MATLAB: Fitting a circle with fitnlm

circle functioncirclefitcirclefittingfitnlmleast squaresnewton methodnlinfitnon-linear regressionnonfitlinnonlinear regression

Hello, I tried to fit following data to a circle with help of fitnlm
i used following circle function to determine the center of the circle and the radius:
X = readmatrix('coordinates.txt') %you can find the coordinats.txt in the attachments
circlefun = @(X, b) (X(:,1).^2 + X(:,2).^2 + b(1)*X(:,1) + b(2)*X(:,2) + b(3));
y = zeros(length(X(:,1)),1);
beta0 = [0 0 400];
mdl = fitnlm(X,y,circlefun, beta0)
it gives me following output:
Error using nlinfit (line 219)
MODELFUN must be a function that returns a vector of fitted values the same size as Y (1000-by-1).  The model function you provided returned a result that was 1-by-1.
One common reason for a size mismatch is using matrix operators (*, /, ^) in your function instead of the corresponding elementwise operators (.*, ./, .^).
Error in NonLinearModel/fitter (line 1127)
                    nlinfit(X,y,F,b0,opts,wtargs{:},errormodelargs{:});
Error in classreg.regr.FitObject/doFit (line 94)
            model = fitter(model);
Error in NonLinearModel.fit (line 1434)
            model = doFit(model);
Error in fitnlm (line 99)
model = NonLinearModel.fit(X,varargin{:});
What I already tried: I used Newton Method for multivariables and the results were quite good in my opinion, but i would like to understand how i can use fitnlm.
Thanks in advance!

Best Answer

The arguments to ‘circlefun’ are reversed. The parameter vector must always be the first argument, and the independent variable vector (or matrix) must always be the second.
This works: 
circlefun = @(b,X) (X(:,1).^2 + X(:,2).^2 + b(1)*X(:,1) + b(2)*X(:,2) + b(3));
and produces: 
mdl = 
Nonlinear regression model:
    y ~ (x1^2 + x2^2 + b1*x1 + b2*x2 + b3)
Estimated Coefficients:
           Estimate        SE        tStat       pValue  
          ___________    _______    _______    __________
    b1        -156.27    0.79825    -195.76             0
    b2         51.732     5.9203     8.7381    9.8825e-18
    b3    -3.4442e+05     3394.1    -101.48             0
Number of observations: 1000, Error degrees of freedom: 997
Root Mean Squared Error: 1.08e+03
R-Squared: -Inf,  Adjusted R-Squared -Inf
F-statistic vs. constant model: 0, p-value = 1
.
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