# Running a function in “for” cycle, containing vpasolve()

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Bogdan MP on 30 Nov 2021
Commented: Bogdan MP on 2 Dec 2021
I have some function in my script that solves a system of nonlinear algebraic equations
function Lam = lambdas1(x1, x2, x3, x4, w1, w2, g, tau, eta, zeta, sigma, eps, kap, gam_1, gam_2)
lam = 0.5 * atanh(-2*g / (w1 + w2 - 2*zeta - 2*eta));
mu = cosh(lam); nu = sinh(lam);
Om = -2*zeta - 2*eta*(nu/mu)^2 + 2*g*(nu/mu) + w2 * (nu/mu)^2 + w1;
A1 = mu^2*w1 + nu^2*w2; A2 = nu^2*w1 + mu^2*w2;
B = mu*nu*(w1 + w2); C = g*(mu^2 + nu^2) - 2*mu*nu*(zeta + eta);
F1 = 2*(zeta*mu^2 + eta*nu^2 - g*mu*nu);
F2 = 2*(zeta*nu^2 + eta*mu^2 - g*mu*nu);
Lam = vpasolve(-kap*(x1)^3 - kap*x2*(x1)^2 + 2*mu*tau*Om*(x1)^2 - 0.5*gam_1*x1 + ...
(A1-F1)*x2 + (B-C)*x4 + 0.5*mu*tau*Om == 0, ...
-(kap*(x1)^2*x2 + kap*(x2)^3 + 8*Om*tau^2*(x1)^3 + 4*mu*Om*tau*x1*x2 + ...
(A1+F1+6*tau^2*Om)*x1 + 0.5*gam_1*x2 - (B+C)*x3 - nu*sigma + eps*mu) == 0, ...
(B+C)*x2 - 0.5*gam_2*x3 + (A2+F2)*x4 == 0, ...
-((C-B)*x1 + (A2-F2)*x3 + 0.5*gam_2*x4 + mu*sigma - eps*nu) == 0, ...
[x1, x2, x3, x4]);
end
Where are real symbolic numbers which I define in the script (outside the sunction). I need to run this function in the cycle like this one (I have a vector ov values of zeta and I wish to solve a system for each of them)
syms x1 x2 x3 x4 real
for k = 1 : some_number
lam = 0.5 * atanh(-2*g / (w1 + w2 - 2*zeta(k) - 2*eta));
mu = cosh(lam);
nu = sinh(lam);
Om = -2*zeta(k) - 2*eta*(nu/mu)^2 + 2*g*(nu/mu) + w2 * (nu/mu)^2 + w1;
A1 = mu^2*w1 + nu^2*w2; A2 = nu^2*w1 + mu^2*w2;
B = mu*nu*(w1 + w2); C = g*(mu^2 + nu^2) - 2*mu*nu*(zeta(k) + eta);
F1 = 2*(zeta(k)*mu^2 + eta*nu^2 - g*mu*nu);
F2 = 2*(zeta(k)*nu^2 + eta*mu^2 - g*mu*nu);
My_roots = vpasolve(-kap*(x1)^3 - kap*x2*(x1)^2 + 2*mu*tau*Om*(x1)^2 - 0.5*gam_1*x1 + ...
(A1-F1)*x2 + (B-C)*x4 + 0.5*mu*tau*Om == 0, ...
-(kap*(x1)^2*x2 + kap*(x2)^3 + 8*Om*tau^2*(x1)^3 + 4*mu*Om*tau*x1*x2 + ...
(A1+F1+6*tau^2*Om)*x1 + 0.5*gam_1*x2 - (B+C)*x3 - nu*sigma + eps*mu) == 0, ...
(B+C)*x2 - 0.5*gam_2*x3 + (A2+F2)*x4 == 0, ...
-((C-B)*x1 + (A2-F2)*x3 + 0.5*gam_2*x4 + mu*sigma - eps*nu) == 0, ...
[x1, x2, x3, x4]);
Solution_I_need(k) = My_roots.x1(1) + 1i*My_roots.x2(1);
end
But even for two iterations, it takes an extra-long time. Could you tell me please, how to deal with it properly?
Bogdan MP on 2 Dec 2021
Did you simply run putting zeta as a symbolic variable? Because when I was trying to obtain the general result this way it was too long and I aborted running.

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