[discussion] Could we remove prod and define * for specific types?

[abelsiqueira]

Having prod, tprod, ctprod and their types makes it difficult for the compiler to guess the types of the outputs, which leads to instability. An alternative could be not assuming that each operator will have prod, and instead define subtypes and * for each one.

Example:

• Remove generic *(A, v);
• Implement subtype MatricialLinearOperator;
• Define *(A, v) for this subtype.

We could then define everything in term of subtypes:

• ScalingLinearOperator for scalar times operator;
• MultiplicationLinearOperator for opA * opB;
• hvcatLinearOperator;
• AdjointLinearOperator (See Create adjoint, transpose and conjugate wrapper types #104);

One downside would be implementing a lot of new types and their interactions. For instance, adjoint of an operator would depend on the operator.

Related to #97 and #104

[abelsiqueira]

I've implemented an early draft here.

• I've removed prod, tprod and ctprod (and F1,F2,F3).
• Created an API for the AbstractLinearOperator.
• Created a DescriptiveLinearOperator which is defined with prod, tprod and ctprod.
• Create a MatricialLinearOperator which is defined by a single matrix.

[dpo]

How does that help with type stability of DescriptiveLinearOperator though?

[abelsiqueira]

I'm still not sure it will. I was trying to have all operations as lazy operators, but I ended having trouble with type instability again (related issue on discourse). It looks like having type stability and speed might not be always possible.

[abelsiqueira]

Having solved #100 and #97, this is less important now. I believe it could be useful for trait-like interfaces in the future, as it allows more specialized code. However, it would be better if we had a strong reason to work on this change, as it is a very large endeavor. I'll close now and leave the discussion for the future.