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https://igit.ific.uv.es/alramos/latticegpu.jl.git
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Groups SU(2) and SU(3) working for arbitrary precision
This commit is contained in:
Alberto Ramos
parent
76d0b66b4b
commit
1416efdbee
2 changed files with 219 additions and 222 deletions
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@ -16,59 +16,56 @@
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using CUDA
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using CUDA
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp
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struct SU2 <: Group
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struct SU2{T} <: Group
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t1::ComplexF64
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t1::Complex{T}
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t2::ComplexF64
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t2::Complex{T}
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end
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end
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SU2() = SU2(1.0, 0.0)
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SU2() = SU2{Float64}(complex(1.0), complex(0.0))
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inverse(b::SU2) = SU2(conj(b.t1), -b.t2)
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SU2(a::T, b::T) where T <: AbstractFloat = SU2{T}(complex(a), complex(b))
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dag(a::SU2) = inverse(a)
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inverse(b::SU2{T}) where T <: AbstractFloat = SU2{T}(conj(b.t1), -b.t2)
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norm(a::SU2) = sqrt(abs2(a.t1) + abs2(a.t2))
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dag(a::SU2{T}) where T <: AbstractFloat = inverse(a)
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norm2(a::SU2) = abs2(a.t1) + abs2(a.t2)
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norm(a::SU2{T}) where T <: AbstractFloat = sqrt(abs2(a.t1) + abs2(a.t2))
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tr(g::SU2) = complex(2.0*real(g.t1), 0.0)
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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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"""
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"""
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function normalize(a::SU2)
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function normalize(a::SU2)
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Return a normalized element of `SU(2)`
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Return a normalized element of `SU(2)`
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"""
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"""
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function normalize(a::SU2)
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function normalize(a::SU2{T}) where T <: AbstractFloat
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dr = sqrt(abs2(a.t1) + abs2(a.t2))
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dr = sqrt(abs2(a.t1) + abs2(a.t2))
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if (dr == 0.0)
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if (dr == 0.0)
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return SU2(0.0)
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return SU2(0.0)
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end
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end
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return SU2(a.t1/dr,a.t2/dr)
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return SU2{T}(a.t1/dr,a.t2/dr)
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end
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end
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Base.:+(a::SU2,b::SU2) = SU2(a.t1+b.t1,a.t2+b.t2)
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Base.:*(a::SU2{T},b::SU2{T}) where T <: AbstractFloat = SU2{T}(a.t1*b.t1-a.t2*conj(b.t2),a.t1*b.t2+a.t2*conj(b.t1))
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Base.:-(a::SU2,b::SU2) = SU2(a.t1-b.t1,a.t2-b.t2)
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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,b::SU2) = SU2(a.t1*b.t1-a.t2*conj(b.t2),a.t1*b.t2+a.t2*conj(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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Base.:/(a::SU2,b::SU2) = SU2(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,b::SU2) = SU2(conj(a.t1)*b.t1+a.t2*conj(b.t2),conj(a.t1)*b.t2-a.t2*conj(b.t1))
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Base.:+(a::SU2) = SU2(a.t1,a.t2)
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Base.:-(a::SU2) = SU2(-a.t1,-a.t2)
