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Kernel: Julia 1.4

Julia 1.4

https://docs.julialang.org/en/v1.4/NEWS/#

In [10]:

VERSION

v"1.4.2"

In [2]:

println("Hello 1.4")

Hello 1.4

In [3]:

using FFTW
using LinearAlgebra
a = 2 * rand(10) .- 1
norm(ifft(fft(a)) - a)

0.0

In [4]:

using PyCall
# pygui(true)
using PyPlot
import Random:seed!; seed!(99)
import LinearAlgebra:norm

function activate(x,W,b)
    return 1 ./ (1 .+ exp.(-(W*x+b)))
end

x1 = [0.1,0.3,0.1,0.6,0.4,0.6,0.5,0.9,0.4,0.7]
x2 = [0.1,0.4,0.5,0.9,0.2,0.3,0.6,0.2,0.4,0.6]
y = [ones(1,5) zeros(1,5) ; zeros(1,5) ones(1,5)]

W2 = 0.5*randn(2,2); W3 = 0.5*randn(3,2); W4 = 0.5*randn(2,3);
b2 = 0.5*randn(2,1); b3 = 0.5*randn(3,1); b4 = 0.5*randn(2,1);

In [5]:

PyPlot.plot(x1, x2)

1-element Array{PyObject,1}:
 PyObject <matplotlib.lines.Line2D object at 0x7f321011f358>

In [6]:

using Pkg

In [7]:

for i = 1:10
    println(i)
end

In [8]:

using NLopt

function myfunc(x::Vector, grad::Vector)
    if length(grad) > 0
        grad[1] = 0
        grad[2] = 0.5/sqrt(x[2])
    end
    return sqrt(x[2])
end

function myconstraint(x::Vector, grad::Vector, a, b)
    if length(grad) > 0
        grad[1] = 3a * (a*x[1] + b)^2
        grad[2] = -1
    end
    (a*x[1] + b)^3 - x[2]
end

opt = Opt(:LD_MMA, 2)
opt.lower_bounds = [-Inf, 0.]
opt.xtol_rel = 1e-4

opt.min_objective = myfunc
inequality_constraint!(opt, (x,g) -> myconstraint(x,g,2,0), 1e-8)
inequality_constraint!(opt, (x,g) -> myconstraint(x,g,-1,1), 1e-8)

(minf,minx,ret) = optimize(opt, [1.234, 5.678])
numevals = opt.numevals # the number of function evaluations
println("got $minf at $minx after $numevals iterations (returned $ret)")

got 0.5443310477213124 at [0.3333333342139688, 0.29629628951338166] after 11 iterations (returned XTOL_REACHED)

In [0]:

In [9]:

using Printf

s = 0
for i = [1 2 5 100 -1 5]
    s = s + i
    @printf("i = %4d  →  s = %4d\n", i, s)
end

i =    1  →  s =    1
i =    2  →  s =    3
i =    5  →  s =    8
i =  100  →  s =  108
i =   -1  →  s =  107
i =    5  →  s =  112

In [2]:

using Pkg
Pkg.add("Turing")

  Resolving package versions...
   Updating `~/.julia/environment/v1.4/Project.toml`
 [no changes]
   Updating `~/.julia/environment/v1.4/Manifest.toml`
 [no changes]

In [3]:

