source: sasmodels/sasmodels/models/two_lorentzian.py @ ef07e95

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since ef07e95 was ef07e95, checked in by Paul Kienzle <pkienzle@…>, 5 years ago

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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 **Date:** pre 2010
30* **Last Modified by:** Piotr rozyczko **Date:** January 29, 2016
31* **Last Reviewed by:** Paul Butler **Date:** March 21, 2016
32"""
33
34import numpy as np
35from numpy import inf, power
36
37name = "two_lorentzian"
38title = "This model calculates an empirical functional form for SAS data \
39characterized by two Lorentzian-type functions."
40description = """I(q) = scale_1/(1.0 + pow((q*length_1),exponent_1))
41             + scale_2/(1.0 + pow((q*length_2),exponent_2) )+ background
42
43             scale_1    = Lorentzian term scaling #1
44             length_1   = Lorentzian screening length #1 [A]
45             exponent_1 = Lorentzian exponent #1
46             scale_2    = Lorentzian term scaling #2
47             length_2   = Lorentzian screening length #2 [A]
48             exponent_2 = Lorentzian exponent #2
49             background = Incoherent background
50        """
51category = "shape-independent"
52
53# pylint: disable=bad-whitespace, line-too-long
54#            ["name", "units", default, [lower, upper], "type", "description"],
55parameters = [["lorentz_scale_1",  "",     10.0, [-inf, inf], "", "First power law scale factor"],
56              ["lorentz_length_1", "Ang", 100.0, [-inf, inf], "", "First Lorentzian screening length"],
57              ["lorentz_exp_1",    "",      3.0, [-inf, inf], "", "First exponent of power law"],
58              ["lorentz_scale_2",  "",      1.0, [-inf, inf], "", "Second scale factor for broad Lorentzian peak"],
59              ["lorentz_length_2", "Ang",  10.0, [-inf, inf], "", "Second Lorentzian screening length"],
60              ["lorentz_exp_2",    "",      2.0, [-inf, inf], "", "Second exponent of power law"],
61             ]
62# pylint: enable=bad-whitespace, line-too-long
63
64
65def Iq(q,
66       lorentz_scale_1=10.0,
67       lorentz_length_1=100.0,
68       lorentz_exp_1=3.0,
69       lorentz_scale_2=1.0,
70       lorentz_length_2=10.0,
71       lorentz_exp_2=2.0):
72
73    """
74    :param q:                   Input q-value (float or [float, float])
75    :param lorentz_scale_1:     Second scale factor for broad Lorentzian peak
76    :param lorentz_length_1:    First Lorentzian screening length
77    :param lorentz_exp_1:       Exponent of the second Lorentz function
78    :param lorentz_scale_2:     Second scale factor for broad Lorentzian peak
79    :param lorentz_length_2:    Second Lorentzian screening length
80    :param lorentz_exp_2:       Exponent of the second Lorentz function
81    :return:                    Calculated intensity
82    """
83# pylint: disable=bad-whitespace
84    intensity  = lorentz_scale_1/(1.0 +
85                                  power(q*lorentz_length_1, lorentz_exp_1))
86    intensity += lorentz_scale_2/(1.0 +
87                                  power(q*lorentz_length_2, lorentz_exp_2))
88# pylint: enable=bad-whitespace
89
90    return intensity
91
92Iq.vectorized = True  # Iq accepts an array of q values
93
94def random():
95    scale = 10**np.random.uniform(0, 4, 2)
96    length = 10**np.random.uniform(1, 4, 2)
97    expon = np.random.uniform(1, 6, 2)
98
99    pars = dict(
100        #background=0,
101        scale=1, # scale provided in model
102        lorentz_scale_1=scale[0],
103        lorentz_length_1=length[0],
104        lorentz_exp_1=expon[0],
105        lorentz_scale_2=scale[1],
106        lorentz_length_2=length[1],
107        lorentz_exp_2=expon[1],
108    )
109    return pars
110
111
112demo = dict(scale=1, background=0.1,
113            lorentz_scale_1=10,
114            lorentz_length_1=100.0,
115            lorentz_exp_1=3.0,
116            lorentz_scale_2=1,
117            lorentz_length_2=10,
118            lorentz_exp_2=2.0)
119
120tests = [
121
122    # Accuracy tests based on content in test/utest_extra_models.py
123    [{'lorentz_scale_1':   10.0,
124      'lorentz_length_1': 100.0,
125      'lorentz_exp_1':      3.0,
126      'lorentz_scale_2':    1.0,
127      'lorentz_length_2':  10.0,
128      'lorentz_exp_2':      2.0,
129      'background':         0.1,
130     }, 0.001, 11.08991],
131
132    [{'lorentz_scale_1':   10.0,
133      'lorentz_length_1': 100.0,
134      'lorentz_exp_1':      3.0,
135      'lorentz_scale_2':    1.0,
136      'lorentz_length_2':  10.0,
137      'lorentz_exp_2':      2.0,
138      'background':         0.1,
139     }, 0.150141, 0.410245],
140
141    [{'lorentz_scale_1':   10.0,
142      'lorentz_length_1': 100.0,
143      'lorentz_exp_1':      3.0,
144      'lorentz_scale_2':    1.0,
145      'lorentz_length_2':  10.0,
146      'lorentz_exp_2':      2.0,
147      'background':         0.1,
148     }, 0.442528, 0.148699],
149
150    # Additional tests with larger range of parameters
151    [{'lorentz_scale_1':   10.0,
152      'lorentz_length_1': 100.0,
153      'lorentz_exp_1':      3.0,
154      'lorentz_scale_2':    1.0,
155      'lorentz_length_2':  10.0,
156      'lorentz_exp_2':      2.0,
157     }, 0.000332070182643, 10.9996228107],
158
159    [{'lorentz_scale_1':  0.0,
160      'lorentz_length_1': 0.0,
161      'lorentz_exp_1':    0.0,
162      'lorentz_scale_2':  0.0,
163      'lorentz_length_2': 0.0,
164      'lorentz_exp_2':    0.0,
165      'background':     100.0
166     }, 5.0, 100.0],
167
168    [{'lorentz_scale_1': 200.0,
169      'lorentz_length_1': 10.0,
170      'lorentz_exp_1':     0.1,
171      'lorentz_scale_2':   0.1,
172      'lorentz_length_2':  5.0,
173      'lorentz_exp_2':     2.0
174     }, 20000., 45.5659201896],
175    ]
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