open Algebra
open Vector
open Matrix

(* Signature of an iterative solver *)
module type Iterative_Solver =
  sig
    type elem
    type argument
    type result
    type norm

    (* Solve A B e = X if norm (AX - B) < e.
       do not forget that norm is the square of the real norm *)
    val solver : elem -> result -> norm -> argument
  end

(* conjugate gradient for symmetric matrices *)

module GC 
  (R : Normed_Field)
  (V : Normed_Vector with type scalar = R.elem and type norm = R.norm)
  (M : Light_Matrix with type scalar = R.elem 
		     and type argument = V.elem
		     and type result = V.elem)
  : Iterative_Solver 
  with type elem = M.elem 
  and type argument = V.elem
  and type result = V.elem
  and type norm = R.norm

(* an interesting exemple (look at the code) of a way
   to apply the GC to a non symmetric matrice *)

module Double_GC 
  (R : Normed_Field)
  (V : Normed_Vector with type scalar = R.elem and type norm = R.norm)
  (M : Light_Matrix with type scalar = R.elem 
		     and type argument = V.elem
		     and type result = V.elem)
  : Iterative_Solver 
  with type elem = M.elem 
  and type argument = V.elem
  and type result = V.elem
  and type norm = R.norm