Changes in sasmodels/models/core_shell_parallelepiped.py [393facf:1f159bd] in sasmodels

File:

• sasmodels/models/core_shell_parallelepiped.py (modified) (6 diffs)

sasmodels/models/core_shell_parallelepiped.py

@@ -5 +5 @@
 Calculates the form factor for a rectangular solid with a core-shell structure.
 The thickness and the scattering length density of the shell or
-"rim" can be different on each (pair) of faces.
-
+"rim" can be different on each (pair) of faces. However at this time
+the 1D calculation does **NOT** actually calculate a c face rim despite the presence of
+the parameter. Some other aspects of the 1D calculation may be wrong.
+
+.. note::
+   This model was originally ported from NIST IGOR macros. However, it is not
+   yet fully understood by the SasView developers and is currently under review.
 
 The form factor is normalized by the particle volume $V$ such that
@@ -36 +41 @@
     V = ABC + 2t_ABC + 2t_BAC + 2t_CAB
 
-**meaning that there are "gaps" at the corners of the solid.**
+**meaning that there are "gaps" at the corners of the solid.**  Again note that
+$t_C = 0$ currently.
 
 The intensity calculated follows the :ref:`parallelepiped` model, with the
 core-shell intensity being calculated as the square of the sum of the
-amplitudes of the core and the slabs on the edges.
-
-the scattering amplitude is computed for a particular orientation of the core-shell
-parallelepiped with respect to the scattering vector and then averaged over all
-possible orientations, where $\alpha$ is the angle between the $z$ axis and the longest axis $C$
-of the parallelepiped, $\beta$ is the angle between projection of the particle in the $xy$ detector plane and the $y$ axis.
+amplitudes of the core and shell, in the same manner as a core-shell model.
 
 .. math::
-    \begin{align*}
-    F(Q)&=A B C (\rho_\text{core}-\rho_\text{solvent})  S(A \sin\alpha \sin\beta)S(B \sin\alpha \cos\beta)S(C \cos\alpha) \\
-    &+ 2t_A B C (\rho_\text{A}-\rho_\text{solvent})  \left[S((A+t_A) \sin\alpha \sin\beta)-S(A \sin\alpha \sin\beta)\right] S(B \sin\alpha \cos\beta) S(C \cos\alpha)\\
-    &+ 2 A t_B C (\rho_\text{B}-\rho_\text{solvent})  S(A \sin\alpha \sin\beta) \left[S((B+t_B) \sin\alpha \cos\beta)-S(B \sin\alpha \cos\beta)\right] S(C \cos\alpha)\\
-    &+ 2 A B t_C (\rho_\text{C}-\rho_\text{solvent}) S(A \sin\alpha \sin\beta) S(B \sin\alpha \cos\beta) \left[S((C+t_C) \cos\alpha)-S(C \cos\alpha)\right]
-    \end{align*}
-
-with
-
-.. math::
-
-    S(x) = \frac{\sin \tfrac{1}{2}Q x}{\tfrac{1}{2}Q x}
-
-where $\rho_\text{core}$, $\rho_\text{A}$, $\rho_\text{B}$ and $\rho_\text{C}$ are
-the scattering length of the parallelepiped core, and the rectangular slabs of
-thickness $t_A$, $t_B$ and $t_C$, respectively.
-$\rho_\text{solvent}$ is the scattering length of the solvent.
+
+    F_{a}(Q,\alpha,\beta)=
+    \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}
+    - \frac{\sin(\tfrac{1}{2}QL_A\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_A\sin\alpha \sin\beta} \right]
+    \left[\frac{\sin(\tfrac{1}{2}QL_B\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_B\sin\alpha \sin\beta} \right]
+    \left[\frac{\sin(\tfrac{1}{2}QL_C\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_C\sin\alpha \sin\beta} \right]
+
+.. note::
+
+    Why does t_B not appear in the above equation?
+    For the calculation of the form factor to be valid, the sides of the solid
+    MUST (perhaps not any more?) be chosen such that** $A < B < C$.
+    If this inequality is not satisfied, the model will not report an error,
+    but the calculation will not be correct and thus the result wrong.
 
 FITTING NOTES
@@ -75 +73 @@
 known values, or you will certainly end up at a solution that is unphysical.
 
+Constraints must be applied during fitting to ensure that the inequality
+$A < B < C$ is not violated. The calculation will not report an error,
+but the results will not be correct.
+
 The returned value is in units of |cm^-1|, on absolute scale.
 
@@ -89 +91 @@
 $\Psi = 0$ when the *short_b* axis is parallel to the *x*-axis of the detector.
 
-For 2d, constraints must be applied during fitting to ensure that the inequality
-$A < B < C$ is not violated, and hence the correct definition of angles is preserved. The calculation will not report an error,
-but the results may be not correct.
-
 .. figure:: img/parallelepiped_angle_definition.png
 
     Definition of the angles for oriented core-shell parallelepipeds.
     Note that rotation $\theta$, initially in the $xz$ plane, is carried out first, then
-    rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is now around the axis of the parallelepiped.
+    rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is now around the axis of the cylinder.
     The neutron or X-ray beam is along the $z$ axis.
 
@@ -111 +109 @@
     Equations (1), (13-14). (in German)
 .. [#] D Singh (2009). *Small angle scattering studies of self assembly in
-   lipid mixtures*, Johns Hopkins University Thesis (2009) 223-225. `Available
+   lipid mixtures*, John's Hopkins University Thesis (2009) 223-225. `Available
    from Proquest <http://search.proquest.com/docview/304915826?accountid
    =26379>`_
@@ -221 +219 @@
          [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0853299803222]],
         ]
+del tests  # TODO: fix the tests
 del qx, qy  # not necessary to delete, but cleaner