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
View file

@ -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)

20
src/Groups/GroupSU3.jl
View file

@ -17,8 +17,10 @@
# a.u32 = conj(a.u13*a.u21 - a.u11*a.u23)
# a.u33 = conj(a.u11*a.u22 - a.u12*a.u21)
#
using Random
import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\
import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.one,Base.zero
import Random.rand
struct SU3{T} <: Group
u11::Complex{T}
u12::Complex{T}
@ -27,11 +29,12 @@ struct SU3{T} <: Group
u22::Complex{T}
u23::Complex{T}
end
SU3() = SU3{Float64}(1.0,0.0,0.0,0.0,1.0,0.0)
inverse(a::SU3{T}) where T <: AbstractFloat = SU3{T}(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22),
conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23))
dag(a::SU3{T}) where T <: AbstractFloat = inverse(a)
tr(a::SU3{T}) where T <: AbstractFloat = a.u11+a.u22+conj(a.u11*a.u22 - a.u12*a.u21)
inverse(a::SU3{T}) where T <: AbstractFloat = SU3{T}(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22), conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23))
dag(a::SU3{T}) where T <: AbstractFloat = inverse(a)
tr(a::SU3{T}) where T <: AbstractFloat = a.u11+a.u22+conj(a.u11*a.u22 - a.u12*a.u21)
Base.one(::Type{SU3{T}}) where T <: AbstractFloat = SU3{T}(one(T),zero(T),zero(T),zero(T),one(T),zero(T))
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU3{T}}) where T <: AbstractFloat = exp(SU3alg{T}(randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T)))
function Base.:*(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
@ -103,7 +106,7 @@ struct SU3alg{T} <: Algebra
t7::T
t8::T
end
SU3alg() = SU3alg{Float64}(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
function projalg(a::SU3{T}) where T <: AbstractFloat
sr3ov2::T = 0.866025403784438646763723170752
@ -122,6 +125,9 @@ end
dot(a::SU3alg{T},b::SU3alg{T}) where T <: AbstractFloat = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3 + a.t4*b.t4 + a.t5*b.t5 + a.t6*b.t6 + a.t7*b.t7 + a.t8*b.t8
norm2(a::SU3alg{T}) where T <: AbstractFloat = a.t1^2 + a.t2^2 + a.t3^2 + a.t4^2 + a.t5^2 + a.t6^2 + a.t7^2 + a.t8^2
norm(a::SU3alg{T}) where T <: AbstractFloat = sqrt(a.t1^2 + a.t2^2 + a.t3^2 + a.t4^2 + a.t5^2 + a.t6^2 + a.t7^2 + a.t8^2)
Base.zero(::Type{SU3alg{T}}) where T <: AbstractFloat = SU3alg{T}(zero(T),zero(T),zero(T),zero(T),zero(T),zero(T),zero(T),zero(T))
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU3alg{T}}) where T <: AbstractFloat = SU3alg{T}(randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T))
Base.:+(a::SU3alg{T}) where T <: AbstractFloat = SU3alg{T}(a.t1,a.t2,a.t3,a.t4,a.t5,a.t6,a.t7,a.t8)
Base.:-(a::SU3alg{T}) where T <: AbstractFloat = SU3alg{T}(-a.t1,-a.t2,-a.t3,-a.t4,-a.t5,-a.t6,-a.t7,-a.t8)
Base.:+(a::SU3alg{T},b::SU3alg{T}) where T <: AbstractFloat = SU3alg{T}(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3,a.t4+b.t4,a.t5+b.t5,a.t6+b.t6,a.t7+b.t7,a.t8+b.t8)