
'''simple docstring'''







from __future__ import annotations


class 						__UpperCAmelCase      :


							def __init__(       self    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								_snake_case   						=		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(lowerCAmelCase_  ) != 0:
									_snake_case   						=		len(rows[0]  )
									if cols == 0:
										raise error
									for row in rows:
										if len(lowerCAmelCase_  ) != cols:
											raise error
										for value in row:
											if not isinstance(lowerCAmelCase_    ,   (int, float)  ):
												raise error
									_snake_case   						=		rows
								else:
									_snake_case   						=		[]


							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								return [[row[i] for row in self.rows] for i in range(len(self.rows[0]  )  )]


							@property
							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								return len(self.rows  )


							@property
							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								return len(self.rows[0]  )


							@property
							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								return (self.num_rows, self.num_columns)


							@property
							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								return self.order[0] == self.order[1]


							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								_snake_case   						=		[
								    [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(lowerCAmelCase_  )


							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								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  lowerCamelCase				(       self  ):





								"""simple docstring"""






								return bool(self.determinant()  )


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								_snake_case   						=		[
								    [
								        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(lowerCAmelCase_  ).determinant()


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								if (row + column) % 2 == 0:
									return self.get_minor(lowerCAmelCase_    ,   lowerCAmelCase_  )
								return -1 * self.get_minor(lowerCAmelCase_    ,   lowerCAmelCase_  )


							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								return Matrix(
								    [
								        [self.get_minor(lowerCAmelCase_    ,   lowerCAmelCase_  ) for column in range(self.num_columns  )]
								        for row in range(self.num_rows  )
								    ]  )


							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								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  lowerCamelCase				(       self  ):





								"""simple docstring"""






								_snake_case   						=		[
								    [self.cofactors().rows[column][row] for column in range(self.num_columns  )]
								    for row in range(self.num_rows  )
								]
								return Matrix(lowerCAmelCase_  )


							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								_snake_case   						=		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  ):





								"""simple docstring"""






								return str(self.rows  )


							def __str__(       self  ):





								"""simple docstring"""






								if self.num_rows == 0:
									return "[]"
								if self.num_rows == 1:
									return "[[" + ". ".join(str(self.rows[0]  )  ) + "]]"
								return (
								    "["
								    + "\n ".join(
								        [
								            '[' + '. '.join([str(lowerCAmelCase_  ) for value in row]  ) + '.]'
								            for row in self.rows
								        ]  )
								    + "]"
								)


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_    ,   lowerCAmelCase_ = None  ):





								"""simple docstring"""






								_snake_case   						=		TypeError('Row must be a list containing all ints and/or floats'  )
								if not isinstance(lowerCAmelCase_    ,   lowerCAmelCase_  ):
									raise type_error
								for value in row:
									if not isinstance(lowerCAmelCase_    ,   (int, float)  ):
										raise type_error
								if len(lowerCAmelCase_  ) != 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(lowerCAmelCase_  )
								else:
									_snake_case   						=		self.rows[0:position] + [row] + self.rows[position:]


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_    ,   lowerCAmelCase_ = None  ):





								"""simple docstring"""






								_snake_case   						=		TypeError(
								    'Column must be a list containing all ints and/or floats'  )
								if not isinstance(lowerCAmelCase_    ,   lowerCAmelCase_  ):
									raise type_error
								for value in column:
									if not isinstance(lowerCAmelCase_    ,   (int, float)  ):
										raise type_error
								if len(lowerCAmelCase_  ) != self.num_rows:
									raise ValueError(
									    'Column must be equal in length to the other columns in the matrix'  )
								if position is None:
									_snake_case   						=		[self.rows[i] + [column[i]] for i in range(self.num_rows  )]
								else:
									_snake_case   						=		[
									    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
									    for i in range(self.num_rows  )
									]


							def __eq__(       self    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								if not isinstance(lowerCAmelCase_    ,   lowerCAmelCase_  ):
									return NotImplemented
								return self.rows == other.rows


							def __ne__(       self    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								return not self == other


							def __neg__(       self  ):





								"""simple docstring"""






								return self * -1


							def __add__(       self    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								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    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								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    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								if isinstance(lowerCAmelCase_    ,   (int, float)  ):
									return Matrix(
									    [[int(element * other  ) for element in row] for row in self.rows]  )
								elif isinstance(lowerCAmelCase_    ,   lowerCAmelCase_  ):
									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(lowerCAmelCase_    ,   lowerCAmelCase_  ) 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    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								if not isinstance(lowerCAmelCase_    ,   lowerCAmelCase_  ):
									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'  )
								_snake_case   						=		self
								for _ in range(other - 1  ):
									result *= self
								return result




							@classmethod
							def  lowerCamelCase				(       cls    ,   lowerCAmelCase_    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								return sum(row[i] * column[i] for i in range(len(lowerCAmelCase_  )  )  )


if __name__ == "__main__":
					import doctest

					doctest.testmod()



'''simple docstring'''







import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
					from transformers import AutoModelForSeqaSeqLM, AutoTokenizer


@require_torch
@require_sentencepiece
@require_tokenizers
class 						__UpperCAmelCase      (					unittest.TestCase						):


							@slow
							def  lowerCamelCase				(       self  ):





								"""simple docstring"""






								_snake_case   						=		AutoModelForSeqaSeqLM.from_pretrained('google/mt5-small'    ,   return_dict=lowerCAmelCase_  ).to(lowerCAmelCase_  )
								_snake_case   						=		AutoTokenizer.from_pretrained('google/mt5-small'  )

								_snake_case   						=		tokenizer('Hello there'    ,   return_tensors='pt'  ).input_ids
								_snake_case   						=		tokenizer('Hi I am'    ,   return_tensors='pt'  ).input_ids

								_snake_case   						=		model(input_ids.to(lowerCAmelCase_  )    ,   labels=labels.to(lowerCAmelCase_  )  ).loss
								_snake_case   						=		-(labels.shape[-1] * loss.item())

								_snake_case   						=		-84.9127
								self.assertTrue(abs(mtf_score - EXPECTED_SCORE  ) < 1E-4  )

