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https://igit.ific.uv.es/alramos/latticegpu.jl.git
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Group SU(3) working
This commit is contained in:
Alberto Ramos
parent
f296fd9768
commit
c341cd24aa
5 changed files with 320 additions and 21 deletions
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@ -11,11 +11,11 @@
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#
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# Use memory efficient representation: Only store
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# first two rows
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# first two rows. Third row constructed on the fly.
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#
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# a.u31 = a.u12*conj(a.u23) - a.u13*conj(a.u22)
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# a.u32 = a.u13*conj(a.u21) - a.u11*conj(a.u23)
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# a.u33 = a.u11*conj(a.u22) - a.u12*conj(a.u21)
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# a.u31 = conj(a.u12*a.u23 - a.u13*a.u22)
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# a.u32 = conj(a.u13*a.u21 - a.u11*a.u23)
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# a.u33 = conj(a.u11*a.u22 - a.u12*a.u21)
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#
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import Base.:*, Base.:+, Base.:-,Base.:/,Base.:\
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@ -27,16 +27,17 @@ struct SU3 <: Group
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u22::ComplexF64
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u23::ComplexF64
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end
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SU3() = SU3(1,0,0,0,1,0)
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inverse(a::SU3) = SU3(conj(a.u11),conj(a.u21),conj(a.u12*conj(a.u23) - a.u13*conj(a.u22)),
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conj(a.u12),conj(a.u22),conj(a.u13*conj(a.u21) - a.u11*conj(a.u23)))
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SU3() = SU3(1.0,0.0,0.0,0.0,1.0,0.0)
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inverse(a::SU3) = SU3(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22),
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conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23))
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dag(a::SU3) = inverse(a)
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tr(g::SU3) = a.u11+a.u22+a.u11*conj(a.u22)-a.u12*conj(a.u21)
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tr(g::SU3) = a.u11+a.u22+a.u11*conj(a.u22)-a.u12*conj(a.u21)
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function Base.:*(a::SU3,b::SU3)
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bu31 = (b.u12*conj(a.u23) - b.u13*conj(b.u22))
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bu32 = (b.u13*conj(b.u21) - b.u11*conj(b.u23))
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bu33 = (b.u11*conj(b.u22) - b.u12*conj(b.u21))
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bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return SU3(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
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a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
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@ -46,3 +47,301 @@ function Base.:*(a::SU3,b::SU3)
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a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33)
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end
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function Base.:/(a::SU3,b::SU3)
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bu31 = conj(b.u12*a.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return SU3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
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a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
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a.u11*conj(bu31) + a.u12*conj(bu32) + a.u13*conj(bu33),
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a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
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a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
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a.u21*conj(bu31) + a.u22*conj(bu32) + a.u23*conj(bu33))
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end
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function Base.:\(a::SU3,b::SU3)
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au31 = conj(a.u12*a.u23 - a.u13*a.u22)
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au32 = conj(a.u13*a.u21 - a.u11*a.u23)
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bu31 = conj(b.u12*a.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return SU3(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + conj(au31)*bu31,
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conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + conj(au31)*bu32,
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conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + conj(au31)*bu33,
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conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + conj(au32)*bu31,
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conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + conj(au32)*bu32,
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conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + conj(au32)*bu33)
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end
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struct SU3alg <: Algebra
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t1::Float64
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t2::Float64
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t3::Float64
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t4::Float64
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t5::Float64
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t6::Float64
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t7::Float64
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t8::Float64
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end
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SU3alg() = SU3alg(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
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function projalg(a::SU3)
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sr3ov2::Float64 = 0.866025403784438646763723170752
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au33 = conj(a.u11*a.u22 - a.u12*a.u21)
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ditr = ( imag(a.u11) + imag(a.u22) + imag(au33) )/3.0
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m12 = (a.u12 - conj(a.u21))/2.0
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m13 = (a.u13 - (a.u12*a.u23 - a.u13*a.u22) )/2.0
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m23 = (a.u23 - (a.u13*a.u21 - a.u11*a.u23) )/2.0
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return SU3alg(imag( m12 ), imag( m13 ), imag( m23 ),
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real( m12 ), real( m13 ), real( m23 ),
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(imag(a.u11)-imag(a.u22))/2.0,
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-sr3ov2*(imag(au33)-ditr))
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end
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dot(a::SU3alg,b::SU3alg) = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3 + a.t4*b.t4 +
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a.t5*b.t5 + a.t6*b.t6 + a.t7*b.t7 + a.t8*b.t8
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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
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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)
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Base.:+(a::SU3alg) = SU3alg(a.t1,a.t2,a.t3,a.t4,a.t5,a.t6,a.t7,a.t8)
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Base.:-(a::SU3alg) = SU3alg(-a.t1,-a.t2,-a.t3,-a.t4,-a.t5,-a.t6,-a.t7,-a.t8)
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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)
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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)
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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)
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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)
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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)
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export SU3, SU3alg, inverse, dag, tr, projalg, expm, exp, norm, norm2
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struct M3x3
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u11::ComplexF64
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u12::ComplexF64
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u13::ComplexF64
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u21::ComplexF64
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u22::ComplexF64
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u23::ComplexF64
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u31::ComplexF64
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u32::ComplexF64
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u33::ComplexF64
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end
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Base.:*(a::M3x3,b::M3x3) = M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
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a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
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a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
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a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
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a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
