Master

src/Dirac/Dirac.jl

@@ -54,15 +54,31 @@ struct DiracWorkspace{T}
     
     function DiracWorkspace(::Type{G}, ::Type{T}, lp::SpaceParm{4,6,B,D}) where {G,T <: AbstractFloat, B,D}
 
+        @timeit "Allocating DiracWorkspace" begin
+            if G == SU3fund
+                sr  = scalar_field(Spinor{4,SU3fund{T}}, lp)
+                sp  = scalar_field(Spinor{4,SU3fund{T}}, lp)
+                sAp = scalar_field(Spinor{4,SU3fund{T}}, lp)
+                st  = scalar_field(Spinor{4,SU3fund{T}}, lp)
+                csw = tensor_field(U3alg{T},lp)
+            elseif G == SU2fund
+                sr  = scalar_field(Spinor{4,SU2fund{T}}, lp)
+                sp  = scalar_field(Spinor{4,SU2fund{T}}, lp)
+                sAp = scalar_field(Spinor{4,SU2fund{T}}, lp)
+                st  = scalar_field(Spinor{4,SU2fund{T}}, lp)
+                csw = tensor_field(U2alg{T},lp)
+            else
                 sr  = scalar_field(Spinor{4,G}, lp)
                 sp  = scalar_field(Spinor{4,G}, lp)
                 sAp = scalar_field(Spinor{4,G}, lp)
                 st  = scalar_field(Spinor{4,G}, lp)
-
+                csw = nothing
-        csw = tensor_field(U3alg{T},lp)
-
-        return new{T}(sr,sp,sAp,st,csw,cs)
             end
+        end
+
+        return new{T}(sr,sp,sAp,st,csw)
+        end
+
 end
 
 export DiracWorkspace, DiracParam

src/Groups/AlgebraU2.jl

@@ -0,0 +1,20 @@
+
+
+
+struct U2alg{T} <: Algebra
+    u11::T
+    u22::T
+    u12::Complex{T}
+end
+
+function antsym(a::SU2{T}) where T <: AbstractFloat
+    return U2alg{T}(2.0*imag(a.t1),-2.0*imag(a.t1),2.0*a.t2)
+end
+
+Base.:*(a::U2alg{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(im*a.u11*b.t1 + a.u12*b.t2,
+                                                                        -conj(a.u12)*b.t1 + im*a.u22*b.t2)
+
+Base.:+(a::U2alg{T},b::U2alg{T}) where T <: AbstractFloat = U2alg{T}(a.u11 + b.u11, a.u22 + b.u22, a.u12 + b.u12)
+
+Base.:*(r::Number, a::U2alg{T}) where T <: AbstractFloat = U2alg{T}(r*a.u11, r*a.u22, r*a.u12)
+

src/Groups/FundamentalSU2.jl

@@ -0,0 +1,72 @@
+
+
+
+SU2fund(a::T, b::T)          where T <: AbstractFloat = SU2fund{T}(complex(a), complex(b))
+
+"""
+    dag(a::SU2fund{T})
+
+Returns the conjugate of a fundamental element. 
+"""
+dag(a::SU2fund{T})                 where T <: AbstractFloat = SU2fund{T}(conj(a.t1), conj(a.t2))
+
+"""
+    norm(a::SU2fund{T})
+
+Returns the norm of a fundamental element. Same result as dot(a,a).
+"""
+norm(a::SU2fund{T})                where T <: AbstractFloat = sqrt((abs2(a.t1) + abs2(a.t2)))
+
+"""
+    norm(a::SU2fund{T})
+
+Returns the norm of a fundamental element. Same result as sqrt(dot(a,a)).
+"""
+norm2(a::SU2fund{T})               where T <: AbstractFloat = (abs2(a.t1) + abs2(a.t2))
+
+"""
+    dot(a::SU2fund{T},b::SU2fund{T})
+
+Returns the scalar product of two fundamental elements. The convention is for the product to the linear in the second argument, and anti-linear in the first argument. 
+"""
+dot(g1::SU2fund{T},g2::SU2fund{T}) where T <: AbstractFloat = conj(g1.t1)*g2.t1+conj(g1.t2)*g2.t2
+
+"""
+    *(g::SU2{T},b::SU2fund{T})
+
+Returns ga
+"""
+Base.:*(g::SU2{T},b::SU2fund{T})     where T <: AbstractFloat = SU2fund{T}(g.t1*b.t1 + g.t2*b.t2,-conj(g.t2)*b.t1 + conj(g.t1)*b.t2)
+                                                                           
+"""
+    \\(g::SU2{T},b::SU2fund{T})
+
+Returns g^dag b
+"""
+Base.:\(g::SU2{T},b::SU2fund{T})     where T <: AbstractFloat = SU2fund{T}(conj(g.t1)*b.t1 - g.t2 * b.t2,conj(g.t2)*b.t1 + g.t1 * b.t2)
+
+"""
+    *(a::SU2alg{T},b::SU2fund{T})
+
+Returns a*b
+"""
+
+Base.:*(a::SU2alg{T},b::SU2fund{T})     where T <: AbstractFloat = SU2fund{T}(complex(0.0, a.t3)*b.t1/2 +  complex(a.t2,a.t1)*b.t2/2,
+                                                                              complex(-a.t2,a.t1)*b.t1/2 + complex(0.0, -a.t3)*b.t1/2)
+
+Base.:+(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1+b.t1,a.t2+b.t2)
+Base.:-(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1-b.t1,a.t2-b.t2)
+Base.:+(a::SU2fund{T})               where T <: AbstractFloat = SU2fund{T}(a.t1,a.t2)
+Base.:-(a::SU2fund{T})               where T <: AbstractFloat = SU2fund{T}(-a.t1,-a.t2)
+imm(a::SU2fund{T})                   where T <: AbstractFloat = SU2fund{T}(complex(-imag(a.t1),real(a.t1)),
+                                                                           complex(-imag(a.t2),real(a.t2)))
+mimm(a::SU2fund{T})                  where T <: AbstractFloat = SU2fund{T}(complex(imag(a.t1),-real(a.t1)),
+                                                                           complex(imag(a.t2),-real(a.t2)))
+
+# Operations with numbers
+Base.:*(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
+Base.:*(b::Number,a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
+Base.:/(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(a.t1/b,a.t2/b)
+
+Base.:*(a::M2x2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.u11*b.t1 + a.u12*b.t2,
+                                                                        a.u21*b.t1 + a.u22*b.t2)

