Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add HeshamFS/materials-simulation-skills --skill nonlinear-solversgit clone --depth 1 https://github.com/HeshamFS/materials-simulation-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/heshamfs/materials-simulation-skills/nonlinear-solvers)<a href="https://agentmods.dev/skills/heshamfs/materials-simulation-skills/nonlinear-solvers"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/nonlinear-solvers.svg" alt="Measured on agentmods" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00153 | $0.04168 |
| Opus 5 | $0.00077 | $0.02084 |
| Sonnet 5 | $0.00031 | $0.00834 |
| Haiku 4.5 | $0.00015 | $0.00417 |
Grade A, and why
nonlinear-solvers scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 8d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 273 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Nonlinear Solvers
Goal
Provide a universal workflow to select a nonlinear solver, configure globalization strategies, and diagnose convergence for root-finding, optimization, and least-squares problems.
Requirements
- Python 3.10+
- NumPy (for Jacobian diagnostics)
- SciPy (optional, for advanced analysis)
Inputs to Gather
| Input | Description | Example |
|---|---|---|
| Problem type | Root-finding, optimization, least-squares | root-finding |
| Problem size | Number of unknowns | n = 10000 |
| Jacobian availability | Analytic, finite-diff, unavailable | analytic |
| Jacobian cost | Cheap or expensive to compute | expensive |
| Constraints | None, bounds, equality, inequality | none |
| Smoothness | Is objective/residual smooth? | yes |
| Residual history | Sequence of residual norms | 1,0.1,0.01,... |
Decision Guidance
Solver Selection Flowchart
Is Jacobian available and cheap?
├── YES → Problem size?
│ ├── Small (n < 1000) → Newton (full)
│ └── Large (n ≥ 1000) → Newton-Krylov
└── NO → Is objective smooth?
├── YES → Memory limited?
│ ├── YES → L-BFGS or Broyden
│ └── NO → BFGS
└── NO → Anderson acceleration or Picard
Quick Reference
| Problem Type | First Choice | Alternative | Globalization |
|---|---|---|---|
| Small root-finding | Newton | Broyden | Line search |
| Large root-finding | Newton-Krylov | Anderson | Trust region |
| Optimization | L-BFGS | BFGS | Wolfe line search |
| Least-squares | Levenberg-Marquardt | Gauss-Newton | Trust region |
| Bound constrained | L-BFGS-B | Trust-region reflective | Projected |
Script Outputs (JSON Fields)
| Script | Key Outputs |
|---|---|
scripts/solver_selector.py |
recommended, alternatives, notes |
scripts/convergence_analyzer.py |
converged, convergence_type, estimated_rate, diagnosis |
scripts/jacobian_diagnostics.py |
condition_number, jacobian_quality, rank_deficient |
scripts/globalization_advisor.py |
strategy, line_search_type, trust_region_type, parameters |
scripts/residual_monitor.py |
patterns_detected, alerts, recommendations |
scripts/step_quality.py |
ratio, step_quality, accept_step, trust_radius_action |
What ships with it
12 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
- CHANGELOG.md 3.7 KB
- evals/evals.json 10 KB
- references/convergence_diagnostics.md 8.5 KB
- references/globalization_strategies.md 8.8 KB
- references/method_catalog.md 9.1 KB
- references/solver_decision_tree.md 8.0 KB
- scripts/convergence_analyzer.py 9.4 KB runs code
- scripts/globalization_advisor.py 9.7 KB runs code
- scripts/jacobian_diagnostics.py 7.9 KB runs code
- scripts/residual_monitor.py 9.4 KB runs code
- scripts/solver_selector.py 12 KB runs code
- scripts/step_quality.py 7.9 KB runs code
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 8d ago First seen · 273 lines · 153 tokens per session scan A 1da26bfcf978
nonlinear-solvers is a skill published in the GitHub repository HeshamFS/materials-simulation-skills (66 stars, last pushed 2mo ago), licensed Apache-2.0. It adds 153 tokens to every session and 4,168 once invoked, about $0.0008 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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