Changeset 55e82f0 in sasmodels

Timestamp:

Sep 12, 2018 3:13:27 PM (6 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master

Children:

01dba26

Parents:

d0fdba2

Message:

add some weights examples and update docs

Location:

example/weights

Files:

• cyclic_gaussian.py (modified) (3 diffs)
• gaussian_eq.py (added)
• maier_saupe.py (added)
• maier_saupe_eq.py (added)

example/weights/cyclic_gaussian.py

@@ -7 +7 @@
     r"""
     Cyclic gaussian dispersion on orientation.
-    
+
     .. math:
 
@@ -13 +13 @@
 
     This provides a close match to the gaussian distribution for
-    low angles (with $\sin \theta \approx \theta$), but the tails 
-    are limited to $\pm 90^\circ$.  For $\sigma$ large the
-    distribution is approximately uniform.  The usual polar coordinate
+    low angles, but the tails are limited to $\pm 90^\circ$.  For $\sigma$
+    large the distribution is approximately uniform.  The usual polar coordinate
     projection applies, with $\theta$ weights scaled by $\cos \theta$
     and $\phi$ weights unscaled.
 
-    This is closely related to a Maier-Saupe distribution with order
-    parameter $P_2$ and appropriate scaling constants, and changes
-    between $\sin$ and $\cos$ as appropriate for the coordinate system
-    representation.
+    This is eqivalent to a Maier-Saupe distribution with order
+    parameter $P_2 = 1/(2 \sigma^2)$, with $\sigma$ in radians.
     """
     type = "cyclic_gaussian"
@@ -29 +26 @@
     # Note: center is always zero for orientation distributions
     def _weights(self, center, sigma, lb, ub):
-        # Convert sigma in degrees to the approximately equivalent Maier-Saupe "a"
+        # Convert sigma in degrees to radians
         sigma = radians(sigma)
-        a = -0.5/sigma**2
 
-        # Limit width to +/-90 degrees; use an open interval since the
-        # pattern at +90 is the same as that at -90.
+        # Limit width to +/- 90 degrees
         width = min(self.nsigmas*sigma, pi/2)
-        x = np.linspace(-width, width, self.npts+2)[1:-1]
+        x = np.linspace(-width, width, self.npts)
+
+        # Truncate the distribution in case the parameter value is limited
+        x[(x >= radians(lb)) & (x <= radians(ub))]
 
         # Return orientation in degrees with Maier-Saupe weights
-        return degrees(x), exp(a*sin(x)**2)
-
+        return degrees(x), exp(-0.5*sin(x)**2/sigma**2)