source: sasmodels/sasmodels/models/linear_pearls.py @ b297ba9

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Last change on this file since b297ba9 was b297ba9, checked in by Paul Kienzle <pkienzle@…>, 7 months ago

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1r"""
2This model provides the form factor for $N$ spherical pearls of radius $R$
3linearly joined by short strings (or segment length or edge separation)
4$l$ $(= A - 2R)$. $A$ is the center-to-center pearl separation distance.
5The thickness of each string is assumed to be negligible.
6
7.. figure:: img/linear_pearls_geometry.jpg
8
9
10Definition
11----------
12
13The output of the scattering intensity function for the linear_pearls model
14is given by (Dobrynin, 1996)
15
16.. math::
17
18    P(Q) = \frac{\text{scale}}{V}\left[ m_{p}^2
19    \left(N+2\sum_{n-1}^{N-1}(N-n)\frac{\sin(qnl)}{qnl}\right)
20    \left( 3\frac{\sin(qR)-qR\cos(qR)}{(qr)^3}\right)^2\right]
21
22where the mass $m_p$ is $(SLD_{pearl}-SLD_{solvent})*(volume\ of\ N\ pearls)$.
23V is the total volume.
24
25The 2D scattering intensity is the same as P(q) above,
26regardless of the orientation of the q vector.
27
28References
29----------
30
31A V Dobrynin, M Rubinstein and S P Obukhov, *Macromol.*,
3229 (1996) 2974-2979
33"""
34
35import numpy as np
36from numpy import inf
37
38name = "linear_pearls"
39title = "Linear pearls model of scattering from spherical pearls."
40description = """
41    Calculate form factor for Pearl Necklace Model
42    [Macromol. 1996, 29, 2974-2979]
43    Parameters:
44
45    sld_pearl: the SLD of the pearl spheres
46    sld_solv: the SLD of the solvent
47    num_pearls: number of the pearls
48    radius: the radius of a pearl
49    edge_separation: the length of string segment; surface to surface
50    """
51category = "shape:sphere"
52
53# pylint: disable=bad-whitespace, line-too-long
54#            ["name", "units", default, [lower, upper], "type", "description"],
55parameters = [
56    ["radius",      "Ang",       80.0, [0, inf],     "", "Radius of the pearls"],
57    ["edge_sep",    "Ang",      350.0, [0, inf],     "", "Length of the string segment - surface to surface"],
58    ["num_pearls",  "",           3.0, [1, inf],     "", "Number of the pearls"],
59    ["sld",   "1e-6/Ang^2", 1.0, [-inf, inf],  "sld", "SLD of the pearl spheres"],
60    ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf],  "sld", "SLD of the solvent"],
61    ]
62# pylint: enable=bad-whitespace, line-too-long
63single = False
64
65source = ["lib/sas_3j1x_x.c", "linear_pearls.c"]
66
67def random():
68    """Return a random parameter set for the model."""
69    radius = 10**np.random.uniform(1, 3) # 1 - 1000
70    edge_sep = 10**np.random.uniform(0, 3)  # 1 - 1000
71    num_pearls = np.round(10**np.random.uniform(0.3, 3)) # 2 - 1000
72    pars = dict(
73        radius=radius,
74        edge_sep=edge_sep,
75        num_pearls=num_pearls,
76    )
77    return pars
78
79_ = """
80Tests temporarily disabled, until single-double precision accuracy issue solved.
81
82tests = [
83    # Accuracy tests based on content in test/utest_model_pearlnecklace.py
84    [{'radius':      20.0,
85      'num_pearls':   2.0,
86      'sld':    1.0,
87      'sld_solvent':  6.3,
88      'edge_sep':   400.0,
89     }, 0.001, 185.135],
90
91    # Additional tests with larger range of parameters
92    [{'radius':     120.0,
93      'num_pearls':   5.0,
94      'sld':    2.0,
95      'sld_solvent':  2.3,
96      'edge_sep':   100.0,
97     }, 0.01, 45.4984],
98
99    [{'radius':       7.0,
100      'num_pearls':   2.0,
101      'sld':   10.0,
102      'sld_solvent': 99.3,
103      'edge_sep':    20.0,
104     }, 1.0, 0.632811],
105    ]
106"""
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