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Added documentation fro Groups module

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This commit is contained in:
Alberto Ramos 2023-01-31 15:52:19 +01:00
parent 63ff01a2be
commit 208d03d245
11 changed files with 294 additions and 31 deletions
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33
src/Groups/GroupSU2.jl
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@ -16,15 +16,39 @@
using CUDA, Random
SU2(a::T, b::T) where T <: AbstractFloat = SU2{T}(complex(a), complex(b))
"""
inverse(g::T) where T <: Group
Returns the group inverse of `g`.
"""
inverse(b::SU2{T}) where T <: AbstractFloat = SU2{T}(conj(b.t1), -b.t2)
"""
dag(g::T) where T <: Group
Returns the group inverse of `g`.
"""
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)
"""
tr(g::T) where T <: Group
Returns the trace of the groups element `g`.
"""
tr(g::SU2{T}) where T <: AbstractFloat = complex(2*real(g.t1), 0.0)
"""
dev_one(T) where T <: Group
Returns the distance to the unit group element
"""
dev_one(g::SU2{T}) where T <: AbstractFloat = sqrt(( abs2(g.t1 - one(T)) + abs2(g.t2))/2)
"""
function unitarize(a::T) where {T <: Group}
unitarize(a::T) where {T <: Group}
Return a unitarized element of the group.
"""
@ -40,6 +64,11 @@ Base.:*(a::SU2{T},b::SU2{T}) where T <: AbstractFloat = SU2{T}(a.t1*b.t1-a.t2*co
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))
"""
isgroup(g::T) where T <: Group
Returns `true` if `g` is a group element, `false` otherwise.
"""
function isgroup(a::SU2{T}) where T <: AbstractFloat
tol = 1.0E-10
if (abs2(a.t1) + abs2(a.t2) - 1.0 < 1.0E-10)