tidy3d.ModeData#

class tidy3d.ModeData#

Bases: tidy3d.components.data.monitor_data.MonitorData

Data associated with a ModeMonitor: modal amplitudes and propagation indices.

Parameters
  • monitor (ModeMonitor) – amps : ModeAmpsDataArray Complex-valued amplitudes associated with the mode.

  • n_complex (ModeIndexDataArray) – Complex-valued effective propagation constants associated with the mode.

Example

>>> from tidy3d import ModeSpec
>>> from tidy3d import ModeAmpsDataArray, ModeIndexDataArray
>>> direction = ["+", "-"]
>>> f = [1e14, 2e14, 3e14]
>>> mode_index = np.arange(5)
>>> index_coords = dict(f=f, mode_index=mode_index)
>>> index_data = ModeIndexDataArray((1+1j) * np.random.random((3, 5)), coords=index_coords)
>>> amp_coords = dict(direction=direction, f=f, mode_index=mode_index)
>>> amp_data = ModeAmpsDataArray((1+1j) * np.random.random((2, 3, 5)), coords=amp_coords)
>>> monitor = ModeMonitor(
...    size=(2,0,6),
...    freqs=[2e14, 3e14],
...    mode_spec=ModeSpec(num_modes=5),
...    name='mode',
... )
>>> data = ModeData(monitor=monitor, amps=amp_data, n_complex=index_data)

