# source:sasmodels/sasmodels/models/gaussian_peak.py@677ccf1

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 677ccf1 was 677ccf1, checked in by Paul Kienzle <pkienzle@…>, 7 years ago

tweak the gaussian formula for efficiency

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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    double scaled_dq = (q - q0)/sigma;
58    return exp(-0.5*scaled_dq*scaled_dq); //sqrt(2*M_PI*sigma*sigma);
59    """
60
61
62Iqxy = """
63    // never called since no orientation or magnetic parameters.
64    //return -1.0;
65    return Iq(sqrt(qx*qx + qy*qy), q0, sigma);
66    """
67
68
69# VR defaults to 1.0
70
71demo = dict(scale=1, background=0, q0=0.05, sigma=0.005)
72oldname = "PeakGaussModel"
73oldpars = dict(sigma='B')
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