



def      UpperCAmelCase__			(				__snake_case				) ->			list[list]:
  _A							     =     current_set.copy()
  for row_index, row in enumerate(__UpperCAmelCase				):
    _A							     =     row[0]
    for column_index, column in enumerate(__UpperCAmelCase				):
      if magnitude == 0:
        _A							     =     column
        continue
      _A							     =     column / magnitude
    # Subtract to cancel term
  _A							     =     current_set[0]
  _A							     =     [first_row]
  _A							     =     current_set[1::]
  for row in current_set:
    _A							     =     []
    # If first term is 0, it is already in form we want, so we preserve it
    if row[0] == 0:
      final_set.append(__UpperCAmelCase				)
      continue
    for column_index in range(len(__UpperCAmelCase				)				):
      temp_row.append(first_row[column_index] - row[column_index]				)
    final_set.append(__UpperCAmelCase				)
  # Create next recursion iteration set
  if len(final_set[0]				) != 3:
    _A							     =     final_set[0]
    _A							     =     []
    _A							     =     []
    for row in final_set[1::]:
      current_first_column.append(row[0]				)
      next_iteration.append(row[1::]				)
    _A							     =     simplify(__UpperCAmelCase				)
    for i in range(len(__UpperCAmelCase				)				):
      resultant[i].insert(0    ,					current_first_column[i]				)
    resultant.insert(0    ,					__UpperCAmelCase				)
    _A							     =     resultant
  return final_set




def      UpperCAmelCase__			(				__snake_case				) ->			list:







  if len(__UpperCAmelCase				) == 0:
    raise IndexError('''solve_simultaneous() requires n lists of length n+1'''				)
  _A							     =     len(__UpperCAmelCase				) + 1
  if any(len(__UpperCAmelCase				) != _length for item in equations				):
    raise IndexError('''solve_simultaneous() requires n lists of length n+1'''				)
  for row in equations:
    if any(not isinstance(__UpperCAmelCase    ,					(int, float)				) for column in row				):
      raise ValueError('''solve_simultaneous() requires lists of integers'''				)
  if len(__UpperCAmelCase				) == 1:
    return [equations[0][-1] / equations[0][0]]
  _A							     =     equations.copy()
  if any(0 in row for row in data_set				):
    _A							     =     data_set.copy()
    _A							     =     []
    for row_index, row in enumerate(__UpperCAmelCase				):
      if 0 not in row:
        _A							     =     data_set.pop(__UpperCAmelCase				)
        break
    if not full_row:
      raise ValueError('''solve_simultaneous() requires at least 1 full equation'''				)
    data_set.insert(0    ,					__UpperCAmelCase				)
  _A							     =     data_set.copy()
  _A							     =     simplify(__UpperCAmelCase				)
  _A							     =     simplified[::-1]
  _A							     =     []
  for row in simplified:
    _A							     =     row[-1]
    if not solutions:
      if row[-2] == 0:
        solutions.append(0				)
        continue
      solutions.append(current_solution / row[-2]				)
      continue
    _A							     =     row.copy()[: len(__UpperCAmelCase				) - 1 :]
    while temp_row[0] == 0:
      temp_row.pop(0				)
    if len(__UpperCAmelCase				) == 0:
      solutions.append(0				)
      continue
    _A							     =     temp_row[1::]
    _A							     =     temp_row[::-1]
    for column_index, column in enumerate(__UpperCAmelCase				):
      current_solution -= column * solutions[column_index]
    solutions.append(__UpperCAmelCase				)
  _A							     =     []
  for item in solutions:
    final.append(float(round(__UpperCAmelCase    ,					5				)				)				)
  return final[::-1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    __lowerCamelCase						=       [
        [2, 1, 1, 1, 1, 4],
        [1, 2, 1, 1, 1, 5],
        [1, 1, 2, 1, 1, 6],
        [1, 1, 1, 2, 1, 7],
        [1, 1, 1, 1, 2, 8],
    ]
    print(solve_simultaneous(eq))
    print(solve_simultaneous([[4, 2]]))






