3j and 6j working and tested

test/runtests.jl

@@ -1,5 +1,96 @@
 using WignerSymbols
 using Base.Test
 
-# write your own tests here
-@test 1 == 2
+smalljlist = 0:1//2:10
+largejlist = 0:1//2:1000
+# test triangle coefficient
+for j1 in smalljlist, j2 in smalljlist
+    for j3 = abs(j1-j2):(j1+j2)
+        @test Δ(j1,j2,j3) ≈ sqrt(factorial(float(j1+j2-j3))*factorial(float(j1-j2+j3))*
+                                    factorial(float(j2+j3-j1))/factorial(float(j1+j2+j3+1)))
+    end
+end
+
+# test 3j:
+#--------
+# test cg orthogonality
+for j1 in smalljlist, j2 in smalljlist
+    d1 = 2*j1+1
+    d2 = 2*j2+1
+    M = zeros(d1*d2, d1*d2)
+    ind1 = 1
+    for m1 in -j1:j1, m2 in -j2:j2
+        ind2 = 1
+        for j3 in abs(j1-j2):(j1+j2)
+            for m3 in -j3:j3
+                M[ind1,ind2] = clebschgordan(j1,m1,j2,m2,j3,m3)
+                ind2 += 1
+            end
+        end
+        ind1 += 1
+    end
+    @test M'*M ≈ one(M)
+end
+
+# test recurrence relations: Phys Rev E 57, 7274 (1998)
+for k = 1:10
+    j2 = convert(BigFloat,rand(0:1//2:1000))
+    j3 = convert(BigFloat,rand(0:1//2:1000))
+    m2 = convert(BigFloat,rand(-j2:j2))
+    m3 = convert(BigFloat,rand(-j3:j3))
+
+    for j in max(abs(j2-j3),abs(m2+m3))+1:(j2+j3)-1
+        X = j*sqrt(((j+1)^2-(j2-j3)^2)*((j2+j3+1)^2-(j+1)^2)*((j+1)^2-(m2+m3)^2))
+        Y = (2*j+1)*((m2+m3)*(j2*(j2+1)-j3*(j3+1)) - (m2-m3)*j*(j+1))
+        Z = (j+1)*sqrt((j^2-(j2-j3)^2)*((j2+j3+1)^2-j^2)*(j^2-(m2+m3)^2))
+        tol = 10*max(abs(X),abs(Y),abs(Z))*eps(BigFloat)
+        @test (X*wigner3j(BigFloat,j+1,j2,j3,-m2-m3,m2,m3) + Z*wigner3j(BigFloat,j-1,j2,j3,-m2-m3,m2,m3))≈(-Y*wigner3j(BigFloat,j,j2,j3,-m2-m3,m2,m3)) atol=tol
+    end
+end
+
+# test 6j
+#----------
+# test orthogonality
+for j1 in smalljlist, j2 in smalljlist, j4 in smalljlist
+    for j5 in max(abs(j1-j2-j4),abs(j1-j2+j4),abs(j1+j2-j4)):(j1+j2+j4)
+        j6range = max(abs(j2-j4),abs(j1-j5)):min((j2+j4),(j1+j5))
+        j3range = max(abs(j1-j2),abs(j4-j5)):min((j1+j2),(j4+j5))
+        @test length(j6range) == length(j3range)
+        M = zeros(length(j3range),length(j6range))
+        for (k2,j6) in enumerate(j6range)
+            for (k1,j3) in enumerate(j3range)
+                M[k1,k2] = sqrt(2*j3+1)*sqrt(2*j6+1)*wigner6j(j1,j2,j3,j4,j5,j6)
+            end
+        end
+        @test M'*M ≈ one(M)
+    end
+end
+
+# test special case
+for j1 in smalljlist, j2 in smalljlist
+    j6 = 0
+    j4 = j2
+    j5 = j1
+    for j3 in abs(j1-j2):(j1+j2)
+        @test wigner6j(j1,j2,j3,j4,j5,j6) ≈ (-1)^(j1+j2+j3)/sqrt((2*j1+1)*(2*j2+1))
+    end
+end
+
+# test recurrence relations: Phys Rev E 57, 7274 (1998)
+for k = 1:10
+    j2 = convert(BigFloat,rand(largejlist))
+    j3 = convert(BigFloat,rand(largejlist))
+    l1 = convert(BigFloat,rand(largejlist))
+    l2 = convert(BigFloat,rand(abs(l1-j3):(l1+j3)))
+    l3 = convert(BigFloat,rand(abs(l1-j2):min(l1+j2)))
+
+    for j in intersect(abs(j2-j3):(j2+j3), abs(l2-l3):(l2+l3))
+        X = j*sqrt(((j+1)^2-(j2-j3)^2)*((j2+j3+1)^2-(j+1)^2)*((j+1)^2-(l2-l3)^2)*((l2+l3+1)^2 - (j+1)^2))
+        Y = (2*j+1)*( j*(j+1)*( -j*(j+1) + j2*(j2+1) + j3*(j3+1) - 2*l1*(l1+1)) +
+                        l2*(l2+1)*( j*(j+1) + j2*(j2+1) - j3*(j3+1) ) +
+                        l3*(l3+1)*( j*(j+1) - j2*(j2+1) + j3*(j3+1) ) )
+        Z = (j+1)*sqrt((j^2-(j2-j3)^2)*((j2+j3+1)^2-j^2)*(j^2-(l2-l3)^2)*((l2+l3+1)^2 - j^2))
+        tol = 10*max(abs(X),abs(Y),abs(Z))*eps(BigFloat)
+        @test (X*wigner6j(BigFloat,j+1,j2,j3,l1,l2,l3) + Z*wigner6j(BigFloat,j-1,j2,j3,l1,l2,l3))≈(-Y*wigner6j(BigFloat,j,j2,j3,l1,l2,l3)) atol=tol
+    end
+end