source: sasmodels/sasmodels/models/two_power_law.py @ 0507e09

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Last change on this file since 0507e09 was 0507e09, checked in by smk78, 7 months ago

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

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Line 
1r"""
2Definition
3----------
4
5The scattering intensity $I(q)$ is calculated as
6
7.. math::
8
9    I(q) = \begin{cases}
10    A q^{-m1} + \text{background} & q <= q_c \\
11    C q^{-m2} + \text{background} & q > q_c
12    \end{cases}
13
14where $q_c$ = the location of the crossover from one slope to the other,
15$A$ = the scaling coefficent that sets the overall intensity of the lower Q
16power law region, $m1$ = power law exponent at low Q, and $m2$ = power law
17exponent at high Q.  The scaling of the second power law region (coefficent C)
18is then automatically scaled to match the first by following formula:
19
20.. math::
21    C = \frac{A q_c^{m2}}{q_c^{m1}}
22
23.. note::
24    Be sure to enter the power law exponents as positive values!
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::
30
31    q = \sqrt{q_x^2 + q_y^2}
32
33
34References
35----------
36
37None.
38
39Source
40------
41
42`two_power_law.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/two_power_law.py>`_
43
44Authorship and Verification
45----------------------------
46
47* **Author:** NIST IGOR/DANSE **Date:** pre 2010
48* **Last Modified by:** Wojciech Wpotrzebowski **Date:** February 18, 2016
49* **Last Reviewed by:** Paul Butler **Date:** March 21, 2016
50* **Source added by :** Steve King **Date:** March 25, 2019
51"""
52
53import numpy as np
54from numpy import inf, power, empty, errstate
55
56name = "two_power_law"
57title = "This model calculates an empirical functional form for SAS data \
58characterized by two power laws."
59description = """
60            I(q) = coef_A*pow(qval,-1.0*power1) + background for q<=q_c
61            =C*pow(qval,-1.0*power2) + background for q>q_c
62            where C=coef_A*pow(q_c,-1.0*power1)/pow(q_c,-1.0*power2).
63
64            coef_A = scaling coefficent
65            q_c = crossover location [1/A]
66            power_1 (=m1) = power law exponent at low Q
67            power_2 (=m2) = power law exponent at high Q
68            background = Incoherent background [1/cm]
69        """
70category = "shape-independent"
71
72# pylint: disable=bad-whitespace, line-too-long
73#   ["name", "units", default, [lower, upper], "type", "description"],
74parameters = [
75    ["coefficent_1", "",       1.0, [-inf, inf], "", "coefficent A in low Q region"],
76    ["crossover",    "1/Ang",  0.04,[0, inf],    "", "crossover location"],
77    ["power_1",      "",       1.0, [0, inf],    "", "power law exponent at low Q"],
78    ["power_2",      "",       4.0, [0, inf],    "", "power law exponent at high Q"],
79    ]
80# pylint: enable=bad-whitespace, line-too-long
81
82
83def Iq(q,
84       coefficent_1=1.0,
85       crossover=0.04,
86       power_1=1.0,
87       power_2=4.0,
88      ):
89    """
90    :param q:                   Input q-value (float or [float, float])
91    :param coefficent_1:        Scaling coefficent at low Q
92    :param crossover:           Crossover location
93    :param power_1:             Exponent of power law function at low Q
94    :param power_2:             Exponent of power law function at high Q
95    :return:                    Calculated intensity
96    """
97    result = empty(q.shape, 'd')
98    index = (q <= crossover)
99    with errstate(divide='ignore'):
100        coefficent_2 = coefficent_1 * power(crossover, power_2 - power_1)
101        result[index] = coefficent_1 * power(q[index], -power_1)
102        result[~index] = coefficent_2 * power(q[~index], -power_2)
103    return result
104
105Iq.vectorized = True  # Iq accepts an array of q values
106
107def random():
108    """Return a random parameter set for the model."""
109    coefficient_1 = 1
110    crossover = 10**np.random.uniform(-3, -1)
111    power_1 = np.random.uniform(1, 6)
112    power_2 = np.random.uniform(1, 6)
113    pars = dict(
114        scale=1, #background=0,
115        coefficient_1=coefficient_1,
116        crossover=crossover,
117        power_1=power_1,
118        power_2=power_2,
119    )
120    return pars
121
122demo = dict(scale=1, background=0.0,
123            coefficent_1=1.0,
124            crossover=0.04,
125            power_1=1.0,
126            power_2=4.0)
127
128tests = [
129    # Accuracy tests based on content in test/utest_extra_models.py
130    [{'coefficent_1':     1.0,
131      'crossover':  0.04,
132      'power_1':    1.0,
133      'power_2':    4.0,
134      'background': 0.0,
135     }, 0.001, 1000],
136
137    [{'coefficent_1':     1.0,
138      'crossover':  0.04,
139      'power_1':    1.0,
140      'power_2':    4.0,
141      'background': 0.0,
142     }, 0.150141, 0.125945],
143
144    [{'coefficent_1':    1.0,
145      'crossover':  0.04,
146      'power_1':    1.0,
147      'power_2':    4.0,
148      'background': 0.0,
149     }, 0.442528, 0.00166884],
150
151    [{'coefficent_1':    1.0,
152      'crossover':  0.04,
153      'power_1':    1.0,
154      'power_2':    4.0,
155      'background': 0.0,
156     }, (0.442528, 0.00166884), 0.00166884],
157
158]
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