# Import libraries.
using Turing, StatsPlots, Random

┌ Info: Precompiling Turing [fce5fe82-541a-59a6-adf8-730c64b5f9a0]
└ @ Base loading.jl:1260
ERROR: LoadError: LoadError: ERROR: LoadError: InterruptException:
Stacktrace:
 [1] top-level scope at /home/user/.julia/packages/DynamicPPL/E1QSS/src/compiler.jl:371
 [2] include(::Module, ::String) at ./Base.jl:377
 [3] include(::String) at /home/user/.julia/packages/DynamicPPL/E1QSS/src/DynamicPPL.jl:1
 [4] top-level scope at /home/user/.julia/packages/DynamicPPL/E1QSS/src/DynamicPPL.jl:103
 [5] include(::Module, ::String) at ./Base.jl:377
 [6] top-level scope at none:2
 [7] eval at ./boot.jl:331 [inlined]
 [8] eval(::Expr) at ./client.jl:449
 [9] top-level scope at ./none:3
in expression starting at /home/user/.julia/packages/DynamicPPL/E1QSS/src/compiler.jl:371
in expression starting at /home/user/.julia/packages/DynamicPPL/E1QSS/src/DynamicPPL.jl:103
InterruptException:
Stacktrace:
 [1] poptaskref(::Base.InvasiveLinkedListSynchronized{Task}) at ./task.jl:702
 [2] wait at ./task.jl:709 [inlined]
 [3] wait(::Base.GenericCondition{Base.Threads.SpinLock}) at ./condition.jl:106
 [4] wait(::Base.Process) at ./process.jl:622
 [5] success at ./process.jl:483 [inlined]
 [6] compilecache(::Base.PkgId, ::String) at ./loading.jl:1262
 [7] _require(::Base.PkgId) at ./loading.jl:1029
 [8] require(::Base.PkgId) at ./loading.jl:927
 [9] require(::Module, ::Symbol) at ./loading.jl:922
 [10] include(::Module, ::String) at ./Base.jl:377
 [11] top-level scope at none:2
 [12] eval at ./boot.jl:331 [inlined]
 [13] eval(::Expr) at ./client.jl:449
 [14] top-level scope at ./none:3
in expression starting at /home/user/.julia/packages/Turing/cReBm/src/Turing.jl:18

Failed to precompile Turing [fce5fe82-541a-59a6-adf8-730c64b5f9a0] to /home/user/.julia/compiled/v1.4/Turing/gm4QC_G6IaO.ji.

Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] compilecache(::Base.PkgId, ::String) at ./loading.jl:1272
 [3] _require(::Base.PkgId) at ./loading.jl:1029
 [4] require(::Base.PkgId) at ./loading.jl:927
 [5] require(::Module, ::Symbol) at ./loading.jl:922
 [6] top-level scope at In[3]:1

In [20]:

# Set the true probability of heads in a coin.
p_true = 0.5

# Iterate from having seen 0 observations to 100 observations.
Ns = 0:100;

# Draw data from a Bernoulli distribution, i.e. draw heads or tails.
Random.seed!(12)
data = rand(Bernoulli(p_true), last(Ns))

# Declare our Turing model.
@model coinflip(y) = begin
    # Our prior belief about the probability of heads in a coin.
    p ~ Beta(1, 1)

    # The number of observations.
    N = length(y)
    for n in 1:N
        # Heads or tails of a coin are drawn from a Bernoulli distribution.
        y[n] ~ Bernoulli(p)
    end
end;

# Settings of the Hamiltonian Monte Carlo (HMC) sampler.
iterations = 1000
ϵ = 0.05
τ = 10

# Start sampling.
chain = sample(coinflip(data), HMC(ϵ, τ), iterations);

# Plot a summary of the sampling process for the parameter p, i.e. the probability of heads in a coin.
histogram(chain[:p])

┌ Info: Precompiling Turing [fce5fe82-541a-59a6-adf8-730c64b5f9a0]
└ @ Base loading.jl:1260

InterruptException:

Stacktrace:
 [1] _include_from_serialized(::String, ::Array{Any,1}) at ./loading.jl:681
 [2] _require_search_from_serialized(::Base.PkgId, ::String) at ./loading.jl:781
 [3] _tryrequire_from_serialized(::Base.PkgId, ::UInt64, ::String) at ./loading.jl:712
 [4] _require_search_from_serialized(::Base.PkgId, ::String) at ./loading.jl:770
 [5] _tryrequire_from_serialized(::Base.PkgId, ::UInt64, ::Nothing) at ./loading.jl:712
 [6] _require_from_serialized(::String) at ./loading.jl:743
 [7] _require(::Base.PkgId) at ./loading.jl:1039
 [8] require(::Base.PkgId) at ./loading.jl:927
 [9] require(::Module, ::Symbol) at ./loading.jl:922
 [10] top-level scope at In[20]:1

