Jacobian accumulation

Benchmarks of SparseDiffEngine — a C engine that assembles sparse derivatives from per-atom closed-form Jacobian blocks — against tools based on automatic/algorithmic differentiation (CasADi, JAX, ADOL-C, the Julia sparse-AD stack SparseConnectivityTracer + SparseMatrixColorings + DifferentiationInterface), against systems that, like the engine, know the structure a priori (the AMPL Solver Library via Pyomo/PyNumero, JuMP/MathOptInterface's matrix assembly), and against CVXPY's cvxcore backends. The recurring question: what do graph coloring, sparsity-pattern detection, and Jacobian accumulation cost, compared to knowing the derivative structure a priori?

Contents

• canonicalization/ — the main experiments: constructing convex-program problem data (P, c, A, b) with the diff engine vs CasADi's symbolic AD, and vs CVXPY's cvxcore backends, over the 25 problems of the public CVXPY benchmark suite. Cold construction and warm parametric re-solves; outputs verified bit-identical across systems before timing. Includes reference results and the mechanism probes (dense-block coloring blow-up, casadi.hessian star-coloring pathology). Backs chapter 4 of the associated thesis and cvxpy#3348. The thesis benchmarks now live in their own repo, SparseDifferentiation/canonicalization-benchmarks.
• jacobian/ — small self-contained sparse-Jacobian comparisons on a tridiagonal system: one script per tool (CasADi, JAX, ADOL-C, SparseDiffEngine, the Julia SCT+SMC+DI stack, AMPL/ASL), illustrating how each recovers — or never needs to recover — the sparsity pattern.

Setup

uv sync            # casadi, numpy, scipy, the CVXPY diff-engine fork, sparsediffpy

# Julia comparisons (SCT+SMC+DI stack, JuMP/MOI): juliaup-installed Julia, then
julia --project=julia -e 'using Pkg; Pkg.instantiate()'

# AMPL/ASL comparison: pyomo + the compiled PyNumero ASL interface
uv sync --extra asl
pyomo build-extensions      # needs cmake + a C++ compiler (or: pyomo download-extensions)

The CVXPY dependency is the diff-engine fork (Transurgeon/cvxpy branch pr-c-resolve-caching, the cvxpy#3348 stack). For warm re-solve benchmarks the engine needs the composite-source refresh fix (SparseDiffEngine #107); see canonicalization/README.md for the version caveat.