Merge pull request #120 from JuliaLinearAlgebra/an/zerosvd

Test svd of zero matrix and fix the sign flipping when there are

Author: andreasnoack

src/svd.jl

@@ -253,12 +253,16 @@ function _svdvals!(B::Bidiagonal{T}; tol = eps(T)) where {T<:Real}
     return sort(abs.(diag(B)), rev = true)
 end
 
+# We want to avoid that zero eigenvalues zero out any singular vectors so we'd
+# have to use a modified sign function
+_sign(x) = ifelse(iszero(x), one(x), sign(x))
+
 function _sort_and_adjust!(U, s, Vᴴ)
     n = length(s)
 
     # Adjust sign of singular values if necessary
     if any(!isposdef, s)
-        rmul!(U, Diagonal(sign.(s)))
+        rmul!(U, Diagonal(_sign.(s)))
         map!(abs, s, s)
     end
 

test/svd.jl

@@ -241,4 +241,11 @@ using Test, GenericLinearAlgebra, LinearAlgebra, Quaternions, DoubleFloats
         BF = GenericLinearAlgebra.bidiagonalize!(copy(A))
         @test (BF.rightQ' * Matrix(I, size(A)...)) * BF.rightQ ≈ I
     end
+
+    @testset "Issue 119" begin
+        F = svd(zeros(BigFloat, 2, 2))
+        @test F.S == zeros(2)
+        @test F.U == I
+        @test F.Vt == I
+    end
 end