source: sasmodels/sasmodels/models/spherical_sld.py @ 9244430

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Last change on this file since 9244430 was 9244430, checked in by wojciech, 8 years ago

Prototype version of sphericalSLD
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1r"""
2This model calculates an empirical functional form for SAS data using SpericalSLD profile
3
4Similarly to the OnionExpShellModel, this model provides the form factor, P(q), for a multi-shell sphere,
5where the interface between the each neighboring shells can be described by one of a number of functions
6including error, power-law, and exponential functions. This model is to calculate the scattering intensity
7by building a continuous custom SLD profile against the radius of the particle. The SLD profile is composed
8of a flat core, a flat solvent, a number (up to 9 ) flat shells, and the interfacial layers between
9the adjacent flat shells (or core, and solvent) (see below).
10Unlike the OnionExpShellModel (using an analytical integration),
11the interfacial layers here are sub-divided and numerically integrated assuming each of the sub-layers are described
12by a line function. The number of the sub-layer can be given by users by setting the integer values of npts_inter
13in the GUI. The form factor is normalized by the total volume of the sphere.
14
15Definition
16----------
17
18The scattering intensity $I(q)$ in 1D is calculated as:
19
20.. math::
21
22    P(q) = \frac{f^2}{V_\text{particle}}
23    f = f_\text{core} + \sum_{\text{inter}_i=0}^N f_text{inter}_i +
24    \sum_{\text{flat}_i=0}^N f_text{flat}_i +f_\text{solvent}
25
26where, for a spherically symmetric particle with a particle density \rho(r)
27
28
29The scaling of the second power law region (coefficent C) is then automatically scaled to
30match the first by following formula
31
32.. math::
33    C = \frac{A}{qc^{-m1} qc^{-m2}}
34
35.. note::
36    Be sure to enter the power law exponents as positive values!
37
38For 2D data the scattering intensity is calculated in the same way as 1D,
39where the $q$ vector is defined as
40
41.. math::
42
43    q = \sqrt{q_x^2 + q_y^2}
44
45
46.. figure:: img/two_power_law_1d.jpg
47
48    1D plot using the default values (w/500 data point).
49
50References
51----------
52L A Feigin and D I Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Press, New York, (1987)
53
54"""
55
56from numpy import inf
57
58name = "spherical_sld"
59title = "Sperical SLD intensity calculation"
60description = """
61            I(q) =
62               background = Incoherent background [1/cm]
63        """
64category = "shere-based"
65
66# pylint: disable=bad-whitespace, line-too-long
67#            ["name", "units", default, [lower, upper], "type", "description"],
68parameters = [["n_shells",       "",         1, [0, 9], "", "number of shells"],
69              ["npts_imter",  "",         35, [0, inf], "", "number of points in each sublayer"],
70              ["sld_solv",     "1/Ang^2",    1E-6,[-inf, inf], "","sld function solvent"],
71              ["func_inter_0",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
72              ["nu_inter_0",       "",         2.5, [-inf, inf], "", "steepness parameter"],
73              ["thick_inter_0",       "Ang",         50, [-inf, inf], "", "intern layer thickness"],
74              ["sld_core_0",       "1/Ang^2",         2.07E-6, [-inf, inf],"", "sld function flat"],
75              ["thick_flat_0",       "Ang",         100, [-inf, inf], "", "flat layer_thickness"],
76              ["func_inter_1",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
77              ["nu_inter_1",       "",         2.5, [-inf, inf], "", "steepness parameter"],
78              ["thick_inter_1",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
79              ["sld_flat_1",       "1/Ang^2",         4.06E-6, [-inf, inf],"", "sld function flat"],
80              ["thick_flat_1",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
81              ["func_inter_2",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
82              ["nu_inter_2",       "",         2.5, [-inf, inf], "", "steepness parameter"],
83              ["thick_inter_2",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
84              ["sld_flat_2",       "1/Ang^2",         3.56E-6, [-inf, inf],"", "sld function flat"],
85              ["thick_flat_2",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
86              ["func_inter_3",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
87              ["nu_inter_3",       "",         2.5, [-inf, inf], "", "steepness parameter"],
88              ["thick_inter_3",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
89              ["sld_flat_3",       "1/Ang^2",         4.06E-6, [-inf, inf],"", "sld function flat"],
90              ["thick_flat_3",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
91              ["func_inter_4",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
92              ["nu_inter_4",       "",         2.5, [-inf, inf], "", "steepness parameter"],
93              ["thick_inter_4",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
