numerical-test-design

name	numerical-test-design
description	Design focused tests for numerical algorithms, convergence behavior, analytic cases, and backend parity.

Numerical Test Design

When to Use

Use when planning or reviewing tests for numerical algorithms, solvers, kernels, or scientific data transforms.

Checklist

• Include analytic or manufactured cases when possible.
• Test limiting cases, zero-size or small-size inputs, invalid inputs, and boundary conditions.
• Use deterministic seeds for stochastic algorithms.
• Test expected convergence rates where relevant.
• Justify tolerances from method order, conditioning, discretization error, or reference precision.
• Add regression tests for known examples or validation fixtures.
• Check CPU/GPU/backend parity where relevant.
• Keep tests small and reproducible.

Output Format

Return:

1. Test objectives.
2. Proposed test cases.
3. Expected results and tolerances.
4. Required fixtures or seeds.
5. Gaps or follow-up validation.

Common Failure Modes

• Golden values are generated by the same implementation under test.
• Stochastic tests are flaky.
• Tests assert overly exact values for approximate methods.
• Convergence tests use too few resolutions.
• Backend parity tests ignore dtype or memory layout differences.