This MR fixes a bunch of smaller issues, making the following changes:
* Template parameters in the documentation are documented with `\tparam` instead
of `\param`
* Superfluous semicolon warnings fixed
* Fixed the type of literals used to initialize float variables
This changeset also includes:
* add HouseholderSequence::conjugateIf
* define int as the StorageIndex type for all dense solvers
* dedicated unit tests, including assertion checking
* _check_solve_assertion(): this method can be implemented in derived solver classes to implement custom checks
* CompleteOrthogonalDecompositions: add applyZOnTheLeftInPlace, fix scalar type in applyZAdjointOnTheLeftInPlace(), add missing assertions
* Cholesky: add missing assertions
* FullPivHouseholderQR: Corrected Scalar type in _solve_impl()
* BDCSVD: Unambiguous return type for ternary operator
* SVDBase: Corrected Scalar type in _solve_impl()
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.
