[Possible Bug] PlainObject in some decompositons but not others

Summary

For some decompositions the typedef PlainObject exists, but in others it does not.

In the godbolt below, Householder QR does not have a PlainObject, but Partial pivot LU and Full pivot QR does.

// Partial Piv LU Plain Type: Eigen::Matrix<double, -1, -1>
  Eigen::MatrixXd A = Eigen::MatrixXd::Random(5, 5);
  std::cout << "Partial Piv LU Plain Type: " <<
   type_name<typename std::decay_t<decltype(A.partialPivLu())>::PlainObject>() << "\n";

// Full Piv Householder QR: Eigen::Matrix<double, -1, -1>
  std::cout << "Full Piv Householder QR: " <<
   type_name<typename std::decay_t<decltype(A.fullPivHouseholderQr())>::PlainObject>() << "\n";

// This errors
  std::cout << "Householder QR: " <<
   type_name<typename std::decay_t<decltype(A.householderQr())>::PlainObject>() << "\n";

https://godbolt.org/z/avr7MrKr3

Is there a reason for that? Further, is there a reason the PlainObject is a Matrix? I understand that some of these are castable to matrices, but they are their own objects that hold more than a matrix does. Or is that not the idea behind PlainObject?

Environment

godbolt

Minimal Example

https://godbolt.org/z/avr7MrKr3

What is the current bug behavior?

Some decompositions have PlainObject while others do not. While we do our template metaprogramming over Eigen this has been a bit of an issue. If it's a feature then it would just be nice to know the intuition behind why some have PlainObject typedefs and others do not.

What is the expected correct behavior?

Personally I would expect the PlainObject of a decomposition to be itself. Though if I'm wrong here I'm fine with that.

Anything else that might help

• Have a plan to fix this issue.

I have no plan in place for a fix as I'm unsure of the intended behavior.