Convolution¶

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In [1]:

import matplotlib.pyplot as plt
import numpy as np

from easydynamics.convolution import Convolution
from easydynamics.sample_model import DampedHarmonicOscillator
from easydynamics.sample_model import DeltaFunction
from easydynamics.sample_model import Gaussian
from easydynamics.sample_model import Lorentzian
from easydynamics.sample_model.component_collection import ComponentCollection
from easydynamics.utils import _detailed_balance_factor as detailed_balance_factor

%matplotlib widget

import matplotlib.pyplot as plt import numpy as np from easydynamics.convolution import Convolution from easydynamics.sample_model import DampedHarmonicOscillator from easydynamics.sample_model import DeltaFunction from easydynamics.sample_model import Gaussian from easydynamics.sample_model import Lorentzian from easydynamics.sample_model.component_collection import ComponentCollection from easydynamics.utils import _detailed_balance_factor as detailed_balance_factor %matplotlib widget

In [2]:

# Standard example of convolution of a sample model with a
# resolution model
sample_components = ComponentCollection()
gaussian = Gaussian(display_name='Gaussian', width=0.5, area=1)
dho = DampedHarmonicOscillator(display_name='DHO', center=1.0, width=0.3, area=2.0)
lorentzian = Lorentzian(display_name='Lorentzian', center=-1.0, width=0.2, area=1.0)
delta = DeltaFunction(display_name='Delta', center=0.4, area=0.5)
sample_components.append_component(gaussian)
# sample_components.append_component(dho)
sample_components.append_component(lorentzian)
sample_components.append_component(delta)

resolution_components = ComponentCollection()
resolution_gaussian = Gaussian(display_name='Resolution Gaussian', width=0.015, area=0.8)
resolution_lorentzian = Lorentzian(display_name='Resolution Lorentzian', width=0.025, area=0.2)
resolution_components.append_component(resolution_gaussian)
resolution_components.append_component(resolution_lorentzian)

energy = np.linspace(-2, 2, 100)

convolver = Convolution(
    sample_components=sample_components, resolution_components=resolution_components, energy=energy
)
y = convolver.convolution()
plt.figure()
plt.plot(energy, y, label='Convoluted Model')
plt.xlabel('Energy (meV)')
plt.ylabel('Intensity (arb. units)')
plt.title('Convolution of Sample Model with Resolution Model')

plt.plot(energy, sample_components.evaluate(energy), label='Sample Model', linestyle='--')
plt.plot(energy, resolution_components.evaluate(energy), label='Resolution Model', linestyle=':')

plt.legend()
# set the limit on the y axis
plt.ylim(0, 6)
plt.show()

# Standard example of convolution of a sample model with a # resolution model sample_components = ComponentCollection() gaussian = Gaussian(display_name='Gaussian', width=0.5, area=1) dho = DampedHarmonicOscillator(display_name='DHO', center=1.0, width=0.3, area=2.0) lorentzian = Lorentzian(display_name='Lorentzian', center=-1.0, width=0.2, area=1.0) delta = DeltaFunction(display_name='Delta', center=0.4, area=0.5) sample_components.append_component(gaussian) # sample_components.append_component(dho) sample_components.append_component(lorentzian) sample_components.append_component(delta) resolution_components = ComponentCollection() resolution_gaussian = Gaussian(display_name='Resolution Gaussian', width=0.015, area=0.8) resolution_lorentzian = Lorentzian(display_name='Resolution Lorentzian', width=0.025, area=0.2) resolution_components.append_component(resolution_gaussian) resolution_components.append_component(resolution_lorentzian) energy = np.linspace(-2, 2, 100) convolver = Convolution( sample_components=sample_components, resolution_components=resolution_components, energy=energy ) y = convolver.convolution() plt.figure() plt.plot(energy, y, label='Convoluted Model') plt.xlabel('Energy (meV)') plt.ylabel('Intensity (arb. units)') plt.title('Convolution of Sample Model with Resolution Model') plt.plot(energy, sample_components.evaluate(energy), label='Sample Model', linestyle='--') plt.plot(energy, resolution_components.evaluate(energy), label='Resolution Model', linestyle=':') plt.legend() # set the limit on the y axis plt.ylim(0, 6) plt.show()

