mirror of
https://igit.ific.uv.es/alramos/latticegpu.jl.git
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SU2 routines re-organized in different files
This commit is contained in:
Alberto Ramos
parent
d11f7eefa3
commit
a27ac98554
4 changed files with 149 additions and 122 deletions
113
src/Groups/AlgebraSU2.jl
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113
src/Groups/AlgebraSU2.jl
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@ -0,0 +1,113 @@
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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: AlgebraSU2.jl
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### created: Sun Oct 3 09:24:25 2021
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###
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SU2alg(x::T) where T <: AbstractFloat = SU2alg{T}(x,0.0,0.0)
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SU2alg(v::Vector{T}) where T <: AbstractFloat = SU2alg{T}(v[1],v[2],v[3])
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projalg(g::SU2{T}) where T <: AbstractFloat = SU2alg{T}(imag(g.t1), real(g.t2), imag(g.t2))
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dot(a::SU2alg{T}, b::SU2alg{T}) where T <: AbstractFloat = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3
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norm(a::SU2alg{T}) where T <: AbstractFloat = sqrt(a.t1^2 + a.t2^2 + a.t3^2)
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norm2(a::SU2alg{T}) where T <: AbstractFloat = a.t1^2 + a.t2^2 + a.t3^2
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Base.:+(a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1,a.t2,a.t3)
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Base.:-(a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(-a.t1,-a.t2,-a.t3)
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Base.:+(a::SU2alg{T},b::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3)
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Base.:-(a::SU2alg{T},b::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1-b.t1,a.t2-b.t2,a.t3-b.t3)
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Base.:*(a::SU2alg{T},b::Number) where T <: AbstractFloat = SU2alg{T}(a.t1*b,a.t2*b,a.t3*b)
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Base.:*(b::Number,a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1*b,a.t2*b,a.t3*b)
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Base.:/(a::SU2alg{T},b::Number) where T <: AbstractFloat = SU2alg{T}(a.t1/b,a.t2/b,a.t3/b)
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"""
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function Base.exp(a::T, t::Number=1) where {T <: Algebra}
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Computes `exp(a)`
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"""
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function Base.exp(a::SU2alg{T}) where T <: AbstractFloat
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rm = sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = 0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0))
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else
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ca = CUDA.cos(rm)
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sa = CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)
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t2 = complex(sa*a.t2,sa*a.t3)
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return SU2{T}(t1,t2)
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end
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function Base.exp(a::SU2alg{T}, t::T) where T <: AbstractFloat
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rm = t*sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = t*(0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0)))
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else
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ca = CUDA.cos(rm)
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sa = t*CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)
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t2 = complex(sa*a.t2,sa*a.t3)
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return SU2{T}(t1,t2)
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end
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"""
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function expm(g::G, a::A) where {G <: Algebra, A <: Algebra}
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Computes `exp(a)*g`
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"""
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function expm(g::SU2{T}, a::SU2alg{T}) where T <: AbstractFloat
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rm = sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = 0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0))
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else
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ca = CUDA.cos(rm)
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sa = CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2)
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t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1)
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return SU2{T}(t1,t2)
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end
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"""
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function expm(g::SU2, a::SU2alg, t::Float64)
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Computes `exp(t*a)*g`
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"""
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function expm(g::SU2{T}, a::SU2alg{T}, t::T) where T <: AbstractFloat
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rm = t*sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = t*(0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0)))
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else
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ca = CUDA.cos(rm)
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sa = t*CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2)
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t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1)
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return SU2{T}(t1,t2)
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end
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@ -15,20 +15,12 @@
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# https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction
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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 SU2{T} <: Group
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t1::Complex{T}
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t2::Complex{T}
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end
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SU2(a::T, b::T) where T <: AbstractFloat = SU2{T}(complex(a), complex(b))
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inverse(b::SU2{T}) where T <: AbstractFloat = SU2{T}(conj(b.t1), -b.t2)
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dag(a::SU2{T}) where T <: AbstractFloat = inverse(a)
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norm(a::SU2{T}) where T <: AbstractFloat = sqrt(abs2(a.t1) + abs2(a.t2))
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norm2(a::SU2{T}) where T <: AbstractFloat = abs2(a.t1) + abs2(a.t2)
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tr(g::SU2{T}) where T <: AbstractFloat = complex(2.0*real(g.t1), 0.0)
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Base.one(::Type{SU2{T}}) where T <: AbstractFloat = SU2{T}(one(T),zero(T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}}) where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)))
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"""
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function normalize(a::T) where {T <: Group}
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@ -47,29 +39,6 @@ Base.:*(a::SU2{T},b::SU2{T}) where T <: AbstractFloat = SU2{T}(a.t1*b.t1-a.t2*co
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Base.:/(a::SU2{T},b::SU2{T}) where T <: AbstractFloat = SU2{T}(a.t1*conj(b.t1)+a.t2*conj(b.t2),-a.t1*b.t2+a.t2*b.t1)
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Base.:\(a::SU2{T},b::SU2{T}) where T <: AbstractFloat = SU2{T}(conj(a.t1)*b.t1+a.t2*conj(b.t2),conj(a.t1)*b.t2-a.t2*conj(b.t1))
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struct SU2alg{T} <: Algebra
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t1::T
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t2::T
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t3::T
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end
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SU2alg(x::T) where T <: AbstractFloat = SU2alg{T}(x,0.0,0.0)
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SU2alg(v::Vector{T}) where T <: AbstractFloat = SU2alg{T}(v[1],v[2],v[3])
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projalg(g::SU2{T}) where T <: AbstractFloat = SU2alg{T}(imag(g.t1), real(g.t2), imag(g.t2))
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dot(a::SU2alg{T}, b::SU2alg{T}) where T <: AbstractFloat = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3
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norm(a::SU2alg{T}) where T <: AbstractFloat = sqrt(a.t1^2 + a.t2^2 + a.t3^2)
