how to minimize a parameter

Hi, mi programm is this one

 function theoretical1
clc; 
clear all; 
close all;
tau1=147;
k0=[150000 1.5 1.5 1.5];
nu=[-1; -5 ;-6];   % stoichiometrical matrix of coefficients
C01 = [0.00005 0.001 0.05];   % initial concentratio of measure j
[time1,C1]= ode45(@myode1,[0 tau1],C01);

 function dC1dt=myode1(t,C)
R1=k0(1)*C(1)^k0(2)*C(2)^k0(3)*C(3)^k0(4);
r1=nu*R1;
dC1dt=r1;
end

 %Volume
 V=0.5;

 %species A B and C refer to KIO3 KI and H

 %Test one
 load ('prova1.mat','seconds','absorbance')
 csi1_1=0.2276*absorbance/1000; %in mol/L (M)
 sec_1=seconds;

 %Initial Concentrations
 C0_1=[0.00005 0.001 0.05]; %species A,B and C

 C0_A_1=C0_1(1); %conc OF IO3- in mol/L
 C0_B_1=C0_1(2); %conc OF I- in mol/L
 C0_C_1=C0_1(3); %conc OF H+ in mol/L

 %Concentration in time
 %from excel plot we know that there is a correlation between   absorbance and
 %the concentration of I2 that follows a linear rule as follows:  C=0.081*A

 C_A_1=C0_A_1-csi1_1;
 CI2_1=absorbance*0.081/1000;
 csi2_1=3*csi1_1-CI2_1; %mol/L
 C_B_1=C0_B_1-5*csi1_1-csi2_1;
 C_C_1=C0_C_1-6*csi1_1;

 C_exp_1=[C_A_1 C_B_1 C_C_1];
 err1=[C1(2)-C_A_1  C1(3)-C_B_1   C1(4)-C_C_1];
  N1=norm(err1);
 end

I have some experimental values of concentration C given and I have to hypothize the values of of the vector k0 in order to calculate a theoretical concentration. What I would like to do now is to minimize the norm N1 by optimizing the values of k0. I know that there are some functions as fminsearch but I really don't know how to use them. Can someone help me with this? Thank you

Answer 1

[Alan Weiss]

Perhaps this example will help.

Alan Weiss

MATLAB mathematical toolbox documentation

[Gisela]

But if my parameters are within an ode, where do I insert this function? Because reading your link I define the function in Fittedcurve, yet I cannot defined the function that way.

[Alan Weiss]

Perhaps this example will help. It uses patternsearch instead of fmincon, but fmincon works, too, especially if you set larger-than-default finite differences.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Star Strider]

I cannot follow your code, but if you want to fit data using an ODE in your objective function, see: Monod kinetics and curve fitting.

[Gisela]

I'm also having a hard time following the link you posted. My problem is basically this: i have vector C_exp_1 which is something I know. Now they tell me the reaction rate is k1C1^a*C2^b*C3^c. Knowing the initial concentration I have to find the values of k1,a,b,c in order to minimize the error between the values present in my vector C_exp_1 and the values of C1, C2 and C3 calculated through the ODE

[Torsten]

Set

B0 = [k1 a b c]

Time = Vector of the times when the measurements were performed
       (threefold repeated) [0 0 0 t1 t1 t1 t2 t2 t2 ... tn tn tn]

Sdata = Vector of concentrations at the time instants for the three components
        [C01 C02 C03 C11 C12 C13 C21 C22 C23 ... Cn1 Cn2 Cn3]

x0 = Vector of initial concentrations [C01 C02 C03]

t in the call to ODE45 = [0 t1 t2 ... tn]

S = [Sv(1,1) Sv(1,2) Sv(1,3) Sv(2,1) Sv(2,2) Sv(2,3) ... Sv(n+1,1) Sv(n+1,2) Sv(n+1,3)]

Best wishes

Torsten.

[Gisela]

To Torsten I'm assuming that S is the error I was talking about. But how do I minimize it? Or the way in which you set it is already minimized?

[Torsten]

Yes, lsqcurvefit automatically forms the sum of squared differences between S and Sdata.

Best wishes

Torsten.