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migrate eigenvalues to Arblib.jl

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kalmarek 2020-11-14 19:23:21 +01:00
parent 8aa4eb9668
commit e01421ace9
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5 changed files with 191 additions and 298 deletions
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Manifest.toml
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@ -2,9 +2,21 @@
[[AbstractAlgebra]] [[AbstractAlgebra]]
deps = ["InteractiveUtils", "LinearAlgebra", "Markdown", "Random", "SparseArrays", "Test"] deps = ["InteractiveUtils", "LinearAlgebra", "Markdown", "Random", "SparseArrays", "Test"]
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[[ArgParse]] [[ArgParse]]
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@ -30,6 +42,12 @@ git-tree-sha1 = "e214a9b9bd1b4e1b4f15b22c0994862b66af7ff7"
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@ -58,10 +76,10 @@ uuid = "0b7ba130-8d10-5ba8-a3d6-c5182647fed9"
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@ -88,22 +106,28 @@ uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
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@ -130,9 +154,15 @@ deps = ["Random", "Serialization", "Sockets"]
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@ -142,49 +172,55 @@ version = "0.2.0"
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@ -202,34 +238,45 @@ deps = ["Markdown"]
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@ -257,11 +304,17 @@ git-tree-sha1 = "51b1db0732bbdcfabb60e36095cc3ed9c0016932"
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@ -269,9 +322,9 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
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@ -281,35 +334,29 @@ version = "0.7.8"
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@ -318,21 +365,21 @@ uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
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version = "1.0.4" version = "1.0.12"
[[Pkg]] [[Pkg]]
deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"] deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
@ -349,12 +396,12 @@ deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
[[PropertyT]] [[PropertyT]]
deps = ["AbstractAlgebra", "Dates", "GroupRings", "Groups", "IntervalArithmetic", "JLD", "JuMP", "LinearAlgebra", "Markdown", "MathProgBase", "Printf", "SparseArrays"] deps = ["AbstractAlgebra", "Dates", "GroupRings", "Groups", "IntervalArithmetic", "JLD", "JuMP", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "38850493c08470c23a8f2d86ad69fc450232c585" git-tree-sha1 = "599ef6d6ba280f3be5dff8d8afdc308fbbcea4df"
repo-rev = "master" repo-rev = "master"
repo-url = "https://github.com/kalmarek/PropertyT.jl" repo-url = "https://github.com/kalmarek/PropertyT.jl"
uuid = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d" uuid = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d"
version = "0.3.1" version = "0.3.2"
[[REPL]] [[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets"] deps = ["InteractiveUtils", "Markdown", "Sockets"]
@ -362,31 +409,26 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
[[RamanujanGraphs]] [[RamanujanGraphs]]
deps = ["LightGraphs", "LinearAlgebra", "Primes"] deps = ["LightGraphs", "LinearAlgebra", "Primes"]
git-tree-sha1 = "f623b007eda4cd5857953ba6735f1d1395175bab" git-tree-sha1 = "41fcab9bc21463a9d52bd481b7986d5271f36607"
repo-rev = "master" repo-rev = "master"
repo-url = "https://github.com/kalmarek/RamanujanGraphs.jl" repo-url = "https://github.com/kalmarek/RamanujanGraphs.jl"
uuid = "e7bd6bc6-b6b8-11e9-1ec2-2f89442c0d6c" uuid = "e7bd6bc6-b6b8-11e9-1ec2-2f89442c0d6c"
version = "0.3.0" version = "0.4.0"
[[Random]] [[Random]]
deps = ["Serialization"] deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
[[RecipesBase]] [[RecipesBase]]
git-tree-sha1 = "54f8ceb165a0f6d083f0d12cb4996f5367c6edbc" git-tree-sha1 = "b4ed4a7f988ea2340017916f7c9e5d7560b52cae"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.0.1" version = "0.8.0"
[[RoundingEmulator]]
git-tree-sha1 = "40b9edad2e5287e05bd413a38f61a8ff55b9557b"
uuid = "5eaf0fd0-dfba-4ccb-bf02-d820a40db705"
version = "0.2.1"
[[SCS]] [[SCS]]
deps = ["BinaryProvider", "Libdl", "LinearAlgebra", "MathOptInterface", "MathProgBase", "SparseArrays"] deps = ["BinaryProvider", "Libdl", "LinearAlgebra", "MathOptInterface", "MathProgBase", "SparseArrays"]
git-tree-sha1 = "5cb256630995eb94526065c4350ce8338947121d" git-tree-sha1 = "936d43feaceae3290472ddf800b496be094d727b"
uuid = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13" uuid = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"
version = "0.6.3" version = "0.6.6"
[[SHA]] [[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@ -406,9 +448,9 @@ uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
[[SimpleTraits]] [[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"] deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "2ee666b24ab8be6a922f9d6c11a86e1a703a7dda" git-tree-sha1 = "daf7aec3fe3acb2131388f93a4c409b8c7f62226"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d" uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.2" version = "0.9.3"
[[Sockets]] [[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc" uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
@ -425,9 +467,9 @@ version = "0.10.3"
[[StaticArrays]] [[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"] deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "5c06c0aeb81bef54aed4b3f446847905eb6cbda0" git-tree-sha1 = "da4cf579416c81994afd6322365d00916c79b8ae"
uuid = "90137ffa-7385-5640-81b9-e52037218182" uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "0.12.3" version = "0.12.5"
[[Statistics]] [[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"] deps = ["LinearAlgebra", "SparseArrays"]
@ -455,14 +497,20 @@ uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
[[Unicode]] [[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
[[ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "c3a5637e27e914a7a445b8d0ad063d701931e9f7"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.9.3"
[[Zlib_jll]] [[Zlib_jll]]
deps = ["Libdl", "Pkg"] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "fdd89e5ab270ea0f2a0174bd9093e557d06d4bfa" git-tree-sha1 = "320228915c8debb12cb434c59057290f0834dbf6"
uuid = "83775a58-1f1d-513f-b197-d71354ab007a" uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.11+16" version = "1.2.11+18"
[[Zstd_jll]] [[Zstd_jll]]
deps = ["Libdl", "Pkg"] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4de91f4313d9e88162d461e282fe3066ab3a3c09" git-tree-sha1 = "6f1abcb0c44f184690912aa4b0ba861dd64f11b9"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.4.5+1" version = "1.4.5+2"

