# source:sasmodels/sasmodels/models/gauss_lorentz_gel.py@0507e09

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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1r"""
2This model calculates the scattering from a gel structure,
3but typically a physical rather than chemical network.
4It is modeled as a sum of a low-q exponential decay (which happens to
5give a functional form similar to Guinier scattering, so interpret with
6care) plus a Lorentzian at higher-q values. See also the gel_fit model.
7
8Definition
9----------
10
11The scattering intensity $I(q)$ is calculated as (Eqn. 5 from the reference)
12
13.. math:: I(q) = I_G(0) \exp(-q^2\Xi ^2/2) + I_L(0)/(1+q^2\xi^2)
14
15$\Xi$ is the length scale of the static correlations in the gel, which can
16be attributed to the "frozen-in" crosslinks. $\xi$ is the dynamic correlation
17length, which can be attributed to the fluctuating polymer chains between
18crosslinks. $I_G(0)$ and $I_L(0)$ are the scaling factors for each of these
20
21.. note::
22    The peaked structure at higher $q$ values (Figure 2 from the reference)
23    is not reproduced by the model. Peaks can be introduced into the model
24    by summing this model with the :ref:gaussian-peak model.
25
26For 2D data the scattering intensity is calculated in the same way as 1D,
27where the $q$ vector is defined as
28
29.. math:: q = \sqrt{q_x^2 + q_y^2}
30
31References
32----------
33
34.. [#] G Evmenenko, E Theunissen, K Mortensen, H Reynaers, *Polymer*, 42 (2001) 2907-2913
35
36Source
37------
38
39gauss_lorentz_gel.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/gauss_lorentz_gel.py>_
40
41Authorship and Verification
42----------------------------
43
44* **Author:**
46* **Last Reviewed by:**
47* **Source added by :** Steve King **Date:** March 25, 2019
48"""
49
50import numpy as np
51from numpy import inf, exp
52
53name = "gauss_lorentz_gel"
54title = "Gauss Lorentz Gel model of scattering from a gel structure"
55description = """
56            Class that evaluates a GaussLorentzGel model.
57
58            I(q) = scale_g*exp(- q^2*Z^2 / 2)+scale_l/(1+q^2*z^2)
59                    + background
60            List of default parameters:
61                scale_g = Gauss scale factor
62                Z = Static correlation length
63                scale_l = Lorentzian scale factor
64                z = Dynamic correlation length
65                background = Incoherent background
66            """
67category = "shape-independent"
69#            ["name", "units", default, [lower, upper], "type", "description"],
70parameters = [["gauss_scale",   "",    100.0,  [-inf, inf], "", "Gauss scale factor"],
71              ["cor_length_static",    "Ang", 100.0,  [0, inf],    "", "Static correlation length"],
72              ["lorentz_scale", "",     50.0,  [-inf, inf], "", "Lorentzian scale factor"],
73              ["cor_length_dynamic",   "Ang",  20.0,  [0, inf],    "", "Dynamic correlation length"],
74             ]
76
77def Iq(q,
78       gauss_scale=100.0,
79       cor_length_static=100.0,
80       lorentz_scale=50.0,
81       cor_length_dynamic=20.0):
82    """
83
84    :param q:                    Input q-value
85    :param gauss_scale:   Gauss scale factor
86    :param cor_length_static:    Static correlation length
87    :param lorentz_scale: Lorentzian scale factor
88    :param cor_length_dynamic:   Dynamic correlation length
89    :return:                     1-D intensity
90    """
91
92    term1 = gauss_scale *\
93            exp(-1.0*q*q*cor_length_static*cor_length_static/2.0)
94    term2 = lorentz_scale /\
95            (1.0+(q*cor_length_dynamic)*(q*cor_length_dynamic))
96
97    return term1 + term2
98
99Iq.vectorized = True  # Iq accepts an array of q values
100
101
102def random():
103    """Return a random parameter set for the model."""
104    gauss_scale = 10**np.random.uniform(1, 3)
105    lorentz_scale = 10**np.random.uniform(1, 3)
106    cor_length_static = 10**np.random.uniform(0, 3)
107    cor_length_dynamic = 10**np.random.uniform(0, 3)
108    pars = dict(
109        #background=0,
110        scale=1,
111        gauss_scale=gauss_scale,
112        lorentz_scale=lorentz_scale,
113        cor_length_static=cor_length_static,
114        cor_length_dynamic=cor_length_dynamic,
115    )
116    return pars
117
118
119demo = dict(scale=1, background=0.1,
120            gauss_scale=100.0,
121            cor_length_static=100.0,
122            lorentz_scale=50.0,
123            cor_length_dynamic=20.0)
124
125tests = [
126
127    # Accuracy tests based on content in test/utest_extra_models.py
128    [{'gauss_scale':  100.0,
129      'cor_length_static':   100.0,
130      'lorentz_scale': 50.0,
131      'cor_length_dynamic':   20.0,
132     }, 0.001, 149.482],
133
134    [{'gauss_scale':  100.0,
135      'cor_length_static':   100.0,
136      'lorentz_scale': 50.0,
137      'cor_length_dynamic':   20.0,
138     }, 0.105363, 9.1913],
139
140    [{'gauss_scale':  100.0,
141      'cor_length_static':   100.0,
142      'lorentz_scale': 50.0,
143      'cor_length_dynamic':   20.0,
144     }, 0.441623, 0.633811],
145
146    # Additional tests with larger range of parameters
147    [{'gauss_scale':  10.0,
148      'cor_length_static':  100.0,
149      'lorentz_scale': 3.0,
150      'cor_length_dynamic':   1.0,
151     }, 0.1, 2.9712970297],
152
153    [{'gauss_scale':  10.0,
154      'cor_length_static':  100.0,
155      'lorentz_scale': 3.0,
156      'cor_length_dynamic':   1.0,
157      'background':         100.0
158     }, 5.0, 100.116384615],
159
160    [{'gauss_scale':  10.0,
161      'cor_length_static':  100.0,
162      'lorentz_scale': 3.0,
163      'cor_length_dynamic':   1.0,
164      'background':           0.0,
165     }, 200., 7.49981250469e-05],
166    ]
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