source: sasmodels/sasmodels/models/gaussian_peak.py @ 9d76d29

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Last change on this file since 9d76d29 was 9d76d29, checked in by Paul Kienzle <pkienzle@…>, 7 years ago

fix up docs to use latex

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Line 
1r"""
2
3Definition
4----------
5
6This model describes a Gaussian shaped peak on a flat background
7
8.. math::
9
10    I(q) = (\text{scale}) \exp\left[ -\tfrac12 (q-q_0)^2 / \sigma^2 \right]
11        + \text{background}
12
13with the peak having height of *scale* centered at $q_0$ and having a standard
14deviation of $\sigma$. The FWHM (full-width half-maximum) is $2.354 \sigma$.
15
16For 2D data, 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
24.. image:: img/gaussian_peak_1d.jpg
25
26    1D plot using the default values (w/500 data points).
27
28Reference
29---------
30
31None.
32"""
33
34from numpy import inf
35
36name = "gaussian_peak"
37title = "Gaussian shaped peak"
38description = """
39    Model describes a Gaussian shaped peak including a flat background
40    Provide F(q) = scale*exp( -1/2 *[(q-q0)/sigma]^2 )+ background
41"""
42category = "shape-independent"
43
44#             ["name", "units", default, [lower, upper], "type","description"],
45parameters = [["q0", "1/Ang", 0.05, [-inf, inf], "", "Peak position"],
46              ["sigma", "1/Ang", 0.005, [0, inf], "",
47               "Peak width (standard deviation)"],
48             ]
49
50# No volume normalization despite having a volume parameter
51# This should perhaps be volume normalized?
52form_volume = """
53    return 1.0;
54    """
55
56Iq = """
57    return exp(-0.5*pow((q - q0)/sigma,2.0));
58    """
59
60
61Iqxy = """
62    // never called since no orientation or magnetic parameters.
63    //return -1.0;
64    return Iq(sqrt(qx*qx + qy*qy), q0, sigma);
65    """
66
67
68# VR defaults to 1.0
69
70demo = dict(scale=1, background=0, q0=0.05, sigma=0.005)
71oldname = "PeakGaussModel"
72oldpars = dict(sigma='B')
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