how to multiply a matrix with every cell of cell array in Matlab?

Question

I have a 4D array A size(l,k,s,r) and a cell array B size(i,j) where in each cell a different 4D array of coefficients size(l,k,s,r) is stored.

I want to make changes in the given array C of size(i,j) = C(i,j) + sum(sum(sum(sum(A.*B{i,j})))) without for loop.

in other words I need to extract one by one all arrays out of cell array B and multiply with A .

with the for loop i do it this way:

for i=1:length_of_first_dimension
    for j=1:length_of_second_dimension
        B_4D=B{i,j};       % extraction of 4D array
        dummy(i,j)=sum(sum(sum(sum(B_4D.*A))));
    end
end
C=C+dummy;

can anyone help me with that?

Answer 1

first, reshape B into a (length_of_first_dimension*length_of_second_dimension) -by- l*k*s*r 2D matrix

rB = cellfun( @(x) x(:).', B, 'uni', 0 ); %'
rB = vertcat(rB{:});

Now, reshape A into a l*k*s*r -by-1 column vector

rA = A(:);

And simply multiply them

rDummy = rB * rA; %// does the elem-wise product and summation quite quickly.  

Reshape the result

dummy = reshape(rDummy, size(B) );
C = C + dummy;

---

As pointed by Divakar a more efficient way to reshape B would be

rB = reshape( cat( 5, B{:} ), numel(A), [] ).';

And a small benchmark can be found here .