# source:sasmodels/sasmodels/models/_spherepy.py@ef07e95

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since ef07e95 was ef07e95, checked in by Paul Kienzle <pkienzle@…>, 7 years ago

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1r"""
2For information about polarised and magnetic scattering, see
3the :doc:magnetic help <../sasgui/perspectives/fitting/mag_help> documentation.
4
5Definition
6----------
7
8The 1D scattering intensity is calculated in the following way (Guinier, 1955)
9
10.. math::
11
12    I(q) = \frac{\text{scale}}{V} \cdot \left[
13        3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3}
14        \right]^2 + \text{background}
15
16where *scale* is a volume fraction, $V$ is the volume of the scatterer,
17$r$ is the radius of the sphere, *background* is the background level and
18*sld* and *sld_solvent* are the scattering length densities (SLDs) of the
19scatterer and the solvent respectively.
20
21Note that if your data is in absolute scale, the *scale* should represent
22the volume fraction (which is unitless) if you have a good fit. If not,
23it should represent the volume fraction times a factor (by which your data
24might need to be rescaled).
25
26The 2D scattering intensity is the same as above, regardless of the
27orientation of $\vec q$.
28
29Validation
30----------
31
32Validation of our code was done by comparing the output of the 1D model
33to the output of the software provided by the NIST (Kline, 2006).
34
35
36References
37----------
38
39A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*,
40John Wiley and Sons, New York, (1955)
41
42* **Last Reviewed by:** S King and P Parker **Date:** 2013/09/09 and 2014/01/06
43"""
44
45import numpy as np
46from numpy import pi, inf, sin, cos, sqrt, log
47
48name = " _sphere (python)"
49title = "PAK testing ideas for Spheres with uniform scattering length density"
50description = """\
51P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr))
52                /(qr)^3]^2 + background
54    V: The volume of the scatter
55    sld: the SLD of the sphere
56    sld_solvent: the SLD of the solvent
57"""
58category = "shape:sphere"
59
60#             ["name", "units", default, [lower, upper], "type","description"],
61parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "",
62               "Layer scattering length density"],
63              ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "",
64               "Solvent scattering length density"],
65              ["radius", "Ang", 50, [0, inf], "volume",
67             ]
68
69
71    return 1.333333333333333 * pi * radius ** 3
72
74    #print "q",q
76    qr = q * radius
77    sn, cn = sin(qr), cos(qr)
78    ## The natural expression for the bessel function is the following:
79    ##     bes = 3 * (sn-qr*cn)/qr**3 if qr>0 else 1
80    ## however, to support vector q values we need to handle the conditional
81    ## as a vector, which we do by first evaluating the full expression
82    ## everywhere, then fixing it up where it is broken.   We should probably
83    ## set numpy to ignore the 0/0 error before we do though...
84    bes = 3 * (sn - qr * cn) / qr ** 3 # may be 0/0 but we fix that next line
85    bes[qr == 0] = 1
86    fq = bes * (sld - sld_solvent) * form_volume(radius)
87    return 1.0e-4 * fq ** 2
88Iq.vectorized = True  # Iq accepts an array of q values
89
90def Iqxy(qx, qy, sld, sld_solvent, radius):
91    return Iq(sqrt(qx ** 2 + qy ** 2), sld, sld_solvent, radius)
92Iqxy.vectorized = True  # Iqxy accepts arrays of qx, qy values
93
95    """
96    Calculate SESANS-correlation function for a solid sphere.
97
98    Wim Bouwman after formulae Timofei Kruglov J.Appl.Cryst. 2003 article
99    """
100    d = z / radius
101    g = np.zeros_like(z)
102    g[d == 0] = 1.
103    low = ((d > 0) & (d < 2))
104    dlow = d[low]
105    dlow2 = dlow ** 2
106    g[low] = (sqrt(1 - dlow2/4.) * (1 + dlow2/8.)
107              + dlow2/2.*(1 - dlow2/16.) * log(dlow / (2. + sqrt(4. - dlow2))))
108    return g
109sesans.vectorized = True  # sesans accepts an array of z values
110