3
Project.toml
View File

@ -1,13 +1,14 @@
[deps] [deps]
AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
Arblib = "fb37089c-8514-4489-9461-98f9c8763369"
ArgParse = "c7e460c6-2fb9-53a9-8c5b-16f535851c63" ArgParse = "c7e460c6-2fb9-53a9-8c5b-16f535851c63"
ArnoldiMethod = "ec485272-7323-5ecc-a04f-4719b315124d"
Arpack = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97" Arpack = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
Dates = "ade2ca70-3891-5945-98fb-dc099432e06a" Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
GroupRings = "0befed6a-bd73-11e8-1e41-a1190947c2f5" GroupRings = "0befed6a-bd73-11e8-1e41-a1190947c2f5"
Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557" Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
PropertyT = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d" PropertyT = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d"
RamanujanGraphs = "e7bd6bc6-b6b8-11e9-1ec2-2f89442c0d6c" RamanujanGraphs = "e7bd6bc6-b6b8-11e9-1ec2-2f89442c0d6c"
SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13" SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"

4
adj_psl2_eigvals.jl
View File

@ -1,12 +1,12 @@
using RamanujanGraphs using RamanujanGraphs
using LinearAlgebra using LinearAlgebra
using Nemo using Arblib
using ArgParse using ArgParse
using Logging using Logging
using Dates using Dates
include("src/nemo_utils.jl") include(joinpath(@__DIR__, "src", "eigen_utils.jl"))
function SL2p_gens(p) function SL2p_gens(p)
if p == 31 if p == 31

43
src/eigen_utils.jl Normal file
View File

@ -0,0 +1,43 @@
function unit_root(order::Integer, pow::Integer = 1; prec = Arblib.DEFAULT_PRECISION[])
@assert order > 0
res = Acb(; prec = prec)
Arblib.unit_root!(res, UInt(order), prec = prec)
return Arblib.pow!(res, res, pow)
end
similarity_transform(A::AcbMatrix) = similarity_transform!(similar(A), A)
function similarity_transform!(res::AcbMatrix, A::AcbMatrix)
@assert size(res) == size(A)
X = similar(A)
X .= rand(Acb(prec = precision(A)), size(X))
Arblib.inv!(res, X)
res = Arblib.mul!(res, A, res)
res = Arblib.mul!(res, X, res)
return res
end
function safe_eigvals(A::AcbMatrix)
λs = Arblib.eig_multiple_rump(similarity_transform(A))
all(isfinite.(λs)) && return λs
throw("Eigenvalue computation was not successful: Arblib returned infinite values.")
end
function count_multiplicites(evs)
λ_m = Vector{Tuple{Acb,Int}}()
sizehint!(λ_m, length(evs))
i = 1
while i <= length(evs)
m = 0
v = evs[i]
while i + m <= length(evs) && isequal(evs[i], evs[i+m])
m += 1
end
@assert m > 0
push!(λ_m, (evs[i], m))
i += m
end
return sort(λ_m, lt = (a, b) -> (real(first(a)) < real(first(b))), rev = true)
end

