source: sasmodels/sasmodels/models/power_law.py @ d86f0fc

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Last change on this file since d86f0fc was 2d81cfe, checked in by Paul Kienzle <pkienzle@…>, 6 years 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"""
28
29import numpy as np
30from numpy import inf, errstate
31
32name = "power_law"
33title = "Simple power law with a flat background"
34
35description = """
36    Evaluates the function
37    I(q) = scale * q^(-power) + background
38    NB: enter power as a positive number!
39    """
40category = "shape-independent"
41
42#             ["name", "units", default, [lower, upper], "type", "description"],
43parameters = [["power", "", 4.0, [-inf, inf], "", "Power law exponent"]]
44
45# NB: Scale and Background are implicit parameters on every model
46def Iq(q, power):
47    # pylint: disable=missing-docstring
48    with errstate(divide='ignore'):
49        result = q**-power
50    return result
51Iq.vectorized = True  # Iq accepts an array of q values
52
53def random():
54    power = np.random.uniform(1, 6)
55    pars = dict(
56        scale=0.1**power*10**np.random.uniform(-4, 2),
57        power=power,
58    )
59    return pars
60
61demo = dict(scale=1.0, power=4.0, background=0.0)
62
63tests = [
64    [{'scale': 1.0, 'power': 4.0, 'background' : 0.0},
65     [0.0106939, 0.469418], [7.64644e+07, 20.5949]],
66    ]
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