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https://igit.ific.uv.es/alramos/latticegpu.jl.git
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Added tests and support for U(1) group
This commit is contained in:
Alberto Ramos
parent
cd6c28ff5f
commit
0587e5ffea
7 changed files with 332 additions and 1 deletions
84
src/Groups/GroupU1.jl
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84
src/Groups/GroupU1.jl
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###
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### "THE BEER-WARE LICENSE":
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### Alberto Ramos wrote this file. As long as you retain this
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### notice you can do whatever you want with this stuff. If we meet some
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### day, and you think this stuff is worth it, you can buy me a beer in
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### return. <alberto.ramos@cern.ch>
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###
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### file: GroupU1.jl
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### created: Tue Sep 21 09:33:44 2021
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###
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using CUDA, Random
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp,Base.zero,Base.one
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import Random.rand
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struct U1{T} <: Group
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t1::T
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t2::T
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end
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U1(a::T) where T <: AbstractFloat = U1{T}(a,zero(T))
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inverse(b::U1{T}) where T <: AbstractFloat = U1{T}(b.t1,-b.t2)
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dag(a::U1{T}) where T <: AbstractFloat = inverse(a)
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norm(a::U1{T}) where T <: AbstractFloat = sqrt(a.t1^2+a.t2^2)
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norm2(a::U1{T}) where T <: AbstractFloat = a.t1^2+a.t2^2
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tr(g::U1{T}) where T <: AbstractFloat = complex(a.t1)
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Base.one(::Type{U1{T}}) where T <: AbstractFloat = U1{T}(one(T), zero(T))
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function Random.rand(rng::AbstractRNG, ::Random.SamplerType{U1{T}}) where T <: AbstractFloat
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r = randn(rng,T)
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return U1{T}(CUDA.cos(r),CUDA.sin(r))
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end
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"""
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function normalize(a::U1)
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Return a normalized element of `SU(2)`
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"""
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function normalize(a::U1{T}) where T <: AbstractFloat
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dr = norm(a)
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return U1{T}(a.t1/dr, a.t2/dr)
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end
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Base.:*(a::U1{T},b::U1{T}) where T <: AbstractFloat = U1{T}(a.t1*b.t1-a.t2*b.t2, a.t1*b.t2+a.t2*b.t1)
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Base.:/(a::U1{T},b::U1{T}) where T <: AbstractFloat = U1{T}(a.t1*b.t1+a.t2*b.t2, -a.t1*b.t2+a.t2*b.t1)
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Base.:\(a::U1{T},b::U1{T}) where T <: AbstractFloat = U1{T}(a.t1*b.t1+a.t2*b.t2, a.t1*b.t2-a.t2*b.t1)
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struct U1alg{T} <: Algebra
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t::T
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end
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projalg(g::U1{T}) where T <: AbstractFloat = U1alg{T}(g.t2)
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dot(a::U1alg{T}, b::U1alg{T}) where T <: AbstractFloat = a.t*b.t
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norm(a::U1alg{T}) where T <: AbstractFloat = abs(a.t)
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norm2(a::U1alg{T}) where T <: AbstractFloat = a.t^2
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Base.zero(::Type{U1alg{T}}) where T <: AbstractFloat = U1alg{T}(zero(T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{U1alg{T}}) where T <: AbstractFloat = U1alg{T}(randn(rng,T))
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Base.:+(a::U1alg{T}) where T <: AbstractFloat = U1alg{T}(a.t)
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Base.:-(a::U1alg{T}) where T <: AbstractFloat = U1alg{T}(-a.t)
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Base.:+(a::U1alg{T},b::U1alg{T}) where T <: AbstractFloat = U1alg{T}(a.t+b.t)
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Base.:-(a::U1alg{T},b::U1alg{T}) where T <: AbstractFloat = U1alg{T}(a.t-b.t)
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Base.:*(a::U1alg{T},b::Number) where T <: AbstractFloat = U1alg{T}(a.t*b)
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Base.:*(b::Number,a::U1alg{T}) where T <: AbstractFloat = U1alg{T}(a.t*b)
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Base.:/(a::U1alg{T},b::Number) where T <: AbstractFloat = U1alg{T}(a.t/b)
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isgroup(a::U1{T}) where T <: AbstractFloat = (abs(a.t) -1.0) < 1.0E-10
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"""
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function Base.exp(a::U1alg, t::Number=1)
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Computes `exp(a)`
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"""
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Base.exp(a::U1alg{T}) where T <: AbstractFloat = U1{T}(CUDA.cos(a.t), CUDA.sin(a.t))
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Base.exp(a::U1alg{T}, t::T) where T <: AbstractFloat = U1{T}(CUDA.cos(t*a.t), CUDA.sin(t*a.t))
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"""
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function expm(g::U1, a::U1alg; t=1)
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Computes `exp(a)*g`
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"""
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expm(g::U1{T}, a::U1alg{T}) where T <: AbstractFloat = U1{T}(CUDA.cos(a.t), CUDA.sin(a.t))*g
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expm(g::U1{T}, a::U1alg{T}, t::T) where T <: AbstractFloat = U1{T}(CUDA.cos(t*a.t), CUDA.sin(t*a.t))*g
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export U1, U1alg, inverse, dag, tr, projalg, expm, exp, norm, norm2, isgroup
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@ -23,6 +23,10 @@ export SU2, SU2alg
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include("GroupSU3.jl")
