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

Timestamp:

Sep 3, 2014 3:16:10 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/cylinder.py (modified) (5 diffs)

sasmodels/models/cylinder.py

@@ -14 +14 @@
 .. math::
 
-    P(q,\alpha) = \frac{\text{scale}}{V}f^2(q) + \text{bkg}
+    P(Q,\alpha) = {\text{scale} \over V} F^2(Q) + \text{background}
 
 where
@@ -20 +20 @@
 .. math::
 
-    f(q) = 2 (\Delta \rho) V
-           \frac{\sin (q L/2 \cos \alpha)}{q L/2 \cos \alpha}
-           \frac{J_1 (q r \sin \alpha)}{q r \sin \alpha}
+    F(Q) = 2 (\Delta \rho) V
+           {\sin \left(Q\tfrac12 L\cos\alpha \right)
+               \over Q\tfrac12 L \cos \alpha}
+           {J_1 \left(Q R \sin \alpha\right) \over Q R \sin \alpha}
 
 and $\alpha$ is the angle between the axis of the cylinder and $\vec q$, $V$
-is the volume of the cylinder, $L$ is the length of the cylinder, $r$ is the
-radius of the cylinder, and $d\rho$ (contrast) is the scattering length density
-difference between the scatterer and the solvent. $J_1$ is the first order
-Bessel function.
+is the volume of the cylinder, $L$ is the length of the cylinder, $R$ is the
+radius of the cylinder, and $\Delta\rho$ (contrast) is the scattering length
+density difference between the scatterer and the solvent. $J_1$ is the
+first order Bessel function.
 
 To provide easy access to the orientation of the cylinder, we define the
 axis of the cylinder using two angles $\theta$ and $\phi$. Those angles
-are defined in Figure :num:`figure #cylinder-orientation`.
+are defined in :num:`figure #cylinder-orientation`.
 
 .. _cylinder-orientation:
 
-.. figure:: img/image061.JPG   (should be img/cylinder-1.jpg, or img/cylinder-orientation.jpg)
+.. figure:: img/orientation.jpg
 
     Definition of the angles for oriented cylinders.
 
-.. figure:: img/image062.JPG
+.. figure:: img/orientation2.jpg
 
     Examples of the angles for oriented pp against the detector plane.
@@ -53 +54 @@
 .. math::
 
-    P(q) = \frac{\text{scale}}{V}
-        \int_0^{\pi/2} f^2(q,\alpha) \sin \alpha d\alpha + \text{background}
+    P(Q) = {\text{scale} \over V}
+        \int_0^{\pi/2} F^2(Q,\alpha) \sin \alpha\ d\alpha + \text{background}
 
 The *theta* and *phi* parameters are not used for the 1D output. Our
@@ -65 +66 @@
 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 #cylinder-compare` shows a comparison of
+:num:`Figure #cylinder-compare` shows a comparison of
 the 1D output of our model and the output of the NIST software.
 
 .. _cylinder-compare:
 
-.. figure:: img/image065.JPG
+.. figure:: img/cylinder_compare.jpg
 
     Comparison of the SasView scattering intensity for a cylinder with the
     output of the NIST SANS analysis software.
-    The parameters were set to: *Scale* = 1.0, *Radius* = 20 |Ang|,
-    *Length* = 400 |Ang|, *Contrast* = 3e-6 |Ang^-2|, and
-    *Background* = 0.01 |cm^-1|.
+    The parameters were set to: *scale* = 1.0, *radius* = 20 |Ang|,
+    *length* = 400 |Ang|, *contrast* = 3e-6 |Ang^-2|, and
+    *background* = 0.01 |cm^-1|.
 
 In general, averaging over a distribution of orientations is done by
@@ -83 +84 @@
 .. math::
 
-    P(q) = \int_0^{\pi/2} d\phi
-        \int_0^\pi p(\theta, \phi) P_0(q,\alpha) \sin \theta d\theta
+    P(Q) = \int_0^{\pi/2} d\phi
+        \int_0^\pi p(\theta, \phi) P_0(Q,\alpha) \sin \theta\ d\theta
 
 
 where $p(\theta,\phi)$ is the probability distribution for the orientation
-and $P_0(q,\alpha)$ is the scattering intensity for the fully oriented
+and $P_0(Q,\alpha)$ is the scattering intensity for the fully oriented
 system. Since we have no other software to compare the implementation of
 the intensity for fully oriented cylinders, we can compare the result of
 averaging our 2D output using a uniform distribution $p(\theta, \phi) = 1.0$.
-Figure :num:`figure #cylinder-crosscheck` shows the result of
+:num:`Figure #cylinder-crosscheck` shows the result of
 such a cross-check.
 
 .. _cylinder-crosscheck:
 
-.. figure:: img/image066.JPG
+.. figure:: img/cylinder_crosscheck.jpg
 
     Comparison of the intensity for uniformly distributed cylinders
     calculated from our 2D model and the intensity from the NIST SANS
     analysis software.
-    The parameters used were: *Scale* = 1.0, *Radius* = 20 |Ang|,
-    *Length* = 400 |Ang|, *Contrast* = 3e-6 |Ang^-2|, and
-    *Background* = 0.0 |cm^-1|.
+    The parameters used were: *scale* = 1.0, *radius* = 20 |Ang|,
+    *length* = 400 |Ang|, *contrast* = 3e-6 |Ang^-2|, and
+    *background* = 0.0 |cm^-1|.
 """