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colPivHouseholderQR -> householderQR ldlt -> llt. The resulting performance differences are significant enough to justify switching. LAPACK's dgels routine used for solving linear least squares problems does not use pivoting either. Similarly, we are not actually using the fact that the matrix being factorized can be indefinite when using LDLT factorization, so its not clear that the performance hit is worth it. These two changes result in Eigen being able to use blocking algorithms, which for Cholesky factorization, brings the performance closer to hardware optimized LAPACK. Similarly for dense QR factorization, on intel there is a 2x speedup. Change-Id: I4459ee0fc8eb87d58e2b299dfaa9e656d539dc5e