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export SU3, SU3alg
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include("GroupU1.jl")
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export U1, U1alg
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export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2, isgroup
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@ -16,7 +16,7 @@ include("Groups/Groups.jl")
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using .Groups
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export Group, Algebra
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export SU2, SU2alg, SU3, SU3alg
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export SU2, SU2alg, SU3, SU3alg, U1, U1alg
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export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2, isgroup
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include("Space/Space.jl")
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40
tests/testU1.jl
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40
tests/testU1.jl
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@ -0,0 +1,40 @@
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using LinearAlgebra, Random
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import Pkg
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#Pkg.activate("/lhome/ific/a/alramos/s.images/julia/workspace/LatticeGPU")
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Pkg.activate("/home/alberto/code/julia/LatticeGPU")
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using LatticeGPU
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T = Float32
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b = rand(U1{T})
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println(b)
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ba = rand(U1alg{T})
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println("Ba: ", ba)
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b = exp(ba)
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println("B: ", b)
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c = exp(ba, convert(T,-1))
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println(typeof(norm2(ba)))
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d = b*c
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println("Test: ", d)
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c = inverse(b)
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println("Inverse B: ", c)
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d = b*c
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println("Test: ", d)
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println("B: ", b)
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println("Ba: ", ba)
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b = expm(b, ba, convert(T,-1))
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println("Test: ", b)
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Ma = Array{U1{T}}(undef, 2)
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rand!(Ma)
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println(Ma)
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fill!(Ma, one(eltype(Ma)))
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println(Ma)
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31
tests/test_SU2.jl
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31
tests/test_SU2.jl
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using LinearAlgebra, Random
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import Pkg
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#Pkg.activate("/lhome/ific/a/alramos/s.images/julia/workspace/LatticeGPU")
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Pkg.activate("/home/alberto/code/julia/LatticeGPU")
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using LatticeGPU
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T = Float32
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b = rand(SU2{T})
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println(b)
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ba = rand(SU2alg{T})
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println("Ba: ", ba)
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b = exp(ba)
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println("B: ", b)
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println(typeof(norm2(ba)))
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c = inverse(b)
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println("Inverse B: ", c)
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d = b*c
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println("Test: ", d)
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Ma = Array{SU2{T}}(undef, 100)
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rand!(Ma)
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println(Ma)
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fill!(Ma, one(eltype(Ma)))
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println(Ma)
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41
tests/test_space.jl
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tests/test_space.jl
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import Pkg
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#Pkg.activate("/lhome/ific/a/alramos/s.images/julia/workspace/LatticeGPU")
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Pkg.activate("/home/alberto/code/julia/LatticeGPU")
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using LatticeGPU, BenchmarkTools
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lp = SpaceParm{4}((8,12,6,6), (8,2,2,3))
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function test_point(pt::NTuple{2,Int64}, lp::SpaceParm)
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ok = true
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println("Global point: ", global_point(pt, lp))
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for id in 1:lp.ndim
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ua, ub = up(pt, id, lp)
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println(" - UP in id $id: ", global_point((ua,ub), lp))
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da, db = dw(pt, id, lp)
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println(" - DW in id $id: ", global_point((da,db), lp), "\n")
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ua2, ub2, da2, db2 = updw(pt, id, lp)
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ok = ok && (ua == ua2)
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ok = ok && (ub == ub2)
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ok = ok && (da == da2)
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ok = ok && (db == db2)
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end
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return ok
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end
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global ok = true
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for i in 1:lp.bsz, j in 1:lp.rsz
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global ok = ok && test_point((i,j), lp)
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end
