lyap-vectors

name	lyap-vectors
description	Identify special vectors spanning Lyapunov partial sums and extract coefficient patterns as functions of k. Use when the user asks for /lyap-vectors, lyap-vectors, Block 4, special Lyapunov vectors, low-rank decomposition of V_k, coefficient pattern extraction, or generating examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b4.json from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b3.json.

Lyap Vectors

Quick Start

Read references/workflow.md, then execute it as the authoritative Block 4 workflow.

Start from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b3.json, rebuild the partial sums using the stored grouping code, and write examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b4.json.

Codex Adaptation

• Reconstruct lyap before searching for vectors; do not infer coefficients from stale printed output.
• Build candidate vectors from tagged iterates, gradients or operator outputs, basis vectors, and meaningful differences.
• Use PEPFlow Lyapunov utilities where available instead of reimplementing linear algebra.
• Track both the rank profile and the chosen basis templates in the output state.
• Keep workflow artifacts under examples_peppy/{ALGO_NAME}/state/.
• When several decompositions are possible, prefer sparse, interpretable vectors that match the algorithm recurrence.
• In the notebook, use the standard Block 4 section order: ## Identify the vectors composing the Lyapunov function, ### Candidate-vector scan, ### Selected basis pattern, ### Coefficient matrices, and ### Block 4 conclusion.

Related Skills

Run lyap-closed-form next to solve the symbolic recursion.