Anyone know if NLopt works with univariate optimization. Tried to run following code:
using NLopt
function myfunc(x, grad)
x.^2
end
opt = Opt(:LD_MMA, 1)
min_objective!(opt, myfunc)
(minf,minx,ret) = optimize(opt, [1.234])
println("got $minf at $minx (returned $ret)")
But get following error message:
> Error evaluating untitled
LoadError: BoundsError: attempt to access 1-element Array{Float64,1}:
1.234
at index [2]
in myfunc at untitled:8
in nlopt_callback_wrapper at /Users/davidzentlermunro/.julia/v0.4/NLopt/src/NLopt.jl:415
in optimize! at /Users/davidzentlermunro/.julia/v0.4/NLopt/src/NLopt.jl:514
in optimize at /Users/davidzentlermunro/.julia/v0.4/NLopt/src/NLopt.jl:520
in include_string at loading.jl:282
in include_string at /Users/davidzentlermunro/.julia/v0.4/CodeTools/src/eval.jl:32
in anonymous at /Users/davidzentlermunro/.julia/v0.4/Atom/src/eval.jl:84
in withpath at /Users/davidzentlermunro/.julia/v0.4/Requires/src/require.jl:37
in withpath at /Users/davidzentlermunro/.julia/v0.4/Atom/src/eval.jl:53
[inlined code] from /Users/davidzentlermunro/.julia/v0.4/Atom/src/eval.jl:83
in anonymous at task.jl:58
while loading untitled, in expression starting on line 13
If this isn't possible, does anyone know if a univariate optimizer where I can specify bounds and an initial condition?
There are a couple of things that you're missing here.
You need to specify the gradient (i.e. first derivative) of your function within the function. See the tutorial and examples on the github page for NLopt. Not all optimization algorithms require this, but the one that you are using LD_MMA looks like it does. See here for a listing of the various algorithms and which require a gradient.
You should specify the tolerance for conditions you need before you "declare victory" ¹ (i.e. decide that the function is sufficiently optimized). This is the xtol_rel!(opt,1e-4) in the example below. See also the ftol_rel! for another way to specify a different tolerance condition. According to the documentation, for example, xtol_rel will "stop when an optimization step (or an estimate of the optimum) changes every parameter by less than tol multiplied by the absolute value of the parameter." and ftol_rel will "stop when an optimization step (or an estimate of the optimum) changes the objective function value by less than tol multiplied by the absolute value of the function value. " See here under the "Stopping Criteria" section for more information on various options here.
The function that you are optimizing should have a unidimensional output. In your example, your output is a vector (albeit of length 1). (x.^2 in your output denotes a vector operation and a vector output). If you "objective function" doesn't ultimately output a unidimensional number, then it won't be clear what your optimization objective is (e.g. what does it mean to minimize a vector? It's not clear, you could minimize the norm of a vector, for instance, but a whole vector - it isn't clear).
Below is a working example, based on your code. Note that I included the printing output from the example on the github page, which can be helpful for you in diagnosing problems.
using NLopt
count = 0 # keep track of # function evaluations
function myfunc(x::Vector, grad::Vector)
if length(grad) > 0
grad[1] = 2*x[1]
end
global count
count::Int += 1
println("f_$count($x)")
x[1]^2
end
opt = Opt(:LD_MMA, 1)
xtol_rel!(opt,1e-4)
min_objective!(opt, myfunc)
(minf,minx,ret) = optimize(opt, [1.234])
println("got $minf at $minx (returned $ret)")
¹ (In the words of optimization great Yinyu Ye.)
