MATLAB: Help with Matrix block multiplication

matrix block multiplicationmatrix manipulationmatrix multiplication

Hi, i need help with block matrix multiplication. I think a practical example should explain what i'm looking for.
Given:
A = rand(3,3); B = rand(9,3);
so basically i have [A] nxn block (generalizing) and [B] (k*n)xn block.
I would like to achieve as a result the equivalent of the following:
[A*B(1:3,:);A*B(4:6,:);A*B(7:9,:)];
possibly without any loops and arrayfun/cellfun.
Thank you in advance.

Best Answer

A = [1 1 0;1 1 0; 1 1 1];
B = [1,2,3;4,5,6;7,8,9;2,6,8;4,1,6;1,12,16;4,2,1;4,9,6;3,8,2];
expected_result=[A*B(1:3,:);A*B(4:6,:);A*B(7:9,:)];
%code starts here
[m,n]=size(A);
[r,c]=size(B);
BB=permute(reshape(B',c,c,[]),[2 1 3]);
[a,b,c]=size(BB);
BBB=reshape(BB,[a b*c]);
A_times_B_slices=A*BBB;
C=permute(reshape(A_times_B_slices,b,a,[]),[2 1 3]);
My_Result=reshape(C,c,[],1)';
isequal(My_Result,expected_result) % to check both the results are the same
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