mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-19 07:20:28 +01:00
Merge pull request #10 from kalmarek/mk/perf_tweaks
Various perf tweaks including moving to sparse matrices where possible
This commit is contained in:
Marek Kaluba
GitHub
commit
0127d05594
@ -1 +0,0 @@
|
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comment: false
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4
.gitignore
vendored
4
.gitignore
vendored
@ -2,7 +2,3 @@
|
||||
*.jl.*.cov
|
||||
*.jl.mem
|
||||
Manifest.toml
|
||||
test/SL*
|
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test/oSL*
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test/SAut*
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test/oSAut*
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28
.travis.yml
28
.travis.yml
@ -1,28 +0,0 @@
|
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# Documentation: http://docs.travis-ci.com/user/languages/julia/
|
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language: julia
|
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os:
|
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- linux
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- osx
|
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julia:
|
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- 1.1
|
||||
- 1.2
|
||||
- 1.3
|
||||
- nightly
|
||||
notifications:
|
||||
email: true
|
||||
matrix:
|
||||
fast_finish: true
|
||||
allow_failures:
|
||||
- julia: nightly
|
||||
- os: osx
|
||||
|
||||
addons:
|
||||
apt:
|
||||
packages:
|
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- hdf5-tools
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|
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## uncomment the following lines to override the default test
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# script:
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# - julia -e 'using Pkg; Pkg.build(); Pkg.test(coverage=true);'
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|
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codecov: true
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@ -8,6 +8,7 @@ Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
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IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
|
||||
JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
|
||||
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
|
||||
ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
|
||||
SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
|
||||
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
|
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SymbolicWedderburn = "858aa9a9-4c7c-4c62-b466-2421203962a2"
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@ -17,9 +18,10 @@ COSMO = "0.8"
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Groups = "0.7"
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IntervalArithmetic = "0.20"
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JuMP = "1.3"
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ProgressMeter = "1.7"
|
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SCS = "1.1.0"
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StaticArrays = "1"
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SymbolicWedderburn = "0.3.1"
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SymbolicWedderburn = "0.3.2"
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julia = "1.6"
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|
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[extras]
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13
README.md
13
README.md
@ -83,7 +83,10 @@ julia> include("test/optimizers.jl");
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Now we have everything what we need to solve the problem!
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```julia
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julia> status, warmstart = PropertyT.solve(opt_problem, scs_optimizer(max_iters=5_000, accel=50, alpha=1.9));
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julia> status, warmstart = PropertyT.solve(
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opt_problem,
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scs_optimizer(max_iters=5_000, accel=50, alpha=1.9),
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);
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------------------------------------------------------------------
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SCS v3.2.1 - Splitting Conic Solver
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(c) Brendan O'Donoghue, Stanford University, 2012
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@ -119,8 +122,12 @@ julia> status
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ALMOST_OPTIMAL::TerminationStatusCode = 7
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```
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The solver didn't manage to solve the problem but it got quite close! (duality gap is ~`1.63e-6`). Let's try once again this time warmstarting the solver:
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```
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julia> status, warmstart = PropertyT.solve(opt_problem, scs_optimizer(max_iters=10_000, accel=50, alpha=1.9), warmstart);
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```julia
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julia> status, warmstart = PropertyT.solve(
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opt_problem,
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scs_optimizer(max_iters=10_000, accel=50, alpha=1.9),
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warmstart,
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);
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------------------------------------------------------------------
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SCS v3.2.1 - Splitting Conic Solver
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(c) Brendan O'Donoghue, Stanford University, 2012
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|
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34
appveyor.yml
34
appveyor.yml
@ -1,34 +0,0 @@
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environment:
|
||||
matrix:
|
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- JULIAVERSION: "julialang/bin/winnt/x86/0.5/julia-0.5-latest-win32.exe"
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||||
- JULIAVERSION: "julialang/bin/winnt/x64/0.5/julia-0.5-latest-win64.exe"
|
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- JULIAVERSION: "julianightlies/bin/winnt/x86/julia-latest-win32.exe"
|
||||
- JULIAVERSION: "julianightlies/bin/winnt/x64/julia-latest-win64.exe"
|
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|
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branches:
