text: __author__ = 'sibirrer'
  
  import numpy as np
  import copy
  from lenstronomy.Util import class_creator
  from lenstronomy.ImSim.image2source_mapping import Image2SourceMapping
  from lenstronomy.LensModel.Solver.solver import Solver
  from lenstronomy.LensModel.lens_param import LensParam
  from lenstronomy.LightModel.light_param import LightParam
  from lenstronomy.PointSource.point_source_param import PointSourceParam
  from lenstronomy.Sampling.special_param import SpecialParam
  
  
  class Param(object):
      """
      class that handles the parameter constraints. In particular when different model profiles share joint constraints.
  
  
      Options between same model classes:
  
      'joint_lens_with_lens':list [[i_lens, k_lens, ['param_name1', 'param_name2', ...]], [...], ...],
      joint parameter between two lens models
  
      'joint_lens_light_with_lens_light':list [[i_lens_light, k_lens_light, ['param_name1', 'param_name2', ...]], [...], ...],
      joint parameter between two lens light models, the second adopts the value of the first
  
      'joint_source_with_source':list [[i_source, k_source, ['param_name1', 'param_name2', ...]], [...], ...],
      joint parameter between two source surface brightness models, the second adopts the value of the first
  
  
      Options between different model classes:
  
      'joint_lens_with_light': list [[i_light, k_lens, ['param_name1', 'param_name2', ...]], [...], ...],
      joint parameter between lens model and lens light model
  
      'joint_source_with_point_source': list [[i_point_source, k_source], [...], ...],
      joint position parameter between lens model and source light model
  
      'joint_lens_light_with_point_source': list [[i_point_source, k_lens_light], [...], ...],
      joint position parameter between lens model and lens light model
  
      'joint_extinction_with_lens_light': list [[i_lens_light, k_extinction, ['param_name1', 'param_name2', ...]], [...], ...],
      joint parameters between the lens surface brightness and the optical depth models
  
      'joint_lens_with_source_light': [[i_source, k_lens, ['param_name1', 'param_name2', ...]], [...], ...],
      joint parameter between lens model and source light model. Samples light model parameter only.
  
      hierarchy is as follows:
      1. Point source parameters are inferred
      2. Lens light joint parameters are set
      3. Lens model joint constraints are set
      4. Lens model solver is applied
      5. Joint source and point source is applied
  
  
      """
  
      def __init__(self, kwargs_model,
                   kwargs_fixed_lens=None, kwargs_fixed_source=None, kwargs_fixed_lens_light=None, kwargs_fixed_ps=None,
                   kwargs_fixed_special=None, kwargs_fixed_extinction=None,
                   kwargs_lower_lens=None, kwargs_lower_source=None, kwargs_lower_lens_light=None, kwargs_lower_ps=None,
                   kwargs_lower_special=None, kwargs_lower_extinction=None,
                   kwargs_upper_lens=None, kwargs_upper_source=None, kwargs_upper_lens_light=None, kwargs_upper_ps=None,
                   kwargs_upper_special=None, kwargs_upper_extinction=None,
                   kwargs_lens_init=None, linear_solver=True, joint_lens_with_lens=[], joint_lens_light_with_lens_light=[],
                   joint_source_with_source=[], joint_lens_with_light=[], joint_source_with_point_source=[],
                   joint_lens_light_with_point_source=[], joint_extinction_with_lens_light=[],
                   joint_lens_with_source_light=[], mass_scaling_list=None, point_source_offset=False,
                   num_point_source_list=None, image_plane_source_list=None, solver_type='NONE', Ddt_sampling=None,
                   source_size=False, num_tau0=0):
          """
  
