How to apply a function that returns non scalar output to arrays using arrayfun?
For example - How to vectorize the following code?
array = magic(5);
A = cell(size(array));
for i=1:5
for j=1:5
A{i,j} = 1:array(i,j);
end
end
This naive attempt to vectorize does not work, because the output is not a scalar
array = magic(5);
result = arrayfun(@(x)(1:x),array);
There are 2 methods to achieve it:
It is possible to set 'UniformOutput' to false. Then, the result is a cell array.
result = arrayfun(@(x)(1:x),array,'UniformOutput',false);
But there is a nice trick that I have found today, the function itself can return a cell. This removes the need of typing 'UniformOutput',false each and every time.
result = arrayfun(@(x){1:x},array)
What is really interesting here that I don't have to type @(X)({1:x}) but I can define it only by using curly bracers @(X){1:x}
Edit(1): As @Jonas correctly points out, there is no wonder that the regular bracers () are not needed, as they are optional. For example, @(x) x+1 is a valid syntax.
Edit(2): There is a small difference between using the curly bracers method or the UniformOutput,false. When the input array is empty, their behavior is different.
arrayfun doesn't really vectorize the code, it just hides the loop (and will allow Matlab to multi-thread, if it's worth the time). Note that the cell "trick" is very useful with accumarray which doesn't have the uniformOutput option.In addition to the answer of Andrey I want to note that it seems, that the first approach, using the option UniformOutput, is slightly faster:
>> tic; cellfun(@(x) {single(x)}, data); toc;
Elapsed time is 0.031817 seconds.
>> tic; cellfun(@(x) single(x), data,'UniformOutput',0); toc;
Elapsed time is 0.025526 seconds.