In [3]:

# Use some of the extra settings for the numerical convolution
sample_components = ComponentCollection()
gaussian = Gaussian(display_name='Gaussian', width=0.3, area=1)
dho = DampedHarmonicOscillator(display_name='DHO', center=1.0, width=0.3, area=2.0)
lorentzian = Lorentzian(display_name='Lorentzian', center=-1.0, width=0.2, area=1.0)
delta = DeltaFunction(display_name='Delta', center=0.4, area=0.5)
sample_components.append_component(gaussian)
sample_components.append_component(dho)
sample_components.append_component(lorentzian)

resolution_components = ComponentCollection()
resolution_gaussian = Gaussian(display_name='Resolution Gaussian', width=0.15, area=0.8)
resolution_lorentzian = Lorentzian(display_name='Resolution Lorentzian', width=0.25, area=0.2)
resolution_components.append_component(resolution_gaussian)
resolution_components.append_component(resolution_lorentzian)

energy = np.linspace(-2, 2, 100)


temperature = 10.0  # Temperature in Kelvin
offset = 0.5
upsample_factor = 5
extension_factor = 0.5
plt.figure()
plt.xlabel('Energy (meV)')
plt.ylabel('Intensity (arb. units)')

convolver = Convolution(
    sample_components=sample_components,
    resolution_components=resolution_components,
    energy=energy - offset,
    upsample_factor=upsample_factor,
    extension_factor=extension_factor,
    temperature=temperature,
    normalize_detailed_balance=True,
)
y = convolver.convolution()


plt.plot(energy, y, label='Convoluted Model')

plt.plot(
    energy,
    sample_components.evaluate(energy - offset)
    * detailed_balance_factor(energy - offset, temperature),
    label='Sample Model with DB',
    linestyle='--',
)

plt.plot(energy, resolution_components.evaluate(energy), label='Resolution Model', linestyle=':')
plt.title('Convolution of Sample Model with Resolution Model with detailed balancing')

plt.legend()
plt.ylim(0, 2.5)
plt.show()

# Use some of the extra settings for the numerical convolution sample_components = ComponentCollection() gaussian = Gaussian(display_name='Gaussian', width=0.3, area=1) dho = DampedHarmonicOscillator(display_name='DHO', center=1.0, width=0.3, area=2.0) lorentzian = Lorentzian(display_name='Lorentzian', center=-1.0, width=0.2, area=1.0) delta = DeltaFunction(display_name='Delta', center=0.4, area=0.5) sample_components.append_component(gaussian) sample_components.append_component(dho) sample_components.append_component(lorentzian) resolution_components = ComponentCollection() resolution_gaussian = Gaussian(display_name='Resolution Gaussian', width=0.15, area=0.8) resolution_lorentzian = Lorentzian(display_name='Resolution Lorentzian', width=0.25, area=0.2) resolution_components.append_component(resolution_gaussian) resolution_components.append_component(resolution_lorentzian) energy = np.linspace(-2, 2, 100) temperature = 10.0 # Temperature in Kelvin offset = 0.5 upsample_factor = 5 extension_factor = 0.5 plt.figure() plt.xlabel('Energy (meV)') plt.ylabel('Intensity (arb. units)') convolver = Convolution( sample_components=sample_components, resolution_components=resolution_components, energy=energy - offset, upsample_factor=upsample_factor, extension_factor=extension_factor, temperature=temperature, normalize_detailed_balance=True, ) y = convolver.convolution() plt.plot(energy, y, label='Convoluted Model') plt.plot( energy, sample_components.evaluate(energy - offset) * detailed_balance_factor(energy - offset, temperature), label='Sample Model with DB', linestyle='--', ) plt.plot(energy, resolution_components.evaluate(energy), label='Resolution Model', linestyle=':') plt.title('Convolution of Sample Model with Resolution Model with detailed balancing') plt.legend() plt.ylim(0, 2.5) plt.show()