



'''simple docstring'''





from __future__ import annotations

from typing import Any


class      __lowerCAmelCase     :
					"""simple docstring"""






					def __init__(     self					:       str				,					_snake_case					:       int				,					_snake_case					:       int				,					_snake_case					:       float = 0					):






								"""simple docstring"""


								A__     , A__       =    row, column
								A__       =    [[default_value for c in range(_snake_case					)] for r in range(_snake_case					)]



					def __str__(     self					:       List[Any]					):






								"""simple docstring"""


								A__       =    F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

								# Make string identifier
								A__       =    0
								for row_vector in self.array:
											for obj in row_vector:
														A__       =    max(_snake_case				,					len(str(_snake_case					)					)					)
								A__       =    F'''%{max_element_length}s'''

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

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



					def __repr__(     self					:       Union[str, Any]					):






								"""simple docstring"""


								return str(self					)



					def     _a							(     self					:       List[Any]				,					_snake_case					:       tuple[int, int]					):






								"""simple docstring"""


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



					def __getitem__(     self					:       List[str]				,					_snake_case					:       tuple[int, int]					):






								"""simple docstring"""


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



					def __setitem__(     self					:       Dict				,					_snake_case					:       tuple[int, int]				,					_snake_case					:       float					):






								"""simple docstring"""


								assert self.validate_indicies(_snake_case					)
								A__       =    value



					def __add__(     self					:       Optional[int]				,					_snake_case					:       Matrix					):






								"""simple docstring"""


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

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



					def __neg__(     self					:       Tuple					):






								"""simple docstring"""


								A__       =    Matrix(self.row				,					self.column					)
								for r in range(self.row					):
											for c in range(self.column					):
														A__       =    -self[r, c]
								return result



					def __sub__(     self					:       Tuple				,					_snake_case					:       Matrix					):






								"""simple docstring"""


								return self + (-another)



					def __mul__(     self					:       str				,					_snake_case					:       int | float | Matrix					):






								"""simple docstring"""


								if isinstance(_snake_case				,					(int, float)					):  # Scalar multiplication
											A__       =    Matrix(self.row				,					self.column					)
											for r in range(self.row					):
														for c in range(self.column					):
																	A__       =    self[r, c] * another
											return result
								elif isinstance(_snake_case				,					_snake_case					):  # Matrix multiplication
											assert self.column == another.row
											A__       =    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:
											A__       =    F'''Unsupported type given for another ({type(_snake_case					)})'''
											raise TypeError(_snake_case					)



					def     _a							(     self					:       List[Any]					):






								"""simple docstring"""


								A__       =    Matrix(self.column				,					self.row					)
								for r in range(self.row					):
											for c in range(self.column					):
														A__       =    self[r, c]
								return result



					def     _a							(     self					:       List[Any]				,					_snake_case					:       Matrix				,					_snake_case					:       Matrix					):






								"""simple docstring"""


								assert isinstance(_snake_case				,					_snake_case					) and isinstance(_snake_case				,					_snake_case					)
								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
								A__       =    v.transpose()
								A__       =    (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 A						(       )						->      None:
										# a^(-1)
										A__       =    Matrix(3 ,	3 ,	0					)
										for i in range(3					):
													A__       =    1
										print(f'''a^(-1) is {ainv}'''					)
										# u, v
										A__       =    Matrix(3 ,	1 ,	0					)
										A__     , A__     , A__       =    1, 2, -3
										A__       =    Matrix(3 ,	1 ,	0					)
										A__     , A__     , A__       =    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(__UpperCamelCase ,	__UpperCamelCase					)}'''					)


							def A						(       )						->      None:
										import doctest

										doctest.testmod()






							testa()









import pytest

import datasets


# Import fixture modules as plugins
SCREAMING_SNAKE_CASE__       =      ['''tests.fixtures.files''', '''tests.fixtures.hub''', '''tests.fixtures.fsspec''']


def A						(       __UpperCamelCase ,	__UpperCamelCase					)						->      Optional[int]:
			# Mark tests as "unit" by default if not marked as "integration" (or already marked as "unit")
			for item in items:
						if any(marker in item.keywords for marker in ['integration', 'unit']					):
									continue
						item.add_marker(pytest.mark.unit					)


def A						(       __UpperCamelCase					)						->      str:
			config.addinivalue_line('markers' ,	'torchaudio_latest: mark test to run with torchaudio>=0.12'					)


@pytest.fixture(autouse=__UpperCamelCase					)
def A						(       __UpperCamelCase ,	__UpperCamelCase					)						->      Union[str, Any]:
			# test_hf_cache_home = tmp_path_factory.mktemp("cache")  # TODO: why a cache dir per test function does not work?
			A__       =    tmp_path_factory.getbasetemp() / 'cache'
			A__       =    test_hf_cache_home / 'datasets'
			A__       =    test_hf_cache_home / 'metrics'
			A__       =    test_hf_cache_home / 'modules'
			monkeypatch.setattr('datasets.config.HF_DATASETS_CACHE' ,	str(__UpperCamelCase					)					)
			monkeypatch.setattr('datasets.config.HF_METRICS_CACHE' ,	str(__UpperCamelCase					)					)
			monkeypatch.setattr('datasets.config.HF_MODULES_CACHE' ,	str(__UpperCamelCase					)					)
			A__       =    test_hf_datasets_cache / 'downloads'
			monkeypatch.setattr('datasets.config.DOWNLOADED_DATASETS_PATH' ,	str(__UpperCamelCase					)					)
			A__       =    test_hf_datasets_cache / 'downloads' / 'extracted'
			monkeypatch.setattr('datasets.config.EXTRACTED_DATASETS_PATH' ,	str(__UpperCamelCase					)					)


@pytest.fixture(autouse=__UpperCamelCase ,	scope='session'					)
def A						(       )						->      Union[str, Any]:
			datasets.disable_progress_bar()


@pytest.fixture(autouse=__UpperCamelCase					)
def A						(       __UpperCamelCase					)						->      int:
			# don't take tests into account when counting downloads
			monkeypatch.setattr('datasets.config.HF_UPDATE_DOWNLOAD_COUNTS' ,	__UpperCamelCase					)






@pytest.fixture
def A						(       __UpperCamelCase					)						->      Any:
			# Required to suppress RemovedIn20Warning when feature(s) are not compatible with SQLAlchemy 2.0
			# To be removed once SQLAlchemy 2.0 supported
			monkeypatch.setattr('sqlalchemy.util.deprecations.SILENCE_UBER_WARNING' ,	__UpperCamelCase					)




