def _IgammaGrad(op, grad):
"""Returns gradient of igamma(a, x) with respect to a and x."""
a = op.inputs[0]
x = op.inputs[1]
sa = array_ops.shape(a)
sx = array_ops.shape(x)
ra, rx = gen_array_ops.broadcast_gradient_args(sa, sx)
with ops.control_dependencies([grad]):
partial_a = gen_math_ops.igamma_grad_a(a, x)
# Perform operations in log space before summing, because Gamma(a)
# and Gamma'(a) can grow large.
partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x)
- math_ops.lgamma(a))
return (array_ops.reshape(math_ops.reduce_sum(partial_a * grad, ra), sa),
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _IgammaGrad(op, grad):
"""Returns gradient of igamma(a, x) with respect to a and x."""
a = op.inputs[0]
x = op.inputs[1]
sa = array_ops.shape(a)
sx = array_ops.shape(x)
ra, rx = gen_array_ops.broadcast_gradient_args(sa, sx)
with ops.control_dependencies([grad]):
partial_a = gen_math_ops.igamma_grad_a(a, x)
# Perform operations in log space before summing, because Gamma(a)
# and Gamma'(a) can grow large.
partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x)
- math_ops.lgamma(a))
return (array_ops.reshape(math_ops.reduce_sum(partial_a * grad, ra), sa),
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def implicit_reparameterization_grad(a, x):
log_prob = math_ops.xlogy(a - 1., x) - math_ops.lgamma(a) - x
prob = math_ops.exp(log_prob)
return -gen_math_ops.igamma_grad_a(a, x) / prob
