[gmx-users] Re: Re: Re: autocorrelation function using g_analyze

[Sung Hyun Park]

>Indeed. The key bit of information not explicitly stated in 8.5, but
>present in g_analyze -h, is that normalization is on by default. The
>correlation function is only dimensionless if it has been normalized
>(subtract mean from all data points, divide by standard deviation). A
>normalized correlation function can readily be negative - consider the
>correlation of two fully-out-of-phase sinusoids.
>
>Mark

Mark,

Thank you for the reply.

However it is not the definition of the autocorrelation function, isn't it?
Autocorrelation function <C(t)> is generally normalized by <C(0)>, and
eq.(8.9) in the manual can be used to calculate <C(t)>. (please
correct me if I'm wrong)
As I mentioned in my original post, the quantity I'm interested in is
a distance correlation hence I believe the autocorrelation should
always be positive.
I just don't see how the autocorrelation function, normalized or not,
can become negative in my case.
If gromacs is indeed doing what you suggested (subtract mean from all
data points, divide by standard deviation), it is not the
autocorrelation function generally defined by any textbook to my
knowledge.(again, please correct me if I'm wrong) Furthermore the
formula you suggested is the correlation of the "fluctuation" of the
quantity, not the correlation of the quantity itself.
Do you know why gromacs calculates the autocorrelation function in
that way instead of using eq (8.9) and normalizing using C(0)? Any
reference would be also helpful.

Thank you again for your kind help!

Regards,
Sung