fitting a circle with fitnlm

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!

Answer 1

[Star Strider]

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

.

[Hoschang Noori]

WTF??? I spend half of the week to figure out how this works XD

Thank you very much!

[Star Strider]

As always, my pleasure!

[Image Analyst]

How do you plot the fitted circle once you have the model?

[Star Strider]

Since it is an implicit equation, the intent appears to be to estimate the parameters. Everything else would be derived from them.

EDIT — (4 Jul 2020 at 17:55)

The plot is relatively straightforward:

B = mdl.Coefficients.Estimate;
Xm = -B(1)/2;
Ym = -B(2)/2;
R = sqrt((Xm^2 + Ym^2) - B(3));

A = atan2(X(:,2)-Ym, X(:,1)-Xm);
Ycir = R*sin(A) + Ym;
Xcir = R*cos(A) + Xm;

figure
plot(X(:,1), X(:,2), 'p')
hold on
plot(Xcir, Ycir, '-r', 'LineWidth',2)
hold off
grid
axis('equal')

producing:

.

Answer 2

[Image Analyst]

You might also be interested in the FAQ: https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data.3F

[Hoschang Noori]

Thanks, I know the FAQ, i saw some posts from you about this elsewhere. :D The solution presented there works quite well for circles with few outliers, but it seems not to be robust enough for my purposes since i have some noise + some more circles in my data.