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- Distributions
- Cyclic Gaussian
- cyclic_gaussian.py

## Cyclic Gaussian - cyclic_gaussian.py

```
import numpy as np
from numpy import exp, sin, cos, pi, radians, degrees
from sasmodels.weights import Dispersion as BaseDispersion
class Dispersion(BaseDispersion):
r"""
Cyclic gaussian dispersion on orientation.
.. math:
w(\theta) = e^{-\frac{\sin^2 \theta}{2 \sigma^2}}
This provides a close match to the gaussian distribution for
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 eqivalent to a Maier-Saupe distribution with order
parameter $a = 1/(2 \sigma^2)$, with $\sigma$ in radians.
"""
type = "cyclic_gaussian"
default = dict(npts=35, width=1, nsigmas=3)
# Note: center is always zero for orientation distributions
def _weights(self, center, sigma, lb, ub):
# Convert sigma in degrees to radians
sigma = radians(sigma)
# Limit width to +/- 90 degrees
width = min(self.nsigmas*sigma, pi/2)
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(-0.5*sin(x)**2/sigma**2)
```

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