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if ok
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println("ALL tests passed")
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else
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println("ERROR in test")
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end
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println(lp)
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131
tests/test_su3.jl
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tests/test_su3.jl
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@ -0,0 +1,131 @@
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using CUDA, LinearAlgebra
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import Pkg
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#Pkg.activate("/lhome/ific/a/alramos/s.images/julia/workspace/LatticeGPU")
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Pkg.activate("/home/alberto/code/julia/LatticeGPU")
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using LatticeGPU
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function g2mat(g::SU3)
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M = Array{ComplexF64, 2}(undef, 3,3)
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M[1,1] = g.u11
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M[1,2] = g.u12
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M[1,3] = g.u13
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M[2,1] = g.u21
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M[2,2] = g.u22
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M[2,3] = g.u23
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M[3,1] = conj(g.u12*g.u23 - g.u13*g.u22)
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M[3,2] = conj(g.u13*g.u21 - g.u11*g.u23)
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M[3,3] = conj(g.u11*g.u22 - g.u12*g.u21)
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return M
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end
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# 0.40284714488721746 + 0.2704272209422031im -0.029482825024553627 - 0.8247329455356851im 0.28771631112777535 + 0.027366985901323956im; -0.08478364480998268 + 0.8226014762207954im -0.4790638417896126 + 0.24301903735299646im -0.022591091614522323 + 0.16452285690920823im; 0.28083864951126214 + 0.04302898862961919im 0.0066864552013863165 - 0.17418727240313508im -0.939634663641523 + 0.07732362776719631im
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T = Float64
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a = rand(SU3alg{T})
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println("Random algebra: ", a)
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g1 = exp(a, 0.2)
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g2 = exp(a, -0.2)
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g = expm(g1, a, -0.2)
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println(g)
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M = [0.40284714488721746 + 0.2704272209422031im -0.029482825024553627 - 0.8247329455356851im 0.28771631112777535 + 0.027366985901323956im; -0.08478364480998268 + 0.8226014762207954im -0.4790638417896126 + 0.24301903735299646im -0.022591091614522323 + 0.16452285690920823im; 0.28083864951126214 + 0.04302898862961919im 0.0066864552013863165 - 0.17418727240313508im -0.939634663641523 + 0.07732362776719631im]
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println(det(M))
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g1 = SU3(M[1,1],M[1,2],M[1,3], M[2,1],M[2,2],M[2,3])
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println("dir: ", g1)
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g2 = exp(a)
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println("exp: ", g2)
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println("dif: ", g2mat(g1)-g2mat(g2))
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g3 = g1/g2
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println(g3)
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println("END")
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ftest(g::Group) = LatticeGPU.tr(g)
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#println(" ## SU(2)")
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#asu2 = SU2alg(0.23, 1.23, -0.34)
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#gsu2 = exp(asu2)
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#
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#eps = 0.001
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#h = SU2alg(eps,0.0,0.0)
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#fp = ftest(exp(h)*gsu2)
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#fm = ftest(exp(h,-1.0)*gsu2)
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#println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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#h = SU2alg(0.0,eps,0.0)
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#fp = ftest(exp(h)*gsu2)
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#fm = ftest(exp(h,-1.0)*gsu2)
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#println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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#h = SU2alg(0.0,0.0,eps)
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#fp = ftest(exp(h)*gsu2)
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#fm = ftest(exp(h,-1.0)*gsu2)
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#println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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#println("Exact derivative: ", -projalg(gsu2))
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println("\n\n ## SU(3)")
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asu3 = SU3alg{T}(0.23, 1.23, -0.34, 2.34, -0.23, 0.23, -1.34, 1.34)
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gsu3 = exp(asu3)
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eps = 0.001
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h = SU3alg{T}(eps,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,eps,0.0,0.0,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,eps,0.0,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,eps,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,eps,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,0.0,eps,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,0.0,0.0,eps,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,0.0,0.0,0.0,eps)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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println("Exact derivative: ", -projalg(gsu3))
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println("\n # Mutiplications")
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g1 = exp(SU3alg{T}(0.23, 1.23, -0.34, 2.34, -0.23, 0.23, -1.34, 1.34))
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g2 = exp(SU3alg{T}(1.23, -0.23, -0.14, 0.4, -1.23, -0.8, -0.34, 0.34))
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a = g1/(g2*g1)
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b = g2*a
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println("b is one: ", b)
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