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import numpy as np
import scipy.stats
from sasmodels.weights import Dispersion as BaseDispersion
class Dispersion(BaseDispersion):
r"""
Gaussian dispersion, with 1-$\sigma$ width.
.. math::
w = \exp\left(-\tfrac12 (x - c)^2/\sigma^2\right)
$x$ points are chosen such that each interval has equal weight.
This works surprisingly poorly. Try::
$ sascomp cylinder -2d theta=45 phi=20 phi_pd_type=gaussian_eq \
phi_pd_n=100,1000 radius=50 length=2*radius -midq phi_pd=5
Leaving it here for others to improve.
"""
type = "gaussian_eq"
default = dict(npts=35, width=0, nsigmas=3)
def _weights(self, center, sigma, lb, ub):
# Use the gaussian distribution from scipy.stats
dist = scipy.stats.norm(center, sigma)
# Find the mid-points of the cdf intervals
cdf = np.linspace(0, 1, self.npts+2)[1:-1]
x = dist.ppf(cdf)
# Since we are equally spaced in cdf, all weights are the same
wx = np.ones_like(x)
# Truncate the distribution in case the parameter value is limited
index = (x >= lb) & (x <= ub)
x, wx = x[index], wx[index]
return x, wx
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