# source:sasmodels/sasmodels/models/sphere.py@ef07e95

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since ef07e95 was ef07e95, checked in by Paul Kienzle <pkienzle@…>, 6 years ago

use consistent formatting for 'Last Reviewed'

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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
39A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*,
40John Wiley and Sons, New York, (1955)
41
42* **Last Reviewed by:** S King and P Parker **Date:** 2013/09/09 and 2014/01/06
43"""
44
45import numpy as np
46from numpy import inf
47
48name = "sphere"
49title = "Spheres with uniform scattering length density"
50description = """\
51P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr))
52                /(qr)^3]^2 + background
54    V: The volume of the scatter
55    sld: the SLD of the sphere
56    sld_solvent: the SLD of the solvent
57"""
58category = "shape:sphere"
59
60#             ["name", "units", default, [lower, upper], "type","description"],
61parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld",
62               "Layer scattering length density"],
63              ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld",
64               "Solvent scattering length density"],
65              ["radius", "Ang", 50, [0, inf], "volume",
67             ]
68
69source = ["lib/sas_3j1x_x.c", "lib/sphere_form.c"]
70
71# No volume normalization despite having a volume parameter
72# This should perhaps be volume normalized?
73form_volume = """
75    """
76
77Iq = """
78    return sphere_form(q, radius, sld, sld_solvent);
79    """
80
82    """
84    """
86
87# VR defaults to 1.0
88
89def random():
91    pars = dict(