CODEWITHSUNDEEP
arraysmatlabmatrix
user2457516
user2457516

Reputation:

MATLAB sum over all elements of array valued expression

So I've been wondering about this for a while now. Summing up over some array variable A is as easy as

sum(A(:))
% or
sum(...sum(sum(A,n),n-2)...,1) % where n is the dimension of A

However once it gets to expressions the (:) doesn't work anymore, like

sum((A-2*A)(:))

is no valid matlab syntax, instead we need to write

foo = A-2*A;
sum(foo(:))
%or the one liner
sum(sum(...sum(A-2*A,n)...,2),1) % n is the dimension of A

The one liner above will only work, if the dimension of A is fixed which, depending on what you are doing, may not necessary be the case. The downside of the two lines is, that foo will be kept in memory until you run clear foo or may not even be possible depending on the size of A and what else is in your workspace.

Is there a general way to circumvent this issue and sum up all elements of an array valued expression in a single line / without creating temporal variables? Something like sum(A-2*A,'-all')?

Edit: It differes from How can I index a MATLAB array returned by a function without first assigning it to a local variable?, as it doesn't concern general (nor specific) indexing of array valued expressions or return values, but rather the summation over each possible index.

While it is possible to solve my problem with the answer given in the link, gnovice says himself that using subref is a rather ugly solution. Further Andras Deak posted a much cleaner way of doing this in the comments below.

Upvotes: 5

Views: 502

Answers (1)

Andras Deak -- Слава Україні
Andras Deak -- Слава Україні

Reputation: 35175

While the answers to the linked duplicate can indeed be applied to your problem, the narrower scope of your question allows us to give a much simpler solution than the answers provided there.

You can sum all the elements in an expression (including the return value of a function) by reshaping your array first to 1d:

sum(reshape(A-2*A,1,[]))
%or even sum(reshape(magic(3),1,[]))

This will reshape your array-valued expression to size [1, N] where N is inferred from the size of the array, i.e. numel(A-2*A) (but the above syntax of reshape will compute the missing dimension for you, no need to evaluate your expression twice). Then a single call to sum will sum all the elements, as needed.

The actual case where you have to resort to something like this is when a function returns an array with an unknown number of dimensions, and you want to use its sum in an anonymous function (making temporary variables unavailable):

fun = @() rand(2*ones(1,randi(10))); %function returning random 2 x 2 x ... x 2 array with randi(10) dimensions
sumfun = @(A) sum(reshape(A,1,[]));
sumfun(fun()) %use it

Upvotes: 10

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