



from __future__ import annotations

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





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , ):
    __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(_UpperCAmelCase				)

    if colsa != 1:
        __a						       =				f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
        raise ValueError(_UpperCAmelCase				)

    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(_UpperCAmelCase				)

    if len(_UpperCAmelCase				) != rowsa:
        __a						       =				(
            '''Number of initial values must be equal to number of rows in coefficient '''
            f'matrix but received {len(_UpperCAmelCase				)} and {rowsa}'
        )
        raise ValueError(_UpperCAmelCase				)

    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(_UpperCAmelCase				)

    # Iterates the whole matrix for given number of times
    for _ in range(_UpperCAmelCase				):
        __a						       =				[]
        for row in range(_UpperCAmelCase				):
            __a						       =				0
            for col in range(_UpperCAmelCase				):
                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(_UpperCAmelCase				)
        __a						       =				new_val

    return [float(_UpperCAmelCase				) for i in new_val]





def      __snake_case	(			_UpperCAmelCase				):
    __a       ,   __a						       =				table.shape

    __a						       =				True

    for i in range(0   , _UpperCAmelCase				):
        __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()









"""simple docstring"""



import importlib.util
import json
import os
import warnings
from dataclasses import dataclass, field

import torch

from ..training_args import TrainingArguments
from ..utils import cached_property, is_sagemaker_dp_enabled, logging


__snake_case   			=    logging.get_logger(__name__)







def   __lowerCAmelCase						(						)	->						str:


    """simple docstring"""





    snake_case    :      Dict      					=    os.getenv("SM_HP_MP_PARAMETERS"						,							"{}" )
    try:
        # Parse it and check the field "partitions" is included, it is required for model parallel.
        snake_case    :      Optional[int]      					=    json.loads(lowercase )
        if "partitions" not in smp_options:
            return False
    except json.JSONDecodeError:
        return False

    # Get the sagemaker specific framework parameters from mpi_options variable.
    snake_case    :      Optional[int]      					=    os.getenv("SM_FRAMEWORK_PARAMS"						,							"{}" )
    try:
        # Parse it and check the field "sagemaker_distributed_dataparallel_enabled".
        snake_case    :      Any      					=    json.loads(lowercase )
        if not mpi_options.get("sagemaker_mpi_enabled"						,							lowercase ):
            return False
    except json.JSONDecodeError:
        return False
    # Lastly, check if the `smdistributed` module is present.
    return importlib.util.find_spec("smdistributed" ) is not None


if is_sagemaker_model_parallel_available():
  import smdistributed.modelparallel.torch as smp

  smp.init()







@dataclass
class _lowerCAmelCase				(      snake_case_	):
   __UpperCAmelCase :       str							  =  field(
       default=''''''    ,							metadata={'''help''': '''Used by the SageMaker launcher to send mp-specific args. Ignored in SageMakerTrainer'''}    ,							)







   def  lowerCamelCase		(	self						)	->		List[Any]:

       '''simple docstring'''




       super().__post_init__()
       warnings.warn(
           "`SageMakerTrainingArguments` is deprecated and will be removed in v5 of Transformers. You can use "
           "`TrainingArguments` instead."						,	UpperCamelCase__						,	)







   @cached_property
   def  lowerCamelCase		(	self						)	->		"torch.device":

       '''simple docstring'''




       logger.info("PyTorch: setting up devices"						)
       if torch.distributed.is_available() and torch.distributed.is_initialized() and self.local_rank == -1:
           logger.warning(
               "torch.distributed process group is initialized, but local_rank == -1. "
               "In order to use Torch DDP, launch your script with `python -m torch.distributed.launch"						)
       if self.no_cuda:
           snake_case    :      Optional[Any]      					=    torch.device("cpu"						)
           snake_case    :      List[Any]      					=    0
       elif is_sagemaker_model_parallel_available():
           snake_case    :      Tuple      					=    smp.local_rank()
           snake_case    :      int      					=    torch.device("cuda"						,	UpperCamelCase__						)
           snake_case    :      Dict      					=    1
       elif is_sagemaker_dp_enabled():
           import smdistributed.dataparallel.torch.torch_smddp  # noqa: F401

           torch.distributed.init_process_group(backend="smddp"						,	timeout=self.ddp_timeout_delta						)
           snake_case    :      Any      					=    int(os.getenv("SMDATAPARALLEL_LOCAL_RANK"						)						)
           snake_case    :      Optional[Any]      					=    torch.device("cuda"						,	self.local_rank						)
           snake_case    :      str      					=    1
       elif self.local_rank == -1:
           # if n_gpu is > 1 we'll use nn.DataParallel.
           # If you only want to use a specific subset of GPUs use `CUDA_VISIBLE_DEVICES=0`
           # Explicitly set CUDA to the first (index 0) CUDA device, otherwise `set_device` will
           # trigger an error that a device index is missing. Index 0 takes into account the
           # GPUs available in the environment, so `CUDA_VISIBLE_DEVICES=1,2` with `cuda:0`
           # will use the first GPU in that env, i.e. GPU#1
           snake_case    :      List[str]      					=    torch.device("cuda:0" if torch.cuda.is_available() else "cpu"						)
           # Sometimes the line in the postinit has not been run before we end up here, so just checking we're not at
           # the default value.
           snake_case    :      Optional[Any]      					=    torch.cuda.device_count()
       else:
           # Here, we'll use torch.distributed.
           # Initializes the distributed backend which will take care of synchronizing nodes/GPUs
           if not torch.distributed.is_initialized():
               torch.distributed.init_process_group(backend="nccl"						,	timeout=self.ddp_timeout_delta						)
           snake_case    :      Any      					=    torch.device("cuda"						,	self.local_rank						)
           snake_case    :      Dict      					=    1

       if device.type == "cuda":
           torch.cuda.set_device(UpperCamelCase__						)

       return device







   @property
   def  lowerCamelCase		(	self						)	->		Optional[int]:

       '''simple docstring'''




       if is_sagemaker_model_parallel_available():
           return smp.dp_size()

       return super().world_size







   @property
   def  lowerCamelCase		(	self						)	->		List[str]:

       '''simple docstring'''




       return not is_sagemaker_model_parallel_available()







   @property
   def  lowerCamelCase		(	self						)	->		str:

       '''simple docstring'''




       return False





