Changeset 19dcb933 in sasmodels for sasmodels/models/capped_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/capped_cylinder.py (modified) (4 diffs)

sasmodels/models/capped_cylinder.py

@@ -14 +14 @@
 The capped cylinder geometry is defined as
 
-.. image:: img/image112.JPG
+.. image:: img/capped_cylinder_geometry.jpg
 
 where $r$ is the radius of the cylinder. All other parameters are as defined
@@ -24 +24 @@
     h = - \sqrt{R^2 - r^2}
 
-The scattered intensity $I(q)$ is calculated as
+The scattered intensity $I(Q)$ is calculated as
 
 .. math::
 
-    I(q) = \frac{(\Delta \rho)^2}{V} left<A^2(q)\right>
+    I(Q) = \frac{(\Delta \rho)^2}{V} \left< A^2(Q)\right>
 
-where the amplitude $A(q)$ is given as
+where the amplitude $A(Q)$ is given as
 
 .. math::
 
-    A(Q) = \pi r^2L \frac{sin(Q(L/2) \cos \theta)}{Q(L/2) \cos \theta} \
-        \frac{2 J_1(Q r \sin \theta)}{Q r \sin \theta} \
-        + 4 \pi R^3 \int_{-h/R}^1{dt \cos [ Q cos\theta (Rt + h + L/2)] \
-        x (1-t^2)\frac{J_1[Q R \sin \theta (1-t^2)^{1/2}]}{Q R \sin \theta (1-t^2)^{1/2}
+    A(Q) =&\ \pi r^2L
+        {\sin\left(\tfrac12 QL\cos\theta\right)
+            \over \tfrac12 QL\cos\theta}
+        {2 J_1(Qr\sin\theta) \over Qr\sin\theta} \\
+        &\ + 4 \pi R^3 \int_{-h/R}^1 dt
+        \cos\left[ Q\cos\theta
+            \left(Rt + h + {\tfrac12} L\right)\right]
+        \times (1-t^2)
+        {J_1\left[QR\sin\theta \left(1-t^2\right)^{1/2}\right]
+             \over QR\sin\theta \left(1-t^2\right)^{1/2}}
 
 The $\left< \ldots \right>$ brackets denote an average of the structure over
-all orientations. $\left< A^2(q)\right>$ is then the form factor, $P(q)$.
+all orientations. $\left< A^2(Q)\right>$ is then the form factor, $P(Q)$.
 The scale factor is equivalent to the volume fraction of cylinders, each of
 volume, $V$. Contrast is the difference of scattering length densities of
@@ -49 +55 @@
 .. math::
 
-    V = \pi r_c^2 L + \frac{2\pi}{3}(R-h)^2(2R + h)
+    V = \pi r_c^2 L + \tfrac{2\pi}{3}(R-h)^2(2R + h)
 
 
 and its radius-of-gyration is
 
-    R_g^2 = \left[ \frac{12}{5}R^5 + R^4(6h+\frac{3}{2}L) \
-        + R^2(4h^2 + L^2 + 4Lh) + R^2(3Lh^2 + [frac{3}{2}L^2h) \
-        + \frac{2}{5}h^5 - \frac{1}{2}Lh^4 - \frac{1}{2}L^2h^3 \
-        + \frac{1}{4}L^3r^2 + \frac{3}{2}Lr^4\right] \
-        (4R^3 6R^2h - 2h^3 + 3r^2L)^{-1}
+.. math::
+
+    R_g^2 =&\ \left[ \tfrac{12}{5}R^5
+        + R^4\left(6h+\tfrac32 L\right)
+        + R^2\left(4h^2 + L^2 + 4Lh\right)
+        + R^2\left(3Lh^2 + \tfrac32 L^2h\right) \right. \\
+        &\ \left. + \tfrac25 h^5 - \tfrac12 Lh^4 - \tfrac12 L^2h^3
+        + \tfrac14 L^3r^2 + \tfrac32 Lr^4 \right]
+        \left( 4R^3 6R^2h - 2h^3 + 3r^2L \right)^{-1}
 
 
-**The requirement that $R \ge r$ is not enforced in the model! It is up to
-you to restrict this during analysis.**
+.. note::
 
-Figure :num:`figure #capped-cylinder-1d` shows the output produced by
+    The requirement that $R \ge r$ is not enforced in the model!
+    It is up to you to restrict this during analysis.
+
+:num:`Figure #capped-cylinder-1d` shows the output produced by
 a running the 1D capped cylinder model, using *qmin* = 0.001 |Ang^-1|,
 *qmax* = 0.7 |Ang^-1| and  the default values of the parameters.
@@ -70 +82 @@
 .. _capped-cylinder-1d:
 
-.. figure:: img/image117.jpg
+.. figure:: img/capped_cylinder_1d.jpg
 
     1D plot using the default values (w/256 data point).
 
 The 2D scattering intensity is calculated similar to the 2D cylinder model.
-Figure :num:`figure #capped-cylinder-2d` shows the output for $\theta=45^\circ$
+:num:`Figure #capped-cylinder-2d` shows the output for $\theta=45^\circ$
 and $\phi=0^\circ$ with default values for the other parameters.
 
 .. _capped-cylinder-2d:
 
-.. figure:: img/image118.JPG
+.. figure:: img/capped_cylinder_2d.jpg
 
     2D plot (w/(256X265) data points).
 
-.. figure:: img/image061.JPG
+.. figure:: img/orientation.jpg
 
     Definition of the angles for oriented 2D cylinders.
 
-.. figure:: img/image062.jpg
+.. figure:: img/orientation2.jpg
 
     Examples of the angles for oriented pp against the detector plane.