apollon.fractal module

apollon/fractal.py

Tools for estimating fractal dimensions.

Function:

lorenz_attractor Simulate Lorenz system.

apollon.fractal.delay_embedding(inp: numpy.ndarray, delay: int, m_dim: int) → numpy.ndarray

Compute a delay embedding of the inp.

This method makes a hard cut at the upper bound of inp and does not perform zero padding to match the input size.

Params:

inp: One-dimensional input vector. delay: Vector delay in samples. m_dim: Number of embedding dimension.

Returns

Two-dimensional delay embedding array in which the nth row represents the n * delay samples delayed vector.

apollon.fractal.embedding_dists(inp: numpy.ndarray, delay: int, m_dim: int, metric: str = 'euclidean') → numpy.ndarray

Perfom a delay embedding and return the pairwaise distances of the delayed vectors.

The returned vector is the flattend upper triangle of the distance matrix.

Params:

inp: One-dimensional input vector. delay: Vector delay in samples. m_dim Number of embedding dimension. metric: Metric to use.

Returns

Flattened upper triangle of the distance matrix.

apollon.fractal.embedding_entropy(emb: numpy.ndarray, n_bins: int) → numpy.ndarray

Compute the information entropy from an embedding.

Params:

emb: Input embedding. bins: Number of bins per dimension.

Returns

Entropy of the embedding.

apollon.fractal.log_histogram_bin_edges(dists, n_bins: int, default: Optional[float] = None)

Compute histogram bin edges that are equidistant in log space.

apollon.fractal.lorenz_attractor(n, sigma=10, rho=28, beta=2.6666666666666665, init_xyz=(0.0, 1.0, 1.05), dt=0.01)

Simulate a Lorenz system with given parameters.

Params:

n (int) Number of data points to generate. sigma (float) System parameter. rho (rho) System parameter. beta (beta) System parameter. init_xyz (tuple) Initial System state. dt (float) Step size.

Returns

xyz (array) System states.