





from typing import Callable, Dict, Optional, Tuple

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)



class    _a     (				__lowercase							):






							"""simple docstring"""

							def __init__(      self				:     List[Any]							,	a				:     Distribution							,	a				:     List[Any]=None							,	a				:     Optional[int]=None							,	a				:     Union[str, Any]=0    )	->Any:
													SCREAMING_SNAKE_CASE__     :				Any   =					1.0 if scale is None else scale
													SCREAMING_SNAKE_CASE__     :				int   =					0.0 if loc is None else loc

													super().__init__(__a							,	[AffineTransform(loc=self.loc							,	scale=self.scale							,	event_dim=__a    )]    )

							@property
							def      A_  (      self				:     Tuple    )	->Union[str, Any]:
													return self.base_dist.mean * self.scale + self.loc

							@property
							def      A_  (      self				:     Dict    )	->List[str]:
													return self.base_dist.variance * self.scale**2






							@property
							def      A_  (      self				:     List[str]    )	->int:
													return self.variance.sqrt()







class    _a     (				nn.Module							):






							"""simple docstring"""

							def __init__(      self				:     Optional[int]							,	a				:     int							,	a				:     Dict[str, int]							,	a				:     Callable[..., Tuple[torch.Tensor]]							,	**a				:     Optional[Any]    )	->None:
													super().__init__(**__a    )
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					args_dim
													SCREAMING_SNAKE_CASE__     :				List[str]   =					nn.ModuleList([nn.Linear(__a							,	__a    ) for dim in args_dim.values()]    )
													SCREAMING_SNAKE_CASE__     :				str   =					domain_map






							def      A_  (      self				:     List[str]							,	a				:     torch.Tensor    )	->Tuple[torch.Tensor]:
													SCREAMING_SNAKE_CASE__     :				List[Any]   =					[proj(__a    ) for proj in self.proj]

													return self.domain_map(*__a    )







class    _a     (				nn.Module							):






							"""simple docstring"""

							def __init__(      self				:     Union[str, Any]							,	a				:     str    )	->Tuple:
													super().__init__()
													SCREAMING_SNAKE_CASE__     :				Any   =					function






							def      A_  (      self				:     str							,	a				:     Union[str, Any]							,	*a				:     Optional[Any]    )	->Any:
													return self.function(__a							,	*__a    )







class    _a     :






							"""simple docstring"""

							snake_case_							 =						42
							snake_case_							 =						42
							snake_case_							 =						42

							def __init__(      self				:     Dict							,	a				:     int = 1    )	->None:
													SCREAMING_SNAKE_CASE__     :				List[Any]   =					dim
													SCREAMING_SNAKE_CASE__     :				List[Any]   =					{k: dim * self.args_dim[k] for k in self.args_dim}

							def      A_  (      self				:     List[str]							,	a				:     Dict    )	->List[Any]:
													if self.dim == 1:
																			return self.distribution_class(*__a    )
													else:
																			return Independent(self.distribution_class(*__a    )							,	1    )

							def      A_  (      self				:     Any							,	a				:     str							,	a				:     Optional[torch.Tensor] = None							,	a				:     Optional[torch.Tensor] = None							,	)	->Distribution:
													SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					self._base_distribution(__a    )
													if loc is None and scale is None:
																			return distr
													else:
																			return AffineTransformed(__a							,	loc=__a							,	scale=__a							,	event_dim=self.event_dim    )

							@property
							def      A_  (      self				:     str    )	->Tuple:
													return () if self.dim == 1 else (self.dim,)

							@property
							def      A_  (      self				:     Union[str, Any]    )	->int:
													return len(self.event_shape    )

							@property
							def      A_  (      self				:     Dict    )	->float:
													return 0.0

							def      A_  (      self				:     Union[str, Any]							,	a				:     int    )	->nn.Module:
													return ParameterProjection(
													    in_features=__a							,	args_dim=self.args_dim							,	domain_map=LambdaLayer(self.domain_map    )							,	)

							def      A_  (      self				:     Any							,	*a				:     torch.Tensor    )	->str:
													raise NotImplementedError()






							@staticmethod
							def      A_  (      a				:     torch.Tensor    )	->torch.Tensor:
													return (x + torch.sqrt(torch.square(__a    ) + 4.0    )) / 2.0







class    _a     (				__lowercase							):






							"""simple docstring"""

							snake_case_							 =						{"df": 1, "loc": 1, "scale": 1}
							snake_case_							 =						StudentT

							@classmethod
							def      A_  (      cls				:     Optional[Any]							,	a				:     torch.Tensor							,	a				:     torch.Tensor							,	a				:     torch.Tensor    )	->Tuple:
													SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					cls.squareplus(__a    ).clamp_min(torch.finfo(scale.dtype    ).eps    )
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					2.0 + cls.squareplus(__a    )
													return df.squeeze(-1    ), loc.squeeze(-1    ), scale.squeeze(-1    )







class    _a     (				__lowercase							):






							"""simple docstring"""

							snake_case_							 =						{"loc": 1, "scale": 1}
							snake_case_							 =						Normal

							@classmethod
							def      A_  (      cls				:     Optional[int]							,	a				:     torch.Tensor							,	a				:     torch.Tensor    )	->str:
													SCREAMING_SNAKE_CASE__     :				int   =					cls.squareplus(__a    ).clamp_min(torch.finfo(scale.dtype    ).eps    )
													return loc.squeeze(-1    ), scale.squeeze(-1    )







class    _a     (				__lowercase							):






							"""simple docstring"""

							snake_case_							 =						{"total_count": 1, "logits": 1}
							snake_case_							 =						NegativeBinomial

							@classmethod
							def      A_  (      cls				:     Tuple							,	a				:     torch.Tensor							,	a				:     torch.Tensor    )	->Union[str, Any]:
													SCREAMING_SNAKE_CASE__     :				int   =					cls.squareplus(__a    )
													return total_count.squeeze(-1    ), logits.squeeze(-1    )

							def      A_  (      self				:     List[Any]							,	a				:     Union[str, Any]    )	->Distribution:
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					distr_args
													if self.dim == 1:
																			return self.distribution_class(total_count=__a							,	logits=__a    )
													else:
																			return Independent(self.distribution_class(total_count=__a							,	logits=__a    )							,	1    )






							def      A_  (      self				:     str							,	a				:     Any							,	a				:     Optional[torch.Tensor] = None							,	a				:     Optional[torch.Tensor] = None    )	->Distribution:
													SCREAMING_SNAKE_CASE__     :				List[str]   =					distr_args

													if scale is not None:
																			# See scaling property of Gamma.
																			logits += scale.log()

													return self._base_distribution((total_count, logits)    )






from __future__ import annotations







def       UpperCAmelCase							(     _lowerCamelCase      :  list			,   _lowerCamelCase      :  int | None = None			,   _lowerCamelCase      :  int | None = None     ):





						'''simple docstring'''


						if start is None:
												SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					0

						if end is None:
												SCREAMING_SNAKE_CASE__     :				Any   =					len(_lowerCamelCase     ) - 1

						if start >= end:
												return

						SCREAMING_SNAKE_CASE__     :				List[str]   =					(start + end) // 2

						slowsort(_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )
						slowsort(_lowerCamelCase			,   mid + 1			,   _lowerCamelCase     )

						if sequence[end] < sequence[mid]:
												SCREAMING_SNAKE_CASE__,							SCREAMING_SNAKE_CASE__     :				Optional[int]   =					sequence[mid], sequence[end]

						slowsort(_lowerCamelCase			,   _lowerCamelCase			,   end - 1     )


if __name__ == "__main__":
				from doctest import testmod

				testmod()