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norm2(a::SU2alg{T}) where T <: AbstractFloat = a.t1^2 + a.t2^2 + a.t3^2
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Base.zero(::Type{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(zero(T),zero(T),zero(T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))
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Base.:+(a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1,a.t2,a.t3)
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Base.:-(a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(-a.t1,-a.t2,-a.t3)
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Base.:+(a::SU2alg{T},b::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3)
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Base.:-(a::SU2alg{T},b::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1-b.t1,a.t2-b.t2,a.t3-b.t3)
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Base.:*(a::SU2alg{T},b::Number) where T <: AbstractFloat = SU2alg{T}(a.t1*b,a.t2*b,a.t3*b)
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Base.:*(b::Number,a::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1*b,a.t2*b,a.t3*b)
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Base.:/(a::SU2alg{T},b::Number) where T <: AbstractFloat = SU2alg{T}(a.t1/b,a.t2/b,a.t3/b)
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function isgroup(a::SU2{T}) where T <: AbstractFloat
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tol = 1.0E-10
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if (abs2(a.t1) + abs2(a.t2) - 1.0 < 1.0E-10)
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@ -79,91 +48,3 @@ function isgroup(a::SU2{T}) where T <: AbstractFloat
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end
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end
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"""
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function Base.exp(a::T, t::Number=1) where {T <: Algebra}
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Computes `exp(a)`
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"""
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function Base.exp(a::SU2alg{T}) where T <: AbstractFloat
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rm = sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = 0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0))
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else
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ca = CUDA.cos(rm)
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sa = CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)
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t2 = complex(sa*a.t2,sa*a.t3)
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return SU2{T}(t1,t2)
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end
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function Base.exp(a::SU2alg{T}, t::T) where T <: AbstractFloat
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rm = t*sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = t*(0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0)))
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else
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ca = CUDA.cos(rm)
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sa = t*CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)
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t2 = complex(sa*a.t2,sa*a.t3)
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return SU2{T}(t1,t2)
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end
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"""
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function expm(g::G, a::A) where {G <: Algebra, A <: Algebra}
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Computes `exp(a)*g`
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"""
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function expm(g::SU2{T}, a::SU2alg{T}) where T <: AbstractFloat
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rm = sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = 0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0))
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else
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ca = CUDA.cos(rm)
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sa = CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2)
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t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1)
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return SU2{T}(t1,t2)
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end
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"""
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function expm(g::SU2, a::SU2alg, t::Float64)
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Computes `exp(t*a)*g`
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"""
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function expm(g::SU2{T}, a::SU2alg{T}, t::T) where T <: AbstractFloat
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rm = t*sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
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if (abs(rm) < 0.05)
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rms = rm^2/2.0
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ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
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sa = t*(0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0)))
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else
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ca = CUDA.cos(rm)
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sa = t*CUDA.sin(rm)/(2.0*rm)
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end
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t1 = complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2)
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t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1)
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return SU2{T}(t1,t2)
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end
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export SU2, SU2alg, inverse, dag, tr, projalg, expm, exp, norm, norm2, isgroup
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@ -12,8 +12,8 @@
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module Groups
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using Random
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.one,Base.zero
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using CUDA, Random
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp,Base.one,Base.zero
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import Random.rand
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abstract type Group end
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@ -21,9 +21,16 @@ abstract type Algebra end
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export Group, Algebra
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include("GroupSU2.jl")
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##
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# SU(2) and 2x2 matrix operations
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##
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include("SU2Types.jl")
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export SU2, SU2alg
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include("GroupSU2.jl")
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include("AlgebraSU2.jl")
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## END SU(2)
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##
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# SU(3) and 3x3 matrix operations
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##
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26
src/Groups/SU2Types.jl
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26
src/Groups/SU2Types.jl
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@ -0,0 +1,26 @@
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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
|
||||
### return. <alberto.ramos@cern.ch>
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###
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### file: SU2Types.jl
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### created: Sun Oct 3 09:22:48 2021
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###
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struct SU2{T} <: Group
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t1::Complex{T}
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t2::Complex{T}
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end
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struct SU2alg{T} <: Algebra
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t1::T
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t2::T
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t3::T
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end
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Base.zero(::Type{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(zero(T),zero(T),zero(T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))
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Base.one(::Type{SU2{T}}) where T <: AbstractFloat = SU2{T}(one(T),zero(T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}}) where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)))
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