Add inline_linear_systems diagnostic

[baggepinnen]

What

Adds inline_linear_systems, a diagnostic that reports the inline linear-solve blocks a compiled system re-solves on every evaluation.

When tearing solves a strongly-connected component of algebraic equations as one linear system, it emits — into equations(sys) / observed(sys) — a square system A x = b that the generated code re-solves at every call (A \ b, or inline_scc_ldiv for the rank-tolerant aggressive reduction). Each solution component appears as an assignment vᵢ ~ (A \ b)[i].

inline_linear_systems(sys) collects these and returns, for each, an InlineLinearSystem with:

• operation — \ or inline_scc_ldiv,
• size — the dimension N of the N×N system,
• variables — the N variables it solves for, in solution order,
• expression — the retained A \ b term, so callers can inspect or numerically evaluate A (e.g. to check conditioning).

Why

It is a diagnostic for understanding a compiled model's per-step cost and structure: large blocks are the dominant linear-algebra work each evaluation, and a singularity-prone block can be traced to the physical quantities it determines. (It grew out of debugging the multibody car/rotorcraft models, where knowing which variables a deficient block solves for was the key to locating the model-level degeneracy.)

Notes

• Block detection matches \ and inline_scc_ldiv by name, so it works whether or not the rank-tolerant op is present (stock systems emit plain \ blocks).
• The walk over the right-hand-side DAG is memoized by object identity (the DAG is heavily shared).
• exported for discoverability — happy to switch to @public/qualified-only if that better matches the package's conventions (it currently exports nothing).

Test

New testset inline_linear_systems diagnostic: a 3-variable algebraic SCC with state/time-dependent coefficients compiles to a single 3×3 inline \ solve; the diagnostic reports size 3 and the three solved variables, and an empty result for a system with no inline solves. Verified locally (9/9 pass).

🤖 Generated with Claude Code

[AayushSabharwal]

Looks great. However, instead of parsing equations what if the code that creates the linsolves in reassemble.jl builds a list of these InlineLinearSystem structs and puts them into the metadata of the simplified system? That way the diagnostic just has to check metadata.

[AayushSabharwal]

Some suggestions around type-stability and redundancy.

[AayushSabharwal]

Hopefully I did this right :D