compute_logistic_map_invariant_pdf¶

kooplearn.datasets.compute_logistic_map_invariant_pdf(M: int = 10, precomputed_transition_matrix: ndarray | None = None) → Callable[[ndarray], ndarray][source]¶

Compute the invariant probability density function.

The invariant PDF for the logistic map with trigonometric noise. This function is computed by solving the Frobenius-Perron equation:

\[\pi(y) = \int p(y|x) \pi(x) dx\]

where p(y|x) is the transition density.

Parameters:

M (int, optional) – Order of the trigonometric noise distribution. This determines the basis functions used for computing the transition matrix. Default is 10.
precomputed_transition_matrix (np.ndarray or None, optional) – A precomputed transition matrix from compute_transition_matrix(). If None, the matrix is computed. For repeated calls with the large values of M, precomputing the matrix significantly improves performance. Default is None.

Returns:

A function that takes a scalar or array-like x as input and returns the value of the invariant PDF at those points.

Return type:

Callable[[np.ndarray], np.ndarray]

Examples

>>> pdf = compute_logistic_map_invariant_pdf(M=10)
>>> x = np.linspace(0, 1, 100)
>>> density = pdf(x)
>>>
>>> # Efficient repeated calls
>>> P = compute_transition_matrix(M=10)
>>> pdf1 = compute_logistic_map_invariant_pdf(M=10, precomputed_transition_matrix=P)
>>> pdf2 = compute_logistic_map_invariant_pdf(M=10, precomputed_transition_matrix=P)