Use dot and views in QR code

stdlib/LinearAlgebra/src/generic.jl

@@ -1490,14 +1490,10 @@ end
  n == 0 && return zero(eltype(x))
  @inbounds begin
  ξ1 = x[1]
- normu = abs2(ξ1)
- for i = 2:n
- normu += abs2(x[i])
- end
+ normu = norm(x)
  if iszero(normu)
  return zero(ξ1/normu)
  end
- normu = sqrt(normu)
  ν = copysign(normu, real(ξ1))
  ξ1 += ν
  x[1] = -ν
@@ -1516,22 +1512,11 @@ end
  throw(DimensionMismatch("reflector has length $(length(x)), which must match the first dimension of matrix A, $m"))
  end
  m == 0 && return A
- @inbounds begin
- for j = 1:n
- # dot
- vAj = A[1, j]
- for i = 2:m
- vAj += x[i]'*A[i, j]
- end
-
- vAj = conj(τ)*vAj
-
- # ger
- A[1, j] -= vAj
- for i = 2:m
- A[i, j] -= x[i]*vAj
- end
- end
+ @inbounds for j = 1:n
+ Aj, xj = view(A, 2:m, j), view(x, 2:m)
+ vAj = conj(τ)*(A[1, j] + dot(xj, Aj))
+ A[1, j] -= vAj
+ axpy!(-vAj, xj, Aj)
  end
  return A
 end