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r"""
Lorentz (Ornstein-Zernicke Model)
Definition
----------
The Ornstein-Zernicke model is defined by
.. math:: I(q)=\frac{\text{scale}}{1+(qL)^2}+\text{background}
The parameter $L$ is the screening length *cor_length*.
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
----------
#. L.S. Qrnstein and F. Zernike, *Proc. Acad. Sci. Amsterdam* 17, 793 (1914),
and *Z. Phys.* 19, 134 (1918), and 27, 761 {1926); referred to as QZ.
Authorship and Verification
----------------------------
* **Author:**
* **Last Modified by:**
* **Last Reviewed by:**
"""
import numpy as np
from numpy import inf
name = "lorentz"
title = "Ornstein-Zernicke correlation length model"
description = """
Model that evaluates a Lorentz (Ornstein-Zernicke) model.
I(q) = scale/( 1 + (q*L)^2 ) + bkd
The model has three parameters:
length = screening Length
scale = scale factor
background = incoherent background
"""
category = "shape-independent"
# ["name", "units", default, [lower, upper], "type","description"],
parameters = [["cor_length", "Ang", 50.0, [0, inf], "", "Screening length"],]
source = ["lorentz.c"]
def random():
"""Return a random parameter set for the model."""
pars = dict(
#background=0,
scale=10**np.random.uniform(1, 4),
cor_length=10**np.random.uniform(0, 3),
)
return pars
# parameters for unit tests
tests = [[{'cor_length': 250}, 0.01, 0.138931]]
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