source: sasmodels/sasmodels/models/core_shell_parallelepiped.py @ 8f04da4

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 8f04da4 was 8f04da4, checked in by Paul Kienzle <pkienzle@…>, 5 years ago

tuned random model generation for more models

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1r"""
2Definition
3----------
4
5Calculates the form factor for a rectangular solid with a core-shell structure.
6The thickness and the scattering length density of the shell or
7"rim" can be different on each (pair) of faces. However at this time
8the 1D calculation does **NOT** actually calculate a c face rim despite the presence of
9the parameter. Some other aspects of the 1D calculation may be wrong.
10
11.. note::
12   This model was originally ported from NIST IGOR macros. However, it is not
13   yet fully understood by the SasView developers and is currently under review.
14
15The form factor is normalized by the particle volume $V$ such that
16
17.. math::
18
19    I(q) = \text{scale}\frac{\langle f^2 \rangle}{V} + \text{background}
20
21where $\langle \ldots \rangle$ is an average over all possible orientations
22of the rectangular solid.
23
24
25The function calculated is the form factor of the rectangular solid below.
26The core of the solid is defined by the dimensions $A$, $B$, $C$ such that
27$A < B < C$.
28
29.. image:: img/core_shell_parallelepiped_geometry.jpg
30
31There are rectangular "slabs" of thickness $t_A$ that add to the $A$ dimension
32(on the $BC$ faces). There are similar slabs on the $AC$ $(=t_B)$ and $AB$
33$(=t_C)$ faces. The projection in the $AB$ plane is then
34
35.. image:: img/core_shell_parallelepiped_projection.jpg
36
37The volume of the solid is
38
39.. math::
40
41    V = ABC + 2t_ABC + 2t_BAC + 2t_CAB
42
43**meaning that there are "gaps" at the corners of the solid.**  Again note that
44$t_C = 0$ currently.
45
46The intensity calculated follows the :ref:`parallelepiped` model, with the
47core-shell intensity being calculated as the square of the sum of the
48amplitudes of the core and shell, in the same manner as a core-shell model.
49
50.. math::
51
52    F_{a}(Q,\alpha,\beta)=
53    \left[\frac{\sin(\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha \sin\beta)}{\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha\sin\beta}
54    - \frac{\sin(\tfrac{1}{2}QL_A\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_A\sin\alpha \sin\beta} \right]
55    \left[\frac{\sin(\tfrac{1}{2}QL_B\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_B\sin\alpha \sin\beta} \right]
56    \left[\frac{\sin(\tfrac{1}{2}QL_C\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_C\sin\alpha \sin\beta} \right]
57
58.. note::
59
60    Why does t_B not appear in the above equation?
61    For the calculation of the form factor to be valid, the sides of the solid
62    MUST (perhaps not any more?) be chosen such that** $A < B < C$.
63    If this inequality is not satisfied, the model will not report an error,
64    but the calculation will not be correct and thus the result wrong.
65
66FITTING NOTES
67If the scale is set equal to the particle volume fraction, $\phi$, the returned
68value is the scattered intensity per unit volume, $I(q) = \phi P(q)$.
69However, **no interparticle interference effects are included in this
70calculation.**
71
72There are many parameters in this model. Hold as many fixed as possible with
73known values, or you will certainly end up at a solution that is unphysical.
74
75Constraints must be applied during fitting to ensure that the inequality
76$A < B < C$ is not violated. The calculation will not report an error,
77but the results will not be correct.
78
79The returned value is in units of |cm^-1|, on absolute scale.
80
81NB: The 2nd virial coefficient of the core_shell_parallelepiped is calculated
82based on the the averaged effective radius $(=\sqrt{(A+2t_A)(B+2t_B)/\pi})$
83and length $(C+2t_C)$ values, after appropriately
84sorting the three dimensions to give an oblate or prolate particle, to give an
85effective radius, for $S(Q)$ when $P(Q) * S(Q)$ is applied.
86
87To provide easy access to the orientation of the parallelepiped, we define the
88axis of the cylinder using three angles $\theta$, $\phi$ and $\Psi$.
89(see :ref:`cylinder orientation <cylinder-angle-definition>`).
90The angle $\Psi$ is the rotational angle around the *long_c* axis against the
91$q$ plane. For example, $\Psi = 0$ when the *short_b* axis is parallel to the
92*x*-axis of the detector.
93
94.. figure:: img/parallelepiped_angle_definition.png
95
96    Definition of the angles for oriented core-shell parallelepipeds.
97
98.. figure:: img/parallelepiped_angle_projection.png
99
100    Examples of the angles for oriented core-shell parallelepipeds against the
101    detector plane.
102
103References
104----------
105
106.. [#] P Mittelbach and G Porod, *Acta Physica Austriaca*, 14 (1961) 185-211
