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enh/global
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.gitignore
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.gitignore
vendored
@ -11,5 +11,3 @@ SL*_*
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*.gws
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.*
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tests*
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*.py
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*.pyc
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65
AutFn.jl
Normal file
65
AutFn.jl
Normal file
@ -0,0 +1,65 @@
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using ArgParse
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###############################################################################
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#
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# Parsing command line
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#
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###############################################################################
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function parse_commandline()
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s = ArgParseSettings()
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@add_arg_table s begin
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"--tol"
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help = "set numerical tolerance for the SDP solver"
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arg_type = Float64
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default = 1e-6
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"--iterations"
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help = "set maximal number of iterations for the SDP solver"
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arg_type = Int
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default = 50000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap"
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arg_type = Float64
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default = Inf
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"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
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arg_type = Int
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required = false
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"--radius"
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help = "Radius of ball B_r(e,S) to find solution over"
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arg_type = Int
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default = 2
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"--warmstart"
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help = "Use warmstart.jld as the initial guess for SCS"
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action = :store_true
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"--nosymmetry"
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help = "Don't use symmetries of the Laplacian"
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action = :store_true
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"N"
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help = "Compute for the automorphisms group of the free group on N generators"
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arg_type = Int
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required = true
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end
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return parse_args(s)
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end
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const PARSEDARGS = parse_commandline()
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#=
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Note that the element
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α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
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which surely belongs to ball of radius 4 in Aut(Fₙ) becomes trivial under the representation
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Aut(Fₙ) → GLₙ(ℤ)⋉ℤⁿ → GL_(n+1)(ℂ).
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Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ(ℂ) (for m ≤ 2n-2) factors through GLₙ(ℤ)⋉ℤⁿ, so will have the same problem.
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We need a different approach: Here we actually compute in (S)Aut(𝔽ₙ)
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=#
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include("CPUselect.jl")
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set_parallel_mthread(PARSEDARGS, workers=true)
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include("main.jl")
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G = PropertyTGroups.SpecialAutomorphismGroup(PARSEDARGS)
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main(G)
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62
FPgroup.jl
Normal file
62
FPgroup.jl
Normal file
@ -0,0 +1,62 @@
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using ArgParse
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function parse_commandline()
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args = ArgParseSettings()
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@add_arg_table args begin
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"--tol"
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help = "set numerical tolerance for the SDP solver"
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arg_type = Float64
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default = 1e-6
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"--iterations"
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help = "set maximal number of iterations for the SDP solver"
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arg_type = Int
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default = 50000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap"
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arg_type = Float64
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default = Inf
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"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
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arg_type = Int
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required = false
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"--radius"
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help = "Radius of ball B_r(e,S) to find solution over"
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arg_type = Int
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default = 2
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"--warmstart"
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help = "Use warmstart.jl as the initial guess for SCS"
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action = :store_true
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"--MCG"
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help = "Compute for mapping class group of surface of genus N"
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arg_type = Int
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required = false
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"--Higman"
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help = "Compute for Higman Group"
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action = :store_true
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"--Caprace"
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help = "Compute for Higman Group"
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action = :store_true
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end
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return parse_args(args)
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end
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const PARSEDARGS = parse_commandline()
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include("CPUselect.jl")
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set_parallel_mthread(PARSEDARGS, workers=false)
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include("main.jl")
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include("FPGroups_GAP.jl")
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if PARSEDARGS["Caprace"]
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G = PropertyTGroups.CapraceGroup(PARSEDARGS)
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elseif PARSEDARGS["Higman"]
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G = PropertyTGroups.HigmanGroup(PARSEDARGS)
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elseif PARSEDARGS["MCG"] != nothing
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G = PropertyTGroups.MappingClassGroup(PARSEDARGS)
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else
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throw("You need to specify one of the --Higman, --Caprace, --MCG N")
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end
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main(G)
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@ -1,10 +1,4 @@
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# DEPRECATED!
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This repository has not been updated for a while!
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If You are interested in replicating results for [1712.07167](https://arxiv.org/abs/1712.07167) please check [these instruction](https://kalmar.faculty.wmi.amu.edu.pl/post/1712.07176/)
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Also [this notebook](https://nbviewer.jupyter.org/gist/kalmarek/03510181bc1e7c98615e86e1ec580b2a) could be of some help. If everything else fails the [zenodo dataset](https://zenodo.org/record/1133440) should contain the last-resort instructions.