|
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only:
|
||||
- master
|
||||
- /release-.*/
|
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|
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notifications:
|
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- provider: Email
|
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on_build_success: false
|
||||
on_build_failure: false
|
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on_build_status_changed: false
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install:
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# Download most recent Julia Windows binary
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- ps: (new-object net.webclient).DownloadFile(
|
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$("http://s3.amazonaws.com/"+$env:JULIAVERSION),
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"C:\projects\julia-binary.exe")
|
||||
# Run installer silently, output to C:\projects\julia
|
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- C:\projects\julia-binary.exe /S /D=C:\projects\julia
|
||||
|
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build_script:
|
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# Need to convert from shallow to complete for Pkg.clone to work
|
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- IF EXIST .git\shallow (git fetch --unshallow)
|
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- C:\projects\julia\bin\julia -e "versioninfo();
|
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Pkg.clone(pwd(), \"Property(T)\"); Pkg.build(\"Property(T)\")"
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|
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test_script:
|
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- C:\projects\julia\bin\julia -e "Pkg.test(\"Property(T)\")"
|
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80
scripts/SpN_Adj.jl
Normal file
80
scripts/SpN_Adj.jl
Normal file
@ -0,0 +1,80 @@
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using LinearAlgebra
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BLAS.set_num_threads(8)
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ENV["OMP_NUM_THREADS"] = 1
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using Groups
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import Groups.MatrixGroups
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include(joinpath(@__DIR__, "../test/optimizers.jl"))
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using PropertyT
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using PropertyT.SymbolicWedderburn
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using PropertyT.PermutationGroups
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using PropertyT.StarAlgebras
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include(joinpath(@__DIR__, "argparse.jl"))
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include(joinpath(@__DIR__, "utils.jl"))
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const N = parsed_args["N"]
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const HALFRADIUS = parsed_args["halfradius"]
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const UPPER_BOUND = parsed_args["upper_bound"]
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const GENUS = 2N
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G = MatrixGroups.SymplecticGroup{GENUS}(Int8)
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RG, S, sizes =
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@time PropertyT.group_algebra(G, halfradius=HALFRADIUS, twisted=true)
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wd = let RG = RG, N = N
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G = StarAlgebras.object(RG)
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P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
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Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
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# Σ = P
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act = PropertyT.action_by_conjugation(G, Σ)
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@info "Computing WedderburnDecomposition"
|
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|
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wdfl = @time SymbolicWedderburn.WedderburnDecomposition(
|
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Float64,
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Σ,
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act,
|
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basis(RG),
|
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StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
|
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)
|
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end
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|
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Δ = RG(length(S)) - sum(RG(s) for s in S)
|
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Δs = PropertyT.laplacians(
|
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RG,
|
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S,
|
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x -> (gx = PropertyT.grading(x); Set([gx, -gx])),
|
||||
)
|
||||
|
||||
# elt = Δ^2
|
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elt = PropertyT.Adj(Δs, :C₂)
|
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unit = Δ
|
||||
|
||||
@time model, varP = PropertyT.sos_problem_primal(
|
||||
elt,
|
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unit,
|
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wd,
|
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upper_bound=UPPER_BOUND,
|
||||
augmented=true,
|
||||
show_progress=true
|
||||
)
|
||||
|
||||
solve_in_loop(
|
||||
model,
|
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wd,
|
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varP,
|
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logdir="./log/Sp($N,Z)/r=$HALFRADIUS/Adj_C₂-InfΔ",
|
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optimizer=cosmo_optimizer(
|
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eps=1e-10,
|
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max_iters=20_000,
|
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accel=50,
|
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alpha=1.95,
|
||||
),
|
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data=(elt=elt, unit=unit, halfradius=HALFRADIUS)
|
||||
)
|
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|
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19
scripts/argparse.jl
Normal file
19
scripts/argparse.jl
Normal file
@ -0,0 +1,19 @@
|
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using ArgParse
|
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|
