Making them trivially copyable allows using std::memcpy() without undefined
behaviors.
Only Matrix and Array with trivially copyable DenseStorage are marked as
trivially copyable with an additional type trait.
As described in http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p0848r3.html
it requires extremely verbose SFINAE to make the special member functions of
fixed-size Matrix and Array trivial, unless C++20 concepts are available to
simplify the selection of trivial special member functions given template
parameters. Therefore only make this feature available to compilers that support
C++20 P0848R3.
Fix#1855.
- Split SpecialFunctions files in to a separate BesselFunctions file.
In particular add:
- Modified bessel functions of the second kind k0, k1, k0e, k1e
- Bessel functions of the first kind j0, j1
- Bessel functions of the second kind y0, y1
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()
This slightly complexifies the type of the expressions and implies that we now have to distinguish between scalar*expr and expr*scalar to catch scalar-multiple expression (e.g., see BlasUtil.h), but this brings several advantages:
- it makes it clear on each side the scalar is applied,
- it clearly reflects that we are dealing with a binary-expression,
- the complexity of the type is hidden through macros defined at the end of Macros.h,
- distinguishing between "scalar op expr" and "expr op scalar" is important to support non commutative fields (like quaternions)
- "scalar op expr" is now fully equivalent to "ConstantExpr(scalar) op expr"
- scalar_multiple_op, scalar_quotient1_op and scalar_quotient2_op are not used anymore in officially supported modules (still used in Tensor)
- 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
TernaryFunctors and their executors allow operations on 3-tuples of inputs.
API fully implemented for Arrays and Tensors based on binary functors.
Ported the cephes betainc function (regularized incomplete beta
integral) to Eigen, with support for CPU and GPU, floats, doubles, and
half types.
Added unit tests in array.cpp and cxx11_tensor_cuda.cu
Collapsed revision
* Merged helper methods for betainc across floats and doubles.
* Added TensorGlobalFunctions with betainc(). Removed betainc() from TensorBase.
* Clean up CwiseTernaryOp checks, change igamma_helper to cephes_helper.
* betainc: merge incbcf and incbd into incbeta_cfe. and more cleanup.
* Update TernaryOp and SpecialFunctions (betainc) based on review comments.
