How to reference multiple matrices in cell arrays using a colon or other special characters rather than a loop?

Is there a way to pull values from multiple arrays without using loops? Specifically, I would like to achieve something like this:

for i = 1:5
    for j = 1:3
        new{i,j} = a1{i,j}./a2{i,j};
    end
end

by doing something simpler and faster like:

new{:,:} = a1{:,:}./a2{:,:};

but this kicks back an error. Assuming all the cell arrays hold appropriately sized matrices, is a loop my only option for this?

Answer 1

[dpb]

That's what cellfun is for...

>> a={rand(2)}; a(2)=a(1);  % a simple test
>> b=a;
>> cellfun(@rdivide,a,b,'uni',0)
ans = 
  [2x2 double]    [2x2 double]
>> ans{:}
ans =
   1     1
   1     1
ans =
   1     1
   1     1
>>

ADDENDUM TO ALTERNATE CONSTRUCTS REQUESTED:

Subscripted assignment

out=cellfun(@(x) x(1:2:end,1:2:end),a,'uni',0);

for fixed subscripts. To include them as a variable, add as additional dummy arguments in the anonymous function definition. Assignment is kinda' the "odd man out" as you see; there isn't another function name as a standin is for other operators such as plus

The interp2 case. Presuming X?,Y? are fixed, then

new=cellfun(@(x) interp2(Xl,Yl,x,Xh,Yh,'cubic'), a, 'uni',0);

The pattern should begin to come apparent; if the operation is a basic one equivalent to a single operation like + you use that function handle name; if it's more complex you invoke another function placing the cell array(s) in the passed-in position(s) in order they're given. Here the operation is simple enough to use an anonymous function; if it's more complex, write a separate function in an m-file and use the handle to it instead.

Seems very complicated at start, granted, but once you get one or two under your belt it'll quickly become easier...

[Stephen23]

Selena G's "Answer" moved here:

Ah, very cool. Thank you.

[Stephen23]

Selena G's comment moved here:

That was very helpful, but I am a beginner when it comes to function handles. How would I apply that for something like this:

for i = 1:5
    for j = 1:3
        new{i,j} = interp2(Xl,Yl,a1{i,j},Xh,Yh,'cubic');
    end
end

or this:

for i = 1:5
    for j = 1:3
        new{i,j} = a1{i,j}(1:2:10,1:2:10);
    end
end