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Larisssa,<br>
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.<br>
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 <br>
<a class="moz-txt-link-freetext" href="http://www.mccannscience.com/fermenta.htm">http://www.mccannscience.com/fermenta.htm</a><br>
if you are interested.<br>
Mike<br>
=======================<br>
<div class="moz-cite-prefix">On 01/07/2013 09:24, Larissa wrote:<br>
</div>
<blockquote
cite="mid:trinity-485c322a-5adf-4cf7-8b6f-fc9c581868e7-1372670654303@3capp-gmx-bs17"
type="cite">
<div style="font-family: Verdana;font-size: 12.0px;">
<div>
<div>Hi,</div>
<div> </div>
<div>so regarding the data..</div>
<div>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...</div>
<div> </div>
<div>does anybody have a hint about the model I could use?:)</div>
<div> </div>
<div> </div>
<div>
<div name="quote" style="margin:10px 5px 5px 10px; padding:
10px 0 10px 10px; border-left:2px solid #C3D9E5;
word-wrap: break-word; -webkit-nbsp-mode: space;
-webkit-line-break: after-white-space;">
<div style="margin:0 0 10px 0;"><b>Gesendet:</b> Montag,
01. Juli 2013 um 11:14 Uhr<br>
<b>Von:</b> "Mike Page [via Scilab / Xcos - Mailing
Lists Archives]" <<a moz-do-not-send="true"
href="/user/SendEmail.jtp?type=node&node=4026926&i=0"
target="_top" rel="nofollow" link="external">[hidden
email]</a>><br>
<b>An:</b> Larissa <<a moz-do-not-send="true"
href="/user/SendEmail.jtp?type=node&node=4026926&i=1"
target="_top" rel="nofollow" link="external">[hidden
email]</a>><br>
<b>Betreff:</b> Re: Convert x, y, z data into a z=f(x,y)
function</div>
<div name="quoted-content">
<div><span class="328270209-01072013"><font
color="#0000ff" face="Arial" size="2">Hi,</font></span></div>
<div> </div>
<div><span class="328270209-01072013"><font
color="#0000ff" face="Arial" size="2">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...).</font></span></div>
<div> </div>
<div><span class="328270209-01072013"><font
color="#0000ff" face="Arial" size="2">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.</font></span></div>
<div> </div>
<div><span class="328270209-01072013"><font
color="#0000ff" face="Arial" size="2">HTH,</font></span></div>
<div><span class="328270209-01072013"><font
color="#0000ff" face="Arial" size="2">Mike.</font></span></div>
<div> </div>
<blockquote style="border-left:2px solid
#CCCCCC;padding:0 1em">
<div class="OutlookMessageHeader" align="left"><font
face="Tahoma" size="2">-----Original Message-----<br>
<b>From:</b> <a moz-do-not-send="true"
target="_top" rel="nofollow" link="external">[hidden
email]</a> [mailto:<a moz-do-not-send="true"
target="_top" rel="nofollow" link="external">[hidden
email]</a>]<b>On Behalf Of </b>Larissa Schultze<br>
<b>Sent:</b> 01 July 2013 09:43<br>
<b>To:</b> International users mailing list for
Scilab.<br>
<b>Subject:</b> Re: [Scilab-users] Convert x, y, z
data into a z=f(x,y) function</font><br>
</div>
<div style="FONT-FAMILY: Verdana;FONT-SIZE: 12.0px;">
<div>
<div>Hello all,</div>
<div> </div>
<div>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...</div>
<div> </div>
<div>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?</div>
<div>I have been searching for it in literature,
but I don't seem to be in the right path...</div>
<div> </div>
<div>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?</div>
<div> </div>
<div>I would be very very thankful for any
help...I'm getting a bit desperate...</div>
<div> </div>
<div>best regards,</div>
<div>Larissa</div>
<div> </div>
<div> </div>
<div> </div>
<div>
<div style="BORDER-LEFT: rgb(195,217,229) 2.0px
solid;PADDING-BOTTOM: 10.0px;MARGIN: 10.0px
5.0px 5.0px 10.0px;PADDING-LEFT:
10.0px;PADDING-RIGHT: 0.0px;PADDING-TOP:
10.0px;">
<div style="MARGIN: 0.0px 0.0px 10.0px;"><b>Gesendet:</b> Dienstag,
25. Juni 2013 um 11:09 Uhr<br>
<b>Von:</b> "CRETE Denis" <<a
moz-do-not-send="true" target="_top"
rel="nofollow" link="external">[hidden
email]</a>><br>
<b>An:</b> "International users mailing list
for Scilab." <<a moz-do-not-send="true"
target="_top" rel="nofollow"
link="external">[hidden email]</a>><br>
<b>Betreff:</b> Re: [Scilab-users] Convert
x, y, z data into a z=f(x,y) function</div>
<div>Hello,<br>
<br>
The general procedure for fitting data in
the case of 2 variables is the following:<br>
// First define your mathematical model by
changing the following line<br>
deff('z=MyFunction(x,y)', 'z=p(1)*x + p(2)*y
+ p(3)*x.*y');<br>
// Store all experimental data in a single
array ExD; X, Y, Z assumed to be 1 x NZ
vectors<br>
ExD=[X;Y;Z];<br>
// Define the error function (to be
minimized with respect to the parameters p)<br>
deff('erro=G(p,ExD)','x=ExD(1),y=ExD(2),
z=ExD(3), erro=z-MyFunction(x,y)')<br>
// Fit experimental data contained in W<br>
// The column vector p0 is an initial guess
of the values for the parameters of your
Model<br>
[p,err]=datafit(G,ExD,p0)<br>
// you can check values generated with<br>
MyFunction(X,Y)<br>
<br>
HTH<br>
Denis<br>
<br>
-----Message d'origine-----<br>
De : <a moz-do-not-send="true"
target="_top" rel="nofollow"
link="external">[hidden email]</a>
[mailto:<a moz-do-not-send="true"
target="_top" rel="nofollow"
link="external">[hidden email]</a>] De la
part de Dang, Christophe<br>
Envoyé : mardi 25 juin 2013 10:20<br>
À : International users mailing list for
Scilab.<br>
Objet : Re: [Scilab-users] Convert x, y, z
data into a z=f(x,y) function<br>
<br>
Hello,<br>
<br>
De la part de Larissa<br>
Envoyé : mardi 25 juin 2013 09:52<br>
<br>
> I conducted an experiment and thus my
results are composed of x,y,z<br>
> data,<br>
[...]<br>
> but I can't figure out how to get an
equation "z=f(x,y)" out of it.<br>
<br>
This is more a math problem than a Scilab
problem.<br>
<br>
You must have a mathematical model, i.e. a
parametric formula, then you can adjust the
parameters by regression (or maximum
likehood).<br>
<br>
You may have theoretical models that derive
from elementary assumptions<br>
-- you usually find such model in the
bibliography --, or use a "nice model that
fit the global shape"<br>
-- you may ask the math laboratory in your
neighbourhood, this is usually polynomials,
exponentials, statistical laws...<br>
<br>
So if you come to us with a parametric
model, we will be able to help you.<br>
<br>
best regards.<br>
<br>
--<br>
Christophe Dang Ngoc Chan<br>
Mechanical calculation engineer<br>
<br>
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