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args_settings = ArgParseSettings()
|
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@add_arg_table! args_settings begin
|
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"-N"
|
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help = "the degree/genus/etc. parameter for a group"
|
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arg_type = Int
|
||||
default = 3
|
||||
"--halfradius", "-R"
|
||||
help = "the halfradius on which perform the sum of squares decomposition"
|
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arg_type = Int
|
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default = 2
|
||||
"--upper_bound", "-u"
|
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help = "set upper bound for the optimization problem to speed-up the convergence"
|
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arg_type = Float64
|
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default = Inf
|
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end
|
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|
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parsed_args = parse_args(ARGS, args_settings)
|
||||
85
scripts/utils.jl
Normal file
85
scripts/utils.jl
Normal file
@ -0,0 +1,85 @@
|
||||
using Dates
|
||||
using Serialization
|
||||
using Logging
|
||||
|
||||
import JuMP
|
||||
|
||||
function get_solution(model)
|
||||
λ = JuMP.value(model[:λ])
|
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Q = real.(sqrt(JuMP.value.(model[:P])))
|
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solution = Dict(:λ => λ, :Q => Q)
|
||||
return solution
|
||||
end
|
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|
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function get_solution(model, wd, varP; logdir)
|
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λ = JuMP.value(model[:λ])
|
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|
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Qs = [real.(sqrt(JuMP.value.(P))) for P in varP]
|
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Q = PropertyT.reconstruct(Qs, wd)
|
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solution = Dict(:λ => λ, :Q => Q)
|
||||
return solution
|
||||
end
|
||||
|
||||
function solve_in_loop(model::JuMP.Model, args...; logdir, optimizer, data)
|
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@info "logging to $logdir"
|
||||
status = JuMP.UNKNOWN_RESULT_STATUS
|
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warm = try
|
||||
solution = deserialize(joinpath(logdir, "solution.sjl"))
|
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warm = solution[:warm]
|
||||
@info "trying to warm-start model with λ=$(solution[:λ])..."
|
||||
warm
|
||||
catch
|
||||
nothing
|
||||
end
|
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old_lambda = 0.0
|
||||
while status != JuMP.OPTIMAL
|
||||
date = now()
|
||||
log_file = joinpath(logdir, "solver_$date.log")
|
||||
@info "Current logfile is $log_file."
|
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isdir(dirname(log_file)) || mkpath(dirname(log_file))
|
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|
||||
λ, flag, certified_λ = let
|
||||
# logstream = current_logger().logger.stream
|
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# v = @ccall setvbuf(logstream.handle::Ptr{Cvoid}, C_NULL::Ptr{Cvoid}, 1::Cint, 0::Cint)::Cint
|
||||
# @warn v
|
||||
status, warm = @time PropertyT.solve(log_file, model, optimizer, warm)
|
||||
|
||||
solution = get_solution(model, args...; logdir=logdir)
|
||||
solution[:warm] = warm
|
||||
|
||||
serialize(joinpath(logdir, "solution_$date.sjl"), solution)
|
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serialize(joinpath(logdir, "solution.sjl"), solution)
|
||||
|
||||
flag, λ_cert = open(log_file, append=true) do io
|
||||
with_logger(SimpleLogger(io)) do
|
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PropertyT.certify_solution(
|
||||
data.elt,
|
||||
data.unit,
|
||||
solution[:λ],
|
||||
solution[:Q],
|
||||
halfradius=data.halfradius,
|
||||
)
|
||||
end
|
||||
end
|
||||
|
||||
solution[:λ], flag, λ_cert
|
||||
end
|
||||
|
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if flag == true && certified_λ ≥ 0
|
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@info "Certification done with λ = $certified_λ"
|
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return certified_λ
|
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else
|
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rel_change = abs(certified_λ - old_lambda) / (abs(certified_λ) + abs(old_lambda))
|
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@info "Certification failed with λ = $λ" certified_λ rel_change
|
||||
end
|
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|
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old_lambda = certified_λ
|
||||
|
||||
if rel_change < 1e-9
|
||||
@info "No progress detected, breaking"
|
||||
break
|
||||
end
|
||||
end
|
||||
|
||||
return status == JuMP.OPTIMAL ? old_lambda : NaN
|
||||
end
|
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@ -1,4 +1,3 @@
|
||||
__precompile__()
|
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module PropertyT
|
||||
|
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using LinearAlgebra
|
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@ -15,6 +14,8 @@ import SymbolicWedderburn.PermutationGroups
|
||||
|
||||
include("constraint_matrix.jl")
|
||||
include("sos_sdps.jl")
|
||||
include("solve.jl")
|
||||
include("reconstruct.jl")
|
||||
include("certify.jl")
|
||||
|
||||
include("sqadjop.jl")
|
||||
@ -28,7 +29,7 @@ include("actions/actions.jl")
|
||||
function group_algebra(G::Groups.Group, S=gens(G); halfradius::Integer, twisted::Bool)
|
||||
S = union!(S, inv.(S))
|
||||
@info "generating wl-metric ball of radius $(2halfradius)"
|
||||
@time E, sizes = Groups.wlmetric_ball_serial(S, radius=2halfradius)
|
||||
@time E, sizes = Groups.wlmetric_ball(S, radius=2halfradius)
|
||||
@info "sizes = $(sizes)"
|
||||
@info "computing the *-algebra structure for G"
|
||||
@time RG = StarAlgebras.StarAlgebra{twisted}(
|
||||
|
||||
@ -4,6 +4,7 @@ StarAlgebras.star(g::Groups.GroupElement) = inv(g)
|
||||
include("alphabet_permutation.jl")
|
||||
|
||||
include("sln_conjugation.jl")
|
||||
include("spn_conjugation.jl")
|
||||
include("autfn_conjugation.jl")
|
||||
|
||||
function SymbolicWedderburn.action(
|
||||
|
||||
@ -1,26 +1,43 @@
|
||||
## Particular definitions for actions on Sp(n,ℤ)
|
||||
|
||||
function _conj(
|
||||
t::MatrixGroups.ElementarySymplectic{N,T},
|
||||
s::MatrixGroups.ElementarySymplectic{N,T},
|
||||
σ::PermutationGroups.AbstractPerm,
|
||||
) where {N,T}
|
||||
@assert iseven(N)
|
||||
@assert degree(σ) == N ÷ 2 "Got degree = $(degree(σ)); N = $N"
|
||||
i = mod1(t.i, N ÷ 2)
|
||||
ib = i == t.i ? 0 : N ÷ 2