In [4]:

using Compat

In [5]:

using PyPlot
x = range(0, stop = 4*pi, length=1000)
y = sin.(3*x + 1.5*cos.(2*x))

plot(x, y, color="red", linewidth=2.0, linestyle="--")

1-element Array{PyCall.PyObject,1}:
 PyObject <matplotlib.lines.Line2D object at 0x7f08fa1982e8>

In [10]:

using SymPy
x = symbols("x")      # or   @vars x, Sym("x"), or  Sym(:x)
y = sin(10 * pi*x)
y(1), y(2.2), y(123456)

(-1.22464679914735e-15, 4.41120439947682e-15, 6.39055017337619e-11)

In [11]:

simplify(diff(sqrt(2 + exp(x)) / (1 + x - cos(x)^2), x))

⎛       2   ⎞  x     ⎛ x    ⎞               
⎝x + sin (x)⎠⋅ℯ  - 2⋅⎝ℯ  + 2⎠⋅(sin(2⋅x) + 1)
────────────────────────────────────────────
                       2    ________        
          ⎛       2   ⎞    ╱  x             
        2⋅⎝x + sin (x)⎠ ⋅╲╱  ℯ  + 2         

In [12]:

using Test

foo(x) = length(x)^2

α = 1

@testset "foo" begin
    @test α == 2-1
    @test π ≈ 3.14 atol=0.01
    @test isapprox(9.81, 10, atol=0.2)
    @test foo("foo") == 9
end

Test Summary: | Pass  Total
foo           |    4      4

Test.DefaultTestSet("foo", Any[], 4, false)

In [0]:

using SpecialMatrices

In [0]:

using ApproxFun

HomotopyContinuation

Taken from https://www.juliahomotopycontinuation.org/examples/cyclooctane/

In [0]:

using HomotopyContinuation, LinearAlgebra, DynamicPolynomials

c² = 2

@polyvar z[1:3, 1:6]
z_vec = vec(z)[1:17] # the 17 variables in a vector
Z = [zeros(3) z[:,1:5] [z[1,6]; z[2,6]; 0] [√c²; 0; 0]] # the eight points in a matrix

# define the functions for cyclooctane:
F1 = [(Z[:, i] - Z[:, i+1]) ⋅ (Z[:, i] - Z[:, i+1]) - c² for i in 1:7]
F2 = [(Z[:, i] - Z[:, i+2]) ⋅ (Z[:, i] - Z[:, i+2]) - 8c²/3 for i in 1:6]
F3 = (Z[:, 7] - Z[:, 1]) ⋅ (Z[:, 7] - Z[:, 1]) - 8c²/3
F4 = (Z[:, 8] - Z[:, 2]) ⋅ (Z[:, 8] - Z[:, 2]) - 8c²/3
f = [F1; F2; F3; F4]

In [2]:

n = 2 # dimension of the cyclooctane variety
N = 17 # ambient dimension
@polyvar Aᵥ[1:n, 1:N] bᵥ[1:n] # variables for the linear equations
p = [vec(Aᵥ); bᵥ] # parameters
F = [f; Aᵥ * z_vec - bᵥ] # the polynomial system we have to solve

# now we solve one particular instance for A,b complex. we use this as start system
A₀ = randn(ComplexF64, n, N)
b₀ = randn(ComplexF64, n)
p₀ = [vec(A₀); b₀]

F₀ = [subs(Fᵢ, p => [vec(A₀); b₀]) for Fᵢ in F]
complex_result = solve(F₀)
S_p₀ = solutions(complex_result)

Tracking 32768 paths... 100%|████████████████████████████████████████| Time: 0:02:32
  # paths tracked:                  32768
  # non-singular solutions (real):  1408 (0)
  # singular solutions (real):      0 (0)
  # total solutions (real):         1408 (0)

