Krylov.jl: A Julia basket of hand-picked Krylov methods
Bibliographic record
Abstract
Krylov v0.10.0 Diff since v0.9.10 Breaking changes solve! is replaced by krylov_solve! Update the API for workspaces (the suffix Solver is now Workspace) Ensure that S is a concrete type in the workspaces Update the API for workspace accessors (not exported anymore) Rename some workspace accessors (iteration_count, solution_count, Aprod_count and Atprod_count) New features Add kdiv!, kscalcopy! and kdivcopy! for the support of custom workspaces Add a generic interface (krylov_workspace, krylov_solve and krylov_solve!) Add documentation on the generic API and the workspace accessors Update the docstrings to add more cross-references Add a function Krylov.elapsed_time Other changes Krylov.jl now requires Julia 1.10 Update the reference of MinAres and CAr Return a nice error if we detect that the preconditioner is not SPD in CG Merged pull requests: Implement Line Search with Negative Curvature Detection for MINRES Based on Liu et al. (2022) (#969) (@farhadrclass) Update the reference of MinAres (#971) (@amontoison) Update the reference of MinAres and CAr (#972) (@amontoison) Don't export Krylov.solve! (#973) (@amontoison) Require Julia 1.10 (#974) (@amontoison) Update the API for workspaces (#975) (@amontoison) S should be a concrete type in the workspaces (#977) (@amontoison) Update Breakage.yml for PRs from a fork (#978) (@amontoison) Add kdiv! -- kscalcopy! -- kdivcopy! (#980) (@amontoison) Add a generic interface for Krylov.jl (#983) (@amontoison) Rename the files krylov_solve.jl and test_solvers.jl (#989) (@amontoison) Use the suffix Workspace instead of Solver (#990) (@amontoison) Return a nice error if we detect the preconditioner is not SPD in CG (#991) (@amontoison) Add references to the generic interface in the docstrings (#992) (@amontoison) krylov_solvers -> krylov_workspaces (#993) (@amontoison) [documentation] Add more cross-references to the in-place methods (#994) (@amontoison) Remove aliases (#995) (@amontoison) Add a function krylov_elapsed_time (#996) (@amontoison) Add a new file krylov_show.jl (#997) (@amontoison) Update the API for workspace accessors (#998) (@amontoison) Polish the API for workspace accessors (#1000) (@amontoison) Closed issues: Improve the documentation of functions Aprod and Atprod (#488) GMRES Fails Silently From Stagnation (#729) StaticArrays support (#766) Remove broadcast in Krylov methods (#930) Unexport Krylov.solve! with the next major release (#934) Add a function to get the timer directly from a KrylovWorkspace (#936) nshifts and S should be the last argument in the Krylov solvers (#946) Require Julia 1.10 for the next major release (#964) Bug Report: CR and CG Solvers Fail with Float16 Precision (#968) Update breakage.yml for PRs from a fork (#976) Add a generic constructor for KrylovSolver and BlockKrylovSolver (#979) Rename the files krylov_solve.jl and test_solvers.jl (#984) Rename the suffix of the workspaces *Solver -> *Workspace (#987)
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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 | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.004 | 0.005 |
| Meta-epidemiology (broad) | 0.003 | 0.006 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.009 | 0.010 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.326 | 0.276 |
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".