Curve Fitting for an equation

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Jay
Jay 2018-9-28
评论： Jay 2019-5-8
Hello
I have an equation like a*(x1^2)+ b(x2^2)+c((x1-x2)^2)+d((x12)^2)=1. Here I have variables of x1, x2, x12. x12 is the variable in the first quardrant. I have data of 12 Points passing through x1, x2 and x12.
I tried fitting the data to the above equation with different ways. But it did not turned out good. I tried with custom equation and some other methods. Could someone help me with getting the coefficients to this equation.
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Jay
Jay 2018-9-28
编辑：Jay 2018-9-28
Hello Torsten
Okay. Can you just eliminate x12 term from the equation and help for the remaining part (a*(x^2)+ b(y^2)+c((x-y)^2)=1). I want to find the values of a,b,c.
Jay
Jay 2018-9-28
Hello Image Analyst
It is not an Ellipse.

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采纳的回答

Torsten
Torsten 2018-10-1
编辑：Torsten 2018-10-1 
function main
xdata = [...];   % x coordinates of your 12 point
ydata = [...];   % y coordaintes of your 12 points
x0 = [1 1 1];      % initial values for a, b and c
x = lsqnonlin(@(x)fun(x,xdata,ydata),x0)
end

function res = fun(x,xdata,ydata)
res = x(1)*xdata.^2+x(2)*ydata.^2+x(3)*(xdata-ydata).^2-1;
end
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Torsten
Torsten 2019-2-11
https://de.mathworks.com/help/matlab/ref/fimplicit.html
Jay
Jay 2019-5-8
Hello Torsten
Do you how to implement this code in python?

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Pratik Bajaria
Pratik Bajaria 2018-9-28
Hello,
Did you try cftool? It does have provision of adding custom equations too.
Regards, Pratik
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Jay
Jay 2018-9-28
Hello
It does'nt work. As I cannot write the above equation as y= f(x).
Pratik Bajaria
Pratik Bajaria 2018-9-29
Well all equations can be written in y=f(x). Take any of the variables to be y (let's say x12) and all the other variables can be x. Since you have data points available try to write x12=f(x1,x2) and it must work.
Regards.

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