Add MATLAB comparison framework for LFM kernel validation

backlog/features/2025-08-15_matlab-comparison-framework.md

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+---
+id: "matlab-comparison-framework"
+title: "Create MATLAB comparison framework for LFM kernel validation"
+status: "In Progress"
+priority: "High"
+created: "2025-08-15"
+last_updated: "2025-08-15"
+owner: "Neil Lawrence"
+github_issue: ""
+dependencies: "lfm-kernel-code-review"
+tags:
+- lfm
+- kernel
+- validation
+- matlab
+- comparison
+---
+
+# Create MATLAB comparison framework for LFM kernel validation
+
+## Description
+Create a comprehensive comparison framework to validate our GPy LFM kernel implementation against the MATLAB reference implementation in GPmat.
+
+## Background
+- We have analyzed the complete MATLAB implementation (SIM, DISIM kernels)
+- Need to validate our GPy implementation against the reference
+- Comparison framework will ensure mathematical correctness and numerical accuracy
+- Will help catch implementation errors and validate parameter handling
+
+## Implementation Tasks
+- [x] Create MATLAB comparison script (`scripts/compare_with_matlab.py`)
+- [ ] Test MATLAB script with existing GPmat installation
+- [ ] Create standard test cases for SIM and DISIM kernels
+- [ ] Implement GPy computation integration in comparison script
+- [ ] Add parameter validation and constraint testing
+- [ ] Create visualization tools for comparison results
+- [ ] Add cross-kernel computation validation
+- [ ] Document comparison methodology and tolerance standards
+
+## Test Cases to Implement
+- [ ] Basic SIM kernel with standard parameters
+- [ ] SIM kernel with fast decay and no delay
+- [ ] Basic DISIM kernel with hierarchical parameters
+- [ ] Edge cases (zero delay, extreme decay values)
+- [ ] Multi-output scenarios
+- [ ] Cross-kernel computations (SIM × RBF, DISIM × SIM)
+
+## Acceptance Criteria
+- [ ] MATLAB comparison script runs successfully
+- [ ] Standard test cases produce consistent results
+- [ ] Comparison framework can detect implementation errors
+- [ ] Tolerance standards defined and documented
+- [ ] Results visualization and reporting implemented
+- [ ] Framework integrated into development workflow
+
+## Implementation Notes
+- Use scipy.io for loading MATLAB .mat files
+- Support both MATLAB and Octave as reference implementations
+- Implement robust error handling for missing dependencies
+- Create standardized test data sets for reproducible comparisons
+- Consider numerical precision differences between platforms
+
+## Related
+- Backlog: lfm-kernel-code-review
+- Backlog: implement-lfm-kernel-core
+- MATLAB Implementation: ~/lawrennd/GPmat/matlab/
+
+## Progress Updates
+
+### 2025-08-15
+Created initial MATLAB comparison framework:
+- Implemented `MATLABComparison` class with automatic MATLAB/Octave detection
+- Created test case generation for SIM and DISIM kernels
+- Added result comparison with tolerance checking
+- Framework ready for integration with GPy implementation
+- Script can generate MATLAB code dynamically for different test cases