[Scilab-users] Convert x, y, z data into a z=f(x,y) function

[Mike Page]

Hi,

You are asking a question which in general has no answer.  There are an infinite number of models which can fit your data.  You need to find some possible candidate model forms based on physical properties and then try fitting to them.  You are probably looking for a fit which leaves residues which are Gaussian and mean zero (but that's not always true...).

Try giving us a clue about where the data come from.  Maybe somebody has the physical background to suggest some models.  If not, try plotting the data and guessing a model from the shape.  To me the shape looks vaguely exponential or logarithmic, so maybe plotting as log-linear or log-log will give a clue.

HTH,
Mike.

  -----Original Message-----
  From: users-bounces at lists.scilab.org [mailto:users-bounces at lists.scilab.org]On Behalf Of Larissa Schultze
  Sent: 01 July 2013 09:43
  To: International users mailing list for Scilab.
  Subject: Re: [Scilab-users] Convert x, y, z data into a z=f(x,y) function


  Hello all,

  first of all, thanks a lot for your effort. I must say that I don't really have anyone to run to for asking about mathematical models - I could go to the mathematicians at the University, but I don't know anyone there and I barelly know where the institute is located...

  therefore I decided to insert my simplest table in here (it is actually very simple) - may be someone here knows which kind of mathematical model I could use?
  I have been searching for it in literature, but I don't seem to be in the right path...

  So attached you will find my data table as well as the scilab commands I used to create the respective graph. I mean, my data is already interpolated...shouldn't it be easy to get a function (z,x,y) out of it?

  I would be very very thankful for any help...I'm getting a bit desperate...

  best regards,
  Larissa



    
  Gesendet: Dienstag, 25. Juni 2013 um 11:09 Uhr
  Von: "CRETE Denis" <denis.crete at thalesgroup.com>
  An: "International users mailing list for Scilab." <users at lists.scilab.org>
  Betreff: Re: [Scilab-users] Convert x, y, z data into a z=f(x,y) function
  Hello,

  The general procedure for fitting data in the case of 2 variables is the following:
  // First define your mathematical model by changing the following line
  deff('z=MyFunction(x,y)', 'z=p(1)*x + p(2)*y + p(3)*x.*y');
  // Store all experimental data in a single array ExD; X, Y, Z assumed to be 1 x NZ vectors
  ExD=[X;Y;Z];
  // Define the error function (to be minimized with respect to the parameters p)
  deff('erro=G(p,ExD)','x=ExD(1),y=ExD(2), z=ExD(3), erro=z-MyFunction(x,y)')
  // Fit experimental data contained in W
  // The column vector p0 is an initial guess of the values for the parameters of your Model
  [p,err]=datafit(G,ExD,p0)
  // you can check values generated with
  MyFunction(X,Y)

  HTH
  Denis

  -----Message d'origine-----
  De : users-bounces at lists.scilab.org [mailto:users-bounces at lists.scilab.org] De la part de Dang, Christophe
  Envoyé : mardi 25 juin 2013 10:20
  À : International users mailing list for Scilab.
  Objet : Re: [Scilab-users] Convert x, y, z data into a z=f(x,y) function

  Hello,

  De la part de Larissa
  Envoyé : mardi 25 juin 2013 09:52

  > I conducted an experiment and thus my results are composed of x,y,z
  > data,
  [...]
  > but I can't figure out how to get an equation "z=f(x,y)" out of it.

  This is more a math problem than a Scilab problem.

  You must have a mathematical model, i.e. a parametric formula, then you can adjust the parameters by regression (or maximum likehood).

  You may have theoretical models that derive from elementary assumptions
  -- you usually find such model in the bibliography --, or use a "nice model that fit the global shape"
  -- you may ask the math laboratory in your neighbourhood, this is usually polynomials, exponentials, statistical laws...

  So if you come to us with a parametric model, we will be able to help you.

  best regards.

  --
  Christophe Dang Ngoc Chan
  Mechanical calculation engineer

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