






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 	_UpperCAmelCase  (  __snake_case		):




      """simple docstring"""



      def __init__(   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase=None    ,	_lowerCAmelCase=None    ,	_lowerCAmelCase=0		):



          '''simple docstring'''
          lowerCAmelCase__   :Any      							=				1.0 if scale is None else scale
          lowerCAmelCase__   :str      							=				0.0 if loc is None else loc

          super().__init__(_lowercase    ,	[AffineTransform(loc=self.loc    ,	scale=self.scale    ,	event_dim=_lowercase		)]		)
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return self.base_dist.mean * self.scale + self.loc
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return self.base_dist.variance * self.scale**2



      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return self.variance.sqrt()







class 	_UpperCAmelCase  (  nn.Module		):




      """simple docstring"""



      def __init__(   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase    ,	_lowerCAmelCase    ,	**_lowerCAmelCase		):



          '''simple docstring'''
          super().__init__(**_lowercase		)
          lowerCAmelCase__   :str      							=				args_dim
          lowerCAmelCase__   :List[Any]      							=				nn.ModuleList([nn.Linear(_lowercase    ,	_lowercase		) for dim in args_dim.values()]		)
          lowerCAmelCase__   :Dict      							=				domain_map



      def 			snake_case_      (   self    ,	_lowerCAmelCase		):



          '''simple docstring'''
          lowerCAmelCase__   :List[Any]      							=				[proj(_lowercase		) for proj in self.proj]

          return self.domain_map(*_lowercase		)







class 	_UpperCAmelCase  (  nn.Module		):




      """simple docstring"""



      def __init__(   self    ,	_lowerCAmelCase		):



          '''simple docstring'''
          super().__init__()
          lowerCAmelCase__   :Optional[int]      							=				function



      def 			snake_case_      (   self    ,	_lowerCAmelCase    ,	*_lowerCAmelCase		):



          '''simple docstring'''
          return self.function(_lowercase    ,	*_lowercase		)







class 	_UpperCAmelCase  :




      """simple docstring"""



      A          =    42
      A          =    42
      A          =    42
      def __init__(   self    ,	_lowerCAmelCase = 1		):



          '''simple docstring'''
          lowerCAmelCase__   :Optional[int]      							=				dim
          lowerCAmelCase__   :str      							=				{k: dim * self.args_dim[k] for k in self.args_dim}
      def 			snake_case_      (   self    ,	_lowerCAmelCase		):



          '''simple docstring'''

          if self.dim == 1:
              return self.distribution_class(*_lowercase		)
          else:
              return Independent(self.distribution_class(*_lowercase		)    ,	1		)
      def 			snake_case_      (   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase = None    ,	_lowerCAmelCase = None    ,	):



          '''simple docstring'''
          lowerCAmelCase__   :Tuple      							=				self._base_distribution(_lowercase		)
          if loc is None and scale is None:
              return distr
          else:
              return AffineTransformed(_lowercase    ,	loc=_lowercase    ,	scale=_lowercase    ,	event_dim=self.event_dim		)
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return () if self.dim == 1 else (self.dim,)
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return len(self.event_shape		)
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return 0.0
      def 			snake_case_      (   self    ,	_lowerCAmelCase		):



          '''simple docstring'''
          return ParameterProjection(
              in_features=_lowercase    ,	args_dim=self.args_dim    ,	domain_map=LambdaLayer(self.domain_map		)    ,	)
      def 			snake_case_      (   self    ,	*_lowerCAmelCase		):



          '''simple docstring'''
          raise NotImplementedError()



      @staticmethod
      def 			snake_case_      (   _lowerCAmelCase		):



          '''simple docstring'''
          return (x + torch.sqrt(torch.square(_lowercase		) + 4.0		)) / 2.0







class 	_UpperCAmelCase  (  __snake_case		):




      """simple docstring"""



      A          =    {'''df''': 1, '''loc''': 1, '''scale''': 1}
      A          =    StudentT
      @classmethod
      def 			snake_case_      (   cls    ,	_lowerCAmelCase    ,	_lowerCAmelCase    ,	_lowerCAmelCase		):



          '''simple docstring'''
          lowerCAmelCase__   :int      							=				cls.squareplus(_lowercase		).clamp_min(torch.finfo(scale.dtype		).eps		)
          lowerCAmelCase__   :Optional[Any]      							=				2.0 + cls.squareplus(_lowercase		)
          return df.squeeze(-1		), loc.squeeze(-1		), scale.squeeze(-1		)







class 	_UpperCAmelCase  (  __snake_case		):




      """simple docstring"""



      A          =    {'''loc''': 1, '''scale''': 1}
      A          =    Normal
      @classmethod
      def 			snake_case_      (   cls    ,	_lowerCAmelCase    ,	_lowerCAmelCase		):



          '''simple docstring'''
          lowerCAmelCase__   :str      							=				cls.squareplus(_lowercase		).clamp_min(torch.finfo(scale.dtype		).eps		)
          return loc.squeeze(-1		), scale.squeeze(-1		)







class 	_UpperCAmelCase  (  __snake_case		):




      """simple docstring"""



      A          =    {'''total_count''': 1, '''logits''': 1}
      A          =    NegativeBinomial
      @classmethod
      def 			snake_case_      (   cls    ,	_lowerCAmelCase    ,	_lowerCAmelCase		):



          '''simple docstring'''
          lowerCAmelCase__   :Union[str, Any]      							=				cls.squareplus(_lowercase		)
          return total_count.squeeze(-1		), logits.squeeze(-1		)
      def 			snake_case_      (   self    ,	_lowerCAmelCase		):



          '''simple docstring'''
          lowerCAmelCase__   :Optional[Any]      							=				distr_args
          if self.dim == 1:
              return self.distribution_class(total_count=_lowercase    ,	logits=_lowercase		)
          else:
              return Independent(self.distribution_class(total_count=_lowercase    ,	logits=_lowercase		)    ,	1		)



      def 			snake_case_      (   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase = None    ,	_lowerCAmelCase = None		):



          '''simple docstring'''
          lowerCAmelCase__   :List[Any]      							=				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

import numpy as np


def 				snake_case__							(							UpperCAmelCase							:  np.ndarray       ):
    lowerCAmelCase__							,lowerCAmelCase__   :List[str]      							=				np.shape(UpperCAmelCase       )
    if rows != columns:
        lowerCAmelCase__   :Tuple      							=				(
            "'table' has to be of square shaped array but got a "
            F'''{rows}x{columns} array:\n{table}'''
        )
        raise ValueError(UpperCAmelCase       )

    lowerCAmelCase__   :Optional[Any]      							=				np.zeros((rows, columns)       )
    lowerCAmelCase__   :Tuple      							=				np.zeros((rows, columns)       )
    for i in range(UpperCAmelCase       ):
        for j in range(UpperCAmelCase       ):
            lowerCAmelCase__   :Any      							=				sum(lower[i][k] * upper[k][j] for k in range(UpperCAmelCase       )       )
            if upper[j][j] == 0:
                raise ArithmeticError("No LU decomposition exists"       )
            lowerCAmelCase__   :Any      							=				(table[i][j] - total) / upper[j][j]
        lowerCAmelCase__   :Tuple      							=				1
        for j in range(UpperCAmelCase    ,			UpperCAmelCase       ):
            lowerCAmelCase__   :Optional[Any]      							=				sum(lower[i][k] * upper[k][j] for k in range(UpperCAmelCase       )       )
            lowerCAmelCase__   :Dict      							=				table[i][j] - total
    return lower, upper


if __name__ == "__main__":
 import doctest

 doctest.testmod()



