Eigen Matrix Assignment Operator with User-Defined Data Types

Question

I am using the Eigen matrix library to deal with matrices of std::complex<T> data types, where T is either of type double or of type ceres::Jet<double,...>. Eigen documentation indicates that << is the correct operator to use for assignment, but it seems that << is not overloaded for matrices of user-defined data types. Is there a different method I can use to initialize Eigen matrices that works for both data types?

Answer 1

The problem with your code is not that Eigen is not overloaded for matrices of user-defined type (it is) but that you have a nested template argument of the type Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic> (where T is something like ceres::Jet<double> resulting in Eigen::Matrix<std::complex<ceres::Jet<double>>, Eigen::Dynamic, Eigen::Dynamic>). You will have to explicitly construct the elements of the nested type T before using the streaming operator <<.

Eigen::Matrix<std::complex<T>, 3, 1> mat;
mat << T{1.0}, T{2.0}, T{3.0};

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More detailed explanation

To further explain this let's start with a simple class we will use for the element type

class SomeClass {
  public:
    constexpr SomeClass(double const& some_data = 0.0) noexcept
      : some_data{some_data} {
      return;
    }

  private:
    double some_data;
};

A matrix of this user-defined type can be successfully assigned with:

Eigen::Matrix<SomeClass, 3, 1> mat;
mat << 1.0, 2.0, 3.0;

The problem only emerges if you apply it to nested element types such as std::complex<SomeClass>. We would like to use the following overload:

CommaInitializer<Derived> Eigen::DenseBase<Derived>::operator<<(const Scalar& s)

where Scalar is the type of the matrix coefficients (element type, e.g. Derived = Eigen::Matrix<std::complex<T>, 3, 1> and Scalar = std::complex<T>):

Eigen::DenseBase<Derived>::Scalar

Therefore when compiling GCC will tell you that it can't match the template:

note: candidate: Eigen::CommaInitializer<Derived> Eigen::DenseBase<Derived>::operator<<(const Scalar&) [with Derived = Eigen::Matrix<std::complex<SomeClass>, 3, 1>; Eigen::DenseBase<Derived>::Scalar = std::complex<SomeClass>
inline CommaInitializer<Derived> DenseBase<Derived>::operator<< (const Scalar& s)

note: no known conversion for argument 1 from ‘double’ to ‘const Scalar& {aka const std::complex<SomeClass>&}’

What you will have to do to make it compile is to construct the elements with a type which can be converted to Scalar and can then call the corresponding streaming operator as follows:

mat << std::complex<SomeClass>{SomeClass{1.0}}, std::complex<SomeClass>{SomeClass{2.0}}, std::complex<SomeClass>{SomeClass{3.0}};

mat << std::complex<SomeClass>{1.0}, std::complex<SomeClass>{2.0}, std::complex<SomeClass>{3.0};

mat << SomeClass{1.0}, SomeClass{2.0}, SomeClass{3.0};

This should be avoidable by changing the Eigen library to something like

CommaInitializer<Derived> Eigen::DenseBase<Derived>::operator<<(Elem const& s)

and require with std::enable_if_t, static_assert or C++20 concepts that Scalar can be constructed by an element of type Elem:

std::is_constructible_v<Scalar, Elem>

If you really need you could try to write an overload for it yourself that makes sure that std::is_constructible_v<Scalar, Elem> but !std::is_same_v<Scalar, Elem> but I personally think it is never a good idea to add such a functionality to an existing library yourself. Somebody else copying fragments of your code and expecting them to work might end up with not working code.

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Alternative options for assignments

As alternatives to assignment with << you could

• Use its constructor
• Initialise the Eigen matrix from an existing C-style array, std::array or std::vector or
• Use its coefficient accessors.

For the first two options you will have to use the same logic as discussed in the previous paragraph or use double braces

Eigen::Matrix<std::complex<SomeClass>, 3, 1> mat = { {1.0, 2.0}, {2.0, 3.0}, {3.0, 4.0} };

or

std::vector<std::complex<SomeClass>> vec = { {1.0, 2.0}, {2.0, 3.0}, {3.0, 4.0} };
Eigen::Matrix<std::complex<SomeClass>, 3, 1> mat{vec.data()};

while something like

mat(0,0) = 1.0;

mat(0,0) = {1.0, 2.0};

will create a complex element with a real part 1.0 and imaginary part 0.0 or 2.0 of type SomeClass without having to call the constructor SomeClass{} explicitly.