Compare commits
No commits in common. "master" and "fix/new_type_system" have entirely different histories.
master
...
fix/new_ty
4
.gitignore
vendored
4
.gitignore
vendored
@ -10,6 +10,4 @@ SL*_*
|
||||
*ipynb*
|
||||
*.gws
|
||||
.*
|
||||
tests*
|
||||
*.py
|
||||
*.pyc
|
||||
*test*
|
||||
|
||||
69
AutFn.jl
Normal file
69
AutFn.jl
Normal file
@ -0,0 +1,69 @@
|
||||
using ArgParse
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Parsing command line
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function parse_commandline()
|
||||
s = ArgParseSettings()
|
||||
|
||||
@add_arg_table s begin
|
||||
"--tol"
|
||||
help = "set numerical tolerance for the SDP solver"
|
||||
arg_type = Float64
|
||||
default = 1e-6
|
||||
"--iterations"
|
||||
help = "set maximal number of iterations for the SDP solver"
|
||||
arg_type = Int
|
||||
default = 50000
|
||||
"--upper-bound"
|
||||
help = "Set an upper bound for the spectral gap"
|
||||
arg_type = Float64
|
||||
default = Inf
|
||||
"--cpus"
|
||||
help = "Set number of cpus used by solver (default: auto)"
|
||||
arg_type = Int
|
||||
required = false
|
||||
"--radius"
|
||||
help = "Radius of ball B_r(e,S) to find solution over"
|
||||
arg_type = Int
|
||||
default = 2
|
||||
"--warmstart"
|
||||
help = "Use warmstart.jld as the initial guess for SCS"
|
||||
action = :store_true
|
||||
"--nosymmetry"
|
||||
help = "Don't use symmetries of the Laplacian"
|
||||
action = :store_true
|
||||
"N"
|
||||
help = "Compute for the automorphisms group of the free group on N generators"
|
||||
arg_type = Int
|
||||
required = true
|
||||
end
|
||||
return parse_args(s)
|
||||
end
|
||||
const PARSEDARGS = parse_commandline()
|
||||
|
||||
#=
|
||||
Note that the element
|
||||
α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
|
||||
which surely belongs to ball of radius 4 in Aut(Fₙ) becomes trivial under the representation
|
||||
Aut(Fₙ) → GLₙ(ℤ)⋉ℤⁿ → GL_(n+1)(ℂ).
|
||||
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.
|
||||
|
||||
We need a different approach: Here we actually compute in (S)Aut(𝔽ₙ)
|
||||
=#
|
||||
|
||||
include("CPUselect.jl")
|
||||
set_parallel_mthread(PARSEDARGS, workers=true)
|
||||
|
||||
include("main.jl")
|
||||
|
||||
G = PropertyTGroups.SpecialAutomorphismGroup(PARSEDARGS)
|
||||
|
||||
if PARSEDARGS["nosymmetry"]
|
||||
main(Standard, G)
|
||||
else
|
||||
main(Symmetrize, G)
|
||||
end
|
||||
62
FPgroup.jl
Normal file
62
FPgroup.jl
Normal file
@ -0,0 +1,62 @@
|
||||
using ArgParse
|
||||
|
||||
function parse_commandline()
|
||||
args = ArgParseSettings()
|
||||
|
||||
@add_arg_table args begin
|
||||
"--tol"
|
||||
help = "set numerical tolerance for the SDP solver"
|
||||
arg_type = Float64
|
||||
default = 1e-6
|
||||
"--iterations"
|
||||
help = "set maximal number of iterations for the SDP solver"
|
||||
arg_type = Int
|
||||
default = 50000
|
||||
"--upper-bound"
|
||||
help = "Set an upper bound for the spectral gap"
|
||||
arg_type = Float64
|
||||
default = Inf
|
||||
"--cpus"
|
||||
help = "Set number of cpus used by solver (default: auto)"
|
||||
arg_type = Int
|
||||
required = false
|
||||
"--radius"
|
||||
help = "Radius of ball B_r(e,S) to find solution over"
|
||||
arg_type = Int
|
||||
default = 2
|
||||
"--warmstart"
|
||||
help = "Use warmstart.jl as the initial guess for SCS"
|
||||
action = :store_true
|
||||
"--MCG"
|
||||
help = "Compute for mapping class group of surface of genus N"
|
||||
arg_type = Int
|
||||
required = false
|
||||
"--Higman"
|
||||
help = "Compute for Higman Group"
|
||||
action = :store_true
|
||||
"--Caprace"
|
||||
help = "Compute for Higman Group"
|
||||
action = :store_true
|
||||
end
|
||||
|
||||
return parse_args(args)
|
||||
end
|
||||
const PARSEDARGS = parse_commandline()
|
||||
|
||||
include("CPUselect.jl")
|
||||
set_parallel_mthread(PARSEDARGS, workers=false)
|
||||
|
||||
include("main.jl")
|
||||
include("FPGroups_GAP.jl")
|
||||
|
||||
if PARSEDARGS["Caprace"]
|
||||
G = PropertyTGroups.CapraceGroup(PARSEDARGS)
|
||||
elseif PARSEDARGS["Higman"]
|
||||
G = PropertyTGroups.HigmanGroup(PARSEDARGS)
|
||||
elseif PARSEDARGS["MCG"] != nothing
|
||||
G = PropertyTGroups.MappingClassGroup(PARSEDARGS)
|
||||
else
|
||||
throw("You need to specify one of the --Higman, --Caprace, --MCG N")
|
||||
end
|
||||
|
||||
main(G)
|
||||
@ -1,10 +1,4 @@
|
||||
# DEPRECATED!
|
||||
|
||||
This repository has not been updated for a while!
|
||||
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/)
|
||||
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.
|
||||
|
||||
This repository contains some legacy code for computations in [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680).
|
||||
This repository contains code for computations in [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680).
|
||||
|
||||
# Installing
|
||||
To run the code You need `julia-v0.5` (should work on `v0.6`, but with warnings).
|
||||
|
||||
66
SLn.jl
Normal file
66
SLn.jl
Normal file
@ -0,0 +1,66 @@
|
||||
using ArgParse
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Parsing command line
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function parse_commandline()
|
||||
settings = ArgParseSettings()
|
||||
|
||||
@add_arg_table settings begin
|
||||
"--tol"
|
||||
help = "set numerical tolerance for the SDP solver"
|
||||
arg_type = Float64
|
||||
default = 1e-6
|
||||
"--iterations"
|
||||
help = "set maximal number of iterations for the SDP solver"
|
||||
arg_type = Int
|
||||
default = 50000
|
||||
"--upper-bound"
|
||||
help = "Set an upper bound for the spectral gap"
|
||||
arg_type = Float64
|
||||
default = Inf
|
||||
"--cpus"
|
||||
help = "Set number of cpus used by solver"
|
||||
arg_type = Int
|
||||
required = false
|
||||
"--radius"
|
||||
help = "Radius of ball B_r(e,S) to find solution over"
|
||||
arg_type = Int
|
||||
default = 2
|
||||
"--warmstart"
|
||||
help = "Use warmstart.jld as the initial guess for SCS"
|
||||
action = :store_true
|
||||
"--nosymmetry"
|
||||
help = "Don't use symmetries of the Laplacian"
|
||||
action = :store_true
|
||||
"-p"
|
||||
help = "Matrices over field of p-elements (p=0 => over ZZ)"
|
||||
arg_type = Int
|
||||
default = 0
|
||||
"-X"
|
||||
help = "Consider EL(N, ZZ⟨X⟩)"
|
||||
action = :store_true
|
||||
"N"
|
||||
help = "Compute with the group generated by elementary matrices of size n×n"
|
||||
arg_type = Int
|
||||
default = 2
|
||||
end
|
||||
return parse_args(settings)
|
||||
end
|
||||
const PARSEDARGS = parse_commandline()
|
||||
|
||||
include("CPUselect.jl")
|
||||
set_parallel_mthread(PARSEDARGS, workers=true)
|
||||
|
||||
include("main.jl")
|
||||
|
||||
G = PropertyTGroups.SpecialLinearGroup(PARSEDARGS)
|
||||
|
||||
if PARSEDARGS["nosymmetry"]
|
||||
main(Standard, G)
|
||||
else
|
||||
main(Symmetrize, G)
|
||||
end
|
||||
@ -1,56 +1,26 @@
|
||||
module PropertyTGroups
|
||||
|
||||
using PropertyT
|
||||
using AbstractAlgebra
|
||||
using Nemo
|
||||
using Groups
|
||||
using GroupRings
|
||||
|
||||
export PropertyTGroup, SymmetrizedGroup, GAPGroup,
|
||||
SpecialLinearGroup,
|
||||
SpecialAutomorphismGroup,
|
||||
HigmanGroup,
|
||||
CapraceGroup,
|
||||
MappingClassGroup
|
||||
|
||||
export PropertyTGroup
|
||||
export PropertyTGroup, SymmetricGroup, GAPGroup
|
||||
|
||||
abstract type PropertyTGroup end
|
||||
|
||||
abstract type SymmetrizedGroup <: PropertyTGroup end
|
||||
abstract type SymmetricGroup <: PropertyTGroup end
|
||||
|
||||
abstract type GAPGroup <: PropertyTGroup end
|
||||
|
||||
function PropertyTGroup(args)
|
||||
if haskey(args, "SL")
|
||||
G = PropertyTGroups.SpecialLinearGroup(args)
|
||||
elseif haskey(args, "SAut")
|
||||
G = PropertyTGroups.SpecialAutomorphismGroup(args)
|
||||
elseif haskey(args, "MCG")
|
||||
G = PropertyTGroups.MappingClassGroup(args)
|
||||
elseif haskey(args, "Higman")
|
||||
G = PropertyTGroups.HigmanGroup(args)
|
||||
elseif haskey(args, "Caprace")
|
||||
G = PropertyTGroups.CapraceGroup(args)
|
||||
else
|
||||
throw("You must provide one of --SL, --SAut, --MCG, --Higman, --Caprace")
|
||||
end
|
||||
return G
|
||||
end
|
||||
|
||||
include("autfreegroup.jl")
|
||||
