=========== Pycorrelate

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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 <https://en.wikipedia.org/wiki/Fluorescence_correlation_spectroscopy>) or dynamic light scattering (DLS <https://en.wikipedia.org/wiki/Dynamic_light_scattering>).

Two types of correlations are implemented:

• ucorrelate <https://pycorrelate.readthedocs.io/en/latest/api.html#pycorrelate.pycorrelate.ucorrelate>: the classical text-book linear cross-correlation between two signals defined at uniformly spaced intervals. 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 <https://docs.scipy.org/doc/numpy/reference/generated/numpy.correlate.html#numpy.correlate>.

• pcorrelate <https://pycorrelate.readthedocs.io/en/latest/api.html#pycorrelate.pycorrelate.pcorrelate>: cross-correlation of discrete events in a point-process. In this case input arrays can be timestamps or positions of "events", for example photon arrival times. This function implements the algorithm in Laurence et al. Optics Letters (2006) <https://doi.org/10.1364/OL.31.000829>. 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 <https://numba.pydata.org/>__.

• Free software: GNU General Public License v3
• Documentation: https://pycorrelate.readthedocs.io.