Show JSON schema
{
   "title": "ModeData",
   "description": "Data associated with a :class:`.ModeMonitor`: modal amplitudes and propagation indices.\n\nParameters\n----------\nmonitor : ModeMonitor\n        amps : ModeAmpsDataArray\n    Complex-valued amplitudes associated with the mode.\nn_complex : ModeIndexDataArray\n    Complex-valued effective propagation constants associated with the mode.\n\nExample\n-------\n>>> from tidy3d import ModeSpec\n>>> from tidy3d import ModeAmpsDataArray, ModeIndexDataArray\n>>> direction = [\"+\", \"-\"]\n>>> f = [1e14, 2e14, 3e14]\n>>> mode_index = np.arange(5)\n>>> index_coords = dict(f=f, mode_index=mode_index)\n>>> index_data = ModeIndexDataArray((1+1j) * np.random.random((3, 5)), coords=index_coords)\n>>> amp_coords = dict(direction=direction, f=f, mode_index=mode_index)\n>>> amp_data = ModeAmpsDataArray((1+1j) * np.random.random((2, 3, 5)), coords=amp_coords)\n>>> monitor = ModeMonitor(\n...    size=(2,0,6),\n...    freqs=[2e14, 3e14],\n...    mode_spec=ModeSpec(num_modes=5),\n...    name='mode',\n... )\n>>> data = ModeData(monitor=monitor, amps=amp_data, n_complex=index_data)",
   "type": "object",
   "properties": {
      "type": {
         "title": "Type",
         "default": "ModeData",
         "enum": [
            "ModeData"
         ],
         "type": "string"
      },
      "monitor": {
         "$ref": "#/definitions/ModeMonitor"
      },
      "amps": {
         "title": "DataArray",
         "description": "Complex-valued amplitudes associated with the mode.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      },
      "n_complex": {
         "title": "DataArray",
         "description": "Complex-valued effective propagation constants associated with the mode.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      }
   },
   "required": [
      "monitor",
      "amps",
      "n_complex"
   ],
   "additionalProperties": false,
   "definitions": {
      "ApodizationSpec": {
         "title": "ApodizationSpec",
         "description": "Stores specifications for the apodizaton of frequency-domain monitors.\n\nParameters\n----------\nstart : Optional[NonNegativeFloat] = None\n    [units = sec].  Defines the time at which the start apodization ends.\nend : Optional[NonNegativeFloat] = None\n    [units = sec].  Defines the time at which the end apodization begins.\nwidth : Optional[PositiveFloat] = None\n    [units = sec].  Characteristic decay length of the apodization function.\n\nExample\n-------\n>>> apod_spec = ApodizationSpec(start=1, end=2, width=0.5)",
         "type": "object",
         "properties": {
            "start": {
               "title": "Start Interval",
               "description": "Defines the time at which the start apodization ends.",
               "units": "sec",
               "minimum": 0,
               "type": "number"
            },
            "end": {
               "title": "End Interval",
               "description": "Defines the time at which the end apodization begins.",
               "units": "sec",
               "minimum": 0,
               "type": "number"
            },
            "width": {
               "title": "Apodization Width",
               "description": "Characteristic decay length of the apodization function.",
               "units": "sec",
               "exclusiveMinimum": 0,
               "type": "number"
            },
            "type": {
               "title": "Type",
               "default": "ApodizationSpec",
               "enum": [
                  "ApodizationSpec"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "ModeSpec": {
         "title": "ModeSpec",
         "description": "Stores specifications for the mode solver to find an electromagntic mode.\nNote, the planar axes are found by popping the injection axis from {x,y,z}.\nFor example, if injection axis is y, the planar axes are ordered {x,z}.\n\nParameters\n----------\nnum_modes : PositiveInt = 1\n    Number of modes returned by mode solver.\ntarget_neff : Optional[PositiveFloat] = None\n    Guess for effective index of the mode.\nnum_pml : Tuple[NonNegativeInt, NonNegativeInt] = (0, 0)\n    Number of standard pml layers to add in the two tangential axes.\nfilter_pol : Optional[Literal['te', 'tm']] = None\n    The solver always computes the ``num_modes`` modes closest to the given ``target_neff``. If ``filter_pol==None``, they are simply sorted in order of decresing effective index. If a polarization filter is selected, the modes are rearranged such that the first ``n_pol`` modes in the list are the ones with the selected polarization fraction larger than or equal to 0.5, while the next ``num_modes - n_pol`` modes are the ones where it is smaller than 0.5 (i.e. the opposite polarization fraction is larger than 0.5). Within each polarization subset, the modes are still ordered by decreasing effective index. ``te``-fraction is defined as the integrated intensity of the E-field component parallel to the first plane axis, normalized to the total in-plane E-field intensity. Conversely, ``tm``-fraction uses the E field component parallel to the second plane axis.\nangle_theta : float = 0.0\n    [units = rad].  Polar angle of the propagation axis from the injection axis.\nangle_phi : float = 0.0\n    [units = rad].  Azimuth angle of the propagation axis in the plane orthogonal to the injection axis.\nprecision : Literal['single', 'double'] = single\n    The solver will be faster and using less memory under single precision, but more accurate under double precision.\nbend_radius : Optional[float] = None\n    [units = um].  A curvature radius for simulation of waveguide bends. Can be negative, in which case the mode plane center has a smaller value than the curvature center along the tangential axis perpendicular to the bend axis.\nbend_axis : Optional[Literal[0, 1]] = None\n    Index into the two tangential axes defining the normal to the plane in which the bend lies. This must be provided if ``bend_radius`` is not ``None``. For example, for a ring in the global xy-plane, and a mode plane in either the xz or the yz plane, the ``bend_axis`` is always 1 (the global z axis).\ntrack_freq : Optional[Literal['central', 'lowest', 'highest']] = central\n    Parameter that turns on/off mode tracking based on their similarity. Can take values ``'lowest'``, ``'central'``, or ``'highest'``, which correspond to mode tracking based on the lowest, central, or highest frequency. If ``None`` no mode tracking is performed.\n\nExample\n-------\n>>> mode_spec = ModeSpec(num_modes=3, target_neff=1.5)",
         "type": "object",
         "properties": {
            "num_modes": {
               "title": "Number of modes",
               "description": "Number of modes returned by mode solver.",
               "default": 1,
               "exclusiveMinimum": 0,
               "type": "integer"
            },
            "target_neff": {
               "title": "Target effective index",
               "description": "Guess for effective index of the mode.",
               "exclusiveMinimum": 0,
               "type": "number"
            },
            "num_pml": {
               "title": "Number of PML layers",
               "description": "Number of standard pml layers to add in the two tangential axes.",
               "default": [
                  0,
                  0
               ],
               "type": "array",
               "minItems": 2,
               "maxItems": 2,
               "items": [
                  {
                     "type": "integer",
                     "minimum": 0
                  },
                  {
                     "type": "integer",
                     "minimum": 0
                  }
               ]
            },
            "filter_pol": {
               "title": "Polarization filtering",