include("speciallinear.jl")
|
||||
|
||||
Comm(x,y) = x*y*x^-1*y^-1
|
||||
|
||||
function generatingset(G::GAPGroup)
|
||||
S = gens(group(G))
|
||||
return unique([S; inv.(S)])
|
||||
end
|
||||
generatingset(G::GAPGroup) = gens(group(G))
|
||||
|
||||
include("mappingclassgroup.jl")
|
||||
include("higman.jl")
|
||||
include("caprace.jl")
|
||||
include("actions.jl")
|
||||
|
||||
end # of module PropertyTGroups
|
||||
|
||||
@ -1,92 +0,0 @@
|
||||
function (p::perm)(A::GroupRingElem)
|
||||
RG = parent(A)
|
||||
result = zero(RG, eltype(A.coeffs))
|
||||
|
||||
for (idx, c) in enumerate(A.coeffs)
|
||||
if c!= zero(eltype(A.coeffs))
|
||||
result[p(RG.basis[idx])] = c
|
||||
end
|
||||
end
|
||||
return result
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# 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
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Action of WreathProductElems on AutGroupElem
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function AutFG_emb(A::AutGroup, g::WreathProductElem)
|
||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
||||
parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
|
||||
elt = A()
|
||||
Id = parent(g.n.elts[1])()
|
||||
flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
|
||||
Groups.r_multiply!(elt, flips, reduced=false)
|
||||
Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
|
||||
return elt
|
||||
end
|
||||
|
||||
function AutFG_emb(A::AutGroup, p::perm)
|
||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
||||
parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(p)) into $A")
|
||||
return A(Groups.perm_autsymbol(p))
|
||||
end
|
||||
|
||||
function (g::WreathProductElem)(a::Groups.Automorphism)
|
||||
A = parent(a)
|
||||
g = AutFG_emb(A,g)
|
||||
res = A()
|
||||
Groups.r_multiply!(res, g.symbols, reduced=false)
|
||||
Groups.r_multiply!(res, a.symbols, reduced=false)
|
||||
Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
|
||||
return res
|
||||
end
|
||||
|
||||
function (p::perm)(a::Groups.Automorphism)
|
||||
g = AutFG_emb(parent(a),p)
|
||||
return g*a*inv(g)
|
||||
end
|
||||
@ -1,13 +1,22 @@
|
||||
struct SpecialAutomorphismGroup{N} <: SymmetrizedGroup
|
||||
struct SpecialAutomorphismGroup <: SymmetricGroup
|
||||
args::Dict{String,Any}
|
||||
group::AutGroup
|
||||
|
||||
function SpecialAutomorphismGroup(args::Dict)
|
||||
N = args["N"]
|
||||
return new(args, AutGroup(FreeGroup(N), special=true))
|
||||
end
|
||||
end
|
||||
|
||||
function SpecialAutomorphismGroup(args::Dict)
|
||||
N = args["SAut"]
|
||||
return SpecialAutomorphismGroup{N}(AutGroup(FreeGroup(N), special=true))
|
||||
end
|
||||
function name(G::SpecialAutomorphismGroup)
|
||||
N = G.args["N"]
|
||||
|
||||
name(G::SpecialAutomorphismGroup{N}) where N = "SAutF$(N)"
|
||||
if G.args["nosymmetry"]
|
||||
return "SAutF$(N)"
|
||||
else
|
||||
return "oSAutF$(N)"
|
||||
end
|
||||
end
|
||||
|
||||
group(G::SpecialAutomorphismGroup) = G.group
|
||||
|
||||
@ -16,6 +25,45 @@ function generatingset(G::SpecialAutomorphismGroup)
|
||||
return unique([S; inv.(S)])
|
||||
end
|
||||
|
||||
function autS(G::SpecialAutomorphismGroup{N}) where N
|
||||
function autS(G::SpecialAutomorphismGroup)
|
||||
N = G.args["N"]
|
||||
return WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Action of WreathProductElems on AutGroupElem
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function AutFG_emb(A::AutGroup, g::WreathProductElem)
|
||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
||||
parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
|
||||
elt = A()
|
||||
Id = parent(g.n.elts[1])()
|
||||
flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
|
||||
Groups.r_multiply!(elt, flips, reduced=false)
|
||||
Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
|
||||
return elt
|
||||
