




# Lint as: python3
import dataclasses
import re
from dataclasses import dataclass
from functools import total_ordering
from typing import Optional, Union


__A   :  Tuple					=      re.compile(R'^(?P<major>\d+)' R'\.(?P<minor>\d+)' R'\.(?P<patch>\d+)$')




@total_ordering
@dataclass
class       lowerCAmelCase__       :


				"""simple docstring"""





				__UpperCAmelCase :     Any       =      42
				__UpperCAmelCase :     Optional[Any]       =      None
				__UpperCAmelCase :     int       =      None
				__UpperCAmelCase :     Dict       =      None
				__UpperCAmelCase :     List[str]       =      None



				def       snake_case    (     self					:	Union[str, Any]						):
						__lowercase				:		int												=				_str_to_version_tuple(self.version_str						)



				def __repr__(     self					:	Tuple						):
						return f'{self.tuple[0]}.{self.tuple[1]}.{self.tuple[2]}'



				@property
				def       snake_case    (     self					:	List[Any]						):
						return self.major, self.minor, self.patch



				def       snake_case    (     self					:	int    ,   lowercase__					:	str						):







						if isinstance(lowercase__    ,   lowercase__						):
								return Version(lowercase__						)
						elif isinstance(lowercase__    ,   lowercase__						):
								return other
						raise TypeError(f'{other} (type {type(lowercase__						)}) cannot be compared to version.'						)



				def __eq__(     self					:	Optional[Any]    ,   lowercase__					:	Tuple						):







						try:
								__lowercase				:		Optional[Any]												=				self._validate_operand(lowercase__						)
						except (TypeError, ValueError):
								return False
						else:
								return self.tuple == other.tuple



				def __lt__(     self					:	Optional[int]    ,   lowercase__					:	Dict						):
						__lowercase				:		str												=				self._validate_operand(lowercase__						)
						return self.tuple < other.tuple



				def __hash__(     self					:	List[Any]						):
						return hash(_version_tuple_to_str(self.tuple						)						)



				@classmethod
				def       snake_case    (     cls					:	Optional[int]    ,   lowercase__					:	Dict						):
						__lowercase				:		Optional[Any]												=				{f.name for f in dataclasses.fields(cls						)}
						return cls(**{k: v for k, v in dic.items() if k in field_names}						)



				def       snake_case    (     self					:	int						):
						return self.version_str





def 						snake_case__       (					_lowerCamelCase				)			->Optional[int]:






		"""simple docstring"""


		__lowercase				:		Optional[int]												=				_VERSION_REG.match(SCREAMING_SNAKE_CASE_				)
		if not res:
				raise ValueError(F'Invalid version \'{version_str}\'. Format should be x.y.z with {{x,y,z}} being digits.'				)
		return tuple(int(SCREAMING_SNAKE_CASE_				) for v in [res.group("major"				), res.group("minor"				), res.group("patch"				)]				)





def 						snake_case__       (					_lowerCamelCase				)			->Optional[int]:






		"""simple docstring"""


		return ".".join(str(SCREAMING_SNAKE_CASE_				) for v in version_tuple				)






"""simple docstring"""







from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase,  )			->list[float]:






		"""simple docstring"""


		__lowercase						,__lowercase				:		Dict												=				coefficient_matrix.shape
		__lowercase						,__lowercase				:		Tuple												=				constant_matrix.shape

		if rowsa != colsa:
				__lowercase				:		str												=				F'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
				raise ValueError(_lowerCamelCase				)

		if colsa != 1:
				__lowercase				:		Dict												=				F'Constant matrix must be nx1 but received {rowsa}x{colsa}'
				raise ValueError(_lowerCamelCase				)

		if rowsa != rowsa:
				__lowercase				:		Optional[Any]												=				(
				    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
				    F'received {rowsa}x{colsa} and {rowsa}x{colsa}'
				)
				raise ValueError(_lowerCamelCase				)

		if len(_lowerCamelCase				) != rowsa:
				__lowercase				:		Dict												=				(
				    "Number of initial values must be equal to number of rows in coefficient "
				    F'matrix but received {len(_lowerCamelCase				)} and {rowsa}'
				)
				raise ValueError(_lowerCamelCase				)

		if iterations <= 0:
				raise ValueError("Iterations must be at least 1"				)

		__lowercase				:		NDArray[floataa]												=				np.concatenate(
		    (coefficient_matrix, constant_matrix),  axis=1				)

		__lowercase						,__lowercase				:		str												=				table.shape

		strictly_diagonally_dominant(_lowerCamelCase				)

		# Iterates the whole matrix for given number of times
		for _ in range(_lowerCamelCase				):
				__lowercase				:		List[Any]												=				[]
				for row in range(_lowerCamelCase				):
						__lowercase				:		Optional[Any]												=				0
						for col in range(_lowerCamelCase				):
								if col == row:
										__lowercase				:		Tuple												=				table[row][col]
								elif col == cols - 1:
										__lowercase				:		Tuple												=				table[row][col]
								else:
										temp += (-1) * table[row][col] * init_val[col]
						__lowercase				:		List[Any]												=				(temp + val) / denom
						new_val.append(_lowerCamelCase				)
				__lowercase				:		Dict												=				new_val

		return [float(_lowerCamelCase				) for i in new_val]

def 						snake_case__       (					_lowerCamelCase				)			->bool:






		"""simple docstring"""


		__lowercase						,__lowercase				:		int												=				table.shape

		__lowercase				:		Optional[int]												=				True

		for i in range(0,  _lowerCamelCase				):
				__lowercase				:		Optional[int]												=				0
				for j in range(0,  cols - 1				):
						if i == j:
								continue
						else:
								total += table[i][j]

				if table[i][i] <= total:
						raise ValueError("Coefficient matrix is not strictly diagonally dominant"				)

		return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
						import doctest

						doctest.testmod()
