mirror of
https://github.com/tgorordo/WignerSymbols.jl.git
synced 2026-06-05 15:42:15 -07:00
205 lines
8.2 KiB
Julia
205 lines
8.2 KiB
Julia
using Test
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using WignerSymbols
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using LinearAlgebra
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using Random
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using Base.Threads
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N = Base.Threads.nthreads()
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Random.seed!(1234)
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smalljlist = 0:1//2:10
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largejlist = 0:1//2:1000
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@threads for i = 1:N
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@testset "triangle coefficient, thread $i" begin
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for k = i:N:length(smalljlist)
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j1 = smalljlist[k]
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for j2 in smalljlist
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for j3 = abs(j1-j2):(j1+j2)
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@test Δ(j1,j2,j3) ≈ sqrt(factorial(big(Int(j1+j2-j3)))*
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factorial(big(Int(j1-j2+j3)))*
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factorial(big(Int(j2+j3-j1)))/
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factorial(big(Int(j1+j2+j3+1))))
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end
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end
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end
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end
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end
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# test 3j:
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#--------
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@threads for i = 1:N
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@testset "clebschgordan: orthogonality relations, thread $i" begin
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for k = i:N:length(smalljlist)
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j1 = smalljlist[k]
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for j2 in smalljlist
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d1::Int = 2*j1+1
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d2::Int = 2*j2+1
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M = zeros(Float64, (d1*d2, d1*d2))
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ind1 = 1
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for m1 in -j1:j1, m2 in -j2:j2
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ind2 = 1
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@inbounds for j3 in abs(j1-j2):(j1+j2), m3 in -j3:j3
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M[ind1,ind2] = clebschgordan(j1,m1,j2,m2,j3,m3)
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ind2 += 1
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end
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ind1 += 1
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end
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@test M'*M ≈ one(M)
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end
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end
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end
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end
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# # test recurrence relations: Phys Rev E 57, 7274 (1998)
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# @threads for i = 1:N
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# @testset "wigner3j: recurrence relations, thread $i" begin
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# for k = 1:div(8,N)
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# j2 = convert(BigFloat, rand(largejlist))
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# j3 = convert(BigFloat, rand(largejlist))
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# m2 = -convert(BigFloat, rand(-j2:0))
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# m3 = convert(BigFloat, rand(-j3:0))
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#
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# for j in max(abs(j2-j3),abs(m2+m3))+1:(j2+j3)-1
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# X = j*sqrt(((j+1)^2-(j2-j3)^2)*((j2+j3+1)^2-(j+1)^2)*((j+1)^2-(m2+m3)^2))
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# Y = (2*j+1)*((m2+m3)*(j2*(j2+1)-j3*(j3+1)) - (m2-m3)*j*(j+1))
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# Z = (j+1)*sqrt((j^2-(j2-j3)^2)*((j2+j3+1)^2-j^2)*(j^2-(m2+m3)^2))
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# tol = 10*max(abs(X),abs(Y),abs(Z))*eps(BigFloat)
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# @test (X*wigner3j(BigFloat,j+1,j2,j3,-m2-m3,m2,m3) +
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# Z*wigner3j(BigFloat,j-1,j2,j3,-m2-m3,m2,m3)) ≈
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# (-Y*wigner3j(BigFloat,j,j2,j3,-m2-m3,m2,m3)) atol=tol
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# end
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# end
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# end
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# end
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@threads for i = 1:N
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@testset "wigner3j: orthogonality relations, thread $i" begin
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# equivalent to Clebsch-Gordan orthogonality, now test using Float32
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for k = i:N:length(smalljlist)
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j1 = smalljlist[k]
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for j2 in smalljlist
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d1::Int = 2*j1+1
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d2::Int = 2*j2+1
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M = zeros(Float32, (d1*d2, d1*d2))
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ind2 = 1
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for m1 in -j1:j1, m2 in -j2:j2
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ind1 = 1
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@inbounds for j3 in abs(j1-j2):(j1+j2), m3 in -j3:j3
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d3::Int = 2*j3+1
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M[ind1,ind2] += sqrt(d3) * wigner3j(Float32, j1, j2, j3, m1, m2, m3)
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ind1 += 1
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end
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ind2 += 1
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end
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@test M'*M ≈ one(M) # orthogonality relation type 1
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@test M*M' ≈ one(M) # orthogonality relation type 2
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end
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end
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end
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end
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# test 6j
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#----------
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@threads for i = 1:N
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@testset "wigner6j: orthogonality relations, thread $i" begin
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for k = i:N:length(smalljlist)
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j1 = smalljlist[k]
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for j2 in smalljlist, j4 in smalljlist
