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#power_law model
#conversion of PowerLawAbsModel.py
#converted by Steve King, Dec 2015
r"""
This model calculates a simple power law with a flat background.
Definition
----------
.. math::
I(q) = \text{scale} \cdot q^{-\text{power}} + \text{background}
Note the minus sign in front of the exponent. The exponent *power*
should therefore be entered as a **positive** number for fitting.
Also note that unlike many other models, *scale* in this model
is NOT explicitly related to a volume fraction. Be careful if
combining this model with other models.
References
----------
None.
Authorship and Verification
----------------------------
* **Author:**
* **Last Modified by:**
* **Last Reviewed by:**
"""
import numpy as np
from numpy import inf, errstate
name = "power_law"
title = "Simple power law with a flat background"
description = """
Evaluates the function
I(q) = scale * q^(-power) + background
NB: enter power as a positive number!
"""
category = "shape-independent"
# ["name", "units", default, [lower, upper], "type", "description"],
parameters = [["power", "", 4.0, [-inf, inf], "", "Power law exponent"]]
# NB: Scale and Background are implicit parameters on every model
def Iq(q, power):
# pylint: disable=missing-docstring
with errstate(divide='ignore'):
result = q**-power
return result
Iq.vectorized = True # Iq accepts an array of q values
def random():
"""Return a random parameter set for the model."""
power = np.random.uniform(1, 6)
pars = dict(
scale=0.1**power*10**np.random.uniform(-4, 2),
power=power,
)
return pars
tests = [
[{'scale': 1.0, 'power': 4.0, 'background' : 0.0},
[0.0106939, 0.469418], [7.64644e+07, 20.5949]],
]
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