





from __future__ import annotations

import math





def 					lowerCAmelCase_			(	__a     ,   __a		)					->		list:







  """simple docstring"""





  if len(__a		) != 2 or len(a[0]		) != 2 or len(__a		) != 2 or len(b[0]		) != 2:
    raise Exception("Matrices are not 2x2"		)
  lowerCamelCase__:				Any        =[
      [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
      [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
  ]
  return new_matrix





def 					lowerCAmelCase_			(	__a     ,   __a		)					->		int:







  """simple docstring"""





  return [
      [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]		)		)]
      for row in range(len(__a		)		)
  ]





def 					lowerCAmelCase_			(	__a     ,   __a		)					->		Tuple:







  """simple docstring"""





  return [
      [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]		)		)]
      for row in range(len(__a		)		)
  ]





def 					lowerCAmelCase_			(	__a		)					->		tuple[list, list, list, list]:







  """simple docstring"""





  if len(__a		) % 2 != 0 or len(a[0]		) % 2 != 0:
    raise Exception("Odd matrices are not supported!"		)

  lowerCamelCase__:				List[Any]        =len(__a		)
  lowerCamelCase__:				List[str]        =matrix_length // 2

  lowerCamelCase__:				Tuple        =[[a[i][j] for j in range(__a     ,   __a		)] for i in range(__a		)]
  lowerCamelCase__:				int        =[
      [a[i][j] for j in range(__a     ,   __a		)] for i in range(__a     ,   __a		)
  ]

  lowerCamelCase__:				Tuple        =[[a[i][j] for j in range(__a		)] for i in range(__a		)]
  lowerCamelCase__:				Any        =[[a[i][j] for j in range(__a		)] for i in range(__a     ,   __a		)]

  return top_left, top_right, bot_left, bot_right





def 					lowerCAmelCase_			(	__a		)					->		tuple[int, int]:







  """simple docstring"""





  return len(__a		), len(matrix[0]		)





def 					lowerCAmelCase_			(	__a		)					->		None:







  """simple docstring"""





  print("\n".join(str(__a		) for line in matrix		)		)





def 					lowerCAmelCase_			(	__a     ,   __a		)					->		list:







  """simple docstring"""





  if matrix_dimensions(__a		) == (2, 2):
    return default_matrix_multiplication(__a     ,   __a		)

  lowerCamelCase__  , lowerCamelCase__  , lowerCamelCase__  , lowerCamelCase__:				List[Any]        =split_matrix(__a		)
  lowerCamelCase__  , lowerCamelCase__  , lowerCamelCase__  , lowerCamelCase__:				Optional[int]        =split_matrix(__a		)

  lowerCamelCase__:				str        =actual_strassen(__a     ,   matrix_subtraction(__a     ,   __a		)		)
  lowerCamelCase__:				Optional[Any]        =actual_strassen(matrix_addition(__a     ,   __a		)     ,   __a		)
  lowerCamelCase__:				Dict        =actual_strassen(matrix_addition(__a     ,   __a		)     ,   __a		)
  lowerCamelCase__:				Union[str, Any]        =actual_strassen(__a     ,   matrix_subtraction(__a     ,   __a		)		)
  lowerCamelCase__:				List[Any]        =actual_strassen(matrix_addition(__a     ,   __a		)     ,   matrix_addition(__a     ,   __a		)		)
  lowerCamelCase__:				str        =actual_strassen(matrix_subtraction(__a     ,   __a		)     ,   matrix_addition(__a     ,   __a		)		)
  lowerCamelCase__:				Tuple        =actual_strassen(matrix_subtraction(__a     ,   __a		)     ,   matrix_addition(__a     ,   __a		)		)

  lowerCamelCase__:				List[str]        =matrix_addition(matrix_subtraction(matrix_addition(__a     ,   __a		)     ,   __a		)     ,   __a		)
  lowerCamelCase__:				Tuple        =matrix_addition(__a     ,   __a		)
  lowerCamelCase__:				List[Any]        =matrix_addition(__a     ,   __a		)
  lowerCamelCase__:				List[Any]        =matrix_subtraction(matrix_subtraction(matrix_addition(__a     ,   __a		)     ,   __a		)     ,   __a		)

