Solve of implicity equations
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Hola que tal, estoy ralizando esta ejecución pero mi variables de interés da NaN
alpha = 0.14; A = 3300; n = 0.01 ; b_2019 = 69100; rho = 0.02
uno_alpha_A = ((1-alpha)*A)
dos_rho = (2+rho)
uno_n = (1+n)
uno_rho = (1+rho)
alpha_A = (alpha*A)
alpha_uno = (alpha-1)
fcn = @(K) (uno_alpha_A*K^(alpha))/(dos_rho*uno_n)-((1+uno_rho*(1+alpha_A*K^alpha_uno)^(-1))/(dos_rho*uno_n))*b_2019 - K;
sols = fzero(fcn, 1)
Alguien me podría a yudar a solucionar este percance, por favor?
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Réponses (2)
Torsten
le 24 Mar 2023
You should first check whether a zero of your function really exists. It doesn't seem to be the case:
alpha = 0.14; A = 3300; n = 0.01 ; b_2019 = 69100; rho = 0.02
uno_alpha_A = ((1-alpha)*A)
dos_rho = (2+rho)
uno_n = (1+n)
uno_rho = (1+rho)
alpha_A = (alpha*A)
alpha_uno = (alpha-1)
fcn = @(K) (uno_alpha_A*K.^(alpha))./(dos_rho*uno_n)-((1+uno_rho*(1+alpha_A*K.^alpha_uno).^(-1))./(dos_rho*uno_n))*b_2019 - K;
K = 0:0.1:10;
plot(K,fcn(K))
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John D'Errico
le 24 Mar 2023
Modifié(e) : John D'Errico
le 24 Mar 2023
alpha = 0.14; A = 3300; n = 0.01 ; b_2019 = 69100; rho = 0.02;
uno_alpha_A = ((1-alpha)*A);
dos_rho = (2+rho);
uno_n = (1+n);
uno_rho = (1+rho);
alpha_A = (alpha*A);
alpha_uno = (alpha-1);
fcn = @(K) (uno_alpha_A*K^(alpha))/(dos_rho*uno_n)-((1+uno_rho*(1+alpha_A*K^alpha_uno)^(-1))/(dos_rho*uno_n))*b_2019 - K;
Sometimes, a symbolic expression can be easier to look at.
syms k
fcn(k)
So we have an expression with powers of k. I suppose it might have a solution. Try plotting it. A basic rule is to ALWAYS PLOT EVERYTHING. And then, plot something else if you can find anything else to plot. Think about what you see.
fplot(fcn,[0,100000])
And that shows no solution so far. It seems to be going asymptotically linearly to -inf for large k. And that makes sense. So I'll narrow the range.
fplot(fcn,[0,100])
That still is going nowhere near zero. I'll narrow the range again.
fplot(fcn,[0,20])
It seems clear this has a maximum value for positive K around K==5, but t is still very far away from zero.
There appear to be no positive solutions. And any negative solutions will generate complex results.
So the failure of fzero to find a root just tells you there is no root.
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Walter Roberson
le 24 Mar 2023
I was confirming your "near 5" for the peak, and showing it is not nearly a zero.
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