Given two 1 x n cells namely, C1 and C2, how do I create a new cell C3 such that C3 = {C1(1) C2(1) C1(2) C2(2) C1(3) C2(3) ... } using a for loop?

For example suppose you are given cells

C1 = {[a1 b1; c1 d1] [a2 b2; c2 d2] [a3 b3; c3 d3] [a4 b4; c4 d4]}; C2 = {[e1 f1; g1 h1] [e2 f2; g2 h2] [e3 f3; g3 h3] [e4 f4; g4 h4]};

(i.e. both cells C1 and C2 contain four 2x2 matrices)

How would I using a for loop create a new cell C3 such that

C3 = {C1{1,1} C2{1,1} C1{1,2} C2{1,2} C1{1,3} C2{1,3} C1{1,4} C2{1,4}}.

Afterwards, I plan to use the function cell2mat() and prod() in order to multiply all the matrices.

Answer 1

[Walter Roberson]

for K = 1 : 1   %it's a loop
  C3 = {C1{1,1} C2{1,1} C1{1,2} C2{1,2} C1{1,3} C2{1,3} C1{1,4} C2{1,4}};
end

Alternately, and less efficiently,

C3 = cell(1,8);
for K = 1 : 4
  C3(2*K-1) = C1(1,K);
  C3(2*K) = C2(1,K);
end

You can cell2mat(C3) but you are going to get out a plain numeric array, 2 x 16 . If you prod() that, you would get out a 1 x 16 result.

[Josh]

Thank you Walter. Do you know of another method that would keep the 2 x 2 matrix format of each element in the cell? I would like to perform a product of each matrix in the cell.

[Walter Roberson]

You mentioned prod() so I will assume you want element-wide multiplication, not algebraic matrix multiplication.

C3 = cat(3, C1{1,1}. C2{1,1}. C1{1,2}, C2{1,2}, C1{1,3}, C2{1,3}, C1{1,4}, C2{1,4});
prod(C3, 3)

[Josh]

I would like to perform algebraic matrix multiplication of each 2x2 matrix.

The cat function does not change the cells to matrices therefore I can not use the prod function.

[Walter Roberson]

You will need a loop to do algebraic matrix multiplication..