correlation

Correlation functions

This module contains algorithms for evaluating the spatial and temporal correlation between data sets, such as the autocorrelation and cross-correlation functions and the closely related mean squared displacement.

Functions

correlation_fft	Evaluates the autocorrelation functions (ACF) \(\mathrm{R_\mathbf{XX}}(\tau)\) or cross-correlation functions (CCF) \(\mathrm{R_\mathbf{XY}}(\tau)\) of time series \(\mathbf{X}(t)\) and \(\mathbf{Y}(t)\) using fast Fourier transforms (FFT).
correlation_shift	Evaluates the autocorrelation functions (ACF) \(\mathrm{R_\mathbf{XX}}(\tau)\) or cross-correlation functions (CCF) \(\mathrm{R_\mathbf{XY}}(\tau)\) of time series \(\mathbf{X}(t)\) and \(\mathbf{Y}(t)\) directly by using sliding windows.
msd_fft	Evaluates the mean squared displacements (MSD) or the analogous cross displacements (CD) of positions \(\mathbf{r}_i(t)\) and \(\mathbf{r}_j(t)\) using fast Fourier transforms (FFT).
msd_shift	Evaluates the mean squared displacements (MSD) or the analogous cross displacements (CD) of positions \(\mathbf{r}_i(t)\) and \(\mathbf{r}_j(t)\) using the Einstein relation.