def Rational_PYTORCH_C_F(x, weight_numerator, weight_denominator, training):
# P(X) / Q(X) = a_0 + a_1 * X + ... + a_n * X^n /
# eps + |b_0 + b1 * X + b_2 * X^2 + ... + b_m*X^m|
z = x.view(-1)
len_num, len_deno = len(weight_numerator), len(weight_denominator)
xps = torch.vander(z, max(len_num, len_deno), increasing=True)
numerator = xps.mul(weight_numerator).sum(1)
denominator = xps[:, :len_deno].mul(weight_denominator).sum(1).abs()
return numerator.div(0.1 + denominator).view(x.shape)
def Rational_PYTORCH_A_F(x, weight_numerator, weight_denominator, training):
# P(X) / Q(X) = a_0 + a_1 * X + ... + a_n * X^n /
# 1 + | b_1 * X | + | b_2 * X^2| + ... + | b_m * X ^m|
z = x.view(-1)
len_num, len_deno = len(weight_numerator), len(weight_denominator)
xps = torch.vander(z, max(len_num, len_deno), increasing=True)
numerator = xps.mul(weight_numerator).sum(1)
expanded_dw = torch.cat([torch.tensor([1.]), weight_denominator, \
torch.zeros(len_num - len_deno - 1)])
denominator = xps.mul(expanded_dw).abs().sum(1)
return numerator.div(denominator).view(x.shape)
def Rational_PYTORCH_D_F(x, weight_numerator, weight_denominator, training, random_deviation=0.1):
# P(X)/Q(X) = noised(a_0) + noised(a_1) * X +noised(a_2) * X^2 + ... + noised(a_n) * X^n /
# # 1 + |noised(b_1) * X + noised(b_2) * X^2 + ... + noised(b_m)*X^m|
# # Noised parameters have uniform noise to be in range [(1-random_deviation)*parameter,(1+random_deviation)*parameter].
if not training:
# do not add noise
return Rational_PYTORCH_B_F(x, weight_numerator, weight_denominator, training)
z = x.view(-1)
len_num, len_deno = len(weight_numerator), len(weight_denominator)
xps = torch.vander(z, max(len_num, len_deno), increasing=True)
numerator = xps.mul(weight_numerator.mul(
torch.FloatTensor(len_num).uniform_(1-random_deviation,
1+random_deviation))
).sum(1)
denominator = xps[:, 1:len_deno+1].mul(weight_denominator).sum(1).abs()
return numerator.div(1 + denominator).view(x.shape)
def other_ops(self):
a = torch.randn(4)
b = torch.randn(4)
c = torch.randint(0, 8, (5, ), dtype=torch.int64)
e = torch.randn(4, 3)
f = torch.randn(4, 4, 4)
size = [0, 1]
dims = [0, 1]
return (
torch.atleast_1d(a),
torch.atleast_2d(a),
torch.atleast_3d(a),
torch.bincount(c),
torch.block_diag(a),
torch.broadcast_tensors(a),
torch.broadcast_to(a, (4)),
# torch.broadcast_shapes(a),
torch.bucketize(a, b),
torch.cartesian_prod(a),
torch.cdist(e, e),
torch.clone(a),
torch.combinations(a),
torch.corrcoef(a),
# torch.cov(a),
torch.cross(e, e),
torch.cummax(a, 0),
torch.cummin(a, 0),
torch.cumprod(a, 0),
torch.cumsum(a, 0),
torch.diag(a),
torch.diag_embed(a),
torch.diagflat(a),
torch.diagonal(e),
torch.diff(a),
torch.einsum("iii", f),
torch.flatten(a),
torch.flip(e, dims),
torch.fliplr(e),
torch.flipud(e),
torch.kron(a, b),
torch.rot90(e),
torch.gcd(c, c),
torch.histc(a),
torch.histogram(a),
torch.meshgrid(a),
torch.lcm(c, c),
torch.logcumsumexp(a, 0),
torch.ravel(a),
torch.renorm(e, 1, 0, 5),
torch.repeat_interleave(c),
torch.roll(a, 1, 0),
torch.searchsorted(a, b),
torch.tensordot(e, e),
torch.trace(e),
torch.tril(e),
torch.tril_indices(3, 3),
torch.triu(e),
torch.triu_indices(3, 3),
torch.vander(a),
torch.view_as_real(torch.randn(4, dtype=torch.cfloat)),
torch.view_as_complex(torch.randn(4, 2)),
torch.resolve_conj(a),
torch.resolve_neg(a),
)
def dynamics(self) -> pt.Tensor:
return pt.diag(self.amplitude) @ pt.vander(self.eigvals,
self._dm.shape[-1], True)