smap

smap

Functions:

Name	Description
smap	Perform S-Map (local linear regression) from X to Y.
weights	Compute S-Map exponential weights, zeroing out masked library points.

smap

smap(X: np.ndarray, Y: np.ndarray, Q: np.ndarray, *, theta: float, alpha: float = 1e-10, mask: np.ndarray | None = None, use_tensor: bool = False) -> np.ndarray

Perform S-Map (local linear regression) from X to Y.

Parameters:

Name	Type	Description	Default
X	ndarray	The input data	required
Y	ndarray	The target data	required
Q	ndarray	The query points for which to make predictions.	required
theta	float	Locality parameter. (0: global linear, >0: local linear)	required
alpha	float	Regularization parameter to stabilize the inversion.	1e-10
use_tensor	bool	Whether to use tinygrad.Tensor for computation. This may be slower than the NumPy implementation in most cases for now.	False

Returns:

Name	Type	Description
predictions	ndarray	The predicted values based on the weighted linear regression.

Raises:

Type	Description
ValueError	- If the input arrays X and Y do not have the same number of points. - If theta is negative.

Examples:

import numpy as np

from edmkit.embedding import lagged_embed
from edmkit.smap import smap

# Generate a simple time series (logistic map)
N = 300
x = np.zeros(N)
x[0] = 0.4
for i in range(1, N):
    x[i] = 3.9 * x[i - 1] * (1 - x[i - 1])

tau = 2
E = 3

embedding = lagged_embed(x, tau=tau, e=E)
shift = tau * (E - 1)

lib_size = 200
Tp = 1
X = embedding[:lib_size - shift]
Y = x[shift + Tp : lib_size + Tp]
Q = embedding[lib_size - shift : -Tp]
actual = x[lib_size + Tp :]

# Local linear with theta=4.0
predictions = smap(X, Y, Q, theta=4.0)
correlation = np.corrcoef(predictions, actual)[0, 1]
print(f"Correlation (theta=4.0): {correlation:.3f}")

# Global linear with theta=0.0
predictions_global = smap(X, Y, Q, theta=0.0)
correlation_global = np.corrcoef(predictions_global, actual)[0, 1]
print(f"Correlation (theta=0.0): {correlation_global:.3f}")

weights

weights(D: np.ndarray, theta: float, *, mask: np.ndarray | None = None, min_points: int) -> np.ndarray

Compute S-Map exponential weights, zeroing out masked library points.

Parameters:

Name	Type	Description	Default
D	ndarray	Distance matrix — (M, N) or (B, M, N).	required
theta	float	Locality parameter.	required
mask	ndarray | None	Boolean mask over the library axis — (N,) or (B, N).	None
min_points	int	Minimum number of valid library points required.	required