end
|
||||
|
||||
function AutFG_emb(A::AutGroup, p::perm)
|
||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
||||
parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
|
||||
return A(Groups.perm_autsymbol(p))
|
||||
end
|
||||
|
||||
function (g::WreathProductElem)(a::Groups.Automorphism)
|
||||
A = parent(a)
|
||||
g = AutFG_emb(A,g)
|
||||
res = A()
|
||||
Groups.r_multiply!(res, g.symbols, reduced=false)
|
||||
Groups.r_multiply!(res, a.symbols, reduced=false)
|
||||
Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
|
||||
return res
|
||||
end
|
||||
|
||||
function (p::perm)(a::Groups.Automorphism)
|
||||
g = AutFG_emb(parent(a),p)
|
||||
return g*a*inv(g)
|
||||
end
|
||||
|
||||
@ -1,4 +1,6 @@
|
||||
struct CapraceGroup <: GAPGroup end
|
||||
struct CapraceGroup <: GAPGroup
|
||||
args::Dict{String,Any}
|
||||
end
|
||||
|
||||
name(G::CapraceGroup) = "CapraceGroup"
|
||||
|
||||
|
||||
@ -1,4 +1,6 @@
|
||||
struct HigmanGroup <: GAPGroup end
|
||||
struct HigmanGroup <: GAPGroup
|
||||
args::Dict{String,Any}
|
||||
end
|
||||
|
||||
name(G::HigmanGroup) = "HigmanGroup"
|
||||
|
||||
|
||||
@ -1,23 +1,26 @@
|
||||
struct MappingClassGroup{N} <: GAPGroup end
|
||||
struct MappingClassGroup <: GAPGroup
|
||||
args::Dict{String,Any}
|
||||
end
|
||||
|
||||
MappingClassGroup(args::Dict) = MappingClassGroup{args["MCG"]}()
|
||||
|
||||
name(G::MappingClassGroup{N}) where N = "MCG(N)"
|
||||
|
||||
function group(G::MappingClassGroup{N}) where N
|
||||
function name(G::MappingClassGroup)
|
||||
N = G.args["MCG"]
|
||||
return "MCG($(N))"
|
||||
end
|
||||
|
||||
function group(G::MappingClassGroup)
|
||||
N = G.args["MCG"]
|
||||
if N < 2
|
||||
throw("Genus must be at least 2!")
|
||||
elseif N == 2
|
||||
MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
|
||||
S = gens(MCGroup)
|
||||
|
||||
n = length(S)
|
||||
N = length(S)
|
||||
A = prod(reverse(S))*prod(S)
|
||||
|
||||
relations = [
|
||||
[Comm(S[i], S[j]) for i in 1:n for j in 1:n if abs(i-j) > 1]...,
|
||||
[S[i]*S[i+1]*S[i]*inv(S[i+1]*S[i]*S[i+1]) for i in 1:G.n-1]...,
|
||||
[Comm(S[i], S[j]) for i in 1:N for j in 1:N if abs(i-j) > 1]...,
|
||||
[S[i]*S[i+1]*S[i]*inv(S[i+1]*S[i]*S[i+1]) for i in 1:N-1]...,
|
||||
(S[1]*S[2]*S[3])^4*inv(S[5])^2,
|
||||
Comm(A, S[1]),
|
||||
A^2
|
||||
|
||||
@ -1,55 +1,40 @@
|
||||
struct SpecialLinearGroup{N} <: SymmetrizedGroup
|
||||
struct SpecialLinearGroup <: SymmetricGroup
|
||||
args::Dict{String,Any}
|
||||
group::AbstractAlgebra.Group
|
||||
p::Int
|
||||
X::Bool
|
||||
|
||||
function SpecialLinearGroup(args::Dict)
|
||||
n = args["N"]
|
||||
p = args["p"]
|
||||
X = args["X"]
|
||||
|
||||
if p == 0
|
||||
G = MatrixSpace(Nemo.ZZ, n, n)
|
||||
else
|
||||
G = MatrixSpace(FiniteField(p), n, n)
|
||||
end
|
||||
return new(args, G)
|
||||
end
|
||||
end
|
||||
|
||||
function SpecialLinearGroup(args::Dict)
|
||||
N = args["SL"]
|
||||
p = args["p"]
|
||||
X = args["X"]
|
||||
function name(G::SpecialLinearGroup)
|
||||
N = G.args["N"]
|
||||
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$p"
|
||||
end
|
||||
return SpecialLinearGroup{N}(G, p, X)
|
||||
end
|
||||
|
||||
function name(G::SpecialLinearGroup{N}) where N
|
||||
if G.p == 0
|
||||
R = (G.X ? "Z[x]" : "Z")
|
||||
if G.args["nosymmetry"]
|
||||
return "SL($N,$R)"
|
||||
else
|
||||
R = "F$(G.p)"
|
||||
return "oSL($N,$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)
|
||||
end
|
||||
|
||||
# r is the injectivity radius of
|
||||
# SL(n, Z[X]) -> SL(n, Z) induced by X -> 100
|
||||
|
||||
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]
|
||||
|
||||
if !X
|
||||
S = [E(idx[1],idx[2],SL) for idx in indexing]
|
||||
else
|
||||
S = [E(i,j,SL,v) for (i,j) in indexing for v in [1, 100*r]]
|
||||
end
|
||||
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)
|
||||
