Fix behaviour of sqrtm on UpperTriangular matrices

JuliaLang · Aug 12, 2015 · 8527eb6 · 8527eb6
1 parent 66f336d
commit 8527eb6
Show file tree

Hide file tree

Showing 3 changed files with 41 additions and 14 deletions.
diff --git a/base/linalg/dense.jl b/base/linalg/dense.jl
@@ -319,7 +319,6 @@ function logm(A::StridedMatrix)
         return retmat
     end
 end
-
 logm(a::Number) = (b = log(complex(a)); imag(b) == 0 ? real(b) : b)
 logm(a::Complex) = log(a)
 
@@ -328,21 +327,27 @@ function sqrtm{T<:Real}(A::StridedMatrix{T})
         return full(sqrtm(Symmetric(A)))
     end
     n = chksquare(A)
-    SchurF = schurfact(complex(A))
-    R = full(sqrtm(UpperTriangular(SchurF[:T])))
-    retmat = SchurF[:vectors]*R*SchurF[:vectors]'
-    all(imag(retmat) .== 0) ? real(retmat) : retmat
+    if istriu(A)
+        return full(sqrtm(UpperTriangular(A)))
+    else
+        SchurF = schurfact(complex(A))
+        R = full(sqrtm(UpperTriangular(SchurF[:T])))
+        return SchurF[:vectors] * R * SchurF[:vectors]'
+    end
 end
 function sqrtm{T<:Complex}(A::StridedMatrix{T})
     if ishermitian(A)
         return full(sqrtm(Hermitian(A)))
     end
     n = chksquare(A)
-    SchurF = schurfact(A)
-    R = full(sqrtm(UpperTriangular(SchurF[:T])))
-    SchurF[:vectors]*R*SchurF[:vectors]'
+    if istriu(A)
+        return full(sqrtm(UpperTriangular(A)))
+    else
+        SchurF = schurfact(A)
+        R = full(sqrtm(UpperTriangular(SchurF[:T])))
+        return SchurF[:vectors] * R * SchurF[:vectors]'
+    end
 end
-
 sqrtm(a::Number) = (b = sqrt(complex(a)); imag(b) == 0 ? real(b) : b)
 sqrtm(a::Complex) = sqrt(a)
 

diff --git a/base/linalg/triangular.jl b/base/linalg/triangular.jl
@@ -1108,11 +1108,25 @@ end
 logm(A::LowerTriangular) = logm(A.').'
 
 function sqrtm{T}(A::UpperTriangular{T})
-    n = size(A, 1)
-    TT = typeof(sqrt(zero(T)))
+    n = chksquare(A)
+    realmatrix = false
+    if isreal(A)
+        realmatrix = true
+        for i = 1:n
+            if real(A[i,i]) < 0
+                realmatrix = false
+                break
+            end
+        end
+    end
+    if realmatrix
+        TT = typeof(sqrt(zero(T)))
+    else
+        TT = typeof(sqrt(complex(-one(T))))
+    end
     R = zeros(TT, n, n)
     for j = 1:n
-        R[j,j] = sqrt(A[j,j])
+        R[j,j] = realmatrix?sqrt(A[j,j]):sqrt(complex(A[j,j]))
         for i = j-1:-1:1
             r = A[i,j]
             for k = i+1:j-1
@@ -1124,7 +1138,7 @@ function sqrtm{T}(A::UpperTriangular{T})
     return UpperTriangular(R)
 end
 function sqrtm{T}(A::UnitUpperTriangular{T})
-    n = size(A, 1)
+    n = chksquare(A)
     TT = typeof(sqrt(zero(T)))
     R = zeros(TT, n, n)
     for j = 1:n

diff --git a/test/linalg/triangular.jl b/test/linalg/triangular.jl
@@ -122,7 +122,7 @@ for elty1 in (Float32, Float64, Complex64, Complex128, BigFloat, Int)
         @test_approx_eq_eps det(A1) det(lufact(full(A1))) sqrt(eps(real(float(one(elty1)))))*n*n
 
         # Matrix square root
-        @test_approx_eq sqrtm(A1) |> t->t*t A1
+        @test sqrtm(A1) |> t->t*t ≈ A1
 
         # naivesub errors
         @test_throws DimensionMismatch naivesub!(A1,ones(elty1,n+1))
@@ -238,6 +238,14 @@ for elty1 in (Float32, Float64, Complex64, Complex128, BigFloat, Int)
     end
 end
 
+# Matrix square root
+Atn = UpperTriangular([-1 1 2; 0 -2 2; 0 0 -3])
+Atp = UpperTriangular([1 1 2; 0 2 2; 0 0 3])
+@test sqrtm(Atn) |> t->t*t ≈ Atn
+@test typeof(sqrtm(Atn)[1,1]) <: Complex
+@test sqrtm(Atp) |> t->t*t ≈ Atp
+@test typeof(sqrtm(Atp)[1,1]) <: Real
+
 Areal   = randn(n, n)/2
 Aimg    = randn(n, n)/2
 A2real  = randn(n, n)/2