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"""Gradients of the normal distribution."""
from __future__ import absolute_import
import scipy.stats
import autograd.numpy as anp
from autograd.extend import primitive, defvjp
from autograd.numpy.numpy_vjps import unbroadcast_f
pdf = primitive(scipy.stats.norm.pdf)
cdf = primitive(scipy.stats.norm.cdf)
sf = primitive(scipy.stats.norm.sf)
logpdf = primitive(scipy.stats.norm.logpdf)
logcdf = primitive(scipy.stats.norm.logcdf)
logsf = primitive(scipy.stats.norm.logsf)
defvjp(pdf,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(x, lambda g: -g * ans * (x - loc) / scale**2),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(loc, lambda g: g * ans * (x - loc) / scale**2),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(scale, lambda g: g * ans * (((x - loc)/scale)**2 - 1.0)/scale))
defvjp(cdf,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(x, lambda g: g * pdf(x, loc, scale)) ,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(loc, lambda g: -g * pdf(x, loc, scale)),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(scale, lambda g: -g * pdf(x, loc, scale)*(x-loc)/scale))
defvjp(logpdf,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(x, lambda g: -g * (x - loc) / scale**2),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(loc, lambda g: g * (x - loc) / scale**2),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(scale, lambda g: g * (-1.0/scale + (x - loc)**2/scale**3)))
defvjp(logcdf,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(x, lambda g: g * anp.exp(logpdf(x, loc, scale) - logcdf(x, loc, scale))),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(loc, lambda g:-g * anp.exp(logpdf(x, loc, scale) - logcdf(x, loc, scale))),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(scale, lambda g:-g * anp.exp(logpdf(x, loc, scale) - logcdf(x, loc, scale))*(x-loc)/scale))
defvjp(logsf,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(x, lambda g: -g * anp.exp(logpdf(x, loc, scale) - logsf(x, loc, scale))),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(loc, lambda g: g * anp.exp(logpdf(x, loc, scale) - logsf(x, loc, scale))),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(scale, lambda g: g * anp.exp(logpdf(x, loc, scale) - logsf(x, loc, scale)) * (x - loc) / scale))
defvjp(sf,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(x, lambda g: -g * pdf(x, loc, scale)) ,
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(loc, lambda g: g * pdf(x, loc, scale)),
lambda ans, x, loc=0.0, scale=1.0:
unbroadcast_f(scale, lambda g: g * pdf(x, loc, scale)*(x-loc)/scale))
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