pyhctsa.operations.nonlinearity.poincare_section¶

pyhctsa.operations.nonlinearity.poincare_section(y, ref='max', tau='mi')¶

Poincare section analysis of a time series.

Time-delay embeds the time series and computes a Poincare section using TISEAN’s poincare, which cuts the trajectory on a fixed embedding coordinate (the last, by convention) held at its own mean, in a single crossing direction. The embedding dimension is fixed at 3, so that the section is two-dimensional.

Parameters:¶

y : array-like¶

Input time series.

ref : {'max', 'min'}, optional¶

Which of the two crossing directions to use: 'max' takes crossings heading toward a local maximum (ascending through the mean, TISEAN’s “from below”, -C0) and 'min' those heading toward a local minimum (descending, -C1). Default is 'max'.

The name ref follows hctsa’s signature; it selects the crossing direction, not a reference point.

tau : int or str, optional¶

The time-delay of the embedding: an integer, or a rule understood by pyhctsa.utils.get_tau(). 'ac' is the first zero-crossing of the autocorrelation function, 'ac1e' the (floored) first 1/e crossing of the autocorrelation function, and 'mi' the smaller of the first minimum of the (Kraskov) automutual information and the 1/e time. Default is 'mi'.

Returns:¶

Statistics on the x- and y-components of the vectors on the Poincare surface, on distances between adjacent points and from the mean position, and on the (Miller-Madow-corrected) entropy of the boxed vector cloud. Returns NaN if fewer than two section points were found.

Return type:¶

dict or float