





from __future__ import annotations

class   lowerCAmelCase				:
 def __init__( self    : Optional[int]     ,	UpperCAmelCase    : list[list[int]]      )     ->      Tuple:
     lowerCamelCase__       : Union[str, Any]   					=						TypeError(
         'Matrices must be formed from a list of zero or more lists containing at '
         'least one and the same number of values, each of which must be of type '
         'int or float.'      )
     if len(UpperCAmelCase      ) != 0:
         lowerCamelCase__       : Union[str, Any]   					=						len(rows[0]      )
         if cols == 0:
             raise error
         for row in rows:
             if len(UpperCAmelCase      ) != cols:
                 raise error
             for value in row:
                 if not isinstance(UpperCAmelCase     ,	(int, float)      ):
                     raise error
         lowerCamelCase__       : Optional[int]   					=						rows
     else:
         lowerCamelCase__       : List[str]   					=						[]
 def 	A_      ( self    : Optional[Any]      )     ->      list[list[int]]:
     return [[row[i] for row in self.rows] for i in range(len(self.rows[0]      )      )]
 @property
 def 	A_      ( self    : Tuple      )     ->      int:
     return len(self.rows      )
 @property
 def 	A_      ( self    : Optional[Any]      )     ->      int:
     return len(self.rows[0]      )
 @property
 def 	A_      ( self    : Optional[int]      )     ->      tuple[int, int]:
     return (self.num_rows, self.num_columns)
 @property
 def 	A_      ( self    : Optional[int]      )     ->      bool:
     return self.order[0] == self.order[1]
 def 	A_      ( self    : List[Any]      )     ->      Matrix:
     lowerCamelCase__       : Optional[int]   					=						[
         [0 if column_num != row_num else 1 for column_num in range(self.num_rows      )]
         for row_num in range(self.num_rows      )
     ]
     return Matrix(UpperCAmelCase      )
 def 	A_      ( self    : str      )     ->      int:
     if not self.is_square:
         return 0
     if self.order == (0, 0):
         return 1
     if self.order == (1, 1):
         return int(self.rows[0][0]      )
     if self.order == (2, 2):
         return int(
             (self.rows[0][0] * self.rows[1][1])
             - (self.rows[0][1] * self.rows[1][0])      )
     else:
         return sum(
             self.rows[0][column] * self.cofactors().rows[0][column]
             for column in range(self.num_columns      )      )
 def 	A_      ( self    : Tuple      )     ->      bool:
     return bool(self.determinant()      )
 def 	A_      ( self    : Any     ,	UpperCAmelCase    : int     ,	UpperCAmelCase    : int      )     ->      int:
     lowerCamelCase__       : Tuple   					=						[
         [
             self.rows[other_row][other_column]
             for other_column in range(self.num_columns      )
             if other_column != column
         ]
         for other_row in range(self.num_rows      )
         if other_row != row
     ]
     return Matrix(UpperCAmelCase      ).determinant()
 def 	A_      ( self    : List[Any]     ,	UpperCAmelCase    : int     ,	UpperCAmelCase    : int      )     ->      int:
     if (row + column) % 2 == 0:
         return self.get_minor(UpperCAmelCase     ,	UpperCAmelCase      )
     return -1 * self.get_minor(UpperCAmelCase     ,	UpperCAmelCase      )
 def 	A_      ( self    : Dict      )     ->      Matrix:
     return Matrix(
         [
             [self.get_minor(UpperCAmelCase     ,	UpperCAmelCase      ) for column in range(self.num_columns      )]
             for row in range(self.num_rows      )
         ]      )
 def 	A_      ( self    : Optional[int]      )     ->      Matrix:
     return Matrix(
         [
             [
                 self.minors().rows[row][column]
                 if (row + column) % 2 == 0
                 else self.minors().rows[row][column] * -1
                 for column in range(self.minors().num_columns      )
             ]
             for row in range(self.minors().num_rows      )
         ]      )
 def 	A_      ( self    : Optional[Any]      )     ->      Matrix:
     lowerCamelCase__       : int   					=						[
         [self.cofactors().rows[column][row] for column in range(self.num_columns      )]
         for row in range(self.num_rows      )
     ]
     return Matrix(UpperCAmelCase      )
 def 	A_      ( self    : Union[str, Any]      )     ->      Matrix:
     lowerCamelCase__       : Any   					=						self.determinant()
     if not determinant:
         raise TypeError('Only matrices with a non-zero determinant have an inverse'      )
     return self.adjugate() * (1 / determinant)
 def __repr__( self    : Optional[int]      )     ->      str:
     return str(self.rows      )
 def __str__( self    : List[Any]      )     ->      str:
     if self.num_rows == 0:
         return "[]"
     if self.num_rows == 1:
         return "[[" + ". ".join(str(self.rows[0]      )      ) + "]]"
     return (
         "["
         + "\n ".join(
             [
                 '[' + '. '.join([str(UpperCAmelCase      ) for value in row]      ) + '.]'
                 for row in self.rows
             ]      )
         + "]"
     )
 def 	A_      ( self    : Union[str, Any]     ,	UpperCAmelCase    : list[int]     ,	UpperCAmelCase    : int | None = None      )     ->      None:
     lowerCamelCase__       : Tuple   					=						TypeError('Row must be a list containing all ints and/or floats'      )
     if not isinstance(UpperCAmelCase     ,	UpperCAmelCase      ):
         raise type_error
     for value in row:
         if not isinstance(UpperCAmelCase     ,	(int, float)      ):
             raise type_error
     if len(UpperCAmelCase      ) != self.num_columns:
         raise ValueError(
             'Row must be equal in length to the other rows in the matrix'      )
     if position is None:
         self.rows.append(UpperCAmelCase      )
     else:
         lowerCamelCase__       : Any   					=						self.rows[0:position] + [row] + self.rows[position:]
 def 	A_      ( self    : int     ,	UpperCAmelCase    : list[int]     ,	UpperCAmelCase    : int | None = None      )     ->      None:
     lowerCamelCase__       : Optional[Any]   					=						TypeError(
         'Column must be a list containing all ints and/or floats'      )
     if not isinstance(UpperCAmelCase     ,	UpperCAmelCase      ):
         raise type_error
     for value in column:
         if not isinstance(UpperCAmelCase     ,	(int, float)      ):
             raise type_error
     if len(UpperCAmelCase      ) != self.num_rows:
         raise ValueError(
             'Column must be equal in length to the other columns in the matrix'      )
     if position is None:
         lowerCamelCase__       : Optional[Any]   					=						[self.rows[i] + [column[i]] for i in range(self.num_rows      )]
     else:
         lowerCamelCase__       : Tuple   					=						[
             self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
             for i in range(self.num_rows      )
         ]
 def __eq__( self    : Any     ,	UpperCAmelCase    : object      )     ->      bool:
     if not isinstance(UpperCAmelCase     ,	UpperCAmelCase      ):
         return NotImplemented
     return self.rows == other.rows
 def __ne__( self    : Dict     ,	UpperCAmelCase    : object      )     ->      bool:
     return not self == other
 def __neg__( self    : Optional[Any]      )     ->      Matrix:
     return self * -1
 def __add__( self    : Optional[Any]     ,	UpperCAmelCase    : Matrix      )     ->      Matrix:
     if self.order != other.order:
         raise ValueError('Addition requires matrices of the same order'      )
     return Matrix(
         [
             [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns      )]
             for i in range(self.num_rows      )
         ]      )
 def __sub__( self    : Tuple     ,	UpperCAmelCase    : Matrix      )     ->      Matrix:
     if self.order != other.order:
         raise ValueError('Subtraction requires matrices of the same order'      )
     return Matrix(
         [
             [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns      )]
             for i in range(self.num_rows      )
         ]      )
 def __mul__( self    : str     ,	UpperCAmelCase    : Matrix | int | float      )     ->      Matrix:
     if isinstance(UpperCAmelCase     ,	(int, float)      ):
         return Matrix(
             [[int(element * other      ) for element in row] for row in self.rows]      )
     elif isinstance(UpperCAmelCase     ,	UpperCAmelCase      ):
         if self.num_columns != other.num_rows:
             raise ValueError(
                 'The number of columns in the first matrix must '
                 'be equal to the number of rows in the second'      )
         return Matrix(
             [
                 [Matrix.dot_product(UpperCAmelCase     ,	UpperCAmelCase      ) for column in other.columns()]
                 for row in self.rows
             ]      )
     else:
         raise TypeError(
             'A Matrix can only be multiplied by an int, float, or another matrix'      )
 def __pow__( self    : Tuple     ,	UpperCAmelCase    : int      )     ->      Matrix:
     if not isinstance(UpperCAmelCase     ,	UpperCAmelCase      ):
         raise TypeError('A Matrix can only be raised to the power of an int'      )
     if not self.is_square:
         raise ValueError('Only square matrices can be raised to a power'      )
     if other == 0:
         return self.identity()
     if other < 0:
         if self.is_invertable():
             return self.inverse() ** (-other)
         raise ValueError(
             'Only invertable matrices can be raised to a negative power'      )
     lowerCamelCase__       : str   					=						self
     for _ in range(other - 1      ):
         result *= self
     return result







