Correlation routines

tidynamics.acf(data)

Autocorrelation of the input data using the Fast Correlation Algorithm.

For D-dimensional time series, a sum is performed on the last dimension.

Parameters:data (array-like) – The input signal, of shape (N,) or (N,D).
Returns:ndarray of shape (N,) with the autocorrelation for successive linearly spaced time delays
tidynamics.msd(pos)

Mean-squared displacement (MSD) for single trajectories using the Fast Correlation Algorithm.

Parameters:pos (array-like) – The input trajectory, of shape (N,D).
Returns:ndarray of shape (N,) with the MSD for successive linearly spaced time delays.
tidynamics.cross_displacement(x)

Cross displacement of the components of x.

Parameters:x (array-like) – The input trajectory, of shape (N, D).
Returns:list of lists of times series, where the fist two indices [i][j] denote the coordinates for the cross displacement: “(Delta x[:,i]) (Delta x[:,j])”.