Module router 

Algorithm router and solver orchestrator.

The SolverRouter inspects a matrix’s SparsityProfile and the caller’s QueryType to select the optimal Algorithm for each solve request. The SolverOrchestrator wraps the router together with concrete solver instances and provides high-level solve / solve_with_fallback entry points.

Routing decision tree

Query	Condition	Algorithm
LinearSystem	diag-dominant + very sparse	Neumann
LinearSystem	low condition number	CG
LinearSystem	else	BMSSP
PageRankSingle	always	ForwardPush
PageRankPairwise	large graph	HybridRandomWalk
PageRankPairwise	small graph	ForwardPush
SpectralFilter	always	Neumann
BatchLinearSystem	large batch	TRUE
BatchLinearSystem	small batch	CG

Fallback chain

When the selected algorithm fails (non-convergence, numerical instability), SolverOrchestrator::solve_with_fallback tries a deterministic chain:

selected algorithm -> CG -> Dense

Structs

RouterConfig

Configuration thresholds that govern the routing decision tree.

SolverOrchestrator

High-level solver facade that combines routing with execution.

SolverRouter

Stateless algorithm selector.