 @classmethod
 def 	A_      ( cls    : Dict     ,	UpperCAmelCase    : list[int]     ,	UpperCAmelCase    : list[int]      )     ->      int:
     return sum(row[i] * column[i] for i in range(len(UpperCAmelCase      )      )      )


if __name__ == "__main__":
    import doctest

    doctest.testmod()












from __future__ import annotations

import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_sentencepiece, require_tf, require_tokenizers, slow


if is_tf_available():
    import tensorflow as tf

    from transformers import AutoTokenizer, TFAutoModelForSeqaSeqLM

@require_tf
@require_sentencepiece
@require_tokenizers
class   lowerCAmelCase				(   unittest.TestCase     ):
 @slow
 def 	A_      ( self    : int      )     ->      Optional[Any]:
     lowerCamelCase__       : Tuple   					=						TFAutoModelForSeqaSeqLM.from_pretrained('google/mt5-small'      )
     lowerCamelCase__       : Any   					=						AutoTokenizer.from_pretrained('google/mt5-small'      )

     lowerCamelCase__       : int   					=						tokenizer('Hello there'     ,	return_tensors='tf'      ).input_ids
     lowerCamelCase__       : int   					=						tokenizer('Hi I am'     ,	return_tensors='tf'      ).input_ids

     lowerCamelCase__       : List[str]   					=						model(UpperCAmelCase     ,	labels=UpperCAmelCase      ).loss
     lowerCamelCase__       : List[Any]   					=						-tf.math.reduce_mean(UpperCAmelCase      ).numpy()

     lowerCamelCase__       : Dict   					=						-2_1.2_2_8_1_6_8
     self.assertTrue(abs(mtf_score - EXPECTED_SCORE      ) < 2e-4      )





