GENERIC INTERFACE EigenN(VRep, MRep);
(*
  Eigenvalues of square matrices.

  In-place ("destructive") eigenvalue and eigenvector computation
  for finite-dimensional linear maps "MRep.T"s.

  It is assumed that each "VRep.T" value is an element of a
  finite-dimensional vector space, and each "MRep.T" is a linear map
  from some finite-dimensional subset of "VRep.T" to itself.
  Conceptually, an "MRep.T" is a two-dimensional array of floats, but
  concretely it could be something else --- say, a triangular matrix,
  a quaternion, a procedure, etc.
  
  Created by J. Stolfi, with contributions by Marcellus R. Macêdo. *)

PROCEDURE SymEigen(
    VAR m: MRep.T;                (* IN: symmetric matrix. OUT: garbage *)
    VAR val: ARRAY OF LONGREAL;   (* OUT: eigenvalues of "M". *)
    VAR vec: ARRAY OF VRep.T;     (* OUT: eigenvectors of "M". *)
    VAR b: ARRAY OF LONGREAL;     (* WORK *)
    VAR z: ARRAY OF LONGREAL;     (* WORK *)
  ); 
  (* 
    Computes the eigenvalues and eigenvectors of the matrix "m", which
    is assumed to be square ("N" by "N") and symmetric.  The "N" unordered
    eigenvalues are returned in "val", and the corresponding
    eigenvectors in "vec".  Matrix "m" is destroyed in the process.
    Parameters "b" AND "z" are work vectors of size "N".
    
    Uses the Jacobi algorithm from Numerical Recipes. *)

END EigenN.