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a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
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a.u31*b.u11 + a.u32*b.u21 + a.u33*b.u31,
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a.u31*b.u12 + a.u32*b.u22 + a.u33*b.u32,
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a.u31*b.u13 + a.u32*b.u23 + a.u33*b.u33)
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function Base.:*(a::SU3,b::M3x3)
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a.u31 = conj(a.u12*a.u23 - a.u13*a.u22)
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a.u32 = conj(a.u13*a.u21 - a.u11*a.u23)
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a.u33 = conj(a.u11*a.u22 - a.u12*a.u21)
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return M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
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a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
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a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
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a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
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a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
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a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
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au31*b.u11 + au32*b.u21 + au33*b.u31,
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au31*b.u12 + au32*b.u22 + au33*b.u32,
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au31*b.u13 + au32*b.u23 + au33*b.u33)
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end
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function Base.:*(a::M3x3,b::SU3)
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bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return M3x3(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
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a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
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a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33,
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a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31,
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a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32,
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a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33,
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a.u31*b.u11 + a.u32*b.u21 + a.u33*bu31,
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a.u31*b.u12 + a.u32*b.u22 + a.u33*bu32,
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a.u31*b.u13 + a.u32*b.u23 + a.u33*bu33)
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end
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function Base.:/(a::M3x3,b::SU3)
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bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return M3x3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
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a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
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a.u11*conj(bu31) + a.u12*conj(bu32) + a.u13*conj(bu33),
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a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
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a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
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a.u21*conj(bu31) + a.u22*conj(bu32) + a.u23*conj(bu33),
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a.u31*conj(b.u11) + a.u32*conj(b.u12) + a.u33*conj(b.u13),
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a.u31*conj(b.u21) + a.u32*conj(b.u22) + a.u33*conj(b.u23),
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a.u31*conj(bu31) + a.u32*conj(bu32) + a.u33*conj(bu33))
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end
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Base.:*(a::Number,b::M3x3) = M3x3(a*b.u11, a*b.u12, a*bu13,
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a*b.u21, a*b.u22, a*bu23,
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a*b.u31, a*b.u32, a*bu33)
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Base.:*(b::M3x3,a::Number) = M3x3(a*b.u11, a*b.u12, a*bu13,
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a*b.u21, a*b.u22, a*bu23,
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a*b.u31, a*b.u32, a*bu33)
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Base.:+(a::M3x3,b::M3x3) = M3x3(a.u11+b.u11, a.u12+b.u12, a.u13+bu13,
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a.u21+b.u21, a.u22+b.u22, a.u23+bu23,
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a.u31+b.u31, a.u32+b.u32, a.u33+bu33)
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Base.:-(a::M3x3,b::M3x3) = M3x3(a.u11-b.u11, a.u12-b.u12, a.u13-bu13,
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a.u21-b.u21, a.u22-b.u22, a.u23-bu23,
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a.u31-b.u31, a.u32-b.u32, a.u33-bu33)
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Base.:-(b::M3x3) = M3x3(-b.u11, -b.u12, -bu13,
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-b.u21, -b.u22, -bu23,
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-b.u31, -b.u32, -bu33)
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Base.:+(b::M3x3) = M3x3(b.u11, b.u12, bu13,
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b.u21, b.u22, bu23,
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b.u31, b.u32, bu33)
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function alg2mat(a::SU3alg)
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x8p = a.t8/3.46410161513775458
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x7p = a.t7/2.0
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u11 = complex(0.0, x7p + x8p)
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u22 = complex(0.0,-x7p + x8p)
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u33 = complex(0.0,-2.0*x8p)
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u12 = complex(a.t4,a.t1)/2.0
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u13 = complex(a.t5,a.t2)/2.0
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u23 = complex(a.t6,a.t3)/2.0
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u21 = -conj(u12)
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u31 = -conj(u13)
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u32 = -conj(u23)
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return M3x3(u11,u12,u13, u21,u22,u23, u31,u32,u33)
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end
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@inline function exp_iter(dch::ComplexF64, tch::Float64)
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c = ( 1.957294106339126128e-20, 4.110317623312164853e-19,
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8.220635246624329711e-18, 1.561920696858622643e-16,
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2.811457254345520766e-15, 4.779477332387385293e-14,
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7.647163731819816473e-13, 1.147074559772972473e-11,
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1.605904383682161451e-10, 2.087675698786809894e-09,
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2.505210838544171879e-08, 2.755731922398589067e-07,
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2.755731922398589065e-06, 2.480158730158730158e-05,
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1.984126984126984127e-04, 1.388888888888888888e-03,
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8.333333333333333333e-03, 4.166666666666666666e-02,
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1.666666666666666666e-01, 0.5, 1.0, 1.0 )
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q0 = complex(c[1])
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q1 = complex(0.0)
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q2 = complex(0.0)
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@inbounds for i in 2:length(c)
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qt0 = q0
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qt1 = q1
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q0 = complex(c[i]) + dch*q2
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q1 = qt0 - tch*q2
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q2 = qt1
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end
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return q0, q1, q2
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end
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function expm(g::SU3, a::SU3alg, t::Number)
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tpw = t^2
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M = alg2mat(a)
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Msq = M*M
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dch = tpw*t*(M.u11*M.u22*M.u33 + M.u13*M.u21*M.u32 +
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M.u31*M.u12*M.u23 - M.u11*M.u23*M.u32 -
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M.u12*M.u21*M.u33 - M.u13*M.u22*M.u31)
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tch = -tpw*(real(Msq.u11)+real(Msq.u22)+real(Msq.u33))/2.0
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q0, q1, q2 = exp_iter(dch, tch)
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q1 = t*q1
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q2 = tpw*q2
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g2 = SU3(q1*M.u11 + q2*Msq.u11+q0, q1*M.u12 + q2*Msq.u12, q1*M.u13 + q2*Msq.u13,
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q1*M.u21 + q2*Msq.u21, q1*M.u22 + q2*Msq.u22+q0, q1*M.u23 + q2*Msq.u23)
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return g2*g
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end
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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
|
||||
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue