Changeset 19dcb933 in sasmodels for sasmodels/models/ellipsoid.py

Timestamp:

Sep 3, 2014 1:16:10 AM (10 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

1c7ffdc

Parents:

87985ca

Message:

build docs for models

File:

• sasmodels/models/ellipsoid.py (modified) (8 diffs)

sasmodels/models/ellipsoid.py

@@ -12 +12 @@
 .. math::
 
-    P(q,\alpha) = \frac{\text{scale}}{V} f^2(q) + \text{background}
+    P(Q,\alpha) = {\text{scale} \over V} F^2(Q) + \text{background}
 
 where
@@ -18 +18 @@
 .. math::
 
-    f(q) = \frac{3 (\Delta rho)) V (\sin[qr(R_p,R_e,\alpha)] \
-                 - \cos[qr(R_p,R_e,\alpha)])}{[qr(R_q,R_b,\alpha)]^3}
+    F(Q) = {3 (\Delta rho)) V (\sin[Qr(R_p,R_e,\alpha)]
+                - \cos[Qr(R_p,R_e,\alpha)])
+            \over [Qr(R_p,R_e,\alpha)]^3 }
 
 and
@@ -25 +26 @@
 .. math::
 
-    r(R_p,R_e,\alpha) = \left[ R_e^2 \sin^2 \alpha + R_p^2 \cos^2 \alpha \right]^{1/2}
+    r(R_p,R_e,\alpha) = \left[ R_e^2 \sin^2 \alpha
+        + R_p^2 \cos^2 \alpha \right]^{1/2}
 
 
@@ -36 +38 @@
 To provide easy access to the orientation of the ellipsoid, we define
 the rotation axis of the ellipsoid using two angles $\theta$ and $\phi$.
-These angles are defined in Figure :num:`figure #cylinder-orientation`.
+These angles are defined in the
+:ref:`cylinder orientation figure <cylinder-orientation>`.
 For the ellipsoid, $\theta$ is the angle between the rotational axis
 and the $z$-axis.
@@ -42 +45 @@
 NB: The 2nd virial coefficient of the solid ellipsoid is calculated based
 on the $R_p$ and $R_e$ values, and used as the effective radius for
-$S(Q)$ when $P(Q) \dot S(Q)$ is applied.
+$S(Q)$ when $P(Q) \cdot S(Q)$ is applied.
 
-.. figure:: img/image121.JPG
+.. _ellipsoid-1d:
+
+.. figure:: img/ellipsoid_1d.JPG
 
     The output of the 1D scattering intensity function for randomly oriented
@@ -54 +59 @@
 use the c-library from NIST.
 
-.. figure:: img/image122.JPG
+.. _ellipsoid-geometry:
+
+.. figure:: img/ellipsoid_geometry.JPG
 
     The angles for oriented ellipsoid.
@@ -63 +70 @@
 Validation of our code was done by comparing the output of the 1D model
 to the output of the software provided by the NIST (Kline, 2006).
-Figure :num:`figure ellipsoid-comparison-1d` below shows a comparison of
+:num:`Figure ellipsoid-comparison-1d` below shows a comparison of
 the 1D output of our model and the output of the NIST software.
 
 .. _ellipsoid-comparison-1d:
 
-.. figure:: img/image123.JPG
+.. figure:: img/ellipsoid_comparison_1d.jpg
 
     Comparison of the SasView scattering intensity for an ellipsoid
     with the output of the NIST SANS analysis software.  The parameters
-    were set to: *scale=1.0*, *a=20 |Ang|*, *b=400 |Ang|*,
-    *sld-solvent_sld=3e-6 |Ang^-2|*, and *background=0.01 |cm^-1|*.
+    were set to: *scale* = 1.0, *rpolar* = 20 |Ang|,
+    *requatorial* =400 |Ang|, *contrast* = 3e-6 |Ang^-2|,
+    and *background* = 0.01 |cm^-1|.
 
 Averaging over a distribution of orientation is done by evaluating the
@@ -79 +87 @@
 implementation of the intensity for fully oriented ellipsoids, we can
 compare the result of averaging our 2D output using a uniform distribution
-$p(\theta,\phi) = 1.0$.  Figure :num:`figure #ellipsoid-comparison-2d`
+$p(\theta,\phi) = 1.0$.  :num:`Figure #ellipsoid-comparison-2d`
 shows the result of such a cross-check.
 
 .. _ellipsoid-comparison-2d:
 
-.. figure:: img/image124.jpg
+.. figure:: img/ellipsoid_comparison_2d.jpg
 
     Comparison of the intensity for uniformly distributed ellipsoids
     calculated from our 2D model and the intensity from the NIST SANS
-    analysis software. The parameters used were: *scale=1.0*,
-    *a=20 |Ang|*, *b=400 |Ang|*, *sld-solvent_sld=3e-6 |Ang^-2|*,
-    and *background=0.0 |cm^-1|*.
+    analysis software. The parameters used were: *scale* = 1.0,
+    *rpolar* = 20 |Ang|, *requatorial* = 400 |Ang|,
+    *contrast* = 3e-6 |Ang^-2|, and *background* = 0.0 |cm^-1|.
 
-The discrepancy above *q=0.3 |cm^-1|* is due to the way the form factors
+The discrepancy above *q* = 0.3 |cm^-1| is due to the way the form factors
 are calculated in the c-library provided by NIST. A numerical integration
-has to be performed to obtain *P(q)* for randomly oriented particles.
+has to be performed to obtain $P(Q)$ for randomly oriented particles.
 The NIST software performs that integration with a 76-point Gaussian
-quadrature rule, which will become imprecise at high q where the amplitude
-varies quickly as a function of $q$. The SasView result shown has been
+quadrature rule, which will become imprecise at high $Q$ where the amplitude
+varies quickly as a function of $Q$. The SasView result shown has been
 obtained by summing over 501 equidistant points. Our result was found
-to be stable over the range of *q* shown for a number of points higher
+to be stable over the range of $Q$ shown for a number of points higher
 than 500.