Solving equation with for loop is slow

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

Answer 1

[Walter Roberson]

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.

[Jack_111]

Walter I didn't get your answer could you please tell me more?

Did you solve the equation at the beginning? How did you get t = roots.....

I tried to get t for more than 2 days and I didn't succeed

[Jack_111]

@Wlater How could I calculate for each loop instance without using the for loop?!

[Walter Roberson]

I solve()'d in Maple. You could do the equivalent using

syms A B i t

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));

tsym = solve(simplify(Equation), t);
tfun = matlabFunction(tsym, 'vars', {'A', 'B', 'i'});

then

for i = 1:length(realA)

    if isnan(B(i,1))
      tCounter(i) = NaN;
    else
      t = tfun(realA, realB, i);
      t(imag(t) ~= 0) = [];
      t(t<0) = [];
      t = min(t);
      tCounter(i) = t;
    end

end

The "for" loop is still there, but the solve() has been done only once, and then each iteration of the loop the anonymous function equivalent of the solution is used, passing in appropriate parameters.

[Jack_111]

It was more than perfect

Big thanks