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This repository contains some legacy code for computations in [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680).
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This repository contains code for computations in [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680).
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# Installing
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To run the code You need `julia-v0.5` (should work on `v0.6`, but with warnings).
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62
SLn.jl
Normal file
62
SLn.jl
Normal file
@ -0,0 +1,62 @@
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using ArgParse
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###############################################################################
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#
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# Parsing command line
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#
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###############################################################################
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function parse_commandline()
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settings = ArgParseSettings()
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@add_arg_table settings begin
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"--tol"
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help = "set numerical tolerance for the SDP solver"
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arg_type = Float64
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default = 1e-6
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"--iterations"
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help = "set maximal number of iterations for the SDP solver"
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arg_type = Int
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default = 50000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap"
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arg_type = Float64
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default = Inf
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"--cpus"
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help = "Set number of cpus used by solver"
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arg_type = Int
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required = false
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"--radius"
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help = "Radius of ball B_r(e,S) to find solution over"
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arg_type = Int
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default = 2
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"--warmstart"
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help = "Use warmstart.jld as the initial guess for SCS"
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action = :store_true
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"--nosymmetry"
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help = "Don't use symmetries of the Laplacian"
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action = :store_true
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"-p"
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help = "Matrices over field of p-elements (p=0 => over ZZ)"
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arg_type = Int
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default = 0
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"-X"
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help = "Consider EL(N, ZZ⟨X⟩)"
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action = :store_true
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"N"
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help = "Compute with the group generated by elementary matrices of size n×n"
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arg_type = Int
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default = 2
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end
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return parse_args(settings)
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end
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const PARSEDARGS = parse_commandline()
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include("CPUselect.jl")
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set_parallel_mthread(PARSEDARGS, workers=true)
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include("main.jl")
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G = PropertyTGroups.SpecialLinearGroup(PARSEDARGS)
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main(G)
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@ -4,7 +4,6 @@ using PropertyT
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using AbstractAlgebra
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using Nemo
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using Groups
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using GroupRings
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export PropertyTGroup, SymmetrizedGroup, GAPGroup,
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SpecialLinearGroup,
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@ -51,6 +50,5 @@ end
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include("mappingclassgroup.jl")
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include("higman.jl")
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include("caprace.jl")
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include("actions.jl")
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end # of module PropertyTGroups
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@ -1,92 +0,0 @@
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function (p::perm)(A::GroupRingElem)
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RG = parent(A)
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result = zero(RG, eltype(A.coeffs))
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for (idx, c) in enumerate(A.coeffs)
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if c!= zero(eltype(A.coeffs))
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result[p(RG.basis[idx])] = c
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end
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end
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return result
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end
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###############################################################################
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#
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# Action of WreathProductElems on Nemo.MatElem
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#
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###############################################################################
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function matrix_emb(n::DirectProductGroupElem, p::perm)
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Id = parent(n.elts[1])()
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elt = diagm([(-1)^(el == Id ? 0 : 1) for el in n.elts])
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return elt[:, p.d]
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end
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function (g::WreathProductElem)(A::MatElem)
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g_inv = inv(g)
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G = matrix_emb(g.n, g_inv.p)
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G_inv = matrix_emb(g_inv.n, g.p)
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M = parent(A)
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return M(G)*A*M(G_inv)
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end
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import Base.*
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doc"""
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*(x::AbstractAlgebra.MatElem, P::Generic.perm)
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> Apply the pemutation $P$ to the rows of the matrix $x$ and return the result.
