Compute average in different columns of cell arrays without considering 0 values

I have a cell array of 30 arrays. Each cell in it is a matrix of thousands rows and let's say several columns.

With a simple example, my cell is C and C{1,1} contains a matrix of single double values like this

C{1,1}=[1 4  5
        2 56 6 
        3 0 0]

C{2,1}=[1 0  0
        2 6  11
        3 0  0]

Also I want to get the mean of all non zeros elements in the 2nd columns in all the cell matrices

If I do

mean(C{1,1}(:,2)) %mean of 2nd column in first cell matrix

but this also includes values where 2nd column is 0 so to remove zero values I did in 3 steps

    A=C{1,1};
    B=A(:,2)>0;
    mean(A(B,2));

or in a single line

mean(C{1,1}(C{1,1}(:,2)>0,2))

So far, this is ok and gives me the average of a the second column in the first cell matrix but then when I wanted to get at once all the averages of the cell matrices and compute its means later with

Averages(:)= mean(C{:,1}(:,2))

but I get an error. I am not removing the zeros here just for the line to be more clear. My problem is how to use the : with the cell matrices. With a for loop, I can do it like this

Averages=zeros(30,1);
for ii=1:30
 Averages(ii)=mean(C{ii,1}(C{ii,1}(:,2)>0,2)); 
end
AvgC=mean(Averages);

But is there a way to do it without for. In other words how can access to the all cells 2nd column at once?

[Image Analyst]

Does each cell contain an array of the same size? Or are they all different sizes? If they're the same size, convert the cell array into a 3D numerical array and then use mean().

And nothing is wrong with a for loop, certainly not for a microscopic for loop of only 30 iterations. It will be so fast you won't believe it.

[etudiant_is]

yes they are of the same size. How do I convert to a 3D array? I have been told that for loops are not optimal so not to use them as much as possible. But I will try it.

[Image Analyst]

Andrei shows you how to convert to a 3D array below. Whoever told you that loops are not optimal forgot to tell you that cell arrays are so much more not optimal than for loops it's not funny. The overhead for a cell array is huge. They are slow and inefficient. You should have never used a cell array for this situation in the first place - that was a bad choice.

For loops are not slow, though for many iterations they may be slower than other vectorized ways. But for less than a few million iterations, for loops are fine, generally finishing in less than a second.

[etudiant_is]

Actually, in this example I have cell arrays of single elements but I have others cells where each element is of different type (matrices, single elements, etc). So I don't think I can do it without cells for these cases. What should I use instead of cells then?

[Image Analyst]

If each column of the cell array is of the same type, like column 1 is all strings, and column 2 is all scalars, then you can use a "table" variable, as long as you have R2013b or later.

Answer 1

[Andrei Bobrov]

z = cat(3,C{:});
x = squeeze(z(:,2,:));
out = (sum(x)./sum(x~=0))';

[etudiant_is]

Thanks a lot, That gives me the same values I got in averages in out. But why do I have to compute out like this and not use instead mean(x)? I tried mean(x) and the result is completely different.

[Andrei Bobrov]

Please give example

[Image Analyst]

The mean will take into account zeros, while Andrei's code does what you asked and does not include zeros.

[etudiant_is]

ok, that was it. Thanks a lot for both of you.