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Groups SU(2) and SU(3) working for arbitrary precision

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This commit is contained in:
Alberto Ramos 2021-09-04 17:40:15 +02:00
parent 76d0b66b4b
commit 1416efdbee
2 changed files with 219 additions and 222 deletions
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85
src/Groups/GroupSU2.jl
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@ -16,59 +16,56 @@
using CUDA
import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp
struct SU2 <: Group
t1::ComplexF64
t2::ComplexF64
struct SU2{T} <: Group
t1::Complex{T}
t2::Complex{T}
end
SU2() = SU2(1.0, 0.0)
inverse(b::SU2) = SU2(conj(b.t1), -b.t2)
dag(a::SU2) = inverse(a)
norm(a::SU2) = sqrt(abs2(a.t1) + abs2(a.t2))
norm2(a::SU2) = abs2(a.t1) + abs2(a.t2)
tr(g::SU2) = complex(2.0*real(g.t1), 0.0)
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)
"""
function normalize(a::SU2)
Return a normalized element of `SU(2)`
"""
function normalize(a::SU2)
function normalize(a::SU2{T}) where T <: AbstractFloat
dr = sqrt(abs2(a.t1) + abs2(a.t2))
if (dr == 0.0)
return SU2(0.0)
end
return SU2(a.t1/dr,a.t2/dr)
return SU2{T}(a.t1/dr,a.t2/dr)
end
Base.:+(a::SU2,b::SU2) = SU2(a.t1+b.t1,a.t2+b.t2)
Base.:-(a::SU2,b::SU2) = SU2(a.t1-b.t1,a.t2-b.t2)
Base.:*(a::SU2,b::SU2) = SU2(a.t1*b.t1-a.t2*conj(b.t2),a.t1*b.t2+a.t2*conj(b.t1))
Base.:/(a::SU2,b::SU2) = SU2(a.t1*conj(b.t1)+a.t2*conj(b.t2),-a.t1*b.t2+a.t2*b.t1)
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))
Base.:+(a::SU2) = SU2(a.t1,a.t2)
Base.:-(a::SU2) = SU2(-a.t1,-a.t2)
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))
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)
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))
struct SU2alg <: Algebra
t1::Float64
t2::Float64
t3::Float64
struct SU2alg{T} <: Algebra
t1::T
t2::T
t3::T
end
SU2alg(x::Real) = SU2alg(x,0.0,0.0)
SU2alg(v::Vector) = SU2alg(v[1],v[2],v[3])
projalg(g::SU2) = SU2alg(imag(g.t1), real(g.t2), imag(g.t2))
dot(a::SU2alg, b::SU2alg) = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3
norm(a::SU2alg) = sqrt(a.t1^2 + a.t2^2 + a.t3^2)
norm2(a::SU2alg) = a.t1^2 + a.t2^2 + a.t3^2
Base.:+(a::SU2alg) = SU2alg(a.t1,a.t2,a.t3)
Base.:-(a::SU2alg) = SU2alg(-a.t1,-a.t2,-a.t3)
Base.:+(a::SU2alg,b::SU2alg) = SU2alg(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3)
Base.:-(a::SU2alg,b::SU2alg) = SU2alg(a.t1-b.t1,a.t2-b.t2,a.t3-b.t3)
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))
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.:+(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)
Base.:-(a::SU2alg{T},b::SU2alg{T}) where T <: AbstractFloat = SU2alg{T}(a.t1-b.t1,a.t2-b.t2,a.t3-b.t3)
Base.:*(a::SU2alg,b::Number) = SU2alg(a.t1*b,a.t2*b,a.t3*b)
Base.:*(b::Number,a::SU2alg) = SU2alg(a.t1*b,a.t2*b,a.t3*b)
Base.:/(a::SU2alg,b::Number) = SU2alg(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)
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 isgroup(a::SU2)
function isgroup(a::SU2{T}) where T <: AbstractFloat
tol = 1.0E-10
if (abs2(a.t1) + abs2(a.t2) - 1.0 < 1.0E-10)
return true
@ -82,7 +79,7 @@ end
Computes `exp(a)`
"""
function Base.exp(a::SU2alg)
function Base.exp(a::SU2alg{T}) where T <: AbstractFloat
rm = sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
if (abs(rm) < 0.05)
@ -96,10 +93,10 @@ function Base.exp(a::SU2alg)
t1 = complex(ca,sa*a.t1)
t2 = complex(sa*a.t2,sa*a.t3)
return SU2(t1,t2)
return SU2{T}(t1,t2)
end
function Base.exp(a::SU2alg, t::Number)
function Base.exp(a::SU2alg{T}, t::T) where T <: AbstractFloat
rm = t*sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
if (abs(rm) < 0.05)
@ -113,7 +110,7 @@ function Base.exp(a::SU2alg, t::Number)
t1 = complex(ca,sa*a.t1)
t2 = complex(sa*a.t2,sa*a.t3)
return SU2(t1,t2)
return SU2{T}(t1,t2)
end
@ -123,7 +120,7 @@ end
Computes `exp(a)*g`
"""
function expm(g::SU2, a::SU2alg)
function expm(g::SU2{T}, a::SU2alg{T}) where T <: AbstractFloat
rm = sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
if (abs(rm) < 0.05)
@ -137,7 +134,7 @@ function expm(g::SU2, a::SU2alg)
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)
return SU2(t1,t2)
return SU2{T}(t1,t2)
end
"""
@ -146,7 +143,7 @@ end
Computes `exp(t*a)*g`
"""
function expm(g::SU2, a::SU2alg, t::Float64)
function expm(g::SU2{T}, a::SU2alg{T}, t::T) where T <: AbstractFloat
rm = t*sqrt( a.t1^2+a.t2^2+a.t3^2 )/2.0
if (abs(rm) < 0.05)
@ -160,7 +157,7 @@ function expm(g::SU2, a::SU2alg, t::Float64)
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)
return SU2(t1,t2)
return SU2{T}(t1,t2)
end