From c341cd24aaa8a7f576968f3198536242f57e5169 Mon Sep 17 00:00:00 2001 From: Alberto Ramos Date: Mon, 19 Jul 2021 00:43:10 +0200 Subject: [PATCH] Group SU(3) working --- src/Groups/GroupSU3.jl | 321 +++++++++++++++++++++++++++++++++++++++-- src/Groups/Groups.jl | 10 +- src/LatticeGPU.jl | 6 +- src/Space/Space.jl | 2 +- src/YM/YM.jl | 2 +- 5 files changed, 320 insertions(+), 21 deletions(-) diff --git a/src/Groups/GroupSU3.jl b/src/Groups/GroupSU3.jl index e4ca91d..dcf9f90 100644 --- a/src/Groups/GroupSU3.jl +++ b/src/Groups/GroupSU3.jl @@ -11,11 +11,11 @@ # # Use memory efficient representation: Only store -# first two rows +# first two rows. Third row constructed on the fly. # -# a.u31 = a.u12*conj(a.u23) - a.u13*conj(a.u22) -# a.u32 = a.u13*conj(a.u21) - a.u11*conj(a.u23) -# a.u33 = a.u11*conj(a.u22) - a.u12*conj(a.u21) +# a.u31 = conj(a.u12*a.u23 - a.u13*a.u22) +# a.u32 = conj(a.u13*a.u21 - a.u11*a.u23) +# a.u33 = conj(a.u11*a.u22 - a.u12*a.u21) # import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\ @@ -27,16 +27,17 @@ struct SU3 <: Group u22::ComplexF64 u23::ComplexF64 end -SU3() = SU3(1,0,0,0,1,0) -inverse(a::SU3) = SU3(conj(a.u11),conj(a.u21),conj(a.u12*conj(a.u23) - a.u13*conj(a.u22)), - conj(a.u12),conj(a.u22),conj(a.u13*conj(a.u21) - a.u11*conj(a.u23))) +SU3() = SU3(1.0,0.0,0.0,0.0,1.0,0.0) +inverse(a::SU3) = SU3(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22), + conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23)) dag(a::SU3) = inverse(a) -tr(g::SU3) = a.u11+a.u22+a.u11*conj(a.u22)-a.u12*conj(a.u21) +tr(g::SU3) = a.u11+a.u22+a.u11*conj(a.u22)-a.u12*conj(a.u21) + function Base.:*(a::SU3,b::SU3) - bu31 = (b.u12*conj(a.u23) - b.u13*conj(b.u22)) - bu32 = (b.u13*conj(b.u21) - b.u11*conj(b.u23)) - bu33 = (b.u11*conj(b.u22) - b.u12*conj(b.u21)) + bu31 = conj(b.u12*b.u23 - b.u13*b.u22) + bu32 = conj(b.u13*b.u21 - b.u11*b.u23) + bu33 = conj(b.u11*b.u22 - b.u12*b.u21) return SU3(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31, a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32, @@ -46,3 +47,301 @@ function Base.:*(a::SU3,b::SU3) a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33) end +function Base.:/(a::SU3,b::SU3) + + bu31 = conj(b.u12*a.u23 - b.u13*b.u22) + bu32 = conj(b.u13*b.u21 - b.u11*b.u23) + bu33 = conj(b.u11*b.u22 - b.u12*b.u21) + + return SU3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13), + a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23), + a.u11*conj(bu31) + a.u12*conj(bu32) + a.u13*conj(bu33), + a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13), + a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23), + a.u21*conj(bu31) + a.u22*conj(bu32) + a.u23*conj(bu33)) + +end + +function Base.:\(a::SU3,b::SU3) + + au31 = conj(a.u12*a.u23 - a.u13*a.u22) + au32 = conj(a.u13*a.u21 - a.u11*a.u23) + bu31 = conj(b.u12*a.u23 - b.u13*b.u22) + bu32 = conj(b.u13*b.u21 - b.u11*b.u23) + bu33 = conj(b.u11*b.u22 - b.u12*b.u21) + + return SU3(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + conj(au31)*bu31, + conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + conj(au31)*bu32, + conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + conj(au31)*bu33, + conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + conj(au32)*bu31, + conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + conj(au32)*bu32, + conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + conj(au32)*bu33) + +end + + + + +struct SU3alg <: Algebra + t1::Float64 + t2::Float64 + t3::Float64 + t4::Float64 + t5::Float64 + t6::Float64 + t7::Float64 + t8::Float64 +end +SU3alg() = SU3alg(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0) +function projalg(a::SU3) + + sr3ov2::Float64 = 0.866025403784438646763723170752 + + au33 = conj(a.u11*a.u22 - a.u12*a.u21) + + ditr = ( imag(a.u11) + imag(a.u22) + imag(au33) )/3.0 + m12 = (a.u12 - conj(a.u21))/2.0 + m13 = (a.u13 - (a.u12*a.u23 - a.u13*a.u22) )/2.0 + m23 = (a.u23 - (a.u13*a.u21 - a.u11*a.u23) )/2.0 + + return SU3alg(imag( m12 ), imag( m13 ), imag( m23 ), + real( m12 ), real( m13 ), real( m23 ), + (imag(a.u11)-imag(a.u22))/2.0, + -sr3ov2*(imag(au33)-ditr)) +end +dot(a::SU3alg,b::SU3alg) = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3 + a.t4*b.t4 + + a.t5*b.t5 + a.t6*b.t6 + a.t7*b.t7 + a.t8*b.t8 +norm2(a::SU3alg) = a.t1^2 + a.t2^2 + a.t3^2 + a.t4^2 + a.t5^2 + a.t6^2 + a.t7^2 + a.t8^2 +norm(a::SU3alg) = sqrt(a.t1^2 + a.t2^2 + a.t3^2 + a.t4^2 + a.t5^2 + a.t6^2 + a.t7^2 + a.t8^2) +Base.:+(a::SU3alg) = SU3alg(a.t1,a.t2,a.t3,a.t4,a.t5,a.t6,a.t7,a.t8) +Base.:-(a::SU3alg) = SU3alg(-a.t1,-a.t2,-a.t3,-a.t4,-a.t5,-a.t6,-a.t7,-a.t8) +Base.:+(a::SU3alg,b::SU3alg) = SU3alg(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3,a.t4+b.t4,a.t5+b.t5,a.t6+b.t6,a.t7+b.t7,a.t8+b.t8) +Base.:-(a::SU3alg,b::SU3alg) = SU3alg(a.t1-b.t1,a.t2-b.t2,a.t3-b.t3,a.t4-b.t4,a.t5-b.t5,a.t6-b.t6,a.t7-b.t7,a.t8-b.t8) +Base.:*(a::SU3alg,b::Number) = SU3alg(b*a.t1,b*a.t2,b*a.t3,b*a.t4,b*a.t5,b*a.t6,b*a.t7,b*a.t8) +Base.:*(b::Number,a::SU3alg) = SU3alg(b*a.t1,b*a.t2,b*a.t3,b*a.t4,b*a.t5,b*a.t6,b*a.t7,b*a.t8) +Base.:/(a::SU3alg,b::Number) = SU3alg(a.t1/b,a.t2/b,a.t3/b,a.t4/b,a.t5/b,a.t6/b,a.t7/b,a.t8/b) + + + +export SU3, SU3alg, inverse, dag, tr, projalg, expm, exp, norm, norm2 + +struct M3x3 + u11::ComplexF64 + u12::ComplexF64 + u13::ComplexF64 + u21::ComplexF64 + u22::ComplexF64 + u23::ComplexF64 + u31::ComplexF64 + u32::ComplexF64 + u33::ComplexF64 +end + +Base.:*(a::M3x3,b::M3x3) = M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31, + a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32, + a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33, + a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31, + a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32, + a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33, + a.u31*b.u11 + a.u32*b.u21 + a.u33*b.u31, + a.u31*b.u12 + a.u32*b.u22 + a.u33*b.u32, + a.u31*b.u13 + a.u32*b.u23 + a.u33*b.u33) + +function Base.:*(a::SU3,b::M3x3) + + a.u31 = conj(a.u12*a.u23 - a.u13*a.u22) + a.u32 = conj(a.u13*a.u21 - a.u11*a.u23) + a.u33 = conj(a.u11*a.u22 - a.u12*a.u21) + + return M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31, + a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32, + a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33, + a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31, + a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32, + a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33, + au31*b.u11 + au32*b.u21 + au33*b.u31, + au31*b.u12 + au32*b.u22 + au33*b.u32, + au31*b.u13 + au32*b.u23 + au33*b.u33) +end + + +function Base.:*(a::M3x3,b::SU3) + + bu31 = conj(b.u12*b.u23 - b.u13*b.u22) + bu32 = conj(b.u13*b.u21 - b.u11*b.u23) + bu33 = conj(b.u11*b.u22 - b.u12*b.u21) + + return M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31, + a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32, + a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33, + a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31, + a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32, + a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33, + a.u31*b.u11 + a.u32*b.u21 + a.u33*bu31, + a.u31*b.u12 + a.u32*b.u22 + a.u33*bu32, + a.u31*b.u13 + a.u32*b.u23 + a.u33*bu33) +end + +function Base.:/(a::M3x3,b::SU3) + + bu31 = conj(b.u12*b.u23 - b.u13*b.u22) + bu32 = conj(b.u13*b.u21 - b.u11*b.u23) + bu33 = conj(b.u11*b.u22 - b.u12*b.u21) + + return M3x3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13), + a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23), + a.u11*conj(bu31) + a.u12*conj(bu32) + a.u13*conj(bu33), + a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13), + a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23), + a.u21*conj(bu31) + a.u22*conj(bu32) + a.u23*conj(bu33), + a.u31*conj(b.u11) + a.u32*conj(b.u12) + a.u33*conj(b.u13), + a.u31*conj(b.u21) + a.u32*conj(b.u22) + a.u33*conj(b.u23), + a.u31*conj(bu31) + a.u32*conj(bu32) + a.u33*conj(bu33)) +end + +Base.:*(a::Number,b::M3x3) = M3x3(a*b.u11, a*b.u12, a*bu13, + a*b.u21, a*b.u22, a*bu23, + a*b.u31, a*b.u32, a*bu33) + +Base.:*(b::M3x3,a::Number) = M3x3(a*b.u11, a*b.u12, a*bu13, + a*b.u21, a*b.u22, a*bu23, + a*b.u31, a*b.u32, a*bu33) + +Base.:+(a::M3x3,b::M3x3) = M3x3(a.u11+b.u11, a.u12+b.u12, a.u13+bu13, + a.u21+b.u21, a.u22+b.u22, a.u23+bu23, + a.u31+b.u31, a.u32+b.u32, a.u33+bu33) + +Base.:-(a::M3x3,b::M3x3) = M3x3(a.u11-b.u11, a.u12-b.u12, a.u13-bu13, + a.u21-b.u21, a.u22-b.u22, a.u23-bu23, + a.u31-b.u31, a.u32-b.u32, a.u33-bu33) + +Base.:-(b::M3x3) = M3x3(-b.u11, -b.u12, -bu13, + -b.u21, -b.u22, -bu23, + -b.u31, -b.u32, -bu33) + +Base.:+(b::M3x3) = M3x3(b.u11, b.u12, bu13, + b.u21, b.u22, bu23, + b.u31, b.u32, bu33) + + +function alg2mat(a::SU3alg) + + x8p = a.t8/3.46410161513775458 + x7p = a.t7/2.0 + u11 = complex(0.0, x7p + x8p) + u22 = complex(0.0,-x7p + x8p) + u33 = complex(0.0,-2.0*x8p) + u12 = complex(a.t4,a.t1)/2.0 + u13 = complex(a.t5,a.t2)/2.0 + u23 = complex(a.t6,a.t3)/2.0 + u21 = -conj(u12) + u31 = -conj(u13) + u32 = -conj(u23) + + return M3x3(u11,u12,u13, u21,u22,u23, u31,u32,u33) +end + +@inline function exp_iter(dch::ComplexF64, tch::Float64) + + c = ( 1.957294106339126128e-20, 4.110317623312164853e-19, + 8.220635246624329711e-18, 1.561920696858622643e-16, + 2.811457254345520766e-15, 4.779477332387385293e-14, + 7.647163731819816473e-13, 1.147074559772972473e-11, + 1.605904383682161451e-10, 2.087675698786809894e-09, + 2.505210838544171879e-08, 2.755731922398589067e-07, + 2.755731922398589065e-06, 2.480158730158730158e-05, + 1.984126984126984127e-04, 1.388888888888888888e-03, + 8.333333333333333333e-03, 4.166666666666666666e-02, + 1.666666666666666666e-01, 0.5, 1.0, 1.0 ) + + q0 = complex(c[1]) + q1 = complex(0.0) + q2 = complex(0.0) + @inbounds for i in 2:length(c) + qt0 = q0 + qt1 = q1 + q0 = complex(c[i]) + dch*q2 + q1 = qt0 - tch*q2 + q2 = qt1 + end + + return q0, q1, q2 +end + + +function expm(g::SU3, a::SU3alg, t::Number) + + tpw = t^2 + M = alg2mat(a) + Msq = M*M + dch = tpw*t*(M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 + + M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 - + M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31) + tch = -tpw*(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0 + + q0, q1, q2 = exp_iter(dch, tch) + + q1 = t*q1 + q2 = tpw*q2 + + g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13, + q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23) + + return