[eigen] Combining different types

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I understand that Eigen does not allow adding vectors of different types. For example, the code

   VectorXf    f(3);
   VectorXd   d(3);

   cout << (f+d) << endl;

yields the compilation error


I also understand the Eigen has this restriction because of the difficulty (correctness?) of doing vectorization with such expressions. However, casting a float vector to a double vector is, of course, inefficient. Does it make sense to move the prohibition of mixing types to be a pre-condition for vectorization, and allow the mixing of types in general in Eigen?

A concrete situation where this is desirable is where a bunch of parameters can be stored in a vector of floats (to save space), but the main calculations are done in double, to maintain sufficient precision.

The following template

   template< typename A, typename B >
   struct promote
     typedef decltype( A(0) + B(0) ) type;

makes the promotion type explicit. [In my actual situation, this does not work with a new scalar type, adouble (from ADOL-C) that I am using, but this can be handled by writing down specializations for the above template].

I have been able to, largely, work around the prohibition of mixing types with adouble by adding small amounts of code to specialize the existing Eigen infrastructure that does the checking. However, I have not been able to solve this definitively, for adouble, and may need to (mildly) constrain my code, instead. It would be more elegant if Eigen, from ground up, allowed the user the option to mix types

Any comments much appreciated ...

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