Solving a nonlinear system of equations in Julia - julia

Question

I can write in function in Matlab in this way:
function res=resid(theta,alpha,beta);
RHS=[];
LHS=[];
RHS= theta-alpha;
LHS= theta*beta;
res = (LHS-RHS);
We set the parameters, call the function:
alpha=0.3;beta=0.95;
a01=[1.0;1.0];
th=fsolve('resid',a01,[],alpha,beta)
This will return [6.0;6.0]. Does the option"[]" signal to fsolve that the input is a vector?
Anyway, how can I implement this in Julia using a NLsolve, Optim or JuMP? The original problem has more than 10 variables, so I would prefer a vector approach.
I can implement the function in Julia:
h! =function (theta)
RHS=[];
LHS=[];
RHS= theta-alpha;
LHS= theta*beta;
res= (LHS-RHS);
return res;
end
But simply using NLsolve:
a01 = [1.0;1.0];
res = nlsolve(h!,a01)
Returns:
MethodError: no method matching (::##17#18)(::Array{Float64,1}, ::Array{Float64,1})
Closest candidates are:
#17(::Any) at In[23]:3
If I alternatively use Optim, I get:
using Optim
optimize(h!, a01)
which returns:
MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type Float64
This may have arisen from a call to the constructor Float64(...),
since type constructors fall back to convert methods.
Thank you for your suggestions!

Answer 1

Following the suggestion by Chris Rackauckas, the solution would be to keep the definition of h:
h =function (theta)
RHS=[];
LHS=[];
RHS= theta-alpha;
LHS= theta*beta;
res= (LHS-RHS);
return res;
end
and to use not_in_place:
a01 = [1.0;1.0];
solve = nlsolve(not_in_place(h),a01)
Returning a solution:
Results of Nonlinear Solver Algorithm
* Algorithm: Trust-region with dogleg and autoscaling
* Starting Point: [1.0,1.0]
* Zero: [6.0,6.0]
* Inf-norm of residuals: 0.000000
* Iterations: 3
* Convergence: true
* |x - x'| < 0.0e+00: false
* |f(x)| < 1.0e-08: true
* Function Calls (f): 4
* Jacobian Calls (df/dx): 4
Thank you!