source: sasmodels/sasmodels/models/two_lorentzian.py @ 48462b0

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 48462b0 was 48462b0, checked in by Paul Kienzle <pkienzle@…>, 7 years ago

tuned random model generation for even more models

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Line 
1r"""
2Definition
3----------
4
5The scattering intensity $I(q)$ is calculated as
6
7.. math::
8
9    I(q) = \frac{A}{1 +(Q\xi_1)^n} + \frac{C}{1 +(Q\xi_2)^m} + \text{B}
10
11where $A$ = Lorentzian scale factor #1, $C$ = Lorentzian scale #2,
12$\xi_1$ and $\xi_2$ are the corresponding correlation lengths, and $n$ and
13$m$ are the respective power law exponents (set $n = m = 2$ for
14Ornstein-Zernicke behaviour).
15
16For 2D data the scattering intensity is calculated in the same way as 1D,
17where the $q$ vector is defined as
18
19.. math::
20
21    q = \sqrt{q_x^2 + q_y^2}
22
23
24References
25----------
26
27None.
28
29**Author:** NIST IGOR/DANSE **on:** pre 2010
30
31**Last Modified by:** Piotr rozyczko **on:** January 29, 2016
32
33**Last Reviewed by:** Paul Butler **on:** March 21, 2016
34"""
35
36from numpy import inf, power
37
38name = "two_lorentzian"
39title = "This model calculates an empirical functional form for SAS data \
40characterized by two Lorentzian-type functions."
41description = """I(q) = scale_1/(1.0 + pow((q*length_1),exponent_1))
42             + scale_2/(1.0 + pow((q*length_2),exponent_2) )+ background
43
44             scale_1    = Lorentzian term scaling #1
45             length_1   = Lorentzian screening length #1 [A]
46             exponent_1 = Lorentzian exponent #1
47             scale_2    = Lorentzian term scaling #2
48             length_2   = Lorentzian screening length #2 [A]
49             exponent_2 = Lorentzian exponent #2
50             background = Incoherent background
51        """
52category = "shape-independent"
53
54# pylint: disable=bad-whitespace, line-too-long
55#            ["name", "units", default, [lower, upper], "type", "description"],
56parameters = [["lorentz_scale_1",  "",     10.0, [-inf, inf], "", "First power law scale factor"],
57              ["lorentz_length_1", "Ang", 100.0, [-inf, inf], "", "First Lorentzian screening length"],
58              ["lorentz_exp_1",    "",      3.0, [-inf, inf], "", "First exponent of power law"],
59              ["lorentz_scale_2",  "",      1.0, [-inf, inf], "", "Second scale factor for broad Lorentzian peak"],
60              ["lorentz_length_2", "Ang",  10.0, [-inf, inf], "", "Second Lorentzian screening length"],
61              ["lorentz_exp_2",    "",      2.0, [-inf, inf], "", "Second exponent of power law"],
62             ]
63# pylint: enable=bad-whitespace, line-too-long
64
65
66def Iq(q,
67       lorentz_scale_1=10.0,
68       lorentz_length_1=100.0,
69       lorentz_exp_1=3.0,
70       lorentz_scale_2=1.0,
71       lorentz_length_2=10.0,
72       lorentz_exp_2=2.0):
73
74    """
75    :param q:                   Input q-value (float or [float, float])
76    :param lorentz_scale_1:     Second scale factor for broad Lorentzian peak
77    :param lorentz_length_1:    First Lorentzian screening length
78    :param lorentz_exp_1:       Exponent of the second Lorentz function
79    :param lorentz_scale_2:     Second scale factor for broad Lorentzian peak
80    :param lorentz_length_2:    Second Lorentzian screening length
81    :param lorentz_exp_2:       Exponent of the second Lorentz function
82    :return:                    Calculated intensity
83    """
84# pylint: disable=bad-whitespace
85    intensity  = lorentz_scale_1/(1.0 +
86                                  power(q*lorentz_length_1, lorentz_exp_1))
87    intensity += lorentz_scale_2/(1.0 +
88                                  power(q*lorentz_length_2, lorentz_exp_2))
89# pylint: enable=bad-whitespace
90
91    return intensity
92
93Iq.vectorized = True  # Iq accepts an array of q values
94
95def random():
96    import numpy as np
97    scale = 10**np.random.uniform(0, 4, 2)
98    length = 10**np.random.uniform(1, 4, 2)
99    expon = np.random.uniform(1, 6, 2)
100
101    pars = dict(
102        #background=0,
103        scale=1, # scale provided in model
104        lorentz_scale_1=scale[0],
105        lorentz_length_1=length[0],
106        lorentz_exp_1=expon[0],
107        lorentz_scale_2=scale[1],
108        lorentz_length_2=length[1],
109        lorentz_exp_2=expon[1],
110    )
111    return pars
112
113
114demo = dict(scale=1, background=0.1,
115            lorentz_scale_1=10,
116            lorentz_length_1=100.0,
117            lorentz_exp_1=3.0,
118            lorentz_scale_2=1,
119            lorentz_length_2=10,
120            lorentz_exp_2=2.0)
121
122tests = [
123
124    # Accuracy tests based on content in test/utest_extra_models.py
125    [{'lorentz_scale_1':   10.0,
126      'lorentz_length_1': 100.0,
127      'lorentz_exp_1':      3.0,
128      'lorentz_scale_2':    1.0,
129      'lorentz_length_2':  10.0,
130      'lorentz_exp_2':      2.0,
131      'background':         0.1,
132     }, 0.001, 11.08991],
133
134    [{'lorentz_scale_1':   10.0,
135      'lorentz_length_1': 100.0,
136      'lorentz_exp_1':      3.0,
137      'lorentz_scale_2':    1.0,
138      'lorentz_length_2':  10.0,
139      'lorentz_exp_2':      2.0,
140      'background':         0.1,
141     }, 0.150141, 0.410245],
142
143    [{'lorentz_scale_1':   10.0,
144      'lorentz_length_1': 100.0,
145      'lorentz_exp_1':      3.0,
146      'lorentz_scale_2':    1.0,
147      'lorentz_length_2':  10.0,
148      'lorentz_exp_2':      2.0,
149      'background':         0.1,
150     }, 0.442528, 0.148699],
151
152    # Additional tests with larger range of parameters
153    [{'lorentz_scale_1':   10.0,
154      'lorentz_length_1': 100.0,
155      'lorentz_exp_1':      3.0,
156      'lorentz_scale_2':    1.0,
157      'lorentz_length_2':  10.0,
158      'lorentz_exp_2':      2.0,
159     }, 0.000332070182643, 10.9996228107],
160
161    [{'lorentz_scale_1':  0.0,
162      'lorentz_length_1': 0.0,
163      'lorentz_exp_1':    0.0,
164      'lorentz_scale_2':  0.0,
165      'lorentz_length_2': 0.0,
166      'lorentz_exp_2':    0.0,
167      'background':     100.0
168     }, 5.0, 100.0],
169
170    [{'lorentz_scale_1': 200.0,
171      'lorentz_length_1': 10.0,
172      'lorentz_exp_1':     0.1,
173      'lorentz_scale_2':   0.1,
174      'lorentz_length_2':  5.0,
175      'lorentz_exp_2':     2.0
176     }, 20000., 45.5659201896],
177    ]
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