# source:sasmodels/sasmodels/models/sphere.py@6140894

ticket-1257-vesicle-productticket_1156ticket_822_more_unit_tests
Last change on this file since 6140894 was 6140894, checked in by richardh, 17 months ago

removed nerge text from model_test, more notes in sphere.py

• Property mode set to 100644
File size: 5.5 KB
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(
90    )
91    return pars
92
93tests = [
94     [{}, 0.2, 0.726362], # each test starts with default parameter values inside { }, unless modified. Then Q and expected value of I(Q)
95     [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1.,
97      0.2, 0.2288431],
99      0.2, 792.0646662454202, 1166737.0473152, 120.0, 7246723.820358589, 1.0], # the longer list here checks  F1, F2, R_eff, volume, volume_ratio = call_Fq(kernel, pars)
100   #  But note P(Q) = F2/volume
101   #  F and F^2 are "unscaled", with for  n <F F*>S(q) or for beta approx I(q) = n [<F F*> + <F><F*> (S(q) - 1)]
102   #  for n the number density and <.> the orientation average, and F = integral rho(r) exp(i q . r) dr.
103   #  The number density is volume fraction divided by particle volume.
104   #  Effectively, this leaves F = V drho form, where form is the usual 3 j1(qr)/(qr) or whatever depending on the shape.
105   # [{"@S": "hardsphere"},
106   #    0.01, 55.881884232102124], # this is current value, not verified elsewhere yet
108   #   0.2, 1.233304061, [1850806.119736], 120.0, 8087664.1226, 1.0], # the longer list here checks  F1, F2, R_eff, volume, volume_ratio = call_Fq(kernel, pars)
109   # [{"@S": "hardsphere"},
110   #     0.2, 0.14730859242492958], #  this is current value, not verified elsewhere yet
111    # [{"@S": "hardsphere"},
112    #    0.1, 0.7940350343811906], #  this is current value, not verified elsewhere yet
113    [{"@S": "hardsphere",
115     "volfraction":0.2,
116     "radius_effective":45.0,     # uses this (check)
117     "structure_factor_mode": 1,  # 0 = normal decoupling approximation, 1 = beta(Q) approx
118     "radius_effective_mode": 0   # equivalent sphere, there is only one valid mode for sphere. says -this used r_eff =0 or default 50?
119     }, 0.01, 1316.2990966463444 ],
120    [{"@S": "hardsphere",
122     "volfraction":0.2,
123     "radius_effective":50.0,        # hard sphere structure factor
124     "structure_factor_mode": 1,  # 0 = normal decoupling approximation, 1 = beta(Q) approx
125     "radius_effective_mode": 0   # this used r_eff =0 or default 50?
126     }, 0.01, 1324.7375636587356 ],
127    [{"@S": "hardsphere",