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struct SU2alg <: Algebra
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struct SU2alg{T} <: Algebra
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t1::Float64
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t1::T
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t2::Float64
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t2::T
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t3::Float64
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t3::T
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end
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end
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SU2alg(x::Real) = SU2alg(x,0.0,0.0)
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SU2alg(x::T) where T <: AbstractFloat = SU2alg{T}(x,0.0,0.0)
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SU2alg(v::Vector) = SU2alg(v[1],v[2],v[3])
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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) = SU2alg(imag(g.t1), real(g.t2), imag(g.t2))
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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, b::SU2alg) = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3
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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) = sqrt(a.t1^2 + a.t2^2 + a.t3^2)
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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) = 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) = SU2alg(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) = SU2alg(-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,b::SU2alg) = SU2alg(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,b::SU2alg) = SU2alg(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,b::Number) = SU2alg(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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Base.:*(b::Number,a::SU2alg) = SU2alg(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,b::Number) = SU2alg(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)
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function isgroup(a::SU2{T}) where T <: AbstractFloat
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tol = 1.0E-10
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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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if (abs2(a.t1) + abs2(a.t2) - 1.0 < 1.0E-10)
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return true
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return true
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@ -82,7 +79,7 @@ end
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Computes `exp(a)`
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Computes `exp(a)`
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"""
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"""
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function Base.exp(a::SU2alg)
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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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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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if (abs(rm) < 0.05)
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@ -96,10 +93,10 @@ function Base.exp(a::SU2alg)
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t1 = complex(ca,sa*a.t1)
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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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t2 = complex(sa*a.t2,sa*a.t3)
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return SU2(t1,t2)
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return SU2{T}(t1,t2)
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end
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end
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function Base.exp(a::SU2alg, t::Number)
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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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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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if (abs(rm) < 0.05)
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@ -113,7 +110,7 @@ function Base.exp(a::SU2alg, t::Number)
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t1 = complex(ca,sa*a.t1)
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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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t2 = complex(sa*a.t2,sa*a.t3)
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return SU2(t1,t2)
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return SU2{T}(t1,t2)
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end