          :param kwargs_model:
          :param kwargs_fixed_lens:
          :param kwargs_fixed_source:
          :param kwargs_fixed_lens_light:
          :param kwargs_fixed_ps:
          :param kwargs_fixed_special:
          :param kwargs_fixed_extinction:
          :param kwargs_lower_lens:
          :param kwargs_lower_source:
          :param kwargs_lower_lens_light:
          :param kwargs_lower_ps:
          :param kwargs_lower_special:
          :param kwargs_lower_extinction:
          :param kwargs_upper_lens:
          :param kwargs_upper_source:
          :param kwargs_upper_lens_light:
          :param kwargs_upper_ps:
          :param kwargs_upper_special:
          :param kwargs_upper_extinction:
          :param kwargs_lens_init:
          :param linear_solver:
          :param joint_lens_with_lens:
          :param joint_lens_light_with_lens_light:
          :param joint_source_with_source:
          :param joint_lens_with_light:
          :param joint_source_with_point_source:
          :param joint_lens_light_with_point_source:
          :param joint_extinction_with_lens_light:
          :param joint_lens_with_source_light:
          :param mass_scaling_list:
          :param point_source_offset:
          :param num_point_source_list:
          :param image_plane_source_list: optional, list of booleans for the source_light components.
           If a component is set =True it will parameterized the positions in the image plane and ray-trace the
           parameters back to the source position on the fly during the fitting.
          :param solver_type:
          :param Ddt_sampling:
          :param source_size:
          :param num_tau0:
          """
  
          self._lens_model_list = kwargs_model.get('lens_model_list', [])
          self._source_light_model_list = kwargs_model.get('source_light_model_list', [])
          self._lens_light_model_list = kwargs_model.get('lens_light_model_list', [])
          self._point_source_model_list = kwargs_model.get('point_source_model_list', [])
          self._optical_depth_model_list = kwargs_model.get('optical_depth_model_list', [])
  
          lens_model_class, source_model_class, _, _, _ = class_creator.create_class_instances(all_models=True, **kwargs_model)
          self._image2SourceMapping = Image2SourceMapping(lensModel=lens_model_class, sourceModel=source_model_class)
  
          if kwargs_fixed_lens is None:
              kwargs_fixed_lens = [{} for i in range(len(self._lens_model_list))]
          if kwargs_fixed_source is None:
              kwargs_fixed_source = [{} for i in range(len(self._source_light_model_list))]
          if kwargs_fixed_lens_light is None:
              kwargs_fixed_lens_light = [{} for i in range(len(self._lens_light_model_list))]
          if kwargs_fixed_ps is None:
              kwargs_fixed_ps = [{} for i in range(len(self._point_source_model_list))]
          if kwargs_fixed_special is None:
              kwargs_fixed_special = {}
  
          self._joint_lens_with_lens = joint_lens_with_lens
          self._joint_lens_light_with_lens_light = joint_lens_light_with_lens_light
          self._joint_source_with_source = joint_source_with_source
  
          self._joint_lens_with_light = joint_lens_with_light
          self._joint_lens_with_source_light = joint_lens_with_source_light
          self._joint_source_with_point_source = copy.deepcopy(joint_source_with_point_source)
          for param_list in self._joint_source_with_point_source:
              if len(param_list) == 2:
                  param_list.append(['center_x', 'center_y'])
          self._joint_lens_light_with_point_source = copy.deepcopy(joint_lens_light_with_point_source)
          for param_list in self._joint_lens_light_with_point_source:
              if len(param_list) == 2:
                  param_list.append(['center_x', 'center_y'])
          if mass_scaling_list is None:
              mass_scaling_list = [False] * len(self._lens_model_list)
          self._mass_scaling_list = mass_scaling_list
          if 1 in self._mass_scaling_list:
              self._num_scale_factor = np.max(self._mass_scaling_list)
              self._mass_scaling = True
          else:
              self._num_scale_factor = 0
              self._mass_scaling = False
          self._point_source_offset = point_source_offset
          if num_point_source_list is None:
              num_point_source_list = [1] * len(self._point_source_model_list)
  
          # Attention: if joint coordinates with other source profiles, only indicate one as bool
          if image_plane_source_list is None:
              image_plane_source_list = [False] * len(self._source_light_model_list)
          self._image_plane_source_list = image_plane_source_list
  
          try:
              self._num_images = num_point_source_list[0]
          except:
              self._num_images = 0
          self._solver_type = solver_type
          if self._solver_type == 'NONE':
              self._solver = False
          else:
              self._solver = True
              self._solver_module = Solver(solver_type=self._solver_type, lensModel=lens_model_class,
                                           num_images=self._num_images)
  
