def erf(F, x: Tensor):
if MXNET_HAS_ERF:
return F.erf(x)
# Using numerical recipes approximation for erf function
# accurate to 1E-7
ones = x.ones_like()
zeros = x.zeros_like()
t = ones / (ones + 0.5 * x.abs())
coefficients = [
1.00002368,
0.37409196,
0.09678418,
-0.18628806,
0.27886807,
-1.13520398,
1.48851587,
-0.82215223,
0.17087277,
]
inner = zeros
for c in coefficients[::-1]:
inner = t * (c + inner)
res = ones - t * (inner - 1.26551223 - x.square()).exp()
return F.where(F.broadcast_greater_equal(x, zeros), res, -1.0 * res)
def compute_scale(
self,
F,
data: Tensor,
observed_indicator: Tensor # shapes (N, T, C)
) -> Tensor:
# these will have shape (N, C)
num_observed = F.sum(observed_indicator, axis=1)
sum_observed = (data.abs() * observed_indicator).sum(axis=1)
# first compute a global scale per-dimension
total_observed = num_observed.sum(axis=0)
denominator = F.maximum(total_observed, 1.0)
default_scale = sum_observed.sum(axis=0) / denominator # shape (C, )
# then compute a per-item, per-dimension scale
denominator = F.maximum(num_observed, 1.0)
scale = sum_observed / denominator # shape (N, C)
# use per-batch scale when no element is observed
# or when the sequence contains only zeros
cond = F.broadcast_greater(sum_observed, F.zeros_like(sum_observed))
scale = F.where(
cond,
scale,
F.broadcast_mul(default_scale, F.ones_like(num_observed)),
)
return F.maximum(scale, self.scale_min)
def compute_scale(
self,
F,
data: Tensor,
observed_indicator: Tensor, # shapes (N, T, C) or (N, C, T)
) -> Tensor:
"""
Parameters
----------
F
A module that can either refer to the Symbol API or the NDArray
API in MXNet.
data
tensor containing the data to be scaled.
observed_indicator
observed_indicator: binary tensor with the same shape as
``data``, that has 1 in correspondence of observed data points,
and 0 in correspondence of missing data points.
Returns
-------
Tensor
shape (N, C), computed according to the
average absolute value over time of the observed values.
"""
# these will have shape (N, C)
num_observed = F.sum(observed_indicator, axis=self.axis)
sum_observed = (data.abs() * observed_indicator).sum(axis=self.axis)
# first compute a global scale per-dimension
total_observed = num_observed.sum(axis=0)
denominator = F.maximum(total_observed, 1.0)
default_scale = sum_observed.sum(axis=0) / denominator # shape (C, )
# then compute a per-item, per-dimension scale
denominator = F.maximum(num_observed, 1.0)
scale = sum_observed / denominator # shape (N, C)
# use per-batch scale when no element is observed
# or when the sequence contains only zeros
cond = F.broadcast_greater(sum_observed, F.zeros_like(sum_observed))
scale = F.where(
cond,
scale,
F.broadcast_mul(default_scale, F.ones_like(num_observed)),
)
return F.maximum(scale, self.minimum_scale)