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Re: Simultaneous Nonlinear Data Fits

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109275] Re: Simultaneous Nonlinear Data Fits
  • From: TheBalrog <TheBalrogEE at gmail.com>
  • Date: Tue, 20 Apr 2010 05:50:33 -0400 (EDT)

I am trying to do something similar but I'm afraid I don't understand all of the syntax or the expressions in either example.  I'd like to post a notebook, but I'm not sure that it's possible on this forum.

In Daniel's example, I cannot identify the expression, and thus cannot replace it with my own.  It seems as though there are three expressions depending on the value of z (although I don't know what the zero means at the end of the If statement).  Also in the FindFit[data,expr,pars,vars] command I do not know what x1,x2 and x3 refer to (are they related to x0?), nor do I understand how this expression relates to the previous one.

In DanO's example I don't understand step 5.  If the expression is myPeak, then why multiply it by KroneckerDelta[index-1]?  Sorry for my ignorance but I'm not a mathematician.

I enclose a function I am familiar with and two datasets I would like to fit; I have also written a Manipulate command so that anyone who would like to help can understand the expression.  The independent variables are "S" and "Inh" and I would like to get a global solution for Vmax, Km and Ki.

Naturally any help is greatly appreciated.

data2D = {{0, 0}, {1, 2.5`}, {2, 3.5`}, {3, 3.8`}, {4, 4}, {0, 0}, {1,
     1}, {2, 1.6`}, {3, 2.1`}, {4, 2.5`}};

data3D = {{0, 0, 0}, {0, 1, 2.5`}, {0, 2, 3.5`}, {0, 3, 3.8`}, {0, 4, 
    4}, {1, 0, 0}, {1, 1, 1.5`}, {1, 2, 2}, {1, 3, 2.3`}, {1, 4, 
    2.5`}};

expr = (Vmax (S))/((1 + Inh/Ki) Km + S);

Manipulate[
 Show[{Plot[(Vmax (S))/(Km (1 + (Inh/Ki)) + S), {S, 0, 4}, 
    PlotRange -> {{0, 5}, {0, 5}}], 
   ListPlot[data2D, PlotMarkers -> {\[FilledCircle], 10}]}], {Vmax, 0,
   5}, {Km, 0, 5}, {Inh, 0, 1}, {Ki, 0.1, 1}]


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