Poly11: "Warning: Equation is badly conditioned. Remove repeated data points or try centering and scaling."

Hi All,

I have the below code running on MATLAB which produces the warning message (also shown below). I am trying to figure out what why the warning message is appering.

My guess is that since the values i use for my fit are similar I get the message but I want to be sure that nothing is going wrong.

I am trying to fully understand things.

Thanks

%INPUT
xy =  [3154384.896 1719923.63; 3155030.31 1719242.07; 3155498.37 1719245.31];

z =

   1.0e+03 *

   5.121466000000001
   5.126727000000000
   5.126100000000000
   
   R = fit(xy, z, 'poly11')    % 'polly11' fit = fit linear polynomial surface. For more info visit: https://www.mathworks.com/help/curvefit/fit.html
coeffs = coeffvalues(R) 
Slopex = coeffs(2) %extract slope x
Slopey = coeffs(3) %extract slope y
   
   
 %OUTPUT
   Warning: Equation is badly conditioned. Remove repeated data points or try centering and scaling. 
> In curvefit.attention.Warning/throw (line 30)
  In fit>iLinearFit (line 672)
  In fit>iFit (line 383)
  In fit (line 108) 

     Linear model Poly11:
     R(x,y) = p00 + p10*x + p01*y
     Coefficients:
       p00 =   2.451e+04
       p10 =   -0.001278
       p01 =   -0.008929


coeffs =

   1.0e+04 *

   2.450931465568791  -0.000000127776324  -0.000000892905436

Answer 1

[Walter Roberson]

The problem is not in the z: the problem is in the y values being very similar.

Your fit can be rewritten as

p = [ones(3,1), xy] \ z

and for that the sensitivity can be estimated by cond([ones(3,1),xy]) which comes out about 1E11 .

[Zachary Ferrie]

Thank you for the help