GPU Refactor: Add array_type parameter and GPU extensions

.claude/skills/test-coverage-benchmark-workflow/SKILL.md

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+---
+name: test-coverage-benchmark-workflow
+description: Run AbstractOperators.jl's long-running test, coverage, and benchmark workflow — filtered TestItemRunner runs, coverage capture, and local/CI AirspeedVelocity benchmark comparisons. Use when running the full test suite, generating coverage, or comparing performance against master.
+---
+
+1. Start from the smallest relevant test scope; prefer a persistent Julia REPL for repeated
+   filtered `TestItemRunner.run_tests(...)` calls.
+2. Fix real implementation bugs in source instead of weakening tests; rerun the same filtered
+   slice until green, then expand to adjacent slices, then run the full suite.
+3. Capture all run logs under `.temp/`.
+4. For performance-sensitive changes, benchmark before and after; run focused ASV filters
+   first, then a single full ASV comparison for final validation. Treat
+   `speedup + uncertainty < 0.95` (master/dirty ratio) as a significant regression.
+5. Prefer representative large inputs for linear and nonlinear operators to reduce
+   microbenchmark noise, but wrap only fast operators in calculus operators to measure the
+   calculus overhead itself.
+6. Use AirspeedVelocity with an explicit script path when comparing against revisions that do
+   not yet contain the benchmark file.
+
+Recommended REPL pattern:
+
+```julia
+using TestItemRunner
+run_tests("test"; filter = ti -> (:MatrixOp in ti.tags) && (:linearoperator in ti.tags))
+```
+
+Main package coverage (also exercises subpackage and extension code — DSPOperators,
+FFTWOperators, NFFTOperators, and WaveletOperators have no standalone `test/` directory, and
+extensions are exercised through the parent package's tests):
+
+```sh
+julia --project=test --code-coverage=user test/runtests.jl
+```
+
+Process coverage after a local run:
+
+```sh
+julia -e 'using Coverage; Coverage.LCOV.writefile("lcov.info", Coverage.process_folder())'
+```
+
+Filtered test run:
+
+```julia
+using TestItemRunner
+TestItemRunner.run_tests(pwd(); filter = ti -> :MatrixOp in ti.tags) # by tag
+TestItemRunner.run_tests(pwd(); filter = ti -> ti.name == "DCT")     # by test name
+```
+
+### Local benchmark comparison with AirspeedVelocity
+
+```sh
+mkdir -p .temp/asv
+benchpkg \
+  --path . \
+  --rev master,dirty \
+  --script benchmark/benchmarks.jl \
+  --output-dir .temp/asv \
+  --exeflags="--threads=4"
+```
+
+Filtered comparison for a single benchmark family:
+
+```sh
+mkdir -p .temp/asv
+benchpkg \
+  --path . \
+  --rev master,dirty \
+  --script benchmark/benchmarks.jl \
+  --output-dir .temp/asv \
+  --exeflags="--threads=4" \
+  --add RecursiveArrayTools \
+  --filter MIMOFilt
+```
+
+Render a comparison table:
+
+```sh
+benchpkgtable \
+  --path . \
+  --rev master,dirty \
+  --input-dir .temp/asv \
+  --ratio \
+  --mode time,memory
+```
+
+### CI benchmark comparison (GitHub Actions)
+
+The GitHub Actions benchmark CI does **not** use the AirspeedVelocity action because the
+root-level Julia workspace (`[workspace]` in `Project.toml`) causes that action's
+revision-management to mis-resolve the monorepo subprojects. Instead, two workflows implement
+a fork-safe two-stage approach:
+
+- **`benchmark.yml`** — unprivileged `pull_request` job that checks out both the base and head
+  revisions, runs `benchmark/compare.jl` against explicit worktree paths, and uploads
+  `body.md`, `pr_number.txt`, and `julia_version.txt` as an artifact.
+- **`post_benchmark_comment.yml`** — privileged `workflow_run` job that downloads the artifact
+  and creates or updates the PR comment.
+
+The comparison table mirrors AirspeedVelocity output with separate Time and Memory sections,
+base/head columns, a ratio column, and emoji indicators:
+
+- 🚀 significant speedup: `ratio − ratio_err > 1.2` (time) or `ratio < 0.5` (memory)
+- 🐢 significant slowdown: `ratio + ratio_err < 0.8` (time) or `ratio > 1.5` (memory)
+
+To run the comparison locally with the same script used by CI:
+
+```sh
+git worktree add .temp/base master
+
+julia --project=benchmark benchmark/compare.jl \
+  --base-dir  .temp/base \
+  --head-dir  . \
+  --output-dir .temp/bench-compare \
+  --pr        0 \
+  --julia-version "$(julia -e 'print(VERSION)')"
+
+cat .temp/bench-compare/body.md
+```