Question

I have the following two vector fields:

>> orient

orient = 

    [1x3 double]    [1x3 double]    [1x3 double]
    [1x3 double]    [1x3 double]    [1x3 double]
    [1x3 double]    [1x3 double]    [1x3 double]

>> distance

distance = 

    [1x3 double]    [1x3 double]    [1x3 double]
    [1x3 double]    [1x3 double]    [1x3 double]
    [1x3 double]    [1x3 double]    [1x3 double]

and I need to take the cross product of pairwise elements i.e.

b = (cross(orient{1,1},distance{1,1}) + cross(orient{1,2},distance{1,2})..... and so on

and then reshape to match the dimensions of distance and orient.

Can I do this without using a for loop?

and what about if I have

orient{1,1} = 

[1x3 double]

distance = 

        [1x3 double]    [1x3 double]    [1x3 double]
        [1x3 double]    [1x3 double]    [1x3 double]
        [1x3 double]    [1x3 double]    [1x3 double]

how do I do

sum1 = (cross(orient{1,1},distance{1,1}) + cross(orient{1,1},distance{1,2}) +…)
sum2 = (cross(orient{1,2},distance{1,1}) + cross(orient{1,2},distance{1,2}) +…)

where each ‘sum’ is just an iteration of a single orient element, crossed with all the elements of distance, and then those cross products are summed. I would then have:

mastersum = sum1 sum2 sum3
            sum4 sum5 sum6
            sum6 sum8 sum9

where

sum1 = 

[1x3 double]

Am I just putting this in a confusing way?

Answer 1

You’ll need to use cellfun to traverse the cell arrays without a for-loop.

For two vector fields (two cell arrays), you should do:

crosses = cellfun(@(u, v)cross(u, v)', orient, distance, 'UniformOutput', 0);
b = sum(cell2mat({crosses{:}})', 1)  %# Summing all vectors in all cells

A similar procedure for single cell from orient, say orient{1, 2}, would be:

u = orient{1, 2};
crosses = cellfun(@(v)cross(u, v)', distance, 'UniformOutput', 0);
b = sum(cell2mat({crosses{:}})', 1)  %# This command remains the same

To get the result for all vectors from orient without a for loop, do instead:

b_func = @(u)sum(cell2mat(cellfun(@(v)cross(u,v)', {distance{:}}, 'Un', 0))', 1);
U = cellfun(b_func, orient, 'UniformOutput', 0)

Now U is also a cell array (of the same dimensions as orient): U{1, 1} has the sum of crosses for orient{1, 1}, U{1, 2} for orient{1, 2}, and so on…