Strong Scaling of The SVD Algorithm For HPC Science: A Petsc-Based Approach
Bibliographic record
Abstract
The Singular Value Decomposition (SVD) algorithm is ubiquitous in many fields of science and technology. It may be used embedded into other advanced algorithms, solvers or data processing chains. In those scenarios dealing with large data volumes expressed as a huge matrix, there is a need for parallel SVD versions to process it efficiently. We present some ideas and results obtained within the PETSc framework, which enable to design promising HPC scalable solvers. The focused SVD implementations have been taken from the SLEPc library, which is seamless plugged into PETSc to extend its capabilities. Besides its implementation, there is also a randomized-SVD and some wrappers to interface ScaLAPACK and others packages intended to extract singular triplets. This work assesses the strong scaling behaviour attained with these SVD implementations at extracting the leading singular values of a population of both sparse and dense squared matrices. A comparison of performance is provided.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".