|
||||
j = mod1(t.j, N ÷ 2)
|
||||
jb = j == t.j ? 0 : N ÷ 2
|
||||
return MatrixGroups.ElementarySymplectic{N}(t.symbol, i^inv(σ) + ib, j^inv(σ) + jb, t.val)
|
||||
@assert PermutationGroups.degree(σ) == N ÷ 2 "Got degree = $(PermutationGroups.degree(σ)); N = $N"
|
||||
n = N ÷ 2
|
||||
@assert 1 ≤ s.i ≤ N
|
||||
@assert 1 ≤ s.j ≤ N
|
||||
if s.symbol == :A
|
||||
@assert 1 ≤ s.i ≤ n
|
||||
@assert 1 ≤ s.j ≤ n
|
||||
i = s.i^inv(σ)
|
||||
j = s.j^inv(σ)
|
||||
else
|
||||
@assert s.symbol == :B
|
||||
@assert xor(s.i > n, s.j > n)
|
||||
if s.i > n
|
||||
i = (s.i - n)^inv(σ) + n
|
||||
j = s.j^inv(σ)
|
||||
elseif s.j > n
|
||||
i = s.i^inv(σ)
|
||||
j = (s.j - n)^inv(σ) + n
|
||||
end
|
||||
end
|
||||
return MatrixGroups.ElementarySymplectic{N}(s.symbol, i, j, s.val)
|
||||
end
|
||||
|
||||
function _conj(
|
||||
t::MatrixGroups.ElementarySymplectic{N,T},
|
||||
s::MatrixGroups.ElementarySymplectic{N,T},
|
||||
x::Groups.Constructions.DirectPowerElement,
|
||||
) where {N,T}
|
||||
@assert Groups.order(Int, parent(x).group) == 2
|
||||
@assert iseven(N)
|
||||
just_one_flips = xor(isone(x.elts[mod1(t.i, N ÷ 2)]), isone(x.elts[mod1(t.j, N ÷ 2)]))
|
||||
return ifelse(just_one_flips, inv(t), t)
|
||||
n = N ÷ 2
|
||||
i, j = ifelse(s.i <= n, s.i, s.i - n), ifelse(s.j <= n, s.j, s.j - n)
|
||||
just_one_flips = xor(isone(x.elts[i]), isone(x.elts[j]))
|
||||
return ifelse(just_one_flips, inv(s), s)
|
||||
end
|
||||
|
||||
action_by_conjugation(sln::Groups.MatrixGroups.SymplecticGroup, Σ::Groups.Group) =
|
||||
|
||||
@ -5,80 +5,50 @@ function augment_columns!(Q::AbstractMatrix)
|
||||
return Q
|
||||
end
|
||||
|
||||
function _fma_SOS_thr!(
|
||||
result::AbstractVector{T},
|
||||
mstructure::AbstractMatrix{<:Integer},
|
||||
Q::AbstractMatrix{T},
|
||||
acc_matrix=zeros(T, size(mstructure)...),
|
||||
) where {T}
|
||||
function __sos_via_sqr!(
|
||||
res::StarAlgebras.AlgebraElement,
|
||||
P::AbstractMatrix;
|
||||
augmented::Bool
|
||||
)
|
||||
StarAlgebras.zero!(res)
|
||||
A = parent(res)
|
||||
b = basis(A)
|
||||
@assert size(A.mstructure) == size(P)
|
||||
e = b[one(b[1])]
|
||||
|
||||
s1, s2 = size(mstructure)
|
||||
|
||||
@inbounds for k = 1:s2
|
||||
let k = k, s1 = s1, s2 = s2, Q = Q, acc_matrix = acc_matrix
|
||||
Threads.@threads for j = 1:s2
|
||||
for i = 1:s1
|
||||
@inbounds acc_matrix[i, j] =
|
||||
muladd(Q[i, k], Q[j, k], acc_matrix[i, j])
|
||||
end
|
||||
for i in axes(A.mstructure, 1)
|
||||
x = StarAlgebras._istwisted(A.mstructure) ? StarAlgebras.star(b[i]) : b[i]
|
||||
for j in axes(A.mstructure, 2)
|
||||
p = P[i, j]
|
||||
xy = b[A.mstructure[i, j]]
|
||||
# either result += P[x,y]*(x*y)
|
||||
res[xy] += p
|
||||
if augmented
|
||||
# or result += P[x,y]*(1-x)*(1-y) == P[x,y]*(2-x-y+xy)
|
||||
y = b[j]
|
||||
res[e] += p
|
||||
res[x] -= p
|
||||
res[y] -= p
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
@inbounds for j = 1:s2
|
||||
for i = 1:s1
|
||||
result[mstructure[i, j]] += acc_matrix[i, j]
|
||||
end
|
||||
end
|
||||
|
||||
return result
|
||||
return res
|
||||
end
|
||||
|
||||
function _cnstr_sos!(res::StarAlgebras.AlgebraElement, Q::AbstractMatrix, cnstrs)
|
||||
function __sos_via_cnstr!(res::StarAlgebras.AlgebraElement, Q²::AbstractMatrix, cnstrs)
|
||||
StarAlgebras.zero!(res)
|
||||
Q² = Q' * Q
|
||||
for (g, A_g) in cnstrs
|
||||
res[g] = dot(A_g, Q²)
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
function _augmented_sos!(res::StarAlgebras.AlgebraElement, Q::AbstractMatrix)
|
||||
A = parent(res)
|
||||
StarAlgebras.zero!(res)
|
||||
Q² = Q' * Q
|
||||
|
||||
N = LinearAlgebra.checksquare(A.mstructure)
|
||||
augmented_basis = [A(1) - A(b) for b in @view basis(A)[1:N]]
|
||||
tmp = zero(res)
|
||||
|
||||
for (j, y) in enumerate(augmented_basis)
|
||||
for (i, x) in enumerate(augmented_basis)
|
||||
# res += Q²[i, j] * x * y
|
||||
|
||||
StarAlgebras.mul!(tmp, x, y)
|
||||
StarAlgebras.mul!(tmp, tmp, Q²[i, j])
|
||||
StarAlgebras.add!(res, res, tmp)
|
||||
end
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
function compute_sos(A::StarAlgebras.StarAlgebra, Q::AbstractMatrix; augmented::Bool)
|
||||
if augmented
|
||||
z = zeros(eltype(Q), length(basis(A)))
|
||||
res = StarAlgebras.AlgebraElement(z, A)
|
||||
return _augmented_sos!(res, Q)
|
||||
cnstrs = constraints(basis(A), A.mstructure; augmented=true)
|
||||
return _cnstr_sos!(res, Q, cnstrs)
|
||||
else
|
||||
@assert size(A.mstructure) == size(Q)
|
||||
z = zeros(eltype(Q), length(basis(A)))
|
||||
|
||||
_fma_SOS_thr!(z, A.mstructure, Q)
|
||||
|
||||
return StarAlgebras.AlgebraElement(z, A)
|
||||
end
|
||||
Q² = Q' * Q
|
||||
res = StarAlgebras.AlgebraElement(zeros(eltype(Q²), length(basis(A))), A)
|
||||
res = __sos_via_sqr!(res, Q², augmented=augmented)
|
||||
return res
|
||||
end
|
||||
|
||||
function sufficient_λ(residual::StarAlgebras.AlgebraElement, λ; halfradius)
|
||||
@ -159,7 +129,7 @@ function certify_solution(
|
||||
true, compute_sos(parent(elt), Q_int, augmented=augmented)
|
||||
end
|
||||
|
||||
@info "Checking in $(eltype(sos_int)) arithmetic with" λ
|
||||
@info "Checking in $(eltype(sos_int)) arithmetic with" λ_int
|
||||
|
||||
λ_certified =
|
||||
sufficient_λ(elt, orderunit, λ_int, sos_int, halfradius=halfradius)
|
||||
|
||||
@ -6,7 +6,8 @@ Roots.Root(e::MatrixGroups.ElementaryMatrix{N}) where {N} =
|
||||
function Roots.Root(s::MatrixGroups.ElementarySymplectic{N}) where {N}
|
||||
if s.symbol === :A
|
||||
return Roots.𝕖(N ÷ 2, s.i) - Roots.𝕖(N ÷ 2, s.j)
|
||||
else#if s.symbol === :B
|
||||
else
|
||||
@assert s.symbol === :B
|
||||
n = N ÷ 2
|
||||
i, j = ifelse(s.i <= n, s.i, s.i - n), ifelse(s.j <= n, s.j, s.j - n)
|
||||
return (-1)^(s.i > s.j) * (Roots.𝕖(n, i) + Roots.𝕖(n, j))
|
||||
|
||||
69
src/reconstruct.jl
Normal file
69
src/reconstruct.jl
Normal file
@ -0,0 +1,69 @@
|
||||
__outer_dim(wd::WedderburnDecomposition) = size(first(direct_summands(wd)), 2)
|
||||
|
||||
function __group_of(wd::WedderburnDecomposition)
|
||||
# this is veeeery hacky... ;)
|
||||
return parent(first(keys(wd.hom.cache)))
|
||||
end
|
||||
|
||||
function reconstruct(
|
||||
Ms::AbstractVector{<:AbstractMatrix},
|
||||
wbdec::WedderburnDecomposition;
|
||||
atol=eps(real(eltype(wbdec))) * 10__outer_dim(wbdec)
|
||||
)
|
||||
n = __outer_dim(wbdec)
|
||||
res = sum(zip(Ms, SymbolicWedderburn.direct_summands(wbdec))) do (M, ds)
|
||||
res = similar(M, n, n)
|
||||
reconstruct!(res, M, ds, __group_of(wbdec), wbdec.hom, atol=atol)
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
function reconstruct!(
|
||||
res::AbstractMatrix,
|
||||
M::AbstractMatrix,
|
||||
ds::SymbolicWedderburn.DirectSummand,
|
||||
G,
|
||||
hom;
|
||||
atol=eps(real(eltype(ds))) * 10max(size(res)...)
|
||||
)
|
||||
res .= zero(eltype(res))
|
||||
U = SymbolicWedderburn.image_basis(ds)
|
||||
d = SymbolicWedderburn.degree(ds)
|
||||
tmp = (U' * M * U) .* d
|
||||
|
||||
res = average!(res, tmp, G, hom)
