lattice/latticegpu.jl
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Working multi-precision simulations

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The pure gauge theory with groups SU(2) and SU(3) is working
properly.
This commit is contained in:
Alberto Ramos 2021-09-20 18:21:16 +02:00
parent 1416efdbee
commit 09a09153b9
8 changed files with 188 additions and 283 deletions
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23
src/Groups/GroupSU2.jl
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@ -13,20 +13,22 @@
# SU(2) group elements represented trough Cayley-Dickson
# construction
# https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction
using CUDA
using CUDA, Random
import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp
import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp,Base.zero,Base.one
import Random.rand
struct SU2{T} <: Group
t1::Complex{T}
t2::Complex{T}
end
SU2() = SU2{Float64}(complex(1.0), complex(0.0))
SU2(a::T, b::T) where T <: AbstractFloat = SU2{T}(complex(a), complex(b))
inverse(b::SU2{T}) where T <: AbstractFloat = SU2{T}(conj(b.t1), -b.t2)
dag(a::SU2{T}) where T <: AbstractFloat = inverse(a)
norm(a::SU2{T}) where T <: AbstractFloat = sqrt(abs2(a.t1) + abs2(a.t2))
norm2(a::SU2{T}) where T <: AbstractFloat = abs2(a.t1) + abs2(a.t2)
tr(g::SU2{T}) where T <: AbstractFloat = complex(2.0*real(g.t1), 0.0)
SU2(a::T, b::T) where T <: AbstractFloat = SU2{T}(complex(a), complex(b))
inverse(b::SU2{T}) where T <: AbstractFloat = SU2{T}(conj(b.t1), -b.t2)
dag(a::SU2{T}) where T <: AbstractFloat = inverse(a)
norm(a::SU2{T}) where T <: AbstractFloat = sqrt(abs2(a.t1) + abs2(a.t2))
norm2(a::SU2{T}) where T <: AbstractFloat = abs2(a.t1) + abs2(a.t2)
tr(g::SU2{T}) where T <: AbstractFloat = complex(2.0*real(g.t1), 0.0)
Base.one(::Type{SU2{T}}) where T <: AbstractFloat = SU2{T}(one(T),zero(T))
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}}) where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)))
"""
function normalize(a::SU2)
@ -56,6 +58,9 @@ projalg(g::SU2{T}) where T <: AbstractFloat = SU2alg{T}(imag(g.t
dot(a::SU2alg{T}, b::SU2alg{T}) where T <: AbstractFloat = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3
norm(a::SU2alg{T}) where T <: AbstractFloat = sqrt(a.t1^2 + a.t2^2 + a.t3^2)
norm2(a::SU2alg{T}) where T <: AbstractFloat = a.t1^2 + a.t2^2 + a.t3^2
Base.zero(::Type{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(zero(T),zero(T),zero(T))
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))
Base.:+(a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1,a.t2,a.t3)
Base.:-(a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(-a.t1,-a.t2,-a.t3)
Base.:+(a::SU2alg{T},b::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3)