MATLAB: How to do parameter fitting for a system of equations with 3 independent variables

fittingmultiple regressionnlinfit

I have a system of 3 equations with 3 independent variables( x1,x2,x3) and correspondingly 3 dependent variables( y1,y2,y3) as follows:

y1=((b1*x1)/(1+(b1*x1)+(b2*x2)+(b3*x3))) + ((b4*x1)/(1+(b1*x1)+(b2*x2)+(b3*x3)));
y2=((b2*x2)/(1+(b1*x1)+(b2*x2)+(b3*x3))) + ((b5*x2)/(1+(b1*x1)+(b2*x2)+(b3*x3)));
y3=((b3*x3)/(1+(b1*x1)+(b2*x2)+(b3*x3))) + ((b6*x3)/(1+(b1*x1)+(b2*x2)+(b3*x3)));

x and y data are available.

I need to fit 6 parameters( b1,b2,b3,b4,b5,b6) in this system.

I tried using nlinfit but couldn't make it work for this case. Suggest me how to solve this problem. Thank you.

Best Answer

xdata = horzcat(x1,x2,x3);
ydata = horzcat(y1,y2,y3);
fun=@(b,xdata) horzcat((b(1)+b(4))*x1./(1+b(1)*x1+b(2)*x2+b(3)*x3),(b(2)+b(5))*x2./(1+b(1)*x1+b(2)*x2+b(3)*x3),(b(3)+b(6))*x3./(1+b(1)*x1+b(2)*x2+b(3)*x3));
b0=[1 ; 1 ; 1 ; 1 ; 1 ; 1];
[x,resnorm] = lsqcurvefit(fun,b0,xdata,ydata);

Best wishes

Torsten.

Related Solutions

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables and a complex function expression

You didn’t show your code, so I’m not certain what you’re doing.

You have to combine your independent variables in a matrix (I prefer column vectors for the independent and dependent variables), present them as one variable, then address the individual columns as the individual variables in your objective function.

For example:

x1x2x3 = [x1(:) x2(:) x3(:)];
y = y(:);
y = (k,x) k(1).*(1-exp(k(2).*x1x2x3(:,1))).*x1x2x3(:,3).^2 + ...

I’m not certain I parsed the parentheses correctly, so I’ll let you sort that.

Here, you would call nlinfit as:

k_est = nlinfit(x1x2x3, y, modelfun, k0);

MATLAB: Isqnonlin command: not enough input parameters error

Hi,

try:

% Sabit degerler
k = 1.38e-23;      % Boltzman sabiti
q = 1.602e-19;     % Elektronun yuku
T = 25+273;        % Sicaklik (K)
Ns = 36;           % Hucre Sayisi
a1 = 2.4;          % Isc
a2 = 21.8;         % Voc
a3 = 17.2;         % Vmpp
a4 = 2.20;         % Impp
a5 = (Ns*k*T)/q;   % Vt
%Is0 = (a1+Ki*dt)/(exp((a2+Kv*dt)/(x3*a5))-1);
x0 = [2.4, 1.2e-7, 1.5, 0.5, 600];
lb = [2, 1e-7, 1.3, 0.3, 400];
ub = [2.6, 5e-7, 1.7, 0.7, 900];
x = lsqnonlin(@(x)myfun(x, a1, a2, a3, a4, a5), x0, lb, ub);
function f = myfun(x, a1, a2, a3, a4, a5)
x1 = x(1);
x2 = x(2);
x3 = x(3);
x4 = x(4);
x5 = x(5);
f(1) = x1-x2*(exp((x4*a1)/(x3*a5))-1)-((x4*a1)/x5)-a1;
f(2) = x2*(exp(a2/(x3*a5))-1)+(a2/x5)-x1;
f(3) = x1-x2*(exp((a3+x4*a4)/(x3*a5))-1)-((a3+x4*a4)/x5)-a4;
f(4) = a3*(((x2/(x3*a5))*exp((a3+x4*a4)/(x3*a5))+(1/x5))/(1+((x4*x2)/(x3*a5))*exp((a3+x4*a4)/(x3*a5))+(x4/x5)))-a4;
f(5) = (((x2/(x3*a5))*exp((x4*a1)/(x3*a5))+(1/x5))/(1+((x4*a1)/(x3*a5))*exp((x4*a1)/(x3*a5))+(x4/x5)))-(1/x5);
end

Best regards

Stephan

Best Answer

Related Solutions

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables and a complex function expression

MATLAB: Isqnonlin command: not enough input parameters error

Related Question