          self._joint_extinction_with_lens_light = joint_extinction_with_lens_light
          # fix parameters joint within the same model types
          kwargs_fixed_lens_updated = self._add_fixed_lens(kwargs_fixed_lens, kwargs_lens_init)
          kwargs_fixed_lens_updated = self._fix_joint_param(kwargs_fixed_lens_updated, self._joint_lens_with_lens)
          kwargs_fixed_lens_updated = self._fix_joint_param(kwargs_fixed_lens_updated, self._joint_lens_with_source_light)
          kwargs_fixed_lens_light_updated = self._fix_joint_param(kwargs_fixed_lens_light, self._joint_lens_light_with_lens_light)
          kwargs_fixed_source_updated = self._fix_joint_param(kwargs_fixed_source, self._joint_source_with_source)
          kwargs_fixed_ps_updated = copy.deepcopy(kwargs_fixed_ps)
          kwargs_fixed_extinction_updated = self._fix_joint_param(kwargs_fixed_extinction, self._joint_extinction_with_lens_light)
          # fix parameters joint with other model types
          kwargs_fixed_lens_updated = self._fix_joint_param(kwargs_fixed_lens_updated, self._joint_lens_with_light)
          kwargs_fixed_source_updated = self._fix_joint_param(kwargs_fixed_source_updated, self._joint_source_with_point_source)
          kwargs_fixed_lens_light_updated = self._fix_joint_param(kwargs_fixed_lens_light_updated,
                                                              self._joint_lens_light_with_point_source)
          self.lensParams = LensParam(self._lens_model_list, kwargs_fixed_lens_updated, num_images=self._num_images,
                                      solver_type=self._solver_type, kwargs_lower=kwargs_lower_lens,
                                      kwargs_upper=kwargs_upper_lens)
          self.lensLightParams = LightParam(self._lens_light_model_list, kwargs_fixed_lens_light_updated, type='lens_light',
                                            linear_solver=linear_solver, kwargs_lower=kwargs_lower_lens_light,
                                            kwargs_upper=kwargs_upper_lens_light)
          self.souceParams = LightParam(self._source_light_model_list, kwargs_fixed_source_updated, type='source_light',
                                        linear_solver=linear_solver, kwargs_lower=kwargs_lower_source,
                                        kwargs_upper=kwargs_upper_source)
          self.pointSourceParams = PointSourceParam(self._point_source_model_list, kwargs_fixed_ps_updated,
                                                    num_point_source_list=num_point_source_list,
                                                    linear_solver=linear_solver, kwargs_lower=kwargs_lower_ps,
                                                    kwargs_upper=kwargs_upper_ps)
          self.extinctionParams = LightParam(self._optical_depth_model_list, kwargs_fixed_extinction_updated,
                                             kwargs_lower=kwargs_lower_extinction, kwargs_upper=kwargs_upper_extinction,
                                             linear_solver=False)
          self.specialParams = SpecialParam(Ddt_sampling=Ddt_sampling, mass_scaling=self._mass_scaling,
                                            kwargs_fixed=kwargs_fixed_special, num_scale_factor=self._num_scale_factor,
                                            kwargs_lower=kwargs_lower_special, kwargs_upper=kwargs_upper_special,
                                            point_source_offset=self._point_source_offset, num_images=self._num_images,
                                            source_size=source_size, num_tau0=num_tau0)
          for lens_source_joint in self._joint_lens_with_source_light:
              i_source = lens_source_joint[0]
              if i_source in self._image_plane_source_list:
                  raise ValueError("linking a source light model with a lens model AND simultaneously parameterizing the"
                                   " source position in the image plane is not valid!")
  
  
      @property
      def num_point_source_images(self):
          return self._num_images
  
      def args2kwargs(self, args, bijective=False):
          """
  
