DEFINITION MODULE SparseL;

   (* EXPORT QUALIFIED Sparse; *)

   FROM NRVect IMPORT Vector;

   TYPE Subroutine = PROCEDURE(Vector, Vector);

   PROCEDURE Sparse(    B,
                        X:   Vector; 
                    VAR rsq: REAL;
                        aSub, aTSub: Subroutine); 
   (*
     Solves the linear system Ax = b for the vector X[0, n-1] given the 
     right-hand vector B[0, n-1], and given two functions, aSub(xIn, xOut) 
     and aTSub(xIn, xOut), which respectively calculate Ax and A^Tx for x
     given as their first arguments, returning the result in their second 
     arguments. These subroutines should take every advantage of the sparseness 
     of the matrix Abf.  On input, X[n] should be set to a first guess
     of the desired solution (all zero components is fine).  On output,
     X is the solution vector, and rsq is the sum of the squares
     of the components of the residual vector Ax-b. If this is not small, 
     then the matrix is numerically singular and the solution represents
     a least-squares best approximation.
   *)

END SparseL.