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end
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@ -123,7 +120,7 @@ end
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Computes `exp(a)*g`
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Computes `exp(a)*g`
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"""
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"""
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function expm(g::SU2, a::SU2alg)
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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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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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if (abs(rm) < 0.05)
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@ -137,7 +134,7 @@ function expm(g::SU2, a::SU2alg)
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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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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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t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1)
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return SU2(t1,t2)
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return SU2{T}(t1,t2)
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end
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end
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"""
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"""
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@ -146,7 +143,7 @@ end
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Computes `exp(t*a)*g`
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Computes `exp(t*a)*g`
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"""
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"""
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function expm(g::SU2, a::SU2alg, t::Float64)
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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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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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if (abs(rm) < 0.05)
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@ -160,7 +157,7 @@ function expm(g::SU2, a::SU2alg, t::Float64)
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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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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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t2 = complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1)
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return SU2(t1,t2)
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return SU2{T}(t1,t2)
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end
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end
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@ -19,50 +19,49 @@
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#
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#
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\
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struct SU3 <: Group
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struct SU3{T} <: Group
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u11::ComplexF64
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u11::Complex{T}
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u12::ComplexF64
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u12::Complex{T}
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u13::ComplexF64
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u13::Complex{T}
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u21::ComplexF64
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u21::Complex{T}
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u22::ComplexF64
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u22::Complex{T}
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u23::ComplexF64
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u23::Complex{T}
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end
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end
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SU3() = SU3(1.0,0.0,0.0,0.0,1.0,0.0)
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SU3() = SU3{Float64}(1.0,0.0,0.0,0.0,1.0,0.0)
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inverse(a::SU3) = SU3(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22),
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inverse(a::SU3{T}) where T <: AbstractFloat = SU3{T}(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22),
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conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23))
