samer@3: % limit - Get the limit of an infinite sequence if it exists
samer@3: %
samer@3: % limit :: 
samer@3: %    (A,A->nonneg) ~ 'metric',
samer@3: %    seq(A),        ~ 'sequence of converging values',
samer@3: %    options {
samer@3: %       maxit :: natural/10e6 ~ 'maximum iterations';
samer@3: %       tol   :: nonneg/1e-5  ~ 'convergence tolerance'
samer@3: %    }
samer@3: % -> A, natural.
samer@3: 
samer@3: function [y,its]=limit(d,X,varargin)
samer@37: 	opts=options('maxit',10e6,'tol',1e-5,varargin{:});
samer@3: 
samer@3: 	tol=opts.tol;
samer@3: 	S.x=head(X);
samer@3: 	S.X=next(X);
samer@3: 	S.f=false;
samer@3: 	S.its=0;
samer@3: 	S=iterate(@converger,S,'its',opts.maxit);
samer@3: 	y=S.x;
samer@3: 	its=S.its;
samer@3: 
samer@3: 	function S=converger(S)
samer@3: 		[xx,S.X]=decons(S.X); 
samer@3: 		S.its=S.its+1;
samer@3: 		if d(S.x,xx)<tol, S=[]; else S.x=xx; end
samer@3: 	end
samer@3: end