107    Equations (1), (13-14). (in German)
108.. [#] D Singh (2009). *Small angle scattering studies of self assembly in
109   lipid mixtures*, John's Hopkins University Thesis (2009) 223-225. `Available
110   from Proquest <http://search.proquest.com/docview/304915826?accountid
111   =26379>`_
112
113Authorship and Verification
114----------------------------
115
116* **Author:** NIST IGOR/DANSE **Date:** pre 2010
117* **Converted to sasmodels by:** Miguel Gonzales **Date:** February 26, 2016
118* **Last Modified by:** Wojciech Potrzebowski **Date:** January 11, 2017
119* **Currently Under review by:** Paul Butler
120"""
121
122import numpy as np
123from numpy import pi, inf, sqrt, cos, sin
124
125name = "core_shell_parallelepiped"
126title = "Rectangular solid with a core-shell structure."
127description = """
128     P(q)=
129"""
130category = "shape:parallelepiped"
131
132#             ["name", "units", default, [lower, upper], "type","description"],
133parameters = [["sld_core", "1e-6/Ang^2", 1, [-inf, inf], "sld",
134               "Parallelepiped core scattering length density"],
135              ["sld_a", "1e-6/Ang^2", 2, [-inf, inf], "sld",
136               "Parallelepiped A rim scattering length density"],
137              ["sld_b", "1e-6/Ang^2", 4, [-inf, inf], "sld",
138               "Parallelepiped B rim scattering length density"],
139              ["sld_c", "1e-6/Ang^2", 2, [-inf, inf], "sld",
140               "Parallelepiped C rim scattering length density"],
141              ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld",
142               "Solvent scattering length density"],
143              ["length_a", "Ang", 35, [0, inf], "volume",
144               "Shorter side of the parallelepiped"],
145              ["length_b", "Ang", 75, [0, inf], "volume",
146               "Second side of the parallelepiped"],
147              ["length_c", "Ang", 400, [0, inf], "volume",
148               "Larger side of the parallelepiped"],
149              ["thick_rim_a", "Ang", 10, [0, inf], "volume",
150               "Thickness of A rim"],
151              ["thick_rim_b", "Ang", 10, [0, inf], "volume",
152               "Thickness of B rim"],
153              ["thick_rim_c", "Ang", 10, [0, inf], "volume",
154               "Thickness of C rim"],
155              ["theta", "degrees", 0, [-360, 360], "orientation",
156               "c axis to beam angle"],
157              ["phi", "degrees", 0, [-360, 360], "orientation",
158               "rotation about beam"],
159              ["psi", "degrees", 0, [-360, 360], "orientation",
160               "rotation about c axis"],
161             ]
162
163source = ["lib/gauss76.c", "core_shell_parallelepiped.c"]
164
165
166def ER(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c):
167    """
168        Return equivalent radius (ER)
169    """
170
171    # surface average radius (rough approximation)
172    surf_rad = sqrt((length_a + 2.0*thick_rim_a) * (length_b + 2.0*thick_rim_b) / pi)
173
174    height = length_c + 2.0*thick_rim_c
175
176    ddd = 0.75 * surf_rad * (2 * surf_rad * height + (height + surf_rad) * (height + pi * surf_rad))
177    return 0.5 * (ddd) ** (1. / 3.)
178
179# VR defaults to 1.0
180
181def random():
182    import numpy as np
183    outer = 10**np.random.uniform(1, 4.7, size=3)
184    thick = np.random.beta(0.5, 0.5, size=3)*(outer-2) + 1
185    length = outer - thick
186    pars = dict(
187        length_a=length[0],
188        length_b=length[1],
189        length_c=length[2],
190        thick_rim_a=thick[0],
191        thick_rim_b=thick[1],
192        thick_rim_c=thick[2],
193    )
194    return pars
195
196# parameters for demo
197demo = dict(scale=1, background=0.0,
198            sld_core=1, sld_a=2, sld_b=4, sld_c=2, sld_solvent=6,
199            length_a=35, length_b=75, length_c=400,
200            thick_rim_a=10, thick_rim_b=10, thick_rim_c=10,
201            theta=0, phi=0, psi=0,
202            length_a_pd=0.1, length_a_pd_n=1,
203            length_b_pd=0.1, length_b_pd_n=1,
204            length_c_pd=0.1, length_c_pd_n=1,
205            thick_rim_a_pd=0.1, thick_rim_a_pd_n=1,
206            thick_rim_b_pd=0.1, thick_rim_b_pd_n=1,
207            thick_rim_c_pd=0.1, thick_rim_c_pd_n=1,
208            theta_pd=10, theta_pd_n=1,
209            phi_pd=10, phi_pd_n=1,
210            psi_pd=10, psi_pd_n=1)
211
212# rkh 7/4/17 add random unit test for 2d, note make all params different, 2d values not tested against other codes or models
213qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.)
214tests = [[{}, 0.2, 0.533149288477],
215         [{}, [0.2], [0.533149288477]],
216         [{'theta':10.0, 'phi':20.0}, (qx, qy), 0.0853299803222],
217         [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0853299803222]],
218        ]
219del qx, qy  # not necessary to delete, but cleaner
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