1408-element Array{Array{Complex{Float64},1},1}:
 [-0.47140452079103157 - 2.422449305177514e-18im, -0.16384237851714517 + 0.2552019284126488im, 1.3479702017333817 + 0.03101915079392895im, -1.0455095604262024 + 0.7933755866659716im, 1.2898783954781725 + 0.5587198843935196im, 1.8765476693717755 + 0.05797937064992404im, 24.735366995427633 + 10.625824542195016im, 13.310996213665462 - 2.2224614153547333im, 9.827663410548107 - 27.61816720417769im, 0.13149256848157667 - 0.08445250104374812im, -0.8930876777097178 + 0.12398508334875953im, 1.450721420349676 - 0.13974025496718226im, 1.1135955726342797 - 0.5858587155439727im, -2.106284509545492 - 0.2071323352891917im, 1.2046193901745286 - 0.5083757604920134im, 1.8856180831641267 + 1.2683105876356778e-43im, -1.3333333333333335 + 1.793662034335766e-43im]
 [-0.47140452079103057 - 6.617828928240829e-16im, -3.4086937947479607 + 2.5181841839755585im, 2.6476833435081675 + 3.2419733360472622im, 2.5052403040075135 + 0.1920065064866999im, 0.34199759439431754 - 0.23177461391707674im, 0.3806202039800047 - 1.0555300903100622im, 1.0604368575965808 + 0.1813209001237161im, 0.7244859857994322 + 0.08213632080142466im, 0.09103514155742315 - 0.5875988778656646im, 0.4465579687900144 + 0.6476897145769915im, 4.79744224240648 - 5.724939885807321im, 6.0270695309569495 + 3.4451037258524315im, 3.2349050935787584 + 0.17689811281980478im, 1.3562883359177793 - 0.06254292757699345im, 0.6060818337742233 - 0.39144986618892147im, 1.885618083164127 + 0.0im, 1.333333333333333 - 1.6704779438076223e-51im]
 [-0.4714045207910317 + 2.0265282535324248e-18im, 1.4773118749787342 + 0.7797185937458206im, -1.1216094256359357 + 1.026995236803861im, -2.2507985671884665 + 0.3579302939650492im, 2.6287604507363715 + 1.3908381809685333im, -1.16891160450314 + 2.438637275661215im, 20.6209669699364 + 7.35413255413667im, 9.82345482600752 - 5.648918321982728im, 3.7300723799894397 - 19.885706215985092im, 5.266097571367884 + 4.762458605040116im, 3.941114654838942 - 0.23080641337503524im, 3.2104992837992636 - 4.635421437460402im, 1.7553112553381764 - 4.130805237382327im, -1.8794037541286512 - 1.4604601975569742im, -4.578911118624116 + 0.29172574153093483im, 1.8856180831641265 + 0.0im, -1.3333333333333335 - 1.925929944387236e-34im]
 [-0.47140452079103146 - 2.9755607998039095e-16im, 0.8886951346725742 - 3.4915979380683106im, -3.724685166573224 - 0.8330814447463443im, 2.248718886520195 - 0.23113787677353967im, 0.6928360631182762 + 0.47195333111145976im, -0.4822327174738021 - 0.3997609743235411im, 3.4150634530832296 - 0.35845638381154493im, 1.0840990026314485 + 0.4974622293345537im, -1.2164062403990406 - 0.5884310340286092im, 2.4033789269324797 - 0.5487946839409098im, 2.261177235656359 + 1.9132022864498959im, -2.9033786108394826 + 0.5135426262402145im, 1.0816482703900105 - 0.44783421615315244im, 2.1175795865742613 + 0.1583333055446281im, -1.0795389380040465 + 0.4485410164513247im, 1.8856180831641265 + 2.7369110631344083e-48im, 1.3333333333333335 + 5.473822126268817e-48im]
 [-0.4714045207910317 + 1.6286824538045384e-17im, 1.5772014810731512 - 0.10584727853837796im, -0.19453682572018186 - 0.8581536367742478im, 7.513661184838595 - 7.634562016147988im, 0.9596918442067405 + 2.934447625084449im, 7.904306671483201 + 6.900965397474049im, 3.4899040302558353 + 0.8479103731336467im, 2.670611902234994 - 0.07333065249240625im, -1.1822719130217272 + 2.578383824569445im, 8.139247137286468 - 0.10790812357479694im, 2.5760663420893133 + 0.4647039212636588im, -0.1633664806374005 + 6.98978136602634im, 11.807711287176083 + 7.413843749082465im, 1.674656360727566 + 2.62118959481686im, -7.9050689147039295 + 10.30292851897507im, 1.8856180831641265 + 0.0im, -1.3333333333333335 - 4.3790577010150533e-47im]
