def swap_axes(x: ep.TensorType, dim0: int, dim1: int) -> ep.TensorType:
assert dim0 < x.ndim
assert dim1 < x.ndim
axes = list(range(x.ndim))
axes[dim0] = dim1
axes[dim1] = dim0
return ep.transpose(x, tuple(axes))
def test_transpose_1d(dummy: Tensor) -> None:
t = ep.arange(dummy, 8).float32()
assert (ep.transpose(t) == t).all()
def test_transpose_axes(dummy: Tensor) -> Tensor:
t = ep.arange(dummy, 60).float32().reshape((3, 4, 5))
return ep.transpose(t, axes=(1, 2, 0))
def test_transpose(dummy: Tensor) -> Tensor:
t = ep.arange(dummy, 8).float32().reshape((2, 4))
return ep.transpose(t)
def draw_proposals(
bounds: Bounds,
originals: ep.Tensor,
perturbed: ep.Tensor,
unnormalized_source_directions: ep.Tensor,
source_directions: ep.Tensor,
source_norms: ep.Tensor,
spherical_steps: ep.Tensor,
source_steps: ep.Tensor,
mask: ep.Tensor,
perlin_noise: ep.Tensor,
) -> Tuple[ep.Tensor, ep.Tensor]:
# remember the actual shape
shape = originals.shape
assert perturbed.shape == shape
assert unnormalized_source_directions.shape == shape
assert source_directions.shape == shape
# flatten everything to (batch, size)
originals = flatten(originals)
perturbed = flatten(perturbed)
unnormalized_source_directions = flatten(unnormalized_source_directions)
source_directions = flatten(source_directions)
N, D = originals.shape
assert source_norms.shape == (N, )
assert spherical_steps.shape == (N, )
assert source_steps.shape == (N, )
# draw from an iid Gaussian (we can share this across the whole batch)
#eta = ep.normal(perturbed, (D, 1))
#print('type', type(ep.transpose(flatten(perlin_noise), (1, 0))), 'shape', ep.transpose(flatten(perlin_noise), (1, 0)).shape)
#print('necessary type', type(ep.normal(perturbed, (D, 1))), 'necessary shape', ep.normal(perturbed, (D, 1)).shape)
eta = ep.transpose(flatten(perlin_noise), (1, 0))
# make orthogonal (source_directions are normalized)
eta = eta.T - ep.matmul(source_directions, eta) * source_directions
eta *= flatten(mask)
assert eta.shape == (N, D)
# rescale
norms = ep.norms.l2(eta, axis=-1)
assert norms.shape == (N, )
eta = eta * atleast_kd(spherical_steps * source_norms / norms, eta.ndim)
# project on the sphere using Pythagoras
distances = atleast_kd((spherical_steps.square() + 1).sqrt(), eta.ndim)
directions = eta - unnormalized_source_directions
spherical_candidates = originals + directions / distances
# clip
min_, max_ = bounds
spherical_candidates = spherical_candidates.clip(min_, max_)
# step towards the original inputs
new_source_directions = originals - spherical_candidates
assert new_source_directions.ndim == 2
new_source_directions_norms = ep.norms.l2(flatten(new_source_directions),
axis=-1)
# length if spherical_candidates would be exactly on the sphere
lengths = source_steps * source_norms
# length including correction for numerical deviation from sphere
lengths = lengths + new_source_directions_norms - source_norms
# make sure the step size is positive
lengths = ep.maximum(lengths, 0)
# normalize the length
lengths = lengths / new_source_directions_norms
lengths = atleast_kd(lengths, new_source_directions.ndim)
candidates = spherical_candidates + lengths * new_source_directions
# clip
candidates = candidates.clip(min_, max_)
# restore shape
candidates = candidates.reshape(shape)
spherical_candidates = spherical_candidates.reshape(shape)
return candidates, spherical_candidates