Comprehensive Testing Framework for Mathematical Algorithms

[ianfd]

Description

Develop a robust testing strategy to ensure correctness, robustness, and reproducibility of mathematical algorithms implemented in single-algebra.

Objectives

• Validate the correctness of all implemented algorithms against reference implementations
• Ensure numerical stability across different data types and input scales
• Verify reproducibility with fixed random seeds where applicable
• Create comprehensive test coverage for core functionality

Key Components to Implement

Correctness Testing

• Implement comparison against reference implementations for SVD/PCA
• Create synthetic datasets with known ground truth results
• Add validation against published results for standard datasets
• Develop numerical accuracy thresholds for floating-point operations

Robustness Testing

• Test algorithms with edge cases (extremely sparse/dense matrices)
• Validate behavior with degenerate inputs (zero variance, constant values)
• Implement stress tests with large matrices and limited memory
• Create fault injection for testing error handling

Reproducibility Testing

• Add seed management for all stochastic algorithms
• Implement deterministic mode for testing environments
• Create cross-platform reproducibility tests
• Verify bit-exact outputs with fixed inputs and seeds

Test Infrastructure

• Develop property-based testing for mathematical properties
• Create benchmark datasets at various scales
• Implement continuous integration test matrix across platforms
• Add performance regression testing

Integration Points

• Should cover all exposed API functions
• Must include both dense and sparse matrix implementations
• Focus especially on chunked computation methods

Technical Notes

• Prioritize testing PCA and chunked methods as specified
• Consider using existing mathematical libraries for validation
• Implement both unit tests and integration tests
• Use parametrized tests for covering multiple scenarios efficiently