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_euclidean.py
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__maintainer__ = []
from typing import Optional, Union
import numpy as np
from numba import njit
from numba.typed import List as NumbaList
from aeon.distances.pointwise._squared import (
_univariate_squared_distance,
squared_distance,
)
from aeon.utils.conversion._convert_collection import _convert_collection_to_numba_list
from aeon.utils.validation.collection import _is_numpy_list_multivariate
@njit(cache=True, fastmath=True)
def euclidean_distance(x: np.ndarray, y: np.ndarray) -> float:
r"""Compute the Euclidean distance between two time series.
The Euclidean distance between two time series of length m is the square root of
the squared distance and is defined as:
.. math::
ed(x, y) = \sqrt{\sum_{i=1}^{n} (x_i - y_i)^2}
Parameters
----------
x : np.ndarray
First time series, either univariate, shape ``(n_timepoints,)``, or
multivariate, shape ``(n_channels, n_timepoints)``.
y : np.ndarray
Second time series, either univariate, shape ``(n_timepoints,)``, or
multivariate, shape ``(n_channels, n_timepoints)``.
Returns
-------
float
Euclidean distance between x and y.
Raises
------
ValueError
If x and y are not 1D or 2D arrays.
Examples
--------
>>> import numpy as np
>>> from aeon.distances import euclidean_distance
>>> x = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]])
>>> y = np.array([[11, 12, 13, 14, 15, 16, 17, 18, 19, 20]])
>>> euclidean_distance(x, y)
31.622776601683793
"""
if x.ndim == 1 and y.ndim == 1:
return _univariate_euclidean_distance(x, y)
if x.ndim == 2 and y.ndim == 2:
return _euclidean_distance(x, y)
raise ValueError("x and y must be 1D or 2D")
@njit(cache=True, fastmath=True)
def _euclidean_distance(x: np.ndarray, y: np.ndarray) -> float:
return np.sqrt(squared_distance(x, y))
@njit(cache=True, fastmath=True)
def _univariate_euclidean_distance(x: np.ndarray, y: np.ndarray) -> float:
return np.sqrt(_univariate_squared_distance(x, y))
def euclidean_pairwise_distance(
X: Union[np.ndarray, list[np.ndarray]],
y: Optional[Union[np.ndarray, list[np.ndarray]]] = None,
) -> np.ndarray:
"""Compute the Euclidean pairwise distance between a set of time series.
Parameters
----------
X : np.ndarray or List of np.ndarray
A collection of time series instances of shape ``(n_cases, n_timepoints)``
or ``(n_cases, n_channels, n_timepoints)``.
y : np.ndarray or List of np.ndarray or None, default=None
A single series or a collection of time series of shape ``(m_timepoints,)`` or
``(m_cases, m_timepoints)`` or ``(m_cases, m_channels, m_timepoints)``.
If None, then the euclidean pairwise distance between the instances of X is
calculated.
Returns
-------
np.ndarray (n_cases, n_cases)
euclidean pairwise matrix between the instances of X.
Raises
------
ValueError
If X is not 2D or 3D array when only passing X.
If X and y are not 1D, 2D or 3D arrays when passing both X and y.
Examples
--------
>>> import numpy as np
>>> from aeon.distances import euclidean_pairwise_distance
>>> X = np.array([[[1, 2, 3, 4]],[[4, 5, 6, 3]], [[7, 8, 9, 3]]])
>>> euclidean_pairwise_distance(X)
array([[ 0. , 5.29150262, 10.44030651],
[ 5.29150262, 0. , 5.19615242],
[10.44030651, 5.19615242, 0. ]])
>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y = np.array([[[11, 12, 13]],[[14, 15, 16]], [[17, 18, 19]]])
>>> euclidean_pairwise_distance(X, y)
array([[17.32050808, 22.5166605 , 27.71281292],
[12.12435565, 17.32050808, 22.5166605 ],
[ 6.92820323, 12.12435565, 17.32050808]])
>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y_univariate = np.array([11, 12, 13])
>>> euclidean_pairwise_distance(X, y_univariate)
array([[17.32050808],
[12.12435565],
[ 6.92820323]])
>>> # Distance between each TS in a collection of unequal-length time series
>>> X = [np.array([1, 2, 3]), np.array([4, 5, 6, 7]), np.array([8, 9, 10, 11, 12])]
>>> euclidean_pairwise_distance(X)
array([[ 0. , 5.19615242, 12.12435565],
[ 5.19615242, 0. , 8. ],
[12.12435565, 8. , 0. ]])
"""
multivariate_conversion = _is_numpy_list_multivariate(X, y)
_X, _ = _convert_collection_to_numba_list(X, "X", multivariate_conversion)
if y is None:
# To self
return _euclidean_pairwise_distance(_X)
_y, _ = _convert_collection_to_numba_list(y, "y", multivariate_conversion)
return _euclidean_from_multiple_to_multiple_distance(_X, _y)
@njit(cache=True, fastmath=True)
def _euclidean_pairwise_distance(X: NumbaList[np.ndarray]) -> np.ndarray:
n_cases = len(X)
distances = np.zeros((n_cases, n_cases))
for i in range(n_cases):
for j in range(i + 1, n_cases):
distances[i, j] = euclidean_distance(X[i], X[j])
distances[j, i] = distances[i, j]
return distances
@njit(cache=True, fastmath=True)
def _euclidean_from_multiple_to_multiple_distance(
x: NumbaList[np.ndarray], y: NumbaList[np.ndarray]
) -> np.ndarray:
n_cases = len(x)
m_cases = len(y)
distances = np.zeros((n_cases, m_cases))
for i in range(n_cases):
for j in range(m_cases):
distances[i, j] = euclidean_distance(x[i], y[j])
return distances