Add an API for n-th order tensor products

Author: amontoison

src/nlp/api.jl

@@ -11,6 +11,7 @@ export jth_hess_coord, jth_hess_coord!, jth_hess
 export jth_hprod, jth_hprod!, ghjvprod, ghjvprod!
 export hess_structure!, hess_structure, hess_coord!, hess_coord
 export hess, hprod, hprod!, hess_op, hess_op!
+export tensor_projection
 export varscale, lagscale, conscale
 
 """
@@ -1298,6 +1299,21 @@ function hess_op!(
   return LinearOperator{T}(nlp.meta.nvar, nlp.meta.nvar, true, true, prod!, prod!, prod!)
 end
 
+"""
+    P = tensor_projection(nlp, n, x, directions, args...)
+
+Returns the projection of the n-th derivative of the objective of `nlp` at `x` along the specified directions.
+
+#### Input arguments
+
+- `nlp::AbstractNLPModel`: An NLP model;
+- `n::Int`: The order of the derivative to compute;
+- `x::AbstractVector`: The point at which the derivative is evaluated;
+- `directions::Tuple{Int, Vararg{Int}}`: A tuple of indices specifying the directions (e.g., `(1, 2)` for a tensor projection along the first and second axes);
+- `args...`: A list of vectors, one for each direction specified in `directions`.
+"""
+function tensor_projection end
+
 function varscale end
 function lagscale end
 function conscale end