How to define ranges for solutions in this example

Hello,

i got the following code to create a formula which includes 4 parameters, which i want to estimate:

syms A B b t0 real

x11=-1;x21=-1;x31=1;x41=1;
x1=[x11;x21;x31;x41];

x12=-1;x22=1;x32=-1;x42=1;
x2=[x12;x22;x32;x42];

t1=98;             t2=52.5;             t3=29;             t4=24;

Versuchsdaten=[t1;t2;t3;t4];

logL=0;
for i=1:length(Versuchsdaten)
    logL=logL+log(b/(exp((A*x1(i)+B*x2(i)+A*B*x1(i)*x2(i)))-t0))+log(((Versuchsdaten(i)-t0)/(exp((A*x1(i)+B*x2(i)+A*B*x1(i)*x2(i)))-t0))).^(b-1)-((Versuchsdaten(i)-t0)/exp((A*x1(i)+B*x2(i)+A*B*x1(i)*x2(i))-t0)).^(b);

end

Now i create four partial derivations:

dLdb=diff(logL,b);
dLdt0=diff(logL,t0);
dLdA=diff(logL,A);
dLdB=diff(logL,B);

After that, im solving this equations:

[b_hat, t0_hat, A_hat, B_hat] = vpasolve([dLdb==0, dLdt0==0, dLdA==0, dLdB==0],[b, t0, A, B]);

And i get following results:

0.22827585315780297509118525877644

-1.1888587849400038882573418242591

-0.10771134364438446209957736245859

-0.050991408729052753335794920302386

The problem is, the solutions must be in defined ranges.

The ranges are: [0 Inf] for b and t0, [-1 1] for A and B. How can i do that? I already tried:

[b_hat, t0_hat, A_hat, B_hat] = vpasolve([dLdb==0, dLdt0==0, dLdA==0, dLdB==0],[b, [0 Inf] t0,[0 Inf] A,[-1 1] B, [-1 1]]);

and

[b_hat, t0_hat, A_hat, B_hat] = vpasolve([dLdb==0, dLdt0==0, dLdA==0, dLdB==0],[b, t0, A, B], [0 Inf], [0 Inf], [-1 1], [-1 1]);

I hope you can understand my problem and try to help me.

Answer 1

[Karan Gill]

To specify ranges for multiple variables, see the last example on Solve Equations Numerically called " Solve Multivariate Equations Using Search Ranges"