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"""
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function *(x::AbstractAlgebra.MatElem, P::Generic.perm)
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z = similar(x)
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m = rows(x)
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n = cols(x)
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for i = 1:m
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for j = 1:n
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z[i, j] = x[i,P[j]]
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end
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end
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return z
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end
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function (p::perm)(A::MatElem)
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length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
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return p*A*inv(p)
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end
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###############################################################################
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#
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# Action of WreathProductElems on AutGroupElem
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#
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###############################################################################
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function AutFG_emb(A::AutGroup, g::WreathProductElem)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
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elt = A()
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Id = parent(g.n.elts[1])()
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flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
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Groups.r_multiply!(elt, flips, reduced=false)
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Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
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return elt
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end
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function AutFG_emb(A::AutGroup, p::perm)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(p)) into $A")
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return A(Groups.perm_autsymbol(p))
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end
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function (g::WreathProductElem)(a::Groups.Automorphism)
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A = parent(a)
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g = AutFG_emb(A,g)
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res = A()
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Groups.r_multiply!(res, g.symbols, reduced=false)
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Groups.r_multiply!(res, a.symbols, reduced=false)
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Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
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return res
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end
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function (p::perm)(a::Groups.Automorphism)
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g = AutFG_emb(parent(a),p)
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return g*a*inv(g)
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end
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@ -1,14 +1,22 @@
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struct SpecialAutomorphismGroup{N} <: SymmetrizedGroup
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struct SpecialAutomorphismGroup <: SymmetrizedGroup
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args::Dict{String,Any}
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group::AutGroup
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N::Int
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function SpecialAutomorphismGroup(args::Dict)
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N = args["SAut"]
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return new(args, AutGroup(FreeGroup(N), special=true), N)
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end
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end
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function SpecialAutomorphismGroup(args::Dict)
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N = args["SAut"]
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return SpecialAutomorphismGroup{N}(AutGroup(FreeGroup(N), special=true))
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function name(G::SpecialAutomorphismGroup)
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if G.args["nosymmetry"]
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return "SAutF$(G.N)"
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else
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return "oSAutF$(G.N)"
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end
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end
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name(G::SpecialAutomorphismGroup{N}) where N = "SAutF$(N)"
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group(G::SpecialAutomorphismGroup) = G.group
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function generatingset(G::SpecialAutomorphismGroup)
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@ -16,6 +24,44 @@ function generatingset(G::SpecialAutomorphismGroup)
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return unique([S; inv.(S)])
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end
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function autS(G::SpecialAutomorphismGroup{N}) where N
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return WreathProduct(PermutationGroup(2), PermutationGroup(N))
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function autS(G::SpecialAutomorphismGroup)
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return WreathProduct(PermutationGroup(2), PermutationGroup(G.N))
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end
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###############################################################################
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#
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# Action of WreathProductElems on AutGroupElem
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#
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###############################################################################
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function AutFG_emb(A::AutGroup, g::WreathProductElem)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
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elt = A()
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Id = parent(g.n.elts[1])()
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flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
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Groups.r_multiply!(elt, flips, reduced=false)
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Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
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return elt
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end
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function AutFG_emb(A::AutGroup, p::perm)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
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return A(Groups.perm_autsymbol(p))
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end
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function (g::WreathProductElem)(a::Groups.Automorphism)
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A = parent(a)
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g = AutFG_emb(A,g)
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res = A()
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Groups.r_multiply!(res, g.symbols, reduced=false)
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Groups.r_multiply!(res, a.symbols, reduced=false)
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Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
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return res
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end
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function (p::perm)(a::Groups.Automorphism)
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g = AutFG_emb(parent(a),p)
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return g*a*inv(g)
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end
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||||
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@ -1,4 +1,6 @@
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struct CapraceGroup <: GAPGroup end
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struct CapraceGroup <: GAPGroup
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args::Dict{String,Any}
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end
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name(G::CapraceGroup) = "CapraceGroup"
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||||
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||||
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||||
@ -1,4 +1,6 @@
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struct HigmanGroup <: GAPGroup end
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struct HigmanGroup <: GAPGroup
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args::Dict{String,Any}
|
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end
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||||
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name(G::HigmanGroup) = "HigmanGroup"
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||||
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||||
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@ -1,14 +1,17 @@
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struct MappingClassGroup{N} <: GAPGroup end
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||||
struct MappingClassGroup <: GAPGroup
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args::Dict{String,Any}
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N::Int
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||||
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MappingClassGroup(args::Dict) = MappingClassGroup{args["MCG"]}()
|
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MappingClassGroup(args) = MappingClassGroup(args, args["MCG"])
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end
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||||
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name(G::MappingClassGroup{N}) where N = "MCG(N)"
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name(G::MappingClassGroup) = "MCG($(G.N))"
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||||
function group(G::MappingClassGroup{N}) where N
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||||
function group(G::MappingClassGroup)
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||||
|
||||
if N < 2
|
||||
if G.N < 2
|
||||
throw("Genus must be at least 2!")