@ -57,6 +42,52 @@ function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
|
||||
return m
|
||||
end
|
||||
|
||||
function autS(G::SpecialLinearGroup{N}) where N
|
||||
function generatingset(G::SpecialLinearGroup)
|
||||
n = G.args["N"]
|
||||
p = G.args["p"]
|
||||
X = G.args["X"]
|
||||
SL = group(G)
|
||||
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||
|
||||
p > 0 && X && throw("SL(n, F_p[x]) not implemented")
|
||||
|
||||
if !X
|
||||
S = [E(idx[1],idx[2],SL) for idx in indexing]
|
||||
else
|
||||
r = G.args["radius"]
|
||||
S = [E(i,j,SL,v) for (i,j) in indexing for v in [1, 100*r]]
|
||||
end
|
||||
return unique([S; inv.(S)])
|
||||
end
|
||||
|
||||
function autS(G::SpecialLinearGroup)
|
||||
N = G.args["N"]
|
||||
return WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# 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)
|
||||
res = M(G_inv)
|
||||
Nemo.mul!(res, A, res)
|
||||
return Nemo.mul!(res, M(G), res)
|
||||
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
|
||||
|
||||
58
logging.jl
58
logging.jl
@ -1,58 +0,0 @@
|
||||
using Memento
|
||||
|
||||
function setup_logging(filename::String, handlername::Symbol=:log)
|
||||
isdir(dirname(filename)) || mkdir(dirname(filename))
|
||||
logger = Memento.config!("info", fmt="{date}| {msg}")
|
||||
handler = DefaultHandler(filename, DefaultFormatter("{date}| {msg}"))
|
||||
logger.handlers[String(handlername)] = handler
|
||||
return logger
|
||||
end
|
||||
|
||||
macro logtime(logger, ex)
|
||||
quote
|
||||
local stats = Base.gc_num()
|
||||
local elapsedtime = Base.time_ns()
|
||||
local val = $(esc(ex))
|
||||
elapsedtime = Base.time_ns() - elapsedtime
|
||||
local diff = Base.GC_Diff(Base.gc_num(), stats)
|
||||
local ts = time_string(elapsedtime,
|
||||
diff.allocd,
|
||||
diff.total_time,
|
||||
Base.gc_alloc_count(diff)
|
||||
)
|
||||
$(esc(info))($(esc(logger)), ts)
|
||||
val
|
||||
end
|
||||
end
|
||||
|
||||
function time_string(elapsedtime, bytes, gctime, allocs)
|
||||
str = @sprintf("%10.6f seconds", elapsedtime/1e9)
|
||||
if bytes != 0 || allocs != 0
|
||||
bytes, mb = Base.prettyprint_getunits(bytes, length(Base._mem_units), Int64(1024))
|
||||
allocs, ma = Base.prettyprint_getunits(allocs, length(Base._cnt_units), Int64(1000))
|
||||
if ma == 1
|
||||
str*= @sprintf(" (%d%s allocation%s: ", allocs, Base._cnt_units[ma], allocs==1 ? "" : "s")
|
||||
else
|
||||
str*= @sprintf(" (%.2f%s allocations: ", allocs, Base._cnt_units[ma])
|
||||
end
|
||||
if mb == 1
|
||||
str*= @sprintf("%d %s%s", bytes, Base._mem_units[mb], bytes==1 ? "" : "s")
|
||||
else
|
||||
str*= @sprintf("%.3f %s", bytes, Base._mem_units[mb])
|
||||
end
|
||||
if gctime > 0
|
||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
||||
end
|
||||
str*=")"
|
||||
elseif gctime > 0
|
||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
||||
end
|
||||
return str
|
||||
end
|
||||
|
||||
import Base: info, @time
|
||||
|
||||
Base.info(x) = info(getlogger(), x)
|
||||
macro time(x)
|
||||
return :(@logtime(getlogger(Main), $(esc(x))))
|
||||
end
|
||||
140
main.jl
140
main.jl
@ -1,61 +1,127 @@
|
||||
using AbstractAlgebra
|
||||
using Nemo
|
||||
using PropertyT
|
||||
using Groups
|
||||
|
||||
include("FPGroups_GAP.jl")
|
||||
using SCS.SCSSolver
|
||||
# using Mosek
|
||||
# using CSDP
|
||||
# using SDPA
|
||||
|
||||
include("groups/Allgroups.jl")
|
||||
using PropertyTGroups
|
||||
|
||||
import PropertyT.Settings
|
||||
struct Symmetrize end
|
||||
struct Standard end
|
||||
|
||||
function summarize(sett::PropertyT.Settings)
|
||||
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)")
|
||||
function summarize(logger, groupdir, iterations, tol, upper_bound, radius, G, S)
|
||||
info(logger, "Group: $groupdir")
|
||||
info(logger, "Iterations: $iterations")
|
||||
info(logger, "Precision: $tol")
