Package evaluation to test BallArithmetic on Julia 1.14.0-DEV.2064 (1d5dcac2d2*) started at 2026-04-21T17:18:54.671 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Activating project at `~/.julia/environments/v1.14` Set-up completed after 14.61s ################################################################################ # Installation # Installing BallArithmetic... Resolving package versions... Updating `~/.julia/environments/v1.14/Project.toml` [77e4f72b] + BallArithmetic v0.1.2 Updating `~/.julia/environments/v1.14/Manifest.toml` [77e4f72b] + BallArithmetic v0.1.2 [0b6fb165] + ChunkCodecCore v1.0.1 [4c0bbee4] + ChunkCodecLibZlib v1.0.0 [55437552] + ChunkCodecLibZstd v1.0.0 [861a8166] + Combinatorics v1.1.0 [34da2185] + Compat v4.18.1 [ffbed154] + DocStringExtensions v0.9.5 [497a8b3b] + DoubleFloats v1.7.1 [5789e2e9] + FileIO v1.18.0 ⌅ [14197337] + GenericLinearAlgebra v0.3.19 [c145ed77] + GenericSchur v0.5.6 [076d061b] + HashArrayMappedTries v0.2.0 [92d709cd] + IrrationalConstants v0.2.6 [033835bb] + JLD2 v0.6.4 [692b3bcd] + JLLWrappers v1.7.1 [2ab3a3ac] + LogExpFunctions v0.3.29 [1914dd2f] + MacroTools v0.5.16 ⌅ [bdf0d083] + MultiFloats v2.3.0 [bac558e1] + OrderedCollections v1.8.1 [aea7be01] + PrecompileTools v1.3.3 [21216c6a] + Preferences v1.5.2 [be4d8f0f] + Quadmath v1.0.1 [ae029012] + Requires v1.3.1 [5eaf0fd0] + RoundingEmulator v0.2.1 [fdea26ae] + SIMD v3.7.2 [7e506255] + ScopedValues v1.6.0 [3cc68bcd] + SetRounding v0.2.1 [276daf66] + SpecialFunctions v2.7.2 [6cdc7f73] + OpenBLASConsistentFPCSR_jll v0.3.30+0 [efe28fd5] + OpenSpecFun_jll v0.5.6+0 [0dad84c5] + ArgTools v1.1.2 [56f22d72] + Artifacts v1.11.0 [2a0f44e3] + Base64 v1.11.0 [ade2ca70] + Dates v1.11.0 [f43a241f] + Downloads v1.7.0 [7b1f6079] + FileWatching v1.11.0 [ac6e5ff7] + JuliaSyntaxHighlighting v1.13.0 [b27032c2] + LibCURL v1.0.0 [76f85450] + LibGit2 v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.13.0 [56ddb016] + Logging v1.11.0 [d6f4376e] + Markdown v1.11.0 [a63ad114] + Mmap v1.11.0 [ca575930] + NetworkOptions v1.3.0 [44cfe95a] + Pkg v1.14.0 [de0858da] + Printf v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v1.0.0 [f489334b] + StyledStrings v1.13.0 [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.3.0+1 [deac9b47] + LibCURL_jll v8.19.0+0 [e37daf67] + LibGit2_jll v1.9.2+0 [29816b5a] + LibSSH2_jll v1.11.3+1 [14a3606d] + MozillaCACerts_jll v2026.3.19 [4536629a] + OpenBLAS_jll v0.3.30+0 [05823500] + OpenLibm_jll v0.8.7+0 [458c3c95] + OpenSSL_jll v3.5.6+0 [efcefdf7] + PCRE2_jll v10.47.0+0 [83775a58] + Zlib_jll v1.3.2+0 [3161d3a3] + Zstd_jll v1.5.7+1 [8e850b90] + libblastrampoline_jll v5.15.0+0 [8e850ede] + nghttp2_jll v1.69.0+0 [3f19e933] + p7zip_jll v17.8.0+0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Installation completed after 5.84s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompiling project... 2.6 s ✓ MultiFloats 7.1 s ✓ IntervalArithmetic 5.1 s ✓ ArbNumerics 2.9 s ✓ DoubleFloats 12.5 s ✓ BallArithmetic ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)')  -> Autodetected symbol suffix "64_"  -> Autodetected interface ILP64 (64-bit)  -> Autodetected normal complex return style  -> Autodetected gfortran calling convention  -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" 7.8 s ✓ BallArithmetic → FFTExt ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)')  -> Autodetected symbol suffix "64_"  -> Autodetected interface ILP64 (64-bit)  -> Autodetected normal complex return style  -> Autodetected gfortran calling convention  -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" 7.9 s ✓ BallArithmetic → ArbNumericsExt ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)')  -> Autodetected symbol suffix "64_"  -> Autodetected interface ILP64 (64-bit)  -> Autodetected normal complex return style  -> Autodetected gfortran calling convention  -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" 8.1 s ✓ BallArithmetic → IntervalArithmeticExt ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)')  -> Autodetected symbol suffix "64_"  -> Autodetected interface ILP64 (64-bit)  -> Autodetected normal complex return style  -> Autodetected gfortran calling convention  -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" 8.4 s ✓ BallArithmetic → DistributedExt ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)')  -> Autodetected symbol suffix "64_"  -> Autodetected interface ILP64 (64-bit)  -> Autodetected normal complex return style  -> Autodetected gfortran calling convention  -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" 8.8 s ✓ BallArithmetic → MultiFloatsExt ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)')  -> Autodetected symbol suffix "64_"  -> Autodetected interface ILP64 (64-bit)  -> Autodetected normal complex return style  -> Autodetected gfortran calling convention  -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" 8.3 s ✓ BallArithmetic → DoubleFloatsExt ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)')  -> Autodetected symbol suffix "64_"  -> Autodetected interface ILP64 (64-bit)  -> Autodetected normal complex return style  -> Autodetected gfortran calling convention  -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" 7.1 s ✓ BallArithmetic → GenericLinearAlgebraExt 12 dependencies successfully precompiled in 87 seconds. 83 already precompiled. 