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pyerrors/examples/02_correlators.ipynb

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In [1]:
import numpy as np
import matplotlib.pyplot as plt
import pyerrors as pe
In [2]:
plt.style.use('./base_style.mplstyle')
plt.rc('text', usetex=True)

We can load data from a preprocessed file which contains a list of pyerror Obs:

In [3]:
correlator_data = pe.input.json.load_json("./data/correlator_test")

Data has been written using pyerrors 2.0.0.
Format version 0.1
Written by fjosw on 2022-01-06 11:11:19 +0100 on host XPS139305, Linux-5.11.0-44-generic-x86_64-with-glibc2.29

Description:  Test data for the correlator example

With this list a Corr object can be initialised

In [4]:
my_correlator = pe.Corr(correlator_data)
In [5]:
my_correlator.print([8, 14])

x0/a	Corr(x0/a)
------------------
8	 548(13)
9	 433(11)
10	 343.1(8.6)
11	 273.2(6.6)
12	 217.5(5.6)
13	 172.9(4.9)
14	 137.6(4.6)

The show method can display the correlator

In [6]:
my_correlator.show()

Manipulating correlators

Corr objects can be shifted

In [7]:
shifted_correlator = my_correlator.roll(20)
shifted_correlator.tag = r'Correlator shifted by $x_0/a=20$'

or symmetrised

In [8]:
symmetrised_correlator = my_correlator.symmetric()
symmetrised_correlator.tag = 'Symmetrised correlator'

We can compare different Corr objects by passing comp to the show method

In [9]:
shifted_correlator.show(comp=symmetrised_correlator, logscale=True)

Effective mass

The effective mass of the correlator can be obtained by calling the m_eff method

In [10]:
m_eff = symmetrised_correlator.m_eff()
m_eff.tag = 'Effective mass'

We can also use the priodicity of the lattice in order to obtain the cosh effective mass

In [11]:
periodic_m_eff = symmetrised_correlator.m_eff('periodic')
periodic_m_eff.tag = 'Cosh effective mass'

We can compare the two and see how the standard effective mass deviates form the plateau at the center of the lattice

In [12]:
periodic_m_eff.show([4,47], comp=m_eff, ylabel=r'$am_\mathrm{eff}$')

Arithmetic operations and mathematical functions are also overloaded for the Corr class. We can compute the difference between the two variants of the effective mass as follows.

In [13]:
difference_m_eff = np.abs(periodic_m_eff - m_eff)
difference_m_eff.show([0, 47], logscale=True)

Derivatives

We can obtain derivatives of correlators in the following way

In [14]:
first_derivative = symmetrised_correlator.deriv()
first_derivative.tag = 'First derivative'
In [15]:
second_derivative = symmetrised_correlator.second_deriv()
second_derivative.tag = 'Second derivative'
In [16]:
symmetrised_correlator.show([5, 20], comp=[first_derivative, second_derivative], y_range=[-500, 1300])

There is a range of addtional methods of the Corr class which can be found in the documentation.

In [ ]:
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