Code is stuck in infinite loop

Trying to find to roots of the function in my code using the incremental search method, but it looks like the code is stuck looping in one condition.

dx=0.1; epsi=0.01; Xi=0.1; Xm=4.0;
F = @(x) 1+5.25*x-sec(sqrt(0.68*x));
a=Xi;
f1=F(a);
b=a+dx;
f2=F(b);
while a<Xm
    a=Xi;
    f1=F(a);
    b=a+dx;
    f2=F(b);
    if abs(f2) > (1/epsi)
        disp ('function approaching infinity at ',a);
        a = a+epsi;
        f1=F(a);
        b=a+dx;
        f2=F(b);
    else
        if  f1*f2 == 0
            disp ('X  is a root',a);
          
            a = a+epsi;
            f1=F(a);
            b=a+dx;
            f2=F(b);
            
        elseif f1*f2 > 0
            if a>Xm
                break;
            else
                a=b;
                f1=F(a);
                b=a+dx;
                f2=F(b);
            end    
        else
            if dx < epsi
                disp ('X is a root',a);
                
                a = a+epsi;
                f1=F(a);
                b=a+dx;
                f2=F(b);
            else
                a=a-dx;
                dx = dx/10;
                f1=F(a);
                b=a+dx;
                f2=F(b);
            end
        end
    end
end

Answer 1

[Geoff Hayes]

haif - part of the problem (of why you are getting stuck in an infinite loop) is due to

dx=0.1; 
epsi=0.01; 
Xi=0.1;   % <----- set here only
Xm=4.0;
F = @(x) 1+5.25*x-sec(sqrt(0.68*x));
a=Xi;     % <------ a initialized to Xi
f1=F(a);
b=a+dx;
f2=F(a)
while a<Xm
    a=Xi; % <------ a reset to static Xi

On each iteration of the loop, the code is always re-assigning a to Xi and since the latter is only set outside the loop, then we are always repeating the same iteration again and again. Try commenting out this line and re-running your code. You'll probably also have a problem with

    disp ('function approaching infinity at ',a);

with a "too many input arguments" error. Just change this to

    disp (sprintf('function approaching infinity at %f',a));

[haif hamza]

Thank you, your solution worked. For the second problem i used fprintf