


'''simple docstring'''




from __future__ import annotations

from typing import Any

def       __UpperCamelCase     (     *_A     :					list[list[int]]					)     ->   list[list[int]]:




	"""simple docstring"""





	if all(_check_not_integer(_A					) for m in matrix_s					):
		for i in matrix_s[1:]:
			_verify_matrix_sizes(matrix_s[0]       , _A					)
		return [[sum(_A					) for t in zip(*_A					)] for m in zip(*_A					)]
	raise TypeError('Expected a matrix, got int/list instead'					)

def       __UpperCamelCase     (     _A     :					list[list[int]]       , _A     :					list[list[int]]					)     ->   list[list[int]]:




	"""simple docstring"""





	if (
	    _check_not_integer(_A					)
	    and _check_not_integer(_A					)
	    and _verify_matrix_sizes(_A       , _A					)
	):
		return [[i - j for i, j in zip(*_A					)] for m in zip(_A       , _A					)]
	raise TypeError('Expected a matrix, got int/list instead'					)

def       __UpperCamelCase     (     _A     :					list[list[int]]       , _A     :					int | float					)     ->   list[list[float]]:




	"""simple docstring"""





	return [[x * n for x in row] for row in matrix]

def       __UpperCamelCase     (     _A     :					list[list[int]]       , _A     :					list[list[int]]					)     ->   list[list[int]]:




	"""simple docstring"""





	if _check_not_integer(_A					) and _check_not_integer(_A					):
		lowerCAmelCase				, lowerCAmelCase       :     Union[str, Any]   				=			_verify_matrix_sizes(_A       , _A					)

	if cols[0] != rows[1]:
		lowerCAmelCase       :     Dict   				=			(
		    'Cannot multiply matrix of dimensions '
		    F"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
		)
		raise ValueError(_A					)
	return [
	    [sum(m * n for m, n in zip(_A       , _A					)					) for j in zip(*_A					)] for i in matrix_a
	]

def       __UpperCamelCase     (     _A     :					int					)     ->   list[list[int]]:




	"""simple docstring"""





	lowerCAmelCase       :     List[str]   				=			int(_A					)
	return [[int(row == column					) for column in range(_A					)] for row in range(_A					)]

def       __UpperCamelCase     (     _A     :					list[list[int]]       , _A     :					bool = True					)     ->   list[list[int]] | map[list[int]]:




	"""simple docstring"""





	if _check_not_integer(_A					):
		if return_map:
			return map(_A       , zip(*_A					)					)
		else:
			return list(map(_A       , zip(*_A					)					)					)
	raise TypeError('Expected a matrix, got int/list instead'					)

def       __UpperCamelCase     (     _A     :					list[list[int]]       , _A     :					int       , _A     :					int					)     ->   list[list[int]]:




	"""simple docstring"""





	lowerCAmelCase       :     Optional[Any]   				=			matrix[:row] + matrix[row + 1 :]
	return [row[:column] + row[column + 1 :] for row in minor]

def       __UpperCamelCase     (     _A     :					list[list[int]]					)     ->   Any:




	"""simple docstring"""





	if len(_A					) == 1:
		return matrix[0][0]

	return sum(
	    x * determinant(minor(_A       , 0       , _A					)					) * (-1) ** i
	    for i, x in enumerate(matrix[0]					)					)

def       __UpperCamelCase     (     _A     :					list[list[int]]					)     ->   list[list[float]] | None:




	"""simple docstring"""





	lowerCAmelCase       :     Tuple   				=			determinant(_A					)
	if det == 0:
		return None

	lowerCAmelCase       :     Tuple   				=			[
	    [determinant(minor(_A       , _A       , _A					)					) for j in range(len(_A					)					)]
	    for i in range(len(_A					)					)
	]

	lowerCAmelCase       :     List[Any]   				=			[
	    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]					)]
	    for row in range(len(_A					)					)
	]
	lowerCAmelCase       :     Optional[Any]   				=			list(transpose(_A					)					)
	return scalar_multiply(_A       , 1 / det					)

def       __UpperCamelCase     (     _A     :					list[list[int]]					)     ->   bool:




	"""simple docstring"""





	return not isinstance(_A       , _A					) and not isinstance(matrix[0]       , _A					)

def       __UpperCamelCase     (     _A     :					list[list[int]]					)     ->   tuple[int, int]:




	"""simple docstring"""





	return len(_A					), len(matrix[0]					)

def       __UpperCamelCase     (     _A     :					list[list[int]]       , _A     :					list[list[int]]					)     ->   tuple[tuple[int, int], tuple[int, int]]:




	"""simple docstring"""





	lowerCAmelCase       :     Tuple   				=			_shape(_A					) + _shape(_A					)
	if shape[0] != shape[3] or shape[1] != shape[2]:
		lowerCAmelCase       :     List[Any]   				=			(
		    'operands could not be broadcast together with shape '
		    F"({shape[0], shape[1]}), ({shape[2], shape[3]})"
		)
		raise ValueError(_A					)
	return (shape[0], shape[2]), (shape[1], shape[3])

def       __UpperCamelCase     (     )     ->   None:




	"""simple docstring"""





	lowerCAmelCase       :     Any   				=			[[12, 10], [3, 9]]
	lowerCAmelCase       :     Any   				=			[[3, 4], [7, 4]]
	lowerCAmelCase       :     List[str]   				=			[[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
	lowerCAmelCase       :     List[Any]   				=			[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
	print(F"Add Operation, {add(_A       , _A					) = } \n"					)
	print(
	    F"Multiply Operation, {multiply(_A       , _A					) = } \n"       , )
	print(F"Identity: {identity(5					)}\n"					)
	print(F"Minor of {matrix_c} = {minor(_A       , 1       , 2					)} \n"					)
	print(F"Determinant of {matrix_b} = {determinant(_A					)} \n"					)
	print(F"Inverse of {matrix_d} = {inverse(_A					)}\n"					)


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				main()




'''simple docstring'''




from collections import OrderedDict
from dataclasses import fields
from typing import Any, Tuple

import numpy as np

from .import_utils import is_torch_available

def       __UpperCamelCase     (     _A     :					List[str]					)     ->   Any:




	"""simple docstring"""





	if is_torch_available():
		import torch

		if isinstance(_A       , torch.Tensor					):
			return True

	return isinstance(_A       , np.ndarray					)






class 			lowerCAmelCase					(					a				):



	def 					lowercase  (       self     ):
		lowerCAmelCase       :     List[str]   				=			fields(self     )

		# Safety and consistency checks
		if not len(snake_case__     ):
			raise ValueError(f"{self.__class__.__name__} has no fields."     )

		lowerCAmelCase       :     List[str]   				=			getattr(self			,       class_fields[0].name     )
		lowerCAmelCase       :     List[Any]   				=			all(getattr(self			,       field.name     ) is None for field in class_fields[1:]     )

		if other_fields_are_none and isinstance(snake_case__			,       snake_case__     ):
			for key, value in first_field.items():
				lowerCAmelCase       :     Optional[int]   				=			value
		else:
			for field in class_fields:
				lowerCAmelCase       :     str   				=			getattr(self			,       field.name     )
				if v is not None:
					lowerCAmelCase       :     Optional[Any]   				=			v



	def __delitem__(       self			,       *snake_case__			,       **snake_case__     ):
		raise Exception(f"You cannot use ``__delitem__`` on a {self.__class__.__name__} instance."     )



	def 					lowercase  (       self			,       *snake_case__			,       **snake_case__     ):
		raise Exception(f"You cannot use ``setdefault`` on a {self.__class__.__name__} instance."     )



	def 					lowercase  (       self			,       *snake_case__			,       **snake_case__     ):
		raise Exception(f"You cannot use ``pop`` on a {self.__class__.__name__} instance."     )



	def 					lowercase  (       self			,       *snake_case__			,       **snake_case__     ):
		raise Exception(f"You cannot use ``update`` on a {self.__class__.__name__} instance."     )



	def __getitem__(       self			,       snake_case__     ):
		if isinstance(snake_case__			,       snake_case__     ):
			lowerCAmelCase       :     Dict   				=			dict(self.items()     )
			return inner_dict[k]
		else:
			return self.to_tuple()[k]



	def __setattr__(       self			,       snake_case__			,       snake_case__     ):
		if name in self.keys() and value is not None:
			# Don't call self.__setitem__ to avoid recursion errors
			super().__setitem__(snake_case__			,       snake_case__     )
		super().__setattr__(snake_case__			,       snake_case__     )



	def __setitem__(       self			,       snake_case__			,       snake_case__     ):
		# Will raise a KeyException if needed
		super().__setitem__(snake_case__			,       snake_case__     )
		# Don't call self.__setattr__ to avoid recursion errors
		super().__setattr__(snake_case__			,       snake_case__     )



	def 					lowercase  (       self     ):
		return tuple(self[k] for k in self.keys()     )