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conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23))
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dag(a::SU3) = inverse(a)
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dag(a::SU3{T}) where T <: AbstractFloat = inverse(a)
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tr(a::SU3) = a.u11+a.u22+conj(a.u11*a.u22 - a.u12*a.u21)
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tr(a::SU3{T}) where T <: AbstractFloat = a.u11+a.u22+conj(a.u11*a.u22 - a.u12*a.u21)
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function Base.:*(a::SU3,b::SU3)
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function Base.:*(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
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bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
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bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return SU3(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
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return SU3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
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a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
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a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
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a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33,
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a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33,
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a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31,
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a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31,
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a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32,
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a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32,
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a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33)
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a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33)
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end
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end
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function Base.:/(a::SU3,b::SU3)
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function Base.:/(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
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bu31 = (b.u12*b.u23 - b.u13*b.u22)
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bu31 = (b.u12*b.u23 - b.u13*b.u22)
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bu32 = (b.u13*b.u21 - b.u11*b.u23)
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bu32 = (b.u13*b.u21 - b.u11*b.u23)
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bu33 = (b.u11*b.u22 - b.u12*b.u21)
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bu33 = (b.u11*b.u22 - b.u12*b.u21)
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return SU3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
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return SU3{T}(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
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a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
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a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
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a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
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a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
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a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
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a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
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a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
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a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
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a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33))
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a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33))
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end
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end
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function Base.:\(a::SU3,b::SU3)
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function Base.:\(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
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au31 = (a.u12*a.u23 - a.u13*a.u22)
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au31 = (a.u12*a.u23 - a.u13*a.u22)
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au32 = (a.u13*a.u21 - a.u11*a.u23)