|
||||
if eltype(res) <: AbstractFloat
|
||||
__droptol!(res, atol) # TODO: is this really necessary?!
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
function __droptol!(M::AbstractMatrix, tol)
|
||||
for i in eachindex(M)
|
||||
if abs(M[i]) < tol
|
||||
M[i] = zero(M[i])
|
||||
end
|
||||
end
|
||||
return M
|
||||
end
|
||||
|
||||
# implement average! for other actions when needed
|
||||
function average!(
|
||||
res::AbstractMatrix,
|
||||
M::AbstractMatrix,
|
||||
G::Groups.Group,
|
||||
hom::SymbolicWedderburn.InducedActionHomomorphism{<:SymbolicWedderburn.ByPermutations}
|
||||
)
|
||||
@assert size(M) == size(res)
|
||||
for g in G
|
||||
gext = SymbolicWedderburn.induce(hom, g)
|
||||
Threads.@threads for c in axes(res, 2)
|
||||
for r in axes(res, 1)
|
||||
res[r, c] += M[r^gext, c^gext]
|
||||
end
|
||||
end
|
||||
end
|
||||
o = Groups.order(Int, G)
|
||||
res ./= o
|
||||
return res
|
||||
end
|
||||
@ -48,10 +48,8 @@ function isorthogonal(α::AbstractRoot{N}, β::AbstractRoot{M}) where {N,M}
|
||||
end
|
||||
|
||||
function _positive_direction(α::Root{N}) where {N}
|
||||
last = -1 / √2^(N - 1)
|
||||
return Root{N,Float64}(
|
||||
SVector(ntuple(i -> ifelse(i == N, last, (√2)^-i), N)),
|
||||
)
|
||||
v = α.coord + 1 / (N * 100) * rand(N)
|
||||
return Root{N,Float64}(v / norm(v, 2))
|
||||
end
|
||||
|
||||
function positive(roots::AbstractVector{<:Root{N}}) where {N}
|
||||
|
||||
63
src/solve.jl
Normal file
63
src/solve.jl
Normal file
@ -0,0 +1,63 @@
|
||||
## Low-level solve
|
||||
|
||||
setwarmstart!(model::JuMP.Model, ::Nothing) = model
|
||||
|
||||
function setwarmstart!(model::JuMP.Model, warmstart)
|
||||
constraint_map = Dict(
|
||||
ct => JuMP.all_constraints(model, ct...) for
|
||||
ct in JuMP.list_of_constraint_types(model)
|
||||
)
|
||||
|
||||
JuMP.set_start_value.(JuMP.all_variables(model), warmstart.primal)
|
||||
|
||||
for (ct, idx) in pairs(constraint_map)
|
||||
JuMP.set_start_value.(idx, warmstart.slack[ct])
|
||||
JuMP.set_dual_start_value.(idx, warmstart.dual[ct])
|
||||
end
|
||||
return model
|
||||
end
|
||||
|
||||
function getwarmstart(model::JuMP.Model)
|
||||
constraint_map = Dict(
|
||||
ct => JuMP.all_constraints(model, ct...) for
|
||||
ct in JuMP.list_of_constraint_types(model)
|
||||
)
|
||||
|
||||
primal = value.(JuMP.all_variables(model))
|
||||
|
||||
slack = Dict(k => value.(v) for (k, v) in constraint_map)
|
||||
duals = Dict(k => JuMP.dual.(v) for (k, v) in constraint_map)
|
||||
|
||||
return (primal=primal, dual=duals, slack=slack)
|
||||
end
|
||||
|
||||
function solve(m::JuMP.Model, optimizer, warmstart=nothing)
|
||||
|
||||
JuMP.set_optimizer(m, optimizer)
|
||||
MOIU.attach_optimizer(m)
|
||||
|
||||
m = setwarmstart!(m, warmstart)
|
||||
|
||||
JuMP.optimize!(m)
|
||||
|
||||
status = JuMP.termination_status(m)
|
||||
|
||||
return status, getwarmstart(m)
|
||||
end
|
||||
|
||||
function solve(solverlog::String, m::JuMP.Model, optimizer, warmstart=nothing)
|
||||
|
||||
isdir(dirname(solverlog)) || mkpath(dirname(solverlog))
|
||||
|
||||
Base.flush(Base.stdout)
|
||||
Base.Libc.flush_cstdio()
|
||||
status, warmstart = open(solverlog, "a+") do logfile
|
||||
redirect_stdout(logfile) do
|
||||
status, warmstart = solve(m, optimizer, warmstart)
|
||||
Base.Libc.flush_cstdio()
|
||||
status, warmstart
|
||||
end
|
||||
end
|
||||
|
||||
return status, warmstart
|
||||
end
|
||||
182
src/sos_sdps.jl
182
src/sos_sdps.jl
@ -160,13 +160,39 @@ sos_problem_primal(
|
||||
kwargs...
|
||||
) = sos_problem_primal(elt, zero(elt), wedderburn; kwargs...)
|
||||
|
||||
function __fast_recursive_dot!(
|
||||
res::JuMP.AffExpr,
|
||||
Ps::AbstractArray{<:AbstractMatrix{<:JuMP.VariableRef}},
|
||||
Ms::AbstractArray{<:AbstractSparseMatrix};
|
||||
)
|
||||
@assert length(Ps) == length(Ms)
|
||||
|
||||
for (A, P) in zip(Ms, Ps)
|
||||
iszero(Ms) && continue
|
||||
rows = rowvals(A)
|
||||
vals = nonzeros(A)
|
||||
for cidx in axes(A, 2)
|
||||
for i in nzrange(A, cidx)
|
||||
ridx = rows[i]
|
||||
val = vals[i]
|
||||
JuMP.add_to_expression!(res, P[ridx, cidx], val)
|
||||
end
|
||||
end
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
import ProgressMeter
|
||||
__show_itrs(n, total) = () -> [(Symbol("constraint"), "$n/$total")]
|
||||
|
||||
function sos_problem_primal(
|
||||
elt::StarAlgebras.AlgebraElement,
|
||||
orderunit::StarAlgebras.AlgebraElement,
|
||||
wedderburn::WedderburnDecomposition;
|
||||
upper_bound=Inf,
|
||||
augmented=iszero(StarAlgebras.aug(elt)) && iszero(StarAlgebras.aug(orderunit)),
|
||||
check_orthogonality=true
|
||||
check_orthogonality=true,
|
||||
show_progress=false
|
||||
)
|
||||
|
||||
@assert parent(elt) === parent(orderunit)
|
||||
@ -194,15 +220,14 @@ function sos_problem_primal(
|
||||
P = map(direct_summands(wedderburn)) do ds
|
||||
dim = size(ds, 1)
|
||||
P = JuMP.@variable(model, [1:dim, 1:dim], Symmetric)
|
||||
@constraint(model, P in PSDCone())
|
||||
JuMP.@constraint(model, P in PSDCone())
|
||||
P
|
||||
end
|
||||
|
||||
begin # preallocating
|
||||
T = eltype(wedderburn)
|
||||
M = zeros.(T, size.(P))
|
||||
Ms = [spzeros.(T, size(p)...) for p in P]
|
||||
M_orb = zeros(T, size(parent(elt).mstructure)...)
|
||||
tmps = SymbolicWedderburn._tmps(wedderburn)
|
||||
end
|
||||
|
||||
X = convert(Vector{T}, StarAlgebras.coeffs(elt))
|
||||
@ -211,142 +236,39 @@ function sos_problem_primal(
|
||||
# defining constraints based on the multiplicative structure
|
||||
cnstrs = constraints(parent(elt), augmented=augmented, twisted=true)
|
||||
|
||||
@info "Adding $(length(invariant_vectors(wedderburn))) constraints"
|
||||
prog = ProgressMeter.Progress(
|
||||
length(invariant_vectors(wedderburn)),
|
||||
dt=1,
|
||||
desc="Adding constraints... ",
|
||||
enabled=show_progress,
|
||||
barlen=60,
|
||||
showspeed=true
|
||||
)
|
||||
|
||||
for (i, iv) in enumerate(invariant_vectors(wedderburn))
|
||||
ProgressMeter.next!(prog, showvalues=__show_itrs(i, prog.n))
|
||||
|
||||
for iv in invariant_vectors(wedderburn)
|
||||
x = dot(X, iv)
|
||||
u = dot(U, iv)
|
||||
|
||||
M_orb = invariant_constraint!(M_orb, basis(parent(elt)), cnstrs, iv)
|
||||
Ms = SymbolicWedderburn.diagonalize!(Ms, M_orb, wedderburn)
|
||||
SparseArrays.droptol!.(Ms, 10 * eps(T) * max(size(M_orb)...))
