How to add more than two elements of a cell, where each element in the cell is a matrix of identicle size?

Hi,

A cell contains N elements, where each element is a square matrix, M1, M2, ...., MN of identicle size (say2x2). To add all matrices i.e., M1+M2+...+MN, I tried to use

"plus(M{1,:})", but works well only when the cell contains only two matrices; else it showed following error

Error using +

Too many input arguments.

The sample Matlab code to add 4 matrices of size 2x2 is show below:

M1 = [1 2; 3 4]
M2 = [2 1; 4 3]
M3 = [2 3; 5 2]
M4 = [1 3; 3 5]

M = cell(1,4);

M{1,1} = M1
M{1,2} = M2
M{1,3} = M3
M{1,4} = M4

S = plus(M{1,:})

The error upon the execution is as follows:

Error using +

Too many input arguments.

Error in celle_add_eg (line 13)

S = plus(M{1,:})

Can anyone kindly suggest the possible solution to this error?

Thanks in advance!!

Answer 1

[Shane L]

Try this:

sum(cat(3, M{:}), 3)

This first concatenates all of the arrays in the cells of M into a three-dimensional numeric array, and then it sums the numeric array along the third dimension.

[Amit Kumar]

Thanks for the reply, but it works only for scalar inputs in the matrix.

If I am trying to use this for symbolic variables, I am getting errror "Input arguments must be two-dimensional."

i tried the following as an example:

syms s

M1 = [s+1 2; 3 4]
M2 = [2 1; 4 3]
M3 = [2 3; 5 2]
M4 = [1 3; 3 5]

M = cell(1,3);

M{1,1} = M1
M{1,2} = M2
M{1,3} = M3
M{1,4} = M4

sum(cat(3, M{:}), 3)

On the execution, I am getting the following error:

Error using symengine

Input arguments must be two-dimensional.

Error in sym/privUnaryOp (line 943)

Csym = mupadmex(op,args{1}.s,varargin{:});

Error in sym/sum (line 54)

s = privUnaryOp(A, 'symobj::prodsumdim', num2str(dim), '_plus');

Error in celle_add_eg (line 16)

sum(cat(3, M{:}), 3)

Kindly, suggest the possible way out for this error.

Thanks.

[Shane L]

Unfortunately, I don't have access to the symbolic toolbox, so I was unable to test this solution for symbolic variables. However, I think you have two options:

1. The simplest option is likely to write a for-loop over the number of cells in M and add each matrix within the loop. This would be the most clear to a reader of the code, too. However, this may take some time if M is very large.
2. If you want to be able to take the sum in one line, here is a way to do it with only 2-D matrices:

reshape(sum(reshape(cat(2,M{:}),[],length(M)),2),size(M{1}))

This concatenates the matrices together in the second dimension, reshapes them in a 2-D array that can be summed over the second dimension, and then reshapes the result back to your original array size. Caveat: I have not been able to test this for symbolic variables. Does this work for you?

[Amit Kumar]

Thanks a lot !! It worked.