



'''simple docstring'''





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 					snake_case			(UpperCamelCase ):



       def __init__(					self  ,UpperCAmelCase_  ,UpperCAmelCase_=None  ,UpperCAmelCase_=None  ,UpperCAmelCase_=0   )	->				Union[str, Any]:
           lowercase__									=    1.0 if scale is None else scale
           lowercase__									=    0.0 if loc is None else loc

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



       @property
       def 				_a   (					self   )	->				int:
           return self.base_dist.mean * self.scale + self.loc



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







       @property
       def 				_a   (					self   )	->				int:
           return self.variance.sqrt()





class 					snake_case			(nn.Module ):



       def __init__(					self  ,UpperCAmelCase_  ,UpperCAmelCase_  ,UpperCAmelCase_  ,**UpperCAmelCase_   )	->				None:
           super().__init__(**UpperCAmelCase_   )
           lowercase__									=    args_dim
           lowercase__									=    nn.ModuleList([nn.Linear(UpperCAmelCase_  ,UpperCAmelCase_   ) for dim in args_dim.values()]   )
           lowercase__									=    domain_map







       def 				_a   (					self  ,UpperCAmelCase_   )	->				Tuple[torch.Tensor]:
           lowercase__									=    [proj(UpperCAmelCase_   ) for proj in self.proj]

           return self.domain_map(*UpperCAmelCase_   )





class 					snake_case			(nn.Module ):



       def __init__(					self  ,UpperCAmelCase_   )	->				str:
           super().__init__()
           lowercase__									=    function







       def 				_a   (					self  ,UpperCAmelCase_  ,*UpperCAmelCase_   )	->				Dict:
           return self.function(UpperCAmelCase_  ,*UpperCAmelCase_   )





class 					snake_case			:
       lowerCAmelCase__	:type
       lowerCAmelCase__	:int
       lowerCAmelCase__	:Dict[str, int]



       def __init__(					self  ,UpperCAmelCase_ = 1   )	->				None:
           lowercase__									=    dim
           lowercase__									=    {k: dim * self.args_dim[k] for k in self.args_dim}



       def 				_a   (					self  ,UpperCAmelCase_   )	->				int:
           if self.dim == 1:
               return self.distribution_class(*UpperCAmelCase_   )
           else:
               return Independent(self.distribution_class(*UpperCAmelCase_   )  ,1   )



       def 				_a   (					self  ,UpperCAmelCase_  ,UpperCAmelCase_ = None  ,UpperCAmelCase_ = None  ,)	->				Distribution:
           lowercase__									=    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 				_a   (					self   )	->				Tuple:
           return () if self.dim == 1 else (self.dim,)



       @property
       def 				_a   (					self   )	->				int:
           return len(self.event_shape   )



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



       def 				_a   (					self  ,UpperCAmelCase_   )	->				nn.Module:
           return ParameterProjection(
               in_features=UpperCAmelCase_  ,args_dim=self.args_dim  ,domain_map=LambdaLayer(self.domain_map   )  ,)



       def 				_a   (					self  ,*UpperCAmelCase_   )	->				int:
           raise NotImplementedError()







       @staticmethod
       def 				_a   (					UpperCAmelCase_   )	->				torch.Tensor:
           return (x + torch.sqrt(torch.square(UpperCAmelCase_   ) + 4.0   )) / 2.0





class 					snake_case			(UpperCamelCase ):
       lowerCAmelCase__	:Dict[str, int]     =       {"df": 1, "loc": 1, "scale": 1}
       lowerCAmelCase__	:type     =       StudentT



       @classmethod
       def 				_a   (					cls  ,UpperCAmelCase_  ,UpperCAmelCase_  ,UpperCAmelCase_   )	->				Union[str, Any]:
           lowercase__									=    cls.squareplus(UpperCAmelCase_   ).clamp_min(torch.finfo(scale.dtype   ).eps   )
           lowercase__									=    2.0 + cls.squareplus(UpperCAmelCase_   )
           return df.squeeze(-1   ), loc.squeeze(-1   ), scale.squeeze(-1   )





class 					snake_case			(UpperCamelCase ):
       lowerCAmelCase__	:Dict[str, int]     =       {"loc": 1, "scale": 1}
       lowerCAmelCase__	:type     =       Normal