Related
I'm trying to solve a nonlinear system of 7 equations with least_squares, as some variables are molar fractions and go between 0 and 1 (fsolve doesnt allow constraints as far as I've read). Heres the main part of the code:
def fun_t(w,x_2):
x_1=1-x_2;
z_A=w[0];
z_B=w[1];
z_AB=w[2];
gamma_A=w[3];
gamma_B=w[4];
gamma_AB=w[5];
eps=w[6]
K_gamma=gamma_AB/(gamma_A*gamma_B)
K=K_gamma*z_AB/(z_A*z_B)
phi_A=z_A*v_A/(z_A*v_A+z_B*v_B+z_AB*v_AB);
phi_B=z_B*v_B/(z_A*v_A+z_B*v_B+z_AB*v_AB);
phi_AB=z_AB*v_AB/(z_A*v_A+z_B*v_B+z_AB*v_AB);
return [z_AB-eps/(1-eps),
z_A-(x_2-eps)/(1-eps),
z_B-(x_1-eps)/(1-eps),
eps-(1-(1-4*K/(K+K_gamma)*x_1*x_2)**0.5)/2,
R*T*np.log(gamma_A)-v_A*(alphaT_AB*phi_B**2+alphaT_AAB*phi_AB**2+(alphaT_AB+alphaT_AAB-alphaT_BAB)*phi_B*phi_AB),
R*T*np.log(gamma_B)-v_B*(alphaT_AB*phi_A**2+alphaT_BAB*phi_AB**2+(alphaT_AB+alphaT_BAB+alphaT_AAB)*phi_A*phi_AB),
R*T*np.log(gamma_AB)-v_AB*(alphaT_AAB*phi_A**2+alphaT_BAB*phi_B**2+(alphaT_AAB+alphaT_BAB-alphaT_AB)*phi_A*phi_B)
]
x_2=np.linspace(0,1,11)
guess=[0.5,0.5,0.5,1,1,1,0.25];
roots_t=np.zeros(shape=(len(x_2),len(guess)))
for i in range(len(x_2)):
roots_t[i] = least_squares(fun_t, guess, bounds = ((0,0,0,-5,-5,-5,0),(1,1,1,5,5,5,0.5)), args=x_2[i])
I get the error TypeError: fun_t() argument after * must be an iterable, not numpy.float64. My goal is to give the elements of the array x_2 as the fuction's second argument in order to get the rest of the variables for a set of compositions. I dont understand why it cant iterate over x_2, as it worked when I was using fsolve.
I'm just starting using python for this kind of calculations, so any help will be much appreciated!
I am trying to find out the parameters for the function below:
$$
\log L(\alpha,\beta,v) = v/\beta(e^{-\beta T} -1) + \alpha/\beta \sum_{i=1}^{n}(e^{-\beta(T-t_i)} -1) + \sum_{i=1}^{N}log(v e^{-\beta t_i} + \alpha \sum_{j=1}^{jmax(t_i)} e^{-\beta(t_i - t_j)}).
$$
However, the conventional methods like fmin, fminsearch are not converging properly. Any suggestions on any other methods or open libraries which I can use?
I was trying CVXPY, but they don't support the division by a variable in the expression.
The problem may not be convex (I have not verified this but it could be why CVXPY refused it). We don't have the data so we cannot try things out, but I can give some general advice:
Provide exact gradients (and 2nd derivatives if needed) or use a modeling system with automatic differentiation. Especially first derivatives should be preferably quite precise. With finite differences you may lose half the precision.
Provide a good starting point. May be using an alternative estimation method.
Some solvers can use bounds on the variables to restrict the feasible region where functions will be evaluated. This can be used to restrict the search to interesting areas only and also to protect operations like division and log functions.
I am programming newtons method, the following code snippet shows what I have done to the main function. I have a data structure with just the function, which is x^2+y^2 for now. the value for data.x0 is [1;1] (close to the solution) and the value for data.e is 0.01
The update xk is running away from the origin instead of towards it. In fact, I can get this code to work for a few problems when I specify data.x0 very close to a local minimum or inside a deep pit on the function. otherwise it diverges even for very simple functions.