g2*g +end + +function expm(g::SU3, a::SU3alg) + + M = alg2mat(a) + Msq = M*M + dch = M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 + + M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 - + M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31 + tch = -(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0 + + q0, q1, q2 = exp_iter(dch, tch) + + g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13, + q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23) + + return g2*g +end + +function Base.exp(a::SU3alg) + + M = alg2mat(a) + Msq = M*M + dch = M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 + + M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 - + M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31 + tch = -(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0 + + q0, q1, q2 = exp_iter(dch, tch) + + g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13, + q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23) + + return g2 +end + +function Base.exp(a::SU3alg, t::Number) + + tpw = t^2 + M = alg2mat(a) + Msq = M*M + dch = tpw*t*(M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 + + M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 - + M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31) + tch = -tpw*(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0 + + q0, q1, q2 = exp_iter(dch, tch) + + q1 = t*q1 + q2 = tpw*q2 + + g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13, + q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23) + + return g2 +end + diff --git a/src/Groups/Groups.jl b/src/Groups/Groups.jl index 691ad29..8e4ed9a 100644 --- a/src/Groups/Groups.jl +++ b/src/Groups/Groups.jl @@ -15,15 +15,15 @@ module Groups abstract type Group end abstract type Algebra end -include("GroupSU2.jl") - export Group, Algebra -export SU2, SU2alg, dag, normalize, inverse, tr, projalg, norm, norm2 -export dot, expm, exp + +include("GroupSU2.jl") +export SU2, SU2alg include("GroupSU3.jl") +export SU3, SU3alg - +export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2 end # module diff --git a/src/LatticeGPU.jl b/src/LatticeGPU.jl index 6280ed7..0ea52ea 100644 --- a/src/LatticeGPU.jl +++ b/src/LatticeGPU.jl @@ -16,8 +16,8 @@ include("Groups/Groups.jl") using .Groups export Group, Algebra -export SU2, SU2alg, dag, normalize, inverse, tr, projalg, norm -export dot, expm, exp +export SU2, SU2alg, SU3, SU3alg +export dot, expm, exp, dag, normalize, inverse, tr, projalg, norm, norm2 include("Space/Space.jl") @@ -30,6 +30,6 @@ include("YM/YM.jl") using .YM export YMworkspace, GaugeParm, force0_wilson!, field, randomn!, zero!, norm2 -export gauge_action, hamiltonian, HMC!, OMF4! +export gauge_action, hamiltonian, plaquette, HMC!, OMF4! end # module diff --git a/src/Space/Space.jl b/src/Space/Space.jl index fa88ec7..229ec45 100644 --- a/src/Space/Space.jl +++ b/src/Space/Space.jl @@ -126,7 +126,7 @@ end return s end -@inline map2latt(th::NTuple{3,Int64},bl::NTuple{3,Int64}) = CartesianIndex(th[1],bl[1],bl[2],bl[2]) +@inline map2latt(th::NTuple{3,Int64},bl::NTuple{3,Int64}) = CartesianIndex(th[1],bl[1],bl[2],bl[3]) export map2latt, up, dw, shift diff --git a/src/YM/YM.jl b/src/YM/YM.jl index bcdc9a2..fb49a71 100644 --- a/src/YM/YM.jl +++ b/src/YM/YM.jl @@ -52,6 +52,6 @@ include("YMact.jl") export krnl_plaq!, force0_wilson! include("YMhmc.jl") -export gauge_action, hamiltonian, HMC!, OMF4! +export gauge_action, hamiltonian, plaquette, HMC!, OMF4! end