How can I find X for given Y value in a fitted curve?

Hi everyone.

I would like to know how to find the X value of a fitted curve given an Y value.

I had some data and fitted them using Gaussian fit. Now they look like this in my workspace:

An example of these functions as seen in the Command Window is:

 f50 = 

     General model Gauss1:
       f50(x) =  a1*exp(-((x-b1)/c1)^2)
     Coefficients (with 95% confidence bounds):
       a1 =        7.81  (7.602, 8.018)
       b1 =  1.497e-013  (-0.001774, 0.001774)
       c1 =     0.08174  (0.07924, 0.08425)

Does someone wonder how to do it?

I really appreciate any help you can provide.

Pablo

Answer 1

[Torsten]

Use the inverse function:

X=b1+c1*(log(a1./Y))^0.5 
or
X=b1-c1*(log(a1./Y))^0.5

Best wishes

Torsten.

[Pablo Martínez Filgueira]

Thank you! It is a good proposal but I have many fits and I have to find a quick way to do it.

Good answer anyway ;)

Answer 2

[Andrei Bobrov]

other variant

X = arrayfun(@(y)fzero(f50(x)-y,1),Y);

[AnaelG]

Brilliant! It took me a while to figure out how to use this. I had to change it a bit to parameterize the X and Y variables index:

X2= arrayfun( @(t)fzero( @(x)fun(x)-Y(t), X(t)) , 1:length(X));

Also zero is a solver, so for best result don't forget to normalize your data.

[Pen-Li (Ben) Yu]

Below is my modification to Andrei's solution:

X = arrayfun(@(y)fzero(@(x)f50(x)-y,x0),Y)

x0 is the initial value for the fzero function Y can be a scalar or a vector

[Christy Zheng]

I'm sorry for my lack of understanding, but to clarify X is the value you are looking for given a Y on the fitted curve. What are x and y referring to?

Answer 3

[Ingrid]

you can do this with the function

Y = feval(cfit,X);

which you could have easily found yourselve if you would have typed

doc cfit

[Pablo Martínez Filgueira]

you could also have read my question to give an answer to it

[Ingrid]

I have read your question but overlooked the fact that you were looking for the X values and not the Y values

in this case you might find this link helpful:

http://www.mathworks.com/matlabcentral/newsreader/view_thread/287031

[Pablo Martínez Filgueira]

thanks, but during the 2 hours before asking this question I also found that topic.

see you