Autocorrelation Function

flipdazed / Hybrid-Monte-Carlo

Used in Deep Machine Learning and Lattice Quantum Chromodynamics

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Autocorrelation Function #13

Closed flipdazed closed 8 years ago

flipdazed commented 8 years ago

Aim Measure autocorrelations : A function of each lattice point varying with number of HMC update steps

Implementation

Record the field configuration at each HMC step
Needs checking: Average across all lattice points for that step
Plot the change over HMC steps
Parameterise with respect to:
- correlation length, c_len
- momentum mixing parameter theta
Comparison with theoretical predictions

flipdazed commented 8 years ago

ADK Measurement of autocorrelations for $\langle\phi^2\rangle$ in one-dimensional free field theory for a single (leapfrog) integrator step as a function of the correlation length $\xi = 1/m$ and the momentum-mixing parameter $\theta$

flipdazed commented 8 years ago

first attempt at autocorrelation function

This is the autocorrelation of <x> as I got confused by the notation when on a coffee downer just before tea time

flipdazed commented 8 years ago

Need to normalise

Correction to the formula: Implicitly assuming <x> = 0 by using the formula:

self.acorr = (shifted*self.samples)[:n-separation] # indexing the 1st index for samples

# ravel() just flattens averything into one dimension
# rather than averaging over each lattice sample and averaging over
# all samples I jsut average the lot saving a calculation
return self.acorr.ravel().mean()

flipdazed commented 8 years ago

Note: should change getTwoPoint() to have similar functionality as getAutocorr() and incorporate c_fn = np.asarray([c.getTwoPoint(separation=i) for i in range(c_len)]) from corr1d_x2.py into correlations/corr.py

flipdazed commented 8 years ago

no point comparing to theory as it is off-topic and it is quite non-trivial to calculate - the face that it behaves as expected is fine and can be verified readily by the integrated autocorrelations