               "description": "The solver always computes the ``num_modes`` modes closest to the given ``target_neff``. If ``filter_pol==None``, they are simply sorted in order of decresing effective index. If a polarization filter is selected, the modes are rearranged such that the first ``n_pol`` modes in the list are the ones with the selected polarization fraction larger than or equal to 0.5, while the next ``num_modes - n_pol`` modes are the ones where it is smaller than 0.5 (i.e. the opposite polarization fraction is larger than 0.5). Within each polarization subset, the modes are still ordered by decreasing effective index. ``te``-fraction is defined as the integrated intensity of the E-field component parallel to the first plane axis, normalized to the total in-plane E-field intensity. Conversely, ``tm``-fraction uses the E field component parallel to the second plane axis.",
               "enum": [
                  "te",
                  "tm"
               ],
               "type": "string"
            },
            "angle_theta": {
               "title": "Polar Angle",
               "description": "Polar angle of the propagation axis from the injection axis.",
               "default": 0.0,
               "units": "rad",
               "type": "number"
            },
            "angle_phi": {
               "title": "Azimuth Angle",
               "description": "Azimuth angle of the propagation axis in the plane orthogonal to the injection axis.",
               "default": 0.0,
               "units": "rad",
               "type": "number"
            },
            "precision": {
               "title": "single or double precision in mode solver",
               "description": "The solver will be faster and using less memory under single precision, but more accurate under double precision.",
               "default": "single",
               "enum": [
                  "single",
                  "double"
               ],
               "type": "string"
            },
            "bend_radius": {
               "title": "Bend radius",
               "description": "A curvature radius for simulation of waveguide bends. Can be negative, in which case the mode plane center has a smaller value than the curvature center along the tangential axis perpendicular to the bend axis.",
               "units": "um",
               "type": "number"
            },
            "bend_axis": {
               "title": "Bend axis",
               "description": "Index into the two tangential axes defining the normal to the plane in which the bend lies. This must be provided if ``bend_radius`` is not ``None``. For example, for a ring in the global xy-plane, and a mode plane in either the xz or the yz plane, the ``bend_axis`` is always 1 (the global z axis).",
               "enum": [
                  0,
                  1
               ],
               "type": "integer"
            },
            "track_freq": {
               "title": "Mode Tracking Frequency",
               "description": "Parameter that turns on/off mode tracking based on their similarity. Can take values ``'lowest'``, ``'central'``, or ``'highest'``, which correspond to mode tracking based on the lowest, central, or highest frequency. If ``None`` no mode tracking is performed.",
               "default": "central",
               "enum": [
                  "central",
                  "lowest",
                  "highest"
               ],
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "ModeSpec",
               "enum": [
                  "ModeSpec"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "ModeMonitor": {
         "title": "ModeMonitor",
         "description": ":class:`Monitor` that records amplitudes from modal decomposition of fields on plane.\n\nParameters\n----------\ncenter : Tuple[float, float, float] = (0.0, 0.0, 0.0)\n    [units = um].  Center of object in x, y, and z.\nsize : Tuple[NonNegativeFloat, NonNegativeFloat, NonNegativeFloat]\n    [units = um].  Size in x, y, and z directions.\nname : ConstrainedStrValue\n    Unique name for monitor.\nfreqs : Union[Tuple[float, ...], Array]\n    [units = Hz].  Array or list of frequencies stored by the field monitor.\napodization : ApodizationSpec = ApodizationSpec(start=None, end=None, width=None, type='ApodizationSpec')\n    Sets parameters of (optional) apodization. Apodization applies a windowing function to the Fourier transform of the time-domain fields into frequency-domain ones, and can be used to truncate the beginning and/or end of the time signal, for example to eliminate the source pulse when studying the eigenmodes of a system. Note: apodization affects the normalization of the frequency-domain fields.\nmode_spec : ModeSpec\n    Parameters to feed to mode solver which determine modes measured by monitor.\n\nExample\n-------\n>>> mode_spec = ModeSpec(num_modes=3)\n>>> monitor = ModeMonitor(\n...     center=(1,2,3),\n...     size=(2,2,0),\n...     freqs=[200e12, 210e12],\n...     mode_spec=mode_spec,\n...     name='mode_monitor')",
         "type": "object",
         "properties": {
            "type": {
               "title": "Type",
               "default": "ModeMonitor",
               "enum": [
                  "ModeMonitor"
               ],
               "type": "string"
            },
            "center": {
               "title": "Center",
               "description": "Center of object in x, y, and z.",
               "default": [
                  0.0,
                  0.0,
                  0.0
               ],
               "units": "um",
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  }
               ]
            },
            "size": {
               "title": "Size",
               "description": "Size in x, y, and z directions.",
               "units": "um",
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "number",
                     "minimum": 0
                  },
                  {
                     "type": "number",
                     "minimum": 0
                  },
                  {
                     "type": "number",
                     "minimum": 0
                  }
               ]
            },
            "name": {
               "title": "Name",
               "description": "Unique name for monitor.",
               "minLength": 1,
               "type": "string"
            },
            "freqs": {
               "title": "Frequencies",
               "description": "Array or list of frequencies stored by the field monitor.",
               "units": "Hz",
               "anyOf": [
                  {
                     "type": "array",
                     "items": {
                        "type": "number"
                     }
                  },
                  {
                     "title": "Array Like",
                     "description": "Accepts sequence (tuple, list, numpy array) and converts to tuple.",
                     "type": "tuple",
                     "properties": {},
                     "required": []
                  }
               ]
            },
            "apodization": {
               "title": "Apodization Specification",
               "description": "Sets parameters of (optional) apodization. Apodization applies a windowing function to the Fourier transform of the time-domain fields into frequency-domain ones, and can be used to truncate the beginning and/or end of the time signal, for example to eliminate the source pulse when studying the eigenmodes of a system. Note: apodization affects the normalization of the frequency-domain fields.",
               "default": {
                  "start": null,
                  "end": null,
                  "width": null,
                  "type": "ApodizationSpec"
               },
               "allOf": [
                  {
                     "$ref": "#/definitions/ApodizationSpec"
                  }
               ]
            },
            "mode_spec": {
               "title": "Mode Specification",
               "description": "Parameters to feed to mode solver which determine modes measured by monitor.",
               "allOf": [
                  {
                     "$ref": "#/definitions/ModeSpec"
                  }
               ]
            }
         },
         "required": [
            "size",
            "name",
            "freqs",
            "mode_spec"
         ],
         "additionalProperties": false
      }
   }
}