src/Groups/Groups.jl

@@ -54,11 +54,12 @@ export Group, Algebra, GMatrix
 # SU(2) and 2x2 matrix operations
 ##
 include("SU2Types.jl")
-export SU2, SU2alg, M2x2
+export SU2, SU2alg, M2x2, SU2fund
 
 include("GroupSU2.jl")
 include("M2x2.jl")
 include("AlgebraSU2.jl")
+include("FundamentalSU2.jl")
 ## END SU(2)
 
 ##
@@ -74,8 +75,10 @@ include("FundamentalSU3.jl")
 export imm, mimm
 ## END SU(3)
 
+
+include("AlgebraU2.jl")
 include("AlgebraU3.jl")
-export U3alg
+export U2alg, U3alg
 
 include("GroupU1.jl")
 export U1, U1alg

src/Groups/SU2Types.jl

@@ -53,3 +53,13 @@ Base.convert(::Type{M2x2{T}}, a::SU2{T}) where T = M2x2{T}(a.t1,a.t2,-conj(a.t2)
 
 Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))
 Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}})    where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)))
+
+
+struct SU2fund{T}
+    t1::Complex{T}
+    t2::Complex{T}
+end
+
+Base.zero(::Type{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(zero(T),zero(T),zero(T))
+Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(complex(randn(rng,T),randn(rng,T)),
+                                                                                                      complex(randn(rng,T),randn(rng,T)))

src/LatticeGPU.jl

@@ -16,7 +16,7 @@ include("Groups/Groups.jl")
 
 using .Groups
 export Group, Algebra, GMatrix
-export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg, SU3fund, U3alg
+export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg, SU3fund, U3alg, SU2fund, U2alg
 export dot, expm, exp, dag, unitarize, inverse, tr, projalg, norm, norm2, isgroup, alg2mat, dev_one, antsym
 
 include("Space/Space.jl")

test/dirac/test_fp_fa.jl

@@ -14,7 +14,7 @@ lp = SpaceParm{4}(size,(4,4,4,4),1,(0,0,0,0,0,0));
 exptheta = exp.(im.*theta./lp.iL);
 
 dpar = DiracParam{Float64}(SU3fund,m,0.0,exptheta,1.0);
-dws = DiracWorkspace(SU3fund{Float64},Float64,lp);
+dws = DiracWorkspace(SU3fund,Float64,lp);
 
 U = fill!(vector_field(SU3{Float64},lp),one(SU3{Float64}));
 psi = scalar_field(Spinor{4,SU3fund{Float64}},lp);
@@ -66,7 +66,7 @@ function fA_test(;theta = (0.5,0.7,1.0,0.0), m = 1.3, size = (8,8,8,16),prec = 1
     exptheta = exp.(im.*theta./lp.iL);
     
     dpar = DiracParam{Float64}(SU3fund,m,0.0,exptheta,1.0);
-    dws = DiracWorkspace(SU3fund{Float64},Float64,lp);
+    dws = DiracWorkspace(SU3fund,Float64,lp);
     
     U = fill!(vector_field(SU3{Float64},lp),one(SU3{Float64}));
     psi = scalar_field(Spinor{4,SU3fund{Float64}},lp);

test/dirac/test_solver_plw.jl

@@ -8,7 +8,7 @@ function Dwpw_test(;p=0,s=1,c=1)
 lp = SpaceParm{4}((16,16,16,16), (4,4,4,4), 0, (0,0,0,0,0,0))
 gp = GaugeParm{Float64}(SU3{Float64}, 6.0, 1.0)
 dpar = DiracParam{Float64}(SU3fund,1.3,0.0,(1.0,1.0,1.0,1.0),0.0)
-dws = DiracWorkspace(SU3fund{Float64},Float64,lp);
+dws = DiracWorkspace(SU3fund,Float64,lp);
 
 p==0 ? p = Int.(round.(lp.iL.*rand(4),RoundUp)) : nothing
 U = fill!(vector_field(SU3{Float64},lp),one(SU3{Float64}))

test/dirac/test_solver_rand.jl

@@ -10,7 +10,7 @@ using CUDA, LatticeGPU, TimerOutputs
     gp = GaugeParm{Float64}(SU3{Float64}, 6.0, 1.0)
     ymws = YMworkspace(SU3, Float64, lp)
     dpar = DiracParam{Float64}(SU3fund,2.3,0.0,(1.0,1.0,1.0,1.0),0.0)
-    dws = DiracWorkspace(SU3fund{Float64},Float64,lp);
+    dws = DiracWorkspace(SU3fund,Float64,lp);
 
     randomize!(ymws.mom, lp, ymws)
     U = exp.(ymws.mom)