0.2232    0.2355    0.1214
    0.1782    0.6873    0.3394
    0.5645    0.4745    0.9763
A(:,:,4) =
    0.5334    0.7559    0.9984
    0.8454    0.7618    0.1065
    0.0549    0.5029    0.3226

>> B = reshape(permute(reshape(A,3,3*N,N),[2 1 3]),3*N,3*N).'
B =
    0.5909    0.6571    0.8082    0.1791    0.6844    0.6286
    0.7118    0.6090    0.7183    0.4164    0.4140    0.5833
    0.4694    0.9588    0.5582    0.1380    0.1099    0.8970
    0.2232    0.2355    0.1214    0.5334    0.7559    0.9984
    0.1782    0.6873    0.3394    0.8454    0.7618    0.1065
    0.5645    0.4745    0.9763    0.0549    0.5029    0.3226

Answer 2

Try the following code:

N = 4;
A = rand(3,3,N^2);                     %# 3-by-3-by-N^2

c1 = squeeze( num2cell(A,[1 2]) );
c2 = cell(N,1);
for i=0:N-1
    c2{i+1} = cat(2, c1{i*N+1:(i+1)*N});
end

B = cat(1, c2{:});                     %# 3N-by-3N