Polar decomposition QDWH #2
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added 25 commits
October 27, 2022 14:56
…oid having a clean up tile in the middle of the W matrix
…ts to slate calls
… != q. Changed dd computing in qdwh for-now and minor changes
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Check for warnings, i.e., add |
added 2 commits
January 30, 2023 13:23
added 3 commits
January 30, 2023 13:48
…trcondest. Reduced the condition number of the tested matrix
mgates3
requested changes
Feb 2, 2023
mgates3
reviewed
Feb 3, 2023
added 6 commits
February 6, 2023 09:38
…or update on gflops count
…from geqrf and geqrf_qdwh_full
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All test passed, except one failure for gels using cholqr. |
mgates3
reviewed
Nov 13, 2023
| lapack::Gflop<scalar_t>::potrf(m) + | ||
| blas::Gflop<scalar_t>::trsm(slate::Side::Left, m, n) ); | ||
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| double gflop_compute_H = blas::Gflop<scalar_t>::her2k(n, m); |
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Currently, this is really gemm, but eventually it should be herk (i.e., herkx) instead of her2k.
(I'll fix.)
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The polar decomposition QDWH of a general matrix A = U * H, where U is orthogonal polar factor and H is hermitian polar factor.
QDWH iterations rely on Cholesky based and QR based iterations to compute the orthogonal polar factor U.
For the QR based iterations, new customized geqrf_qdwh_full and unmqr_qdwh_full are included to take advantage of the identity structure of the matrix involved during the QR based iterations.
The 2-norm estimate (norm2est) of the original matrix is required, the norm2est using power iteration is implemented and called in QDWH.
The following figure present the performance of SLATE_QDWH on Summit using various number of nodes.
