MATLAB: Peculiar behavior regarding matrix operations

divisionmatricesmatrixmultiplicationorderpeculiarweird

Hi,
I just discovered something that I found really weird when I was working with some element-wise multiplication and division for large matrices. I found that the order in which I carry out the operations gives me different results, the line of code giving this behavior is the following:
efrog2=efrog./abs(efrog).*spectrogram;
where efrog and spectrogram are 1325×1325 (efrog contains complex values) matrices. Now if I change the order to:
efrog3=spectrogram.*efrog./abs(efrog);
I get a different result, I if look at the maximum difference I get:
max(max(abs(efrog3-efrog2)))=6.0024e+08
However, if I change the order to:
efrog4=efrog.*spectrogram./abs(efrog);
I get:
max(max(abs(efrog3-efrog4)))=0
I tried the same thing with small 4×4 matrices, but for them the order (as one would suspect) didn't matter. Does anybody have any idea about what is going on here?
Thanks in advance
Cheers
Robert

Best Answer

Congratulations. You are the 10 millionth person to have discovered that floating point operations can have subtly different results depending on the order in which those operations were performed. Of course, you award for having done so will be your name appearing in USA today, the Washington Post, and Time magazine, to name just a few. No money though.
Essentially, the basic properties of arithmetic that you learned in grade school no longer EXACTLY apply in floating point arithmetic. In fact, that which you do on a computer only resembles/approximates true mathematics when done in floating point arithmetic.
http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
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