I want to compute the derivatives of a non-analytic function. I see there are packages available (for example, DERIVESTsuite) to compute the numerical derivatives but they do not have any option to put constraints on the parameter space. Please suggest some ways to compute the numerical derivatives with constraints on the parameter. I have only one constraint: the parameters can take only positive values.
For example, suppose I have a function f(x) which is defined as a MATLAB function,
where x=[x1,x2] is a vector with x1>0 and x2>0
and I want to compute Jacobian of f(x) w.r.t. x.
The problem is that the function f(x) cannot be computed for negative values of either x1 or x2. So, if my program tries to compute the partial derivative of f(x) w.r.t. x1 at x1=0 using the formula
it will give an error.