## RMS error of matrices

on 6 Apr 2011

### Walter Roberson (view profile)

Hi,
I have 2 large matrixes (2048x2048), and have taken one away from the other to get a 'difference' matrix. I want to quantify this matrix by using an RMS error, however if I use a standard RMS error formula I get another 2048x2048 matrix.
Is there a way to get a single representative RMS value out?
Thanks,
Richard

### Walter Roberson (view profile)

on 6 Apr 2011

Isn't it usually
sqrt(mean(A(:).^2 - B(:).^2))

### darksideofthemoon101 (view profile)

on 6 Apr 2011

I've been using
rms = sqrt((A - B)^2))
How dissimilar are these equations?

Walter Roberson

### Walter Roberson (view profile)

on 6 Apr 2011
When A and B are arrays then A-B is an array, and (A-B)^2 is
(A-B)*(A-B) which is a matrix multiplication which will produce an output the same size as A (in this case.) sqrt() of that would then be the same size.
Nothing in your code calculates the _mean_ portion of "RMS". Root MEAN square.
Possibly I should have suggested
sqrt(mean((A(:)-B(:)).^2))
but I am too tired to look up the definition at the moment.