How does one solve the roots of a symbolic polynomial in a loop?

Hello,

I am attempting to fit data that involves solving a fifth order polynomial for the real positive root. I need to calculate the real positive root over a set of values, so I was trying to use syms with a loop in order to get the root with each iteration of the symbolic polynomial. It should have five roots, though I just need one. I'm not very good at using syms so I am likely confusing some syntax. It tells me the error "Conversion to logical from sym is not possible". I imagine this is because MatLab thinks I am still using a symbolic variable when doing the logic check, which it doesn't understand. Though I thought my program has converted back to numerical at that point. Does anyone know a good way to do this?

Thank you.

syms X Y

for i = 1:length(injections)

Y = C1(i,1).*X + C2.*X + C3(i,1).*X +

C4(i,1).*X^2 + C5.*X^2 + C6(i,1).*X^2 + C7(i,1).*X^3 +

C8.*X^3 + C9(i,1).*X^3 + C10(i,1).*X^4 + C11.*X^4 +

C12(i,1).*X^4 + C13.*X^5;

realposans(:,i) = solve(Y == 0,'Real',true);

for j = 1:size(realposans,1)

if realposans(j,i) > 0

LF(i,1) = realposans(j,i);

end

end

end

Answer 1

[Star Strider]

Maybe I’m missing something, but wouldn’t it be easier to cast your equation as:

K5*x^5 + K4*x^4 + K3*X^3 + K2*x^2 + K1*x + (K0-Y)

with:

K5 = C13(i,1),   K4 = (C10(i,1) + C11(i,1) + C12(i,1)), K3 = ... etc.

then use roots as:

K5 = 6;
K4 = 5;
K3 = 4;
K2 = 3;
K1 = 2;
K0 = 1;
r = roots([K5 K4 K3 K2 K1 K0]);

rr = r(imag(r) == 0)

Loop with values of C1 ... C13, assign rr(i) with the loop index, and avoid the Symbolic Math Toolbox entirely. The Symbolic Toolbox has its strengths, but looping to solve equations such as yours is not one of them.

[Erick Alejandro]

Earlier I was doing something like this though it was taking too long so I thought that I could save time and just do my final substitution and calculation at the very end. This looks good though, thank you.

[Star Strider]

My pleasure!

[Erick Alejandro]

Yes! I have tried it now and it works much faster with the imag(r) == 0. I did not know about this command. I think I had a problem before using isreal because it only works if all the elements of the array are real.

[Star Strider]

I’m pleased it worked for you!