Merge pull request #26 from JuliaLinearAlgebra/an/degenerate

Add a slight perturbation to initial α if it is one so ensure that

src/svd.jl

@@ -15,7 +15,6 @@ function _biLanczosIterations!(A, stepsize, αs, βs, U, V, μs, νs, maxνs, ma
     β = βs[iter]
 
     for j = iter .+ (1:stepsize)
-
         # The v step
         vOld = v
         ## apply operator
@@ -127,6 +126,11 @@ function biLanczos(A,
     v = A'initvec
     rmul!(v, inv(nrmInit))
     α = norm(v)
+    if isone(α)
+        # We need v to change when scaled with α.
+        # Otherwise the basis generation might break down.
+        α = nextfloat(α)
+    end
     rmul!(v, inv(α))
     V = fill(v, 1)
     αs = fill(α, 1)

test/runtests.jl

@@ -36,3 +36,7 @@ end
     data = rand(1:100, 50, 50)
     @test @inferred(TSVD.tsvd(data, 2))[2] ≈ svdvals(data)[1:2]
 end
+
+@testset "Issue 25. Degenerate basis" begin
+  @test tsvd([1 0 ; 0 1], 1, initvec=[1.0; 0.0])[2] ≈ [1.0]
+end