Some Eigen objects, such as those returned by matrix.diagonal() and
matrix.block() have non-standard stride values because they are
basically just maps onto the underlying matrix without copying it (for
example, the primary diagonal of a 3x3 matrix is a vector-like object
with .src equal to the full matrix data, but with stride 4). Returning
such an object from a pybind11 method breaks, however, because pybind11
assumes vectors have stride 1, and that matrices have strides equal to
the number of rows/columns or 1 (depending on whether the matrix is
stored column-major or row-major).
This commit fixes the issue by making pybind11 use Eigen's stride
methods when copying the data.
Eigen::Ref is a common way to pass eigen dense types without needing a
template, e.g. the single definition `void
func(Eigen::Ref<Eigen::MatrixXd> x)` can be called with any double
matrix-like object.
The current pybind11 eigen support fails with internal errors if
attempting to bind a function with an Eigen::Ref<...> argument because
Eigen::Ref<...> satisfies the "is_eigen_dense" requirement, but can't
compile if actually used: Eigen::Ref<...> itself is not default
constructible, and so the argument std::tuple containing an
Eigen::Ref<...> isn't constructible, which results in compilation
failure.
This commit adds support for Eigen::Ref<...> by giving it its own
type_caster implementation which consists of an internal type_caster of
the referenced type, load/cast methods that dispatch to the internal
type_caster, and a unique_ptr to an Eigen::Ref<> instance that gets
set during load().
There is, of course, no performance advantage for pybind11-using code of
using Eigen::Ref<...>--we are allocating a matrix of the derived type
when loading it--but this has the advantage of allowing pybind11 to bind
transparently to C++ methods taking Eigen::Refs.
Add and declare to Python functions
double_mat_cm() --- compute 2* a column-major matrix
double_mat_rm() --- compute 2* a row-major matrix
to 'eigen.cpp' tests / example.
