Sum over part of array without knowing array size

I currently have a function that takes a two dimensional (2D) array as one of its inputs. Part of the function code sums over all but the first column of this input array, i.e.:

function DoSomething( Array2D, OtherInputs)
    ...
    SumOverColumns = sum(Array2D(:, 2:end), 2);
    ...
end

I want to expand the use of the function so that the array can be 3D or more. However, I still want to be able so sum over all columns except the first one. I can't think of a general way to do this because I think that I need to specify ":" for every other dimension.

Any help would be much appreciated.

[Cedric]

You need to define a little more precisely what happens with higher dimensions, and what it is that you want to output. In 2D you are summing over the 2nd dimension excluding the first column and outputting a column vector of sums. What happens in 3D? Do you still need to sum over the 2nd dimension only excluding the first column of each page (and hence output a 2D array of sums), or do you need to sum over dimensions 2 and 3 excluding the first, simultaneously (output a vector) or separately (output two 2D arrays)?

[JE]

Hi Cedric

In the following, I've used a1 to denote the size of dimension 1 (of the input array), a2 for the size of the 2nd dimension and so on.

Yes, in the 2D example, the result is a column vector (e.g., a1 x 1).

For 3D, I want the output to be a1 x 1 x a3. For 4D, I want the output to be a1 x 1 x a3 x a4. and so on.

Answer 1

[John D'Errico]

Or more? How many more dimensions? Really high dimensional arrays will be huge, so it makes little sense to have a 300 dimensional array. Even a 2- dimensional array actually has infinitely many trailing singleton dimensions. So a 5x6 array is actually implicitly of size

[5,6,1,1,1,1,1,1,1,1, ...]

Suppose you are willing to assume your array will have no more than 5 dimensions in the future. Then the trivial solution is:

SumOverColumns = sum(Array2D(:, 2:end, :, :, :), 2);

There are ways to do this with more potential dimensions, but why bother?

[JE]

Hi John

Thanks for your input.

I'd considered that as a solution. However, my main concern is that however many ":" I input, it will end up being one too few at some point in the future, creating a hard to find bug!

Ideally, I'd like something more general (but I accept that solution might not exist).

[John D'Errico]

If you really cannot limit the number of dimensions, then this will work:

S = size(ArrayNd);
S(2) = S(2) - 1;
SumOverColumns = reshape(sum(ArrayNd(:, 2:end,:), 2),S);

[JE]

Hi John

That works with one slight change to the 2nd line:

S = size(ArrayNd);
S(2) = 1;
SumOverColumns = reshape(sum(ArrayNd(:, 2:end,:), 2),S);

Thanks very much!

[John D'Errico]

Oops, yes. You were summing on that dimension. Yes.