Let f : T^m -> S^n be a function that takes m elements of type T as input and returns n elements of type S as output.
The l batch of f is
Batch(l, f) : (T^m)^l -> (S^n)^l
the l vectorize of f is
Vectorize(l, f) : (T^l)^m -> (S^l)^n
Batch(l, f)(X) = Vectorize(k, f)(X^T) where X^T is the transpose of X.
Let f : T^m -> S^n be a function that takes m elements of type T as input and returns n elements of type S as output.
The l batch of f is
Batch(l, f) : (T^m)^l -> (S^n)^l
the l vectorize of f is
Vectorize(l, f) : (T^l)^m -> (S^l)^n
Batch(l, f)(X) = Vectorize(k, f)(X^T) where X^T is the transpose of X.