 [-0.47140452079103273 - 2.300198559466298e-16im, 0.6864263968540075 + 8.293384853722484im, -8.39917942631617 + 0.6777802918494329im, -2.1527879309937235 - 0.024799481351254173im, 0.8647872671915876 + 13.489633620771004im, -13.515680610851247 + 0.8670707569888416im, 6.173243179922792 + 2.035582328461635im, 4.182870492767442 - 0.7043149550745138im, -1.936910481147947 + 3.4530016710606244im, 4.916750580363144 + 1.2868171608914283im, 2.953858516527601 - 0.46747574906528566im, -1.2622941390540123 + 2.4898769575163184im, -4.945358476758881 - 4.233992247692672im, 4.248448257157288 + 1.4969423149173797im, 4.5445854232569936 - 7.324333812906591im, 1.885618083164127 + 5.345529420184391e-51im, 1.333333333333333 + 4.276423536147513e-50im]
 [-0.47140452079103096 - 3.567553603052717e-16im, -2.6591470212879242 + 2.227908580596266im, -2.400369858953108 - 2.4680931747652393im, -2.2874026513483465 + 0.41936124226406835im, -1.4814373075800487 - 1.7005716515192872im, 1.45652558152636 - 1.0710709726850682im, -0.6911665099096699 + 0.48937338394048246im, -1.542264281655869 - 1.0901195097569725im, 1.6226759959309947 - 1.5202058999093628im, -0.1548732137313416 - 0.23790971062048658im, -0.03880849489265388 - 0.7587270155365943im, 1.2192946833278848 - 1.2519809928346468im, 2.2201321780921885 - 2.474438187591074im, 1.715064740870276 + 0.874846011036299im, 2.9425736730194982 + 0.16780489003009705im, 1.885618083164127 - 1.5482306977974587e-47im, 1.3333333333333333 - 2.1895288505075267e-47im]
 [-0.4714045207910311 + 3.3320935660482274e-16im, -2.6116311888968333 + 2.6481641874217603im, -2.823257257925051 - 2.4496627665709902im, 2.0315768314827345 - 1.022370882693332im, -2.487471429587334 - 1.485838735638739im, 0.9853628910797673 - 1.6430052522468568im, 0.7328330295247414 + 0.5252640701489933im, -0.2477945796018222 - 0.3731159530770196im, 0.5549378940505199 - 0.5228143776804759im, 0.7396893182526616 + 0.7044135578346908im, 0.1645838635805236 - 1.256950665922701im, 2.1957203480458554 - 0.30142848863938165im, 2.324296457074964 - 0.43847509040642757im, 1.6782371068572128 + 0.15502435490388478im, 1.3838236271851092 + 0.10036037247604107im, 1.885618083164127 - 2.5366211752713563e-43im, 1.3333333333333333 - 3.587324068671532e-43im]
 [-0.47140452079103146 - 1.3895044915021593e-18im, -1.335890569804467 + 0.005446137141163444im, 0.06805731679703328 + 0.10690170566729205im, -32.56901144352285 - 0.6808675495405753im, 12.285114172023555 - 1.4676285758911252im, 0.11947612994623184 - 34.694782944752376im, -45.83369328550179 - 0.4883888317559811im, 16.43877656924994 - 2.247020613452205im, -0.29979964551946986 - 48.5055029784775im, 20.74485489831559 + 2.2684050123980266im, 3.225160943348284 + 0.8094409673313138im, -2.41217448523765 + 19.264866460853934im, 15.173467967107053 + 1.7561867821854384im, 2.8646310468291376 + 0.6209057913567545im, -1.8711592773154386 + 13.864392539910838im, 1.885618083164127 + 0.0im, -1.333333333333333 - 4.1053665947016125e-48im]
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 ⋮
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In [3]:

tracker = pathtracker(F; parameters=p, generic_parameters=p₀)

# we compute 100 random intersections
data = [randn(n*N+n) for _ in 1:100]
Ω = map(data) do pp
    # We want to store all solutions. Create an empty array.
    S_p = similar(S_p₀, 0)
    for s in S_p₀
        result = track(tracker, s; target_parameters=pp, details=:minimal)
        # check that the tracking was successfull and that we have a real solution
        if is_success(result) && is_real(result)
            # only store the solutions
            push!(S_p, solution(result))
        end
    end
    # return an array of type Array{Float64}
    # (and not Array{ComplexF64})
    real.(S_p)
end
Ω = vcat(Ω...)

794-element Array{Array{Float64,1},1}:
 [-0.47140452079103135, -1.0450657970165176, 0.8280188751979082, -1.4072716179482827, -1.8276293465988476, 0.1126538863121203, -0.8376968482498709, -2.2386216369390524, -1.114810947808969, 0.40168704888186707, -2.8742312373669674, -0.870009004649992, 1.4568131830371633, -1.9849387596762313, -1.1796341492122016, 1.8856180831641267, -1.3333333333333335]
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 [-0.47140452079103135, 0.5688017280450942, 1.205919720358985, 0.5977128843453564, 0.6779325040459827, 2.1252012048695135, 1.8268372586051689, 0.5826892079122182, 1.4322495563816835, 2.6120256632155607, -0.44511280121441993, 2.004178047804024, 2.436053346594702, -1.6387250796453514, 1.2663952392742992, 1.885618083164127, -1.3333333333333333]
 [-0.47140452079103135, 1.01949229960036, 0.8593097397524063, 0.4316252259992146, 1.1841663907997846, 1.9351441694392368, 1.627661339317607, 0.48210822114837515, 1.6583555460026036, 1.557007062856779, -0.8114597072614212, 2.225532756235336, 2.121345375684943, -1.7499911498072265, 1.3307249556283274, 1.885618083164127, -1.3333333333333333]
 [-0.4714045207910314, -0.3319457266763361, -1.2913519320150868, -1.1636789711744073, 0.7730066623061634, -1.8389250352883042, -0.2399382336337838, 1.6519958612844385, -2.4505466813142074, 0.43716421875665873, 2.392379002822633, -1.4538696660816486, 1.7467379744631204, 1.8824348666505366, -1.2958394273658649, 1.885618083164127, 1.3333333333333333]
 ⋮
 [-0.47140452079103135, -1.2853862909988014, -0.3543442686006406, -1.154243984951937, -1.8565385995716481, 0.7445257449115834, -0.35991563623008005, -2.879022773747076, 1.3133566406772785, 0.6575314149834368, -3.2472149558150063, 0.40273267051122896, 0.8805576408434317, -2.18867586046699, -0.5081758244532483, 1.8856180831641267, -1.3333333333333335]
 [-0.47140452079103135, -1.331970902557534, 0.06026020675244135, -0.24866558258536722, -1.8526866816721754, 1.356116079443554, 0.1639434382464032, -3.2017746379204057, 1.257548933628023, 0.849603921829774, -3.396995004067007, 0.03617318886566478, 0.9463332722875073, -2.1654206629515245, -0.6522075742778064, 1.885618083164127, -1.3333333333333333]
 [-0.47140452079103135, 0.9320244950983979, 0.9534716137957935, -0.24176879652005476, 0.4310655026500103, 2.255895324430562, 0.12209530444594109, -0.9333608168502115, 2.178799704040771, -0.23418087515015426, -1.4452596279691334, 0.9095373627466455, 0.8401672166594262, -2.2029560318847454, 0.38831539743967297, 1.8856180831641267, -1.3333333333333335]
