Multiply matrices in cell array Matlab?

Question

I have a cell array of `cell(1, n)` called `A`, with each cell entry containing a matrix of `mxn`. So, in effect, my cell array contains `n` matrices of size `mxn`. I then have another cell array called `B`, with `n` `pxm` matrices stored in it. What I need to do is multiply the two against each other, as in: `A[1] * B[1]`, `A[2] * B[2]`, ..., `A[n] * B[n]`. I then need to store the results as individual matrices of their own, and sum them up. The matrices are conformal for multiplication, but because cell array `B` contains less rows than cell array `A`, when I use `cellfun(@times A, B, 'UniformOutput', true)` I get an `unequal matrices` error. This seems to indicate that `cellfun` can only multiply individual cells when the matrices have equal numbers of rows and columns. Now, I could perform this by using various loops, or by calling `cell2mat` and `mat2cell`, and so on. I could also just store everything as a matrix array rather than using cells... but - I would prefer to use cell…

Accepted Answer

To do this with `cellfun`, just define your own anonymous function:

```
C = cellfun(@(a,b) a*b, A, B, 'UniformOutput', 0);
```

Now, as you posed the question, you cannot multiply A*B, because the inner dimensions don't agree. Instead, I tested this with B*A, where the dimensions do agree: p=1, m=3, n=3.

```
A = {eye(3), rand(3), magic(3)};
B = {[1 2 3], [3 5 1], [7 8 8]};

C = cellfun(@(a,b) b*a, A, B, 'UniformOutput', 0);

Cmat = cat(3, C{:});
S = sum(Cmat, 3);
```

The sum is done by concatenating each array of `C` over a third dimension then summing over it.

Multiply matrices in cell array Matlab?

Solution

Problem