oneMKL potrf on GPU reports the failing column relative to its 32-column panel #755

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'.

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

1. Report the bug to Intel, which is the real fix.
2. 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.