  # construct the new matrix from our 4 quadrants
  lowerCamelCase__:				str        =[]
  for i in range(len(__a		)		):
    new_matrix.append(top_left[i] + top_right[i]		)
  for i in range(len(__a		)		):
    new_matrix.append(bot_left[i] + bot_right[i]		)
  return new_matrix





def 					lowerCAmelCase_			(	__a     ,   __a		)					->		list:







  """simple docstring"""





  if matrix_dimensions(__a		)[1] != matrix_dimensions(__a		)[0]:
    lowerCamelCase__:				int        =(
        "Unable to multiply these matrices, please check the dimensions.\n"
        F"""Matrix A: {matrixa}\n"""
        F"""Matrix B: {matrixa}"""
    )
    raise Exception(__a		)
  lowerCamelCase__:				Optional[Any]        =matrix_dimensions(__a		)
  lowerCamelCase__:				Optional[int]        =matrix_dimensions(__a		)

  if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
    return [matrixa, matrixa]

  lowerCamelCase__:				str        =max(*__a     ,   *__a		)
  lowerCamelCase__:				Tuple        =int(math.pow(2     ,   math.ceil(math.loga(__a		)		)		)		)
  lowerCamelCase__:				Optional[Any]        =matrixa
  lowerCamelCase__:				Tuple        =matrixa

  # Adding zeros to the matrices so that the arrays dimensions are the same and also
  # power of 2
  for i in range(0     ,   __a		):
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]     ,   __a		):
        new_matrixa[i].append(0		)
    else:
      new_matrixa.append([0] * maxim		)
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]     ,   __a		):
        new_matrixa[i].append(0		)
    else:
      new_matrixa.append([0] * maxim		)

  lowerCamelCase__:				List[str]        =actual_strassen(__a     ,   __a		)

  # Removing the additional zeros
  for i in range(0     ,   __a		):
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]     ,   __a		):
        final_matrix[i].pop()
    else:
      final_matrix.pop()
  return final_matrix


if __name__ == "__main__":
     __A     =    [
         [2, 3, 4, 5],
         [6, 4, 3, 1],
         [2, 3, 6, 7],
         [3, 1, 2, 4],
         [2, 3, 4, 5],
         [6, 4, 3, 1],
         [2, 3, 6, 7],
         [3, 1, 2, 4],
         [2, 3, 4, 5],
         [6, 2, 3, 1],
     ]
     __A     =    [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
     print(strassen(matrixa, matrixa))








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        _SCREAMING_SNAKE_CASE						(     __SCREAMING_SNAKE_CASE   ):







 '''simple docstring'''

 def __init__(self    :       int	,			UpperCAmelCase_    :       Distribution	,			UpperCAmelCase_    :       Dict=None	,			UpperCAmelCase_    :       Tuple=None	,			UpperCAmelCase_    :       Tuple=0)	->Optional[int]:



   '''simple docstring'''



   lowerCamelCase__:				Optional[Any]        =1.0 if scale is None else scale
   lowerCamelCase__:				List[Any]        =0.0 if loc is None else loc

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

 @property
 def 							SCREAMING_SNAKE_CASE_ (self    :       Union[str, Any])	->int:



   '''simple docstring'''



   return self.base_dist.mean * self.scale + self.loc

 @property
 def 							SCREAMING_SNAKE_CASE_ (self    :       int)	->Dict:



   '''simple docstring'''



   return self.base_dist.variance * self.scale**2







 @property
 def 							SCREAMING_SNAKE_CASE_ (self    :       int)	->Optional[Any]:



   '''simple docstring'''



   return self.variance.sqrt()



class        _SCREAMING_SNAKE_CASE						(     nn.Module   ):