|
||||
|
||||
M = SymbolicWedderburn.diagonalize!(M, M_orb, wedderburn, tmps)
|
||||
SymbolicWedderburn.zerotol!.(M, atol=1e-12)
|
||||
|
||||
M_dot_P = sum(dot(M[π], P[π]) for π in eachindex(M) if !iszero(M[π]))
|
||||
# @info [nnz(m) / length(m) for m in Ms]
|
||||
|
||||
if feasibility_problem
|
||||
JuMP.@constraint(model, x == M_dot_P)
|
||||
JuMP.@constraint(
|
||||
model,
|
||||
x == __fast_recursive_dot!(JuMP.AffExpr(), P, Ms)
|
||||
)
|
||||
else
|
||||
JuMP.@constraint(model, x - λ * u == M_dot_P)
|
||||
JuMP.@constraint(
|
||||
model,
|
||||
x - λ * u == __fast_recursive_dot!(JuMP.AffExpr(), P, Ms)
|
||||
)
|
||||
end
|
||||
end
|
||||
ProgressMeter.finish!(prog)
|
||||
return model, P
|
||||
end
|
||||
|
||||
function reconstruct(Ps, wd::WedderburnDecomposition)
|
||||
N = size(first(direct_summands(wd)), 2)
|
||||
P = zeros(eltype(wd), N, N)
|
||||
return reconstruct!(P, Ps, wd)
|
||||
end
|
||||
|
||||
function group_of(wd::WedderburnDecomposition)
|
||||
# this is veeeery hacky... ;)
|
||||
return parent(first(keys(wd.hom.cache)))
|
||||
end
|
||||
|
||||
# TODO: move to SymbolicWedderburn
|
||||
SymbolicWedderburn.action(wd::WedderburnDecomposition) =
|
||||
SymbolicWedderburn.action(wd.hom)
|
||||
|
||||
function reconstruct!(
|
||||
res::AbstractMatrix,
|
||||
Ps,
|
||||
wedderburn::WedderburnDecomposition,
|
||||
)
|
||||
G = group_of(wedderburn)
|
||||
|
||||
act = SymbolicWedderburn.action(wedderburn)
|
||||
|
||||
@assert act isa SymbolicWedderburn.ByPermutations
|
||||
|
||||
for (π, ds) in pairs(direct_summands(wedderburn))
|
||||
Uπ = SymbolicWedderburn.image_basis(ds)
|
||||
|
||||
# LinearAlgebra.mul!(tmp, Uπ', P[π])
|
||||
# LinearAlgebra.mul!(tmp2, tmp, Uπ)
|
||||
tmp2 = Uπ' * Ps[π] * Uπ
|
||||
if eltype(res) <: AbstractFloat
|
||||
SymbolicWedderburn.zerotol!(tmp2, atol=1e-12)
|
||||
end
|
||||
tmp2 .*= SymbolicWedderburn.degree(ds)
|
||||
|
||||
@assert size(tmp2) == size(res)
|
||||
|
||||
for g in G
|
||||
p = SymbolicWedderburn.induce(wedderburn.hom, g)
|
||||
for c in axes(res, 2)
|
||||
for r in axes(res, 1)
|
||||
res[r, c] += tmp2[r^p, c^p]
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
res ./= Groups.order(Int, G)
|
||||
|
||||
return res
|
||||
end
|
||||
|
||||
##
|
||||
# Low-level solve
|
||||
|
||||
setwarmstart!(model::JuMP.Model, ::Nothing) = model
|
||||
|
||||
function setwarmstart!(model::JuMP.Model, warmstart)
|
||||
constraint_map = Dict(
|
||||
ct => JuMP.all_constraints(model, ct...) for
|
||||
ct in JuMP.list_of_constraint_types(model)
|
||||
)
|
||||
|
||||
JuMP.set_start_value.(JuMP.all_variables(model), warmstart.primal)
|
||||
|
||||
for (ct, idx) in pairs(constraint_map)
|
||||
JuMP.set_start_value.(idx, warmstart.slack[ct])
|
||||
JuMP.set_dual_start_value.(idx, warmstart.dual[ct])
|
||||
end
|
||||
return model
|
||||
end
|
||||
|
||||
function getwarmstart(model::JuMP.Model)
|
||||
constraint_map = Dict(
|
||||
ct => JuMP.all_constraints(model, ct...) for
|
||||
ct in JuMP.list_of_constraint_types(model)
|
||||
)
|
||||
|
||||
primal = value.(JuMP.all_variables(model))
|
||||
|
||||
slack = Dict(k => value.(v) for (k, v) in constraint_map)
|
||||
duals = Dict(k => JuMP.dual.(v) for (k, v) in constraint_map)
|
||||
|
||||
return (primal=primal, dual=duals, slack=slack)
|
||||
end
|
||||
|
||||
function solve(m::JuMP.Model, optimizer, warmstart=nothing)
|
||||
|
||||
JuMP.set_optimizer(m, optimizer)
|
||||
MOIU.attach_optimizer(m)
|
||||
|
||||
m = setwarmstart!(m, warmstart)
|
||||
|
||||
JuMP.optimize!(m)
|
||||
Base.Libc.flush_cstdio()
|
||||
|
||||
status = JuMP.termination_status(m)
|
||||
|
||||
return status, getwarmstart(m)
|
||||
end
|
||||
|
||||
function solve(solverlog::String, m::JuMP.Model, optimizer, warmstart=nothing)
|
||||
|
||||
isdir(dirname(solverlog)) || mkpath(dirname(solverlog))
|
||||
|
||||
Base.flush(Base.stdout)
|
||||
Base.Libc.flush_cstdio()
|
||||
status, warmstart = open(solverlog, "a+") do logfile
|
||||
redirect_stdout(logfile) do
|
||||
status, warmstart = solve(m, optimizer, warmstart)
|
||||
status, warmstart
|
||||
end
|
||||
end
|
||||
|
||||
return status, warmstart
|
||||
end
|
||||
|
||||
@ -1,20 +1,3 @@
|
||||
function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
|
||||
@time sos_problem =
|
||||
PropertyT.sos_problem_primal(elt, unit, upper_bound=upper_bound)
|
||||
|
||||
status, _ = PropertyT.solve(sos_problem, optimizer)
|
||||
P = JuMP.value.(sos_problem[:P])
|
||||
Q = real.(sqrt(P))
|
||||
certified, λ_cert = PropertyT.certify_solution(
|
||||
elt,
|
||||
unit,
|
||||
JuMP.objective_value(sos_problem),
|
||||
Q,
|
||||
halfradius=halfradius,
|
||||
)
|
||||
return status, certified, λ_cert
|
||||
end
|
||||
|
||||
@testset "1703.09680 Examples" begin
|
||||
|
||||
@testset "SL(2,Z)" begin
|
||||
@ -79,15 +62,15 @@ end
|
||||
@test λ > 1
|
||||
|
||||
m = PropertyT.sos_problem_dual(elt, unit)
