source: sasmodels/sasmodels/models/pringle.py @ 0507e09

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 0507e09 was 0507e09, checked in by smk78, 5 months ago

Added link to source code to each model. Closes #883

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Line 
1r"""
2Definition
3----------
4
5The form factor for this bent disc is essentially that of a hyperbolic
6paraboloid and calculated as
7
8.. math::
9
10    P(q) = (\Delta \rho )^2 V \int^{\pi/2}_0 d\psi \sin{\psi} sinc^2
11    \left( \frac{qd\cos{\psi}}{2} \right)
12    \left[ \left( S^2_0+C^2_0\right) + 2\sum_{n=1}^{\infty}
13     \left( S^2_n+C^2_n\right) \right]
14
15where
16
17.. math::
18
19    C_n = \frac{1}{r^2}\int^{R}_{0} r dr\cos(qr^2\alpha \cos{\psi})
20    J_n\left( qr^2\beta \cos{\psi}\right)
21    J_{2n}\left( qr \sin{\psi}\right)
22
23.. math::
24
25    S_n = \frac{1}{r^2}\int^{R}_{0} r dr\sin(qr^2\alpha \cos{\psi})
26    J_n\left( qr^2\beta \cos{\psi}\right)
27    J_{2n}\left( qr \sin{\psi}\right)
28
29and $\Delta \rho \text{ is } \rho_{pringle}-\rho_{solvent}$, $V$ is the volume of
30the disc, $\psi$ is the angle between the normal to the disc and the q vector,
31$d$ and $R$ are the "pringle" thickness and radius respectively, $\alpha$ and
32$\beta$ are the two curvature parameters, and $J_n$ is the n\ :sup:`th` order
33Bessel function of the first kind.
34
35.. figure:: img/pringles_fig1.png
36
37    Schematic of model shape (Graphic from Matt Henderson, matt@matthen.com)
38
39Reference
40---------
41
42.. [#] Karen Edler, Universtiy of Bath, Private Communication. 2012. Derivation by Stefan Alexandru Rautu.
43.. [#] L. Onsager, *Ann. New York Acad. Sci.*, 51 (1949) 627-659
44
45Source
46------
47
48`pringle.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/pringle.py>`_
49
50`pringle.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/pringle.c>`_
51
52Authorship and Verification
53----------------------------
54
55* **Author:** Andrew Jackson **Date:** 2008
56* **Last Modified by:** Wojciech Wpotrzebowski **Date:** March 20, 2016
57* **Last Reviewed by:** Andrew Jackson **Date:** September 26, 2016
58* **Source added by :** Steve King **Date:** March 25, 2019
59"""
60
61import numpy as np
62from numpy import inf
63
64name = "pringle"
65title = "The Pringle model provides the form factor, $P(q)$, for a 'pringle' \
66or 'saddle-shaped' disc that is bent in two directions."
67description = """\
68
69"""
70category = "shape:cylinder"
71
72# pylint: disable=bad-whitespace, line-too-long
73#   ["name", "units", default, [lower, upper], "type","description"],
74parameters = [
75    ["radius",      "Ang",         60.0,   [0, inf],    "volume", "Pringle radius"],
76    ["thickness",   "Ang",         10.0,   [0, inf],    "volume", "Thickness of pringle"],
77    ["alpha",       "",            0.001,  [-inf, inf], "volume", "Curvature parameter alpha"],
78    ["beta",        "",            0.02,   [-inf, inf], "volume", "Curvature paramter beta"],
79    ["sld", "1e-6/Ang^2",  1.0,    [-inf, inf], "sld", "Pringle sld"],
80    ["sld_solvent", "1e-6/Ang^2",  6.3,    [-inf, inf], "sld", "Solvent sld"]
81    ]
82# pylint: enable=bad-whitespace, line-too-long
83
84
85source = ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c",
86          "lib/sas_JN.c", "lib/gauss76.c", "pringle.c"]
87effective_radius_type = [
88    "equivalent cylinder excluded volume",
89    "equivalent volume sphere",
90    "radius"]
91
92def random():
93    """Return a random parameter set for the model."""
94    alpha, beta = 10**np.random.uniform(-1, 1, size=2)
95    radius = 10**np.random.uniform(1, 3)
96    thickness = 10**np.random.uniform(0.7, 2)
97    pars = dict(
98        radius=radius,
99        thickness=thickness,
100        alpha=alpha,
101        beta=beta,
102    )
103    return pars
104
105tests = [
106    [{'scale' : 1.0,
107      'radius': 60.0,
108      'thickness': 10.0,
109      'alpha': 0.001,
110      'beta': 0.02,
111      'sld': 1.0,
112      'sld_solvent': 6.3,
113      'background': 0.001,
114     }, 0.1, 9.87676],
115
116    [{'scale' : 1.0,
117      'radius': 60.0,
118      'thickness': 10.0,
119      'alpha': 0.001,
120      'beta': 0.02,
121      'sld': 1.0,
122      'sld_solvent': 6.3,
123      'background': 0.001,
124     }, 0.01, 290.56723],
125
126    [{'scale' : 1.0,
127      'radius': 60.0,
128      'thickness': 10.0,
129      'alpha': 0.001,
130      'beta': 0.02,
131      'sld': 1.0,
132      'sld_solvent': 6.3,
133      'background': 0.001,
134     }, 0.001, 317.40847],
135]
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