Ternary DimProd<> or compose DimProd<> results?

nalgebra
1

(How) Is it possible to constrain a dimension trait to be the product of three other dimensions? e.g. Can one declare a structure with field of type VectorN<f64, DimProd<M, DimProd<N, P>>> where M, N, and P implement DimName?

For context I’d like to implement a 2-d convolution operation to pool sub matrices. For pooling scalars, the following skeleton suffices, even being able to compute multiple values/characteristics for each pool.

pub struct Pooler2d<'a, NumRows, NumCols, NumOutputs>
where
    NumRows: DimName + DimMul<NumCols>,
    NumCols: DimName, 
    NumOutputs: DimName,
{
    op: &'a dyn Operator<DimProd<NumRows, NumCols>, NumOutputs>,
}

Where Operator<NumInputs: DimName, NumOutputs: DimName> is a trait with a method f(x: &VectorN<f64, NumInputs>) -> Vector<f64, NumOutputs>.

I’d like to be able to extend Pooler2d, however, to take as input multiple scalars or a vector for each element in the pool (effectively pooling in three dimensions), but I cannot get the type with the following field with a nested DimProd to compile

   NumChannels: DimName + DimMul<NumRows>,
...
    op: &'a dyn Operator<DimProd<NumChannels, DimProd<NumRows, NumCols>>, NumOutputs>,

The error is something like

error[E0277]: cannot multiply `<NumChannels as DimName>::Value` by `_`
  --> src/img/conv2d.rs:31:12
   |
31 |     model: &'a dyn Model<DimProd<NumChannels, DimProd<NumRows, NumCols>>, NumOutputs>,
   |            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ no implementation for `<NumChannels as DimName>::Value * _`
   |
   = help: the trait `Mul<_>` is not implemented for `<NumChannels as DimName>::Value`
   = note: required because of the requirements on the impl of `DimMul<<NumRows as DimMul<NumCols>>::Output>` for `NumChannels`

Am I just lost in the weeds and should consider dynamically sized vectors and matrices? Operating on VectorN<f64, xxx> instead of f64? Thanks for any attention reading this far.

2

Fiddling some, I can chain dimensional products:

NumChannels: DimName + DimMul<DimProd<NumRows, NumCols>>,
...
op: &'a dyn Operator<DimProd<NumChannels, DimProd<NumRows, NumCols>>, NumOutputs>,