7 dependencies had output during precompilation: ┌ BallArithmetic → ArbNumericsExt │ ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees │ └ correct floating point rounding mode over all threads. │ [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads │ Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') │ -> Autodetected symbol suffix "64_" │ -> Autodetected interface ILP64 (64-bit) │ -> Autodetected normal complex return style │ -> Autodetected gfortran calling convention │ -> CBLAS detected │ Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" └ ┌ BallArithmetic → DoubleFloatsExt │ ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees │ └ correct floating point rounding mode over all threads. │ [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads │ Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') │ -> Autodetected symbol suffix "64_" │ -> Autodetected interface ILP64 (64-bit) │ -> Autodetected normal complex return style │ -> Autodetected gfortran calling convention │ -> CBLAS detected │ Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" └ ┌ BallArithmetic → IntervalArithmeticExt │ ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees │ └ correct floating point rounding mode over all threads. │ [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads │ Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') │ -> Autodetected symbol suffix "64_" │ -> Autodetected interface ILP64 (64-bit) │ -> Autodetected normal complex return style │ -> Autodetected gfortran calling convention │ -> CBLAS detected │ Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" └ ┌ BallArithmetic → DistributedExt │ ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees │ └ correct floating point rounding mode over all threads. │ [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads │ Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') │ -> Autodetected symbol suffix "64_" │ -> Autodetected interface ILP64 (64-bit) │ -> Autodetected normal complex return style │ -> Autodetected gfortran calling convention │ -> CBLAS detected │ Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" └ ┌ BallArithmetic → MultiFloatsExt │ ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees │ └ correct floating point rounding mode over all threads. │ [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads │ Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') │ -> Autodetected symbol suffix "64_" │ -> Autodetected interface ILP64 (64-bit) │ -> Autodetected normal complex return style │ -> Autodetected gfortran calling convention │ -> CBLAS detected │ Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" └ ┌ BallArithmetic → FFTExt │ ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees │ └ correct floating point rounding mode over all threads. │ [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads │ Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') │ -> Autodetected symbol suffix "64_" │ -> Autodetected interface ILP64 (64-bit) │ -> Autodetected normal complex return style │ -> Autodetected gfortran calling convention │ -> CBLAS detected │ Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" └ ┌ BallArithmetic → GenericLinearAlgebraExt │ ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees │ └ correct floating point rounding mode over all threads. │ [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads │ Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') │ -> Autodetected symbol suffix "64_" │ -> Autodetected interface ILP64 (64-bit) │ -> Autodetected normal complex return style │ -> Autodetected gfortran calling convention │ -> CBLAS detected │ Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" └ Precompilation completed after 114.53s ################################################################################ # Testing # Testing BallArithmetic Status `/tmp/jl_0rF2jl/Project.toml` [7e558dbc] ArbNumerics v1.6.3 [77e4f72b] BallArithmetic v0.1.2 [497a8b3b] DoubleFloats v1.7.1 [7a1cc6ca] FFTW v1.10.0 ⌅ [14197337] GenericLinearAlgebra v0.3.19 [c145ed77] GenericSchur v0.5.6 ⌅ [d1acc4aa] IntervalArithmetic v0.20.9 [033835bb] JLD2 v0.6.4 ⌅ [bdf0d083] MultiFloats v2.3.0 [8ba89e20] Distributed v1.11.0 [37e2e46d] LinearAlgebra v1.13.0 [9a3f8284] Random v1.11.0 [8dfed614] Test v1.11.0 Status `/tmp/jl_0rF2jl/Manifest.toml` [621f4979] AbstractFFTs v1.5.0 [7e558dbc] ArbNumerics v1.6.3 [77e4f72b] BallArithmetic v0.1.2 [96374032] CRlibm v1.0.2 [0b6fb165] ChunkCodecCore v1.0.1 [4c0bbee4] ChunkCodecLibZlib v1.0.0 [55437552] ChunkCodecLibZstd v1.0.0 [861a8166] Combinatorics v1.1.0 [34da2185] Compat v4.18.1 [ffbed154] DocStringExtensions v0.9.5 [497a8b3b] DoubleFloats v1.7.1 [90fa49ef] ErrorfreeArithmetic v0.5.2 [7a1cc6ca] FFTW v1.10.0 [fa42c844] FastRounding v0.3.1 [5789e2e9] FileIO v1.18.0 ⌅ [14197337] GenericLinearAlgebra v0.3.19 [c145ed77] GenericSchur v0.5.6 [076d061b] HashArrayMappedTries v0.2.0 ⌅ [d1acc4aa] IntervalArithmetic v0.20.9 [92d709cd] IrrationalConstants v0.2.6 [033835bb] JLD2 v0.6.4 [692b3bcd] JLLWrappers v1.7.1 [2ab3a3ac] LogExpFunctions v0.3.29 [1914dd2f] MacroTools v0.5.16 ⌅ [bdf0d083] MultiFloats v2.3.0 [bac558e1] OrderedCollections v1.8.1 [aea7be01] PrecompileTools v1.3.3 [21216c6a] Preferences v1.5.2 [be4d8f0f] Quadmath v1.0.1 [0d4725de] Readables v0.3.3 [3cdcf5f2] RecipesBase v1.3.4 [189a3867] Reexport v1.2.2 [ae029012] Requires v1.3.1 [5eaf0fd0] RoundingEmulator v0.2.1 [fdea26ae] SIMD v3.7.2 [7e506255] ScopedValues v1.6.0 [3cc68bcd] SetRounding v0.2.1 [276daf66] SpecialFunctions v2.7.2 [90137ffa] StaticArrays v1.9.18 [1e83bf80] StaticArraysCore v1.4.4 [4e9b3aee] CRlibm_jll v1.0.1+0 [f5851436] FFTW_jll v3.3.11+0 [e134572f] FLINT_jll v301.400.1+0 [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0 [856f044c] MKL_jll v2025.2.0+0 [656ef2d0] OpenBLAS32_jll v0.3.30+0 [6cdc7f73] OpenBLASConsistentFPCSR_jll v0.3.30+0 [efe28fd5] OpenSpecFun_jll v0.5.6+0 [1317d2d5] oneTBB_jll v2022.0.0+1 [0dad84c5] ArgTools v1.1.2 [56f22d72] Artifacts v1.11.0 [2a0f44e3] Base64 v1.11.0 [ade2ca70] Dates v1.11.0 [8ba89e20] Distributed v1.11.0 [f43a241f] Downloads v1.7.0 [7b1f6079] FileWatching v1.11.0 [b77e0a4c] InteractiveUtils v1.11.0 [ac6e5ff7] JuliaSyntaxHighlighting v1.13.0 [4af54fe1] LazyArtifacts v1.11.0 [b27032c2] LibCURL