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Hi there, I have X1, X2 and Y1 data set and a function of x=f(y,B), but not y=g(x,B), where B is a vector of parameters. Unfortunately, the inverse function of f can't be solved analytically. So I am stuck with x=f(y,B).
The problem is I want to estimate the parameter values of the function, based on X1 and Y1, so that I can use it to estimate Y2 from X2, numerically.
Is it possible at all to estimate parameter values based on SSE regarding Y1, and not X1? NonLinearModel.fit and nlinfit do not seem to offer the option.
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If you have the Optimization Toolbox, maybe you can express g(x,B) in the following way and pass it to your favorite solver,
g=@(x,B) fsolve(@(y) f(y,B)-x , y0);
You could also generalize this by making the initial guess y0 a more general function of (x,B), if you know a good custom initialization scheme.