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Re: inverse of calculation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97620] Re: inverse of calculation
  • From: dh <dh at metrohm.com>
  • Date: Tue, 17 Mar 2009 04:59:06 -0500 (EST)
  • References: <gphdoe$oit$1@smc.vnet.net>


Hi Erik,

if a numerical approximation is good enough you may simply calculate the 

function to inverse for a number of {x,y} points. Then you exchange the 

x and y: {y,x} and use Interpolation to get a function. Take care that 

the function is invertible (no zeros). E.g.:

f1[x_] := Exp[x];

f2[x_] := x^2;

f3[x_] := f2[f1[x]];

Plot[f3[x], {x, 0, 3}]

dat = Reverse /@ Table[{x, f3[x]}, {x, 0, 3, .1}];

ListPlot[dat]

f4 = Interpolation[dat]

Plot[f4[x], {x, 1, 400}]



hope this helps, Daniel



Erik Henriksen wrote:

> hello everyone,

> 

> 

> i need assistance in inverting a calculation.  currently, i do the 

> following:

> 

> i have a dataset, D(x).  i wrote a notebook for a physical model of 

> the process that produces the data.  there is a model function, 

> d(a,b,c,x), where a,b,c are parameters i twiddle to get the best fit 

> (or ultimately let mathematica's nonlinearmodelfit do it for me).  

> there are also other physical inputs, call them e(x), that describe 

> parts of the system i'm studying.  in the end, i plot a curve F( e(x), 

> d(a,b,c,x) ), and by varying the model parameters i try to find the 

> d() that makes F look the most like D.

> 

> i'd like to flip this process around.

> 

> that is, i'd like to invert the calculation such that i input D(x) (or 

> a smooth interpolation of it)  into Finv ( e(x), D(x) ) and get back a 

> curve d(x).

> 

> with a single function, i might just invert it.  however, F() here is 

> actually a set of nested functions F(G(H(e(x),d(x))))=96 there's a 

> number of effects i'm modeling=96, and so i'm unsure how to proceed.  

> heck, i'm not sure it can be done in principle.

> 

> 

> 

> thank you very much for any help.

> 

> best,

> erik

> 

> 




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