|
||||
elseif N == 2
|
||||
elseif G.N == 2
|
||||
MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
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||||
S = gens(MCGroup)
|
||||
|
||||
@ -28,7 +31,7 @@ function group(G::MappingClassGroup{N}) where N
|
||||
return MCGroup
|
||||
|
||||
else
|
||||
MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
|
||||
MCGroup = Groups.FPGroup(["a$i" for i in 0:2G.N])
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||||
S = gens(MCGroup)
|
||||
|
||||
a0 = S[1]
|
||||
@ -73,7 +76,7 @@ function group(G::MappingClassGroup{N}) where N
|
||||
(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
|
||||
end
|
||||
|
||||
# push!(relations, X*n(N)*inv(n(N)*X))
|
||||
# push!(relations, X*n(G.N)*inv(n(G.N)*X))
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||||
|
||||
relations = [relations; [inv(rel) for rel in relations]]
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||||
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
|
||||
|
||||
@ -1,44 +1,60 @@
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||||
struct SpecialLinearGroup{N} <: SymmetrizedGroup
|
||||
struct SpecialLinearGroup <: SymmetrizedGroup
|
||||
args::Dict{String,Any}
|
||||
group::AbstractAlgebra.Group
|
||||
p::Int
|
||||
X::Bool
|
||||
N::Int
|
||||
|
||||
function SpecialLinearGroup(args::Dict)
|
||||
n = args["SL"]
|
||||
p = args["p"]
|
||||
X = args["X"]
|
||||
|
||||
if p == 0
|
||||
G = MatrixSpace(Nemo.ZZ, n, n)
|
||||
else
|
||||
R = Nemo.NmodRing(UInt(p))
|
||||
G = MatrixSpace(R, n, n)
|
||||
end
|
||||
return new(args, G, n)
|
||||
end
|
||||
end
|
||||
|
||||
function SpecialLinearGroup(args::Dict)
|
||||
N = args["SL"]
|
||||
p = args["p"]
|
||||
X = args["X"]
|
||||
function name(G::SpecialLinearGroup)
|
||||
p = G.args["p"]
|
||||
X = G.args["X"]
|
||||
|
||||
if p == 0
|
||||
G = MatrixSpace(Nemo.ZZ, N, N)
|
||||
R = (X ? "Z[x]" : "Z")
|
||||
else
|
||||
R = Nemo.NmodRing(UInt(p))
|
||||
G = MatrixSpace(R, N, N)
|
||||
R = "F$p"
|
||||
end
|
||||
return SpecialLinearGroup{N}(G, p, X)
|
||||
end
|
||||
|
||||
function name(G::SpecialLinearGroup{N}) where N
|
||||
if G.p == 0
|
||||
R = (G.X ? "Z[x]" : "Z")
|
||||
if G.args["nosymmetry"]
|
||||
return "SL($(G.N),$R)"
|
||||
else
|
||||
R = "F$(G.p)"
|
||||
return "oSL($(G.N),$R)"
|
||||
end
|
||||
return SL($(G.N),$R)
|
||||
end
|
||||
|
||||
group(G::SpecialLinearGroup) = G.group
|
||||
|
||||
function generatingset(G::SpecialLinearGroup{N}) where N
|
||||
G.p > 0 && G.X && throw("SL(n, F_p[x]) not implemented")
|
||||
SL = group(G)
|
||||
return generatingset(SL, G.X)
|
||||
function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
|
||||
@assert i≠j
|
||||
m = one(M)
|
||||
m[i,j] = val
|
||||
return m
|
||||
end
|
||||
|
||||
# r is the injectivity radius of
|
||||
# SL(n, Z[X]) -> SL(n, Z) induced by X -> 100
|
||||
function generatingset(G::SpecialLinearGroup)
|
||||
p = G.args["p"]
|
||||
X = G.args["X"]
|
||||
p > 0 && X && throw("SL(n, F_p[x]) not implemented")
|
||||
SL = group(G)
|
||||
r = G.args["radius"]
|
||||
return generatingset(SL, r, X)
|
||||
end
|
||||
|
||||
|
||||
function generatingset(SL::MatSpace, radius::Integer, X::Bool=false)
|
||||
|
||||
function generatingset(SL::MatSpace, X::Bool=false, r=5)
|
||||
n = SL.cols
|
||||
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||
|
||||
@ -50,13 +66,49 @@ function generatingset(SL::MatSpace, X::Bool=false, r=5)
|
||||
return unique([S; inv.(S)])
|
||||
end
|
||||
|
||||
function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
|
||||
@assert i≠j
|
||||
m = one(M)
|
||||
m[i,j] = val
|
||||
return m
|
||||
function autS(G::SpecialLinearGroup)
|
||||
return WreathProduct(PermutationGroup(2), PermutationGroup(G.N))
|
||||
end
|
||||
|
||||
function autS(G::SpecialLinearGroup{N}) where N
|
||||
return WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
||||
###############################################################################
|
||||
#
|
||||
# Action of WreathProductElems on Nemo.MatElem
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function matrix_emb(n::DirectProductGroupElem, p::perm)
|
||||
Id = parent(n.elts[1])()
|
||||
elt = diagm([(-1)^(el == Id ? 0 : 1) for el in n.elts])
|
||||
return elt[:, p.d]
|
||||
end
|
||||
|
||||
function (g::WreathProductElem)(A::MatElem)
|
||||
g_inv = inv(g)
|
||||
G = matrix_emb(g.n, g_inv.p)
|
||||
G_inv = matrix_emb(g_inv.n, g.p)
|
||||
M = parent(A)
|
||||
return M(G)*A*M(G_inv)
|
||||
end
|
||||
|
||||
import Base.*
|
||||
|
||||
doc"""
|
||||
*(x::AbstractAlgebra.MatElem, P::Generic.perm)
|
||||
> Apply the pemutation $P$ to the rows of the matrix $x$ and return the result.
