# source:sasmodels/sasmodels/models/sphere.py@934a001

ticket_1156ticket_822_more_unit_tests
Last change on this file since 934a001 was 934a001, checked in by richardh, 15 months ago

tidied up unit tests in sphere, now understand beta approx ones

• Property mode set to 100644
File size: 7.1 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*,
40   John Wiley and Sons, New York, (1955)
41
42Source
43------
44
45sphere.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/sphere.py>_
46
47sphere.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/sphere.c>_
48
49Authorship and Verification
50----------------------------
51
52* **Author:**
54* **Last Reviewed by:** S King and P Parker **Date:** 2013/09/09 and 2014/01/06
55* **Source added by :** Steve King **Date:** March 25, 2019
56"""
57
58import numpy as np
59from numpy import inf
60
61name = "sphere"
62title = "Spheres with uniform scattering length density"
63description = """\
64P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr))
65                /(qr)^3]^2 + background
67    V: The volume of the scatter
68    sld: the SLD of the sphere
69    sld_solvent: the SLD of the solvent
70"""
71category = "shape:sphere"
72
73#             ["name", "units", default, [lower, upper], "type","description"],
74parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld",
75               "Layer scattering length density"],
76              ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld",
77               "Solvent scattering length density"],
78              ["radius", "Ang", 50, [0, inf], "volume",
80             ]
81
82source = ["lib/sas_3j1x_x.c", "sphere.c"]
83have_Fq = True
85
86def random():
87    """Return a random parameter set for the model."""
89    pars = dict(
91    )
92    return pars
93#2345678901234567890123456789012345678901234567890123456789012345678901234567890
94tests = [
95     [{}, 0.2, 0.726362], # each test starts with default parameter values
96     #            inside { }, unless modified. Then Q and expected value of I(Q)
97     # putting None for an expected result will pass the test if there are no
98     # errors from the routine, but without any check on the value of the result
99    [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1.,
101     [1.34836265e+04, 6.20114062e+00, 1.04733914e-01]],
102     [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1.,
103     #  careful tests here R=120 Pd=.2, then with S(Q) at default Reff=50
104     #  (but this gets changed to 120) phi=0,2
106      [0.01,0.1,0.2], [1.74395295e+04, 3.68016987e+00, 2.28843099e-01]],
107     # a list of Q values and list of expected results is also possible
108    [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1.,
110      0.01, 335839.88055473, 1.41045057e+11, 120.0, 8087664.122641933, 1.0],
111     # the longer list here checks  F1, F2, R_eff, volume, volume_ratio
113      0.1, 482.93824329, 29763977.79867414, 120.0, 8087664.122641933, 1.0],
115      0.2, 1.23330406, 1850806.1197361, 120.0, 8087664.122641933, 1.0],
116   #  But note P(Q) = F2/volume
117   #  F and F^2 are "unscaled", with for  n <F F*>S(q) or for beta approx
118   #          I(q) = n [<F F*> + <F><F*> (S(q) - 1)]
119   #  for n the number density and <.> the orientation average, and
120   #  F = integral rho(r) exp(i q . r) dr.
121   #  The number density is volume fraction divided by particle volume.
122   #  Effectively, this leaves F = V drho form, where form is the usual
123   #  3 j1(qr)/(qr) or whatever depending on the shape.
124   # @S RESULTS using F1 and F2 from the longer test strng above:
125   #
126   # I(Q) = (F2 + F1^2*(S(Q) -1))*volfraction*scale/Volume  + background
127   #
128   # with by default scale=1.0, background=0.001
129   # NOTE currently S(Q) volfraction is also included in scaling
130   #  structure_factor_mode 0 = normal decoupling approx,
131   #                        1 = beta(Q) approx
133   #                        1 is use radius from F2(Q)
134   #    (sphere only has two choices, other models may have more)
135    [{"@S": "hardsphere",
137     #"radius_effective":50.0,    # hard sphere structure factor
138     "structure_factor_mode": 1,  # mode 0 = normal decoupling approx,
139     #                                   1 = beta(Q) approx
140     "radius_effective_mode": 0   # this used default hardsphere Reff=50
141     }, [0.01,0.1,0.2], [1.32473756e+03, 7.36633631e-01, 4.67686201e-02]  ],
142    [{"@S": "hardsphere",
144     "volfraction":0.2,
145     "radius_effective":45.0,     # explicit Reff over rides either 50 or 120
146     "structure_factor_mode": 1,  # beta approx
148     }, 0.01, 1316.2990966463444 ],
149    [{"@S": "hardsphere",
151     "volfraction":0.2,
152     "radius_effective":120.0,    # over ride Reff
153     "structure_factor_mode": 1,  # beta approx
154     "radius_effective_mode": 0   # (mode=1 here also uses 120)
155     }, [0.01,0.1,0.2], [1.57928589e+03, 7.37067923e-01, 4.67686197e-02  ]],
156    [{"@S": "hardsphere",
158     "volfraction":0.2,
159     #"radius_effective":120.0,   # hard sphere structure factor
160     "structure_factor_mode": 0,  # normal decoupling approximation
161     "radius_effective_mode": 1   # this uses 120 from the form factor
162     }, [0.01,0.1,0.2], [1.10112335e+03, 7.41366536e-01, 4.66630207e-02]],
163    [{"@S": "hardsphere",