Allow 0x0 matrices for exp, inv, sqrt (#991)

* Allow 0x0 matrices for exp, sqrt

* Implement inv for 0x0 matrices

* Update test/expm.jl

Co-authored-by: Mateusz Baran <[email protected]>

* Update test/inv.jl

Co-authored-by: Mateusz Baran <[email protected]>

* Update test/sqrtm.jl

Co-authored-by: Mateusz Baran <[email protected]>

* Bump patch version to 1.3.5

Co-authored-by: Mateusz Baran <[email protected]>

Author: eschnett

Project.toml

@@ -1,6 +1,6 @@
 name = "StaticArrays"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.3.4"
+version = "1.3.5"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/expm.jl

@@ -1,5 +1,12 @@
 @inline exp(A::StaticMatrix) = _exp(Size(A), A)
 
+@inline function _exp(::Size{(0,0)}, A::StaticMatrix)
+    T = typeof(exp(zero(eltype(A))))
+    newtype = similar_type(A,T)
+
+    (newtype)()
+end
+
 @inline function _exp(::Size{(1,1)}, A::StaticMatrix)
     T = typeof(exp(zero(eltype(A))))
     newtype = similar_type(A,T)

src/inv.jl

@@ -5,6 +5,8 @@
     _inv(Size(A_S),A_S)
 end
 
+@inline _inv(::Size{(0,0)}, A) = similar_type(A,typeof(inv(one(eltype(A)))))()
+
 @inline _inv(::Size{(1,1)}, A) = similar_type(A)(inv(A[1]))
 
 @inline function _inv(::Size{(2,2)}, A)

src/sqrtm.jl

@@ -1,6 +1,10 @@
 
 @inline sqrt(A::StaticMatrix) = _sqrt(Size(A),A)
 
+@inline function _sqrt(::Size{(0,0)}, A::SA) where {SA<:StaticArray}
+    similar_type(A,typeof(sqrt(zero(eltype(A)))))()
+end
+
 @inline function _sqrt(::Size{(1,1)}, A::SA) where {SA<:StaticArray}
     s = sqrt(A[1,1])
     similar_type(SA,typeof(s))(s)

test/expm.jl

@@ -1,6 +1,7 @@
 using StaticArrays, Test, LinearAlgebra
 
 @testset "Matrix exponential" begin
+    @test exp(SMatrix{0,0,Int}())::SMatrix === SMatrix{0,0,Float64}()
     @test exp(@SMatrix [2])::SMatrix ≈ SMatrix{1,1}(exp(2))
     @test exp(@SMatrix [5 2; -2 1])::SMatrix ≈ exp([5 2; -2 1])
     @test exp(@SMatrix [4 2; -2 1])::SMatrix ≈ exp([4 2; -2 1])

test/inv.jl

@@ -19,6 +19,7 @@ function almost_singular_matrix(N, rank, ϵ)
 end
 
 @testset "Matrix inverse" begin
+    @test inv(SMatrix{0,0,Int}())::SMatrix === SMatrix{0,0,Float64}()
     @test inv(@SMatrix [2])::SMatrix ≈ @SMatrix [0.5]
     @test inv(@SMatrix [1 2; 2 1])::SMatrix ≈ [-1/3 2/3; 2/3 -1/3]
     @test inv(@SMatrix [1 2 0; 2 1 0; 0 0 1])::SMatrix ≈ [-1/3 2/3 0; 2/3 -1/3 0; 0 0 1]

test/sqrtm.jl

@@ -1,6 +1,7 @@
 using StaticArrays, Test
 
 @testset "Matrix square root" begin
+    @test sqrt(SMatrix{0,0,Int}())::SMatrix === SMatrix{0,0,Float64}()
     @test sqrt(@SMatrix [2])::SMatrix ≈ SMatrix{1,1}(sqrt(2))
     @test sqrt(@SMatrix [5 2; -2 1])::SMatrix ≈ sqrt([5 2; -2 1])
     @test sqrt(@SMatrix [4 2; -2 1])::SMatrix ≈ sqrt([4 2; -2 1])