 '''simple docstring'''

 def __init__(self    :       Tuple	,			UpperCAmelCase_    :       int	,			UpperCAmelCase_    :       Dict[str, int]	,			UpperCAmelCase_    :       Callable[..., Tuple[torch.Tensor]]	,			**UpperCAmelCase_    :       Dict)	->None:



   '''simple docstring'''



   super().__init__(**UpperCAmelCase_)
   lowerCamelCase__:				Tuple        =args_dim
   lowerCamelCase__:				Any        =nn.ModuleList([nn.Linear(UpperCAmelCase_	,			UpperCAmelCase_) for dim in args_dim.values()])
   lowerCamelCase__:				Any        =domain_map







 def 							SCREAMING_SNAKE_CASE_ (self    :       Optional[Any]	,			UpperCAmelCase_    :       torch.Tensor)	->Tuple[torch.Tensor]:



   '''simple docstring'''



   lowerCamelCase__:				Any        =[proj(UpperCAmelCase_) for proj in self.proj]

   return self.domain_map(*UpperCAmelCase_)



class        _SCREAMING_SNAKE_CASE						(     nn.Module   ):







 '''simple docstring'''

 def __init__(self    :       str	,			UpperCAmelCase_    :       Optional[Any])	->Optional[int]:



   '''simple docstring'''



   super().__init__()
   lowerCamelCase__:				Any        =function







 def 							SCREAMING_SNAKE_CASE_ (self    :       Dict	,			UpperCAmelCase_    :       Optional[Any]	,			*UpperCAmelCase_    :       Union[str, Any])	->Union[str, Any]:



   '''simple docstring'''



   return self.function(UpperCAmelCase_	,			*UpperCAmelCase_)



class        _SCREAMING_SNAKE_CASE						:







 '''simple docstring'''
 lowercase_		=      42
 lowercase_		=      42
 lowercase_		=      42

 def __init__(self    :       str	,			UpperCAmelCase_    :       int = 1)	->None:



   '''simple docstring'''



   lowerCamelCase__:				List[str]        =dim
   lowerCamelCase__:				int        ={k: dim * self.args_dim[k] for k in self.args_dim}

 def 							SCREAMING_SNAKE_CASE_ (self    :       int	,			UpperCAmelCase_    :       str)	->Optional[Any]:



   '''simple docstring'''



   if self.dim == 1:
     return self.distribution_class(*UpperCAmelCase_)
   else:
     return Independent(self.distribution_class(*UpperCAmelCase_)	,			1)

 def 							SCREAMING_SNAKE_CASE_ (self    :       Any	,			UpperCAmelCase_    :       List[Any]	,			UpperCAmelCase_    :       Optional[torch.Tensor] = None	,			UpperCAmelCase_    :       Optional[torch.Tensor] = None	,			)	->Distribution:



   '''simple docstring'''



   lowerCamelCase__:				Optional[Any]        =self._base_distribution(UpperCAmelCase_)
   if loc is None and scale is None:
     return distr
   else:
     return AffineTransformed(UpperCAmelCase_	,			loc=UpperCAmelCase_	,			scale=UpperCAmelCase_	,			event_dim=self.event_dim)

 @property
 def 							SCREAMING_SNAKE_CASE_ (self    :       int)	->Tuple:



   '''simple docstring'''



   return () if self.dim == 1 else (self.dim,)

 @property
 def 							SCREAMING_SNAKE_CASE_ (self    :       Optional[Any])	->int:



   '''simple docstring'''



   return len(self.event_shape)

 @property
 def 							SCREAMING_SNAKE_CASE_ (self    :       Tuple)	->float:



   '''simple docstring'''



   return 0.0

 def 							SCREAMING_SNAKE_CASE_ (self    :       str	,			UpperCAmelCase_    :       int)	->nn.Module:



