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 beita6969/ScienceClaw --skill linear-solversgit clone --depth 1 https://github.com/beita6969/ScienceClawWrote 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/beita6969/scienceclaw/linear-solvers)<a href="https://agentmods.dev/skills/beita6969/scienceclaw/linear-solvers"><img src="https://agentmods.dev/badge/skills/beita6969/scienceclaw/linear-solvers/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/beita6969/scienceclaw/linear-solvers"><img src="https://agentmods.dev/badge/skills/beita6969/scienceclaw/linear-solvers.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector pass
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 | $0.00055 | $0.01537 |
| Opus 5 | $0.00028 | $0.00768 |
| Sonnet 5 | $0.00011 | $0.00307 |
| Haiku 4.5 | $0.00006 | $0.00154 |
Grade A, and why
linear-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 7d 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 — 166 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Linear Solvers
Goal
Provide a universal workflow to select a solver, assess conditioning, and diagnose convergence for linear systems arising in numerical simulations.
Requirements
- Python 3.8+
- NumPy, SciPy (for matrix operations)
- See individual scripts for dependencies
Inputs to Gather
| Input | Description | Example |
|---|---|---|
| Matrix size | Dimension of system | n = 1000000 |
| Sparsity | Fraction of nonzeros | 0.01% |
| Symmetry | Is A = Aᵀ? | yes |
| Definiteness | Is A positive definite? | yes (SPD) |
| Conditioning | Estimated condition number | 10⁶ |
Decision Guidance
Solver Selection Flowchart
Is matrix small (n < 5000) and dense?
├── YES → Use direct solver (LU, Cholesky)
└── NO → Is matrix symmetric?
├── YES → Is it positive definite?
│ ├── YES → Use CG with AMG/IC preconditioner
│ └── NO → Use MINRES
└── NO → Is it nearly symmetric?
├── YES → Use BiCGSTAB
└── NO → Use GMRES with ILU/AMG
Quick Reference
| Matrix Type | Solver | Preconditioner |
|---|---|---|
| SPD, sparse | CG | AMG, IC |
| Symmetric indefinite | MINRES | ILU |
| Nonsymmetric | GMRES, BiCGSTAB | ILU, AMG |
| Dense | LU, Cholesky | None |
| Saddle point | Schur complement, Uzawa | Block preconditioner |
Script Outputs (JSON Fields)
| Script | Key Outputs |
|---|---|
scripts/solver_selector.py |
recommended, alternatives, notes |
scripts/convergence_diagnostics.py |
rate, stagnation, recommended_action |
scripts/sparsity_stats.py |
nnz, density, bandwidth, symmetry |
scripts/preconditioner_advisor.py |
suggested, notes |
scripts/scaling_equilibration.py |
row_scale, col_scale, notes |
scripts/residual_norms.py |
residual_norms, relative_norms, converged |
Workflow
- Characterize matrix - symmetry, definiteness, sparsity
- Analyze sparsity - Run
scripts/sparsity_stats.py - Select solver - Run
scripts/solver_selector.py - Choose preconditioner - Run
scripts/preconditioner_advisor.py - Apply scaling - If ill-conditioned, use
scripts/scaling_equilibration.py - Monitor convergence - Use
scripts/convergence_diagnostics.py - Diagnose issues - Check residual history with
scripts/residual_norms.py
What ships with it
10 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.
- references/convergence_patterns.md 10 KB
- references/preconditioner_catalog.md 8.0 KB
- references/scaling_guidelines.md 8.3 KB
- references/solver_decision_tree.md 7.9 KB
- scripts/convergence_diagnostics.py 2.2 KB runs code
- scripts/preconditioner_advisor.py 3.3 KB runs code
- scripts/residual_norms.py 5.5 KB runs code
- scripts/scaling_equilibration.py 4.2 KB runs code
- scripts/solver_selector.py 4.4 KB runs code
- scripts/sparsity_stats.py 2.7 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.
- 7d ago First seen · 166 lines · 55 tokens per session scan A 924c9c02c5f3
linear-solvers is a skill published in the GitHub repository beita6969/ScienceClaw (898 stars, last pushed 3mo ago), licensed MIT. It adds 55 tokens to every session and 1,537 once invoked, about $0.0003 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 2026-09-03.
Other skills, from other repositories
biopython
Comprehensive molecular biology toolkit. Use for sequence manipulation, file parsing (FASTA/GenBank/PDB), phylogenetics, and programmatic NCBI/PubMed access (Bio.Entrez). Best for batch processing, custom bioinformatics pipelines, BLAST automation. For quick lookups use gget; for multi-service integration use…
scanpy
Standard single-cell RNA-seq analysis pipeline. Use for QC, normalization, dimensionality reduction (PCA/UMAP/t-SNE), clustering, differential expression, and visualization. Best for exploratory scRNA-seq analysis with established workflows. For deep learning models use scvi-tools; for data format questions use…
structure-prediction
Protein structure prediction from sequence. ESMFold-based, single GPU, no MSA needed. Predicts 3D structures with pLDDT confidence scores for drug discovery targets.
smiles-validation
Strict SMILES validation, structural comparison, and modification verification. Catches invalid LLM-generated molecules.
anomaly-characterization
SOP: Describe and classify anomalous phenomena that existing theory cannot explain.
biomcp
Search and retrieve biomedical data - genes, variants, clinical trials, diagnostic tests, articles, drugs, diseases, pathways, proteins, adverse events, pharmacogenomics, and phenotype-disease matching. Use for gene function, variant pathogenicity, trials, diagnostics, drug safety, pathway context, disease workups…