# Basic math operations on contents of a cell array

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Bill Tubbs on 4 Nov 2020
Commented: Bill Tubbs on 4 Nov 2020
Is there any reason why basic math operations don't work with cell arrays? Seems to me it would extremely useful and efficient if you could do the following:
C = [0.7152 1.0000];
A = [0.6807 0; 0 1.0000];
Apows = {A,A^2,A^3};
C*Apows
Result:
Undefined operator '*' for input arguments of type 'cell'.
Expected:
{C*Apows{1},C*Apows{2},C*Apows{3}} =
1×3 cell array
{1×2 double} {1×2 double} {1×2 double}
Is this the only/best way to do this (which I got from this answer):
cellfun(@(x) C*x,Apows,'UniformOutput',false);
ans =
1×3 cell array
{1×2 double} {1×2 double} {1×2 double}

Matt J on 4 Nov 2020
Edited: Matt J on 4 Nov 2020
Is there any reason why basic math operations don't work with cell arrays? Seems to me it would extremely useful and efficient if you could do the following:
Cell arrays are designed for containing objects of different types and sizes. They are a fundamentally inefficient way to hold objects that are all the same size, partly because their contents are not guaranteed to be held contiguously in RAM. Because a better data type is usually available for the situations you describe, TMW hasn't bothered to define such operations for cells. You could write cell-like class with overloaded arithmetic operations if you wished, but it would be syntactic sugar, and nothing more.
For the scenario in your example, moreover, the best method is in any case a simple for loop. This accomplishes the whole operation with just 3 multiplications with A, unlike the approach you presented which first forms Apow.
out=cell(1,4);
out{1}=C;
for i=2:4
out{i}=out{i-1}*A;
end
out=out(2:end);
Bill Tubbs on 4 Nov 2020
It could be argued that the applicability of cellfun is so great that it could be replaced with a dedicated language feature. E.g. something similar to list comprehensions in Python. Maybe something like this:
{C*x for x=Apows}
(would produce a cell array)

James Tursa on 4 Nov 2020
I suppose only TMW could give you their reasons for not implementing numeric operations on cell arrays. Maybe they simply didn't want to expend the effort when cellfun( ) would suffice.
One other option for you is to stack your matrices in a single array:
Apows = cat(3,A,A^2,A^3);
Then you can use a variety of options for doing the page matrix multiplies:
pagemtimes (R2020b)
Some options from the FEX:
MULTIPROD:
MTIMESX: (C-mex code requiring C compiler) needs updated build routine for later MATLAB versions
MMX: (C-mex code requiring C compiler)
Bill Tubbs on 4 Nov 2020
Thanks, these alternatives to using cellarrays seem to be exactly what I am actually looking for in this case where the computations are matrix operations. I will look into these...

R2020a

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