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au32 = (a.u13*a.u21 - a.u11*a.u23)
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@ -70,16 +69,15 @@ function Base.:\(a::SU3,b::SU3)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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|
||||||
return SU3(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + (au31)*bu31,
|
return SU3{T}(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + (au31)*bu31,
|
||||||
conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + (au31)*bu32,
|
conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + (au31)*bu32,
|
||||||
conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + (au31)*bu33,
|
conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + (au31)*bu33,
|
||||||
conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + (au32)*bu31,
|
conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + (au32)*bu31,
|
||||||
conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + (au32)*bu32,
|
conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + (au32)*bu32,
|
||||||
conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + (au32)*bu33)
|
conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + (au32)*bu33)
|
||||||
|
|
||||||
end
|
end
|
||||||
|
|
||||||
function isgroup(a::SU3)
|
function isgroup(a::SU3{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
tol = 1.0E-10
|
tol = 1.0E-10
|
||||||
g = a/a
|
g = a/a
|
||||||
|
|
@ -95,176 +93,178 @@ function isgroup(a::SU3)
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
|
|
||||||
struct SU3alg <: Algebra
|
struct SU3alg{T} <: Algebra
|
||||||
t1::Float64
|
t1::T
|
||||||
t2::Float64
|
t2::T
|
||||||
t3::Float64
|
t3::T
|
||||||
t4::Float64
|
t4::T
|
||||||
t5::Float64
|
t5::T
|
||||||
t6::Float64
|
t6::T
|
||||||
t7::Float64
|
t7::T
|
||||||
t8::Float64
|
t8::T
|
||||||
end
|
end
|
||||||
SU3alg() = SU3alg(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
|
SU3alg() = SU3alg{Float64}(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
|
||||||
function projalg(a::SU3)
|
function projalg(a::SU3{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
sr3ov2::Float64 = 0.866025403784438646763723170752
|
sr3ov2::T = 0.866025403784438646763723170752
|
||||||
|
|
||||||
ditr = ( imag(a.u11) + imag(a.u22) + 2.0*imag(a.u11*a.u22 - a.u12*a.u21) )/3.0
|
ditr = ( imag(a.u11) + imag(a.u22) + 2.0*imag(a.u11*a.u22 - a.u12*a.u21) )/3.0
|
||||||
m12 = (a.u12 - conj(a.u21))/2.0
|
m12 = (a.u12 - conj(a.u21))/2.0
|
||||||
m13 = (a.u13 - (a.u12*a.u23 - a.u13*a.u22) )/2.0
|
m13 = (a.u13 - (a.u12*a.u23 - a.u13*a.u22) )/2.0
|
||||||
m23 = (a.u23 - (a.u13*a.u21 - a.u11*a.u23) )/2.0
|
m23 = (a.u23 - (a.u13*a.u21 - a.u11*a.u23) )/2.0
|
||||||
|
|
||||||
return SU3alg(imag( m12 ), imag( m13 ), imag( m23 ),
|
return SU3alg{T}(imag( m12 ), imag( m13 ), imag( m23 ),
|
||||||
real( m12 ), real( m13 ), real( m23 ),
|
real( m12 ), real( m13 ), real( m23 ),
|
||||||
(imag(a.u11)-imag(a.u22))/2.0,
|
(imag(a.u11)-imag(a.u22))/2.0,
|
||||||
sr3ov2*(ditr))
|
sr3ov2*(ditr))
|
||||||
end
|
end
|
||||||
|
|
||||||
dot(a::SU3alg,b::SU3alg) = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3 + a.t4*b.t4 +
|
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
|
||||||
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
|
||||||
norm2(a::SU3alg) = 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)
|
||||||
norm(a::SU3alg) = 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.:+(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) = SU3alg(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) = SU3alg(-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)
|
||||||
Base.:+(a::SU3alg,b::SU3alg) = SU3alg(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)
|
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)
|
||||||
Base.:-(a::SU3alg,b::SU3alg) = SU3alg(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)
|
Base.:*(a::SU3alg{T},b::Number) where T <: AbstractFloat = SU3alg{T}(b*a.t1,b*a.t2,b*a.t3,b*a.t4,b*a.t5,b*a.t6,b*a.t7,b*a.t8)
|
||||||
Base.:*(a::SU3alg,b::Number) = SU3alg(b*a.t1,b*a.t2,b*a.t3,b*a.t4,b*a.t5,b*a.t6,b*a.t7,b*a.t8)
|
Base.:*(b::Number,a::SU3alg{T}) where T <: AbstractFloat = SU3alg{T}(b*a.t1,b*a.t2,b*a.t3,b*a.t4,b*a.t5,b*a.t6,b*a.t7,b*a.t8)
|
||||||
Base.:*(b::Number,a::SU3alg) = SU3alg(b*a.t1,b*a.t2,b*a.t3,b*a.t4,b*a.t5,b*a.t6,b*a.t7,b*a.t8)
|
Base.:/(a::SU3alg{T},b::Number) where T <: AbstractFloat = SU3alg{T}(a.t1/b,a.t2/b,a.t3/b,a.t4/b,a.t5/b,a.t6/b,a.t7/b,a.t8/b)
|
||||||
Base.:/(a::SU3alg,b::Number) = SU3alg(a.t1/b,a.t2/b,a.t3/b,a.t4/b,a.t5/b,a.t6/b,a.t7/b,a.t8/b)
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
export SU3, SU3alg, inverse, dag, tr, projalg, expm, exp, norm, norm2, isgroup
|
export SU3, SU3alg, inverse, dag, tr, projalg, expm, exp, norm, norm2, isgroup
|
||||||
|
|
||||||
struct M3x3
|
struct M3x3{T}
|
||||||
u11::ComplexF64
|
u11::Complex{T}
|
