From 3f71a5222f90badb0ffcdcc67a74c3c056f024fc Mon Sep 17 00:00:00 2001 From: Alberto Ramos Date: Sun, 3 Oct 2021 18:22:32 +0200 Subject: [PATCH] Cleaned up groups modules --- src/Groups/AlgebraSU2.jl | 34 ++++++++++++++++------ src/Groups/AlgebraSU3.jl | 15 ---------- src/Groups/Groups.jl | 5 ++-- src/Groups/M2x2.jl | 62 ++++++++++++++++++++++++++++++++++++++++ src/Groups/M3x3.jl | 15 ++++++++++ src/Groups/SU2Types.jl | 14 +++++++-- src/Groups/SU3Types.jl | 2 ++ src/LatticeGPU.jl | 4 +-- tests/test_SU2.jl | 25 ++++++++++++++-- tests/test_su3.jl | 5 ++++ 10 files changed, 149 insertions(+), 32 deletions(-) create mode 100644 src/Groups/M2x2.jl diff --git a/src/Groups/AlgebraSU2.jl b/src/Groups/AlgebraSU2.jl index dea936f..ec6a853 100644 --- a/src/Groups/AlgebraSU2.jl +++ b/src/Groups/AlgebraSU2.jl @@ -11,7 +11,7 @@ SU2alg(x::T) where T <: AbstractFloat = SU2alg{T}(x,0.0,0.0) SU2alg(v::Vector{T}) where T <: AbstractFloat = SU2alg{T}(v[1],v[2],v[3]) -projalg(g::SU2{T}) where T <: AbstractFloat = SU2alg{T}(imag(g.t1), real(g.t2), imag(g.t2)) +projalg(g::SU2{T}) where T <: AbstractFloat = SU2alg{T}(imag(g.t2), real(g.t2), imag(g.t1)) 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 @@ -25,6 +25,22 @@ Base.:*(a::SU2alg{T},b::Number) where T <: AbstractFloat = SU2alg{T}(a.t1*b,a Base.:*(b::Number,a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1*b,a.t2*b,a.t3*b) Base.:/(a::SU2alg{T},b::Number) where T <: AbstractFloat = SU2alg{T}(a.t1/b,a.t2/b,a.t3/b) +function alg2mat(a::SU2alg{T}) where T <: AbstractFloat + + u11::Complex{T} = complex(0.0, a.t3)/2 + u22::Complex{T} = conj(u11) + u12::Complex{T} = complex(a.t2,a.t1)/2 + u21::Complex{T} = -conj(u12) + + return M2x2{T}(u11,u12,u21,u22) +end + +Base.:*(a::SU2alg,b::SU2) = alg2mat(a)*b +Base.:*(a::SU2,b::SU2alg) = a*alg2mat(b) +Base.:/(a::SU2alg,b::SU2) = alg2mat(a)/b +Base.:\(a::SU2,b::SU2alg) = a\alg2mat(b) + + """ function Base.exp(a::T, t::Number=1) where {T <: Algebra} @@ -42,8 +58,8 @@ function Base.exp(a::SU2alg{T}) where T <: AbstractFloat sa = CUDA.sin(rm)/(2.0*rm) end - t1 = complex(ca,sa*a.t1) - t2 = complex(sa*a.t2,sa*a.t3) + t1 = complex(ca,sa*a.t3) + t2 = complex(sa*a.t2,sa*a.t1) return SU2{T}(t1,t2) end @@ -59,8 +75,8 @@ function Base.exp(a::SU2alg{T}, t::T) where T <: AbstractFloat sa = t*CUDA.sin(rm)/(2.0*rm) end - t1 = complex(ca,sa*a.t1) - t2 = complex(sa*a.t2,sa*a.t3) + t1 = complex(ca,sa*a.t3) + t2 = complex(sa*a.t2,sa*a.t1) return SU2{T}(t1,t2) end @@ -83,8 +99,8 @@ function expm(g::SU2{T}, a::SU2alg{T}) where T <: AbstractFloat sa = CUDA.sin(rm)/(2.0*rm) end - t1 = complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2) - t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1) + t1 = complex(ca,sa*a.t3)*g.t1-complex(sa*a.t2,sa*a.t1)*conj(g.t2) + t2 = complex(ca,sa*a.t3)*g.t2+complex(sa*a.t2,sa*a.t1)*conj(g.t1) return SU2{T}(t1,t2) end @@ -106,8 +122,8 @@ function expm(g::SU2{T}, a::SU2alg{T}, t::T) where T <: AbstractFloat sa = t*CUDA.sin(rm)/(2.0*rm) end - t1 = complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2) - t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1) + t1 = complex(ca,sa*a.t3)*g.t1-complex(sa*a.t2,sa*a.t1)*conj(g.t2) + t2 = complex(ca,sa*a.t3)*g.t2+complex(sa*a.t2,sa*a.t1)*conj(g.t1) return SU2{T}(t1,t2) end diff --git a/src/Groups/AlgebraSU3.jl b/src/Groups/AlgebraSU3.jl index 77cab59..107ab4a 100644 --- a/src/Groups/AlgebraSU3.jl +++ b/src/Groups/AlgebraSU3.jl @@ -24,21 +24,6 @@ function projalg(a::SU3{T}) where T <: AbstractFloat sr3ov2*(ditr)) end -function projalg(a::M3x3{T}) where T <: AbstractFloat - - sr3ov2::T = 0.866025403784438646763723170752 - - ditr = ( imag(a.u11) + imag(a.u22) + 2.0*imag(a.u33) )/3.0 - m12 = (a.u12 - conj(a.u21))/2.0 - m13 = (a.u13 - conj(a.u31))/2.0 - m23 = (a.u23 - conj(a.u32))/2.0 - - return SU3alg{T}(imag( m12 ), imag( m13 ), imag( m23 ), - real( m12 ), real( m13 ), real( m23 ), - (imag(a.u11)-imag(a.u22))/2.0, - sr3ov2*(ditr)) -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) diff --git a/src/Groups/Groups.jl b/src/Groups/Groups.jl index 138f535..b049cd9 100644 --- a/src/Groups/Groups.jl +++ b/src/Groups/Groups.jl @@ -25,9 +25,10 @@ export Group, Algebra # SU(2) and 2x2 matrix operations ## include("SU2Types.jl") -export SU2, SU2alg +export SU2, SU2alg, M2x2 include("GroupSU2.jl") +include("M2x2.jl") include("AlgebraSU2.jl") ## END SU(2) @@ -46,7 +47,7 @@ include("GroupU1.jl") export U1, U1alg -export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2, isgroup +export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2, isgroup, alg2mat end # module diff --git a/src/Groups/M2x2.jl b/src/Groups/M2x2.jl new file mode 100644 index 0000000..19e23bd --- /dev/null +++ b/src/Groups/M2x2.jl @@ -0,0 +1,62 @@ +### +### "THE BEER-WARE LICENSE": +### Alberto Ramos wrote this file. As long as you retain this +### notice you can do whatever you want with this stuff. If we meet some +### day, and you think this stuff is worth it, you can buy me a beer in +### return. +### +### file: M3x3.jl +### created: Sun Oct 3 09:03:34 2021 +### + + +Base.:*(a::M2x2{T},b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(a.u11*b.u11 + a.u12*b.u21, + a.u11*b.u12 + a.u12*b.u22, + a.u21*b.u11 + a.u22*b.u21, + a.u21*b.u12 + a.u22*b.u22) + +Base.:*(a::SU2{T},b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(a.t1*b.u11+a.t2*b.u21, + a.t1*b.u12+a.t2*b.u22, + -conj(a.t2)*b.u11+conj(a.t1)*b.u21, + -conj(a.t2)*b.u12+conj(a.t1)*b.u22) + +Base.:*(a::M2x2{T},b::SU2{T}) where T <: AbstractFloat = M2x2{T}(a.u11*b.t1-a.u12*conj(b.t2), + a.u11*b.t2+a.u12*conj(b.t1), + a.u21*b.t1-a.u22*conj(b.t2), + -a.u21*b.t2+a.u22*conj(b.t1)) + +Base.:/(a::M2x2{T},b::SU2{T}) where T <: AbstractFloat = M2x2{T}(a.u11*conj(b.t1)-a.u12*conj(b.t2), + a.u11*b.t2+a.u12*b.t1, + a.u21*conj(b.t1)-a.u22*conj(b.t2), + -a.u21*b.t2+a.u22*b.t1) + +Base.:\(a::SU2{T},b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(conj(a.t1)*b.u11+a.t2*b.u21, + conj(a.t1)*b.u12+a.t2*b.u22, + -conj(a.t2)*b.u11+a.t1*b.u21, + -conj(a.t2)*b.u12+a.t1*b.u22) + +Base.:*(a::Number,b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(a*b.u11, a*b.u12, + a*b.u21, a*b.u22) + +Base.:*(b::M2x2{T},a::Number) where T <: AbstractFloat = M2x2{T}(a*b.u11, a*b.u12, + a*b.u21, a*b.u22) + +Base.:+(a::M2x2{T},b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(a.u11+b.u11, a.u12+b.u12, + a.u21+b.u21, a.u22+b.u22) + +Base.:-(a::M2x2{T},b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(a.u11-b.u11, a.u12-b.u12, + a.u21-b.u21, a.u22-b.u22) + +Base.:-(b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(-b.u11, -b.u12, + -b.u21, -b.u22) + +Base.:+(b::M2x2{T}) where T <: AbstractFloat = M2x2{T}(b.u11, b.u12, + b.u21, b.u22) + +function projalg(a::M2x2{T}) where T <: AbstractFloat + + m12 = (a.u12 - conj(a.u21))/2 + + return SU2alg{T}(imag( m12 ), real( m12 ), (imag(a.u11) - imag(a.u22))/2) +end + diff --git a/src/Groups/M3x3.jl b/src/Groups/M3x3.jl index 9a1b83b..30866f0 100644 --- a/src/Groups/M3x3.jl +++ b/src/Groups/M3x3.jl @@ -113,3 +113,18 @@ Base.:-(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(-b.u11, -b.u12 