MATLAB: Error encountered using ‘fzero’

error fzeroMATLAB

Hello, I have a question regarding fzero. my code is as follows:
syms P
N=-P;
a=50; b=20;  h0=50; E=200;n=1.5;
 h1=40;
l=100;
I0=b*h0^3/12; I1=b*h1^3/12;
L0=sqrt(P/(E*I0-P*n));%L0=simplify(L00);
L1=sqrt(P/(E*I1-P*n));%L1=simplify(L11);
v=0.3;
s=0.5; 
f=1.93-3.07*s+14.53*s^2-25.11*s^3+25.8*s^4;
k=(E*I1)/(6*pi*h1*f*(1-v^2)); 
m=(E*I1+n*N)/N;
x=(E*I1+n*N)/(E*I0+n*N);
a11=(L0*a)-sin(L0*a);
a12=cos(L0*a)-1;
a13=(-tan(L1*l)*cos(L1*a))+sin(L1*a)-(a*(m*L1^3+L1)*((tan(L1*l)*sin(L1*l))+cos(L1*l)));
a14=1;
a21=(-L0*cos(L0*a))+L0+((E*I0+n*N)*L0^2*sin(L0*a));
a22=(-L0*cos(L0*a))-((E*I0+n*N)*L0^2*cos(L0*a));
a23=(k*L1*((tan(L1*l)*sin(L1*a))+cos(L1*a)))-((m*L1^3+L1)*((tan(L1*l)*sin(L1*l))+cos(L1*l)));
a24=0;
a31=L0^2*sin(L0*a);
a32=-L0^2*cos(L0*a);
a33=x*L1^2*((tan(L1*l)*cos(L1*a))-sin(L1*a));
a34=0;
a41=L0^3*cos(L0*a);
a42=L0^3*sin(L0*a);
a43=-x*L1^3*((tan(L1*l)*sin(L1*a))+cos(L1*a));
a44=0;
A=[a11 a12 a13 a14;a21 a22 a23 a24;a31 a32 a33 a34;a41 a42 a43 a44];
delta1=det(A);
delta2=subs(delta1);
delta=simplify(delta2);
% P=vpasolve(delta,P,1e3);
F=matlabFunction(delta);
P1=[];
for j = 0.01:10
    PP = fzero(F, j);
    P1 = [P1; PP];
end
P_cr = min(P1(P1 > 0))
It reports the following kind of errors,
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -2.5228 is 3.3961e-18-1.174e-23i.)
Check function or try again with a different starting value.
P_cr =
  0×1 empty double column vector
My question is that, how could i get positive real solutions. I shall be very thankful if somone can help me regarding this problem.

Best Answer

First of all, it looks like P is maybe supposed to be restricted to be a positive number, and when it's not, your function returns a complex number. However, fzero doesn't respect bounds on the search variable (P in your case): it looks for any value of P that zeros the function, regardless of whether P is postiive or negative. If it encounters a complex function value at some point, however (e.g., in your case if it evaluates F(P) for P<0), fzero doesn't know how to proceed, so it stops and reports an error. This is what you're seeing I believe.
There are various ways you can fix this problem, but the simplest to implement in your case is probably just to do a variable transformation like logP = log(P), P = exp(logP). For any real value of logP, P will be positive here, so you can use fzero to search among values of logP instead of directly for P. Here's how you might implement this:
% Replace the first line of your posted code with the following two:
syms logP
P = exp(logP);
. 
. % Then everything is the same until...
.
% replacing what you had, starting from the line P1=[];
logP1=[];
for j = log(0.01:10)
    logPP = fzero(F, j);
    logP1 = [logP1; logPP];
end
P1 = exp(logP1);
P_cr = min(P1(P1 > 0))
I think this should do what you want.
A couple of other comments/pointers:
  • Do you really need to do this with symbolic variables? Couldn't you just write a regular MATLAB function called F.m that contains everything up to just before you start the fzero loop, but where logP is the argument passed into the function, and excluding the syms and the call to matlabFunction? Symbolic math is slow, so if you can avoid it you should.
  • You have some crazy scaling on these values. For values of P between 0 and 10, the absolute value of F is on the order of 10^(-16) or smaller, but if you inspect F, these values are arrived at using some intermediate numbers that are on the order of like 10^(+15). That tells me that your F value is likely seriously compromised by numerical precision issues. Are you sure you haven't made a mistake somewhere in your code? It would be pretty unusual to encounter something like this in the real world.
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