|
||||
info(logger, "Upper bound: $upper_bound")
|
||||
info(logger, "Radius: $radius")
|
||||
info(logger, "Threads: $(Threads.nthreads())")
|
||||
info(logger, "Workers: $(workers())")
|
||||
info(logger, string(G))
|
||||
info(logger, "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::SymmetricGroup)
|
||||
radius = Gr.args["radius"]
|
||||
tol = Gr.args["tol"]
|
||||
iterations = Gr.args["iterations"]
|
||||
upper_bound = Gr.args["upper-bound"]
|
||||
warm = Gr.args["warmstart"]
|
||||
N = Gr.args["N"]
|
||||
return radius, tol, iterations, upper_bound, warm, N
|
||||
end
|
||||
|
||||
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
|
||||
|
||||
scs_solver(tol, iterations) = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=10)
|
||||
|
||||
main(G::SymmetricGroup) = main(Symmetrize, G)
|
||||
|
||||
function main(::Type{Symmetrize}, Gr::SymmetricGroup)
|
||||
|
||||
radius, tol, iterations, upper_bound, warm, N = params(Gr)
|
||||
|
||||
groupdir = "$(PropertyTGroups.name(Gr))_r$radius"
|
||||
isdir(groupdir) || mkdir(groupdir)
|
||||
logger = PropertyT.setup_logging(joinpath(groupdir, "$(upper_bound)"), :fulllog)
|
||||
|
||||
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(logger, 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)
|
||||
else
|
||||
autS = PropertyTGroups.autS(Gr)
|
||||
return PropertyT.Settings(gr_name, G, S, r, sol, ub, tol, ws, autS)
|
||||
end
|
||||
end
|
||||
autS = PropertyTGroups.autS(Gr)
|
||||
info(logger, "Symmetrising with $(autS)")
|
||||
|
||||
function main(::PropertyTGroup, sett::PropertyT.Settings)
|
||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
||||
solver = scs_solver(tol, iterations)
|
||||
|
||||
summarize(sett)
|
||||
# solver = Mosek.MosekSolver(
|
||||
# MSK_DPAR_INTPNT_CO_TOL_REL_GAP=tol,
|
||||
# MSK_IPAR_INTPNT_MAX_ITERATIONS=iterations,
|
||||
# QUIET=false)
|
||||
|
||||
# solver = CSDP.CSDPSolver(axtol=tol, atytol=tol, objtol=tol, minstepp=tol*10.0^-1, minstepd=tol*10.0^-1)
|
||||
|
||||
# solver = SDPA.SDPASolver(epsilonStar=tol, epsilonDash=tol)
|
||||
|
||||
sett = Settings(groupdir, N, G, S, autS,
|
||||
radius, solver, upper_bound, tol, warm, logger)
|
||||
return PropertyT.check_property_T(sett)
|
||||
end
|
||||
|
||||
function main(::GAPGroup, sett::PropertyT.Settings)
|
||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
||||
function main(::Type{Standard}, Gr::SymmetricGroup)
|
||||
|
||||
summarize(sett)
|
||||
radius, tol, iterations, upper_bound, warm, _ = params(Gr)
|
||||
|
||||
S = [s for s in sett.S if s.symbols[1].pow == 1]
|
||||
relations = [k*inv(v) for (k,v) in sett.G.rels]
|
||||
groupdir = "$(PropertyTGroups.name(Gr))_r$radius"
|
||||
isdir(groupdir) || mkdir(groupdir)
|
||||
logger = PropertyT.setup_logging(joinpath(groupdir, "$(upper_bound)"), :fulllog)
|
||||
|
||||
prepare_pm_delta(PropertyT.prepath(sett), GAP_groupcode(S, relations), sett.radius)
|
||||
G = PropertyTGroups.group(Gr)
|
||||
S = PropertyTGroups.generatingset(Gr)
|
||||
|
||||
summarize(logger, groupdir, iterations, tol, upper_bound, radius, G, S)
|
||||
|
||||
solver = scs_solver(tol, iterations)
|
||||
|
||||
return PropertyT.check_property_T(groupdir, S, G(),
|
||||
solver, upper_bound, tol, radius, warm)
|
||||
|
||||
return PropertyT.check_property_T(sett)
|
||||
end
|
||||
|
||||
|
||||
function main(Gr::GAPGroup)
|
||||
|
||||
radius, tol, iterations, upper_bound, warm = params(Gr)
|
||||
|
||||
groupdir = "$(PropertyTGroups.name(Gr))_r$radius"
|
||||
isdir(groupdir) || mkdir(groupdir)
|
||||
logger = PropertyT.setup_logging(joinpath(groupdir, "$(upper_bound)"), :fulllog)
|
||||
|
||||
G = PropertyTGroups.group(Gr)
|
||||
S = PropertyTGroups.generatingset(Gr)
|
||||
|
||||
relations = [k*inv(v) for (k,v) in G.rels]
|
||||
prepare_pm_delta(groupdir, GAP_groupcode(S, relations), radius)