|
||||
"""
|
||||
function *(x::AbstractAlgebra.MatElem, P::Generic.perm)
|
||||
z = similar(x)
|
||||
m = rows(x)
|
||||
n = cols(x)
|
||||
for i = 1:m
|
||||
for j = 1:n
|
||||
z[i, j] = x[i,P[j]]
|
||||
end
|
||||
end
|
||||
return z
|
||||
end
|
||||
|
||||
function (p::perm)(A::MatElem)
|
||||
length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
|
||||
return p*A*inv(p)
|
||||
end
|
||||
|
||||
94
main.jl
94
main.jl
@ -1,61 +1,87 @@
|
||||
using PropertyT
|
||||
|
||||
using SCS.SCSSolver
|
||||
# using Mosek
|
||||
# using CSDP
|
||||
# using SDPA
|
||||
|
||||
scs_solver(tol, iterations) = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=1)
|
||||
|
||||
# solver = Mosek.MosekSolver(
|
||||
# MSK_DPAR_INTPNT_CO_TOL_REL_GAP=tol,
|
||||
# MSK_IPAR_INTPNT_MAX_ITERATIONS=iterations,
|
||||
# QUIET=false)
|
||||
|
||||
# solver = CSDP.CSDPSolver(axtol=tol, atytol=tol, objtol=tol, minstepp=tol*10.0^-1, minstepd=tol*10.0^-1)
|
||||
|
||||
# solver = SDPA.SDPASolver(epsilonStar=tol, epsilonDash=tol)
|
||||
|
||||
include("FPGroups_GAP.jl")
|
||||
|
||||
include("groups/Allgroups.jl")
|
||||
using PropertyTGroups
|
||||
|
||||
import PropertyT.Settings
|
||||
|
||||
function summarize(sett::PropertyT.Settings)
|
||||
function summarize(groupdir, iterations, tol, upper_bound, radius, G, S)
|
||||
info("Group: $groupdir")
|
||||
info("Iterations: $iterations")
|
||||
info("Precision: $tol")
|
||||
info("Upper bound: $upper_bound")
|
||||
info("Radius: $radius")
|
||||
info("Threads: $(Threads.nthreads())")
|
||||
info("Workers: $(workers())")
|
||||
info("GroupDir: $(PropertyT.prepath(sett))")
|
||||
info(string(sett.G))
|
||||
info("with generating set of size $(length(sett.S))")
|
||||
|
||||
info("Radius: $(sett.radius)")
|
||||
info("Precision: $(sett.tol)")
|
||||
info("Upper bound: $(sett.upper_bound)")
|
||||
info("Solver: $(sett.solver)")
|
||||
info(string(G))
|
||||
info("with generating set of size $(length(S))")
|
||||
end
|
||||
|
||||
function Settings(Gr::PropertyTGroup, args, solver)
|
||||
r = get(args, "radius", 2)
|
||||
gr_name = PropertyTGroups.name(Gr)*"_r$r"
|
||||
function params(Gr::PropertyTGroup)
|
||||
radius = Gr.args["radius"]
|
||||
tol = Gr.args["tol"]
|
||||
iterations = Gr.args["iterations"]
|
||||
upper_bound = Gr.args["upper-bound"]
|
||||
warm = Gr.args["warmstart"]
|
||||
return radius, tol, iterations, upper_bound, warm
|
||||
end
|
||||
|
||||
function Settings(Gr::PropertyTGroup)
|
||||
r = Gr.args["radius"]
|
||||
ub = Gr.args["upper-bound"]
|
||||
groupdir = "$(PropertyTGroups.name(Gr))_r$r"
|
||||
|
||||
radius, tol, iterations, upper_bound, warm = params(Gr)
|
||||
|
||||
G = PropertyTGroups.group(Gr)
|
||||
S = PropertyTGroups.generatingset(Gr)
|
||||
|
||||
sol = solver
|
||||
ub = get(args,"upper-bound", Inf)
|
||||
tol = get(args,"tol", 1e-10)
|
||||
ws = get(args, "warmstart", false)
|
||||
summarize(groupdir, iterations, tol, upper_bound, radius, G, S)
|
||||
|
||||
if get(args, "nosymmetry", false)
|
||||
return PropertyT.Settings(gr_name, G, S, r, sol, ub, tol, ws)
|
||||
solver = scs_solver(tol, iterations)
|
||||
|
||||
return PropertyT.Settings(groupdir, G, S, radius,
|
||||
solver, upper_bound, tol, warm)
|
||||
end
|
||||
|
||||
function main(Gr::SymmetrizedGroup)
|
||||
sett = Settings(Gr)
|
||||
|
