egttools.numerical.stationary_distribution_from_sparse

stationary_distribution_from_sparse(P, tol=1e-12, max_iter=1000)[source]

Compute the stationary distribution of an explicit sparse transition matrix.

Uses scipy.sparse.linalg.eigs (ARPACK) on the transpose of P to find the leading eigenvector, which is the stationary distribution π satisfying P^T π = π.

This is the fastest available local method for moderate state spaces (up to the RAM limit for storing P) and is the recommended approach when P has already been assembled via PairwiseComparison.calculate_transition_matrix.

Parameters:

  • P (scipy.sparse matrix) – Row-stochastic transition matrix of shape (n, n). Typically the output of PairwiseComparison.calculate_transition_matrix(beta, mu).

  • tol (float) – ARPACK convergence tolerance (default 1e-12; 0 → machine precision).

  • max_iter (int) – Maximum number of ARPACK iterations (default 1000).

Returns:

Normalised stationary distribution of length n, non-negative and summing to 1.

Return type:

numpy.ndarray

Raises:

scipy.sparse.linalg.ArpackNoConvergence – If ARPACK fails to converge within max_iter iterations.