v1.0.0 [76f85450] LibGit2 v1.11.0 [8f399da3] Libdl v1.11.0 [37e2e46d] LinearAlgebra v1.13.0 [56ddb016] Logging v1.11.0 [d6f4376e] Markdown v1.11.0 [a63ad114] Mmap v1.11.0 [ca575930] NetworkOptions v1.3.0 [44cfe95a] Pkg v1.14.0 [de0858da] Printf v1.11.0 [9a3f8284] Random v1.11.0 [ea8e919c] SHA v1.0.0 [9e88b42a] Serialization v1.11.0 [6462fe0b] Sockets v1.11.0 [f489334b] StyledStrings v1.13.0 [fa267f1f] TOML v1.0.3 [a4e569a6] Tar v1.10.0 [8dfed614] Test v1.11.0 [cf7118a7] UUIDs v1.11.0 [4ec0a83e] Unicode v1.11.0 [e66e0078] CompilerSupportLibraries_jll v1.3.0+1 [781609d7] GMP_jll v6.3.0+2 [deac9b47] LibCURL_jll v8.19.0+0 [e37daf67] LibGit2_jll v1.9.2+0 [29816b5a] LibSSH2_jll v1.11.3+1 [3a97d323] MPFR_jll v4.2.2+0 [14a3606d] MozillaCACerts_jll v2026.3.19 [4536629a] OpenBLAS_jll v0.3.30+0 [05823500] OpenLibm_jll v0.8.7+0 [458c3c95] OpenSSL_jll v3.5.6+0 [efcefdf7] PCRE2_jll v10.47.0+0 [83775a58] Zlib_jll v1.3.2+0 [3161d3a3] Zstd_jll v1.5.7+1 [8e850b90] libblastrampoline_jll v5.15.0+0 [8e850ede] nghttp2_jll v1.69.0+0 [3f19e933] p7zip_jll v17.8.0+0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. Testing Running tests... ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees └ correct floating point rounding mode over all threads. [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads ┌ Warning: Global bound failed: ‖I - Gg‖₂ >= 1, eigenvectors not sufficiently orthogonal └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/eigenvalues/verified_gev.jl:239 ┌ Warning: Eigenvector bound 1: ρᵢ ≤ 0 or infinite, eigenvalues not separated └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/eigenvalues/verified_gev.jl:426 ┌ Warning: Eigenvector bound 2: ρᵢ ≤ 0 or infinite, eigenvalues not separated └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/eigenvalues/verified_gev.jl:426 ┌ Warning: Eigenvector bound 3: ρᵢ ≤ 0 or infinite, eigenvalues not separated └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/eigenvalues/verified_gev.jl:426 ┌ Warning: Some eigenvector bounds are infinite └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/eigenvalues/verified_gev.jl:573 ┌ Warning: Global bound failed: ‖I - Gg‖₂ >= 1, eigenvectors not sufficiently orthogonal └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/eigenvalues/verified_gev.jl:239 ┌ Warning: triangular_sylvester_miyajima_enclosure(BallMatrix): separation ≤ 0 after accounting for radii. Perturbation bound is infinite. └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/linear_system/sylvester.jl:299 ┌ Warning: MiyajimaM4 via `rigorous_svd(A; method=MiyajimaM4())` falls back to M1 bounds. Use `rigorous_svd_m4(A)` for the full Theorem 11 eigendecomposition-based approach. └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/svd.jl:358 === Miyajima M1 vs Rump Original Comparison === σ1: M1 radius = 3.9968028886505635e-14, Rump radius = 4.440892098500626e-14 Improvement: 10.0% σ2: M1 radius = 3.68594044175552e-14, Rump radius = 3.9968028886505635e-14 Improvement: 7.8% σ3: M1 radius = 3.3861802251067274e-14, Rump radius = 3.497202527569243e-14 Improvement: 3.2% [ Info: Refining SVD at precision 106 bits (step 1/2) [ Info: After refinement: max radius = 1.010000000000000036231063791790297732838075500660934835650550667196512222290039e-10 [ Info: Refining SVD at precision 212 bits (step 2/2) [ Info: After refinement: max radius = 1.010000000000000036231063791790297732838075500660934835650550667196512222290039e-10 ┌ Warning: Maximum refinement iterations reached. Final max radius: 1.010000000000000036231063791790297732838075500660934835650550667196512222290039e-10, target: 1.0e-10 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:467 [ Info: Refining SVD at precision 106 bits (step 1/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 212 bits (step 2/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 424 bits (step 3/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 848 bits (step 4/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 1024 bits (step 5/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 ┌ Warning: Maximum precision reached without achieving tolerance └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:461 ┌ Warning: Maximum refinement iterations reached. Final max radius: 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10, target: 1.0e-12 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:467 [ Info: Refining SVD at precision 106 bits (step 1/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 212 bits (step 2/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 424 bits (step 3/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 848 bits (step 4/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 [ Info: Refining SVD at precision 1024 bits (step 5/5) [ Info: After refinement: max radius = 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10 ┌ Warning: Maximum precision reached without achieving tolerance └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:461 ┌ Warning: Maximum refinement iterations reached. Final max radius: 3.0000000000000001092965919464932247374966411967989188269712030887603759765625e-10, target: 1.0e-12 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:467 [ Info: Refining SVD at precision 106 bits (step 1/3) [ Info: After refinement: max radius = 2.000000000000000072864394630995483158331094131199279217980802059173583984375e-10 [ Info: Refining SVD at precision 128 bits (step 2/3) [ Info: After refinement: max radius = 2.000000000000000072864394630995483158331094131199279217980802059173583984375e-10 ┌ Warning: Maximum precision reached without achieving tolerance └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:461 ┌ Warning: Maximum refinement iterations reached. Final max radius: 2.000000000000000072864394630995483158331094131199279217980802059173583984375e-10, target: 