source: sasmodels/sasmodels/models/correlation_length.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, 6 months ago

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

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1#correlation length model
2# Note: model title and parameter table are inserted automatically
3r"""
4Definition
5----------
6
7The scattering intensity I(q) is calculated as
8
9.. math::
10    I(Q) = \frac{A}{Q^n} + \frac{C}{1 + (Q\xi)^m} + \text{background}
11
12The first term describes Porod scattering from clusters (exponent = $n$) and
13the second term is a Lorentzian function describing scattering from
14polymer chains (exponent = $m$). This second term characterizes the
15polymer/solvent interactions and therefore the thermodynamics. The two
16multiplicative factors $A$ and $C$, and the two exponents $n$ and $m$ are
17used as fitting parameters. (Respectively *porod_scale*, *lorentz_scale*,
18*porod_exp* and *lorentz_exp* in the parameter list.) The remaining
19parameter $\xi$ (*cor_length* in the parameter list) is a correlation
20length for the polymer chains. Note that when $m=2$ this functional form
21becomes the familiar Lorentzian function. Some interpretation of the
22values of $A$ and $C$ may be possible depending on the values of $m$ and $n$.
23
24For 2D data: The 2D scattering intensity is calculated in the same way as 1D,
25where the q vector is defined as
26
27.. math::  q = \sqrt{q_x^2 + q_y^2}
28
29References
30----------
31
32.. [#] B Hammouda, D L Ho and S R Kline, Insight into Clustering in Poly(ethylene oxide) Solutions, Macromolecules, 37 (2004) 6932-6937
33
34Source
35------
36
37`correlation_length.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/correlation_length.py>`_
38
39Authorship and Verification
40----------------------------
41
42* **Author:**
43* **Last Modified by:**
44* **Last Reviewed by:**
45* **Source added by :** Steve King **Date:** March 25, 2019
46"""
47
48from numpy import inf, errstate
49
50name = "correlation_length"
51title = """Calculates an empirical functional form for SAS data characterized
52by a low-Q signal and a high-Q signal."""
53description = """
54"""
55category = "shape-independent"
56# pylint: disable=bad-continuation, line-too-long
57#             ["name", "units", default, [lower, upper], "type","description"],
58parameters = [
59              ["lorentz_scale", "", 10.0, [0, inf], "", "Lorentzian Scaling Factor"],
60              ["porod_scale", "", 1e-06, [0, inf], "", "Porod Scaling Factor"],
61              ["cor_length", "Ang", 50.0, [0, inf], "", "Correlation length, xi, in Lorentzian"],
62              ["porod_exp", "", 3.0, [0, inf], "", "Porod Exponent, n, in q^-n"],
63              ["lorentz_exp", "1/Ang^2", 2.0, [0, inf], "", "Lorentzian Exponent, m, in 1/( 1 + (q.xi)^m)"],
64             ]
65# pylint: enable=bad-continuation, line-too-long
66
67def Iq(q, lorentz_scale, porod_scale, cor_length, porod_exp, lorentz_exp):
68    """
69    1D calculation of the Correlation length model
70    """
71    with errstate(divide='ignore'):
72        porod = porod_scale / q**porod_exp
73        lorentz = lorentz_scale / (1.0 + (q * cor_length)**lorentz_exp)
74    inten = porod + lorentz
75    return inten
76Iq.vectorized = True
77
78# parameters for demo
79demo = dict(lorentz_scale=10.0, porod_scale=1.0e-06, cor_length=50.0,
80            porod_exp=3.0, lorentz_exp=2.0, background=0.1,
81           )
82
83tests = [[{}, 0.001, 1009.98],
84         [{}, 0.150141, 0.175645],
85         [{}, 0.442528, 0.0213957]]
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