Changeset dbf1a60 in sasmodels for sasmodels/models/parallelepiped.py

Timestamp:

Mar 11, 2018 2:29:41 PM (6 years ago)

Author:

butler

Branches:

master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

9616dfe

Parents:

367886f

Message:

Add comments to c code and clean documentatin

Added comments to c code in both parallelepiped and core shell
parallelepiped noting the change of integration varialbes in the
computation. Cleaned up and final corrections to the core shell
documentation and did some cleaning of parallelipiped. In particular
tried to bring a bit more consistency between the docs.

addresses #896

File:

• sasmodels/models/parallelepiped.py (modified) (4 diffs)

sasmodels/models/parallelepiped.py

@@ -39 +39 @@
 
     I(q) = \frac{\text{scale}}{V} (\Delta\rho \cdot V)^2
-           \left< P(q, \alpha) \right> + \text{background}
+           \left< P(q, \alpha, \beta) \right> + \text{background}
 
 where the volume $V = A B C$, the contrast is defined as
-$\Delta\rho = \rho_\text{p} - \rho_\text{solvent}$,
-$P(q, \alpha)$ is the form factor corresponding to a parallelepiped oriented
-at an angle $\alpha$ (angle between the long axis C and $\vec q$),
-and the averaging $\left<\ldots\right>$ is applied over all orientations.
+$\Delta\rho = \rho_\text{p} - \rho_\text{solvent}$, $P(q, \alpha, \beta)$
+is the form factor corresponding to a parallelepiped oriented
+at an angle $\alpha$ (angle between the long axis C and $\vec q$), and $\beta$
+( the angle between the projection of the particle in the $xy$ detector plane
+and the $y$ axis) and the averaging $\left<\ldots\right>$ is applied over all
+orientations.
 
 Assuming $a = A/B < 1$, $b = B /B = 1$, and $c = C/B > 1$, the
-form factor is given by (Mittelbach and Porod, 1961)
+form factor is given by (Mittelbach and Porod, 1961 [#Mittelbach]_)
 
 .. math::
@@ -66 +68 @@
     \mu &= qB
 
-The scattering intensity per unit volume is returned in units of |cm^-1|.
+where substitution of $\sigma = cos\alpha$ and $\beta = \pi/2 \ u$ have been
+applied.
 
 NB: The 2nd virial coefficient of the parallelepiped is calculated based on
@@ -120 +123 @@
 .. math::
 
-    P(q_x, q_y) = \left[\frac{\sin(\tfrac{1}{2}qA\cos\alpha)}{(\tfrac{1}{2}qA\cos\alpha)}\right]^2
-                  \left[\frac{\sin(\tfrac{1}{2}qB\cos\beta)}{(\tfrac{1}{2}qB\cos\beta)}\right]^2
-                  \left[\frac{\sin(\tfrac{1}{2}qC\cos\gamma)}{(\tfrac{1}{2}qC\cos\gamma)}\right]^2
+    P(q_x, q_y) = \left[\frac{\sin(\tfrac{1}{2}qA\cos\alpha)}{(\tfrac{1}
+                   {2}qA\cos\alpha)}\right]^2
+                  \left[\frac{\sin(\tfrac{1}{2}qB\cos\beta)}{(\tfrac{1}
+                   {2}qB\cos\beta)}\right]^2
+                  \left[\frac{\sin(\tfrac{1}{2}qC\cos\gamma)}{(\tfrac{1}
+                   {2}qC\cos\gamma)}\right]^2
 
 with
@@ -160 +166 @@
 ----------
 
-P Mittelbach and G Porod, *Acta Physica Austriaca*, 14 (1961) 185-211
-
-R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854
+.. [#Mittelbach] P Mittelbach and G Porod, *Acta Physica Austriaca*,
+   14 (1961) 185-211
+.. [#] R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854
 
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