||||||
u12::ComplexF64
|
u12::Complex{T}
|
||||||
u13::ComplexF64
|
u13::Complex{T}
|
||||||
u21::ComplexF64
|
u21::Complex{T}
|
||||||
u22::ComplexF64
|
u22::Complex{T}
|
||||||
u23::ComplexF64
|
u23::Complex{T}
|
||||||
u31::ComplexF64
|
u31::Complex{T}
|
||||||
u32::ComplexF64
|
u32::Complex{T}
|
||||||
u33::ComplexF64
|
u33::Complex{T}
|
||||||
end
|
end
|
||||||
|
|
||||||
Base.:*(a::M3x3,b::M3x3) = M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
|
Base.:*(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
|
||||||
a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
|
a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
|
||||||
a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
|
a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
|
||||||
a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
|
a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
|
||||||
a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
|
a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
|
||||||
a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
|
a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
|
||||||
a.u31*b.u11 + a.u32*b.u21 + a.u33*b.u31,
|
a.u31*b.u11 + a.u32*b.u21 + a.u33*b.u31,
|
||||||
a.u31*b.u12 + a.u32*b.u22 + a.u33*b.u32,
|
a.u31*b.u12 + a.u32*b.u22 + a.u33*b.u32,
|
||||||
a.u31*b.u13 + a.u32*b.u23 + a.u33*b.u33)
|
a.u31*b.u13 + a.u32*b.u23 + a.u33*b.u33)
|
||||||
|
|
||||||
function Base.:*(a::SU3,b::M3x3)
|
function Base.:*(a::SU3{T},b::M3x3{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
a.u31 = conj(a.u12*a.u23 - a.u13*a.u22)
|
a.u31 = conj(a.u12*a.u23 - a.u13*a.u22)
|
||||||
a.u32 = conj(a.u13*a.u21 - a.u11*a.u23)
|
a.u32 = conj(a.u13*a.u21 - a.u11*a.u23)
|
||||||
a.u33 = conj(a.u11*a.u22 - a.u12*a.u21)
|
a.u33 = conj(a.u11*a.u22 - a.u12*a.u21)
|
||||||
|
|
||||||
return M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
|
return M3x3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
|
||||||
a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
|
a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
|
||||||
a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
|
a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
|
||||||
a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
|
a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
|
||||||
a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
|
a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
|
||||||
a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
|
a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
|
||||||
au31*b.u11 + au32*b.u21 + au33*b.u31,
|
au31*b.u11 + au32*b.u21 + au33*b.u31,
|
||||||
au31*b.u12 + au32*b.u22 + au33*b.u32,
|
au31*b.u12 + au32*b.u22 + au33*b.u32,
|
||||||
au31*b.u13 + au32*b.u23 + au33*b.u33)
|
au31*b.u13 + au32*b.u23 + au33*b.u33)
|
||||||
end
|
end
|
||||||
|
|
||||||
|
|
||||||
function Base.:*(a::M3x3,b::SU3)
|
function Base.:*(a::M3x3{T},b::SU3{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
|
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
|
||||||
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
|
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
|
||||||
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
|
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
|
||||||
|
|
||||||
return M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
|
return M3x3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
|
||||||
a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
|
a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
|
||||||
a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33,
|
a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33,
|
||||||
a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31,
|
a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31,
|
||||||
a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32,
|
a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32,
|
||||||
a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33,
|
a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33,
|
||||||
a.u31*b.u11 + a.u32*b.u21 + a.u33*bu31,
|
a.u31*b.u11 + a.u32*b.u21 + a.u33*bu31,
|
||||||
a.u31*b.u12 + a.u32*b.u22 + a.u33*bu32,
|
a.u31*b.u12 + a.u32*b.u22 + a.u33*bu32,
|
||||||
a.u31*b.u13 + a.u32*b.u23 + a.u33*bu33)
|
a.u31*b.u13 + a.u32*b.u23 + a.u33*bu33)
|
||||||
end
|
end
|
||||||
|
|
||||||
function Base.:/(a::M3x3,b::SU3)
|
function Base.:/(a::M3x3{T},b::SU3{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
bu31 = (b.u12*b.u23 - b.u13*b.u22)
|
bu31 = (b.u12*b.u23 - b.u13*b.u22)
|
||||||
bu32 = (b.u13*b.u21 - b.u11*b.u23)
|
bu32 = (b.u13*b.u21 - b.u11*b.u23)
|
||||||
bu33 = (b.u11*b.u22 - b.u12*b.u21)
|
bu33 = (b.u11*b.u22 - b.u12*b.u21)
|
||||||
|
|
||||||
return M3x3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
|
return M3x3{T}(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
|
||||||
a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
