lattice/latticegpu.jl
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Working HMC for one scalar coupled to SU(2)

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This commit is contained in:
Alberto Ramos 2021-10-13 14:17:34 +02:00
parent bd88c213d7
commit 4f9ddb7026
7 changed files with 192 additions and 34 deletions
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139
tests/test_SU2.jl
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@ -50,3 +50,142 @@ println(mp)
println(projalg(mp))
println(projalg(ga))
println("## HERE test SU(2) fundamental")
a = rand(SU2fund{T})
println(a)
ft(x) = LatticeGPU.dot(x,x)
f2(x) = LatticeGPU.tr(dag(x)*x)
f3(x) = LatticeGPU.norm2(x)
S = ft(a)
println("Check 1: ", S)
S = f2(a)
println("Check 2: ", S)
S = f3(a)
println("Check 3: ", S)
h = 0.000001
xh = SU2fund{T}(a.t1+h, a.t2)
Sp = ft(xh)
xh = SU2fund{T}(a.t1-h, a.t2)
Sm = ft(xh)
println("Numerical derivative: ", (Sp-Sm)/(2*h))
xh = SU2fund{T}(a.t1, a.t2+h)
Sp = ft(xh)
xh = SU2fund{T}(a.t1, a.t2-h)
Sm = ft(xh)
println("Numerical derivative: ", (Sp-Sm)/(2*h))
h = 0.000001im
xh = SU2fund{T}(a.t1+h, a.t2)
Sp = ft(xh)
xh = SU2fund{T}(a.t1-h, a.t2)
Sm = ft(xh)
println("Numerical derivative: ", 1im * (Sp-Sm)/(2*h))
xh = SU2fund{T}(a.t1, a.t2+h)
Sp = ft(xh)
xh = SU2fund{T}(a.t1, a.t2-h)
Sm = ft(xh)
println("Numerical derivative: ", 1im * (Sp-Sm)/(2*h))
ad = a
println("Exact derivative: ", ad)
println("## Hamiltonian dynamics")
println(" # Mass terms")
H(p,a) = LatticeGPU.norm2(p)/2 + LatticeGPU.norm2(a)
function MD!(p, a, ns, ee)
for i in 1:ns
p = p - ee*a
a = a + ee*p
p = p - ee*a
end
return p, a
end
a = rand(SU2fund{T})
p = rand(SU2fund{T})
println(H(p,a))
ee = 0.0001
ns = 10000
p, a = MD!(p, a, ns, ee)
println(H(p,a))
println(" # Interaction terms")
H(p,a, M,kap) = LatticeGPU.norm2(p)/2 - (2*kap)*LatticeGPU.dot(a, M)
function MD!(p, a, M, kap, ns, ee)
for i in 1:ns
p = p + 0.5*( (2*kap)*ee*M )
a = a + ee*p
p = p + 0.5*( (2*kap)*ee*M )
end
return p, a
end
a = rand(SU2fund{T})
p = rand(SU2fund{T})
M = rand(SU2fund{T})
kap = 0.5
println(H(p,a, M,kap))
ee = 0.0001
ns = 10000
p, a = MD!(p, a, M,kap, ns, ee)
println(H(p,a, M,kap))
println(" # Gauge Interaction terms")
H(p,a, M,kap) = LatticeGPU.norm2(p)/2 - (2*kap)*LatticeGPU.tr(a*M)
function MD!(p, a, M, kap, ns, ee)
for i in 1:ns
p = p + 0.5*( - (2*kap)*ee*projalg(a*M) )
a = expm(a, p, ee)
p = p + 0.5*( - (2*kap)*ee*projalg(a*M) )
end
return p, a
end
a = rand(SU2{T})
p = rand(SU2alg{T})
M = rand(SU2fund{T})
#M = SU2fund{T}(0.0+rand()im, rand()+rand()im)
kap = 1.1
println(H(p,a, M,kap))
ee = 0.0001
ns = 10000
p, a = MD!(p, a, M,kap, ns, ee)
println(H(p,a, M,kap))
println(" # Gauge Interaction terms")
H(p,a, M1,M2,kap) = LatticeGPU.norm2(p)/2 - (2*kap)*LatticeGPU.dot(M1,a*M2)
#H(p,a, M1,M2,kap) = LatticeGPU.norm2(p)/2 - (2*kap)*LatticeGPU.tr(a*(M2*dag(M1)))
function MD!(p, a, M1, M2, kap, ns, ee)
for i in 1:ns
p = p + 0.5*( - (2*kap)*ee*projalg(a*M2*dag(M1)) )
a = expm(a, p, ee)
p = p + 0.5*( - (2*kap)*ee*projalg(a*M2*dag(M1)) )
end
return p, a
end
a = rand(SU2{T})
p = rand(SU2alg{T})
M1 = rand(SU2fund{T})
M2 = rand(SU2fund{T})
#M = SU2fund{T}(0.0+rand()im, rand()+rand()im)
kap = 1.1
println(H(p,a, M1,M2,kap))
ee = 0.0001
ns = 10000
p, a = MD!(p, a, M1,M2,kap, ns, ee)
println(H(p,a, M1,M2,kap))