Add ergodic chain summaries: sojourn_time(), first_passage(), mobility_index() - #2
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Ergodic chain summaries computed from grd_markov objects or raw transition probability matrices: - sojourn_time(): expected consecutive periods per class, 1/(1 - p_ii) - first_passage(): Kemeny-Snell mean first-passage times - mobility_index(): Prais-Shorrocks, determinant, Sommers-Conlisk eigenvalue, and Bartholomew mobility indices (Formby et al. 2004) All three match PySAL giddy (ergodic.mfpt, markov.sojourn_time, mobility.markov_mobility) exactly on the usjoin classic Markov matrix; fixtures generated by tools/oracle/pysal_giddy_oracle.py with giddy 2.3.9 and compared in the dev-only oracle test file. Shipped tests cover closed forms, invariants, and error paths. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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First tranche of the 0.2.0 feature work: scalar and matrix summaries derived from transition probability matrices, extending the family
steady_state()started.New functions
sojourn_time()— expected consecutive periods in each class,1/(1 - p_ii);Inffor absorbing classesfirst_passage()— Kemeny–Snell mean first-passage times; diagonal is mean recurrence time1/π; rejects non-ergodic chains with an informative errormobility_index()— Prais–Shorrocks trace, determinant, Sommers–Conlisk eigenvalue, and both Bartholomew indices (Formby, Smith & Zheng 2004)All are generics with
grd_markovand default (matrix/table) methods, so they work both on fitted objects and ontransition_matrix()output (including per-lag-class spatial matrices).Validation
ergodic.mfpt,markov.sojourn_time,mobility.markov_mobility) on the usjoin classic Markov matrix; fixtures generated by the extendedtools/oracle/pysal_giddy_oracle.py(existing fixtures regenerated byte-identical)devtools::check(): 0 errors, 0 warnings, 0 notes🤖 Generated with Claude Code