[eigen] Combining different types

[Norman Goldstein <normvcr@xxxxxxxxx>]

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

YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY

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 ...