          :param args: tuple of parameter values (float, strings, ...)
          :param bijective: boolean, if True (default) returns the parameters in the form as they are sampled
           (e.g. if image_plane_source_list is set =True it returns the position in the image plane coordinates),
           if False, returns the parameters in the form to render a model (e.g. image_plane_source_list positions are
           ray-traced back to the source plane).
          :return: keyword arguments sorted in lenstronomy conventions
          """
          i = 0
          args = np.atleast_1d(args)
          kwargs_lens, i = self.lensParams.getParams(args, i)
          kwargs_source, i = self.souceParams.getParams(args, i)
          kwargs_lens_light, i = self.lensLightParams.getParams(args, i)
          kwargs_ps, i = self.pointSourceParams.getParams(args, i)
          kwargs_special, i = self.specialParams.getParams(args, i)
          kwargs_extinction, i = self.extinctionParams.getParams(args, i)
          # update lens_light joint parameters
          kwargs_lens_light = self._update_lens_light_joint_with_point_source(kwargs_lens_light, kwargs_ps)
          kwargs_lens_light = self._update_joint_param(kwargs_lens_light, kwargs_lens_light, self._joint_lens_light_with_lens_light)
          # update lens_light joint with lens model parameters
          kwargs_lens = self._update_joint_param(kwargs_lens_light, kwargs_lens, self._joint_lens_with_light)
          kwargs_lens = self._update_joint_param(kwargs_source, kwargs_lens, self._joint_lens_with_source_light)
          # update extinction model with lens light model
          kwargs_extinction = self._update_joint_param(kwargs_lens_light, kwargs_extinction, self._joint_extinction_with_lens_light)
          # update lens model joint parameters (including scaling)
          kwargs_lens = self._update_joint_param(kwargs_lens, kwargs_lens, self._joint_lens_with_lens)
          kwargs_lens = self.update_lens_scaling(kwargs_special, kwargs_lens)
          # update point source constraint solver
          if self._solver is True:
              x_pos, y_pos = kwargs_ps[0]['ra_image'], kwargs_ps[0]['dec_image']
              kwargs_lens = self._solver_module.update_solver(kwargs_lens, x_pos, y_pos)
          # update source joint with point source
          kwargs_source = self._update_source_joint_with_point_source(kwargs_lens, kwargs_source, kwargs_ps, kwargs_special,
                                                                          image_plane=bijective)
          # update source joint with source
          kwargs_source = self._update_joint_param(kwargs_source, kwargs_source, self._joint_source_with_source)
          # optional revert lens_scaling for bijective
  
          if bijective is True:
              kwargs_lens = self.update_lens_scaling(kwargs_special, kwargs_lens, inverse=True)
          kwargs_return = {'kwargs_lens': kwargs_lens, 'kwargs_source': kwargs_source,
                           'kwargs_lens_light': kwargs_lens_light, 'kwargs_ps': kwargs_ps,
                           'kwargs_special': kwargs_special, 'kwargs_extinction': kwargs_extinction}
          return kwargs_return
  
      def kwargs2args(self, kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None,
                      kwargs_special=None, kwargs_extinction=None):
          """
          inverse of getParam function
          :param kwargs_lens: keyword arguments depending on model options
          :param kwargs_source: keyword arguments depending on model options
          :return: tuple of parameters
          """
  
          args = self.lensParams.setParams(kwargs_lens)
          args += self.souceParams.setParams(kwargs_source)
          args += self.lensLightParams.setParams(kwargs_lens_light)
          args += self.pointSourceParams.setParams(kwargs_ps)
          args += self.specialParams.setParams(kwargs_special)
          args += self.extinctionParams.setParams(kwargs_extinction)
          return args
  
      def param_limits(self):
          """
  
          :return: lower and upper limits of the arguments being sampled
          """
          lower_limit = self.kwargs2args(kwargs_lens=self.lensParams.lower_limit,
                                         kwargs_source=self.souceParams.lower_limit,
                                         kwargs_lens_light=self.lensLightParams.lower_limit,
                                         kwargs_ps=self.pointSourceParams.lower_limit,
                                         kwargs_special=self.specialParams.lower_limit,
                                         kwargs_extinction=self.extinctionParams.lower_limit)
          upper_limit = self.kwargs2args(kwargs_lens=self.lensParams.upper_limit,
                                         kwargs_source=self.souceParams.upper_limit,
                                         kwargs_lens_light=self.lensLightParams.upper_limit,
                                         kwargs_ps=self.pointSourceParams.upper_limit,
                                         kwargs_special=self.specialParams.upper_limit,
                                         kwargs_extinction=self.extinctionParams.upper_limit)
          return lower_limit, upper_limit
  
      def num_param(self):
          """
  
          :return: number of parameters involved (int)
          """
          num, list = self.lensParams.num_param()
          _num, _list = self.souceParams.num_param()
          num += _num
          list += _list
          _num, _list = self.lensLightParams.num_param()
          num += _num
          list += _list
          _num, _list = self.pointSourceParams.num_param()
          num += _num
          list += _list
          _num, _list = self.specialParams.num_param()
          num += _num
          list += _list
          _num, _list = self.extinctionParams.num_param()
          num += _num
          list += _list
          return num, list
  
      def num_param_linear(self):
          """
  
