source: sasmodels/sasmodels/models/porod.py @ 19b6d28

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Last change on this file since 19b6d28 was 19b6d28, checked in by Doucet, Mathieu <doucetm@…>, 7 years ago

Add porod model

  • Property mode set to 100644
File size: 1.2 KB
Line 
1r"""
2This model fits the Porod function
3
4.. math::
5
6    I(q) = C/q^4
7    \\
8    C = 2\pi (\Delta\rho)^2 S_v
9
10to the data directly without any need for linearisation (cf. Log I(q) vs Log q).
11
12Here $C$ is the scale factor and $S_v$ is the specific surface area (ie, surface area / volume)
13of the sample, and $\Delta\rho$ is the contrast factor.
14
15For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as
16
17.. math::
18    q = \sqrt{q_x^2+q_y^2}
19
20"""
21
22from numpy import sqrt, power
23
24name = "porod"
25title = "Porod function"
26description = """\
27          I(q) = scale/q^4 + background
28"""
29
30category = "shape-independent"
31
32parameters = []
33
34def Iq(q):
35    """
36    @param q: Input q-value
37    """
38    return 1.0/power(q,4)
39
40Iq.vectorized = True  # Iq accepts an array of q values
41
42def Iqxy(qx, qy, *args):
43    """
44    @param qx:   Input q_x-value
45    @param qy:   Input q_y-value
46    @param args: Remaining arguments
47    """
48    return Iq(sqrt(qx ** 2 + qy ** 2), *args)
49
50Iqxy.vectorized = True # Iqxy accepts an array of qx, qy values
51
52demo = dict(scale=1.5, background=0.5)
53
54oldname = "PorodModel"
55oldpars = dict(scale='scale', background='background')
56
57tests = [[{'scale': 0.00001, 'background':0.01}, 0.04, 3.916250]]
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