|
||||
|
||||
S = unique([S; inv.(S)])
|
||||
|
||||
summarize(logger, groupdir, iterations, tol, upper_bound, radius, G, S)
|
||||
|
||||
solver = scs_solver(tol, iterations)
|
||||
|
||||
return PropertyT.check_property_T(groupdir, S, G(),
|
||||
solver, upper_bound, tol, radius, warm)
|
||||
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)
|
||||
108
run.jl
108
run.jl
@ -1,108 +0,0 @@
|
||||
using ArgParse
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Parsing command line
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function parse_commandline()
|
||||
settings = ArgParseSettings()
|
||||
|
||||
@add_arg_table settings begin
|
||||
"--tol"
|
||||
help = "set numerical tolerance for the SDP solver"
|
||||
arg_type = Float64
|
||||
default = 1e-6
|
||||
"--iterations"
|
||||
help = "set maximal number of iterations for the SDP solver"
|
||||
arg_type = Int
|
||||
default = 50000
|
||||
"--upper-bound"
|
||||
help = "Set an upper bound for the spectral gap"
|
||||
arg_type = Float64
|
||||
default = Inf
|
||||
"--cpus"
|
||||
help = "Set number of cpus used by solver"
|
||||
arg_type = Int
|
||||
required = false
|
||||
"--radius"
|
||||
help = "Radius of ball B_r(e,S) to find solution over"
|
||||
arg_type = Int
|
||||
default = 2
|
||||
"--warmstart"
|
||||
help = "Use warmstart.jld as the initial guess for SCS"
|
||||
action = :store_true
|
||||
"--nosymmetry"
|
||||
help = "Don't use symmetries of the Laplacian"
|
||||
action = :store_true
|
||||
|
||||
"--SL "
|
||||
help = "GROUP: the group generated by elementary matrices of size n by n"
|
||||
arg_type = Int
|
||||
required = false
|
||||
"-p"
|
||||
help = "Matrices over field of p-elements (p=0 => over ZZ) [only with --SL]"
|
||||
arg_type = Int
|
||||
default = 0
|
||||
"-X"
|
||||
help = "Consider EL(N, ZZ⟨X⟩) [only with --SL]"
|
||||
action = :store_true
|
||||
|
||||
"--SAut"
|
||||
help = "GROUP: the automorphisms group of the free group on N generators"
|
||||
arg_type = Int
|
||||
required = false
|
||||
|
||||
"--MCG"
|
||||
help = "GROUP: mapping class group of surface of genus N"
|
||||
arg_type = Int
|
||||
required = false
|
||||
|
||||
"--Higman"
|
||||
help = "GROUP: the Higman Group"
|
||||
action = :store_true
|
||||
|
||||
"--Caprace"
|
||||
help = "GROUP: for Caprace Group"
|
||||
action = :store_true
|
||||
end
|
||||
return parse_args(settings)
|
||||
end
|
||||
|
||||
const PARSEDARGS = parse_commandline()
|
||||
|
||||
set_parallel_mthread(PARSEDARGS, workers=false)
|
||||
|
||||
include("CPUselect.jl")
|
||||
include("logging.jl")
|
||||
include("main.jl")
|
||||
|
||||
using SCS.SCSSolver
|
||||
# using Mosek
|
||||
# using CSDP
|
||||
# using SDPA
|
||||
|
||||
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)
|
||||
isdir(fullpath) || mkpath(fullpath)
|
||||
setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
||||
|
||||
main(Gr, sett)
|
||||
222
runtests.jl
222
runtests.jl
@ -1,222 +0,0 @@
|
||||
using Base.Test
|
||||
|
||||
include("main.jl")
|
||||
|
||||
testdir = "tests_"*string(now())
|
||||
mkdir(testdir)
|
||||
include("logging.jl")
|
||||
logger=setup_logging(joinpath(testdir, "tests.log"))
|
||||
info(testdir)
|
||||
|
||||
cd(testdir)
|
||||
|
||||
# groupname = name(G)
|
||||
# ub = PARSEDARGS["upper-bound"]
|
||||
#
|
||||
# fullpath = joinpath(groupname, string(ub))
|
||||
# isdir(fullpath) || mkpath(fullpath)
|
||||
|
||||
separator(n=60) = info("\n"*("\n"*"="^n*"\n"^3)*"\n")
|
||||
|
||||
|
||||
function SL_tests(args)
|
||||
|
||||
|
||||
args["SL"] = 2
|
||||
args["p"] = 3
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == true
|
||||
separator()
|
||||
|
||||
let args = args
|
||||
args["SL"] = 2
|
||||
args["p"] = 5
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
separator()
|
||||
|
||||
args["warmstart"] = true
