ALPS 2 Tutorials:MC-01 Equilibration

Revision as of 18:20, 28 August 2013 by Tamama (talk | contribs) (A convenient tool: steady_state_check)

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Rule of thumb: All Monte Carlo simulations have to be equilibrated before taking measurements.

Example: Quantum Monte Carlo (directed worm algorithm) simulations

As an example, we consider a Quantum Monte Carlo simulation implemented in the directed worm algorithm for boson Hubbard model in square lattice geometry of size 202.

Using command line

The parameter file parm1a:

LATTICE="square lattice"
MODEL="boson Hubbard"





We first convert the input parameters to XML and then run the application dwa:

parameter2xml parm1a

Detailed information regarding the Density measurements, for example, can be extracted from:

h5dump -g /simulation/results/Density parm1a.task1.out.h5

or its (binned) timeseries from:

h5dump -g /simulation/results/Density/timeseries parm1a.task1.out.h5

We can extract the timeseries data into a CSV file:

h5dump -d /simulation/results/Density/timeseries/data -w 1 -y -o parm1a.task1.out.density.timeseries.csv parm1a.task1.out.h5

and plot it using your favourite graphical plotter, say xmgrace:

xmgrace parm1a.task1.out.density.timeseries.csv

or, say gnuplot:

gnuplot <<@@
set datafile separator ','
plot "parm1a.task1.out.density.timeseries.csv"

Based on the timeseries, the user will then judge for himself/herself whether the simulation has reached equilibration.

Using Python

The following describes what is going on within the script file

The headers:

import pyalps

Set up a python list of parameters (python) dictionaries:

parms = [{
  'LATTICE'         : "square lattice",          
  'MODEL'           : "boson Hubbard",
  'L'               : 20,
  'Nmax'            : 20,
  't'               : 1.,
  'U'               : 16.,
  'mu'              : 32.,
  'T'               : 1.,
  'THERMALIZATION'  : 10000,
  'SWEEPS'          : 100000,
  'SKIP'            : 400

Write into XML input file:

input_file = pyalps.writeInputFiles('parm1a',parms)

and run the application dwa:

pyalps.runApplication('dwa', input_file, Tmin=10, writexml=True)

We first get the list of all hdf5 result files via:

files = pyalps.getResultFiles(prefix='parm1a', format='hdf5')

and then extract, say the timeseries of the Density measurements:

ar = pyalps.hdf5.h5ar(files[0])
density_timeseries = ar['/simulation/results']['Density']['timeseries']['data']

We can then visualize graphically:

import matplotlib.pyplot as plt

Based on the timeseries, the user will then judge for himself/herself whether the simulation has reached equilibration.

A convenient tool: steady_state_check

ALPS Python provides a convenient tool to check whether a measurement observable(s) has (have) reached steady state equilibrium.

Here is one example:

pyalps.steady_state_check(files[0], 'Density')

and another one:

pyalps.steady_state_check(files[0], ['Density', 'Energy Density'])


Using Vistrails