||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
||||
|
||||
if Gr.args["nosymmetry"]
|
||||
return PropertyT.check_property_T(PropertyT.Naive, sett)
|
||||
else
|
||||
autS = PropertyTGroups.autS(Gr)
|
||||
return PropertyT.Settings(gr_name, G, S, r, sol, ub, tol, ws, autS)
|
||||
info("Symmetrising with $(autS)")
|
||||
sett.autS = autS
|
||||
return PropertyT.check_property_T(PropertyT.Symmetrize, sett)
|
||||
end
|
||||
end
|
||||
|
||||
function main(::PropertyTGroup, sett::PropertyT.Settings)
|
||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
||||
|
||||
summarize(sett)
|
||||
|
||||
return PropertyT.check_property_T(sett)
|
||||
end
|
||||
|
||||
function main(::GAPGroup, sett::PropertyT.Settings)
|
||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
||||
|
||||
summarize(sett)
|
||||
function main(Gr::GAPGroup)
|
||||
sett = Settings(Gr)
|
||||
|
||||
S = [s for s in sett.S if s.symbols[1].pow == 1]
|
||||
relations = [k*inv(v) for (k,v) in sett.G.rels]
|
||||
|
||||
prepare_pm_delta(PropertyT.prepath(sett), GAP_groupcode(S, relations), sett.radius)
|
||||
|
||||
return PropertyT.check_property_T(sett)
|
||||
return PropertyT.check_property_T(PropertyT.Naive, sett)
|
||||
end
|
||||
|
||||
@ -1,197 +0,0 @@
|
||||
using AbstractAlgebra
|
||||
using Groups
|
||||
using GroupRings
|
||||
using PropertyT
|
||||
|
||||
using SCS
|
||||
solver(tol, iterations) =
|
||||
SCSSolver(linearsolver=SCS.Direct,
|
||||
eps=tol, max_iters=iterations,
|
||||
alpha=1.95, acceleration_lookback=1)
|
||||
|
||||
include("../main.jl")
|
||||
|
||||
using PropertyTGroups
|
||||
|
||||
args = Dict("SAut" => 5, "upper-bound" => 50.0, "radius" => 2, "nosymmetry"=>false, "tol"=>1e-12, "iterations" =>200000, "warmstart" => true)
|
||||
|
||||
Gr = PropertyTGroups.PropertyTGroup(args)
|
||||
sett = PropertyT.Settings(Gr, args,
|
||||
solver(args["tol"], args["iterations"]))
|
||||
|
||||
@show sett
|
||||
|
||||
fullpath = PropertyT.fullpath(sett)
|
||||
isdir(fullpath) || mkpath(fullpath)
|
||||
# setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
||||
|
||||
function small_generating_set(RG::GroupRing{AutGroup{N}}, n) where N
|
||||
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||
|
||||
rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing]
|
||||
lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing]
|
||||
gen_set = RG.group.([rmuls; lmuls])
|
||||
|
||||
return [gen_set; inv.(gen_set)]
|
||||
end
|
||||
|
||||
function computeX(RG::GroupRing{AutGroup{N}}) where N
|
||||
Tn = small_generating_set(RG, N-1)
|
||||
|
||||
ℤ = Int64
|
||||
Δn = length(Tn)*one(RG, ℤ) - RG(Tn, ℤ);
|
||||
|
||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
||||
|
||||
@time X = sum(σ(Δn)*sum(τ(Δn) for τ ∈ Alt_N if τ ≠ σ) for σ in Alt_N);
|
||||
return X
|
||||
end
|
||||
|
||||
function Sq(RG::GroupRing{AutGroup{N}}) where N
|
||||
T2 = small_generating_set(RG, 2)
|
||||
ℤ = Int64
|
||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
||||
|
||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
||||
elt = sum(σ(Δ₂)^2 for σ in Alt_N)
|
||||
return elt
|
||||
end
|
||||
|
||||
function Adj(RG::GroupRing{AutGroup{N}}) where N
|
||||
T2 = small_generating_set(RG, 2)
|
||||
|
||||
ℤ = Int64
|
||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
||||
|
||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
