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

Answer 2

[guy tau]

Hi @Wlater, a very late replay, buy unfortentaly, i'm currently dealing with a simialr issue, and hopfully you can assisit me as well.

I have large table of data (~30000 rows), in which I use the solver function on some of the varibles from the table to predect and compare to a known sampled varible.

I tried your suggested code, wrtiren as:

syms a.var1 a.var2 a.var3 a.var4 i X
Equation = ((a.var1(i) -c1*(X)^4)- (c2*a.var2(i)*(6.105.*exp((c3*X)./(x+c4)) -a.var3(i)))  - (c5*(x-a.var4(i)))) = 0;
tsym = solve(simplify(Equation), X);
tfun = matlabFunction(tsym, 'vars', {'a.var1', 'a.var2', 'a.var3', 'a.var4','i'});
for i = 1:height(a)
    t(i) = tfun(a.var1,a.var2,a.var3,a.var4, i);
end

where

c1,c2,c3,c4 and c5 are constants

and a.var1 to a.var 4 are the varibiles from the table

Unfortunately I got the follwing error back

Error using sym/subsindex

Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic variables, and function body must be sym expression.

Error in indexing (line 1075)

R_tilde = builtin('subsref',L_tilde,Idx);

Related documentation

I assume the problem is realted to the index table, but i'm struggling the find the solution

If other solution pop's to your mind that will be great as well.

currently, letting the loop run by just using solver is just to slow...