add sqrtm

Author: marius311

src/StaticArrays.jl

@@ -8,7 +8,7 @@ import Base: getindex, setindex!, size, similar, vec, show,
              length, convert, promote_op, map, map!, reduce, reducedim, mapreducedim,
              mapreduce, broadcast, broadcast!, conj, transpose, ctranspose,
              hcat, vcat, ones, zeros, eye, one, cross, vecdot, reshape, fill,
-             fill!, det, inv, eig, eigvals, expm, trace, vecnorm, norm, dot, diagm,
+             fill!, det, inv, eig, eigvals, expm, sqrtm, trace, vecnorm, norm, dot, diagm,
              sum, diff, prod, count, any, all, minimum,
              maximum, extrema, mean, copy, rand, randn, randexp, rand!, randn!,
              randexp!, normalize, normalize!, read, read!, write

src/sqrtm.jl

@@ -0,0 +1,10 @@
+@inline sqrtm(A::StaticMatrix) = _sqrtm(Size(A),A)
+
+@inline function _sqrtm(::Size{(2,2)}, A::StaticMatrix)
+    a,b,c,d = A
+    s = sqrtm(a*d-b*c)
+    t = inv(sqrtm(a+d+2s))
+    similar_type(typeof(A),typeof(t))(t*(a+s), t*b, t*c, t*(d+s))
+end
+
+@inline _sqrtm(s::Size, A::StaticArray) = s(Base.sqrtm(Array(A)))