How to define ranges for solutions in this example

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Ronald Singer
Ronald Singer 2017-7-25
编辑： Karan Gill 2017-10-17
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.

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采纳的回答

Karan Gill
Karan Gill 2017-7-25
编辑：Karan Gill 2017-10-17
To specify ranges for multiple variables, see the last example on Solve Equations Numerically called " Solve Multivariate Equations Using Search Ranges"

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