gnuplot-info

[Gnuplot-info] Fitting and inverse function

[Theo <th...@gm...>]

Hi all,

I have a function e.g. like
f(x,T1,T2,T3,R1,R2,R3) = R1*exp(-x/T1) + R2*exp(-x/T2) + R3*exp(-x/T3)

When using

fit f(x,T1,T2,T3,R1,R2,R3) 'FileName.dat' using 1:2 via T1,T2,T3,R1,R2,R3

I nicely get the best fitting constants T1,T2,T3,R1,R2,R3

Now, I now would like to know what is x if y = f(x) = 0.5 and place it 
as a label. The problem is that the above function can not be simply 
rewritten as inverse function x = g(y)

At least as an approximation, how could I extract x?
Can I use the fitting capability of gnuplot to do that? I don't see how 
to do it. Any ideas?

Thanks,
Theo.

Re: [Gnuplot-info] Fitting and inverse function

[Hans-Bernhard B. <HBB...@t-...>]

On 10.04.2013 19:46, Theo wrote:
> Now, I now would like to know what is x if y = f(x) = 0.5 and place it
> as a label. The problem is that the above function can not be simply
> rewritten as inverse function x = g(y)
>
> At least as an approximation, how could I extract x?
> Can I use the fitting capability of gnuplot to do that? I don't see how
> to do it. Any ideas?

This might work (didn't try):

   fit f(x0,T1,T2,T3,R1,R2,R3) '-' via x0
     0.5
   E

Re: [Gnuplot-info] Fitting and inverse function

[Theo <th...@gm...>]

Thank you, Bernhard.

The code gives an error message:

Read 1 points
          No data to fit
          "Test.gp", line 186: error during fit

However, with adding an additional data point it works:

fit f(x0) '-' via x0
  0.5
  0.5
E