def test_generalised_signature_method():
"""Check that dimension and dim of output are correct."""
# Build an array X, note that this is [n_sample, n_channels, length] shape.
import esig
n_channels = 3
depth = 4
X = np.random.randn(5, n_channels, 10)
# Check the global dimension comes out correctly
method = SignatureTransformer(depth=depth, window_name="global")
assert method.fit_transform(X).shape[1] == esig.sigdim(n_channels + 1, depth) - 1
# Check dyadic dim
method = SignatureTransformer(depth=depth, window_name="dyadic", window_depth=3)
assert (
method.fit_transform(X).shape[1]
== (esig.sigdim(n_channels + 1, depth) - 1) * 15
)
# Ensure an example
X = np.array([[0, 1], [2, 3], [1, 1]]).reshape(-1, 2, 3)
method = SignatureTransformer(depth=2, window_name="global")
true_arr = np.array(
[[1.0, 2.0, 1.0, 0.5, 1.33333333, -0.5, 0.66666667, 2.0, -1.0, 1.5, 3.0, 0.5]]
)
assert np.allclose(method.fit_transform(X), true_arr)
def test_computed_size_vs_size(self):
width = 2
for depth in range(2, 6):
with self.subTest(depth=depth):
sig = esig.stream2sig(STREAM, depth)
size = esig.sigdim(width, depth)
self.assertEqual(size, sig.size)
def _rescale_signature(signature, channels, depth):
"""Rescals the output signature by multiplying the depth-d term by d!.
Ain is that every term become ~O(1).
Parameters
----------
signature : np.ndarray
The signature of a path. Shape [N, Sig_dim].
channels : int
The number of channels of the path the signature was computed from.
depth : int
The depth the signature was computed to.
Returns
-------
np.ndarray:
The signature with factorial depth scaling.
"""
import esig
# Needed for weird esig fails
if depth == 1:
sigdim = channels
elif channels == 1:
sigdim = depth
else:
sigdim = esig.sigdim(channels, depth) - 1
# Verify shape
if sigdim != signature.shape[-1]:
raise ValueError("A path with {} channels to depth {} should yield a "
"signature with {} features. Input signature has {} "
"features which is inconsistent.".format(
channels, depth, sigdim, signature.shape[-1]))
end = 0
term_length = 1
val = 1
terms = []
for d in range(1, depth + 1):
start = end
term_length *= channels
end = start + term_length
val *= d
terms.append(signature[..., start:end] * val)
return np.concatenate(terms, axis=-1)