Fix to_boundary for complex numbers (#928)

src/krylov_utils.jl

@@ -336,12 +336,12 @@ kcopy!(n :: Integer, y :: AbstractVector{T}, x :: AbstractVector{T}) where T <:
 
 kfill!(x :: AbstractArray{T}, val :: T) where T <: FloatOrComplex = fill!(x, val)
 
+kref!(n, x, y, c, s) = reflect!(x, y, c, s)
+
 kgeqrf!(A :: AbstractMatrix{T}, tau :: AbstractVector{T}) where T <: BLAS.BlasFloat = LAPACK.geqrf!(A, tau)
 korgqr!(A :: AbstractMatrix{T}, tau :: AbstractVector{T}) where T <: BLAS.BlasFloat = LAPACK.orgqr!(A, tau)
 kormqr!(side :: Char, trans :: Char, A :: AbstractMatrix{T}, tau :: AbstractVector{T}, C :: AbstractMatrix{T}) where T <: BLAS.BlasFloat = LAPACK.ormqr!(side, trans, A, tau, C)
 
-kref!(n, x, y, c, s) = reflect!(x, y, c, s)
-
 macro kswap!(x, y)
   quote
     local tmp = $(esc(x))
@@ -377,10 +377,10 @@ function to_boundary(n :: Int, x :: AbstractVector{FC}, d :: AbstractVector{FC},
   else
     # (dᴴMd) σ² + (xᴴMd + dᴴMx) σ + (xᴴMx - Δ²).
     mulorldiv!(z, M, x, ldiv)
-    rxd = dot(z, d)
-    xNorm2 = dot(z, x)
+    rxd = kdot(n, z, d)
+    xNorm2 = kdotr(n, z, x)
     mulorldiv!(z, M, d, ldiv) 
-    dNorm2 = dot(z, d)
+    dNorm2 = kdotr(n, z, d)
   end 
   dNorm2 == zero(T) && error("zero direction")
   flip && (rxd = -rxd)
@@ -390,7 +390,7 @@ function to_boundary(n :: Int, x :: AbstractVector{FC}, d :: AbstractVector{FC},
 
   # q₂ = ‖d‖², q₁ = xᴴd + dᴴx, q₀ = ‖x‖² - Δ²
   # ‖x‖² ≤ Δ² ⟹ (q₁)² - 4 * q₂ * q₀ ≥ 0
-  roots = roots_quadratic(dNorm2, 2 * rxd, xNorm2 - radius2)
+  roots = roots_quadratic(dNorm2, 2 * real(rxd), xNorm2 - radius2)
 
   return roots  # `σ1` and `σ2`
 end