attribute amps: tidy3d.components.data.data_array.ModeAmpsDataArray [Required]#

Complex-valued amplitudes associated with the mode.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

attribute monitor: tidy3d.components.monitor.ModeMonitor [Required]#
attribute n_complex: tidy3d.components.data.data_array.ModeIndexDataArray [Required]#

Complex-valued effective propagation constants associated with the mode.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

classmethod add_type_field() None#

Automatically place “type” field with model name in the model field dictionary.

classmethod construct(_fields_set: Optional[SetStr] = None, **values: Any) Model#

Creates a new model setting __dict__ and __fields_set__ from trusted or pre-validated data. Default values are respected, but no other validation is performed. Behaves as if Config.extra = ‘allow’ was set since it adds all passed values

copy(**kwargs) tidy3d.components.base.Tidy3dBaseModel#

Copy a Tidy3dBaseModel. With deep=True as default.

dict(*, include: Optional[Union[AbstractSetIntStr, MappingIntStrAny]] = None, exclude: Optional[Union[AbstractSetIntStr, MappingIntStrAny]] = None, by_alias: bool = False, skip_defaults: Optional[bool] = None, exclude_unset: bool = False, exclude_defaults: bool = False, exclude_none: bool = False) DictStrAny#

Generate a dictionary representation of the model, optionally specifying which fields to include or exclude.

classmethod dict_from_file(fname: str, group_path: Optional[str] = None) dict#

Loads a dictionary containing the model from a .yaml, .json, or .hdf5 file.

