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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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