       @classmethod
       def 				_a   (					cls  ,UpperCAmelCase_  ,UpperCAmelCase_   )	->				Union[str, Any]:
           lowercase__									=    cls.squareplus(UpperCAmelCase_   ).clamp_min(torch.finfo(scale.dtype   ).eps   )
           return loc.squeeze(-1   ), scale.squeeze(-1   )





class 					snake_case			(UpperCamelCase ):
       lowerCAmelCase__	:Dict[str, int]     =       {"total_count": 1, "logits": 1}
       lowerCAmelCase__	:type     =       NegativeBinomial



       @classmethod
       def 				_a   (					cls  ,UpperCAmelCase_  ,UpperCAmelCase_   )	->				List[Any]:
           lowercase__									=    cls.squareplus(UpperCAmelCase_   )
           return total_count.squeeze(-1   ), logits.squeeze(-1   )



       def 				_a   (					self  ,UpperCAmelCase_   )	->				Distribution:
           lowercase__							,							lowercase__									=    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 				_a   (					self  ,UpperCAmelCase_  ,UpperCAmelCase_ = None  ,UpperCAmelCase_ = None   )	->				Distribution:
           lowercase__							,							lowercase__									=    distr_args

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

           return self._base_distribution((total_count, logits)   )









'''simple docstring'''





def 							lowerCamelCase	(					):





    '''simple docstring'''


    return [list(range(1_000 - i  ,-1_000 - i  ,-1							)							) for i in range(1_000							)]


SCREAMING_SNAKE_CASE__          =  generate_large_matrix()
SCREAMING_SNAKE_CASE__          =  (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    assert all(row == sorted(_snake_case  ,reverse=_snake_case							) for row in grid							)
    assert all(list(_snake_case							) == sorted(_snake_case  ,reverse=_snake_case							) for col in zip(*_snake_case							)							)




def 							lowerCamelCase	(					_snake_case	:    list[int]							):





    '''simple docstring'''


    lowercase__									=    0
    lowercase__									=    len(_snake_case							) - 1

    # Edge cases such as no values or all numbers are negative.
    if not array or array[0] < 0:
        return 0

    while right + 1 > left:
        lowercase__									=    (left + right) // 2
        lowercase__									=    array[mid]

        # Num must be negative and the index must be greater than or equal to 0.
        if num < 0 and array[mid - 1] >= 0:
            return mid

        if num >= 0:
            lowercase__									=    mid + 1
        else:
            lowercase__									=    mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
    return len(_snake_case							)




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    lowercase__									=    0
    lowercase__									=    len(grid[0]							)

    for i in range(len(_snake_case							)							):
        lowercase__									=    find_negative_index(grid[i][:bound]							)
        total += bound
    return (len(_snake_case							) * len(grid[0]							)) - total




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    return len([number for row in grid for number in row if number < 0]							)




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    lowercase__									=    0
    for row in grid:
        for i, number in enumerate(_snake_case							):
            if number < 0:
                total += len(_snake_case							) - i
                break
    return total




def 							lowerCamelCase	(					):





    '''simple docstring'''


    from timeit import timeit

    print("Running benchmarks"							)
    lowercase__									=    (
        "from __main__ import count_negatives_binary_search, "
        "count_negatives_brute_force, count_negatives_brute_force_with_break, grid"
    )
    for func in (
        "count_negatives_binary_search",  # took 0.7727 seconds
        "count_negatives_brute_force_with_break",  # took 4.6505 seconds
        "count_negatives_brute_force",  # took 12.8160 seconds
    ):
        lowercase__									=    timeit(f'''{func}(grid=grid)'''  ,setup=_snake_case  ,number=500							)
        print(f'''{func}() took {time:0.4f} seconds'''							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()




