fitting a circle with fitnlm
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Hoschang Noori
am 4 Jul. 2020
Bearbeitet: Star Strider
am 4 Jul. 2020
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!
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Star Strider
am 4 Jul. 2020
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
.
4 Kommentare
Star Strider
am 4 Jul. 2020
Bearbeitet: Star Strider
am 4 Jul. 2020
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:
.
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Image Analyst
am 4 Jul. 2020
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
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