function [p,normr] = polyfit(x,y,n)
// adattamento function del Matlab
//POLYFIT Fit polynomial to data.
//   POLYFIT(X,Y,N) finds the coefficients of a polynomial P(X) of
//   degree N that fits the data, P(X(I))~=Y(I), in a least-squares sense.
//
//   [P] = POLYFIT(X,Y,N) returns the polynomial coefficients P 
//
//   See also  POLYVAL.
// The regression problem is formulated in matrix format as:
//
//    y = V*p    or
//
//          3  2
//    y = [x  x  x  1] [p3
//                      p2
//                      p1
//                      p0]
//
// where the vector p contains the coefficients to be found.  For a
// 7th order polynomial, matrix V would be:
//
// V = [x.^7 x.^6 x.^5 x.^4 x.^3 x.^2 x ones(size(x))];

if size(x)~=size(y)
    error('X and Y vectors must be the same size.')
end

x = x(:);
y = y(:);


 

//% Construct Vandermonde matrix.
V(1:length(x),n+1) = ones(length(x),1);
for j = n:-1:1
   V(:,j) = x.*V(:,j+1);
end

//!% Solve least squares problem
[Q,R] = qr(V);

getf("solu.sci");
c=Q'*y;
p = solu(R,c(1:n+1));
pause
if size(R,2) > size(R,1)
   warning('Polynomial is not unique; degree >= number of data points.')
   
elseif size(R,1)~= size(R,2)
 
    warning('Polynomial approximation; degree < number of data points.')
   
 
elseif 1/rcond(R) > 1.0e10
    
        warning(sprintf( ...
            ['Polynomial is badly conditioned. Remove repeated data points\n' ...
                '         or try centering and scaling as described in HELP POLYFIT.']))
  
end
r = y - V*p;
normr=norm(r,2);
p = p.';          //!% Polynomial coefficients are row vectors by convention.
endfunction