199
src/nemo_utils.jl
View File

@ -1,199 +0,0 @@
const libarb = Nemo.libarb
Base.hash(a::acb, h::UInt) = h
Base.reim(x::acb) = reim(convert(ComplexF64, x))
function root_of_unity(CC::AcbField, p, k = 1)
@assert p > 0
res = zero(CC)
ccall(
(:acb_unit_root, libarb),
Cvoid,
(Ref{acb}, Culong, Clong),
res,
p,
prec(CC),
)
return res^k
end
import Base.adjoint
function Base.adjoint(m::acb_mat)
res = zero(m)
ccall(
(:acb_mat_conjugate_transpose, libarb),
Cvoid,
(Ref{acb_mat}, Ref{acb_mat}),
res,
m,
)
return res
end
using Random
import Base.rand
rand(rng::AbstractRNG, rs::Random.SamplerTrivial{AcbField}) =
(CC = rs[]; CC(rand(Float64), rand(Float64)))
import Nemo.acb_struct
mutable struct AcbVector <: AbstractVector{acb_struct}
ptr::Ptr{acb_struct}
length::Int
precision::Int
function AcbVector(n::Integer, precision::Integer)
v = new(
ccall((:_acb_vec_init, libarb), Ptr{acb_struct}, (Clong,), n),
n,
precision,
)
finalizer(clear!, v)
return v
end
end
Base.cconvert(::Type{Ptr{acb_struct}}, acb_v::AcbVector) = acb_v.ptr
Base.size(acb_v::AcbVector) = (acb_v.length,)
Base.precision(acb_v::AcbVector) = acb_v.precision
function clear!(acb_v::AcbVector)
ccall(
(:_acb_vec_clear, libarb),
Cvoid,
(Ptr{acb_struct}, Clong),
acb_v,
length(acb_v),
)
end
Base.@propagate_inbounds function Base.getindex(acb_v::AcbVector, i::Integer)
@boundscheck checkbounds(acb_v, i)
return unsafe_load(acb_v.ptr, i)
end
_get_ptr(acb_v::AcbVector, i::Int = 1) =
acb_v.ptr + (i - 1) * sizeof(acb_struct)
function AcbVector(v::AbstractVector{acb}, p = prec(parent(first(v))))
acb_v = AcbVector(length(v), p)
for (i, val) in zip(eachindex(acb_v), v)
ccall(
(:acb_set, libarb),
Cvoid,
(Ptr{acb_struct}, Ref{acb}),
_get_ptr(acb_v, i),
val,
)
end
return acb_v
end
function approx_eig_qr!(v::AcbVector, R::acb_mat, A::acb_mat)
ccall(
(:acb_mat_approx_eig_qr, libarb),
Cint,
(
Ptr{acb_struct},
Ptr{Cvoid},
Ref{acb_mat},
Ref{acb_mat},
Ptr{Cvoid},
Int,
Int,
),
v,
C_NULL,
R,
A,
C_NULL,
0,
prec(parent(A)),
)
return v
end
function (C::AcbField)(z::acb_struct)
res = zero(C)
ccall((:acb_set, libarb), Cvoid, (Ref{acb}, Ref{acb_struct}), res, z)
return res
end
function LinearAlgebra.eigvals(A::acb_mat)
n = nrows(A)
CC = base_ring(A)
p = prec(CC)
λ_approx = AcbVector(n, p)
R_approx = similar(A)
v = approx_eig_qr!(λ_approx, R_approx, A)
λ = AcbVector(n, p)
b = ccall(
(:acb_mat_eig_multiple, libarb),
Cint,
(Ptr{acb_struct}, Ref{acb_mat}, Ptr{acb_struct}, Ref{acb_mat}, Int),
λ,
A,
λ_approx,
R_approx,
p,
)
return CC.(λ)
end
function eigvals_rump(A::acb_mat)
n = nrows(A)
CC = base_ring(A)
p = prec(CC)
λ_approx = AcbVector(n, p)
R_approx = similar(A)
v = approx_eig_qr!(λ_approx, R_approx, A)
λ = AcbVector(n, p)
b = ccall(
(:acb_mat_eig_multiple_rump, libarb),
Cint,
(Ptr{acb_struct}, Ref{acb_mat}, Ptr{acb_struct}, Ref{acb_mat}, Int),
λ,
A,
λ_approx,
R_approx,
p,
)
return CC.(λ)
end
function _count_multiplicites(evs)
λ_m = Vector{Tuple{acb,Int}}()
sizehint!(λ_m, length(evs))
i = 1
while i <= length(evs)
m = 0
v = evs[i]
while i + m <= length(evs) && isequal(evs[i], evs[i+m])
m += 1
end
push!(λ_m, (evs[i], m))
i += m
end
return sort(
λ_m,
lt = (a, b) -> (real(first(a)) < real(first(b))),
rev = true,
)
end
function safe_eigvals(m::acb_mat)
# evs = eigvals_rump(m)
# all(isfinite.(evs)) && return evs
CC = base_ring(m)
X = matrix(CC, rand(CC, size(m)))
evs = eigvals_rump(X * m * inv(X))
return evs
all(isfinite.(evs)) && return evs
throw(ArgumentError("Could not compute eigenvalues"))
end