Merge pull request #212 from marius311/MM/sqrtm

add sqrtm

Author: c42f

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
@@ -91,6 +91,7 @@ include("inv.jl")
 include("solve.jl")
 include("eigen.jl")
 include("expm.jl")
+include("sqrtm.jl")
 include("cholesky.jl")
 include("deque.jl")
 include("io.jl")

src/sqrtm.jl

@@ -0,0 +1,19 @@
+@inline sqrtm(A::StaticMatrix) = _sqrtm(Size(A),A)
+
+@inline function _sqrtm(::Size{(1,1)}, A::SA) where {SA<:StaticArray}
+    s = sqrtm(A[1,1])
+    similar_type(SA,typeof(s))(s)
+end
+
+@inline function _sqrtm(::Size{(2,2)}, A::SA) where {SA<:StaticArray}
+    a,b,c,d = A
+    if a==b==c==d==0
+        zero(A)
+    else
+        s = sqrtm(a*d-b*c)
+        t = inv(sqrtm(a+d+2s))
+        similar_type(SA,typeof(t))(t*(a+s), t*b, t*c, t*(d+s))
+    end
+end
+
+@inline _sqrtm(s::Size, A::StaticArray) = s(Base.sqrtm(Array(A)))

test/runtests.jl

@@ -27,6 +27,7 @@ using Base.Test
     include("solve.jl") # Strange inference / world-age error
     include("eigen.jl")
     include("expm.jl")
+    include("sqrtm.jl")
     include("chol.jl")
     include("deque.jl")
     include("io.jl")

test/sqrtm.jl

@@ -0,0 +1,7 @@
+@testset "Matrix square root" begin
+    @test sqrtm(@SMatrix [2])::SMatrix ≈ SMatrix{1,1}(sqrtm(2))
+    @test sqrtm(@SMatrix [5 2; -2 1])::SMatrix ≈ sqrtm([5 2; -2 1])
+    @test sqrtm(@SMatrix [4 2; -2 1])::SMatrix ≈ sqrtm([4 2; -2 1])
+    @test sqrtm(@SMatrix [4 2; 2 1])::SMatrix ≈ sqrtm([4 2; 2 1])
+    @test sqrtm(@SMatrix [1 2 0; 2 1 0; 0 0 1])::SizedArray{Tuple{3,3}} ≈ sqrtm([1 2 0; 2 1 0; 0 0 1])
+end