module Jacobian

def dfdxi(f,fx,x,i)
  nRetry = 0
  n = x.size
  xSave = x[i]
  ok = 0
  ratio = f.ten*f.ten*f.ten
  dx = x[i].abs/ratio
  dx = fx[i].abs/ratio if isEqual(dx,f.zero,f.zero,f.eps)
  dx = f.one/f.ten     if isEqual(dx,f.zero,f.zero,f.eps)
  until ok>0 do
    deriv = []
    nRetry += 1
    if nRetry > 100
      raise "Singular Jacobian matrix. No change at x[" + i.to_s + "]"
    end
    dx = dx*f.two
    x[i] += dx
    fxNew = f.values(x)
    for j in 0...n do
      if !isEqual(fxNew[j],fx[j],f.zero,f.eps) then
        ok += 1
        deriv <<= (fxNew[j]-fx[j])/dx
      else
        deriv <<= f.zero
      end
    end
    x[i] = xSave
  end
  deriv
end