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
separator()
|
||||
|
||||
args["upper-bound"] = 0.1
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == true
|
||||
separator()
|
||||
end
|
||||
|
||||
args["SL"] = 2
|
||||
args["p"] = 7
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
separator()
|
||||
|
||||
args["SL"] = 3
|
||||
args["p"] = 7
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == true
|
||||
separator()
|
||||
|
||||
# begin
|
||||
# args["iterations"] = 25000
|
||||
# args["N"] = 3
|
||||
# args["p"] = 0
|
||||
# args["upper-bound"] = Inf
|
||||
#
|
||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
||||
# @test main(G) == false
|
||||
# separator()
|
||||
#
|
||||
# args["warmstart"] = false
|
||||
# args["upper-bound"] = 0.27
|
||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
||||
# @test main(G) == false
|
||||
# separator()
|
||||
#
|
||||
# args["warmstart"] = true
|
||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
||||
# @test main(G) == true
|
||||
# separator()
|
||||
# end
|
||||
|
||||
return 0
|
||||
end
|
||||
|
||||
function SAut_tests(args)
|
||||
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
separator()
|
||||
|
||||
args["warmstart"] = true
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
separator()
|
||||
|
||||
args["upper-bound"] = 0.1
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
separator()
|
||||
|
||||
return 0
|
||||
end
|
||||
|
||||
@testset "Groups with(out) (T)" begin
|
||||
|
||||
@testset "GAPGroups" begin
|
||||
args = Dict(
|
||||
"Higman" => true,
|
||||
"iterations"=>5000,
|
||||
"tol"=>1e-7,
|
||||
"upper-bound"=>Inf,
|
||||
"cpus"=>2,
|
||||
"radius"=>2,
|
||||
"warmstart"=>false,
|
||||
"nosymmetry"=>true,
|
||||
)
|
||||
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
|
||||
args = Dict(
|
||||
"Caprace" => true,
|
||||
"iterations"=>5000,
|
||||
"tol"=>1e-7,
|
||||
"upper-bound"=>Inf,
|
||||
"cpus"=>2,
|
||||
"radius"=>2,
|
||||
"warmstart"=>false,
|
||||
"nosymmetry"=>true,
|
||||
)
|
||||
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
|
||||
args = Dict(
|
||||
"MCG" => 3,
|
||||
"iterations"=>5000,
|
||||
"tol"=>1e-7,
|
||||
"upper-bound"=>Inf,
|
||||
"cpus"=>2,
|
||||
"radius"=>2,
|
||||
"warmstart"=>false,
|
||||
"nosymmetry"=>true,
|
||||
)
|
||||
|
||||
G = PropertyTGroup(args)
|
||||
@test main(G) == false
|
||||
end
|
||||
|
||||
@testset "SLn's" begin
|
||||
@testset "Non-Symmetrized" begin
|
||||
|
||||
args = Dict(
|
||||
"SL" => 2,
|
||||
"p" => 3,
|
||||
"X" => false,
|
||||
"iterations"=>50000,
|
||||
"tol"=>1e-7,
|
||||
"upper-bound"=>Inf,
|
||||
"cpus"=>2,
|
||||
"radius"=>2,
|
||||
"warmstart"=>false,
|
||||
"nosymmetry"=>true,
|
||||
)
|
||||
|
||||
SL_tests(args)
|
||||
end
|
||||
|
||||
@testset "Symmetrized" begin
|
||||
|
||||
args = Dict(
|
||||
"SL" => 2,
|
||||
"p" => 3,
|
||||
"X" => false,
|
||||
"iterations"=>20000,
|
||||
"tol"=>1e-7,
|
||||
"upper-bound"=>Inf,
|
||||
"cpus"=>2,
|
||||
"radius"=>2,
|
||||
"warmstart"=>false,
|
||||
"nosymmetry"=>false,
|
||||
)
|
||||
|
||||
SL_tests(args)
|
||||
end
|
||||
end
|
||||
|
||||
@testset "SAutF_n's" begin
|
||||
|
||||
@testset "Non-Symmetrized" begin
|
||||
|
||||
args = Dict(
|
||||
"SAut" => 2,
|
||||
"iterations"=>5000,
|
||||
"tol"=>1e-7,
|
||||
"upper-bound"=>Inf,
|
||||
"cpus"=>2,
|
||||
"radius"=>2,
|
||||
"warmstart"=>false,
|
||||
"nosymmetry"=>true,
|
||||
)
|
||||
SAut_tests(args)
|
||||
end
|
||||
|
||||
@testset "Symmetrized" begin
|
||||
args = Dict(
|
||||
"SAut" => 3,
|
||||
"iterations"=>500,
|
||||
"tol"=>1e-7,
|
||||
"upper-bound"=>Inf,
|
||||
"cpus"=>2,
|
||||
"radius"=>2,
|
||||
"warmstart"=>false,
|
||||
"nosymmetry"=>false,
|
||||
)
|
||||
SAut_tests(args)
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
end
|
||||
Loading…
Reference in New Issue
Block a user