Why is subtracting different sized matrices not giving me an error? What is matlab calculating?

I was trying to write up a code for R^2 analysis and when calculating residual sum of squares I realised my model data and my real data were not the same size.

Yet somehow matlab is calculating something and giving me a matric answer. I'm confused about what it's doing. In my code fft_x is a (1000x1 double) and sxx is (1x3328 double) and so is ssres. In an ideal world where my model data and real data match in size, I would have expected a scalar. In this unfortunate case, I was expecting an error. But I'm ot getting an error. What's happening?

ssres=sum((fft_x - sxx).^2);

Answer 1

[James Tursa]

See documentation on "implicit expansion"

https://www.mathworks.com/help/matlab/matlab_prog/compatible-array-sizes-for-basic-operations.html?searchHighlight=implicit%20expansion&s_tid=doc_srchtitle

Answer 2

[KSSV]

What you are doing is not correct. Note that

fft_x - sxx

will be a matrix of size 1000X3328. It will subtract the respective elements. As you are calculating sum, it comes to 1X3328. YOu need to get them to same size either by using interpolation (interp1) or by removing some terms. Note that both the terms should be either row or column arrays.