1.0e-100 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:467 [ Info: Refining SVD at precision 106 bits (step 1/2) [ Info: After refinement: max radius = 1.999999999999999997638618709119797394268658145832784356343836462448629002085647e-14 [ Info: Refining SVD at precision 212 bits (step 2/2) [ Info: After refinement: max radius = 1.999999999999999997638618709119797394268658145832784356343836462448629002085647e-14 ┌ Warning: Maximum refinement iterations reached. Final max radius: 1.999999999999999997638618709119797394268658145832784356343836462448629002085647e-14, target: 1.0e-18 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/decompositions/svd/adaptive_ogita_svd.jl:467 All adaptive Ogita SVD tests passed! All sub-ε certification tests passed! ┌ Warning: ogita_svd_cascade not available (MultiFloats extension not loaded) └ @ Main ~/.julia/packages/BallArithmetic/TCPcX/test/test_decompositions/test_svd/test_precision_cascade_svd.jl:149 All precision cascade SVD tests passed! All GenericLinearAlgebra SVD tests passed! μ=0.1: ψ=1.0512492197250396, 1/(1-μ)=1.1111111111111112, ratio=0.9461242977525356 μ=0.3: ψ=1.1611874208078345, 1/(1-μ)=1.4285714285714286, ratio=0.8128311945654841 μ=0.5: ψ=1.2807764064044154, 1/(1-μ)=2.0, ratio=0.6403882032022077 μ=0.7: ψ=1.4094810050208548, 1/(1-μ)=3.333333333333333, ratio=0.42284430150625646 μ=0.9: ψ=1.5465856099730657, 1/(1-μ)=10.000000000000002, ratio=0.15465856099730654 μ=1.0: ψ=1.6180339887498951 (old bound would be undefined) μ=1.5: ψ=2.0000000000000004 (old bound would be undefined) μ=2.0: ψ=2.4142135623730954 (old bound would be undefined) μ=3.0: ψ=3.3027756377319957 (old bound would be undefined) m=2: 2023=3.9331911336341423, 2024=4.175866137491631, true=4.752337568743529 Improvement: 1.0616992654596127 m=5: 2023=3.9679950469851963, 2024=4.3461389863276985, true=4.752337568743529 Improvement: 1.0952984907654582 m=9: 2023=4.318544168103696, 2024=4.53580609932415, true=4.752337568743529 Improvement: 1.0503090677699043 Test case where 2023 may fail: Oishi 2023: verified=true, ‖A⁻¹B‖=0.9682458365518543, ‖CA⁻¹‖=0.9682458365518543 Rump-Oishi 2024: verified=true, σ_min_lower=0.04912566814016744, true=0.06350832689629163 Fast γ bound test: With fast γ: used=true, σ_min_lower=0.8483739911363939 Without fast γ: σ_min_lower=0.8483739911363939 Optimal block size: m=14, σ_min_lower=1.033555379145975, true=1.0753086208212534 Paper Example 3 (k=0.9, n=50, m=20): True ‖G⁻¹‖ ≈ 2.3881899286854913 Oishi 2023: ‖G⁻¹‖ ≤ 3.7548445188744894 Rump-Oishi 2024: ‖G⁻¹‖ ≤ 2.9231444178655694 m=1: σ_min_lower=3.923554137443023, σ_true=4.752337568743529, ratio=0.825605100792613 m=3: σ_min_lower=3.8974112726755794, σ_true=4.752337568743529, ratio=0.8201040469660946 m=5: σ_min_lower=3.9679950469851963, σ_true=4.752337568743529, ratio=0.8349564797507207 m=9: σ_min_lower=4.318544168103696, σ_true=4.752337568743529, ratio=0.908719994241797 Optimal block size: m=11, σ_min_lower=9.519969928682382, σ_true=9.811379604392224 Comparison with SVD methods: True σ_min = 9.350992551270204 Oishi 2023 lower bound = 8.085625816068415 SVD lower bound = 9.35099255127012 BigFloat (256-bit) Oishi 2023: σ_min_lower = 9.191957147103954 σ_true ≈ 9.723832868730351 Ratio = 0.9453018445702837 ┌ Warning: ‖F‖ = 1.0 ≥ 1, bound may be loose or invalid └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/norm_bounds/rump_oishi_2024.jl:126 ┌ Warning: ‖F‖ = 1.0 ≥ 1, bound may be loose or invalid └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/norm_bounds/rump_oishi_2024.jl:126 [ Info: ("Computing exclusion circle ", 2.0) Triangular inverse bounds: ‖U⁻¹‖_∞: bound=0.9128772424635796, true=0.9111811522730199, ratio=1.0018614193086948 ‖U⁻¹‖_1: bound=0.8609286289455271, true=0.8609286289455271, ratio=1.0 ‖U⁻¹‖_2: bound=0.8865225054953445, true=0.8613924430892194, ratio=1.0291737669719982 Sylvester oracle residual: 7.244937139023184e-17 Precomputation results: Sylvester Resolvent Bound Diagnostics ======================================== Matrix size: 20 × 20 Split index k: 5 Small block: 5 × 5 Large block: 15 × 15 Norms: ‖R‖₂ (residual): 1.5146726115701608e-16 ‖T₁₂‖₂ (coupling): 0.9668861315505904 κ₂(S(X̃)) (penalty): 1.2113445869329509 Quality indicators: reduction = r/‖T₁₂‖: 1.5665470443154334e-16 ✓ excellent penalty = κ₂(S): 1.2113445869329509 ✓ excellent net = pen × red: 1.8976282823073138e-16 ✓ excellent V1 resolvent bound at z=3.5 + 1.0im: Certified bound: 2.541622398227329 True value: 1.6018451276178394 Overestimation: 1.586684227086963x z = 3.5 + 1.0im ‖(zI-T)⁻¹‖₂ ≤ 2.541622398227329 Components: M_A=1.5994662571305527, M_D=0.4799070762220216, coupling=1.5863904348338518e-16 V2 resolvent bound at z=3.5 + 1.0im: z = 3.5 + 1.0im V2 bound: ‖(zI-T)⁻¹‖₂ ≤ 2.541622398227329 V1 bound: ‖(zI-T)⁻¹‖₂ ≤ 2.541622398227329 Improvement: 0.0% Components: M_A = 1.5994662571305527 M_D = 0.4799070762220216 M_AR = 2.2119661188953638e-16 (V2) coupling_v1 = 1.5863904348338518e-16 coupling_v2 = 1.0615381928212467e-16 tightening = 0.669153172833159 ‖Δ‖ = 3.6806987487581356e-32 True value: 1.6018451276178394 V1 vs V2 comparison: z=5.0 + 1.0im: V1: 18.399471566472585 (1.1742577699309849x) V2: 18.399471566472585 (1.1742577699309849x) Improvement: 0.0% Tightening ratio: 0.6908664295633616 z=10.0 + 2.0im: V1: 15.858072374164827 (1.2751491961616843x) V2: 15.858072374164827 (1.2751491961616843x) Improvement: 0.0% Tightening ratio: 1.0 z=15.0 + 0.5im: V1: 0.6184895053567019 (1.5095219658494603x) V2: 0.6184895053567019 (1.5095219658494603x) Improvement: 0.0% Tightening ratio: 1.0 z at T11 eigenvalue: success=false, reason=σ_min(A_z) ≤ 0: z is at or very near an eigenvalue of T11 z at T22 eigenvalue: success=false, bound=Inf Optimal split selection: V1: best_k=2, bound=2.476596824830035 V2: best_k=2, bound=2.476596824830035 V3 resolvent bound at z=3.5 + 1.0im: z = 3.5 + 1.0im V3 bound: ‖(zI-T)⁻¹‖₂ ≤ 2.623348329760588 V1 bound: ‖(zI-T)⁻¹‖₂ ≤ 2.541622398227329 Overall improvement: -3.2% Components: M_A = 1.5994662571305527 M_D (V3 Neumann) = 0.5467693775584367 M_D (V1 triang.) = 0.4799070762220216 M_D improvement: -13.9% M_AR = 2.2119661188953638e-16 coupling = 1.209435338008769e-16 Neumann diagnostics: α = ‖N_z‖₂ ≤ 0.16755060243148837 gap = 1-α = 0.8324493975685117 ‖(D_z)_d⁻¹‖₂ = 0.4551578389574307 Neumann certified: true True value: 1.6018451276178394 Neumann certified with α=0.16755060243148837 Collatz-Neumann internals: α = ‖N_z‖₂ ≤ 0.54540470150115 ‖(D_z)_d⁻¹‖₂ = 2.3410722167984566 Neumann success: true M_D = 5.149794167535542 gap = 0.45459529849885005 True ‖D_z⁻¹‖₂ = 2.3554473459897243 V1 vs V2 vs V3 comparison at z=10.0 + 2.0im: True: 12.436248575381669 V1: 15.858072374164827 (1.2751491961616843x) V2: 15.858072374164827 (1.2751491961616843x) V3: 15.858072374164827 (1.2751491961616843x) V3 M_D: 13.675081145578726 vs V1 M_D: 13.675081145578726 V3 α: 1.6940147452062948, gap: -0.6940147452062948 Neumann failure test: α = 27.134392242348735 success = false V3 overall success: true Neumann certified: false Bound: 14255.69963463909, true: 2768.028970862225 Norm estimators test: True ‖M‖₂: 5.210165605358989 OneInfNorm: 10.554175709158052 (2.025689106369749x) FrobeniusNorm: 9.924437504287397 (1.904821891664917x) RowCol2Norm: 3.9261666916894815 Neumann 1/∞ bound test: α∞ = 0.2979944143372266 α₁ = 0.18352572319755067 Success: true M_D = 0.529117238238481 (true: 0.40188256505977316) Parametric framework comparison at z=10.0 + 2.0im: True: 12.436248575381669 V1: 15.858072374164832 (1.2751491961616848x) V2: 15.858072374164832 (1.2751491961616848x) V2.5: 15.858072374164832 (1.2751491961616848x) V3: 15.858072374164832 (1.2751491961616848x) compare_all_configs test: Best method: V3 V3: 49.91346715102321 V1: 49.91346715102321 V2: 49.91346715102321 V2.5: 49.91346715102321 SVDWarmStart test: z1 = 10.0 + 2.0im, z2 = 10.05 + 2.02im Cold start: 9.538910025360337 Warm start: 9.5389100253754 Relative difference: 1.5789780594670992e-12 Off-diagonal direct bound test: Product bound (M_A·r·M_D): 6.482932214636611e-16 Direct bound (M_off): 4.304455211854661e-17 Tightening ratio: 0.06639673328893413 Residual fallback — small well-conditioned: Direct max radius: 2.1705188888032406e-15 Residual max radius: 2.1705188888032406e-15 Residual fallback — k=4 coupling: Direct max radius: 1.1660230302462319e-15 Residual max radius: 1.1660230302462319e-15 All verified H-matrix linear system tests passed! ┌ Warning: Krawczyk Sylvester: Estimated contraction >= 1 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/linear_system/krawczyk_complete.jl:313 ┌ Warning: Krawczyk Sylvester: Estimated contraction >= 1 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/linear_system/krawczyk_complete.jl:313 ┌ Warning: Krawczyk Sylvester: Estimated contraction >= 1 └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/linear_system/krawczyk_complete.jl:313 ┌ Warning: Gaussian elimination: Zero pivot at last position, matrix may be singular └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/linear_system/gaussian_elimination.jl:170 ┌ Warning: LDLT factorization failed: MethodError(LinearAlgebra.ldlt, ([3.0 1.0; 1.0 2.0],), 0x000000000000a14b), falling back to LU └ @ BallArithmetic ~/.julia/packages/BallArithmetic/TCPcX/src/linear_system/preconditioning.jl:156 ✓ All Horáček method tests completed successfully! ┌ Info: Processed 4 arcs (serial) │ remaining = 4 └ new_ratio = 0.0 ┌ Info: Processed 8 arcs (serial) │ remaining = 0 └ new_ratio = 0.0 [ Info: The ϵ in the Schur theorems 2.6645352591003765e-15 ┌ Info: Processed 4 arcs (serial) │ remaining = 4 └ new_ratio = 0.0 ┌ Info: Processed 8 arcs (serial) │ remaining = 0 └ new_ratio = 0.0 [ Info: The ϵ in the Schur theorems 2.6645352591003765e-15 ┌ Info: Processed 4 arcs (serial) │ remaining = 4 └ new_ratio = 0.0 ┌ Info: Processed 8 arcs (serial) │ remaining = 0 └ new_ratio = 0.0 [ Info: The ϵ in the Schur theorems 2.6645352591003765e-15 From worker 2: ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees From worker 2: └ correct floating point rounding mode over all threads. From worker 2: [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads [ Info: Starting adaptive refinement, arcs, 8, pending, 0 ┌ Info: Pending from snapshot │ length(pending) = 0 └ id_counter = 1 [ Info: Waited for all pending to be computed, arcs, 8, pending, 0 [ Info: Waiting for all pending jobs... ┌ Info: Waiting for pending └ length(pending) = 5 [ Info: Restarting refinement cycle with new arcs: 8 [ Info: Processed 4 arcs... ┌ Info: Remaining arcs └ length(arcs) = 4 ┌ Info: Pending jobs └ length(pending) = 0 ┌ Info: New arcs ratio └ new / check_interval = 0.0 [ Info: Saved in /tmp/jl_hUlQzUxe1M_A.jld2, arcs 4, pending 0 [ Info: Processed 8 arcs... ┌ Info: Remaining arcs └ length(arcs) = 0 ┌ Info: Pending jobs └ length(pending) = 0 ┌ Info: New arcs ratio └ new / check_interval = 0.0 [ Info: Saved in /tmp/jl_hUlQzUxe1M_B.jld2, arcs 0, pending 0 [ Info: Waiting for all pending jobs... [ Info: Restarting refinement cycle with new arcs: 0 [ Info: Adaptive refinement complete [ Info: The ϵ in the Schur theorems 2.6645352591003765e-15 ┌ Info: certification worker stopped after channels closed │ reason = InvalidStateException: Channel is closed. │ reason_message = "InvalidStateException: Channel is closed." │ exception = │ InvalidStateException: Channel is closed. │ Stacktrace: │ [1] remotecall_fetch(f::Function, w::Distributed.Worker, args::Distributed.RRID; kwargs::@Kwargs{}) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:467 │ [2] remotecall_fetch(f::Function, w::Distributed.Worker, args::Distributed.RRID) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:456 │ [3] remotecall_fetch │ @ /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:494 [inlined] │ [4] call_on_owner │ @ /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:567 [inlined] │ [5] fetch(r::Future) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:621 │ [6] _run_certification_distributed(A::BallMatrix{Float64, ComplexF64, Ball{Float64, ComplexF64}, Matrix{ComplexF64}, Matrix{Float64}}, circle::BallArithmetic.CertifScripts.CertificationCircle, worker_ids::Vector{Int64}; schur_data::Nothing, polynomial::Nothing, η::Float64, check_interval::Int64, snapshot_path::Nothing, log_io::IOBuffer, channel_capacity::Int64, Cbound::Float64, cleanup_workers::Bool, use_ogita_cache::Bool, ogita_distance_threshold::Float64, ogita_quality_threshold::Float64, ogita_iterations::Int64, use_bigfloat_ogita::Bool, target_precision::Int64, max_ogita_iterations::Int64, use_parametric::Bool, parametric_k::Nothing, parametric_config::ResolventBoundConfig, parametric_distance_threshold::Float64) │ @ DistributedExt ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:263 │ [7] _run_certification_distributed │ @ ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:49 [inlined] │ [8] run_certification(A::BallMatrix{Float64, ComplexF64, Ball{Float64, ComplexF64}, Matrix{ComplexF64}, Matrix{Float64}}, circle::BallArithmetic.CertifScripts.CertificationCircle, num_workers::Int64; kwargs::@Kwargs{η::Float64, check_interval::Int64, log_io::IOBuffer, channel_capacity::Int64}) │ @ DistributedExt ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:392 [inlined] │ [9] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:34 │ [10] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [11] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:37 [inlined] │ [12] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [13] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:6 │ [14] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [15] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:74 [inlined] │ [16] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [17] top-level scope │ @ none:6 │ [18] eval(m::Module, e::Any) │ @ Core ./boot.jl:517 │ [19] exec_options(opts::Base.JLOptions) │ @ Base ./client.jl:318 │ [20] _start() └ @ Base ./client.jl:593 From worker 2: Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') From worker 2: -> Autodetected symbol suffix "64_" From worker 2: -> Autodetected interface ILP64 (64-bit) From worker 2: -> Autodetected normal complex return style From worker 2: -> Autodetected gfortran calling convention From worker 2: -> CBLAS detected From worker 2: Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" From worker 3: ┌ Info: Switching to OpenBLAS with ConsistentFPCSR = 1 flag enabled, guarantees From worker 3: └ correct floating point rounding mode over all threads. From worker 3: [ Info: OpenBLAS is giving correct rounding on a (1024,1024) test matrix on 1 threads [ Info: Starting adaptive refinement, arcs, 8, pending, 0 ┌ Info: Pending from snapshot │ length(pending) = 0 └ id_counter = 1 [ Info: Waited for all pending to be computed, arcs, 8, pending, 0 [ Info: Waiting for all pending jobs... ┌ Info: Waiting for pending └ length(pending) = 5 [ Info: Restarting refinement cycle with new arcs: 8 [ Info: Processed 4 arcs... ┌ Info: Remaining arcs └ length(arcs) = 4 ┌ Info: Pending jobs └ length(pending) = 0 ┌ Info: New arcs ratio └ new / check_interval = 0.0 [ Info: Saved in /tmp/jl_RitwPeV8xA_A.jld2, arcs 4, pending 0 [ Info: Processed 8 arcs... ┌ Info: Remaining arcs └ length(arcs) = 0 ┌ Info: Pending jobs └ length(pending) = 0 ┌ Info: New arcs ratio └ new / check_interval = 0.0 [ Info: Saved in /tmp/jl_RitwPeV8xA_B.jld2, arcs 0, pending 0 [ Info: Waiting for all pending jobs... [ Info: Restarting refinement cycle with new arcs: 0 [ Info: Adaptive refinement complete [ Info: The ϵ in the Schur theorems 2.6645352591003765e-15 ┌ Info: certification worker stopped after channels closed │ reason = InvalidStateException: Channel is closed. │ reason_message = "InvalidStateException: Channel is closed." │ exception = │ InvalidStateException: Channel is closed. │ Stacktrace: │ [1] remotecall_fetch(f::Function, w::Distributed.Worker, args::Distributed.RRID; kwargs::@Kwargs{}) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:467 │ [2] remotecall_fetch(f::Function, w::Distributed.Worker, args::Distributed.RRID) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:456 │ [3] remotecall_fetch │ @ /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:494 [inlined] │ [4] call_on_owner │ @ /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:567 [inlined] │ [5] fetch(r::Future) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:621 │ [6] _run_certification_distributed(A::BallMatrix{Float64, ComplexF64, Ball{Float64, ComplexF64}, Matrix{ComplexF64}, Matrix{Float64}}, circle::BallArithmetic.CertifScripts.CertificationCircle, worker_ids::Vector{Int64}; schur_data::Nothing, polynomial::Nothing, η::Float64, check_interval::Int64, snapshot_path::Nothing, log_io::IOBuffer, channel_capacity::Int64, Cbound::Float64, cleanup_workers::Bool, use_ogita_cache::Bool, ogita_distance_threshold::Float64, ogita_quality_threshold::Float64, ogita_iterations::Int64, use_bigfloat_ogita::Bool, target_precision::Int64, max_ogita_iterations::Int64, use_parametric::Bool, parametric_k::Nothing, parametric_config::ResolventBoundConfig, parametric_distance_threshold::Float64) │ @ DistributedExt ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:263 │ [7] collect(A::Vector{Int64}) │ @ Base ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:49 [inlined] │ [8] run_certification(A::BallMatrix{Float64, ComplexF64, Ball{Float64, ComplexF64}, Matrix{ComplexF64}, Matrix{Float64}}, circle::BallArithmetic.CertifScripts.CertificationCircle, pool::WorkerPool; kwargs::@Kwargs{η::Float64, check_interval::Int64, log_io::IOBuffer, channel_capacity::Int64}) │ @ DistributedExt ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:398 │ [9] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:34 │ [10] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [11] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:44 [inlined] │ [12] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [13] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:6 │ [14] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [15] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:74 [inlined] │ [16] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [17] top-level scope │ @ none:6 │ [18] eval(m::Module, e::Any) │ @ Core ./boot.jl:517 │ [19] exec_options(opts::Base.JLOptions) │ @ Base ./client.jl:318 │ [20] _start() └ @ Base ./client.jl:593 [ Info: Starting adaptive refinement, arcs, 8, pending, 0 ┌ Info: Pending from snapshot │ length(pending) = 0 └ id_counter = 1 [ Info: Waited for all pending to be computed, arcs, 8, pending, 0 [ Info: Waiting for all pending jobs... ┌ Info: Waiting for pending └ length(pending) = 5 [ Info: Restarting refinement cycle with new arcs: 8 [ Info: Processed 4 arcs... ┌ Info: Remaining arcs └ length(arcs) = 4 ┌ Info: Pending jobs └ length(pending) = 0 ┌ Info: New arcs ratio └ new / check_interval = 0.0 [ Info: Saved in /tmp/jl_bIdcnw1UPy_A.jld2, arcs 4, pending 0 [ Info: Processed 8 arcs... ┌ Info: Remaining arcs └ length(arcs) = 0 ┌ Info: Pending jobs └ length(pending) = 0 ┌ Info: New arcs ratio └ new / check_interval = 0.0 [ Info: Saved in /tmp/jl_bIdcnw1UPy_B.jld2, arcs 0, pending 0 [ Info: Waiting for all pending jobs... [ Info: Restarting refinement cycle with new arcs: 0 [ Info: Adaptive refinement complete [ Info: The ϵ in the Schur theorems 2.6645352591003765e-15 ┌ Info: certification worker stopped after channels closed │ reason = InvalidStateException: Channel is closed. │ reason_message = "InvalidStateException: Channel is closed." │ exception = │ InvalidStateException: Channel is closed. │ Stacktrace: │ [1] remotecall_fetch(f::Function, w::Distributed.Worker, args::Distributed.RRID; kwargs::@Kwargs{}) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:467 │ [2] remotecall_fetch(f::Function, w::Distributed.Worker, args::Distributed.RRID) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:456 │ [3] remotecall_fetch │ @ /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:494 [inlined] │ [4] call_on_owner │ @ /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:567 [inlined] │ [5] fetch(r::Future) │ @ Distributed /opt/julia/share/julia/stdlib/v1.14/Distributed/src/remotecall.jl:621 │ [6] _run_certification_distributed(A::BallMatrix{Float64, ComplexF64, Ball{Float64, ComplexF64}, Matrix{ComplexF64}, Matrix{Float64}}, circle::BallArithmetic.CertifScripts.CertificationCircle, worker_ids::Vector{Int64}; schur_data::Nothing, polynomial::Nothing, η::Float64, check_interval::Int64, snapshot_path::Nothing, log_io::IOBuffer, channel_capacity::Int64, Cbound::Float64, cleanup_workers::Bool, use_ogita_cache::Bool, ogita_distance_threshold::Float64, ogita_quality_threshold::Float64, ogita_iterations::Int64, use_bigfloat_ogita::Bool, target_precision::Int64, max_ogita_iterations::Int64, use_parametric::Bool, parametric_k::Nothing, parametric_config::ResolventBoundConfig, parametric_distance_threshold::Float64) │ @ DistributedExt ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:263 │ [7] collect(A::Vector{Int64}) │ @ Base ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:49 [inlined] │ [8] run_certification(A::BallMatrix{Float64, ComplexF64, Ball{Float64, ComplexF64}, Matrix{ComplexF64}, Matrix{Float64}}, circle::BallArithmetic.CertifScripts.CertificationCircle, pool::WorkerPool; kwargs::@Kwargs{η::Float64, check_interval::Int64, log_io::IOBuffer, channel_capacity::Int64}) │ @ DistributedExt ~/.julia/packages/BallArithmetic/TCPcX/ext/DistributedExt.jl:398 │ [9] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:34 │ [10] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [11] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:48 [inlined] │ [12] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [13] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:6 │ [14] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [15] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:74 [inlined] │ [16] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [17] top-level scope │ @ none:6 │ [18] eval(m::Module, e::Any) │ @ Core ./boot.jl:517 │ [19] exec_options(opts::Base.JLOptions) │ @ Base ./client.jl:318 │ [20] _start() └ @ Base ./client.jl:593 From worker 3: Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') From worker 3: -> Autodetected symbol suffix "64_" From worker 3: -> Autodetected interface ILP64 (64-bit) From worker 3: -> Autodetected normal complex return style From worker 3: -> Autodetected gfortran calling convention From worker 3: -> CBLAS detected From worker 3: Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" Error encountered while load FileIO.File{FileIO.DataFormat{:JLD2}, String}("/tmp/jl_hmqrgF/snap3_B.jld2"). Fatal error: ┌ Warning: Could not load snapshot file /tmp/jl_hmqrgF/snap3_B.jld2, possibly corrupted. Trying backup. │ exception = │ EOFError: read end of file │ Stacktrace: │ [1] jldopen(fname::String, wr::Bool, create::Bool, truncate::Bool, iotype::Type{JLD2.MmapIO}; fallback::Type{IOStream}, compress::Bool, mmaparrays::Bool, typemap::Function, parallel_read::Bool, plain::Bool) │ @ JLD2 ~/.julia/packages/JLD2/qcxKY/src/JLD2.jl:242 │ [2] jldopen │ @ ~/.julia/packages/JLD2/qcxKY/src/JLD2.jl:174 [inlined] │ [3] jldopen(fname::String, mode::String; iotype::Type{JLD2.MmapIO}, kwargs::@Kwargs{}) │ @ JLD2 ~/.julia/packages/JLD2/qcxKY/src/JLD2.jl:296 [inlined] │ [4] jldopen(fname::String, mode::String) │ @ JLD2 ~/.julia/packages/JLD2/qcxKY/src/JLD2.jl:290 [inlined] │ [5] fileio_load(f::FileIO.File{FileIO.DataFormat{:JLD2}, String}; nested::Bool, kwargs::@Kwargs{}) │ @ JLD2 ~/.julia/packages/JLD2/qcxKY/src/fileio.jl:38 │ [6] fileio_load(f::FileIO.File{FileIO.DataFormat{:JLD2}, String}) │ @ JLD2 ~/.julia/packages/JLD2/qcxKY/src/fileio.jl:37 │ [7] action(::Symbol, ::Vector{Union{Base.PkgId, Module}}, ::FileIO.Formatted; options::@Kwargs{}) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:219 │ [8] action │ @ ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:196 [inlined] │ [9] _isurl(path::String) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:185 [inlined] │ [10] checkpath_load(file::String) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:185 [inlined] │ [11] load(::String; options::@Kwargs{}) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:113 │ [12] choose_snapshot_to_load(basepath::String) │ @ BallArithmetic.CertifScripts ~/.julia/packages/BallArithmetic/TCPcX/src/pseudospectra/CertifScripts.jl:1010 │ [13] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:315 [inlined] │ [14] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [15] (::var"#340#341"{Module})(dir::String) │ @ Main ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:305 │ [16] mktempdir(fn::var"#340#341"{Module}, parent::String; prefix::String) │ @ Base.Filesystem ./file.jl:936 │ [17] mktempdir(fn::Function, parent::String) │ @ Base.Filesystem ./file.jl:932 │ [18] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:269 │ [19] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [20] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:271 [inlined] │ [21] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [22] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:6 │ [23] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [24] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:74 [inlined] │ [25] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [26] top-level scope │ @ none:6 │ [27] eval(m::Module, e::Any) │ @ Core ./boot.jl:517 │ [28] exec_options(opts::Base.JLOptions) │ @ Base ./client.jl:318 │ [29] _start() │ @ Base ./client.jl:593 │ Stacktrace: │ [1] handle_error(e::EOFError, q::Base.PkgId, bt::Vector{Union{Ptr{Nothing}, Base.InterpreterIP}}) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/error_handling.jl:73 │ [2] handle_exceptions(exceptions::Vector{Tuple{Any, Union{Base.PkgId, Module}, Vector}}, action::String) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/error_handling.jl:66 │ [3] action(::Symbol, ::Vector{Union{Base.PkgId, Module}}, ::FileIO.Formatted; options::@Kwargs{}) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:228 │ [4] action │ @ ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:196 [inlined] │ [5] _isurl(path::String) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:185 [inlined] │ [6] checkpath_load(file::String) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:185 [inlined] │ [7] load(::String; options::@Kwargs{}) │ @ FileIO ~/.julia/packages/FileIO/ZlWq2/src/loadsave.jl:113 │ [8] choose_snapshot_to_load(basepath::String) │ @ BallArithmetic.CertifScripts ~/.julia/packages/BallArithmetic/TCPcX/src/pseudospectra/CertifScripts.jl:1010 │ [9] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:315 [inlined] │ [10] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [11] (::var"#340#341"{Module})(dir::String) │ @ Main ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:305 │ [12] mktempdir(fn::var"#340#341"{Module}, parent::String; prefix::String) │ @ Base.Filesystem ./file.jl:936 │ [13] mktempdir(fn::Function, parent::String) │ @ Base.Filesystem ./file.jl:932 │ [14] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:269 │ [15] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [16] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/test_certification/test_certifscripts.jl:271 [inlined] │ [17] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [18] top-level scope │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:6 │ [19] macro expansion │ @ /opt/julia/share/julia/stdlib/v1.14/Test/src/Test.jl:2246 [inlined] │ [20] macro expansion │ @ ~/.julia/packages/BallArithmetic/TCPcX/test/runtests.jl:74 [inlined] │ [21] include(mapexpr::Function, mod::Module, _path::String) │ @ Base ./Base.jl:327 │ [22] top-level scope │ @ none:6 │ [23] eval(m::Module, e::Any) │ @ Core ./boot.jl:517 │ [24] exec_options(opts::Base.JLOptions) │ @ Base ./client.jl:318 │ [25] _start() │ @ Base ./client.jl:593 └ @ BallArithmetic.CertifScripts ~/.julia/packages/BallArithmetic/TCPcX/src/pseudospectra/CertifScripts.jl:1013 SVD refinement timing (n=50, 3 runs): Double64 (2 iters): 0.292s BigFloat (2 iters): 12.353s Speedup: 42.3× Quadratic convergence test: Iteration 1: residual = 2.7321155727500664e-26 Iteration 2: residual = 3.47854823219106e-31 Iteration 3: residual = 4.072230442138127e-31 Iteration 4: residual = 3.237772987016434e-31 Test Summary: | Pass Broken Total Time BallArithmetic.jl | 2417 15 2432 28m52.6s Generating forwards to /home/pkgeval/.julia/artifacts/dbf2792c710de82713d9ff1fea46d24ec811e15b/lib/libopenblas64_.so (clear: 0, verbose: 1, suffix_hint: '(null)') -> Autodetected symbol suffix "64_" -> Autodetected interface ILP64 (64-bit) -> Autodetected normal complex return style -> Autodetected gfortran calling convention -> CBLAS detected Processed 5146 symbols; forwarded 5067 symbols with 64-bit interface and mangling to a suffix of "64_" Testing BallArithmetic tests passed Testing completed after 1747.43s PkgEval succeeded after 1897.55s