   '''simple docstring'''



   return ParameterProjection(
       in_features=UpperCAmelCase_	,			args_dim=self.args_dim	,			domain_map=LambdaLayer(self.domain_map)	,			)

 def 							SCREAMING_SNAKE_CASE_ (self    :       Any	,			*UpperCAmelCase_    :       torch.Tensor)	->Any:



   '''simple docstring'''



   raise NotImplementedError()







 @staticmethod
 def 							SCREAMING_SNAKE_CASE_ (UpperCAmelCase_    :       torch.Tensor)	->torch.Tensor:



   '''simple docstring'''



   return (x + torch.sqrt(torch.square(UpperCAmelCase_) + 4.0)) / 2.0



class        _SCREAMING_SNAKE_CASE						(     __SCREAMING_SNAKE_CASE   ):







 '''simple docstring'''
 lowercase_		=      {"df": 1, "loc": 1, "scale": 1}
 lowercase_		=      StudentT

 @classmethod
 def 							SCREAMING_SNAKE_CASE_ (cls    :       Optional[int]	,			UpperCAmelCase_    :       torch.Tensor	,			UpperCAmelCase_    :       torch.Tensor	,			UpperCAmelCase_    :       torch.Tensor)	->Dict:



   '''simple docstring'''



   lowerCamelCase__:				str        =cls.squareplus(UpperCAmelCase_).clamp_min(torch.finfo(scale.dtype).eps)
   lowerCamelCase__:				Any        =2.0 + cls.squareplus(UpperCAmelCase_)
   return df.squeeze(-1), loc.squeeze(-1), scale.squeeze(-1)



class        _SCREAMING_SNAKE_CASE						(     __SCREAMING_SNAKE_CASE   ):







 '''simple docstring'''
 lowercase_		=      {"loc": 1, "scale": 1}
 lowercase_		=      Normal

 @classmethod
 def 							SCREAMING_SNAKE_CASE_ (cls    :       Optional[Any]	,			UpperCAmelCase_    :       torch.Tensor	,			UpperCAmelCase_    :       torch.Tensor)	->Optional[Any]:



   '''simple docstring'''



   lowerCamelCase__:				List[Any]        =cls.squareplus(UpperCAmelCase_).clamp_min(torch.finfo(scale.dtype).eps)
   return loc.squeeze(-1), scale.squeeze(-1)



class        _SCREAMING_SNAKE_CASE						(     __SCREAMING_SNAKE_CASE   ):







 '''simple docstring'''
 lowercase_		=      {"total_count": 1, "logits": 1}
 lowercase_		=      NegativeBinomial

 @classmethod
 def 							SCREAMING_SNAKE_CASE_ (cls    :       Optional[int]	,			UpperCAmelCase_    :       torch.Tensor	,			UpperCAmelCase_    :       torch.Tensor)	->List[str]:



   '''simple docstring'''



   lowerCamelCase__:				Tuple        =cls.squareplus(UpperCAmelCase_)
   return total_count.squeeze(-1), logits.squeeze(-1)

 def 							SCREAMING_SNAKE_CASE_ (self    :       Tuple	,			UpperCAmelCase_    :       Tuple)	->Distribution:



   '''simple docstring'''



   lowerCamelCase__  , lowerCamelCase__:				Any        =distr_args
   if self.dim == 1:
     return self.distribution_class(total_count=UpperCAmelCase_	,			logits=UpperCAmelCase_)
   else:
     return Independent(self.distribution_class(total_count=UpperCAmelCase_	,			logits=UpperCAmelCase_)	,			1)







 def 							SCREAMING_SNAKE_CASE_ (self    :       Union[str, Any]	,			UpperCAmelCase_    :       Optional[Any]	,			UpperCAmelCase_    :       Optional[torch.Tensor] = None	,			UpperCAmelCase_    :       Optional[torch.Tensor] = None)	->Distribution:



   '''simple docstring'''



   lowerCamelCase__  , lowerCamelCase__:				Union[str, Any]        =distr_args

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

   return self._base_distribution((total_count, logits))

