Components¶

Components are the basic ingredients for all models. Currently, the available components are Gaussian, Lorentzian, Voigt (the convolution of a Gaussian with a Lorentzian), delta function, damped harmonic oscillator and polynomial. This notebooks shows how to use the components.

Note in particular that a Gaussian, Lorentzian, Voigt or delta function where the center has not been given will be centered at 0.

In [1]:

import matplotlib.pyplot as plt
import numpy as np
import scipp as sc

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 import Polynomial

%matplotlib widget

import matplotlib.pyplot as plt import numpy as np import scipp as sc 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 import Polynomial %matplotlib widget

In [2]:

# Creating a component
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)
polynomial = Polynomial(display_name='Polynomial', coefficients=[0.1, 0, 0.5])  # y=0.1+0.5*x^2

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

plt.figure()
y = gaussian.evaluate(x)
plt.plot(x, y, label='Gaussian')
y = dho.evaluate(x)
plt.plot(x, y, label='DHO')
y = lorentzian.evaluate(x)
plt.plot(x, y, label='Lorentzian')
y = polynomial.evaluate(x)
plt.plot(x, y, label='Polynomial')
plt.legend()
plt.show()

# Creating a component 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) polynomial = Polynomial(display_name='Polynomial', coefficients=[0.1, 0, 0.5]) # y=0.1+0.5*x^2 x = np.linspace(-2, 2, 100) plt.figure() y = gaussian.evaluate(x) plt.plot(x, y, label='Gaussian') y = dho.evaluate(x) plt.plot(x, y, label='DHO') y = lorentzian.evaluate(x) plt.plot(x, y, label='Lorentzian') y = polynomial.evaluate(x) plt.plot(x, y, label='Polynomial') plt.legend() plt.show()

In [3]:

# The area under the DHO curve is indeed equal to the area parameter.
xx = np.linspace(-15, 15, 10000)
yy = dho.evaluate(xx)
area = np.trapezoid(yy, xx)
print(f'Area under DHO curve: {area:.4f}')

# The area under the DHO curve is indeed equal to the area parameter. xx = np.linspace(-15, 15, 10000) yy = dho.evaluate(xx) area = np.trapezoid(yy, xx) print(f'Area under DHO curve: {area:.4f}')

Area under DHO curve: 1.9999

In [4]:

delta = DeltaFunction(display_name='Delta', center=0.0, area=1.0)
x1 = np.linspace(-2, 2, 100)
y = delta.evaluate(x1)
x2 = np.linspace(-2, 2, 51)
y2 = delta.evaluate(x2)
plt.figure()
plt.plot(x1, y, label='Delta Function')
plt.plot(x2, y2, label='Delta Function (coarser)')
plt.legend()
plt.show()
# The area under the Delta function is indeed equal to
# the area parameter.
xx = np.linspace(-2, 2, 10000)
yy = delta.evaluate(xx)
area = np.trapezoid(y, x1)
print(area)

delta = DeltaFunction(display_name='Delta', center=0.0, area=1.0) x1 = np.linspace(-2, 2, 100) y = delta.evaluate(x1) x2 = np.linspace(-2, 2, 51) y2 = delta.evaluate(x2) plt.figure() plt.plot(x1, y, label='Delta Function') plt.plot(x2, y2, label='Delta Function (coarser)') plt.legend() plt.show() # The area under the Delta function is indeed equal to # the area parameter. xx = np.linspace(-2, 2, 10000) yy = delta.evaluate(xx) area = np.trapezoid(y, x1) print(area)

0.9999999999999999

In [5]:

x1 = sc.linspace(dim='x', start=-2.0, stop=2.0, num=100, unit='meV')
x2 = sc.linspace(dim='x', start=-2.0 * 1e3, stop=2.0 * 1e3, num=101, unit='microeV')

polynomial = Polynomial(display_name='Polynomial', coefficients=[0.1, 0, 0.5])  # y=0.1+0.5*x^2
y1 = polynomial.evaluate(x1)
y2 = polynomial.evaluate(x2)

plt.figure()
plt.plot(x1.values, y1, label='Polynomial meV', color='blue')
plt.plot(x2.values / 1000, y2, label='Polynomial microeV', linestyle='dashed', color='orange')
plt.legend()
plt.show()

x1 = sc.linspace(dim='x', start=-2.0, stop=2.0, num=100, unit='meV') x2 = sc.linspace(dim='x', start=-2.0 * 1e3, stop=2.0 * 1e3, num=101, unit='microeV') polynomial = Polynomial(display_name='Polynomial', coefficients=[0.1, 0, 0.5]) # y=0.1+0.5*x^2 y1 = polynomial.evaluate(x1) y2 = polynomial.evaluate(x2) plt.figure() plt.plot(x1.values, y1, label='Polynomial meV', color='blue') plt.plot(x2.values / 1000, y2, label='Polynomial microeV', linestyle='dashed', color='orange') plt.legend() plt.show()

/home/runner/work/dynamics-lib/dynamics-lib/src/easydynamics/sample_model/components/model_component.py:152: UserWarning: Input x has unit µeV, but Polynomial component                         has unit meV.                             Converting Polynomial to µeV.
  warnings.warn(