# Problem with NaN's when plugging minimizing vectors (NLopt) back into function
**URL:** https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154
**Category:** General Usage
**Tags:** optimization
**Created:** [August 4, 2019, 8:59pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154 "2019-08-04T20:59:22Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@CPPhysics](https://discourse.julialang.org/u/CPPhysics)
#### Post date: [August 4, 2019, 8:59pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/1 "2019-08-04T20:59:22Z")
Hello, first off I don’t have a working example due to research privacy and I know that will make things much harder to debug. But I would like to see if anyone recognizes this problem by chance.
I have a function, which I minimize using NLopt and the algorithm PRAXIS. This goes smoothly, I take the minimizer (which I name minx) and copy the vector itself, and paste it into another cell and label it something to save it for later.
When I then go back to plug the vector back into the function later to get the results again, all I get returned from the function is NaN, and when I `@show` various parts of the function, they are all NaN’s as well. I have not had any other problems with this function and it behaves normally otherwise.
When plugging minx (I have NLopt save the minimizer to minx immediately) back into the function immediately after the minimizing run, I have no problems, I get the results that I should and no NaN’s. Therefore the problem is in copying and saving the vector, and then restarting the kernel, losing the saved minx, and trying to plug back in the same vector (now saved as a different variable) back into the function. I don’t change anything about the function or the minx array between restarts.
Let me know if this rings any bells for anyone. If not, that’s okay. It is not holding me back too much it is just very strange and a bit frustrating.
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [August 4, 2019, 10:19pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/2 "2019-08-04T22:19:22Z")
Have you tried to replicate the problem without the optimization? Or have you been able to determine at which step the problem arises. It is very difficult to help you with a so very generalized problem statement.
---
### Author:  [@CPPhysics](https://discourse.julialang.org/u/CPPhysics)
#### Post date: [August 5, 2019, 9:05pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/3 "2019-08-05T21:05:42Z")
I will try to narrow it down some. Something else of note is that (say I save a minimizing vector as X0) if I pass X0 to NLopt to use as a starting vector, nothing goes wrong, the optimization run goes normally. And the problem only happens with vectors I have previously used in the optimization. So the problem doesn’t arrive normally, passing other random vectors to the function doesn’t give any NaN’s.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [August 5, 2019, 9:23pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/4 "2019-08-05T21:23:01Z")
Without a minimal working example, it’s impossible to say. However,
> I take the minimizer (which I name minx) and copy the vector itself, and paste it into another cell and label it something to save it for later.
You’re probably not copying the full `Float64` value. Consider
```Julia
julia> rand(3)
3-element Array{Float64,1}:
0.5154380997179793
0.4773473251211171
0.7388211634374753
julia> [rand(3)]
1-element Array{Array{Float64,1},1}:
[0.45449, 0.408123, 0.295315]
```
---
### Author:  [@CPPhysics](https://discourse.julialang.org/u/CPPhysics)
#### Post date: [August 5, 2019, 9:32pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/5 "2019-08-05T21:32:19Z")
Thank you, this is very helpful. I am working on a working example now.
---
### Author:  [@CPPhysics](https://discourse.julialang.org/u/CPPhysics)
#### Post date: [August 5, 2019, 11:49pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/6 "2019-08-05T23:49:13Z")
Here is a working example. With `D_2 = 4`, I get `NaN` when trying to use `XD8G200`, but `1` when I pass a random vector, and I get `1` when using `XD8G200` with either `D_2 = 2` or `D_2 = 3`. `tr(ExpTL)` should always be `1`. I have found when I remove `0.5*` from the construction of `F`, I don’t get `NaN` but I get zero not `1` so that is not a change I can make. There might be a problem with the math itself and if that is a case, I will take another look at it but so far I have found no errors.
