jwscook

using ForwardDiff, StaticArrays

function jacobi(f, x)
  x_real = @SArray [real(x), imag(x)]
  function f_real(v)
    z = complex(v[1], v[2])
    result = f(z)
    return @SArray [real(result), imag(result)]
  end
  J = ForwardDiff.jacobian(f_real, x_real)

jwscook

using LinearAlgebra

"Compute Givens rotation parameters to zero out b"
function givens_rotation(a, b)
  T = promote_type(typeof(a), typeof(b))
  if iszero(b)
    return one(T), zero(T)
  elseif abs(b) > abs(a)
    t = a / b
    s = 1 / sqrt(1 + t^2)