how to calculate the variance between columns of matrices

Hi I have two matrices a = [NaN 2 3 ; 2 NaN 4 ; 5 NaN 4] and b = [4 2 3 ; 5 NaN 4 ; 7 NaN 9]

What I want to do is create one matrix that shows the variance between each column (between the values located in the same position in each of the two matrices). How to do that? Thanks!!

Answer 1

[Greg Heath]

>> var(b-a) = [ NaN NaN 8.3333 ]

However, I have no idea what the variance of the difference between two matrices is supposed to represent

Hope this helps

Thank you for formally accepting my answer

Greg

[Matt J]

A Commented:

Hi Greg, Thanks for your reply. Ok I'll put in this way: a = [NaN 2 3 ; 2 NaN 4 ; 5 NaN 4] b = [4 2 3 ; 5 NaN 4 ; 7 NaN 9] c= [4 NaN 2 ; 5 8 4 ; 8 NaN 9]

the outup matrix should be [ 0 0 .33; 3 0 0; 2.3 NaN 8.33 ] so the variance should be calculate for each matrix positions considering the values of a, b and c matrixes output matrix format = [ var((a(1,1),b(1,1),c(1,1) var((a(1,2),b(1,2),c(1,1) (...) var((a(2,1),b(2,1),c(2,1) (...) ] Any suggestions? Thanks

Answer 2

[Greg Heath]

No. The output is

 >> output    = reshape(var([a(:)';b(:)';c(:)']),3,3)

output =

          NaN          NaN      0.33333
            3          NaN            0
       2.3333          NaN       8.3333

Hope this helps.

Thank you for formally accepting my answer

Greg

Answer 3

[Guillaume]

To calculate the element-wise variance (mean / sum / etc.) of several matrices of the same size, just concatenate them along a new dimension and apply the function along that dimension:

together = cat(3, a, b, c); %concatenate along 3rd dimension
elementwisevar = var(together, 0, 3); %variance along 3rd dimension
%or as a one liner:
elementwisevar = var(cat(3, a, b, c), 0, 3);

By definition, NaN propagates to any calculation you make. It doesn't make much sense to me, but if you want to replace the NaNs with 0:

 elementwisevar(isnan(elementwisevar)) = 0;