Parameters
  • fname (str) – Full path to the .yaml or .json file to load the Tidy3dBaseModel from.

  • group_path (str, optional) – Path to a group inside the file to use as the base level.

Returns

A dictionary containing the model.

Return type

dict

Example

>>> simulation = Simulation.from_file(fname='folder/sim.json') 
classmethod dict_from_hdf5(fname: str, group_path: str = '') dict#

Loads a dictionary containing the model contents from a .hdf5 file.

Parameters
  • fname (str) – Full path to the .hdf5 file to load the Tidy3dBaseModel from.

  • group_path (str, optional) – Path to a group inside the file to selectively load a sub-element of the model only.

Returns

Dictionary containing the model.

Return type

dict

Example

>>> sim_dict = Simulation.dict_from_hdf5(fname='folder/sim.hdf5') 
classmethod dict_from_json(fname: str) dict#

Load dictionary of the model from a .json file.

Parameters

fname (str) – Full path to the .json file to load the Tidy3dBaseModel from.

Returns

A dictionary containing the model.

Return type

dict

Example

>>> sim_dict = Simulation.dict_from_json(fname='folder/sim.json') 
classmethod dict_from_yaml(fname: str) dict#

Load dictionary of the model from a .yaml file.

Parameters

fname (str) – Full path to the .yaml file to load the Tidy3dBaseModel from.

Returns

A dictionary containing the model.

Return type

dict

Example

>>> sim_dict = Simulation.dict_from_yaml(fname='folder/sim.yaml') 
classmethod from_file(fname: str, group_path: Optional[str] = None, **parse_obj_kwargs) tidy3d.components.base.Tidy3dBaseModel#

Loads a Tidy3dBaseModel from .yaml, .json, or .hdf5 file.

Parameters
  • fname (str) – Full path to the .yaml or .json file to load the Tidy3dBaseModel from.

  • group_path (str, optional) – Path to a group inside the file to use as the base level. Only for .hdf5 files. Starting / is optional.

  • **parse_obj_kwargs – Keyword arguments passed to either pydantic’s parse_obj function when loading model.

Returns

An instance of the component class calling load.

Return type

Tidy3dBaseModel

Example

>>> simulation = Simulation.from_file(fname='folder/sim.json') 
classmethod from_hdf5(fname: str, group_path: str = '', **parse_obj_kwargs) tidy3d.components.base.Tidy3dBaseModel#

Loads Tidy3dBaseModel instance to .hdf5 file.

Parameters
  • fname (str) – Full path to the .hdf5 file to load the Tidy3dBaseModel from.

  • group_path (str, optional) – Path to a group inside the file to selectively load a sub-element of the model only. Starting / is optional.

  • **parse_obj_kwargs – Keyword arguments passed to pydantic’s parse_obj method.

Example

>>> simulation.to_hdf5(fname='folder/sim.hdf5') 
classmethod from_json(fname: str, **parse_obj_kwargs) tidy3d.components.base.Tidy3dBaseModel#

Load a Tidy3dBaseModel from .json file.

Parameters

fname (str) – Full path to the .json file to load the Tidy3dBaseModel from.

Returns

  • Tidy3dBaseModel – An instance of the component class calling load.

  • **parse_obj_kwargs – Keyword arguments passed to pydantic’s parse_obj method.

Example

>>> simulation = Simulation.from_json(fname='folder/sim.json') 
classmethod from_orm(obj: Any) Model#
classmethod from_yaml(fname: str, **parse_obj_kwargs) tidy3d.components.base.Tidy3dBaseModel#

Loads Tidy3dBaseModel from .yaml file.

Parameters
  • fname (str) – Full path to the .yaml file to load the Tidy3dBaseModel from.

  • **parse_obj_kwargs – Keyword arguments passed to pydantic’s parse_obj method.

