linear-solvers

linear-solvers is a skill for Claude Code from beita6969/ScienceClaw. It costs 55 tokens per session (1,537 once invoked), scanned A, original, MIT.

A guide for choosing numerical methods to solve systems of linear equations, written as Ax=b. It covers dense and sparse matrices, convergence problems, and preconditioners that can improve solver behaviour.

In plain words
What is it for?
Use it to choose among LU, Cholesky, CG, MINRES, GMRES, or BiCGSTAB for numerical simulations and large matrix problems.
Why use it?
It helps select a suitable solver from the matrix's size and properties and diagnose cases where an iterative solver stalls.

Skill for Claude Code

Written for Claude Code: allowed-tools in frontmatter.

Good fit Use it to choose among LU, Cholesky, CG, MINRES, GMRES, or BiCGSTAB for numerical simulations and large matrix problems.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/beita6969/scienceclaw/linear-solvers
Install

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.

Any agent
npx skills add beita6969/ScienceClaw --skill linear-solvers
Clone the repo
git clone --depth 1 https://github.com/beita6969/ScienceClaw

Made for: Claude Code.

Wrote this? Show the measurements

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README.md
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agentmods 80×15 button for linear-solvers

Your own site · 80×15
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Per session 55 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 1,537 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe. Third-party audits
  • NVIDIA SkillSpector pass 7 Sept 2026
How audits are shown
Origin original No closer match found in the catalogue.
Token cost

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.

ModelPer sessionOnce 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

Measured 7d ago against content hash 924c9c02c5f3, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-10, from the pricing page.

Security

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.

The scan reads SKILL.md. This mod also ships 6 executable files (scripts/convergence_diagnostics.py, scripts/preconditioner_advisor.py, scripts/residual_norms.py, …), listed below but not scanned — reading those needs a real analyzer, not pattern matching.

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.

skills/linear-solvers/SKILL.md · 166 lines

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

  1. Characterize matrix - symmetry, definiteness, sparsity
  2. Analyze sparsity - Run scripts/sparsity_stats.py
  3. Select solver - Run scripts/solver_selector.py
  4. Choose preconditioner - Run scripts/preconditioner_advisor.py
  5. Apply scaling - If ill-conditioned, use scripts/scaling_equilibration.py
  6. Monitor convergence - Use scripts/convergence_diagnostics.py
  7. Diagnose issues - Check residual history with scripts/residual_norms.py

Read the full file on GitHub · 166 lines

Changes

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.

  1. 7d ago First seen · 166 lines · 55 tokens per session scan A 924c9c02c5f3

Subscribe to this mod's changes

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.

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