          :return: number of linear basis set coefficients that are solved for
          """
          num = 0
          num += self.souceParams.num_param_linear()
          num += self.lensLightParams.num_param_linear()
          num += self.pointSourceParams.num_param_linear()
          return num
  
      def image2source_plane(self, kwargs_source, kwargs_lens, image_plane=False):
          """
          maps the image plane position definition of the source plane
  
          :param kwargs_source:
          :param kwargs_lens:
          :return:
          """
          kwargs_source_copy = copy.deepcopy(kwargs_source)
          for i, kwargs in enumerate(kwargs_source_copy):
              if self._image_plane_source_list[i] is True and not image_plane:
                  if 'center_x' in kwargs:
                      x_mapped, y_mapped = self._image2SourceMapping.image2source(kwargs['center_x'], kwargs['center_y'],
                                                                                  kwargs_lens, index_source=i)
                      kwargs['center_x'] = x_mapped
                      kwargs['center_y'] = y_mapped
          return kwargs_source_copy
  
      def _update_source_joint_with_point_source(self, kwargs_lens_list, kwargs_source_list, kwargs_ps, kwargs_special, image_plane=False):
          kwargs_source_list = self.image2source_plane(kwargs_source_list, kwargs_lens_list, image_plane=image_plane)
  
          for setting in self._joint_source_with_point_source:
              i_point_source, k_source, param_list = setting
              if 'ra_source' in kwargs_ps[i_point_source]:
                  x_mapped = kwargs_ps[i_point_source]['ra_source']
                  y_mapped = kwargs_ps[i_point_source]['dec_source']
              else:
                  x_pos, y_pos = kwargs_ps[i_point_source]['ra_image'], kwargs_ps[i_point_source]['dec_image']
                  #x_pos, y_pos = self.real_image_positions(x_pos, y_pos, kwargs_special)
                  x_mapped, y_mapped = self._image2SourceMapping.image2source(x_pos, y_pos, kwargs_lens_list,
                                                                              index_source=k_source)
              for param_name in param_list:
                  if param_name == 'center_x':
                      kwargs_source_list[k_source][param_name] = np.mean(x_mapped)
                  elif param_name == 'center_y':
                      kwargs_source_list[k_source][param_name] = np.mean(y_mapped)
                  else:
                      kwargs_source_list[k_source][param_name] = kwargs_ps[i_point_source][param_name]
          return kwargs_source_list
  
      def _update_lens_light_joint_with_point_source(self, kwargs_lens_light_list, kwargs_ps):
  
          for setting in self._joint_lens_light_with_point_source:
              i_point_source, k_lens_light, param_list = setting
              if 'ra_image' in kwargs_ps[i_point_source]:
                  x_mapped = kwargs_ps[i_point_source]['ra_image']
                  y_mapped = kwargs_ps[i_point_source]['dec_image']
              else:
                  raise ValueError("Joint lens light with point source not possible as point source is defined in the source plane!")
              for param_name in param_list:
                  if param_name == 'center_x':
                      kwargs_lens_light_list[k_lens_light][param_name] = np.mean(x_mapped)
                  elif param_name == 'center_y':
                      kwargs_lens_light_list[k_lens_light][param_name] = np.mean(y_mapped)
          return kwargs_lens_light_list
  
      @staticmethod
      def _update_joint_param(kwargs_list_1, kwargs_list_2, joint_setting_list):
          """
  
          :param kwargs_list_1: list of keyword arguments
          :param kwargs_list_2: list of keyword arguments
          :param joint_setting_list: [[i_1, k_2, ['param_name1', 'param_name2', ...]], [...], ...]
          :return: udated kwargs_list_2 with arguments from kwargs_list_1 as defined in joint_setting_list
          """
          for setting in joint_setting_list:
              i_1, k_2, param_list = setting
              for param_name in param_list:
                  kwargs_list_2[k_2][param_name] = kwargs_list_1[i_1][param_name]
          return kwargs_list_2
  
      @staticmethod
      def _fix_joint_param(kwargs_list_2, joint_setting_list):
          """
  
          :param kwargs_list_2: list of keyword arguments
          :param joint_setting_list: [[i_1, k_2, ['param_name1', 'param_name2', ...]], [...], ...]
          :return: fixes entries in kwargs_list_2 that are joint with other kwargs_list as defined in joint_setting_list
          """
          kwargs_list_2_update = copy.deepcopy(kwargs_list_2)
          for setting in joint_setting_list:
              i_1, k_2, param_list = setting
              for param_name in param_list:
                  kwargs_list_2_update[k_2][param_name] = 0
          return kwargs_list_2_update
  
      def update_lens_scaling(self, kwargs_special, kwargs_lens, inverse=False):
          """
          multiplies the scaling parameters of the profiles
  
          :param args:
          :param kwargs_lens:
          :param i:
          :param inverse:
          :return:
          """
          kwargs_lens_updated = copy.deepcopy(kwargs_lens)
          if self._mass_scaling is False:
              return kwargs_lens_updated
          scale_factor_list = np.array(kwargs_special['scale_factor'])
          if inverse is True:
              scale_factor_list = 1. / np.array(kwargs_special['scale_factor'])
          for i, kwargs in enumerate(kwargs_lens_updated):
              if self._mass_scaling_list[i] is not False:
                  scale_factor = scale_factor_list[self._mass_scaling_list[i] - 1]
                  if 'theta_E' in kwargs:
                      kwargs['theta_E'] *= scale_factor
                  elif 'alpha_Rs' in kwargs:
                      kwargs['alpha_Rs'] *= scale_factor
                  elif 'alpha_1' in kwargs:
                      kwargs['alpha_1'] *= scale_factor
                  elif 'sigma0' in kwargs:
                      kwargs['sigma0'] *= scale_factor
                  elif 'k_eff' in kwargs:
                      kwargs['k_eff'] *= scale_factor
          return kwargs_lens_updated
  
      def _add_fixed_lens(self, kwargs_fixed, kwargs_init):
          kwargs_fixed_update = copy.deepcopy(kwargs_fixed)
          if self._solver is True:
              if kwargs_init is None:
                  raise ValueError("kwargs_lens_init must be specified when the point source solver is enabled!")
              kwargs_fixed_update = self._solver_module.add_fixed_lens(kwargs_fixed_update, kwargs_init)
          return kwargs_fixed_update
  
      def check_solver(self, kwargs_lens, kwargs_ps):
          """
          test whether the image positions map back to the same source position
          :param kwargs_lens:
          :param kwargs_ps:
          :return: Euclidean distance between the rayshooting of the image positions
          """
          if self._solver is True:
              image_x, image_y = kwargs_ps[0]['ra_image'], kwargs_ps[0]['dec_image']
              dist = self._solver_module.check_solver(image_x, image_y, kwargs_lens)
              return np.max(dist)
          else:
              return 0
  
      def check_positive_flux(self, kwargs_source, kwargs_lens_light, kwargs_ps):
          pos_bool_ps = self.pointSourceParams.check_positive_flux(kwargs_ps)
          pos_bool_source = self.souceParams.check_positive_flux_profile(kwargs_source)
          pos_bool_lens_light = self.lensLightParams.check_positive_flux_profile(kwargs_lens_light)
          if pos_bool_ps is True and pos_bool_source is True and pos_bool_lens_light is True:
              return True
          else:
              return False
  
      def print_setting(self):
          """
          prints the setting of the parameter class
  
          :return:
          """
          num, param_list = self.num_param()
          num_linear = self.num_param_linear()
  
          print("The following model options are chosen:")
          print("Lens models:", self._lens_model_list)
          print("Source models:", self._source_light_model_list)
          print("Lens light models:", self._lens_light_model_list)
          print("Point source models:", self._point_source_model_list)
          print("===================")
          print("The following parameters are being fixed:")
          print("Lens:", self.lensParams.kwargs_fixed)
          print("Source:", self.souceParams.kwargs_fixed)
          print("Lens light:", self.lensLightParams.kwargs_fixed)
          print("Point source:", self.pointSourceParams.kwargs_fixed)
          print("===================")
          print("Joint parameters for different models")
          print("Joint lens with lens:", self._joint_lens_with_lens)
          print("Joint lens light with lens light:", self._joint_lens_light_with_lens_light)
          print("Joint source with source:", self._joint_source_with_source)
          print("Joint lens with light:", self._joint_lens_with_light)
          print("Joint source with point source:", self._joint_source_with_point_source)
          print("Joint lens light with point source:", self._joint_lens_light_with_point_source)
          print("===================")
          print("Number of non-linear parameters being sampled: ", num)
          print("Parameters being sampled: ", param_list)
          print("Number of linear parameters being solved for: ", num_linear)
  