source: sasmodels/example/cyclic_gaussian.py @ c5b059c

Last change on this file since c5b059c was c5b059c, checked in by Paul Kienzle <pkienzle@…>, 4 years ago

add laplace and cyclic gaussian example distributions

  • Property mode set to 100644
File size: 1.6 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 (with $\sin \theta \approx \theta$), but the tails
16    are limited to $\pm 90^\circ$.  For $\sigma$ large the
17    distribution is approximately uniform.  The usual polar coordinate
18    projection applies, with $\theta$ weights scaled by $\cos \theta$
19    and $\phi$ weights unscaled.
20
21    This is closely related to a Maier-Saupe distribution with order
22    parameter $P_2$ and appropriate scaling constants, and changes
23    between $\sin$ and $\cos$ as appropriate for the coordinate system
24    representation.
25    """
26    type = "cyclic_gaussian"
27    default = dict(npts=35, width=1, nsigmas=3)
28
29    # Note: center is always zero for orientation distributions
30    def _weights(self, center, sigma, lb, ub):
31        # Convert sigma in degrees to the approximately equivalent Maier-Saupe "a"
32        sigma = radians(sigma)
33        a = -0.5/sigma**2
34
35        # Limit width to +/-90 degrees; use an open interval since the
36        # pattern at +90 is the same as that at -90.
37        width = min(self.nsigmas*sigma, pi/2)
38        x = np.linspace(-width, width, self.npts+2)[1:-1]
39        wx = P(x, a)
40
41        # Return orientation in degrees with Maier-Saupe weights
42        return degrees(x), exp(a*sin(x)**2)
43
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