Solve matrix in the equation

Dear Matlab experts,

I would like to get b values, but I think my coding is wrong. Please let me know how to get the b values.

syms b G = [7340, 7194]; G1 = [4516.881,5002.953]; M1 =[ 5222.328, 6009.419]; M2 =[3264.034, 2632.621]; P1 =[3000, 3025]; P2 =[10000, 10051]; Out=solve(G1 == G*(P1*exp(-b*M1/P1)/( P1*exp(-b*M1/P1)+ P2*exp(-b*M2/P2))), b) Out=double(out)

Thank you very much in advance.

Sincerely yours,

Redwood

Answer 1

[Roger Stafford]

You can't use the 'solve' function with vector inputs in that manner. You should leave all six parameters as symbols and let 'solve' obtain a general solution for 'b' as a function of them. Then use matlab to evaluate this function for your vector inputs.

Actually you don't even need 'solve' in this very elementary case. You can solve it yourself with simple algebra. The following equations are equivalent:

 G1 = G*(P1*exp(-b*M1/P1)/(P1*exp(-b*M1/P1)+ P2*exp(-b*M2/P2)))

 G1/G = 1/(1+P2/P1*exp(-b*(M2/P2-M1/P1)))

 P2/P1*exp(-b*(M2/P2-M1/P1)) = G/G1 - 1

 exp(-b*(M2/P2-M1/P1)) = (G/G1-1)*P1/P2

 -b*(M2/P2-M1/P1) = log((G/G1-1)*P1/P2)

 b = -log((G/G1-1)*P1/P2)/(M2/P2-M1/P1)

This last equation is your general solution for b in terms of the six parameters, so evaluate it directly with matlab:

 b = -log((G./G1-1).*P1./P2)./(M2./P2-M1./P1);

Answer 2

[Zhang lu]

syms b G G1 M1 M2 P1 P2
Out=solve('G*(P1*exp(-b*M1/P1)/( P1*exp(-b*M1/P1)+ P2*exp(-b*M2/P2)))-G1', b)
G = [7340, 7194];
G1 = [4516.881,5002.953]; 
M1 =[ 5222.328, 6009.419];  
M2 =[3264.034, 2632.621]; 
P1 =[3000, 3025]; 
P2 =[10000, 10051]; 
Out=subs(Out)