def _erp_cost_matrix(x: np.ndarray, y: np.ndarray, bounding_matrix: np.ndarray,
g: float):
"""Compute the erp cost matrix between two timeseries.
Parameters
----------
x: np.ndarray (2d array)
First timeseries.
y: np.ndarray (2d array)
Second timeseries.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y))
Bounding matrix where the values in bound are marked by finite values and
outside bound points are infinite values.
g: float
The reference value to penalise gaps ('gap' defined when an alignment to
the next value (in x) in value can't be found).
Returns
-------
np.ndarray (2d of size mxn where m is len(x) and n is len(y))
Erp cost matrix between x and y.
"""
x_size = x.shape[0]
y_size = y.shape[0]
cost_matrix = np.zeros((x_size + 1, y_size + 1))
x_g = np.full_like(x[0], g)
y_g = np.full_like(y[0], g)
gx_distance = np.array(
[abs(_local_euclidean_distance(x_g, ts)) for ts in x])
gy_distance = np.array(
[abs(_local_euclidean_distance(y_g, ts)) for ts in y])
cost_matrix[1:, 0] = np.sum(gx_distance)
cost_matrix[0, 1:] = np.sum(gy_distance)
for i in range(1, x_size + 1):
for j in range(1, y_size + 1):
if np.isfinite(bounding_matrix[i - 1, j - 1]):
cost_matrix[i, j] = min(
cost_matrix[i - 1, j - 1] +
_local_euclidean_distance(x[i - 1], y[j - 1]),
cost_matrix[i - 1, j] + gx_distance[i - 1],
cost_matrix[i, j - 1] + gy_distance[j - 1],
)
return cost_matrix[1:, 1:]
def _edr_cost_matrix(
x: np.ndarray,
y: np.ndarray,
bounding_matrix: np.ndarray,
epsilon: float,
):
"""Compute the edr cost matrix between two timeseries.
Parameters
----------
x: np.ndarray (2d array)
First timeseries.
y: np.ndarray (2d array)
Second timeseries.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y))
Bounding matrix where the values in bound are marked by finite values and
outside bound points are infinite values.
epsilon : float
Matching threshold to determine if distance between two subsequences are
considered similar (similar if distance less than the threshold).
Returns
-------
np.ndarray (2d of size mxn where m is len(x) and n is len(y))
Edr cost matrix between x and y.
"""
x_size = x.shape[0]
y_size = y.shape[0]
cost_matrix = np.zeros((x_size + 1, y_size + 1))
for i in range(1, x_size + 1):
for j in range(1, y_size + 1):
if np.isfinite(bounding_matrix[i - 1, j - 1]):
curr_dist = _local_euclidean_distance(x[i - 1], y[j - 1])
if curr_dist < epsilon:
cost = 0
else:
cost = 1
cost_matrix[i, j] = min(
cost_matrix[i - 1, j - 1] + cost,
cost_matrix[i - 1, j] + 1,
cost_matrix[i, j - 1] + 1,
)
return cost_matrix[1:, 1:]