|
a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
|
||||||
a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
|
a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
|
||||||
a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
|
a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
|
||||||
a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
|
a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
|
||||||
a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33),
|
a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33),
|
||||||
a.u31*conj(b.u11) + a.u32*conj(b.u12) + a.u33*conj(b.u13),
|
a.u31*conj(b.u11) + a.u32*conj(b.u12) + a.u33*conj(b.u13),
|
||||||
a.u31*conj(b.u21) + a.u32*conj(b.u22) + a.u33*conj(b.u23),
|
a.u31*conj(b.u21) + a.u32*conj(b.u22) + a.u33*conj(b.u23),
|
||||||
a.u31*(bu31) + a.u32*(bu32) + a.u33*(bu33))
|
a.u31*(bu31) + a.u32*(bu32) + a.u33*(bu33))
|
||||||
end
|
end
|
||||||
|
|
||||||
Base.:*(a::Number,b::M3x3) = M3x3(a*b.u11, a*b.u12, a*bu13,
|
Base.:*(a::Number,b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a*b.u11, a*b.u12, a*bu13,
|
||||||
a*b.u21, a*b.u22, a*bu23,
|
a*b.u21, a*b.u22, a*bu23,
|
||||||
a*b.u31, a*b.u32, a*bu33)
|
a*b.u31, a*b.u32, a*bu33)
|
||||||
|
|
||||||
Base.:*(b::M3x3,a::Number) = M3x3(a*b.u11, a*b.u12, a*bu13,
|
Base.:*(b::M3x3{T},a::Number) where T <: AbstractFloat = M3x3{T}(a*b.u11, a*b.u12, a*bu13,
|
||||||
a*b.u21, a*b.u22, a*bu23,
|
a*b.u21, a*b.u22, a*bu23,
|
||||||
a*b.u31, a*b.u32, a*bu33)
|
a*b.u31, a*b.u32, a*bu33)
|
||||||
|
|
||||||
Base.:+(a::M3x3,b::M3x3) = M3x3(a.u11+b.u11, a.u12+b.u12, a.u13+bu13,
|
Base.:+(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11+b.u11, a.u12+b.u12, a.u13+bu13,
|
||||||
a.u21+b.u21, a.u22+b.u22, a.u23+bu23,
|
a.u21+b.u21, a.u22+b.u22, a.u23+bu23,
|
||||||
a.u31+b.u31, a.u32+b.u32, a.u33+bu33)
|
a.u31+b.u31, a.u32+b.u32, a.u33+bu33)
|
||||||
|
|
||||||
Base.:-(a::M3x3,b::M3x3) = M3x3(a.u11-b.u11, a.u12-b.u12, a.u13-bu13,
|
Base.:-(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11-b.u11, a.u12-b.u12, a.u13-bu13,
|
||||||
a.u21-b.u21, a.u22-b.u22, a.u23-bu23,
|
a.u21-b.u21, a.u22-b.u22, a.u23-bu23,
|
||||||
a.u31-b.u31, a.u32-b.u32, a.u33-bu33)
|
a.u31-b.u31, a.u32-b.u32, a.u33-bu33)
|
||||||
|
|
||||||
Base.:-(b::M3x3) = M3x3(-b.u11, -b.u12, -bu13,
|
Base.:-(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(-b.u11, -b.u12, -bu13,
|
||||||
-b.u21, -b.u22, -bu23,
|
-b.u21, -b.u22, -bu23,
|
||||||
-b.u31, -b.u32, -bu33)
|
-b.u31, -b.u32, -bu33)
|
||||||
|
|
||||||
Base.:+(b::M3x3) = M3x3(b.u11, b.u12, bu13,
|
Base.:+(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(b.u11, b.u12, bu13,
|
||||||
b.u21, b.u22, bu23,
|
b.u21, b.u22, bu23,
|
||||||
b.u31, b.u32, bu33)
|
b.u31, b.u32, bu33)
|
||||||
|
|
||||||
|
|
||||||
function alg2mat(a::SU3alg)
|
function alg2mat(a::SU3alg{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
x8p = a.t8/3.46410161513775458
|
two::T = 2.0
|
||||||
x7p = a.t7/2.0
|
rct::T = 3.46410161513775458
|
||||||
u11 = complex(0.0, x7p + x8p)
|
|
||||||
u22 = complex(0.0,-x7p + x8p)
|
|
||||||
u33 = complex(0.0,-2.0*x8p)
|
|
||||||
u12 = complex(a.t4,a.t1)/2.0
|
|
||||||
u13 = complex(a.t5,a.t2)/2.0
|
|
||||||
u23 = complex(a.t6,a.t3)/2.0
|
|
||||||
u21 = -conj(u12)
|
|
||||||
u31 = -conj(u13)
|
|
||||||
u32 = -conj(u23)
|
|
||||||
|
|
||||||
return M3x3(u11,u12,u13, u21,u22,u23, u31,u32,u33)
|
x8p::T = a.t8/rct
|
||||||
|
x7p::T = a.t7/two
|
||||||
|
u11::Complex{T} = complex(0.0, x7p + x8p)
|
||||||
|
u22::Complex{T} = complex(0.0,-x7p + x8p)
|
||||||
|
u33::Complex{T} = complex(0.0,-2.0*x8p)
|
||||||
|
u12::Complex{T} = complex(a.t4,a.t1)/two
|
||||||
|
u13::Complex{T} = complex(a.t5,a.t2)/two
|
||||||
|
u23::Complex{T} = complex(a.t6,a.t3)/two
|
||||||
|
u21::Complex{T} = -conj(u12)
|
||||||
|
u31::Complex{T} = -conj(u13)
|
||||||
|
u32::Complex{T} = -conj(u23)
|
||||||
|
|
||||||
|
return M3x3{T}(u11,u12,u13, u21,u22,u23, u31,u32,u33)
|
||||||
end
|
end
|
||||||
|
|
||||||
@inline function exp_iter(dch::ComplexF64, tch::Float64)
|
@inline function exp_iter(dch::Complex{T}, tch::T) where T <: AbstractFloat
|
||||||
|
|
||||||
c = ( 1.957294106339126128e-20, 4.110317623312164853e-19,
|
c::NTuple{22, T} = ( 1.957294106339126128e-20, 4.110317623312164853e-19,
|
||||||
8.220635246624329711e-18, 1.561920696858622643e-16,
|
8.220635246624329711e-18, 1.561920696858622643e-16,
|
||||||
2.811457254345520766e-15, 4.779477332387385293e-14,
|
2.811457254345520766e-15, 4.779477332387385293e-14,
|
||||||
7.647163731819816473e-13, 1.147074559772972473e-11,
|
7.647163731819816473e-13, 1.147074559772972473e-11,
|
||||||
1.605904383682161451e-10, 2.087675698786809894e-09,
|
1.605904383682161451e-10, 2.087675698786809894e-09,
|
||||||
2.505210838544171879e-08, 2.755731922398589067e-07,
|
2.505210838544171879e-08, 2.755731922398589067e-07,
|
||||||
2.755731922398589065e-06, 2.480158730158730158e-05,
