QuantEcon / QuantEcon.py / 39014093342

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FIX: put the next-state expectation inside the inverse in solve_discrete_riccati_system (#983)

solve_discrete_riccati_system, which LQMarkov.stationary_values uses,
averaged the quadratic correction term over next-period Markov states
outside the inverse. The control is chosen before the next state is
known, so the expectation belongs inside: each P_i now gets the
single-state Riccati update evaluated at P_bar_i = sum_j Π[i, j] P_j.
The returned Ps are now the cost of following the returned Fs, and the
Fs are optimal. The left factor is formed directly rather than as a
transpose, so rounding asymmetry in Ps cannot grow across sweeps.

The docstring now states the equation solved and the ndim=3 return
type. The TestLQMarkov reference values are regenerated, and three
tests are added: Ps equal the exact cost of following Fs, perturbing
Fs does not lower that cost, and identical regimes match LQ.

Fixes #982

Assisted-by: Claude Code (Claude Sonnet 5.5)
Assisted-by: Claude Code (Claude Opus 5.5)
Signed-off-by: Gaurav Jadhav <gaurav.vjadhav01@gmail.com>
Co-authored-by: Matt McKay <mmcky@users.noreply.github.com>
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

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