Solve of implicity equations

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?

Answer 1

[Torsten]

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

rho = 0.0200

uno_alpha_A = ((1-alpha)*A)

uno_alpha_A = 2838

dos_rho = (2+rho)

dos_rho = 2.0200

uno_n = (1+n)

uno_n = 1.0100

uno_rho = (1+rho)

uno_rho = 1.0200

alpha_A = (alpha*A)

alpha_A = 462.0000

alpha_uno = (alpha-1)

alpha_uno = -0.8600

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))

Answer 2

[John D'Errico]

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)

ans = 

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])

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

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])

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

That still is going nowhere near zero. I'll narrow the range again.

fplot(fcn,[0,20])

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

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.

[Walter Roberson]

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;
syms k
F = fcn(k)

F = 

criticals = solve(diff(F,k),k, 'returnconditions', true)

criticals = struct with fields:
             k: z2^50
    parameters: z2
    conditions: z2^129 + (7439124*z2^86)/10201 + (341723844*z2^43)/10201 + (140019541200*z2^36)/10201 - 424027850400/10201 == 0 & -pi/50 < angle(z2) & angle(z2) <= pi/50

best = vpasolve(diff(F,k),k,5)

best = 

4.6384218721011299497817383048764

subs(F,k,best)

ans = 

limit(F,k,0), vpa(ans)

ans = 

ans = 

[John D'Errico]

But, apparently, a negative root.

[Walter Roberson]

I was confirming your "near 5" for the peak, and showing it is not nearly a zero.