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https://igit.ific.uv.es/alramos/latticegpu.jl.git
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145 lines
4.1 KiB
Julia
145 lines
4.1 KiB
Julia
using CUDA, LinearAlgebra
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import Pkg
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#Pkg.activate("/lhome/ific/a/alramos/s.images/julia/workspace/LatticeGPU")
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Pkg.activate("/home/alberto/code/julia/LatticeGPU")
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using LatticeGPU
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function g2mat(g::SU3)
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M = Array{ComplexF64, 2}(undef, 3,3)
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M[1,1] = g.u11
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M[1,2] = g.u12
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M[1,3] = g.u13
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M[2,1] = g.u21
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M[2,2] = g.u22
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M[2,3] = g.u23
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M[3,1] = conj(g.u12*g.u23 - g.u13*g.u22)
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M[3,2] = conj(g.u13*g.u21 - g.u11*g.u23)
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M[3,3] = conj(g.u11*g.u22 - g.u12*g.u21)
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return M
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end
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# 0.40284714488721746 + 0.2704272209422031im -0.029482825024553627 - 0.8247329455356851im 0.28771631112777535 + 0.027366985901323956im; -0.08478364480998268 + 0.8226014762207954im -0.4790638417896126 + 0.24301903735299646im -0.022591091614522323 + 0.16452285690920823im; 0.28083864951126214 + 0.04302898862961919im 0.0066864552013863165 - 0.17418727240313508im -0.939634663641523 + 0.07732362776719631im
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T = Float64
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a = rand(SU3alg{T})
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println("Random algebra: ", a)
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g1 = exp(a, 0.2)
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g2 = exp(a, -0.2)
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g = g1*g2
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println("One?: ", g)
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M = [0.40284714488721746 + 0.2704272209422031im -0.029482825024553627 - 0.8247329455356851im 0.28771631112777535 + 0.027366985901323956im; -0.08478364480998268 + 0.8226014762207954im -0.4790638417896126 + 0.24301903735299646im -0.022591091614522323 + 0.16452285690920823im; 0.28083864951126214 + 0.04302898862961919im 0.0066864552013863165 - 0.17418727240313508im -0.939634663641523 + 0.07732362776719631im]
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println(det(M))
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g1 = SU3(M[1,1],M[1,2],M[1,3], M[2,1],M[2,2],M[2,3])
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println("dir: ", g1)
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g2 = exp(a)
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println("exp: ", g2)
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println("dif: ", g2mat(g1)-g2mat(g2))
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g3 = g1/g2
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println(g3)
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println("END")
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ftest(g::Group) = LatticeGPU.tr(g)
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#println(" ## SU(2)")
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#asu2 = SU2alg(0.23, 1.23, -0.34)
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#gsu2 = exp(asu2)
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#
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#eps = 0.001
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#h = SU2alg(eps,0.0,0.0)
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#fp = ftest(exp(h)*gsu2)
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#fm = ftest(exp(h,-1.0)*gsu2)
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#println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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#h = SU2alg(0.0,eps,0.0)
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#fp = ftest(exp(h)*gsu2)
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#fm = ftest(exp(h,-1.0)*gsu2)
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#println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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#h = SU2alg(0.0,0.0,eps)
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#fp = ftest(exp(h)*gsu2)
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#fm = ftest(exp(h,-1.0)*gsu2)
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#println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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#println("Exact derivative: ", -projalg(gsu2))
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println("\n\n ## SU(3)")
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asu3 = SU3alg{T}(0.23, 1.23, -0.34, 2.34, -0.23, 0.23, -1.34, 1.34)
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gsu3 = exp(asu3)
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eps = 0.001
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h = SU3alg{T}(eps,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,eps,0.0,0.0,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,eps,0.0,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,eps,0.0,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,eps,0.0,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,0.0,eps,0.0,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,0.0,0.0,eps,0.0)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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h = SU3alg{T}(0.0,0.0,0.0,0.0,0.0,0.0,0.0,eps)
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fp = ftest(exp(h)*gsu3)
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fm = ftest(exp(h,-1.0)*gsu3)
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println("Numerical derivative: ", (fp-fm)/(2.0*eps))
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println("Exact derivative: ", -projalg(gsu3))
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println("\n # Mutiplications")
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g1 = exp(SU3alg{T}(0.23, 1.23, -0.34, 2.34, -0.23, 0.23, -1.34, 1.34))
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g2 = exp(SU3alg{T}(1.23, -0.23, -0.14, 0.4, -1.23, -0.8, -0.34, 0.34))
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a = g1/(g2*g1)
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b = g2*a
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println("b is one: ", b)
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println("## Aqui test M3x3")
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ba = rand(SU3alg{T})
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ga = exp(ba)
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println("Matrix: ", alg2mat(ba))
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println("Exp: ", ga)
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println("## Final tests: ")
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g1 = exp(SU3alg{T}(6.23, 1.23, -0.34, 2.34, -0.23, 0.23, -8.34, 8.34))
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println(g1)
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println(isgroup(g1))
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g1 = unitarize(g1)
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println(g1)
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println(isgroup(g1))
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