||||
|
||||
adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
|
||||
adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 1]
|
||||
|
||||
@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
|
||||
# return RG(elt.coeffs÷factorial(N-2)^2)
|
||||
return elt
|
||||
end
|
||||
|
||||
function Op(RG::GroupRing{AutGroup{N}}) where N
|
||||
T2 = small_generating_set(RG, 2)
|
||||
|
||||
ℤ = Int64
|
||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
||||
|
||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
||||
|
||||
adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
|
||||
adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 0]
|
||||
|
||||
@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
|
||||
# return RG(elt.coeffs÷factorial(N-2)^2)
|
||||
return elt
|
||||
end
|
||||
|
||||
const ELT_FILE = joinpath(dirname(PropertyT.filename(sett, :Δ)), "SqAdjOp_coeffs.jld")
|
||||
const WARMSTART_FILE = PropertyT.filename(sett, :warmstart)
|
||||
|
||||
if isfile(PropertyT.filename(sett,:Δ)) && isfile(ELT_FILE) &&
|
||||
isfile(PropertyT.filename(sett, :OrbitData))
|
||||
# cached
|
||||
Δ = PropertyT.loadGRElem(PropertyT.filename(sett,:Δ), sett.G)
|
||||
RG = parent(Δ)
|
||||
orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
|
||||
sq_c, adj_c, op_c = load(ELT_FILE, "Sq", "Adj", "Op")
|
||||
# elt = ELT_FILE, sett.G)
|
||||
sq = GroupRingElem(sq_c, RG)
|
||||
adj = GroupRingElem(adj_c, RG)
|
||||
op = GroupRingElem(op_c, RG);
|
||||
else
|
||||
info("Compute Laplacian")
|
||||
Δ = PropertyT.Laplacian(sett.S, sett.radius)
|
||||
RG = parent(Δ)
|
||||
|
||||
info("Compute Sq, Adj, Op")
|
||||
@time sq, adj, op = Sq(RG), Adj(RG), Op(RG)
|
||||
|
||||
PropertyT.saveGRElem(PropertyT.filename(sett, :Δ), Δ)
|
||||
save(ELT_FILE, "Sq", sq.coeffs, "Adj", adj.coeffs, "Op", op.coeffs)
|
||||
|
||||
info("Compute OrbitData")
|
||||
if !isfile(PropertyT.filename(sett, :OrbitData))
|
||||
orbit_data = PropertyT.OrbitData(parent(Y), sett.autS)
|
||||
save(PropertyT.filename(sett, :OrbitData), "OrbitData", orbit_data)
|
||||
else
|
||||
orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
|
||||
end
|
||||
end;
|
||||
|
||||
orbit_data = PropertyT.decimate(orbit_data);
|
||||
|
||||
elt = adj+2op;
|
||||
|
||||
const SOLUTION_FILE = PropertyT.filename(sett, :solution)
|
||||
|
||||
if !isfile(SOLUTION_FILE)
|
||||
|
||||
SDP_problem, varλ, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=sett.upper_bound)
|
||||
|
||||
begin
|
||||
using SCS
|
||||
scs_solver = SCS.SCSSolver(linearsolver=SCS.Direct,
|
||||
eps=sett.tol,
|
||||
max_iters=args["iterations"],
|
||||
alpha=1.95,
|
||||
acceleration_lookback=1)
|
||||
|
||||
JuMP.setsolver(SDP_problem, scs_solver)
|
||||
end
|
||||
|
||||
λ = Ps = nothing
|
||||
ws = PropertyT.warmstart(sett)
|
||||
|
||||
# using ProgressMeter
|
||||
|
||||
# @showprogress "Running SDP optimization step... " for i in 1:args["repetitions"]
|
||||
while true
|
||||
λ, Ps, ws = PropertyT.solve(PropertyT.filename(sett, :solverlog),
|
||||
SDP_problem, varλ, varP, ws);
|
||||
|
||||
if all((!isnan).(ws[1]))
|
||||
save(WARMSTART_FILE, "warmstart", ws, "λ", λ, "Ps", Ps)
|
||||
save(WARMSTART_FILE[1:end-4]*"_$(now()).jld", "warmstart", ws, "λ", λ, "Ps", Ps)
|
||||
else
|
||||
warn("No valid solution was saved!")
