I am trying to use Boost.Units with Eigen 3.3.1, but after following the instructions here, and some pieces of informations found around, I still cannot figure out how to make norm() work.
Here is what I have so far (sorry for the long code block):
#include <boost/units/quantity.hpp>
#include <boost/units/systems/si/length.hpp>
#include <boost/units/systems/si/area.hpp>
#include <boost/units/cmath.hpp>
#include <Eigen/Geometry>
namespace Eigen {
//specialization of numeric traits
using boost::units::quantity;
template <typename Unit, typename Scalar>
struct NumTraits<quantity<Unit, Scalar>>
: GenericNumTraits<quantity<Unit, Scalar>>
{
typedef quantity<Unit, Scalar> Real;
typedef quantity<Unit, Scalar> NonInteger;
typedef quantity<Unit, Scalar> Nested;
typedef quantity<Unit, Scalar> Literal;
static inline Real epsilon() { return quantity<Unit, Scalar>(0); }
static inline Real dummy_precision() { return quantity<Unit, Scalar>(1e-6 * Unit()); }
static inline Real digits10() { return quantity<Unit, Scalar>(0); }
enum {
IsComplex = 0,
IsInteger = 0,
IsSigned = 1,
RequireInitialization = 1,
ReadCost = 1,
AddCost = 3,
MulCost = 3
};
};
//specialization of sum operator
template <typename Unit, typename Scalar>
struct ScalarBinaryOpTraits<quantity<Unit, Scalar>, quantity<Unit, Scalar>, internal::scalar_sum_op<quantity<Unit, Scalar>, quantity<Unit, Scalar>>> {
typedef typename boost::units::add_typeof_helper<quantity<Unit, Scalar>, quantity<Unit, Scalar>>::type ReturnType;
};
//specialization of product operator
template <typename Unit, typename Scalar>
struct ScalarBinaryOpTraits<Scalar, quantity<Unit, Scalar>,internal::scalar_product_op<Scalar, quantity<Unit, Scalar>>> {
typedef Scalar X;
typedef quantity<Unit, Scalar> Y;
typedef typename boost::units::multiply_typeof_helper<X, Y>::type ReturnType;
};
template <typename Unit, typename Scalar>
struct ScalarBinaryOpTraits<quantity<Unit, Scalar>, Scalar, internal::scalar_product_op<quantity<Unit, Scalar>, Scalar>> {
typedef quantity<Unit, Scalar> X;
typedef Scalar Y;
typedef typename boost::units::multiply_typeof_helper<X, Y>::type ReturnType;
};
template <typename Unit, typename Scalar>
struct ScalarBinaryOpTraits<quantity<Unit, Scalar>, quantity<Unit, Scalar>, internal::scalar_product_op<quantity<Unit, Scalar>, quantity<Unit, Scalar>>> {
typedef quantity<Unit, Scalar> X;
typedef quantity<Unit, Scalar> Y;
typedef typename boost::units::multiply_typeof_helper<X, Y>::type ReturnType;
};
namespace internal {
//specialization for abs2()
template<typename Unit, typename Scalar>
struct abs2_impl<quantity<Unit, Scalar>>
{
typedef quantity<Unit, Scalar> X;
typedef quantity<Unit, Scalar> Y;
typedef typename boost::units::multiply_typeof_helper<X, Y>::type ReturnType;
EIGEN_DEVICE_FUNC
static inline ReturnType run(const quantity<Unit, Scalar>& x)
{
return x * x;
}
};
} // namespace internal
} // namespace Eigen
namespace boost {
namespace units {
//required functions
using namespace boost::units::si;
inline quantity<area, double> abs2(const quantity<length, double>& x) { return x * x; }
} // namespace units
} // namespace boost
int main(int /*argc*/, char** /*argv[]*/)
{
//unit typedefs
using namespace boost::units;
using namespace boost::units::si;
using Length = quantity<length, double>;
using Area = quantity<area, double>;
//eigen typedefs
using LengthVector = Eigen::Matrix<Length, 3, 1>;
using AreaVector = Eigen::Matrix<Area, 3, 1>;
using LengthMatrix = Eigen::Matrix<Length, 3, 3>;
//test norm
LengthVector vector1;
Length result4 = vector1.norm();
}
But this fails to compile (gcc 5.4.0) with an error like
could not convert "boost::units::sqrt... (some undecipherable template error)"
and
could not convert "Eigen::internal::abs2_impl... (some obscure template error)"
As shown above, Eigen3
norm()
function makes use of thesquaredNorm()
. However, the declaration ofsquaredNorm()
requires the return type should be same to the Matrix element typeDerived
, which means the return value units should be same to the matrix element units. For example, a displacement vector of meter units, its squaredNorm should return a value with meter_squared unit, which conflicts with the declaration. So it may not be possible to usesquaredNorm()
ornorm()
directly without changing the implementation of Eigen.My idea is to write a utility function outside of Eigen to implement
squaredNorm()
,norm()
andnormalized()
:https://github.com/iastate-robotics/eigen3-units