Base.:+(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(b.u11, b.u12, bu13, b.u21, b.u22, bu23, b.u31, b.u32, bu33) +function projalg(a::M3x3{T}) where T <: AbstractFloat + + sr3ov2::T = 0.866025403784438646763723170752 + + ditr = ( imag(a.u11) + imag(a.u22) + 2.0*imag(a.u33) )/3.0 + m12 = (a.u12 - conj(a.u21))/2.0 + m13 = (a.u13 - conj(a.u31))/2.0 + m23 = (a.u23 - conj(a.u32))/2.0 + + return SU3alg{T}(imag( m12 ), imag( m13 ), imag( m23 ), + real( m12 ), real( m13 ), real( m23 ), + (imag(a.u11)-imag(a.u22))/2.0, + sr3ov2*(ditr)) +end + diff --git a/src/Groups/SU2Types.jl b/src/Groups/SU2Types.jl index e6e5340..d36ec33 100644 --- a/src/Groups/SU2Types.jl +++ b/src/Groups/SU2Types.jl @@ -14,6 +14,13 @@ struct SU2{T} <: Group t2::Complex{T} end +struct M2x2{T} + u11::Complex{T} + u12::Complex{T} + u21::Complex{T} + u22::Complex{T} +end + struct SU2alg{T} <: Algebra t1::T t2::T @@ -21,6 +28,9 @@ struct SU2alg{T} <: Algebra end Base.zero(::Type{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(zero(T),zero(T),zero(T)) +Base.zero(::Type{M2x2{T}}) where T <: AbstractFloat = M2x2{T}(zero(T),zero(T),zero(T),zero(T)) +Base.one(::Type{SU2{T}}) where T <: AbstractFloat = SU2{T}(one(T),zero(T)) +Base.one(::Type{M2x2{T}}) where T <: AbstractFloat = M2x2{T}(one(T),zero(T),zero(T),one(T)) + Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)) -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))) +Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}}) where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))) diff --git a/src/Groups/SU3Types.jl b/src/Groups/SU3Types.jl index ae08832..82c751f 100644 --- a/src/Groups/SU3Types.jl +++ b/src/Groups/SU3Types.jl @@ -39,6 +39,8 @@ struct M3x3{T} u32::Complex{T} u33::Complex{T} end +Base.one(::Type{M3x3{T}}) where T <: AbstractFloat = M3x3{T}(one(T),zero(T),zero(T),zero(T),one(T),zero(T),zero(T),zero(T),one(T)) +Base.zero(::Type{M3x3{T}}) where T <: AbstractFloat = M3x3{T}(zero(T),zero(T),zero(T),zero(T),zero(T),zero(T),zero(T),zero(T),zero(T)) struct SU3alg{T} <: Algebra t1::T diff --git a/src/LatticeGPU.jl b/src/LatticeGPU.jl index 5be9f7b..5ca9987 100644 --- a/src/LatticeGPU.jl +++ b/src/LatticeGPU.jl @@ -16,8 +16,8 @@ include("Groups/Groups.jl") using .Groups export Group, Algebra -export SU2, SU2alg, SU3, SU3alg, M3x3, U1, U1alg -export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2, isgroup +export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg +export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2, isgroup, alg2mat include("Space/Space.jl") diff --git a/tests/test_SU2.jl b/tests/test_SU2.jl index 423b722..12f3739 100644 --- a/tests/test_SU2.jl +++ b/tests/test_SU2.jl @@ -6,7 +6,7 @@ Pkg.activate("/home/alberto/code/julia/LatticeGPU") using LatticeGPU -T = Float32 +T = Float64 b = rand(SU2{T}) println(b) @@ -23,9 +23,30 @@ println("Inverse B: ", c) d = b*c println("Test: ", d) -Ma = Array{SU2{T}}(undef, 100) +c = exp(ba, -1.0) +println("Inverse B: ", c) + +d = b*c +println("Test: ", d) + +Ma = Array{SU2{T}}(undef, 2) rand!(Ma) println(Ma) fill!(Ma, one(eltype(Ma))) println(Ma) + +println("## Aqui test M2x2") +ba = rand(SU2alg{T}) +ga = exp(ba) +println("Matrix: ", alg2mat(ba)) +println("Exp: ", ga) + + +mo = one(M2x2{T}) +println(mo) +mp = mo*ga +println(mp) +println(projalg(mp)) +println(projalg(ga)) + diff --git a/tests/test_su3.jl b/tests/test_su3.jl index 7660309..191de72 100644 --- a/tests/test_su3.jl +++ b/tests/test_su3.jl @@ -129,3 +129,8 @@ b = g2*a println("b is one: ", b) +println("## Aqui test M3x3") +ba = rand(SU3alg{T}) +ga = exp(ba) +println("Matrix: ", alg2mat(ba)) +println("Exp: ", ga)