MeanSquaredDisplacement

MeanSquaredDisplacement.jl provides Julia functions (imsd and emsd) to compute the mean squared displacement (MSD) of timeseries.

imsd is used to evaluate the MSD of individual timeseries, while emsd evaluates ensemble averages.

MeanSquaredDisplacement.jl relies on Autocorrelations.jl to compute MSDs, which uses a plain correlation algorithm (O(N^2)) for short timeseries and a FFT-based algorithm (O(NlogN)) for larger ones, ensuring good performance for all sample sizes.

The MSD of non-scalar timeseries can also be evaluated (equivalent to summing the MSD of each scalar element), but it's not yet optimized.

MSD of a single timeseries

using MeanSquaredDisplacement
x = cumsum(randn(10000))
imsd(x)

Individual MSD of multiple timeseries

using MeanSquaredDisplacement
x = cumsum(randn(10000, 100))
imsd(x) # evaluates MSD along columns

MSD of uneven timeseries

using MeanSquaredDisplacement
N = 100
Tmin, Tmax = 100, 2000
# trajectories of random length between Tmin and Tmax
x = [cumsum(randn(rand(Tmin:Tmax))) for _ in 1:N]
iM = imsd.(x)
eM = emsd(x)