[Scilab-users] Convert x, y, z data into a z=f(x,y) function
Michael J. McCann
mccannscience at comcast.net
Mon Jul 1 13:00:53 CEST 2013
Larisssa,
Now we have a clue. Many years ago I worked on dynamic system models of
fermentation. What I did was to create a differential equation set to
account for the identifiable "species" --- abstract idea which includes
various bio-chemical generic classes -- and running those models and
experimenting it became possible to get a working model, by choosing
parameters. When that reached its limit, moving on to more complex
models enabled us (me and a micologist) to create a model good enough to
predict the performance of an industrial process.
In your case I'd start with a very simple model, and I'd expect
that since the growth rate in biomass would initially probably increase
in proportion to the mass present the model would give an exponential
initial rate, then as the algae blocked the light it wanted and the
other key food sources (dissolved oxygen?) were depleted, the rate would
decline. In the work I did in the past we got into the metabolic
pathways and energy balances with heat and synthesis reaction rates,
but I'd start with something simpler in your case to see how simple a
model would explain the process. I would be a good candidate for a model
in Xcos. You can look into my website
http://www.mccannscience.com/fermenta.htm
if you are interested.
Mike
=======================
On 01/07/2013 09:24, Larissa wrote:
> Hi,
> so regarding the data..
> it was an experiment related to algal biomass yield (g/m²) ("z")
> according to time (0-25days, the "x"-data) and light intensity
> (25-1000µmol*m^-1*s^-1, the "y" values). Increase in biomass might
> have been exponential right at the beginning, but with increasing time
> I guess it turned out to be linear...
> does anybody have a hint about the model I could use?:)
> *Gesendet:* Montag, 01. Juli 2013 um 11:14 Uhr
> *Von:* "Mike Page [via Scilab / Xcos - Mailing Lists Archives]"
> <[hidden email] </user/SendEmail.jtp?type=node&node=4026926&i=0>>
> *An:* Larissa <[hidden email]
> </user/SendEmail.jtp?type=node&node=4026926&i=1>>
> *Betreff:* Re: Convert x, y, z data into a z=f(x,y) function
> ?
> 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:* [hidden email] [mailto:[hidden email]]*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" <[hidden email]>
> *An:* "International users mailing list for Scilab." <[hidden email]>
> *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 : [hidden email] [mailto:[hidden email]] 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
>
> ______________________________________________________________________
>
> This e-mail may contain confidential and/or privileged
> information. If you are not the intended recipient (or have
> received this e-mail in error), please notify the sender
> immediately and destroy this e-mail. Any unauthorized copying,
> disclosure or distribution of the material in this e-mail is
> strictly forbidden.
> ______________________________________________________________________
> _______________________________________________
> users mailing list
> [hidden email]
> http://lists.scilab.org/mailman/listinfo/users
> _______________________________________________
> users mailing list
> [hidden email]
> http://lists.scilab.org/mailman/listinfo/users
>
>
> _______________________________________________
> users mailing list
> [hidden email]
> http://lists.scilab.org/mailman/listinfo/users
>
> ------------------------------------------------------------------------
> If you reply to this email, your message will be added to the
> discussion below:
> http://mailinglists.scilab.org/Convert-x-y-z-data-into-a-z-f-x-y-function-tp4026897p4026925.html
> To unsubscribe from Convert x, y, z data into a z=f(x,y) function,
> click here.
> NAML
> <http://mailinglists.scilab.org/template/NamlServlet.jtp?macro=macro_viewer&id=instant_html%21nabble%3Aemail.naml&base=nabble.naml.namespaces.BasicNamespace-nabble.view.web.template.NabbleNamespace-nabble.view.web.template.NodeNamespace&breadcrumbs=notify_subscribers%21nabble%3Aemail.naml-instant_emails%21nabble%3Aemail.naml-send_instant_email%21nabble%3Aemail.naml>
>
> ------------------------------------------------------------------------
> View this message in context: Aw: Re: Convert x, y, z data into a
> z=f(x,y) function
> <http://mailinglists.scilab.org/Convert-x-y-z-data-into-a-z-f-x-y-function-tp4026897p4026926.html>
> Sent from the Scilab users - Mailing Lists Archives mailing list
> archive
> <http://mailinglists.scilab.org/Scilab-users-Mailing-Lists-Archives-f2602246.html>
> at Nabble.com.
>
>
> _______________________________________________
> users mailing list
> users at lists.scilab.org
> http://lists.scilab.org/mailman/listinfo/users
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20130701/5aed1271/attachment.htm>
More information about the users
mailing list