Fzero with defined scalar parameters

Hello, I am approaching to MATLAB by myself, but I have a problem: I'm writing a script, that I will simplify as follow

   k=0.1805;                    
n=4;                         
r_t=1.78e-3;                 
I=151;                       
d_r=0.06;                    
d=0.0009/d_r;                                    
delt=10;                    
f=0.907;                         % Parameter that I want to set and change when needed
r_c=r_t*sqrt(f);                 
q_r=0.0072*((1+2/n)/((1+(4/n))^(3/10)))*(I^(7/5))/(r_t*sqrt(f))^(12/5)    
y=k*delt/((q_r)*d_r*r_t*sqrt(f))  
x=fzero('( exp(-(x^2)))/(x*sqrt(pi))+erf(x) -1-0.1805*10/((0.0072*((1+2/4)/((1+(4/4))^(3/10)))*(151^(7/5))/(1.78e-3*sqrt(0.907))^(12/5)*(0.06)*(1.78e-3)*sqrt(0.907)))',3)

Now the problem arises when I compute x: it is computed as the zero of exp(-(x^2)))/(x*sqrt(pi))+erf(x) -y , but I can't introduce "y" in the string of fzero, so I've inserted all the numerical expression. This is a big deal, because everytime I want to change "f" I have to find it in the string and change its value, while I would like to substitute it only once, when I define it. If I want to change any other parameter, the problem is still the same... I've read about fmin, function_handle etc etc, but I was not able to understand those tools, because by now I know very little about MATLAB. Could you kindly help me to solve this particular problem? Please, I beg you also to be detailed, because nothing is so obvious to me, now. Thanks a lot!

Answer 1

[Matt J]

You should not be using strings to specify the function whose root you are trying to find. It's a deprecated syntax. You should be using anonymous functions

   y=1;
   fun=@(x) exp(-(x^2))/(x*sqrt(pi))+erf(x) -y;

   x=fzero(fun,x0)

For other options, see also Passing Extra Parameters.

Answer 2

[Thorsten]

If FUN is parameterized, you can use anonymous functions to capture the problem-dependent parameters. Suppose you want to solve the equation given in the function myfun, which is parameterized by its second argument c. Here myfun is an M-file function such as

        function f = myfun(x,c)
        f = cos(c*x);

To solve the equation for a specific value of c, first assign the value to c. Then create a one-argument anonymous function that captures that value of c and calls myfun with two arguments. Finally, pass this anonymous function to FZERO:

        c = 2; % define parameter first
        x = fzero(@(x) myfun(x,c),0.1)

In your case use y instead of c and define myfun as exp(-(x^2)))/(x*sqrt(pi))+erf(x)

Answer 3

[Francesco]

Thank you both, you help me to save a lot of time!