source: sasmodels/sasmodels/models/guinier.py @ 2d81cfe

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 2d81cfe was 2d81cfe, checked in by Paul Kienzle <pkienzle@…>, 19 months ago

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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
29import numpy as np
30from numpy import inf
31
32name = "guinier"
33title = ""
34description = """
35 I(q) = scale.exp ( - rg^2 q^2 / 3.0 )
36
37    List of default parameters:
38    scale = scale
39    rg = Radius of gyration
40"""
41category = "shape-independent"
42
43#             ["name", "units", default, [lower, upper], "type","description"],
44parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]]
45
46Iq = """
47    double exponent = rg*rg*q*q/3.0;
48    double value = exp(-exponent);
49    return value;
50"""
51
52def random():
53    scale = 10**np.random.uniform(1, 4)
54    # Note: compare.py has Rg cutoff of 1e-30 at q=1 for guinier, so use that
55    # log_10 Ae^(-(q Rg)^2/3) = log_10(A) - (q Rg)^2/ (3 ln 10) > -30
56    #   => log_10(A) > Rg^2/(3 ln 10) - 30
57    q_max = 1.0
58    rg_max = np.sqrt(90*np.log(10) + 3*np.log(scale))/q_max
59    rg = 10**np.random.uniform(0, np.log10(rg_max))
60    pars = dict(
61        #background=0,
62        scale=scale,
63        rg=rg,
64    )
65    return pars
66
67# parameters for demo
68demo = dict(scale=1.0, rg=60.0)
69
70# parameters for unit tests
71tests = [[{'rg' : 31.5}, 0.005, 0.992756]]
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