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r"""
This model describes a Lorentzian shaped peak on a flat background.
Definition
----------
The scattering intensity $I(q)$ is calculated as
.. math::
I(q) = \frac{scale}{\bigl(1+\bigl(\frac{q-q_0}{B}\bigr)^2\bigr)} + background
with the peak having height of $I_0$ centered at $q_0$ and having
a HWHM (half-width half-maximum) of B.
For 2D data the scattering intensity is calculated in the same way as 1D,
where the $q$ vector is defined as
.. math::
q = \sqrt{q_x^2 + q_y^2}
References
----------
None.
Authorship and Verification
----------------------------
* **Author:**
* **Last Modified by:**
* **Last Reviewed by:**
"""
import numpy as np
from numpy import inf
name = "peak_lorentz"
title = "A Lorentzian peak on a flat background"
description = """\
Class that evaluates a Lorentzian shaped peak.
F(q) = scale/(1+[(q-q0)/B]^2 ) + background
The model has three parameters:
scale = scale
peak_pos = peak position
peak_hwhm = half-width-half-maximum of peak
background= incoherent background"""
category = "shape-independent"
# ["name", "units", default, [lower, upper], "type", "description"],
parameters = [["peak_pos", "1/Ang", 0.05, [-inf, inf], "", "Peak postion in q"],
["peak_hwhm", "1/Ang", 0.005, [-inf, inf], "", "HWHM of peak"],
]
def Iq(q, peak_pos, peak_hwhm):
"""
Return I(q)
"""
inten = (1/(1+((q-peak_pos)/peak_hwhm)**2))
return inten
Iq.vectorized = True # Iq accepts an array of q values
def random():
"""Return a random parameter set for the model."""
peak_pos = 10**np.random.uniform(-3, -1)
peak_hwhm = peak_pos * 10**np.random.uniform(-3, 0)
pars = dict(
#background=0,
scale=10**np.random.uniform(2, 6),
peak_pos=peak_pos,
peak_hwhm=peak_hwhm,
)
return pars
tests = [[{'scale':100.0, 'background':1.0}, 0.001, 2.0305]]
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