source: sasmodels/sasmodels/models/guinier.py @ 58c3367

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Last change on this file since 58c3367 was 40a87fa, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

lint and latex cleanup

  • Property mode set to 100644
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Line 
1r"""
2Definition
3----------
4
5This model fits the Guinier function
6
7.. math::
8
9    I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2R_g^2}{3} \right]}
10            + \text{background}
11
12to the data directly without any need for linearisation (*cf*. the usual
13plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to restrict the data
14range to include small q only, where the Guinier approximation actually
15applies. See also the guinier_porod model.
16
17For 2D data the scattering intensity is calculated in the same way as 1D,
18where the $q$ vector is defined as
19
20.. math:: q = \sqrt{q_x^2 + q_y^2}
21
22References
23----------
24
25A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*,
26John Wiley & Sons, New York (1955)
27"""
28
29from numpy import inf
30
31name = "guinier"
32title = ""
33description = """
34 I(q) = scale.exp ( - rg^2 q^2 / 3.0 )
35 
36    List of default parameters:
37    scale = scale
38    rg = Radius of gyration
39"""
40category = "shape-independent"
41
42#             ["name", "units", default, [lower, upper], "type","description"],
43parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]]
44
45Iq = """
46    double exponent = rg*rg*q*q/3.0;
47    double value = exp(-exponent);
48    return value;
49"""
50
51# parameters for demo
52demo = dict(scale=1.0, rg=60.0)
53
54# parameters for unit tests
55tests = [[{'rg' : 31.5}, 0.005, 0.992756]]
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