


'''simple docstring'''



from __future__ import annotations

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






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Optional[Any]						,				_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       List[str]						,				_SCREAMING_SNAKE_CASE				:       List[Any]						,				):
					__a      :	Tuple    =  coefficient_matrix.shape
					__a      :	Dict    =  constant_matrix.shape

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

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

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

					if len(lowercase__       ) != rowsa:
										__a      :	List[str]    =  (
										    'Number of initial values must be equal to number of rows in coefficient '
										    F"""matrix but received {len(lowercase__       )} and {rowsa}"""
										)
										raise ValueError(lowercase__       )

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

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

					__a      :	Any    =  table.shape

					strictly_diagonally_dominant(lowercase__       )

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

					return [float(lowercase__       ) for i in new_val]






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Optional[int]       ):
					__a      :	Union[str, Any]    =  table.shape

					__a      :	List[str]    =  True

					for i in range(0						,				lowercase__       ):
										__a      :	str    =  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 os
import socket
from contextlib import contextmanager

import torch

from ..commands.config.default import write_basic_config  # noqa: F401
from ..state import PartialState
from .dataclasses import DistributedType
from .imports import is_deepspeed_available, is_tpu_available
from .transformer_engine import convert_model
from .versions import is_torch_version


if is_deepspeed_available():
	from deepspeed import DeepSpeedEngine

if is_tpu_available(check_device=False):
	import torch_xla.core.xla_model as xm






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Optional[Any]       ):
					if is_torch_version('<'						,				'2.0.0'       ) or not hasattr(_SCREAMING_SNAKE_CASE						,				'_dynamo'       ):
										return False
					return isinstance(_SCREAMING_SNAKE_CASE						,				torch._dynamo.eval_frame.OptimizedModule       )






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Optional[Any]						,				_SCREAMING_SNAKE_CASE				:       bool = True       ):
					__a      :	int    =  (torch.nn.parallel.DistributedDataParallel, torch.nn.DataParallel)

					__a      :	Any    =  is_compiled_module(_SCREAMING_SNAKE_CASE       )
					if is_compiled:
										__a      :	List[Any]    =  model
										__a      :	Union[str, Any]    =  model._orig_mod

					if is_deepspeed_available():
										options += (DeepSpeedEngine,)

					while isinstance(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ):
										__a      :	Union[str, Any]    =  model.module

					if not keep_fpaa_wrapper:
										__a      :	Optional[Any]    =  getattr(_SCREAMING_SNAKE_CASE						,				'forward'       )
										__a      :	str    =  model.__dict__.pop('_original_forward'						,				_SCREAMING_SNAKE_CASE       )
										if original_forward is not None:
															while hasattr(_SCREAMING_SNAKE_CASE						,				'__wrapped__'       ):
																				__a      :	Any    =  forward.__wrapped__
																				if forward == original_forward:
																									break
															__a      :	str    =  forward
										if getattr(_SCREAMING_SNAKE_CASE						,				'_converted_to_transformer_engine'						,				_SCREAMING_SNAKE_CASE       ):
															convert_model(_SCREAMING_SNAKE_CASE						,				to_transformer_engine=_SCREAMING_SNAKE_CASE       )

					if is_compiled:
										__a      :	List[str]    =  model
										__a      :	Optional[int]    =  compiled_model

					return model






def   lowerCamelCase							():
					PartialState().wait_for_everyone()






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       Tuple       ):
					if PartialState().distributed_type == DistributedType.TPU:
										xm.save(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
					elif PartialState().local_process_index == 0:
										torch.save(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )






@contextmanager
def   lowerCamelCase							(**_SCREAMING_SNAKE_CASE				:       Tuple       ):
					for key, value in kwargs.items():
										__a      :	Optional[int]    =  str(_SCREAMING_SNAKE_CASE       )

					yield

					for key in kwargs:
										if key.upper() in os.environ:
															del os.environ[key.upper()]






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Dict       ):
					if not hasattr(_SCREAMING_SNAKE_CASE						,				'__qualname__'       ) and not hasattr(_SCREAMING_SNAKE_CASE						,				'__name__'       ):
										__a      :	List[Any]    =  getattr(_SCREAMING_SNAKE_CASE						,				'__class__'						,				_SCREAMING_SNAKE_CASE       )
					if hasattr(_SCREAMING_SNAKE_CASE						,				'__qualname__'       ):
										return obj.__qualname__
					if hasattr(_SCREAMING_SNAKE_CASE						,				'__name__'       ):
										return obj.__name__
					return str(_SCREAMING_SNAKE_CASE       )






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       List[str]       ):
					for key, value in source.items():
										if isinstance(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ):
															__a      :	int    =  destination.setdefault(_SCREAMING_SNAKE_CASE						,				{}       )
															merge_dicts(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
										else:
															__a      :	Tuple    =  value

					return destination






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int = None       ):
					if port is None:
										__a      :	List[str]    =  29_500
					with socket.socket(socket.AF_INET						,				socket.SOCK_STREAM       ) as s:
										return s.connect_ex(('localhost', port)       ) == 0



