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

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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Line
1r"""
2For information about polarised and magnetic scattering, see
3the :ref:magnetism documentation.
4
5Definition
6----------
7
8The 1D scattering intensity is calculated in the following way (Guinier, 1955)
9
10.. math::
11
12    I(q) = \frac{\text{scale}}{V} \cdot \left[
13        3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3}
14        \right]^2 + \text{background}
15
16where *scale* is a volume fraction, $V$ is the volume of the scatterer,
17$r$ is the radius of the sphere and *background* is the background level.
18*sld* and *sld_solvent* are the scattering length densities (SLDs) of the
19scatterer and the solvent respectively, whose difference is $\Delta\rho$.
20
21Note that if your data is in absolute scale, the *scale* should represent
22the volume fraction (which is unitless) if you have a good fit. If not,
23it should represent the volume fraction times a factor (by which your data
24might need to be rescaled).
25
26The 2D scattering intensity is the same as above, regardless of the
27orientation of $\vec q$.
28
29Validation
30----------
31
32Validation of our code was done by comparing the output of the 1D model
33to the output of the software provided by the NIST (Kline, 2006).
34
35
36References
37----------
38
39.. [#] A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955)
40
41Source
42------
43
44sphere.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/sphere.py>_
45
46sphere.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/sphere.c>_
47
48Authorship and Verification
49----------------------------
50
51* **Author:**
53* **Last Reviewed by:** S King and P Parker **Date:** 2013/09/09 and 2014/01/06
54* **Source added by :** Steve King **Date:** March 25, 2019
55"""
56
57import numpy as np
58from numpy import inf
59
60name = "sphere"
61title = "Spheres with uniform scattering length density"
62description = """\
63P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr))
64                /(qr)^3]^2 + background
66    V: The volume of the scatter
67    sld: the SLD of the sphere
68    sld_solvent: the SLD of the solvent
69"""
70category = "shape:sphere"
71
72#             ["name", "units", default, [lower, upper], "type","description"],
73parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld",
74               "Layer scattering length density"],
75              ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld",
76               "Solvent scattering length density"],
77              ["radius", "Ang", 50, [0, inf], "volume",
79             ]
80
81source = ["lib/sas_3j1x_x.c", "sphere.c"]
82have_Fq = True
84
85def random():
86    """Return a random parameter set for the model."""
88    pars = dict(