 [-0.47140452079103135, 0.3679173693238242, 1.2815672386291774, 0.6244321855761877, 0.5092826715975187, 2.1642663744004276, 1.35218173878464, -0.7024428590980487, 2.2101120510280303, 0.5163116058573611, -1.7698625448089045, 1.8076989107889583, 0.880053542638232, -2.188854086096631, 0.506876904611235, 1.8856180831641267, -1.3333333333333335]
 [-0.47140452079103135, 0.8992220279562192, 0.9844681417984447, -0.36940639328957986, 0.2974265106095656, 2.2601791346521045, -0.2974969423649234, -1.1074046953571175, 2.1143082547277396, -0.2995808043087642, -1.4393209965358302, 0.7395983847801785, 0.8547910717990976, -2.1977857183165703, 0.4360249382054165, 1.8856180831641267, -1.3333333333333335]
 [-0.4714045207910314, 0.8613176413096886, 1.0177964917145728, 0.12683490797560132, 0.5073924416390924, 2.2493997309548326, 0.8146520248827888, -0.7197007799260432, 2.1039698878056985, 0.027345694779926544, -1.6140083353630406, 1.342154464708827, 0.8267112507634773, -2.2077134342509668, 0.33789903730921056, 1.8856180831641267, -1.3333333333333335]
 [-0.4714045207910314, 0.8712797093877704, 1.0092816483950058, -0.43554722286892456, 0.2089773317170862, 2.258309196016548, -0.5722910285252211, -1.184177076602339, 2.0572571475445525, 0.7087823260572257, -1.7712678186017947, 1.9381961512552355, 0.9198157188404517, -2.1747960338829686, 0.599304861193794, 1.885618083164127, -1.3333333333333333]
 [-0.4714045207910314, 0.469041544066437, 1.2481096937839842, 0.5205290772709177, 0.2621468369827796, 2.2346502744073273, 0.39629547925267644, -1.0444505583051868, 2.761308854276814, 1.3818037363130589, -1.8800986613869521, 2.1864473726295777, 1.059946716920792, -2.1252522443844453, 0.831343029853193, 1.8856180831641267, -1.3333333333333335]
 [-0.47140452079103135, -0.8786811225498685, 1.0028445854928274, -0.07185062875982146, -0.40213126979484587, 2.272985099452554, -0.30997838203832173, 0.9897303041854314, 2.3505514065431945, -0.14735821610210365, 1.5678791324987185, 1.0702004335866186, 1.1618566113395445, 2.089221655677693, 0.9512108998774896, 1.8856180831641267, 1.3333333333333333]
 [-0.4714045207910314, -0.924192810319554, 0.9610647361813994, -0.8111061496177753, -0.23664128857047134, 2.1492884980684344, 0.2681040423276839, 0.5890630990015677, 2.541101751985818, 0.34378838053421523, 1.706979912189246, 1.6782379853676186, 1.685959470668116, 1.9039233127424469, 1.2785004942721274, 1.885618083164127, 1.3333333333333333]
 [-0.4714045207910314, -0.44933198582759326, 1.2553400114271869, 0.4497336631353765, -0.08227642507109022, 2.2636924604401742, 0.7239562680491822, 1.3019590142501025, 2.1704497047883162, -0.05397967596205814, 1.8678579001534423, 1.1338330360294633, 0.7866715253305094, 2.221869614936215, 0.05310121750928835, 1.8856180831641267, 1.3333333333333335]
 [-0.47140452079103135, -0.8400429977026833, 1.035425294161036, -0.024580865906231788, -0.3464959763419161, 2.283127165258978, 0.9988763672529918, 0.6067800831313921, 2.0738425592099214, 0.42189699558027854, 1.8459559727803165, 1.71116099202328, 0.8464829524921471, 2.2007230820669967, 0.40967450981856396, 1.8856180831641267, 1.3333333333333335]

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using JuMP
using Ipopt
m = Model(with_optimizer(Ipopt.Optimizer, print_level=0))
@variable(m, 0 <= x <= 2 )
@variable(m, 0 <= y <= 30 )
@objective(m, Min, x*x+ 2x*y + y*y )
@constraint(m, x + y >= 1 )
optimize!(m)
println(termination_status(m))
println("| x = ", JuMP.value(x), "| y = ", JuMP.value(y))

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