There seems to be a gcc 4.7 bug that incorrectly flags the current
3x3 inverse as using uninitialized memory. I'm *pretty* sure it's
a false positive, but it's hard to trigger. The same warning
does not trigger with clang or later compiler versions.
In trying to find a work-around, this implementation turns out to be
faster anyways for static-sized matrices.
```
name old cpu/op new cpu/op delta
BM_Inverse3x3<DynamicMatrix3T<float>> 423ns ± 2% 433ns ± 3% +2.32% (p=0.000 n=98+96)
BM_Inverse3x3<DynamicMatrix3T<double>> 425ns ± 2% 427ns ± 3% +0.48% (p=0.003 n=99+96)
BM_Inverse3x3<StaticMatrix3T<float>> 7.10ns ± 2% 0.80ns ± 1% -88.67% (p=0.000 n=114+112)
BM_Inverse3x3<StaticMatrix3T<double>> 7.45ns ± 2% 1.34ns ± 1% -82.01% (p=0.000 n=105+111)
BM_AliasedInverse3x3<DynamicMatrix3T<float>> 409ns ± 3% 419ns ± 3% +2.40% (p=0.000 n=100+98)
BM_AliasedInverse3x3<DynamicMatrix3T<double>> 414ns ± 3% 413ns ± 2% ~ (p=0.322 n=98+98)
BM_AliasedInverse3x3<StaticMatrix3T<float>> 7.57ns ± 1% 0.80ns ± 1% -89.37% (p=0.000 n=111+114)
BM_AliasedInverse3x3<StaticMatrix3T<double>> 9.09ns ± 1% 2.58ns ±41% -71.60% (p=0.000 n=113+116)
```
(cherry picked from commit 5ad8b9bfe2bf75620bc89467c5cc051fc2a597df)
For empty or single-column matrices, the current `PartialPivLU`
currently dereferences a `nullptr` or accesses memory out-of-bounds.
Here we adjust the checks to avoid this.
(cherry picked from commit 154f00e9eacaec5667215784c7601b55024e2f61)
We can't make guarantees on alignment for existing calls to `pset`,
so we should default to loading unaligned. But in that case, we should
just use `ploadu` directly. For loading constants, this load should hopefully
get optimized away.
This is causing segfaults in Google Maps.
(cherry picked from commit 12e8d57108c50d8a63605c6eb0144c838c128337)
Implemented fast size-4 matrix inverse (mimicking Inverse_SSE.h) using NEON intrinsics.
```
Benchmark Time CPU Time Old Time New CPU Old CPU New
--------------------------------------------------------------------------------------------------------
BM_float -0.1285 -0.1275 568 495 572 499
BM_double -0.2265 -0.2254 638 494 641 496
```
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()
- 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
