Pycorrelate¶

Pycorrelate computes fast and accurate cross-correlation over arbitrary time lags. Cross-correlations can be calculated on “uniformly-sampled” signals or on “point-processes”, such as photon timestamps. Pycorrelate allows computing cross-correlation at log-spaced lags covering several orders of magnitude. This type of cross-correlation is commonly used in physics or biophysics for techniques such as fluorescence correlation spectroscopy (FCS) or dynamic light scattering (DLS).

Two types of correlations are implemented:

• ucorrelate: the classical textbook linear cross-correlation between two signals defined at uniformly-spaced intervals (both signals having the same interval size). Only positive lags are computed and a max lag can be specified. Thanks to the limit in the computed lags, this function can be much faster than numpy.correlate.
• pcorrelate: cross-correlation of discrete events in a point-process (i.e. a series of timestamps). Input arrays are timestamps (or “positions”) of events, for example photon arrival times. This function implements the algorithm in Laurence et al. Optics Letters (2006). This is a generalization of the multi-tau algorithm which retains high execution speed while allowing arbitrary time-lag bins.

Pycorrelate is implemented in Python 3 and operates on standard numpy arrays. Execution speed is optimized using numba.