My intuition tells me it is a result of using the hessian and gradient functions from the symbolic toolbox instead of analytic methods as I had been warned of. Any thoughts?
xk=data.x0
grad=gradient(data.f)
grad_xk=double(subs(grad,[x;y],xk))
hess=hessian(data.f)
norm_grad_xk=0;
for i=1:length(grad_xk)
norm_grad_xk=norm_grad_xk+grad_xk(i)^2;
end
norm_grad_xk=sqrt(norm_grad_xk)
mag_fun_xk=double(subs(data.f,[x;y],xk))
while (norm_grad_xk)>data.e*(1+abs(mag_fun_xk))
hess_xk=double(subs(hess,[x;y],xk))
invhess_xk=inv(hess_xk)
xk=xk-invhess_xk*grad_xk
% ll=horzcat(ll,xk)
norm_grad_xk=0;
for i=1:length(grad_xk)
norm_grad_xk=norm_grad_xk+grad_xk(i)^2
end
norm_grad_xk=sqrt(norm_grad_xk)
mag_fun_xk=double(subs(data.f,[x;y],xk))
end
I've created an interprter for a simple language. It is AST based (to be more exact, an irregular heterogeneous AST) with visitors executing and evaluating nodes. However I've noticed that it is extremely slow compared to "real" interpreters. For testing I've ran this code:
i = 3
j = 3
has = false
while i < 10000
j = 3
has = false
while j <= i / 2
if i % j == 0 then
has = true
end
j = j+2
end
if has == false then
puts i
end
i = i+2
end
In both ruby and my interpreter (just finding primes primitively). Ruby finished under 0.63 second, and my interpreter was over 15 seconds.
I develop the interpreter in C++ and in Visual Studio, so I've used the profiler to see what takes the most time: the evaluation methods.
50% of the execution time was to call the abstract evaluation method, which then casts the passed expression and calls the proper eval method. Something like this:
Value * eval (Exp * exp)
{
switch (exp->type)
{
case EXP_ADDITION:
eval ((AdditionExp*) exp);
break;
...
}
}
I could put the eval methods into the Exp nodes themselves, but I want to keep the nodes clean (Terence Parr saied something about reusability in his book).
Also at evaluation I always reconstruct the Value object, which stores the result of the evaluated expression. Actually Value is abstract, and it has derived value classes for different types (That's why I work with pointers, to avoid object slicing at returning). I think this could be another reason of slowness.
How could I make my interpreter as optimized as possible? Should I create bytecodes out of the AST and then interpret bytecodes instead? (As far as I know, they could be much faster)
Here is the source if it helps understanding my problem: src
Note: I haven't done any error handling yet, so an illegal statement or an error will simply freeze the program. (Also sorry for the stupid "error messages" :))
The syntax is pretty simple, the currently executed file is in OTZ1core/testfiles/test.txt (which is the prime finder).
I appreciate any help I can get, I'm really beginner at compilers and interpreters.
One possibility for a speed-up would be to use a function table instead of the switch with dynamic retyping. Your call to the typed-eval is going through at least one, and possibly several, levels of indirection. If you distinguish the typed functions instead by name and give them identical signatures, then pointers to the various functions can be packed into an array and indexed by the type member.
value (*evaltab[])(Exp *) = { // the order of functions must match
Exp_Add, // the order type values
//...
};
Then the whole switch becomes:
evaltab[exp->type](exp);
1 indirection, 1 function call. Fast.
I have written a finite volume model. The parameter n represents the number of volumes. After translating, the parameter can't be modified. Dymola gives this message:
Warning: Setting n has no effect in model.
After translation you can only set literal start-values and non-evaluated parameters.
I think the problem is that the parameter n is used in the equation section. There I use the following code:
equation
...
for i in 2:n-1 loop
T[i] = some equation
end for
I also use n for the calculation of the initial values of T.
The purpose is to make a script that repeatedly executes the model but with a different n.
How can I do this?
The issue here is that your parameter n affects the number of variables in the problem. Dymola (and all other Modelica compilers I know of) evaluate such parameters at compile time. In other words, they hard code the value at compile time into the model.
One potential workaround in your case is to perform the translation or simulation inside your loop. Note that in the translate and simulate commands in Dymola you can include modifications. Just add them after the model name. For example MyModel would become MyModel(n=10).