numerical-patterns

Numerical computing patterns for C++20 including matrix operations, iterative solvers, numerical stability, data pipelines, and HPC I/O with MPI-IO and HDF5.

Quality

67%

Does it follow best practices?

Impact

Pending

No eval scenarios have been run

Securityby

Passed

No known issues

Optimize this skill with Tessl

npx tessl skill review --optimize ./skills/numerical-patterns/SKILL.md

Quality

Discovery

82%

Based on the skill's description, can an agent find and select it at the right time? Clear, specific descriptions lead to better discovery.

This description excels at specificity and distinctiveness, listing concrete numerical computing capabilities tied to a specific language (C++20) and technology stack (MPI-IO, HDF5). Its main weakness is the absence of an explicit 'Use when...' clause, which would help Claude know exactly when to select this skill. The trigger terms are strong and domain-appropriate.

Suggestions

Add a 'Use when...' clause such as 'Use when the user asks about numerical computing in C++, matrix math, iterative solvers, HPC data I/O, MPI-IO, or HDF5 integration.'

Consider adding a few more user-facing trigger variations like 'scientific computing', 'linear algebra', or 'high-performance computing' to capture broader user phrasing.

Dimension	Reasoning	Score
Specificity	Lists multiple specific concrete actions/domains: matrix operations, iterative solvers, numerical stability, data pipelines, and HPC I/O with MPI-IO and HDF5. These are concrete, well-defined technical capabilities.	3 / 3
Completeness	Clearly answers 'what does this do' with specific capabilities, but lacks an explicit 'Use when...' clause or equivalent trigger guidance. Per rubric guidelines, missing 'Use when' caps completeness at 2.	2 / 3
Trigger Term Quality	Includes strong natural keywords a user would use: 'matrix operations', 'iterative solvers', 'numerical stability', 'HPC', 'MPI-IO', 'HDF5', 'C++20', 'numerical computing', 'data pipelines'. Good coverage of domain-specific terms users would naturally mention.	3 / 3
Distinctiveness Conflict Risk	Highly distinctive niche combining C++20, numerical computing, HPC I/O, MPI-IO, and HDF5. Very unlikely to conflict with other skills given the specific technology stack and domain focus.	3 / 3
	Total	11 / 12 Passed

Implementation

52%

Reviews the quality of instructions and guidance provided to agents. Good implementation is clear, handles edge cases, and produces reliable results.

This skill provides a solid reference library of numerical computing patterns in C++20 with concrete, executable code examples covering matrix operations, solvers, stability techniques, and HPC I/O. However, it reads more like a code cookbook than an actionable skill—it lacks workflow guidance on when/how to apply these patterns, validation steps for numerical correctness, and decision criteria for choosing between approaches. The content is also quite long for a SKILL.md and would benefit from progressive disclosure.

Suggestions

Add workflow guidance: when to choose dense vs sparse matrices, when to use CG vs GMRES, and decision criteria based on problem characteristics (symmetry, conditioning, size).

Include validation/verification steps for numerical operations—e.g., how to check convergence, verify numerical stability, and test with known analytical solutions.

Split detailed implementations into separate reference files (e.g., SOLVERS.md, HPC_IO.md) and keep SKILL.md as a concise overview with brief examples and navigation links.

Remove or significantly trim the incomplete GMRES implementation (which has placeholder comments) and the generic DataPipeline pattern, which doesn't add numerical-computing-specific value.

Dimension	Reasoning	Score
Conciseness	The skill is mostly code examples which are inherently dense, but it's quite long (~400 lines) and includes patterns Claude likely already knows (basic dense matrix class, CSR format, CG method). The GMRES implementation is incomplete with placeholder comments, wasting tokens. Some sections like the DataPipeline pattern are generic C++ patterns not specific to numerical computing.	2 / 3
Actionability	The code examples are concrete, executable (or near-executable), and copy-paste ready. Dense matrix, sparse matrix, CG solver, Kahan summation, MPI-IO, HDF5 writer, and binary I/O all provide complete, working implementations with proper includes and usage examples.	3 / 3
Workflow Clarity	There are no workflows, sequences, or validation checkpoints. The skill is a collection of code snippets without guidance on when to use each pattern, how they connect, or how to verify correctness. The 'Key Principles' at the end mention testing but provide no concrete validation steps. For numerical computing where stability issues are critical, the lack of verification workflows is a significant gap.	1 / 3
Progressive Disclosure	The content is organized into clear sections (Matrix Operations, Iterative Solvers, Numerical Stability, Data Pipelines, HPC I/O) which aids navigation. However, it's a monolithic file with ~400 lines of inline code that could benefit from splitting detailed implementations into separate reference files, keeping SKILL.md as an overview with brief examples and links.	2 / 3
	Total	8 / 12 Passed

Validation

100%

Warnings & errors only

Checks the skill against the spec for correct structure and formatting. All validation checks must pass before discovery and implementation can be scored.

Validation — 11 / 11 Passed

Validation for skill structure

No warnings or errors.

Repository: ysyecust/everything-claude-code
Commit: 79cc4e3

Reviewed: 8 days ago

Table of Contents

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