Implicit Function Curve Fitting

 

This example shows the equation text for a curve fit in which the fit model is defined implicitly. In this particular example, the data in the table is fit by an ellipse that is defined implicitly.

When using the implicit function in curve fitting, you can set the value of maxroots to any value which is sufficient to locate one solution. However, if maxroots is greater than 1, you must set the value of firstroot to 1 (or follow the call of the implicit function with a method of selecting one solution), for otherwise the returned values cannot be properly matched to the independent variable values.

-2.0000 0.1000
-1.5000 0.3000
-1.0000 0.4000
-0.5000 0.6000
0.0000 0.5000
0.5000 0.6000
1.0000 0.5000
1.5000 0.2500
2.0000 0.1000
[Variables]
x=col(1
y=col(2)
[Parameters]
a = .01
b = .01
[Equation]
k(u,v)=a*v^2+b*u^2-1
f=implicit(k(u,v),0,10,x)
fit f to y
[Constraints]
a>0
b>0
[Options]
tolerance=1e-010
stepsize=1
iterations=200

Try SigmaPlot FREE for 30 Days!