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This change also adds additional checks for non-increasing diagonal in R11 to existing unit tests, and adds a new unit test with the Kahan matrix, which consistently fails for the original code. Benchmark timings on Intel(R) Xeon(R) CPU E5-1650 v3 @ 3.50GHz. Code compiled with AVX & FMA. I just ran on square matrices of 3 difference sizes. Benchmark Time(ns) CPU(ns) Iterations ------------------------------------------------------- Before: BM_EigencolPivQR/64 53677 53627 12890 BM_EigencolPivQR/512 15265408 15250784 46 BM_EigencolPivQR/4k 15403556228 15388788368 2 After (non-vectorized version): Benchmark Time(ns) CPU(ns) Iterations Degradation -------------------------------------------------------------------- BM_EigencolPivQR/64 63736 63669 10844 18.5% BM_EigencolPivQR/512 16052546 16037381 43 5.1% BM_EigencolPivQR/4k 15149263620 15132025316 2 -2.0% Performance-wise there seems to be a ~18.5% degradation for small (64x64) matrices, probably due to the cost of more O(min(m,n)^2) sqrt operations that are not needed for the unstable formula.
Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
For more information go to http://eigen.tuxfamily.org/.