oneMKL potrf on GPU reports the failing column relative to its 32-column panel
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评估
调研方向
Start with the onemkl<T>potrf shim and the LinearAlgebra.LAPACK.potrf! changes referenced in #754; compare the raw oneMKL info with the failing diagonal entry in the reproducer. Check the existing @test_broken coverage and add a focused regression test for the affected GPU types. Done means the reported failure column is correct, with a raw-shim test retaining coverage of oneMKL's behavior if a workaround is added.
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描述
On the GPU, oneMKL's potrf returns the wrong info when the matrix stops being positive definite after column 32. This is oneMKL 2026.1, through oneAPI_Support_jll 0.11.0, on an Intel Data Center GPU Max 1100.
- Real types get the column's position inside its 32-column panel, i.e.
(j - 1) % 32 + 1. - Complex types get
panel * 1024 + position.
Columns 1 to 32 are reported correctly. The shim onemkl<T>potrf returns computation_error::info() unchanged, so the wrong value comes from oneMKL itself, not from oneAPI.jl.
Reproducer
using oneAPI, LinearAlgebra
using oneAPI: Support, sycl_queue, global_queue
n, j = 100, 50
G = randn(n, n); S = Matrix(Hermitian(G * G' / n + n * I)); S[j, j] = -1
A = oneMatrix(S)
q = sycl_queue(global_queue(oneAPI.context(A), oneAPI.device(A)))
lw = Support.onemklDpotrf_scratchpad_size(q, 'L', n, n)
Support.onemklDpotrf(q, 'L', n, A, n, oneVector{Float64}(undef, lw), lw) # returns 18, expected 50
Observed values for an HPD matrix with A[j, j] = -1. Results are the same for 'L' and 'U'.
| type | n | j | info |
|---|---|---|---|
| Float32 / Float64 | 50 | 17 | 17 |
| Float32 / Float64 | 50 | 33 | 1 |
| Float32 / Float64 | 100 | 50 | 18 |
| Float32 / Float64 | 100 | 100 | 4 |
| Float32 / Float64 | 257 | 257 | 1 |
| ComplexF32 / ComplexF64 | 100 | 50 | 1042 |
| ComplexF32 / ComplexF64 | 100 | 97 | 3073 |
| ComplexF32 / ComplexF64 | 257 | 254 | 7198 |
In every case the factor itself still follows LAPACK potf2. The first diagonal entry that is not a finite positive number is exactly column j, so a caller can recover the right column from the diagonal. getrf's info is correct. The environment variables OverrideDefaultFP64Settings and IGC_EnableDPEmulation make no difference.
Impact. cholesky, issuccess and isposdef only check whether info is nonzero, so they are unaffected. Only the exact column number is wrong, for example in a PosDefException. #754 makes LinearAlgebra.LAPACK.potrf! return info and marks these cases @test_broken.
Possible handling
- Report the bug to Intel, which is the real fix.
- Optionally work around it in Julia: when
info > 0, take the first non-positive diagonal entry as the column. This costs one small diagonal copy on the failure path only, since the shim already synchronizes. If you prefer to carry a workaround, a separate test on the raw shim would keep tracking the oneMKL bug.
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