|
2.755731922398589065e-06, 2.480158730158730158e-05,
|
||||||
1.984126984126984127e-04, 1.388888888888888888e-03,
|
1.984126984126984127e-04, 1.388888888888888888e-03,
|
||||||
8.333333333333333333e-03, 4.166666666666666666e-02,
|
8.333333333333333333e-03, 4.166666666666666666e-02,
|
||||||
1.666666666666666666e-01, 0.5, 1.0, 1.0 )
|
1.666666666666666666e-01, 0.5, 1.0, 1.0 )
|
||||||
|
|
||||||
q0 = complex(c[1])
|
q0 = complex(c[1])
|
||||||
q1 = complex(0.0)
|
q1 = complex(0.0)
|
||||||
|
|
@ -281,78 +281,78 @@ end
|
||||||
end
|
end
|
||||||
|
|
||||||
|
|
||||||
function expm(g::SU3, a::SU3alg, t::Number)
|
function expm(g::SU3{T}, a::SU3alg{T}, t::Number) where T <: AbstractFloat
|
||||||
|
|
||||||
tpw = t^2
|
tpw = t^2
|
||||||
M = alg2mat(a)
|
M = alg2mat(a)
|
||||||
Msq = M*M
|
Msq = M*M
|
||||||
dch = tpw*t*(M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
dch::Complex{T} = tpw*t*(M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
||||||
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
||||||
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31)
|
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31)
|
||||||
tch = -tpw*(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
tch::T = -tpw*(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
||||||
|
|
||||||
q0, q1, q2 = exp_iter(dch, tch)
|
q0, q1, q2 = exp_iter(dch, tch)
|
||||||
|
|
||||||
q1 = t*q1
|
q1 = t*q1
|
||||||
q2 = tpw*q2
|
q2 = tpw*q2
|
||||||
|
|
||||||
g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
g2 = SU3{T}(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
||||||
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
||||||
|
|
||||||
return g2*g
|
return g2*g
|
||||||
end
|
end
|
||||||
|
|
||||||
function expm(g::SU3, a::SU3alg)
|
function expm(g::SU3{T}, a::SU3alg{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
M = alg2mat(a)
|
M = alg2mat(a)
|
||||||
Msq = M*M
|
Msq = M*M
|
||||||
dch = M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
dch::Complex{T} = M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
||||||
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
||||||
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31
|
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31
|
||||||
tch = -(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
tch::T = -(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
||||||
|
|
||||||
q0, q1, q2 = exp_iter(dch, tch)
|
q0, q1, q2 = exp_iter(dch, tch)
|
||||||
|
|
||||||
g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
g2 = SU3{T}(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
||||||
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
||||||
|
|
||||||
return g2*g
|
return g2*g
|
||||||
end
|
end
|
||||||
|
|
||||||
function Base.exp(a::SU3alg)
|
function Base.exp(a::SU3alg{T}) where T <: AbstractFloat
|
||||||
|
|
||||||
M = alg2mat(a)
|
M = alg2mat(a)
|
||||||
Msq = M*M
|
Msq = M*M
|
||||||
dch = M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
dch::Complex{T} = M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
||||||
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
||||||
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31
|
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31
|
||||||
tch = -(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
tch::T = -(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
||||||
|
|
||||||
q0, q1, q2 = exp_iter(dch, tch)
|
q0, q1, q2 = exp_iter(dch, tch)
|
||||||
|
|
||||||
g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
g2 = SU3{T}(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
||||||
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
||||||
|
|
||||||
return g2
|
return g2
|
||||||
end
|
end
|
||||||
|
|
||||||
function Base.exp(a::SU3alg, t::Number)
|
function Base.exp(a::SU3alg{T}, t::Number) where T <: AbstractFloat
|
||||||
|
|
||||||
tpw = t^2
|
tpw = t^2
|
||||||
M = alg2mat(a)
|
M = alg2mat(a)
|
||||||
Msq = M*M
|
Msq = M*M
|
||||||
dch = tpw*t*(M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
dch::Complex{T} = tpw*t*(M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
|
||||||
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
|
||||||
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31)
|
M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31)
|
||||||
tch = -tpw*(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
tch::T = -tpw*(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
|
||||||
|
|
||||||
q0, q1, q2 = exp_iter(dch, tch)
|
q0, q1, q2 = exp_iter(dch, tch)
|
||||||
|
|
||||||
q1 = t*q1
|
q1 = t*q1
|
||||||
q2 = tpw*q2
|
q2 = tpw*q2
|
||||||
|
|
||||||
g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
g2 = SU3{T}(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
|
||||||
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
|
||||||
|
|
||||||
return g2
|
return g2
|
||||||
end
|
end
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue