Fix complex GMRES inner products - #378
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Summary
Fix the complex-valued inner products used by device code and GMRES Arnoldi orthogonalization.
Fixes #377
Root cause
The device implementation of
dotc(...)insrc/blas.cucallsCublas::dot(...).For complex double precision, this maps to the unconjugated
cublasZdotu, whiledotc(x, y)is expected to compute the Hermitian inner productx^H y.After restoring the correct
dotcsemantics, the GMRES Modified Gram-Schmidt projection also needs its arguments swapped. The current expression computesw^H v_k, whereas Arnoldi orthogonalization requiresv_k^H w.Changes
Cublas::dotc(...)in the two device implementations ofdotc(...).dot(w, v_k)todot(v_k, w).Testing
Tested using the 3x3 complex reproducer from #377 with:
dZZI10Results:
2.955383e-054.981581e-16The same reproducer was also tested after applying the patch to the current
mainbranch.Full reproduction details and logs are available in #377.