add matrix exponentials

src/Quaternion.jl

@@ -293,3 +293,25 @@ function slerp(qa::Quaternion{T}, qb::Quaternion{T}, t::T) where {T}
         qa.v3 * ratio_a + qm.v3 * ratio_b,
     )
 end
+
+function _complex_representation(A::Matrix{Quaternion{T}}) where {T}
+	# convert a quatenion matrix to corresponding complex matrix
+	a = map(t->t.s, A)
+    b = map(t->t.v1, A)
+    c = map(t->t.v2, A)
+    d = map(t->t.v3, A)
+
+	return [a+im*b c+im*d;-c+im*d a-im*b]
+end
+
+function _quaternion_representation(A::Matrix{Complex{T}}) where {T}
+	n = round(Int, size(A, 1)/2)
+    a = real(A[1:n, 1:n])
+    b = imag(A[1:n, 1:n])
+    c = real(A[1:n, n+1:2n])
+    d = imag(A[1:n, n+1:2n])
+    return [Quaternion(a[i,j], b[i,j], c[i,j], d[i,j]) for i in 1:n, j in 1:n]
+end
+
+# A quick way of doing the quaternionic matrix exponential
+exp(A::Matrix{Quaternion{T}}) where {T} = _quaternion_representation(exp(_complex_representation(A)))

src/Quaternions.jl

@@ -4,8 +4,8 @@ module Quaternions
 
   import Base: +, -, *, /, ^
   import Base: abs, abs2, angle, conj, cos, exp, inv, isfinite, log, real, sin, sqrt
-  import Base: convert, promote_rule, float
-  import LinearAlgebra: norm, normalize
+  import Base: convert, promote_rule, float, imag
+  import LinearAlgebra: norm, normalize, exp
 
   include("Quaternion.jl")
   include("Octonion.jl")
@@ -32,4 +32,5 @@ module Quaternions
   export qrotation
   export rotationmatrix
   export slerp
+  export exp
 end