Add normalize function (#28)

* Add `normalize`

* Bump version

Author: moble

Project.toml

@@ -1,7 +1,7 @@
 name = "Quaternionic"
 uuid = "0756cd96-85bf-4b6f-a009-b5012ea7a443"
 authors = ["Michael Boyle <michael.oliver.boyle@gmail.com>"]
-version = "0.1.0"
+version = "0.2.0"
 
 [deps]
 LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"

src/Quaternionic.jl

@@ -8,7 +8,7 @@ export AbstractQuaternion
 export Quaternion, QuaternionF64, QuaternionF32, QuaternionF16, imx, imy, imz, 𝐢, 𝐣, 𝐤
 export Rotor, RotorF64, RotorF32, RotorF16
 export QuatVec, QuatVecF64, QuatVecF32, QuatVecF16
-export (⋅), (×), (×̂)
+export (⋅), (×), (×̂), normalize
 export abs2vec, absvec
 export from_float_array, to_float_array,
     from_euler_angles, to_euler_angles,

src/algebra.jl

@@ -117,3 +117,19 @@ vector is returned.
         return axb / av
     end
 end
+
+"""
+    normalize(q)
+
+Return a copy of this quaternion, normalized.
+
+Note that this returns the same type as the input quaternion.  If you want to
+convert to a `Rotor`, just call `Rotor(q)`, which includes a normalization
+step.
+"""
+@inline function normalize(q::AbstractQuaternion)
+    return q / abs(q)
+end
+@inline function normalize(q::Rotor)
+    return Rotor(q)  # already normalizes
+end

test/basis.jl

@@ -67,6 +67,36 @@
                     @test basis[i1] - basis[i2] == Q{T}(s...)
                 end
             end
+
+            # Normalization
+            for q in basis
+                n = normalize(q)
+                @test typeof(n) === Q{float(T)}
+                if Q === QuatVec && q == u
+                    continue
+                end
+                @test q == n
+                @test q == normalize(2n)
+            end
+        end
+
+        let Q = Rotor
+            # Define basis elements
+            u = Q{T}(1)
+            i = Q{T}(𝐢)
+            j = Q{T}(𝐣)
+            k = Q{T}(𝐤)
+            basis = [u, i, j, k]
+
+            # Normalization
+            for q in basis
+                n = normalize(q)
+                @test typeof(n) === Q{float(T)}
+                @test q == n
+                @test q == normalize(2n)
+                twoq = Q{T}(2*(q.components))  # Won't normalize
+                @test q == normalize(twoq)
+            end
         end
 
         let Q = QuatVec