MATLAB: Solving equation with for loop is slow

for loop

I have an equation (5th order Polynomial) and I have to solve it every time for different variables A,B and Coeff as written down. And the coefficient are quite alot (100000) I had no other way than using the for loop to do it but it is incredibely slow. Could anyone please give me a suggestion to make it faster or if there is another way to solve the equation faster.
This is my code:
    tCounter = zeros(length(A),1); 
    for i = 1:length(A)
    syms t
    Check = (isnan(B(i,1))==1);
    if Check ==1
    tCounter(i) = NaN;
    else
    Equation = -(Coeff(21).*((B(i,2) + t*A(i,2)).^5) + (Coeff(20).*((B(i,2) + t*A(i,2)).^4)).*(B(i,1) + t*A(i,1)) + Coeff(19).*((B(i,2) + t*A(i,2)).^4) + (Coeff(18).*((B(i,2) + t*A(i,2)).^3)).*((B(i,1) + t*A(i,1)).^2) + (Coeff(17).*((B(i,2) + t*A(i,2)).^3)).*(B(i,1) + t*A(i,1)) + Coeff(16).*((B(i,2) + t*A(i,2)).^3) + (Coeff(15).*((B(i,2) + t*A(i,2)).^2)).*((B(i,1) + t*A(i,1)).^3) + (Coeff(14).*((B(i,2) + t*A(i,2)).^2)).*((B(i,1) + t*A(i,1)).^2) + (Coeff(13).*((B(i,2) + t*A(i,2)).^2)).*(B(i,1) + t*A(i,1)) + Coeff(12).*((B(i,2) + t*A(i,2)).^2) + (Coeff(11).*((B(i,2) + t*A(i,2)))).*((B(i,1) + t*A(i,1)).^4) + (Coeff(10).*(B(i,2) + t*A(i,2))).*((B(i,1) + t*A(i,1)).^3) + (Coeff(9).*(B(i,2) + t*A(i,2))).*((B(i,1) + t*A(i,1)).^2) + (Coeff(8).*(B(i,2) + t*A(i,2))).*((B(i,1) + t*A(i,1))) + (Coeff(7).*(B(i,2) + t*A(i,2))) + Coeff(6).*((B(i,1) + t*A(i,1)).^5) + Coeff(5).*((B(i,1) + t*A(i,1)).^4) + Coeff(4).*((B(i,1) + t*A(i,1)).^3) + Coeff(3).*((B(i,1) + t*A(i,1)).^2) + Coeff(2).*(B(i,1) + t*A(i,1)) + Coeff(1)) + Thickness - (B(i,3) + t*A(i,3));
    t = solve(Equation,t);
    t = double (t);
    t(imag(t) ~= 0) = [];
    t(t<0) = [];
    t = min(t);
    tCounter(i) = t;
    end
    end
Many thanks in advance

