Re: Operating on multi-dimensional arrays

On 2008-02-21 13:45:57 -0500, Doug Schwarz <see@xxxxxxxxxxxxxxxxxxx> said:

In article <47bdba3b$0$293$b45e6eb0@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Arthur G <gorramfreak+news@xxxxxxxxx> wrote:

I have a general question about how best to perform operations across
multiple dimensions of multi-dimensional arrays. But let me start with
the specific example of summing across "slabs" of a 3D array.

If I want to find the "row-wise" sums, I can think of two possiblities:

sum1a = sum(sum(x, 2), 3); % Sum across columns, then slabs
sum1b = sum(x(:,:), 2); % Convert to 2D and then sum

I like the second way because I only have to use sum once, but it only
works because I am maintaining the first dimensions and "collapsing"
dimensions 2 and 3 into one.

So if I want to find the "column-wise" sum, I can still use option 1:

sum2a = sum(sum(x, 1), 3); % Sum across rows, then slabs

But approach 2 requires permuting before reshaping:

xTemp = permute(x, [2 1 3]);
sum2b = sum(xTemp(:,:));

Does anyone know of a nicer way to perform operations like sum, max,
etc. across *multiple* dimensions, that doesn't require permuting or
reshaping? Applying the operation multiple times ("Approach 1" above)
also doesn't work for me, because it requires a fixed number of
dimensions, and I'm working with anywhere from 3D to 6D arrays.

--Arthur


We can't use permute or reshape and you don't want to use sum multiple
times. You've pretty much eliminated every approach I can think of to
solve your problem.

Forgetting about your restrictions, I would use a loop. Say you want to
sum across dimensions, dims = [2 3], you could use

function y = sum_mutidim(x,dims)
y = x;
for i = 1:length(dims)
y = sum(y,dims(i));
end


Untested, but should work.

Thanks. Your solution is nice. In fact, it's pretty much exactly what I was converging on: it is very similiar to the "normal" sum, but with a little more generalization.

Also, I don't *mind* the summing multiple times, since that's probably more efficient than permute/reshape. But I still wonder if there's a more efficient way that doesn't generate intermediate arrays. I doubt it would be as readable though, so I will probably stick with your solution unless I run into speed/memory problems.

Thanks again,
Arthur

.

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