Fix type instability in matrix log and add missing exp(::Matrix{Complex{<:Integer}}) (#23707)

* Matrices: exp and log minor changes

Add `exp` for matrices of complex integers and fix type instability in `log`
by wrapping sym/herm in `full`.

* Add tests

* Avoid multiple testset loops

Author: Evey

base/linalg/dense.jl

@@ -462,12 +462,17 @@ julia> exp(A)
 ```
 """
 exp(A::StridedMatrix{<:BlasFloat}) = exp!(copy(A))
-exp(A::StridedMatrix{<:Integer}) = exp!(float(A))
+exp(A::StridedMatrix{<:Union{Integer,Complex{<:Integer}}}) = exp!(float.(A))
 
 ## Destructive matrix exponential using algorithm from Higham, 2008,
 ## "Functions of Matrices: Theory and Computation", SIAM
 function exp!(A::StridedMatrix{T}) where T<:BlasFloat
     n = checksquare(A)
+    if T <: Real
+        if issymmetric(A)
+            return full(exp(Symmetric(A)))
+        end
+    end
     if ishermitian(A)
         return full(exp(Hermitian(A)))
     end
@@ -592,11 +597,13 @@ julia> log(A)
 """
 function log(A::StridedMatrix{T}) where T
     # If possible, use diagonalization
-    if issymmetric(A) && T <: Real
-        return log(Symmetric(A))
+    if T <: Real
+        if issymmetric(A)
+            return full(log(Symmetric(A)))
+        end
     end
     if ishermitian(A)
-        return log(Hermitian(A))
+        return full(log(Hermitian(A)))
     end
 
     # Use Schur decomposition

test/linalg/dense.jl

@@ -423,6 +423,14 @@ end
         @test exp(log(A7)) ≈ A7
     end
 
+    @testset "Integer promotion tests" begin
+        for (elty1, elty2) in ((Int64, Float64), (Complex{Int64}, Complex{Float64}))
+            A4int  = convert(Matrix{elty1}, [1 2; 3 4])
+            A4float  = convert(Matrix{elty2}, A4int)
+            @test exp(A4int) == exp(A4float)
+        end
+    end
+
     A8 = 100 * [-1+1im 0 0 1e-8; 0 1 0 0; 0 0 1 0; 0 0 0 1]
     @test exp(log(A8)) ≈ A8
 end
@@ -450,6 +458,12 @@ end
     A12 = convert(Matrix{elty}, [1 -1; 1 -1])
     @test typeof(log(A12)) == Array{Complex{Float64}, 2}
 
+    A13 = convert(Matrix{elty}, [2 0; 0 2])
+    @test typeof(log(A13)) == Array{elty, 2}
+
+    T = elty == Float64 ? Symmetric : Hermitian
+    @test typeof(log(T(A13))) == T{elty, Array{elty, 2}}
+
     A1  = convert(Matrix{elty}, [4 2 0; 1 4 1; 1 1 4])
     logA1 = convert(Matrix{elty}, [1.329661349 0.5302876358 -0.06818951543;
                                     0.2310490602 1.295566591 0.2651438179;