|
||||
PropertyT.solve(m, scs_optimizer(
|
||||
eps=1e-10,
|
||||
PropertyT.solve(m, cosmo_optimizer(
|
||||
eps=1e-6,
|
||||
max_iters=5_000,
|
||||
accel=50,
|
||||
alpha=1.9,
|
||||
))
|
||||
|
||||
@test JuMP.termination_status(m) in (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
|
||||
@test JuMP.objective_value(m) ≈ 1.5 atol = 1e-3
|
||||
@test JuMP.objective_value(m) ≈ 1.5 atol = 1e-2
|
||||
end
|
||||
|
||||
@testset "SAut(F₂)" begin
|
||||
|
||||
@ -1,44 +1,3 @@
|
||||
function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimizer)
|
||||
@assert aug(elt) == aug(unit) == 0
|
||||
@time sos_problem, Ps =
|
||||
PropertyT.sos_problem_primal(elt, unit, wd, upper_bound=upper_bound)
|
||||
|
||||
@time status, _ = PropertyT.solve(sos_problem, optimizer)
|
||||
|
||||
Q = let Ps = Ps
|
||||
flPs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
|
||||
PropertyT.reconstruct(flPs, wd)
|
||||
end
|
||||
|
||||
λ = JuMP.value(sos_problem[:λ])
|
||||
|
||||
sos = let RG = parent(elt), Q = Q
|
||||
z = zeros(eltype(Q), length(basis(RG)))
|
||||
res = AlgebraElement(z, RG)
|
||||
cnstrs = PropertyT.constraints(basis(RG), RG.mstructure, augmented=true)
|
||||
PropertyT._cnstr_sos!(res, Q, cnstrs)
|
||||
end
|
||||
|
||||
residual = elt - λ * unit - sos
|
||||
λ_fl = PropertyT.sufficient_λ(residual, λ, halfradius=2)
|
||||
|
||||
λ_fl < 0 && return status, false, λ_fl
|
||||
|
||||
sos = let RG = parent(elt), Q = [PropertyT.IntervalArithmetic.@interval(q) for q in Q]
|
||||
z = zeros(eltype(Q), length(basis(RG)))
|
||||
res = AlgebraElement(z, RG)
|
||||
cnstrs = PropertyT.constraints(basis(RG), RG.mstructure, augmented=true)
|
||||
PropertyT._cnstr_sos!(res, Q, cnstrs)
|
||||
end
|
||||
|
||||
λ_int = PropertyT.IntervalArithmetic.@interval(λ)
|
||||
|
||||
residual_int = elt - λ_int * unit - sos
|
||||
λ_int = PropertyT.sufficient_λ(residual_int, λ_int, halfradius=2)
|
||||
|
||||
return status, λ_int > 0, PropertyT.IntervalArithmetic.inf(λ_int)
|
||||
end
|
||||
|
||||
@testset "1712.07167 Examples" begin
|
||||
|
||||
@testset "SAut(F₃)" begin
|
||||
|
||||
@ -1,59 +0,0 @@
|
||||
@testset "Correctness of HPC SOS computation" begin
|
||||
|
||||
function prepare(G_name, λ, S_size)
|
||||
pm = load("$G_name/delta.jld", "pm")
|
||||
P = load("$G_name/$λ/solution.jld", "P")
|
||||
@time Q = real(sqrt(P))
|
||||
|
||||
Δ_coeff = SparseVector(maximum(pm), collect(1:1+S_size), [S_size; ((-1.0) for i in 1:S_size)...])
|
||||
|
||||
Δ²_coeff = GroupRings.GRmul!(spzeros(length(Δ_coeff)), Δ_coeff, Δ_coeff, pm)
|
||||
|
||||
eoi = Δ²_coeff - λ*Δ_coeff
|
||||
|
||||
Q = PropertyT.augIdproj(Q)
|
||||
|
||||
return eoi, pm, Q
|
||||
end
|
||||
|
||||
#########################################################
|
||||
NAME = "SL(3,Z)"
|
||||
eoi, pm, Q = prepare(NAME, 0.1, 3*2*2)
|
||||
|
||||
@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
|
||||
@time sos_hpc = PropertyT.compute_SOS(pm, Q)
|
||||
|
||||
@test norm(sos_sqr - sos_hpc, 1) < 3e-12
|
||||
@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
|
||||
|
||||
#########################################################
|
||||
NAME = "SL(3,Z)_orbit"
|
||||
eoi, pm, Q = prepare(NAME, 0.27, 3*2*2)
|
||||
|
||||
@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
|
||||
@time sos_hpc = PropertyT.compute_SOS(pm, Q)
|
||||
|
||||
@test norm(sos_sqr - sos_hpc, 1) < 5e-12
|
||||
@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
|
||||
|
||||
#########################################################
|
||||
NAME = "SL(4,Z)_orbit"
|
||||
eoi, pm, Q = prepare(NAME, 1.3, 4*3*2)
|
||||
|
||||
@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
|
||||
@time sos_hpc = PropertyT.compute_SOS(pm, Q)
|
||||
|
||||
@test norm(sos_sqr - sos_hpc, 1) < 2e-10
|
||||
@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
|
||||
|
||||
#########################################################
|
||||
NAME = "SAut(F3)_orbit"
|
||||
eoi, pm, Q = prepare(NAME, 0.15, 4*3*2*2)
|
||||
|
||||
@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
|
||||
@time sos_hpc = PropertyT.compute_SOS(pm, Q)
|
||||
|
||||
@test norm(sos_sqr - sos_hpc, 1) < 6e-11
|
||||
@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
|
||||
|
||||
end
|
||||
41
test/check_positivity.jl
Normal file
41
test/check_positivity.jl
Normal file
@ -0,0 +1,41 @@
|
||||
function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
|
||||
@time sos_problem =
|
||||
PropertyT.sos_problem_primal(elt, unit, upper_bound=upper_bound)
|
||||
|
||||
status, _ = PropertyT.solve(sos_problem, optimizer)
|
||||
P = JuMP.value.(sos_problem[:P])
|
||||
Q = real.(sqrt(P))
|
||||
certified, λ_cert = PropertyT.certify_solution(
|
||||
elt,
|
||||
unit,
|
||||
JuMP.objective_value(sos_problem),
|
||||
Q,
|
||||
halfradius=halfradius,
|
||||
)
|
||||
return status, certified, λ_cert
|
||||
end
|
||||
