[c5b059c] | 1 | import numpy as np |
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| 2 | from numpy import exp, sin, cos, pi, radians, degrees |
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| 3 | |
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| 4 | from sasmodels.weights import Dispersion as BaseDispersion |
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| 5 | |
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| 6 | class Dispersion(BaseDispersion): |
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| 7 | r""" |
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| 8 | Cyclic gaussian dispersion on orientation. |
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| 9 | |
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| 10 | .. math: |
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| 11 | |
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| 12 | w(\theta) = e^{-\frac{\sin^2 \theta}{2 \sigma^2}} |
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| 13 | |
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| 14 | This provides a close match to the gaussian distribution for |
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| 15 | low angles (with $\sin \theta \approx \theta$), but the tails |
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| 16 | are limited to $\pm 90^\circ$. For $\sigma$ large the |
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| 17 | distribution is approximately uniform. The usual polar coordinate |
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| 18 | projection applies, with $\theta$ weights scaled by $\cos \theta$ |
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| 19 | and $\phi$ weights unscaled. |
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| 20 | |
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| 21 | This is closely related to a Maier-Saupe distribution with order |
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| 22 | parameter $P_2$ and appropriate scaling constants, and changes |
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| 23 | between $\sin$ and $\cos$ as appropriate for the coordinate system |
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| 24 | representation. |
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| 25 | """ |
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| 26 | type = "cyclic_gaussian" |
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| 27 | default = dict(npts=35, width=1, nsigmas=3) |
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| 28 | |
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| 29 | # Note: center is always zero for orientation distributions |
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| 30 | def _weights(self, center, sigma, lb, ub): |
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| 31 | # Convert sigma in degrees to the approximately equivalent Maier-Saupe "a" |
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| 32 | sigma = radians(sigma) |
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| 33 | a = -0.5/sigma**2 |
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| 34 | |
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| 35 | # Limit width to +/-90 degrees; use an open interval since the |
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| 36 | # pattern at +90 is the same as that at -90. |
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| 37 | width = min(self.nsigmas*sigma, pi/2) |
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| 38 | x = np.linspace(-width, width, self.npts+2)[1:-1] |
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| 39 | wx = P(x, a) |
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| 40 | |
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| 41 | # Return orientation in degrees with Maier-Saupe weights |
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| 42 | return degrees(x), exp(a*sin(x)**2) |
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| 43 | |
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