Matlab: Matrix multiplication of many matrices in cell arrays

Question

I have a cell array size 1x200x201, in each cell is 2x2 matrix. I need to multiply the matrices in a way that I would get resulting matrix: 2x2x201. Which means: Cell_M{1,1,1}* Cell_M{1,2,1}*Cell_M{1,3,1}*... and so on up to 200, and the same up to 201 ( Cell_M{1,1,2}* Cell_M{1,2,2}*Cell_M{1,3,2}*... ). Cell arrays is just a way for handling the data. Is any effective way to do this multiplications?

Answer 1

Floating-point matrix multiplication is not associative in general, so A*B*C*D is ambiguous. In this code I assume you are looking for ((A*B)*C)*D

d=size(Cell_M); 
P = cell(d(1), 1, d(3)); 
P(:)={eye(2)}; 
for k=1:d(2), 
    P = cellfun(@mtimes, P(:,1,:), Cell_M(:,k,:), 'UniformOutput', false); 
end
P = squeeze(P);

Now P will be a cell array of 201 elements where each element is a 2-by-2 matrix.