Normal MLE using fminunc

Hi,

I am using the following code to estimate the MLE for the normal distribution.

1.load normaldata.dat
2.global x N
3.x = normaldata;
4.N = length(x);
5.theta0 = zeros(2,1);
6.[thetac,fval,output] = fminunc(@Norm,theta0);
7.thetac(2) = exp(thetac(2)); 

8.function output = NORM(theta)
9.    global x N
10.    theta(2) = exp(theta(2)); 
11.    output = 0;
12.    
13.    for n = 1:N
14.       output = output + (1/(2*theta(2)))*(-(x(n)-theta(1))^2);
15.    end
16.    
17.    output = output - ((N/2)*(log(theta(2))));
18.    output = -output;
19.    end

It gives me the right answer, but I dont understand why we are setting sigma to exp(sigma) (refer to lines 7 and 10). Im guessing because we want sigma to be positive, in which case I understand why theta(2) = exp(theta(2)) in line 10 is present. But what is the relevance of theta(2) = exp(theta(2)) in line 7, surely it should be theta(2) = log(theta(2))???