





import pytest

from datasets.utils.sharding import _distribute_shards, _number_of_shards_in_gen_kwargs, _split_gen_kwargs





@pytest.mark.parametrize(
    "kwargs, expected"     ,   [
        ({"num_shards": 0, "max_num_jobs": 1}, []),
        ({"num_shards": 10, "max_num_jobs": 1}, [range(10		)]),
        ({"num_shards": 10, "max_num_jobs": 10}, [range(__a     ,   i + 1		) for i in range(10		)]),
        ({"num_shards": 1, "max_num_jobs": 10}, [range(1		)]),
        ({"num_shards": 10, "max_num_jobs": 3}, [range(0     ,   4		), range(4     ,   7		), range(7     ,   10		)]),
        ({"num_shards": 3, "max_num_jobs": 10}, [range(0     ,   1		), range(1     ,   2		), range(2     ,   3		)]),
    ]     ,   )
def 					lowerCAmelCase_			(	__a     ,   __a		)					->		Dict:







  """simple docstring"""





  lowerCamelCase__:				Tuple					  =_distribute_shards(**__a		)
  assert out == expected





@pytest.mark.parametrize(
    "gen_kwargs, max_num_jobs, expected"     ,   [
        ({"foo": 0}, 10, [{"foo": 0}]),
        ({"shards": [0, 1, 2, 3]}, 1, [{"shards": [0, 1, 2, 3]}]),
        ({"shards": [0, 1, 2, 3]}, 4, [{"shards": [0]}, {"shards": [1]}, {"shards": [2]}, {"shards": [3]}]),
        ({"shards": [0, 1]}, 4, [{"shards": [0]}, {"shards": [1]}]),
        ({"shards": [0, 1, 2, 3]}, 2, [{"shards": [0, 1]}, {"shards": [2, 3]}]),
    ]     ,   )
def 					lowerCAmelCase_			(	__a     ,   __a     ,   __a		)					->		str:







  """simple docstring"""





  lowerCamelCase__:				Optional[Any]					  =_split_gen_kwargs(__a     ,   __a		)
  assert out == expected






@pytest.mark.parametrize(
    "gen_kwargs, expected"     ,   [
        ({"foo": 0}, 1),
        ({"shards": [0]}, 1),
        ({"shards": [0, 1, 2, 3]}, 4),
        ({"shards": [0, 1, 2, 3], "foo": 0}, 4),
        ({"shards": [0, 1, 2, 3], "other": (0, 1)}, 4),
        ({"shards": [0, 1, 2, 3], "shards2": [0, 1]}, RuntimeError),
    ]     ,   )
def 					lowerCAmelCase_			(	__a     ,   __a		)					->		List[Any]:







  """simple docstring"""





  if expected is RuntimeError:
    with pytest.raises(__a		):
      _number_of_shards_in_gen_kwargs(__a		)
  else:
    lowerCamelCase__:				Dict					  =_number_of_shards_in_gen_kwargs(__a		)
    assert out == expected








from __future__ import annotations

from typing import Any



class        _SCREAMING_SNAKE_CASE						:







 '''simple docstring'''

 def __init__(self    :       Tuple	,			UpperCAmelCase_    :       int	,			UpperCAmelCase_    :       int	,			UpperCAmelCase_    :       float = 0)	->None:



   '''simple docstring'''



   lowerCamelCase__  , lowerCamelCase__:				Any        =row, column
   lowerCamelCase__:				List[str]        =[[default_value for c in range(UpperCAmelCase_)] for r in range(UpperCAmelCase_)]

 def __str__(self    :       Tuple)	->str:



   '''simple docstring'''



   lowerCamelCase__:				Union[str, Any]        =F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

   # Make string identifier
   lowerCamelCase__:				List[str]        =0
   for row_vector in self.array:
     for obj in row_vector:
       lowerCamelCase__:				int        =max(UpperCAmelCase_	,			len(str(UpperCAmelCase_)))
   lowerCamelCase__:				Any        =F"""%{max_element_length}s"""

   # Make string and return
   def single_line(UpperCAmelCase_    :       list[float]) -> str:
     nonlocal string_format_identifier
     lowerCamelCase__:				Tuple        ="["
     line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
     line += "]"
     return line

   s += "\n".join(single_line(UpperCAmelCase_) for row_vector in self.array)
   return s

 def __repr__(self    :       Optional[int])	->str:



   '''simple docstring'''



   return str(self)

 def 							SCREAMING_SNAKE_CASE_ (self    :       Optional[int]	,			UpperCAmelCase_    :       tuple[int, int])	->bool:



   '''simple docstring'''



   if not (isinstance(UpperCAmelCase_	,			(list, tuple)) and len(UpperCAmelCase_) == 2):
     return False
   elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
     return False
   else:
     return True

 def __getitem__(self    :       int	,			UpperCAmelCase_    :       tuple[int, int])	->Any:



   '''simple docstring'''



   assert self.validate_indicies(UpperCAmelCase_)
   return self.array[loc[0]][loc[1]]

 def __setitem__(self    :       Optional[Any]	,			UpperCAmelCase_    :       tuple[int, int]	,			UpperCAmelCase_    :       float)	->None:



   '''simple docstring'''



   assert self.validate_indicies(UpperCAmelCase_)
   lowerCamelCase__:				str        =value

 def __add__(self    :       Dict	,			UpperCAmelCase_    :       Matrix)	->Matrix:



   '''simple docstring'''



   assert isinstance(UpperCAmelCase_	,			UpperCAmelCase_)
   assert self.row == another.row and self.column == another.column

   # Add
   lowerCamelCase__:				Dict        =Matrix(self.row	,			self.column)
   for r in range(self.row):
     for c in range(self.column):
       lowerCamelCase__:				List[str]        =self[r, c] + another[r, c]
   return result

 def __neg__(self    :       str)	->Matrix:



   '''simple docstring'''



   lowerCamelCase__:				List[Any]        =Matrix(self.row	,			self.column)
   for r in range(self.row):
     for c in range(self.column):
       lowerCamelCase__:				Union[str, Any]        =-self[r, c]
   return result

 def __sub__(self    :       str	,			UpperCAmelCase_    :       Matrix)	->Matrix:



   '''simple docstring'''



   return self + (-another)

 def __mul__(self    :       List[str]	,			UpperCAmelCase_    :       int | float | Matrix)	->Matrix:



   '''simple docstring'''



   if isinstance(UpperCAmelCase_	,			(int, float)):  # Scalar multiplication
     lowerCamelCase__:				List[Any]        =Matrix(self.row	,			self.column)
     for r in range(self.row):
       for c in range(self.column):
         lowerCamelCase__:				Union[str, Any]        =self[r, c] * another
     return result
   elif isinstance(UpperCAmelCase_	,			UpperCAmelCase_):  # Matrix multiplication
     assert self.column == another.row
     lowerCamelCase__:				Dict        =Matrix(self.row	,			another.column)
     for r in range(self.row):
       for c in range(another.column):
         for i in range(self.column):
           result[r, c] += self[r, i] * another[i, c]
     return result
   else:
     lowerCamelCase__:				int        =F"""Unsupported type given for another ({type(UpperCAmelCase_)})"""
     raise TypeError(UpperCAmelCase_)

 def 							SCREAMING_SNAKE_CASE_ (self    :       Optional[Any])	->Matrix:



   '''simple docstring'''



   lowerCamelCase__:				Optional[Any]        =Matrix(self.column	,			self.row)
   for r in range(self.row):
     for c in range(self.column):
       lowerCamelCase__:				Optional[int]        =self[r, c]
   return result







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



   '''simple docstring'''



   assert isinstance(UpperCAmelCase_	,			UpperCAmelCase_) and isinstance(UpperCAmelCase_	,			UpperCAmelCase_)
   assert self.row == self.column == u.row == v.row  # u, v should be column vector
   assert u.column == v.column == 1  # u, v should be column vector

   # Calculate
   lowerCamelCase__:				Tuple        =v.transpose()
   lowerCamelCase__:				Optional[Any]        =(v_t * self * u)[0, 0] + 1
   if numerator_factor == 0:
     return None  # It's not invertable
   return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":





     def 					lowerCAmelCase_			(	)					->		None:







       """simple docstring"""





       lowerCamelCase__:				List[str]        =Matrix(3     ,   3     ,   0		)
       for i in range(3		):
         lowerCamelCase__:				Union[str, Any]        =1
       print(F"""a^(-1) is {ainv}"""		)
       # u, v
       lowerCamelCase__:				Optional[int]        =Matrix(3     ,   1     ,   0		)
       lowerCamelCase__  , lowerCamelCase__  , lowerCamelCase__:				int        =1, 2, -3
       lowerCamelCase__:				Optional[Any]        =Matrix(3     ,   1     ,   0		)
       lowerCamelCase__  , lowerCamelCase__  , lowerCamelCase__:				Any        =4, -2, 5
       print(F"""u is {u}"""		)
       print(F"""v is {v}"""		)
       print(F"""uv^T is {u * v.transpose()}"""		)
       # Sherman Morrison
       print(F"""(a + uv^T)^(-1) is {ainv.sherman_morrison(__a     ,   __a		)}"""		)





     def 					lowerCAmelCase_			(	)					->		None:







       """simple docstring"""





       import doctest

       doctest.testmod()






     testa()

