"""The Lorentzian resolution subclass"""
import numpy as np
from MDMC.resolution.resolution import Resolution
from MDMC.common.resolution_functions import lorentzian
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class LorentzianResolution(Resolution):
"""
A class for applying a Lorentzian resolution to an :any:`Observable`.
"""
def __init__(self, e_res: float):
self.e_res = e_res / 1000
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def apply(self, FQt, t, Q):
N_Q, N_T = np.shape(FQt)
window = self.window_in_t(t[:N_T])
return np.broadcast_to(window, (N_Q, N_T)) * FQt
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def window_in_w(self, w: np.ndarray) -> np.ndarray:
"""
Calculate the Lorentzian window function in frequency space.
Parameters
----------
w : ~numpy.ndarray
An array of frequencies.
Returns
-------
~numpy.ndarray
The Lorentzian window over the frequency array `w`.
"""
window = lorentzian(w, self.e_res)
return window
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def window_in_t(self, t: np.ndarray) -> np.ndarray:
"""
Calculate the Lorentzian window function in time space.
Parameters
----------
t : ~numpy.ndarray
An array of time points.
Returns
-------
~numpy.ndarray
The Lorentzian window over the time array `t`.
"""
# The Lorentzian window in time space (i.e. the Fourier transform centred around zero)
# The Fourier transform of the Lorentzian is
# F(k) = e^((2 * pi * i) * k * x_0) - Gamma * pi * |k|
# where x_0 is the offset and Gamma the FWHM.
# thus as the instrument resolution function is centred around x_0, this simplifies to
# e^(-Gamma * pi * |k|).
window = np.exp((-self.e_res * np.pi * np.abs(t)))
return window
def __repr__(self):
"""
Represent a ``LorentzianResolution`` object as the given FWHM energy resolution.
"""
return "Resolution" + str({'lorentzian': self.e_res})