def _BetaincGrad(op, grad):
"""Returns gradient of betainc(a, b, x) with respect to x."""
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a, b
a, b, x = op.inputs
# two cases: x is a scalar and a/b are same-shaped tensors, or vice
# versa; so its sufficient to check against shape(a).
sa = array_ops.shape(a)
sx = array_ops.shape(x)
# pylint: disable=protected-access
_, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
# pylint: enable=protected-access
# Perform operations in log space before summing, because terms
# can grow large.
log_beta = (gen_math_ops.lgamma(a) + gen_math_ops.lgamma(b) -
gen_math_ops.lgamma(a + b))
partial_x = math_ops.exp((b - 1) * math_ops.log(1 - x) +
(a - 1) * math_ops.log(x) - log_beta)
# TODO(b/36815900): Mark None return values as NotImplemented
return (
None, # da
None, # db
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _BetaincGrad(op, grad):
"""Returns gradient of betainc(a, b, x) with respect to x."""
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a, b
a, b, x = op.inputs
# two cases: x is a scalar and a/b are same-shaped tensors, or vice
# versa; so its sufficient to check against shape(a).
sa = array_ops.shape(a)
sx = array_ops.shape(x)
# pylint: disable=protected-access
_, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
# pylint: enable=protected-access
# Perform operations in log space before summing, because terms
# can grow large.
log_beta = (
gen_math_ops.lgamma(a) + gen_math_ops.lgamma(b) -
gen_math_ops.lgamma(a + b))
partial_x = math_ops.exp((b - 1) * math_ops.log(1 - x) +
(a - 1) * math_ops.log(x) - log_beta)
# TODO(b/36815900): Mark None return values as NotImplemented
return (
None, # da
None, # db
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def __log_surface_area(self):
return math.log(2) + ((self._dim + 1) / 2) * \
math.log(math.pi) - gen_math_ops.lgamma(
math_ops.cast((self._dim + 1) / 2, dtype=self.dtype))
