text: __author__ = 'sibirrer'
  
  
  import numpy as np
  from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
  
  __all__ = ['PointMass']
  
  
  class PointMass(LensProfileBase):
      """
      class to compute the physical deflection angle of a point mass, given as an Einstein radius
      """
      param_names = ['theta_E', 'center_x', 'center_y']
      lower_limit_default = {'theta_E': 0, 'center_x': -100, 'center_y': -100}
      upper_limit_default = {'theta_E': 100, 'center_x': 100, 'center_y': 100}
  
      def __init__(self):
          self.r_min = 10**(-25)
          super(PointMass, self).__init__()
          # alpha = 4*const.G * (mass*const.M_sun)/const.c**2/(r*const.Mpc)
  
      def function(self, x, y, theta_E, center_x=0, center_y=0):
          """
  
          :param x: x-coord (in angles)
          :param y: y-coord (in angles)
          :param theta_E: Einstein radius (in angles)
          :return: lensing potential
          """
          x_ = x - center_x
          y_ = y - center_y
          a = np.sqrt(x_**2 + y_**2)
          if isinstance(a, int) or isinstance(a, float):
              r = max(self.r_min, a)
          else:
              r = np.empty_like(a)
              r[a > self.r_min] = a[a > self.r_min]  #in the SIS regime
              r[a <= self.r_min] = self.r_min
          phi = theta_E**2*np.log(r)
          return phi
  
      def derivatives(self, x, y, theta_E, center_x=0, center_y=0):
          """
  
          :param x: x-coord (in angles)
          :param y: y-coord (in angles)
          :param theta_E: Einstein radius (in angles)
          :return: deflection angle (in radian)
          """
          x_ = x - center_x
          y_ = y - center_y
          a = np.sqrt(x_**2 + y_**2)
          if isinstance(a, int) or isinstance(a, float):
              r = max(self.r_min, a)
          else:
              r = np.empty_like(a)
              r[a > self.r_min] = a[a > self.r_min]  #in the SIS regime
              r[a <= self.r_min] = self.r_min
          alpha = theta_E**2/r
          return alpha*x_/r, alpha*y_/r
  
      def hessian(self, x, y, theta_E, center_x=0, center_y=0):
          """
  
          :param x: x-coord (in angles)
          :param y: y-coord (in angles)
          :param theta_E: Einstein radius (in angles)
          :return: hessian matrix (in radian)
          """
          x_ = x - center_x
          y_ = y - center_y
          C = theta_E**2
          a = x_**2 + y_**2
          if isinstance(a, int) or isinstance(a, float):
              r2 = max(self.r_min**2, a)
          else:
              r2 = np.empty_like(a)
              r2[a > self.r_min**2] = a[a > self.r_min**2]  #in the SIS regime
              r2[a <= self.r_min**2] = self.r_min**2
          f_xx = C * (y_**2-x_**2)/r2**2
          f_yy = C * (x_**2-y_**2)/r2**2
          f_xy = -C * 2*x_*y_/r2**2
          return f_xx, f_yy, f_xy
  