|
||||
function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimizer)
|
||||
@assert aug(elt) == aug(unit) == 0
|
||||
@time sos_problem, Ps =
|
||||
PropertyT.sos_problem_primal(elt, unit, wd, upper_bound=upper_bound)
|
||||
|
||||
@time status, _ = PropertyT.solve(sos_problem, optimizer)
|
||||
|
||||
Q = let Ps = Ps
|
||||
Qs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
|
||||
PropertyT.reconstruct(Qs, wd)
|
||||
end
|
||||
|
||||
λ = JuMP.value(sos_problem[:λ])
|
||||
|
||||
certified, λ_cert = PropertyT.certify_solution(
|
||||
elt,
|
||||
unit,
|
||||
λ,
|
||||
Q,
|
||||
halfradius=halfradius
|
||||
)
|
||||
return status, certified, λ_cert
|
||||
end
|
||||
|
||||
@ -46,6 +46,28 @@
|
||||
|
||||
|
||||
@testset "Symplectic group" begin
|
||||
@testset "Sp2(ℤ)" begin
|
||||
genus = 2
|
||||
halfradius = 1
|
||||
|
||||
SpN = MatrixGroups.SymplecticGroup{2genus}(Int8)
|
||||
|
||||
RSpN, S_sp, sizes_sp = PropertyT.group_algebra(SpN, halfradius=halfradius, twisted=true)
|
||||
|
||||
Δ, Δs = let RG = RSpN, S = S_sp, ψ = identity
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
Δs = PropertyT.laplacians(
|
||||
RG,
|
||||
S,
|
||||
x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])),
|
||||
)
|
||||
Δ, Δs
|
||||
end
|
||||
|
||||
sq = sum(Δᵢ^2 for Δᵢ in values(Δs))
|
||||
@test PropertyT.Adj(Δs, :C₂) + sq == Δ^2
|
||||
end
|
||||
|
||||
genus = 3
|
||||
halfradius = 1
|
||||
|
||||
@ -63,7 +85,7 @@
|
||||
Δ, Δs
|
||||
end
|
||||
|
||||
@testset "Adj correctness: genus=$genus" begin
|
||||
@testset "Adj numerics for genus=$genus" begin
|
||||
|
||||
all_subtypes = (
|
||||
:A₁, :C₁, Symbol("A₁×A₁"), Symbol("C₁×C₁"), Symbol("A₁×C₁"), :A₂, :C₂
|
||||
|
||||
80
test/quick_tests.jl
Normal file
80
test/quick_tests.jl
Normal file
@ -0,0 +1,80 @@
|
||||
@testset "Quick tests" begin
|
||||
|
||||
@testset "SL(2,F₇)" begin
|
||||
N = 2
|
||||
p = 7
|
||||
halfradius = 3
|
||||
G = MatrixGroups.SpecialLinearGroup{N}(SymbolicWedderburn.Characters.FiniteFields.GF{p})
|
||||
RG, S, sizes = PropertyT.group_algebra(G, halfradius=3, twisted=true)
|
||||
|
||||
Δ = let RG = RG, S = S
|
||||
RG(length(S)) - sum(RG(s) for s in S)
|
||||
end
|
||||
|
||||
elt = Δ^2
|
||||
unit = Δ
|
||||
ub = 0.58578# Inf# 1.5
|
||||
|
||||
@testset "standard formulation" begin
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
unit,
|
||||
upper_bound=ub,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(
|
||||
eps=1e-7,
|
||||
max_iters=5_000,
|
||||
accel=50,
|
||||
alpha=1.95,
|
||||
)
|
||||
)
|
||||
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test certified
|
||||
@test λ_cert > 5857 // 10000
|
||||
|
||||
m = PropertyT.sos_problem_dual(elt, unit)
|
||||
PropertyT.solve(m, cosmo_optimizer(
|
||||
eps=1e-7,
|
||||
max_iters=10_000,
|
||||
accel=50,
|
||||
alpha=1.95,
|
||||
))
|
||||
|
||||
@test JuMP.termination_status(m) in (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
|
||||
@test JuMP.objective_value(m) ≈ λ_cert atol = 1e-2
|
||||
end
|
||||
|
||||
@testset "Wedderburn decomposition" begin
|
||||
P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
|
||||
Σ = PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
|
||||
act = PropertyT.action_by_conjugation(G, Σ)
|
||||
|
||||
wd = WedderburnDecomposition(
|
||||
Float64,
|
||||
Σ,
|
||||
act,
|
||||
basis(RG),
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[halfradius]]),
|
||||
)
|
||||
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
unit,
|
||||
wd,
|
||||
upper_bound=ub,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(
|
||||
eps=1e-7,
|
||||
max_iters=10_000,
|
||||
accel=50,
|
||||
alpha=1.9,
|
||||
),
|
||||
)
|
||||
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test certified
|
||||
@test λ_cert > 5857 // 10000
|
||||
end
|
||||
end
|
||||
end
|
||||
@ -1,8 +1,6 @@
|
||||
using Test
|
||||
using LinearAlgebra
|
||||
using SparseArrays
|
||||
BLAS.set_num_threads(1)
|
||||
ENV["OMP_NUM_THREADS"] = 4
|
||||
|
||||
using Groups
|
||||
using Groups.GroupsCore
|
||||
@ -14,15 +12,18 @@ using SymbolicWedderburn.StarAlgebras
|
||||
using SymbolicWedderburn.PermutationGroups
|
||||
|
||||
include("optimizers.jl")
|
||||
include("check_positivity.jl")
|
||||
include("quick_tests.jl")
|
||||
|
||||
@testset "PropertyT" begin
|
||||
if haskey(ENV, "FULL_TEST") || haskey(ENV, "CI")
|
||||
@testset "PropertyT" begin
|
||||
include("constratint_matrices.jl")
|
||||
include("actions.jl")
|
||||
|
||||
include("constratint_matrices.jl")
|
||||
include("actions.jl")
|
||||
include("1703.09680.jl")
|
||||
include("1712.07167.jl")
|
||||
include("1812.03456.jl")
|
||||
|
||||
include("1703.09680.jl")
|
||||
include("1712.07167.jl")
|
||||
include("1812.03456.jl")
|
||||
|
||||
include("graded_adj.jl")
|
||||
include("graded_adj.jl")
|
||||
end
|
||||
end
|
||||
|
||||
Loading…
Reference in New Issue
Block a user