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

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Last change on this file since 0507e09 was 0507e09, checked in by smk78, 3 months ago

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

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Line 
1r"""
2Definition
3----------
4
5This model calculates an empirical functional form for SAS data characterized
6by a broad scattering peak. Many SAS spectra are characterized by a broad peak
7even though they are from amorphous soft materials. For example, soft systems
8that show a SAS peak include copolymers, polyelectrolytes, multiphase systems,
9layered structures, etc.
10
11The d-spacing corresponding to the broad peak is a characteristic distance
12between the scattering inhomogeneities (such as in lamellar, cylindrical, or
13spherical morphologies, or for bicontinuous structures).
14
15The scattering intensity $I(q)$ is calculated as
16
17.. math:: I(q) = \frac{A}{q^n} + \frac{C}{1 + (|q - q_0|\xi)^m} + B
18
19Here the peak position is related to the d-spacing as $q_0 = 2\pi / d_0$.
20
21$A$ is the Porod law scale factor, $n$ the Porod exponent, $C$ is the
22Lorentzian scale factor, $m$ the exponent of $q$, $\xi$ the screening length,
23and $B$ the flat background.
24
25For 2D data the scattering intensity is calculated in the same way as 1D,
26where the $q$ vector is defined as
27
28.. math:: q = \sqrt{q_x^2 + q_y^2}
29
30References
31----------
32
33None.
34
35Source
36------
37
38`broad_peak.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/broad_peak.py>`_
39
40Authorship and Verification
41----------------------------
42
43* **Author:** NIST IGOR/DANSE **Date:** pre 2010
44* **Last Modified by:** Paul kienle **Date:** July 24, 2016
45* **Last Reviewed by:** Richard Heenan **Date:** March 21, 2016
46* **Source added by :** Steve King **Date:** March 25, 2019
47"""
48
49import numpy as np
50from numpy import inf, errstate
51
52name = "broad_peak"
53title = "Broad Lorentzian type peak on top of a power law decay"
54description = """\
55      I(q) = scale_p/pow(q,exponent)+scale_l/
56      (1.0 + pow((fabs(q-q_peak)*length_l),exponent_l) )+ background
57
58      List of default parameters:
59      porod_scale = Porod term scaling
60      porod_exp = Porod exponent
61      lorentz_scale = Lorentzian term scaling
62      lorentz_length = Lorentzian screening length [A]
63      peak_pos = peak location [1/A]
64      lorentz_exp = Lorentzian exponent
65      background = Incoherent background"""
66category = "shape-independent"
67
68# pylint: disable=bad-whitespace, line-too-long
69#             ["name", "units", default, [lower, upper], "type", "description"],
70parameters = [["porod_scale",    "",  1.0e-05, [-inf, inf], "", "Power law scale factor"],
71              ["porod_exp",      "",      3.0, [-inf, inf], "", "Exponent of power law"],
72              ["lorentz_scale",  "",     10.0, [-inf, inf], "", "Scale factor for broad Lorentzian peak"],
73              ["lorentz_length", "Ang",  50.0, [-inf, inf], "", "Lorentzian screening length"],
74              ["peak_pos",       "1/Ang", 0.1, [-inf, inf], "", "Peak position in q"],
75              ["lorentz_exp",    "",      2.0, [-inf, inf], "", "Exponent of Lorentz function"],
76             ]
77# pylint: enable=bad-whitespace, line-too-long
78
79def Iq(q,
80       porod_scale=1.0e-5,
81       porod_exp=3.0,
82       lorentz_scale=10.0,
83       lorentz_length=50.0,
84       peak_pos=0.1,
85       lorentz_exp=2.0):
86    """
87    :param q:              Input q-value
88    :param porod_scale:    Power law scale factor
89    :param porod_exp:      Exponent of power law
90    :param lorentz_scale:  Scale factor for broad Lorentzian peak
91    :param lorentz_length: Lorentzian screening length
92    :param peak_pos:       Peak position in q
93    :param lorentz_exp:    Exponent of Lorentz function
94    :return:               Calculated intensity
95    """
96    z = abs(q - peak_pos) * lorentz_length
97    with errstate(divide='ignore'):
98        inten = (porod_scale / q ** porod_exp
99                 + lorentz_scale / (1 + z ** lorentz_exp))
100    return inten
101Iq.vectorized = True  # Iq accepts an array of q values
102
103def random():
104    """Return a random parameter set for the model."""
105    pars = dict(
106        scale=1,
107        porod_scale=10**np.random.uniform(-8, -5),
108        porod_exp=np.random.uniform(1, 6),
109        lorentz_scale=10**np.random.uniform(0.3, 6),
110        lorentz_length=10**np.random.uniform(0, 2),
111        peak_pos=10**np.random.uniform(-3, -1),
112        lorentz_exp=np.random.uniform(1, 4),
113    )
114    pars['lorentz_length'] /= pars['peak_pos']
115    pars['lorentz_scale'] *= pars['porod_scale'] / pars['peak_pos']**pars['porod_exp']
116    #pars['porod_scale'] = 0.
117    return pars
118
119demo = dict(scale=1, background=0,
120            porod_scale=1.0e-05, porod_exp=3,
121            lorentz_scale=10, lorentz_length=50, peak_pos=0.1, lorentz_exp=2)
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