Best Answer

solve() generically outside of the loop and then subs() or matlabFunction() to get code executed for each loop instance.
t = roots( [Coeff(6)*A(i, 1)^5+Coeff(11)*A(i, 1)^4*A(i, 2)+Coeff(15)*A(i, 1)^3*A(i, 2)^2+Coeff(18)*A(i, 1)^2*A(i, 2)^3+Coeff(20)*A(i, 1)*A(i, 2)^4+Coeff(21)*A(i, 2)^5,
            (5*Coeff(6)*B(i, 1)+Coeff(11)*B(i, 2)+Coeff(5))*A(i, 1)^4+(2*(2*Coeff(11)*B(i, 1)+Coeff(15)*B(i, 2)+(1/2)*Coeff(10)))*A(i, 1)^3*A(i, 2)+(3*Coeff(15)*B(i, 1)+3*Coeff(18)*B(i, 2)+Coeff(14))*A(i, 1)^2*A(i, 2)^2+(2*Coeff(18)*B(i, 1)+4*Coeff(20)*B(i, 2)+Coeff(17))*A(i, 1)*A(i, 2)^3+(Coeff(20)*B(i, 1)+5*Coeff(21)*B(i, 2)+Coeff(19))*A(i, 2)^4,
            (10*Coeff(6)*B(i, 1)^2+Coeff(15)*B(i, 2)^2+(4*Coeff(11)*B(i, 2)+4*Coeff(5))*B(i, 1)+Coeff(10)*B(i, 2)+Coeff(4))*A(i, 1)^3+(3*(2*Coeff(11)*B(i, 1)^2+Coeff(18)*B(i, 2)^2+(2*Coeff(15)*B(i, 2)+Coeff(10))*B(i, 1)+(2/3)*Coeff(14)*B(i, 2)+(1/3)*Coeff(9)))*A(i, 1)^2*A(i, 2)+(3*Coeff(15)*B(i, 1)^2+6*Coeff(20)*B(i, 2)^2+(6*Coeff(18)*B(i, 2)+2*Coeff(14))*B(i, 1)+3*Coeff(17)*B(i, 2)+Coeff(13))*A(i, 1)*A(i, 2)^2+(Coeff(18)*B(i, 1)^2+10*Coeff(21)*B(i, 2)^2+(4*Coeff(20)*B(i, 2)+Coeff(17))*B(i, 1)+4*Coeff(19)*B(i, 2)+Coeff(16))*A(i, 2)^3,
            (10*Coeff(6)*B(i, 1)^3+Coeff(18)*B(i, 2)^3+(6*Coeff(11)*B(i, 2)+6*Coeff(5))*B(i, 1)^2+Coeff(14)*B(i, 2)^2+(3*Coeff(15)*B(i, 2)^2+3*Coeff(10)*B(i, 2)+3*Coeff(4))*B(i, 1)+Coeff(9)*B(i, 2)+Coeff(3))*A(i, 1)^2+(4*Coeff(11)*B(i, 1)^3+4*Coeff(20)*B(i, 2)^3+(6*Coeff(15)*B(i, 2)+3*Coeff(10))*B(i, 1)^2+3*Coeff(17)*B(i, 2)^2+(6*Coeff(18)*B(i, 2)^2+4*Coeff(14)*B(i, 2)+2*Coeff(9))*B(i, 1)+2*Coeff(13)*B(i, 2)+Coeff(8))*A(i, 1)*A(i, 2)+(Coeff(15)*B(i, 1)^3+10*Coeff(21)*B(i, 2)^3+(3*Coeff(18)*B(i, 2)+Coeff(14))*B(i, 1)^2+6*Coeff(19)*B(i, 2)^2+(6*Coeff(20)*B(i, 2)^2+3*Coeff(17)*B(i, 2)+Coeff(13))*B(i, 1)+3*Coeff(16)*B(i, 2)+Coeff(12))*A(i, 2)^2,
            (5*Coeff(6)*A(i, 1)+Coeff(11)*A(i, 2))*B(i, 1)^4+(Coeff(20)*A(i, 1)+5*Coeff(21)*A(i, 2))*B(i, 2)^4+(4*Coeff(5)*A(i, 1)+Coeff(10)*A(i, 2)+(4*Coeff(11)*A(i, 1)+2*Coeff(15)*A(i, 2))*B(i, 2))*B(i, 1)^3+(Coeff(17)*A(i, 1)+4*Coeff(19)*A(i, 2))*B(i, 2)^3+((3*Coeff(15)*A(i, 1)+3*Coeff(18)*A(i, 2))*B(i, 2)^2+3*Coeff(4)*A(i, 1)+Coeff(9)*A(i, 2)+(3*Coeff(10)*A(i, 1)+2*Coeff(14)*A(i, 2))*B(i, 2))*B(i, 1)^2+(Coeff(13)*A(i, 1)+3*Coeff(16)*A(i, 2))*B(i, 2)^2+Coeff(2)*A(i, 1)+Coeff(7)*A(i, 2)+A(i, 3)+((2*Coeff(18)*A(i, 1)+4*Coeff(20)*A(i, 2))*B(i, 2)^3+(2*Coeff(14)*A(i, 1)+3*Coeff(17)*A(i, 2))*B(i, 2)^2+2*Coeff(3)*A(i, 1)+Coeff(8)*A(i, 2)+(2*Coeff(9)*A(i, 1)+2*Coeff(13)*A(i, 2))*B(i, 2))*B(i, 1)+(Coeff(8)*A(i, 1)+2*Coeff(12)*A(i, 2))*B(i, 2),
             Coeff(6)*B(i, 1)^5+Coeff(21)*B(i, 2)^5+(Coeff(11)*B(i, 2)+Coeff(5))*B(i, 1)^4+Coeff(19)*B(i, 2)^4+(Coeff(15)*B(i, 2)^2+Coeff(10)*B(i, 2)+Coeff(4))*B(i, 1)^3+Coeff(16)*B(i, 2)^3+(Coeff(18)*B(i, 2)^3+Coeff(14)*B(i, 2)^2+Coeff(9)*B(i, 2)+Coeff(3))*B(i, 1)^2+Coeff(12)*B(i, 2)^2-Thickness+(Coeff(20)*B(i, 2)^4+Coeff(17)*B(i, 2)^3+Coeff(13)*B(i, 2)^2+Coeff(8)*B(i, 2)+Coeff(2))*B(i, 1)+Coeff(7)*B(i, 2)+B(i, 3)+Coeff(1) ] );
and then do the filtering like you had before.
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