Fixed #12294 and added logm for a few classes of special matrices

base/linalg/dense.jl

@@ -286,9 +286,14 @@ function logm(A::StridedMatrix)
 
     # Use Schur decomposition
     n = chksquare(A)
-    S,Q,d = schur(complex(A))
-    R = logm(UpperTriangular(S))
-    retmat = Q * R * Q'
+    if istriu(A)
+        retmat = full(logm(UpperTriangular(complex(A))))
+        d = diag(A)
+    else
+        S,Q,d = schur(complex(A))
+        R = logm(UpperTriangular(S))
+        retmat = Q * R * Q'
+    end
 
     # Check whether the matrix has nonpositive real eigs
     np_real_eigs = false

base/linalg/diagonal.jl

@@ -119,6 +119,7 @@ end
 eye{T}(::Type{Diagonal{T}}, n::Int) = Diagonal(ones(T,n))
 
 expm(D::Diagonal) = Diagonal(exp(D.diag))
+logm(D::Diagonal) = Diagonal(log(D.diag))
 sqrtm(D::Diagonal) = Diagonal(sqrt(D.diag))
 
 #Linear solver

base/linalg/triangular.jl

@@ -910,7 +910,7 @@ function logm{T<:Union{Float64,Complex{Float64}}}(A0::UpperTriangular{T})
          2.879093714241194e-001]
     tmax = size(theta, 1)
     n = size(A0, 1)
-    A = A0
+    A = copy(A0)
     p = 0
     m = 0
 
@@ -919,7 +919,7 @@ function logm{T<:Union{Float64,Complex{Float64}}}(A0::UpperTriangular{T})
     dm1 = Array(T, n)
     s = 0
     for i = 1:n
-        dm1[i] = dm1[i] - 1.
+        dm1[i] = d[i] - 1.
     end
     while norm(dm1, Inf) > theta[tmax]
         for i = 1:n
@@ -1078,6 +1078,7 @@ function logm{T<:Union{Float64,Complex{Float64}}}(A0::UpperTriangular{T})
     return UpperTriangular(Y)
 
 end
+logm(A::LowerTriangular) = logm(A.').'
 
 function sqrtm{T}(A::UpperTriangular{T})
     n = size(A, 1)

test/linalg3.jl

@@ -182,6 +182,9 @@ for elty in (Float64, Complex{Float64})
     @test contains(s, "WARNING: Matrix with nonpositive real eigenvalues, a nonprimary matrix logarithm will be returned.")
     redirect_stderr(OLD_STDERR)
 
+    A7  = convert(Matrix{elty}, [1 0 0 1e-8; 0 1 0 0; 0 0 1 0; 0 0 0 1])
+    @test_approx_eq expm(logm(A7)) A7
+
 end
 
 A8 = 100 * [-1+1im 0 0 1e-8; 0 1 0 0; 0 0 1 0; 0 0 0 1];