function [Xnew,spare]=LM(X,F,G,Ini,spare);

%	This function implements a Levenberg Marquadt Increment, according to 
%	the algorithm given in 'Practical Methods of Optimization', Vol I, by
%	R.Fletcher, pp.84
%
%	In the first call, Ini should be set equal to 1, 
%	0 afterwards
%
%	Input Arguments:
%		X - design variables
%		F - the error vector obtained using the variables X
%		G - The Jacobian matrix of the problem at point X
%		spare - a vector containing previous values; its format is
%			known by the functions WrapSpare and UnWrapSpare
%
%	Output Arguments
%		Xnew - the new design variables
%		spare
%
%	Written on 16, June, 1990 by Antonio Ruano

[m,nvars]=size(G);
[k,l]=size(X);
if k==1
  row=1;
else
  row=0;
end;

X=X(:);
F=F(:);

if Ini~=1
  % not initialization
  [Xold,Fold,Gold,Eold,Fest,lambda]=UnWrapSp(spare,m,nvars);
  ESN=F'*F;
  ESO=Fold'*Fold;
  ESE=Fest'*Fest;

  DeltaF=ESO-ESN;
  DeltaQ=ESO-ESE;

  r=DeltaF/DeltaQ;
  if r<.25
    lambda=lambda*4;
  elseif r>.75
    lambda=lambda/2;
  end;
  
  if r>0
    % the test point is accepted
    Xold=X;
    Gold=G;
    Fold=F;
    Eold=G'*F;
  end;

else
  %  It's initialization
  lambda=1;
  Xold=X;
  Gold=G;
  Fold=F;
  Eold=G'*F;
end;
%  Compute new point and the estimated sum of squares
sd =-(Gold'*Gold+lambda*eye(nvars))\Eold;
Xnew=Xold+sd;
if row==1
  Xnew=Xnew';
end;
Fest=Gold*sd+Fold;
spare=WrapSpar(Xold,Fold,Gold,Eold,Fest,lambda);