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  • sasmodels/models/triaxial_ellipsoid.py

    r9b79f29 r0881f4e  
    1616    \frac{X^2}{R_a^2} + \frac{Y^2}{R_b^2} + \frac{Z^2}{R_c^2} = 1 
    1717 
    18 the scattering for randomly oriented particles is defined by the average over all orientations $\Omega$ of: 
     18the scattering for randomly oriented particles is defined by the average over 
     19all orientations $\Omega$ of: 
    1920 
    2021.. math:: 
    2122 
    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} 
    2325 
    2426where 
     
    3840 .. math:: 
    3941 
    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 
    4144 
    4245with $e = \cos\gamma \sin\phi$, $f = \cos\gamma \cos\phi$ and $g = \sin\gamma$. 
     
    6972.. figure:: img/elliptical_cylinder_angle_definition.png 
    7073 
    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. 
    7377 
    7478The angle $\psi$ is the rotational angle around its own $c$ axis 
     
    114118* **Last Modified by:** Paul Kienzle (improved calculation) **Date:** April 4, 2017 
    115119* **Last Reviewed by:** Paul Kienzle & Richard Heenan **Date:**  April 4, 2017 
    116  
    117120""" 
    118121 
     
    122125title = "Ellipsoid of uniform scattering length density with three independent axes." 
    123126 
    124 description = """\ 
     127description = """ 
    125128Note: During fitting ensure that the inequality ra<rb<rc is not 
    126129        violated. Otherwise the calculation will 
     
    140143              ["radius_polar", "Ang", 10, [0, inf], "volume", 
    141144               "Polar radius, Rc"], 
    142               ["theta", "degrees", 60, [-360, 360], "orientation", 
    143                "polar axis to beam angle"], 
    144               ["phi", "degrees", 60, [-360, 360], "orientation", 
    145                "rotation about beam"], 
    146               ["psi", "degrees", 60, [-360, 360], "orientation", 
    147                "rotation about polar axis"], 
     145              ["theta", "degrees", 60, [-inf, inf], "orientation", 
     146               "In plane angle"], 
     147              ["phi", "degrees", 60, [-inf, inf], "orientation", 
     148               "Out of plane angle"], 
     149              ["psi", "degrees", 60, [-inf, inf], "orientation", 
     150               "Out of plane angle"], 
    148151             ] 
    149152 
     
    157160    from .ellipsoid import ER as ellipsoid_ER 
    158161 
    159     # now that radii can be in any size order, radii need sorting a,b,c where a~b and c is either much smaller 
    160     # or much larger 
     162    # now that radii can be in any size order, radii need sorting a,b,c 
     163    # where a~b and c is either much smaller or much larger 
    161164    radii = np.vstack((radius_equat_major, radius_equat_minor, radius_polar)) 
    162165    radii = np.sort(radii, axis=0) 
     
    178181 
    179182q = 0.1 
    180 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     183# april 6 2017, rkh add unit tests 
     184#     NOT compared with any other calc method, assume correct! 
    181185# add 2d test after pull #890 
    182186qx = q*cos(pi/6.0) 
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