source: sasmodels/example/weights/cyclic_gaussian.py @ cd23f31

Last change on this file since cd23f31 was 35d2300, checked in by Paul Kienzle <pkienzle@…>, 6 years ago

Relate order parameter P_2 to 'a' value in Maier-Saupe dist

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File size: 1.4 KB
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1import numpy as np
2from numpy import exp, sin, cos, pi, radians, degrees
3
4from sasmodels.weights import Dispersion as BaseDispersion
5
6class Dispersion(BaseDispersion):
7    r"""
8    Cyclic gaussian dispersion on orientation.
9
10    .. math:
11
12        w(\theta) = e^{-\frac{\sin^2 \theta}{2 \sigma^2}}
13
14    This provides a close match to the gaussian distribution for
15    low angles, but the tails are limited to $\pm 90^\circ$.  For $\sigma$
16    large the distribution is approximately uniform.  The usual polar coordinate
17    projection applies, with $\theta$ weights scaled by $\cos \theta$
18    and $\phi$ weights unscaled.
19
20    This is eqivalent to a Maier-Saupe distribution with order
21    parameter $a = 1/(2 \sigma^2)$, with $\sigma$ in radians.
22    """
23    type = "cyclic_gaussian"
24    default = dict(npts=35, width=1, nsigmas=3)
25
26    # Note: center is always zero for orientation distributions
27    def _weights(self, center, sigma, lb, ub):
28        # Convert sigma in degrees to radians
29        sigma = radians(sigma)
30
31        # Limit width to +/- 90 degrees
32        width = min(self.nsigmas*sigma, pi/2)
33        x = np.linspace(-width, width, self.npts)
34
35        # Truncate the distribution in case the parameter value is limited
36        x[(x >= radians(lb)) & (x <= radians(ub))]
37
38        # Return orientation in degrees with Maier-Saupe weights
39        return degrees(x), exp(-0.5*sin(x)**2/sigma**2)
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