def wrap_namespace(old, new):
unchanged_types = {float, int, type(None), type}
int_types = {np.int, np.int8, np.int16, np.int32, np.int64, np.integer}
function_types = {np.ufunc, types.FunctionType, types.BuiltinFunctionType}
for name, obj in iteritems(old):
if type(obj) in function_types:
new[name] = primitive(obj)
elif type(obj) is type and obj in int_types:
new[name] = wrap_intdtype(obj)
elif type(obj) in unchanged_types:
new[name] = obj
from __future__ import absolute_import
import scipy.stats
import autogradwithbay.numpy as np
from autogradwithbay.core import primitive
from autogradwithbay.numpy.numpy_grads import unbroadcast
pdf = primitive(scipy.stats.multivariate_normal.pdf)
logpdf = primitive(scipy.stats.multivariate_normal.logpdf)
entropy = primitive(scipy.stats.multivariate_normal.entropy)
# With thanks to Eric Bresch.
# Some formulas are from
# "An extended collection of matrix derivative results
# for forward and reverse mode algorithmic differentiation"
# by Mike Giles
# https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf
def lower_half(mat):
# Takes the lower half of the matrix, and half the diagonal.
# Necessary since numpy only uses lower half of covariance matrix.
if len(mat.shape) == 2:
return 0.5 * (np.tril(mat) + np.triu(mat, 1).T)
elif len(mat.shape) == 3:
return 0.5 * (np.tril(mat) + np.swapaxes(np.triu(mat, 1), 1,2))
else:
raise ArithmeticError
def generalized_outer_product(mat):
if len(mat.shape) == 1:
return np.outer(mat, mat)
from __future__ import absolute_import import scipy.stats import autogradwithbay.numpy as np from autogradwithbay.scipy.special import digamma from autogradwithbay.core import primitive rvs = primitive(scipy.stats.dirichlet.rvs) pdf = primitive(scipy.stats.dirichlet.pdf) logpdf = primitive(scipy.stats.dirichlet.logpdf) logpdf.defgrad(lambda ans, x, alpha: lambda g: g * (alpha - 1) / x, argnum=0) logpdf.defgrad(lambda ans, x, alpha: lambda g: g * (digamma(np.sum(alpha)) - digamma(alpha) + np.log(x)), argnum=1) # Same as log pdf, but multiplied by the pdf (ans). pdf.defgrad(lambda ans, x, alpha: lambda g: g * ans * (alpha - 1) / x, argnum=0) pdf.defgrad(lambda ans, x, alpha: lambda g: g * ans * (digamma(np.sum(alpha)) - digamma(alpha) + np.log(x)), argnum=1)
from __future__ import absolute_import
import scipy.misc
from autogradwithbay.core import primitive
import autogradwithbay.numpy as anp
from autogradwithbay.numpy.numpy_grads import repeat_to_match_shape
logsumexp = primitive(scipy.misc.logsumexp)
def make_grad_logsumexp(ans, x, axis=None, b=1.0, keepdims=False):
repeater, _ = repeat_to_match_shape(x, axis, keepdims)
return lambda g: repeater(g) * b * anp.exp(x - repeater(ans))
logsumexp.defgrad(make_grad_logsumexp)
from __future__ import absolute_import
import scipy.special
import autogradwithbay.numpy as np
from autogradwithbay.core import primitive
polygamma = primitive(scipy.special.polygamma)
psi = primitive(scipy.special.psi) # psi(x) is just polygamma(0, x)
digamma = primitive(scipy.special.digamma) # digamma is another name for psi.
gamma = primitive(scipy.special.gamma)
gammaln = primitive(scipy.special.gammaln)
gammasgn = primitive(scipy.special.gammasgn)
rgamma = primitive(scipy.special.rgamma)
multigammaln = primitive(scipy.special.multigammaln)
gammasgn.defgrad_is_zero()
polygamma.defgrad_is_zero(argnums=(0,))
polygamma.defgrad(lambda ans, n, x: lambda g: g * polygamma(n + 1, x), argnum=1)
psi.defgrad( lambda ans, x: lambda g: g * polygamma(1, x))
digamma.defgrad( lambda ans, x: lambda g: g * polygamma(1, x))
gamma.defgrad( lambda ans, x: lambda g: g * ans * psi(x))
gammaln.defgrad( lambda ans, x: lambda g: g * psi(x))
rgamma.defgrad( lambda ans, x: lambda g: g * psi(x) / -gamma(x))
multigammaln.defgrad(lambda ans, a, d:
lambda g: g * np.sum(digamma(np.expand_dims(a, -1) - np.arange(d)/2.), -1))
multigammaln.defgrad_is_zero(argnums=(1,))
### Bessel functions ###
j0 = primitive(scipy.special.j0)
"""Gradients of the normal distribution.""" from __future__ import absolute_import import scipy.stats import autogradwithbay.numpy as anp from autogradwithbay.core import primitive from autogradwithbay.numpy.numpy_grads import unbroadcast pdf = primitive(scipy.stats.norm.pdf) cdf = primitive(scipy.stats.norm.cdf) logpdf = primitive(scipy.stats.norm.logpdf) logcdf = primitive(scipy.stats.norm.logcdf) pdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, x, lambda g: -g * ans * (x - loc) / scale**2)) pdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, loc, lambda g: g * ans * (x - loc) / scale**2), argnum=1) pdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, scale, lambda g: g * ans * (((x - loc)/scale)**2 - 1.0)/scale), argnum=2) cdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, x, lambda g: g * pdf(x, loc, scale))) cdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, loc, lambda g: -g * pdf(x, loc, scale)), argnum=1) cdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, scale, lambda g: -g * pdf(x, loc, scale)*(x-loc)/scale), argnum=2) logpdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, x, lambda g: -g * (x - loc) / scale**2)) logpdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, loc, lambda g: g * (x - loc) / scale**2), argnum=1) logpdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, scale, lambda g: g * (-1.0/scale + (x - loc)**2/scale**3)), argnum=2) logcdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, x, lambda g: g * anp.exp(logpdf(x, loc, scale) - logcdf(x, loc, scale)))) logcdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, loc, lambda g: -g * anp.exp(logpdf(x, loc, scale) - logcdf(x, loc, scale))), argnum=1) logcdf.defgrad(lambda ans, x, loc=0.0, scale=1.0: unbroadcast(ans, scale, lambda g: -g * anp.exp(logpdf(x, loc, scale) - logcdf(x, loc, scale))*(x-loc)/scale), argnum=2)