|
||||
end
|
||||
end
|
||||
|
||||
info("Reconstructing P...")
|
||||
@time P = PropertyT.reconstruct(Ps, orbit_data);
|
||||
save(SOLUTION_FILE, "λ", λ, "P", P)
|
||||
end
|
||||
|
||||
P, λ = load(SOLUTION_FILE, "P", "λ")
|
||||
@show λ;
|
||||
|
||||
@time const Q = real(sqrtm(P));
|
||||
|
||||
function SOS_residual(eoi::GroupRingElem, Q::Matrix)
|
||||
RG = parent(eoi)
|
||||
@time sos = PropertyT.compute_SOS(RG, Q);
|
||||
return eoi - sos
|
||||
end
|
||||
|
||||
info("Floating Point arithmetic:")
|
||||
EOI = elt - λ*Δ
|
||||
b = SOS_residual(EOI, Q)
|
||||
@show norm(b, 1);
|
||||
|
||||
info("Interval arithmetic:")
|
||||
using IntervalArithmetic
|
||||
Qint = PropertyT.augIdproj(Q);
|
||||
@assert all([zero(eltype(Q)) in sum(view(Qint, :, i)) for i in 1:size(Qint, 2)])
|
||||
|
||||
EOI_int = elt - @interval(λ)*Δ;
|
||||
Q_int = PropertyT.augIdproj(Q);
|
||||
@assert all([zero(eltype(Q)) in sum(view(Q_int, :, i)) for i in 1:size(Q_int, 2)])
|
||||
b_int = SOS_residual(EOI_int, Q_int)
|
||||
@show norm(b_int, 1);
|
||||
|
||||
info("λ is certified to be > ", (@interval(λ) - 2^2*norm(b_int,1)).lo)
|
||||
29
run.jl
29
run.jl
@ -78,31 +78,10 @@ include("CPUselect.jl")
|
||||
include("logging.jl")
|
||||
include("main.jl")
|
||||
|
||||
using SCS.SCSSolver
|
||||
# using Mosek
|
||||
# using CSDP
|
||||
# using SDPA
|
||||
const G = PropertyTGroups.PropertyTGroup(PARSEDARGS)
|
||||
|
||||
solver(tol, iterations) =
|
||||
SCSSolver(linearsolver=SCS.Direct,
|
||||
eps=tol, max_iters=iterations,
|
||||
alpha=1.95, acceleration_lookback=1)
|
||||
|
||||
# Mosek.MosekSolver(
|
||||
# MSK_DPAR_INTPNT_CO_TOL_REL_GAP=tol,
|
||||
# MSK_IPAR_INTPNT_MAX_ITERATIONS=iterations,
|
||||
# QUIET=false)
|
||||
|
||||
# CSDP.CSDPSolver(axtol=tol, atytol=tol, objtol=tol, minstepp=tol*10.0^-1, minstepd=tol*10.0^-1)
|
||||
|
||||
# SDPA.SDPASolver(epsilonStar=tol, epsilonDash=tol)
|
||||
|
||||
const Gr = PropertyTGroups.PropertyTGroup(PARSEDARGS)
|
||||
const sett = PropertyT.Settings(Gr, PARSEDARGS,
|
||||
solver(PARSEDARGS["tol"], PARSEDARGS["iterations"]))
|
||||
|
||||
fullpath = PropertyT.fullpath(sett)
|
||||
fullpath = joinpath(name(G), string(G.args["upper-bound"]))
|
||||
isdir(fullpath) || mkpath(fullpath)
|
||||
setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
||||
logger=setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
||||
|
||||
main(Gr, sett)
|
||||
main(G)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user