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Commit 4848407
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Refactor gpu_stump to Use Covariance-Based Pearson Correlation
Overview
This PR transitions the core distance computation within the gpu_stump implementation from the original sliding dot-product (QT) approach to a sliding covariance-based Pearson correlation approach.
The original sliding dot-product implementation was mathematically sound for most typical scenarios but was susceptible to catastrophic cancellation in extreme edge cases (where QT and m * μ_Q * M_T are both very large numbers but their difference is very small). By maintaining a sliding covariance directly within the kernel, we avoid this cancellation and guarantee significantly higher numerical stability for extreme-valued inputs.
Key Changes
Covariance Kernel Implementation (_compute_and_update_PI_kernel):
Replaced the inner sliding QT loop with a direct sliding cov_out update.
Introduced μ_Q_m_1 and M_T_m_1 as kernel arguments to correctly calculate the sliding update across moving windows.
Computes Pearson correlation and subsequent Euclidean distances directly from the stabilized sliding covariance arrays.
NaN and Inf Data Correctness:
Maintained rigorous correctness for NaN and Inf inputs by ensuring the algebraic mean of the zero-filled overlapping region (μ_Q_m_1) is read explicitly from global memory.
core.preprocess explicitly flags NaN-containing windows with np.inf. By retaining the dedicated μ_Q_m_1 array (which operates cleanly on the zero-filled T_A_pre underneath), we prevent these np.inf flags from poisoning the sliding covariance diagonals, preserving STUMPY's expected NaN masking logic and unit test parity.
Multi-GPU / Process Pool Updates:
Plumbed the new required precalculated sliding-mean arrays (μ_Q_m_1_fname, M_T_m_1_fname) and base covariance files (cov_fname, cov_first_fname) through the _gpu_stump multi-process driver loop and temporary file system.
Performance & Math Considerations:
The shift from a dot-product update to a full covariance update inherently adds an ~8% computational and memory bandwidth overhead (due to the physically unavoidable μ_Q_m_1 extra global memory load per thread required to maintain NaN-stability).
The inner loop mathematics use a 5-op formula (adj_cov_a_j * cov_b_i - adj_cov_c_j * cov_d_i) to compute the exact covariance differential while preserving all necessary algebraic boundaries.
Testing
✅ Passed black, isort, and flake8 compliance.
✅ Custom docstring.py fully conforms with the updated kernel signatures.
✅ Successfully passes all NUMBA_ENABLE_CUDASIM=1 tests (test_gpu_stump.py).
✅ Perfect parity with stumpy.stump (CPU) matrix profile results (including robust test_gpu_stump_nan_inf_A_B_join validation tests).
✅ Maintained 100% Code Coverage across the test suite.
Impact
This brings the numerical stability of gpu_stump perfectly in line with STUMPY's CPU implementations, eliminating catastrophic cancellation vulnerabilities at the cost of a minor (~8%) acceptable kernel overhead.1 parent f5b5424 commit 4848407
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