61 KiB
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import pyerrors as pe
plt.style.use('./base_style.mplstyle')
import shutil
usetex = shutil.which('latex') != ''
plt.rc('text', usetex=usetex)
We can load data from a preprocessed file which contains a list of pyerror
Obs
:
correlator_data = pe.input.json.load_json("./data/correlator_test")
With this list a Corr
object can be initialised
my_correlator = pe.Corr(correlator_data)
my_correlator.gamma_method()
my_correlator.print([8, 14])
The show
method can display the correlator.
my_correlator.show()
Manipulating correlators¶
Arithmetic operations are overloaded for Corr
objects as is the case for Obs
objects.
new_correlator = 1 + 1 / my_correlator ** 2
In addition to that various useful methods for the manipulation of Corr
objects are implemented. A correlator can for example be periodically shifted
shifted_correlator = my_correlator.roll(20)
shifted_correlator.tag = r'Correlator shifted by $x_0/a=20$'
or symmetrised
symmetrised_correlator = my_correlator.symmetric()
symmetrised_correlator.tag = 'Symmetrised correlator'
The full list of Corr
methods can be found in the documentation.
We can visually compare different Corr
objects by passing comp
to the show
method. The argument auto_gamma
tells show
to calculate the y-errors using the gamma method with the default parameters.
shifted_correlator.show(comp=symmetrised_correlator, logscale=True, auto_gamma=True)
Effective mass¶
The effective mass of the correlator can be obtained by calling the m_eff
method
m_eff = symmetrised_correlator.m_eff()
m_eff.tag = 'Effective mass'
We can also use the periodicity of the lattice in order to obtain the cosh effective mass
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 from the plateau at the center of the lattice
periodic_m_eff.show([4,47], comp=m_eff, ylabel=r'$am_\mathrm{eff}$', auto_gamma=True)
Derivatives¶
We can obtain derivatives of correlators in the following way
first_derivative = symmetrised_correlator.deriv()
first_derivative.tag = 'First derivative'
second_derivative = symmetrised_correlator.second_deriv()
second_derivative.tag = 'Second derivative'
symmetrised_correlator.show([5, 20], comp=[first_derivative, second_derivative], y_range=[-500, 1300], auto_gamma=True)
Missing Values¶
Apart from the build-in functions, another benefit of using Corr
objects is that they can handle missing values.
We will create a second correlator with missing values.
new_content=[(my_correlator.content[i] if i not in [6,8,9,12,14,15,20] else None ) for i in range(my_correlator.T) ] # We reuse the old example and replace a few values with None
correlator_incomplete=pe.Corr(new_content)
correlator_incomplete.print([0, 22]) # Print the correlator in the range 0 - 22
We see that this is still a valid correlator. It is just missing some values. When we perform operations, which generate new correlators, the missing values are handled automatically.
Some functions might also return correlators with missing values. We already looked at the derivative.
The symmertic derivative is not defined for the first and last timeslice. Whatever operation is performed on a Corr
object, the correlators keeps its length T. So there will never be confusion about how to count timeslices. One can also take a plateau or perform a fit, even though some values might be missing.