The previous "Scalar" semantic was obsolete since we allow for different scalar types in the source and destination expressions.
On can still specialize on scalar types through SFINAE and/or assignment functor.
- Replace internal::scalar_product_traits<A,B> by Eigen::ScalarBinaryOpTraits<A,B,OP>
- Remove the "functor_is_product_like" helper (was pretty ugly)
- Currently, OP is not used, but it is available to the user for fine grained tuning
- Currently, only the following operators have been generalized: *,/,+,-,=,*=,/=,+=,-=
- TODO: generalize all other binray operators (comparisons,pow,etc.)
- TODO: handle "scalar op array" operators (currently only * is handled)
- TODO: move the handling of the "void" scalar type to ScalarBinaryOpTraits
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.
bug #877, bug #572: Get rid of Index conversion warnings, summary of changes:
- Introduce a global typedef Eigen::Index making Eigen::DenseIndex and AnyExpr<>::Index deprecated (default is std::ptrdiff_t).
- Eigen::Index is used throughout the API to represent indices, offsets, and sizes.
- Classes storing an array of indices uses the type StorageIndex to store them. This is a template parameter of the class. Default is int.
- Methods that *explicitly* set or return an element of such an array take or return a StorageIndex type. In all other cases, the Index type is used.
