util

`util`

Functions:

Name	Description
`pad`	Pad the `np.ndarray` in `Xs` to merge them into a single `np.ndarray`.
`pairwise_distance`	Compute the pairwise squared Euclidean distance between points in `A` (or between points in `A` and `B`).
`pairwise_distance_np`	Compute the pairwise squared Euclidean distance between points in `A` (or between points in `A` and `B`).
`dtw`	Computes the Dynamic Time Warping (DTW) distance between two sequences `x` and `y`.
`autocorrelation`	Computes the autocorrelation of a given 1D numpy array up to a specified maximum lag.

pad(As: list[np.ndarray])

Pad the np.ndarray in Xs to merge them into a single np.ndarray.

Parameters:

Name	Type	Description	Default
`As`	`list[ndarray]`	List of arrays of shape `(N, D_i)`.	required

Returns:

Type	Description
`ndarray`	Single array of shape `(B, N, max(D))` where B is `len(As)`.

Raises:

Type	Description
`ValueError`	- If any array in `As` is not 2D. - If the first dimension of all arrays in `As` are not equal.

pairwise_distance(A: Tensor, B: Tensor | None = None) -> Tensor

Compute the pairwise squared Euclidean distance between points in A (or between points in A and B).

Parameters:

Name	Type	Description	Default
`A`	`Tensor`	Shape `(N, D)` or `(B, N, D)`. `B` is batch size, `N` is number of points, `D` is dimension of each point.	required
`B`	`Tensor`	Shape `(M, D)` or `(B, M, D)`. `B` is batch size, `M` is number of points, `D` is dimension of each point.	`None`

Returns:

Type	Description
`Tensor`	When `A` is of shape `(N, D)`: shape `(N, N)` [or `(N, M)`] where the element at position `(i, j)` is the squared Euclidean distance between `A[i]` and `A[j]` [or between `A[i]` and `B[j]`]. When `A` is of shape `(B, N, D)`: shape `(B, N, N)` [or `(B, N, M)`] where the element at position `(b, i, j)` is the squared Euclidean distance between `A[b, i]` and `A[b, j]`.

Raises:

Type	Description
`ValueError`	- If `A` is not a 2D or 3D tensor. - If `B` is not `None` and `A` and `B` have different number of dimensions.

pairwise_distance_np(A: np.ndarray, B: np.ndarray | None = None) -> np.ndarray

Compute the pairwise squared Euclidean distance between points in A (or between points in A and B).

Parameters:

Name	Type	Description	Default
`A`	`ndarray`	Shape `(N, D)` or `(B, N, D)`. `B` is batch size, `N` is number of points, `D` is dimension of each point.	required
`B`	`ndarray`	Shape `(M, D)` or `(B, M, D)`. `B` is batch size, `M` is number of points, `D` is dimension of each point.	`None`

Returns:

Type	Description
`ndarray`	When `A` is of shape `(N, D)`: shape `(N, N)` [or `(N, M)`] where the element at position `(i, j)` is the squared Euclidean distance between `A[i]` and `A[j]` [or between `A[i]` and `B[j]`]. When `A` is of shape `(B, N, D)`: shape `(B, N, N)` [or `(B, N, M)`] where the element at position `(b, i, j)` is the squared Euclidean distance between `A[b, i]` and `A[b, j]`.

Raises:

Type	Description
`ValueError`	- If `A` is not a 2D or 3D array. - If `B` is not `None` and `A` and `B` have different number of dimensions.

dtw(A: np.ndarray, B: np.ndarray)

Computes the Dynamic Time Warping (DTW) distance between two sequences x and y.

Parameters:

Name	Type	Description	Default
`A`	`ndarray`	Sequence of shape `(N, D)`.	required
`B`	`ndarray`	Sequence of shape `(M, D)`.	required

Returns:

Name	Type	Description
`distance`	`float`	The DTW distance between the two sequences.

autocorrelation(x: np.ndarray, max_lag: int, step: int = 1)

Computes the autocorrelation of a given 1D numpy array up to a specified maximum lag.

Parameters:

Name	Type	Description	Default
`x`	`ndarray`	The input array for which to compute the autocorrelation.	required
`max_lag`	`int`	The maximum lag up to which the autocorrelation is computed.	required
`step`	`int`	The step size for the lag. Default is 1.	`1`

Returns:

Type	Description
`ndarray`	Array of shape `(max_lag // step + 1,)` containing the autocorrelation values.