94              ["sld_flat_4",       "1/Ang^2",         3.5E-6, [-inf, inf],"", "sld function flat"],
95              ["thick_flat_4",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
96              ["func_inter_5",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
97              ["nu_inter_5",       "",         2.5, [-inf, inf], "", "steepness parameter"],
98              ["thick_inter_5",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
99              ["sld_flat_5",       "1/Ang^2",         4.06E-6, [-inf, inf],"", "sld function flat"],
100              ["thick_flat_5",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
101              ["func_inter_6",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
102              ["nu_inter_6",       "",         2.5, [-inf, inf], "", "steepness parameter"],
103              ["thick_inter_6",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
104              ["sld_flat_6",       "1/Ang^2",         3.5E-6, [-inf, inf],"", "sld function flat"],
105              ["thick_flat_6",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
106              ["func_inter_7",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
107              ["nu_inter_7",       "",         2.5, [-inf, inf], "", "steepness parameter"],
108              ["thick_inter_7",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
109              ["sld_flat_7",       "1/Ang^2",         4.06E-6, [-inf, inf],"", "sld function flat"],
110              ["thick_flat_7",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
111              ["func_inter_8",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
112              ["nu_inter_8",       "",         2.5, [-inf, inf], "", "steepness parameter"],
113              ["thick_inter_8",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
114              ["sld_flat_8",       "1/Ang^2",         3.5E-6, [-inf, inf],"", "sld function flat"],
115              ["thick_flat_8",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
116              ["func_inter_9",       "",         0, [0, 4], "", "'Erf(|nu|*z)':0, 'RPower(z^|nu|)':1, 'LPower(z^|nu|)':2, 'RExp(-|nu|*z)':3, 'LExp(-|nu|*z)':4"],
117              ["nu_inter_9",       "",         2.5, [-inf, inf], "", "steepness parameter"],
118              ["thick_inter_9",       "Ang",         50.0, [-inf, inf], "", "intern layer thickness"],
119              ["sld_flat_9",       "1/Ang^2",         4.06E-6, [-inf, inf],"", "sld function flat"],
120              ["thick_flat_9",       "Ang",         100.0, [-inf, inf], "", "flat layer_thickness"],
121              ]
122# pylint: enable=bad-whitespace, line-too-long
123source = ["lib/librefl.c", "spherical_sld.c"]
124
125
126#TODO: Not clear if dispersion function is needed
127#def _set_dispersion(self):
128#        """
129#        Setting dispersion for all shells
130#        """
131#        ##set dispersion from model
132#        for name , value in self.model.dispersion.iteritems():
133#
134#            nshell = -1
135#            if name.split('_')[0] == 'thick':
136#                while nshell < 1:
137#                    nshell += 1
138#                    if name.split('_')[1] == 'inter%s' % str(nshell):
139#                        self.dispersion[name] = value
140#                    else:
141#                        continue
142#            else:
143#                self.dispersion[name] = value
144
145
146def ER(radius):
147        """
148        Calculate the effective radius for P(q)*S(q)
149        Tale different radius values from corresponding shells
150
151        :return: the value of the effective radius
152        """
153
154        return radius
155
156
157demo = dict(scale=1, background=0.1,
158        n_shells=1,
159        npts_inter=35,
160        sld_solv=1E-6,
161        func_inter_1=0.0,
162        nu_inter_1=2.5,
163        thick_inter_1=50,
164        sld_flat_1=4E-6,
165        thick_flat_1=100,
166        func_inter_0=0.0,
167        nu_inter_0=2.5,
168        rad_core_0=50.0,
169        std_core_0=2.07E-6,
170        thick_core_0=50
171    )
172
173oldname = "SphericalSLDModel"
174oldpars = dict(
175        npts_inter='npts_imter',
176        sld_solv='sld_solv',
177        func_inter_1='func_inter_1',
178        nu_inter_1='nu_inter',
179        thick_inter_1='thick_inter1',
180        sld_flat_1='sld_flat1',
181        thick_flat_1='thick_flat1',
182        func_inter_0='nu_inter0',
183        nu_inter_0='nu_inter0',
184        rad_core_0='rad_core0',
185        std_core_0='std_core0',
186        thick_core_0='thick_core0',
187        background='background')
188
189tests = [
190    # Accuracy tests based on content in test/utest_extra_models.py
191    [{'npts_iter':35,
192        'sld_solv':1E-6,
193        'func_inter_1':0.0,
194        'nu_inter':2.5,
195        'thick_inter_1':50,
196        'sld_flat_1':4E-6,
197        'thick_flat_1':100,
198        'func_inter_0':0.0,
199        'nu_inter_0':2.5,
200        'rad_core_0':50.0,
201        'std_core_0':2.07E-6,
202        'thick_core':50,
203        'background': 0.0,
204    }, 0.001, 1000],
205]
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