%
%  ITIMP
%
%     This command script simulates a single iteration of the iterative
%  improvement (refinement) method of error estimation, applied to the 
%  system of equations:
%
%                       A x = b
%
%  and in a simulated,specified digit (rounding) machine.   The script 
%  has no calling arguments, however the variables
%
%           A         =  the (square) matrix
%           b         =  the right-hand side (column) vector 
%           NDIGITS   =  the number of simulated digits of precision
%           x         =  the current (approximate) computed solution
%           niter     =  the number of iterations already completed
%           [ L U P ] =  the output of the  lu_chop( A , NDIGITS ) ,
%                        command, i.e. the permutation (P), lower (L)
%                        and upper (L) triangular matrices such that
%
%                                     PA = LU
%
%   must be defined prior to invoking the script.  Note that  A , P, L , U
%   and  NDIGITS   must be upper case, and   b , x , and   niter   lower!!!
%
%   On exit, the resulting updated solution vector, i.e.   
%
%                        x + e 
%
%   where   e   is the (computed) error estimate from the iterative
%   refinement algorithm, is found. along with the iteration number,
%   in the last row of the array named   data , specifically
%
%                   data  =  [  data ; niter (x + e)'  ]
%   
%
    r = calc_resid_chop( A, b, x , 2*NDIGITS )  ;
%
    z = fwd_solve_chop( L , P*r ) ;
    e = bwd_solve_chop( U ,  z  ) ;
% 
    niter = niter + 1 ;
%
    x = chop( x + e, NDIGITS) ;
    data = [ data ; niter  x' ] ;