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for j5 in max(abs(j1-j2-j4),abs(j1-j2+j4),abs(j1+j2-j4)):(j1+j2+j4)
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j6range = max(abs(j2-j4),abs(j1-j5)):min((j2+j4),(j1+j5))
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j3range = max(abs(j1-j2),abs(j4-j5)):min((j1+j2),(j4+j5))
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@test length(j6range) == length(j3range)
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M = zeros(Float64, (length(j3range), length(j6range)))
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for (k2,j6) in enumerate(j6range)
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for (k1,j3) in enumerate(j3range)
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M[k1,k2] = sqrt(2*j3+1)*sqrt(2*j6+1)*wigner6j(j1,j2,j3,j4,j5,j6)
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end
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end
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@test M'*M ≈ one(M)
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end
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end
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end
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end
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end
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@threads for i = 1:N
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@testset "wigner6j: special cases, thread $i" begin
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for k = i:N:length(smalljlist)
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j1 = smalljlist[k]
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for j2 in smalljlist
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j6 = 0
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j4 = j2
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j5 = j1
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for j3 in abs(j1-j2):(j1+j2)
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@test wigner6j(j1,j2,j3,j4,j5,j6) ≈
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(-1)^(j1+j2+j3)/sqrt((2*j1+1)*(2*j2+1))
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end
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end
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end
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end
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end
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@threads for i = 1:N
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@testset "wigner6j: recurrence relation, thread $i" begin
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for k = 1:div(8,N)
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j2 = convert(BigFloat,rand(largejlist))
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j3 = convert(BigFloat,rand(largejlist))
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l1 = convert(BigFloat,rand(largejlist))
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l2 = convert(BigFloat,rand(abs(l1-j3):(l1+j3)))
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l3 = convert(BigFloat,rand(abs(l1-j2):min(l1+j2)))
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for j in intersect(abs(j2-j3):(j2+j3), abs(l2-l3):(l2+l3))
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X = j * sqrt( ((j+1)^2-(j2-j3)^2) * ((j2+j3+1)^2-(j+1)^2) *
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((j+1)^2-(l2-l3)^2) * ((l2+l3+1)^2 - (j+1)^2) )
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Y = (2*j+1) * ( j*(j+1)*( -j*(j+1) + j2*(j2+1) + j3*(j3+1) - 2*l1*(l1+1)) +
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l2*(l2+1)*( j*(j+1) + j2*(j2+1) - j3*(j3+1) ) +
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l3*(l3+1)*( j*(j+1) - j2*(j2+1) + j3*(j3+1) ) )
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Z = (j+1) * sqrt( (j^2-(j2-j3)^2) * ((j2+j3+1)^2-j^2) *
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(j^2-(l2-l3)^2) * ((l2+l3+1)^2-j^2) )
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tol = 10 * max(abs(X), abs(Y), abs(Z)) * eps(BigFloat)
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@test (X*wigner6j(BigFloat, j+1, j2, j3, l1, l2, l3) +
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Z*wigner6j(BigFloat, j-1, j2, j3, l1, l2, l3)) ≈
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(-Y*wigner6j(BigFloat, j, j2, j3, l1, l2, l3)) atol=tol
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end
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end
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end
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end
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@threads for i = 1:N
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@testset "recoupling relation between 3j/CG and 6j/racahW symbols, thread $i" begin
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smallerjlist = 0:1//2:5
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for k = i:N:length(smallerjlist)
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j1 = smallerjlist[k]
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for j2 in smallerjlist, j3 in smallerjlist
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m1range = -j1:j1
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m2range = -j2:j2
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m3range = -j3:j3
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V1 = Array{Float64}(undef, length(m1range),length(m2range),length(m3range))
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V2 = Array{Float64}(undef, length(m1range),length(m2range),length(m3range))
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for J in max(abs(j1-j2-j3),abs(j1-j2+j3),abs(j1+j2-j3)):(j1+j2+j3)
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J12range = max(abs(j1-j2),abs(J-j3)):min((j1+j2),(J+j3))
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J23range = max(abs(j2-j3),abs(j1-J)):min((j2+j3),(j1+J))
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for J12 in J12range, J23 in J23range
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M = rand(-J:J) # only test for one instance of M in -J:J
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# should be independent of M anyway
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fill!(V1,0)
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fill!(V2,0)
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for (k1,m1) in enumerate(m1range), (k2,m2) in enumerate(m2range)
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abs(m1+m2)<=J12 || continue
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for (k3,m3) in enumerate(m3range)
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abs(m2+m3)<=J23 || continue
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m1+m2+m3==M || continue
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V1[k1,k2,k3] = clebschgordan(j1,m1,j2,m2,J12) *
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clebschgordan(J12,m1+m2,j3,m3,J)
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V2[k1,k2,k3] = clebschgordan(j2,m2,j3,m3,J23) *
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clebschgordan(j1,m1,J23,m2+m3,J)
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end
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end
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@test racahW(j1,j2,J,j3,J12,J23) ≈
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dot(V2,V1)/sqrt((2*J12+1)*(2*J23+1)) atol=10*eps(Float64)
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end
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end
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end
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end
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end
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end
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