






"""simple docstring"""



from __future__ import annotations

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

def 			_snake_case    (					lowerCamelCase__     :   Optional[Any]    ,						lowerCamelCase__     :   List[str]    ,						lowerCamelCase__     :   Optional[int]    ,						lowerCamelCase__     :   Union[str, Any]    ,						)    ->     Union[str, Any]:
							lowerCamelCase_							,						lowerCamelCase_	:							Optional[int]									=coefficient_matrix.shape
							lowerCamelCase_							,						lowerCamelCase_	:							Optional[int]									=constant_matrix.shape

							if rowsa != colsa:
														lowerCamelCase_	:							Optional[Any]									=F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
														raise ValueError(lowerCamelCase__  )

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

							if rowsa != rowsa:
														lowerCamelCase_	:							str									=(
														    "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:
														lowerCamelCase_	:							List[Any]									=(
														    "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"  )

							lowerCamelCase_	:							List[str]									=np.concatenate(
							    (coefficient_matrix, constant_matrix)    ,						axis=1  )

							lowerCamelCase_							,						lowerCamelCase_	:							List[Any]									=table.shape

							strictly_diagonally_dominant(lowerCamelCase__  )

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

							return [float(lowerCamelCase__  ) for i in new_val]

def 			_snake_case    (					lowerCamelCase__     :   Tuple  )    ->     List[str]:
							lowerCamelCase_							,						lowerCamelCase_	:							List[str]									=table.shape

							lowerCamelCase_	:							Optional[int]									=True

							for i in range(0    ,						lowerCamelCase__  ):
														lowerCamelCase_	:							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()











"""simple docstring"""



import torch

def 			_snake_case    (					)    ->     Union[str, Any]:
							if torch.cuda.is_available():
														lowerCamelCase_	:							int									=torch.cuda.device_count()
							else:
														lowerCamelCase_	:							List[str]									=0
							print(F"""Successfully ran on {num_gpus} GPUs"""  )


if __name__ == "__main__":
						main()



