Non-seg-fault HMC. Energy not conserved.

This commit is contained in:
Alberto Ramos 2021-07-17 18:43:33 +02:00
parent 5bb4f28c8b
commit f296fd9768
8 changed files with 172 additions and 40 deletions

View file

@ -13,8 +13,9 @@
# SU(2) group elements represented trough Cayley-Dickson
# construction
# https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction
using CUDA
import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\
import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\,Base.exp
struct SU2 <: Group
t1::ComplexF64
t2::ComplexF64
@ -23,7 +24,8 @@ 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))
tr(g::SU2) = 2.0*real(a.t1)
norm2(a::SU2) = abs2(a.t1) + abs2(a.t2)
tr(g::SU2) = complex(2.0*real(g.t1), 0.0)
"""
function normalize(a::SU2)
@ -55,14 +57,16 @@ 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)
Base.:*(a::SU2alg,b::Real) = SU2alg(a.t1*b,a.t2*b,a.t3*b)
Base.:*(b::Real,a::SU2alg) = SU2alg(a.t1*b,a.t2*b,a.t3*b)
Base.:/(a::SU2alg,b::Real) = 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.:*(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)
"""
@ -78,11 +82,13 @@ function Base.exp(a::SU2alg)
ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
sa = 0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0))
else
ca = cos(rm)
sa = sin(rm)/(2.0*rm)
ca = CUDA.cos(rm)
sa = CUDA.sin(rm)/(2.0*rm)
end
return SU2(complex(ca,sa*a.t1),complex(sa*a.t2,sa*a.t3))
t1 = complex(ca,sa*a.t1)
t2 = complex(sa*a.t2,sa*a.t3)
return SU2(t1,t2)
end
function Base.exp(a::SU2alg, t::Number)
@ -93,11 +99,13 @@ function Base.exp(a::SU2alg, t::Number)
ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
sa = t*(0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0)))
else
ca = cos(rm)
sa = t*sin(rm)/(2.0*rm)
ca = CUDA.cos(rm)
sa = t*CUDA.sin(rm)/(2.0*rm)
end
return SU2(complex(ca,sa*a.t1),complex(sa*a.t2,sa*a.t3))
t1 = complex(ca,sa*a.t1)
t2 = complex(sa*a.t2,sa*a.t3)
return SU2(t1,t2)
end
@ -115,12 +123,13 @@ function expm(g::SU2, a::SU2alg)
ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
sa = 0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0))
else
ca = cos(rm)
sa = sin(rm)/(2.0*rm)
ca = CUDA.cos(rm)
sa = CUDA.sin(rm)/(2.0*rm)
end
return SU2(complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2),
complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1))
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)
end
"""
@ -137,10 +146,12 @@ function expm(g::SU2, a::SU2alg, t::Float64)
ca = 1.0 - rms *(1.0 - (rms/6.0 )*(1.0 - rms/15.0))
sa = t*(0.5 - rms/6.0*(1.0 - (rms/10.0)*(1.0 - rms/21.0)))
else
ca = cos(rm)
sa = t*sin(rm)/(2.0*rm)
ca = CUDA.cos(rm)
sa = t*CUDA.sin(rm)/(2.0*rm)
end
return SU2(complex(ca,sa*a.t1)*g.t1-complex(sa*a.t2,sa*a.t3)*conj(g.t2),
complex(ca,sa*a.t1)*g.t2+complex(sa*a.t2,sa*a.t3)*conj(g.t1))
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)
end

View file

@ -17,7 +17,8 @@ abstract type Algebra end
include("GroupSU2.jl")
export SU2, SU2alg, dag, normalize, inverse, tr, projalg, norm
export Group, Algebra
export SU2, SU2alg, dag, normalize, inverse, tr, projalg, norm, norm2
export dot, expm, exp
include("GroupSU3.jl")