Changeset 34a9e4e in sasmodels


Ignore:
Timestamp:
Apr 11, 2017 6:11:36 AM (8 months ago)
Author:
richardh
Branches:
master, boltzmann, costrafo411, doc_update, generic_integration_loop, ticket-1043, ticket-786
Children:
9ed43f4
Parents:
e645373
Message:

more docs fixes

Location:
sasmodels/models
Files:
2 edited

Legend:

Unmodified
Added
Removed
  • sasmodels/models/parallelepiped.py

    r9802ab3 r34a9e4e  
    2222.. note:: 
    2323 
    24    The edge of the solid used to have to satisfy the condition that $A < B < C$. 
    25    After some improvements to the effective radius calculation, used with 
    26    an S(Q), it is beleived that this is no longer the case. 
     24The three dimensions of the parallelepiped (strictly here a cuboid) may be given in  
     25$any$ size order. To avoid multiple fit solutions, especially 
     26with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may  
     27be a number of closely similar "best fits", so some trial and error, or fixing of some  
     28dimensions at expected values, may help. 
    2729 
    2830The 1D scattering intensity $I(q)$ is calculated as: 
  • sasmodels/models/triaxial_ellipsoid.py

    re645373 r34a9e4e  
    6666    r^2 &= b^2(p_a \sin^2(\phi)(1 - u^2) + 1 + p_c u^2) 
    6767 
     68Though for convenience we describe the three radii of the ellipsoid as equatorial 
     69and polar, they may be given in $any$ size order. To avoid multiple solutions, especially 
     70with Monte-Carlo fit methods, it may be advisable to restrict their ranges. For typical 
     71small angle diffraction situations there may be a number of closely similar "best fits", 
     72so some trial and error, or fixing of some radii at expected values, may help. 
     73     
    6874To provide easy access to the orientation of the triaxial ellipsoid, 
    6975we define the axis of the cylinder using the angles $\theta$, $\phi$ 
    70 and $\psi$. These angles are defined analogously to the elliptical_cylinder below 
     76and $\psi$. These angles are defined analogously to the elliptical_cylinder below, note that 
     77angle $\phi$ is now NOT the same as in the equations above. 
    7178 
    7279.. figure:: img/elliptical_cylinder_angle_definition.png 
    7380 
    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. 
     81    Definition of angles for oriented triaxial ellipsoid, where radii are for illustration here  
     82    $a < b << c$ and angle $\Psi$ is a rotation around the axis of the particle. 
    7783 
    7884For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,  
     
    8389.. figure:: img/triaxial_ellipsoid_angle_projection.png 
    8490 
    85     Some example angles for oriented ellipsoid. 
     91    Some examples for an oriented triaxial ellipsoid. 
    8692 
    8793The radius-of-gyration for this system is  $R_g^2 = (R_a R_b R_c)^2/5$. 
     
    9298 
    9399NB: The 2nd virial coefficient of the triaxial solid ellipsoid is 
    94 calculated based on the polar radius $R_p = R_c$ and equatorial 
    95 radius $R_e = \sqrt{R_a R_b}$, and used as the effective radius for 
     100calculated after sorting the three radii to give the most appropriate 
     101prolate or oblate form, from the new polar radius $R_p = R_c$ and effective equatorial 
     102radius,  $R_e = \sqrt{R_a R_b}$, to then be used as the effective radius for 
    96103$S(q)$ when $P(q) \cdot S(q)$ is applied. 
    97104 
     
    125132 
    126133description = """ 
    127    Note - fitting ensure that the inequality ra<rb<rc is not 
    128    violated. Otherwise the calculation may not be correct. 
     134   Triaxial ellipsoid - see main documentation. 
    129135""" 
    130136category = "shape:ellipsoid" 
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