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inverse of calculation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97525] inverse of calculation
  • From: Erik Henriksen <erikku at caltech.edu>
  • Date: Sat, 14 Mar 2009 18:14:31 -0500 (EST)

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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