




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


__lowerCAmelCase		:				str       			=		re.compile(r'^(?P<major>\d+)' r'\.(?P<minor>\d+)' r'\.(?P<patch>\d+)$')




@total_ordering
@dataclass
class     snake_case__							:
				"""simple docstring"""



				SCREAMING_SNAKE_CASE_       :							str
				SCREAMING_SNAKE_CASE_       :							Optional[str]							 =					None
				SCREAMING_SNAKE_CASE_       :							Optional[Union[str, int]]							 =					None
				SCREAMING_SNAKE_CASE_       :							Optional[Union[str, int]]							 =					None
				SCREAMING_SNAKE_CASE_       :							Optional[Union[str, int]]							 =					None





				def 							__UpperCAmelCase							(      self				:     Tuple							)					->     Optional[Any]:
							a    ,		a    ,		a    =			_str_to_version_tuple(self.version_str							)





				def __repr__(      self				:     List[str]							)					->     Dict:
							return f"""{self.tuple[0]}.{self.tuple[1]}.{self.tuple[2]}"""





				@property
				def 							__UpperCAmelCase							(      self				:     Tuple							)					->     Any:
							return self.major, self.minor, self.patch





				def 							__UpperCAmelCase							(      self				:     List[str]					,      __lowerCamelCase				:     Optional[int]							)					->     Optional[Any]:
							if isinstance(__lowerCamelCase					,      __lowerCamelCase							):
										return Version(__lowerCamelCase							)
							elif isinstance(__lowerCamelCase					,      __lowerCamelCase							):
										return other
							raise TypeError(f"""{other} (type {type(__lowerCamelCase							)}) cannot be compared to version."""							)





				def __eq__(      self				:     int					,      __lowerCamelCase				:     Any							)					->     Optional[int]:
							try:
										a    =			self._validate_operand(__lowerCamelCase							)
							except (TypeError, ValueError):
										return False
							else:
										return self.tuple == other.tuple





				def __lt__(      self				:     Optional[Any]					,      __lowerCamelCase				:     Union[str, Any]							)					->     Dict:
							a    =			self._validate_operand(__lowerCamelCase							)
							return self.tuple < other.tuple





				def __hash__(      self				:     Any							)					->     Optional[Any]:
							return hash(_version_tuple_to_str(self.tuple							)							)





				@classmethod
				def 							__UpperCAmelCase							(      cls				:     Optional[Any]					,      __lowerCamelCase				:     Dict							)					->     Any:
							a    =			{f.name for f in dataclasses.fields(cls							)}
							return cls(**{k: v for k, v in dic.items() if k in field_names}							)





				def 							__UpperCAmelCase							(      self				:     List[Any]							)					->     str:
							return self.version_str




def 			__magic_name__				( A		:					Optional[int]   ):






			'''simple docstring'''







			a    =			_VERSION_REG.match(A   )
			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(A   ) for v in [res.group("major"   ), res.group("minor"   ), res.group("patch"   )]   )






def 			__magic_name__				( A		:					Optional[Any]   ):






			'''simple docstring'''







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












from __future__ import annotations

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




def 			__magic_name__				( A		:					NDArray[floataa],  A		:					NDArray[floataa],  A		:					list[int],  A		:					int,  ):






			'''simple docstring'''







			a    ,		a    =			coefficient_matrix.shape
			a    ,		a    =			constant_matrix.shape

			if rowsa != colsa:
						a    =			F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
						raise ValueError(A   )

			if colsa != 1:
						a    =			F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
						raise ValueError(A   )

			if rowsa != rowsa:
						a    =			(
						    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
						    F"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
						)
						raise ValueError(A   )

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

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

			a    =			np.concatenate(
			    (coefficient_matrix, constant_matrix),  axis=1   )

			a    ,		a    =			table.shape

			strictly_diagonally_dominant(A   )

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

			return [float(A   ) for i in new_val]




def 			__magic_name__				( A		:					NDArray[floataa]   ):






			'''simple docstring'''







			a    ,		a    =			table.shape

			a    =			True

			for i in range(0,  A   ):
						a    =			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()






