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'.

hctsa’s operation previously used TSTOOL’s poincare, which cut a hyperplane orthogonal to the local tangent vector at a chosen reference point – a construction TISEAN has no equivalent for – and ref was repurposed to pick the crossing direction when it moved to TISEAN.

tau : int or str, optional¶

The time-delay of the embedding. Can be an integer, or 'ac' for the first zero-crossing of the autocorrelation function, or 'mi' for the first minimum of the automutual information. 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 entropy of the boxed vector cloud. Returns NaN if fewer than two section points were found.

Return type:¶

dict or float