# source:sasmodels/sasmodels/models/power_law.py@0507e09

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Last change on this file since 0507e09 was 0507e09, checked in by smk78, 6 months ago

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1#power_law model
2#conversion of PowerLawAbsModel.py
3#converted by Steve King, Dec 2015
4
5r"""
6This model calculates a simple power law with a flat background.
7
8Definition
9----------
10
11.. math::
12
13    I(q) = \text{scale} \cdot q^{-\text{power}} + \text{background}
14
15Note the minus sign in front of the exponent. The exponent *power*
16should therefore be entered as a **positive** number for fitting.
17
18Also note that unlike many other models, *scale* in this model
19is NOT explicitly related to a volume fraction. Be careful if
20combining this model with other models.
21
22
23References
24----------
25
26None.
27
28Source
29------
30
31power_law.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/power_law.py>_
32
33Authorship and Verification
34----------------------------
35
36* **Author:**
38* **Last Reviewed by:**
39* **Source added by :** Steve King **Date:** March 25, 2019
40"""
41
42import numpy as np
43from numpy import inf, errstate
44
45name = "power_law"
46title = "Simple power law with a flat background"
47
48description = """
49    Evaluates the function
50    I(q) = scale * q^(-power) + background
51    NB: enter power as a positive number!
52    """
53category = "shape-independent"
54
55#             ["name", "units", default, [lower, upper], "type", "description"],
56parameters = [["power", "", 4.0, [-inf, inf], "", "Power law exponent"]]
57
58# NB: Scale and Background are implicit parameters on every model
59def Iq(q, power):
60    # pylint: disable=missing-docstring
61    with errstate(divide='ignore'):
62        result = q**-power
63    return result
64Iq.vectorized = True  # Iq accepts an array of q values
65
66def random():
67    """Return a random parameter set for the model."""
68    power = np.random.uniform(1, 6)
69    pars = dict(
70        scale=0.1**power*10**np.random.uniform(-4, 2),
71        power=power,
72    )
73    return pars
74
75demo = dict(scale=1.0, power=4.0, background=0.0)
76
77tests = [
78    [{'scale': 1.0, 'power': 4.0, 'background' : 0.0},
79     [0.0106939, 0.469418], [7.64644e+07, 20.5949]],
80    ]
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