Returns

An instance of the component class calling from_yaml.

Return type

Tidy3dBaseModel

Example

>>> simulation = Simulation.from_yaml(fname='folder/sim.yaml') 
classmethod generate_docstring() str#

Generates a docstring for a Tidy3D mode and saves it to the __doc__ of the class.

classmethod get_sub_model(group_path: str, model_dict: dict | list) dict#

Get the sub model for a given group path.

static get_tuple_group_name(index: int) str#

Get the group name of a tuple element.

static get_tuple_index(key_name: str) int#

Get the index into the tuple based on its group name.

help(methods: bool = False) None#

Prints message describing the fields and methods of a Tidy3dBaseModel.

Parameters

methods (bool = False) – Whether to also print out information about object’s methods.

Example

>>> simulation.help(methods=True) 
json(*, include: Optional[Union[AbstractSetIntStr, MappingIntStrAny]] = None, exclude: Optional[Union[AbstractSetIntStr, MappingIntStrAny]] = None, by_alias: bool = False, skip_defaults: Optional[bool] = None, exclude_unset: bool = False, exclude_defaults: bool = False, exclude_none: bool = False, encoder: Optional[Callable[[Any], Any]] = None, models_as_dict: bool = True, **dumps_kwargs: Any) unicode#

Generate a JSON representation of the model, include and exclude arguments as per dict().

encoder is an optional function to supply as default to json.dumps(), other arguments as per json.dumps().

normalize(source_spectrum_fn) tidy3d.components.data.monitor_data.ModeData#

Return copy of self after normalization is applied using source spectrum function.

classmethod parse_file(path: Union[str, pathlib.Path], *, content_type: unicode = None, encoding: unicode = 'utf8', proto: pydantic.parse.Protocol = None, allow_pickle: bool = False) Model#
classmethod parse_obj(obj: Any) Model#
classmethod parse_raw(b: Union[str, bytes], *, content_type: unicode = None, encoding: unicode = 'utf8', proto: pydantic.parse.Protocol = None, allow_pickle: bool = False) Model#
classmethod schema(by_alias: bool = True, ref_template: unicode = '#/definitions/{model}') DictStrAny#
classmethod schema_json(*, by_alias: bool = True, ref_template: unicode = '#/definitions/{model}', **dumps_kwargs: Any) unicode#
to_file(fname: str) None#

Exports Tidy3dBaseModel instance to .yaml, .json, or .hdf5 file

Parameters

fname (str) – Full path to the .yaml or .json file to save the Tidy3dBaseModel to.

Example

>>> simulation.to_file(fname='folder/sim.json') 
to_hdf5(fname: str) None#

Exports Tidy3dBaseModel instance to .hdf5 file.

Parameters

fname (str) – Full path to the .hdf5 file to save the Tidy3dBaseModel to.

Example

>>> simulation.to_hdf5(fname='folder/sim.hdf5') 
to_json(fname: str) None#

Exports Tidy3dBaseModel instance to .json file

Parameters

fname (str) – Full path to the .json file to save the Tidy3dBaseModel to.

Example

>>> simulation.to_json(fname='folder/sim.json') 
to_yaml(fname: str) None#

Exports Tidy3dBaseModel instance to .yaml file.

Parameters

fname (str) – Full path to the .yaml file to save the Tidy3dBaseModel to.

Example

>>> simulation.to_yaml(fname='folder/sim.yaml') 
classmethod tuple_to_dict(tuple_values: tuple) dict#

How we generate a dictionary mapping new keys to tuple values for hdf5.

classmethod update_forward_refs(**localns: Any) None#

Try to update ForwardRefs on fields based on this Model, globalns and localns.

updated_copy(**kwargs) tidy3d.components.base.Tidy3dBaseModel#

Make copy of a component instance with **kwargs indicating updated field values.

classmethod validate(value: Any) Model#
property k_eff#

Imaginary part of the propagation index.

property n_eff#

Real part of the propagation index.

property symmetry_expanded_copy: tidy3d.components.data.monitor_data.MonitorData#

Return copy of self with symmetry applied.