```julia
D_2 = 4
D = 2*D_2
using LinearAlgebra
function ETest(x::Array)
S1 = [0 1; 0 0]
A = reshape(Complex.(x[1:2:2*D_2^2-1],x[2:2:2*D_2^2]),D_2,D_2)
B = reshape(Complex.(x[2*D_2^2+1:2:4*(D_2^2)-1],x[2*D_2^2+2:2:4*(D_2^2)]),D_2,D_2)
C = kron(S1,Diagonal(ones(D_2)))
E = kron(Diagonal(ones(2)),A) + kron(S1,B)
H = reshape(x[4*D_2^2+1:4*D_2^2+(2D_2)^2],D,D)
H = Hermitian(Complex.(H,LowerTriangular(H)'-Diagonal(H)))
F = -im*H - 0.5*(C'*C + E'*E)
I = kron(F,Diagonal(ones(D))) + kron(Diagonal(ones(D)),conj(F)) + kron(C,conj(C)) + kron(E,conj(E))
J = x[4*D_2^2+(2D_2)^2+1]
G = x[4*D_2^2+(2D_2)^2+2]
L = 2.0
ExpT = exp(I)
ExpTL = ExpT^L
epsilon = norm(ExpTL-ExpT,2)/1_000_000
while norm(ExpTL-ExpT,2) > epsilon
ExpT = ExpTL
ExpTL = ExpT*ExpT
end
return tr(ExpTL)
end
XD8G200 = [-1.59374,-5.2499, 1.67174, -1.98958, -0.647899, 6.07679, 1.75827, -4.27265, 2.96154, -1.68131, -0.723875, -2.21622, -1.43416, 0.746147, 5.63919, 1.9931, 2.90512, 0.742848, -3.68103, 0.2776, -2.41628, 3.89632, -8.49975, -4.41796, -5.06176, -3.10374, 8.03138, -1.23213, 1.58675, 2.90112, 1.55164, 2.37669, -2.04646, 0.924121, 0.139059, -2.68708, 1.31853, -0.58986, 2.27582, -0.669315, -0.365731, -2.18405, 1.05335, 0.182093, 0.261764, 1.15751, 1.45095, 1.20171, -0.224569, 2.11413, -1.10776, -2.29912, 0.32957, -1.24015, 0.927298, -0.693715, 0.168881, 1.13747, -0.161536, -0.747931, -0.0125401, -0.577182, -0.31807, 0.0709998, 1.21963, -3.78828, 3.18148, -5.90588, -6.8576, 2.22467, 24.6244, -23.6736, 0.922213, -2.682, -1.59649, 4.73233, 20.2889, 1.37649, -27.4573, 44.7773, 6.01401, -1.93724, 3.19959, 1.72178, 2.2031, -0.980421, -13.4228, 12.3053, -0.405479, 3.12535, -0.256148, -0.0570012, 2.87966, 0.364477, -12.8079, 12.7975, 24.8966, -10.8566, -15.2349, -10.306, -5.34033, -3.3093, 4.65935, -4.26519, 4.51724, -2.40256, -0.495797, 0.31801, -2.48692, -2.72646, -5.89435, 5.61049, -16.2209, -8.38797, 13.4124, 8.94201, 6.46931, 0.158825, 3.15498, -10.7349, 41.1833, -9.70869, -30.2226, -22.3293, -6.48997, -1.12033, -0.123085, -0.573403, 1.67974, -1.66205];
ETest(XD8G200)
#or
ETest(randn(4*D_2^2+(2D_2)^2+2))
```
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [August 6, 2019, 6:16am UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/7 "2019-08-06T06:16:35Z")
Don’t use globals, there is no reason the `D` and `D_2` cannot be just arguments to `ETest`.
I don’t know what you are trying to do here, but
```julia
while norm(ExpTL-ExpT,2) > epsilon
ExpT = ExpTL
ExpTL = ExpT*ExpT
end
```
is effectively just squaring `ExpTL` after the first step, a numerically unstable algorithm. `ExpTL` just blows up. This is the part that is giving you `NaN`s with the given `XD8G200` value.
---
### Author:  [@CPPhysics](https://discourse.julialang.org/u/CPPhysics)
#### Post date: [August 6, 2019, 7:26pm UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/8 "2019-08-06T19:26:38Z")
Okay, I have been worried about that loop for a long time. Here’s what I wanted it to do:
I have a matrix `ExpT = e^(IL)`. In my calculations, I need to use the value of `ExpT` as L goes to infinity. Basically this matrix will converge at some point as L increases, and I want to use that converged value. This loop was the way that I tried to “take L to infinity” with lack of a better construction. Do you have any suggestions for how to better construct this loop in order to do what I would like it do to?
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [August 7, 2019, 5:15am UTC](https://discourse.julialang.org/t/problem-with-nans-when-plugging-minimizing-vectors-nlopt-back-into-function/27154/9 "2019-08-07T05:15:54Z")
I would recommend looking at the famous [“19 dubious ways” article](https://www.cs.cornell.edu/cv/ResearchPDF/19ways+.pdf), especially decomposition methods (Section 6), but I did not study your problem in detail.