Changeset 48438f9 in sasmodels for sasmodels/models/triaxial_ellipsoid.py
- Timestamp:
- Apr 8, 2017 5:51:51 AM (7 years ago)
- Branches:
- master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- 3401a7a
- Parents:
- 9b79f29 (diff), 85190c2 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
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sasmodels/models/triaxial_ellipsoid.py
r9b79f29 r48438f9 16 16 \frac{X^2}{R_a^2} + \frac{Y^2}{R_b^2} + \frac{Z^2}{R_c^2} = 1 17 17 18 the scattering for randomly oriented particles is defined by the average over all orientations $\Omega$ of: 18 the scattering for randomly oriented particles is defined by the average over 19 all orientations $\Omega$ of: 19 20 20 21 .. math:: 21 22 22 P(q) = \text{scale}(\Delta\rho)^2\frac{V}{4 \pi}\int_\Omega \Phi^2(qr) d\Omega + \text{background} 23 P(q) = \text{scale}(\Delta\rho)^2\frac{V}{4 \pi}\int_\Omega\Phi^2(qr)\,d\Omega 24 + \text{background} 23 25 24 26 where … … 38 40 .. math:: 39 41 40 \langle\Phi^2\rangle = \int_0^{2\pi} \int_{-\pi/2}^{\pi/2} \Phi^2(qr) \cos \gamma\,d\gamma d\phi 42 \langle\Phi^2\rangle = \int_0^{2\pi} \int_{-\pi/2}^{\pi/2} \Phi^2(qr) 43 \cos \gamma\,d\gamma d\phi 41 44 42 45 with $e = \cos\gamma \sin\phi$, $f = \cos\gamma \cos\phi$ and $g = \sin\gamma$. … … 69 72 .. figure:: img/elliptical_cylinder_angle_definition.png 70 73 71 Definition of angles for oriented triaxial ellipsoid, where radii shown here are $a < b << c$ 72 and angle $\Psi$ is a rotation around the axis of the particle. 74 Definition of angles for oriented triaxial ellipsoid, where radii shown 75 here are $a < b << c$ and angle $\Psi$ is a rotation around the axis 76 of the particle. 73 77 74 78 The angle $\psi$ is the rotational angle around its own $c$ axis … … 115 119 * **Last Reviewed by:** Paul Kienzle & Richard Heenan **Date:** April 4, 2017 116 120 117 """118 119 121 from numpy import inf, sin, cos, pi 120 122 … … 122 124 title = "Ellipsoid of uniform scattering length density with three independent axes." 123 125 124 description = """ \126 description = """ 125 127 Note: During fitting ensure that the inequality ra<rb<rc is not 126 128 violated. Otherwise the calculation will … … 157 159 from .ellipsoid import ER as ellipsoid_ER 158 160 159 # now that radii can be in any size order, radii need sorting a,b,c where a~b and c is either much smaller160 # or much larger161 # now that radii can be in any size order, radii need sorting a,b,c 162 # where a~b and c is either much smaller or much larger 161 163 radii = np.vstack((radius_equat_major, radius_equat_minor, radius_polar)) 162 164 radii = np.sort(radii, axis=0) … … 178 180 179 181 q = 0.1 180 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 182 # april 6 2017, rkh add unit tests 183 # NOT compared with any other calc method, assume correct! 181 184 # add 2d test after pull #890 182 185 qx = q*cos(pi/6.0)
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