'''simple docstring'''

import dataclasses
import json
import warnings
from dataclasses import dataclass, field
from time import time
from typing import List

from ..utils import logging


a   	=    logging.get_logger(__name__)

def     __magic_name__							(				__UpperCAmelCase=None				,						__UpperCAmelCase=None   )    ->       Dict:

   '''simple docstring'''







   return field(default_factory=lambda: default				,						metadata=__UpperCAmelCase   )







@dataclass
class __a			:
   __UpperCamelCase :			List[str]						   =						list_field(
       default=[], metadata={
           'help': (
               'Model checkpoints to be provided to the AutoModel classes. Leave blank to benchmark the base version'
               ' of all available models'
           )
       }, )

   __UpperCamelCase :			List[int]						   =						list_field(
       default=[8], metadata={'help': 'List of batch sizes for which memory and time performance will be evaluated'}      )

   __UpperCamelCase :			List[int]						   =						list_field(
       default=[8, 32, 128, 512], metadata={'help': 'List of sequence lengths for which memory and time performance will be evaluated'}, )

   __UpperCamelCase :			bool						   =						field(
       default=_snake_case, metadata={'help': 'Whether to benchmark inference of model. Inference can be disabled via --no-inference.'}, )
   __UpperCamelCase :			bool						   =						field(
       default=_snake_case, metadata={'help': 'Whether to run on available cuda devices. Cuda can be disabled via --no-cuda.'}, )
   __UpperCamelCase :			bool						   =						field(
       default=_snake_case, metadata={'help': 'Whether to run on available tpu devices. TPU can be disabled via --no-tpu.'}      )
   __UpperCamelCase :			bool						   =						field(default=_snake_case, metadata={'help': 'Use FP16 to accelerate inference.'}      )
   __UpperCamelCase :			bool						   =						field(default=_snake_case, metadata={'help': 'Benchmark training of model'}      )
   __UpperCamelCase :			bool						   =						field(default=_snake_case, metadata={'help': 'Verbose memory tracing'}      )
   __UpperCamelCase :			bool						   =						field(
       default=_snake_case, metadata={'help': 'Whether to perform speed measurements. Speed measurements can be disabled via --no-speed.'}, )
   __UpperCamelCase :			bool						   =						field(
       default=_snake_case, metadata={
           'help': 'Whether to perform memory measurements. Memory measurements can be disabled via --no-memory'
       }, )
   __UpperCamelCase :			bool						   =						field(default=_snake_case, metadata={'help': 'Trace memory line by line'}      )
   __UpperCamelCase :			bool						   =						field(default=_snake_case, metadata={'help': 'Save result to a CSV file'}      )
   __UpperCamelCase :			bool						   =						field(default=_snake_case, metadata={'help': 'Save all print statements in a log file'}      )
   __UpperCamelCase :			bool						   =						field(default=_snake_case, metadata={'help': 'Whether to print environment information'}      )
   __UpperCamelCase :			bool						   =						field(
       default=_snake_case, metadata={
           'help': (
               'Whether to use multiprocessing for memory and speed measurement. It is highly recommended to use'
               ' multiprocessing for accurate CPU and GPU memory measurements. This option should only be disabled'
               ' for debugging / testing and on TPU.'
           )
       }, )
   __UpperCamelCase :			str						   =						field(
       default=F'inference_time_{round(time()      )}.csv', metadata={'help': 'CSV filename used if saving time results to csv.'}, )
   __UpperCamelCase :			str						   =						field(
       default=F'inference_memory_{round(time()      )}.csv', metadata={'help': 'CSV filename used if saving memory results to csv.'}, )
   __UpperCamelCase :			str						   =						field(
       default=F'train_time_{round(time()      )}.csv', metadata={'help': 'CSV filename used if saving time results to csv for training.'}, )
   __UpperCamelCase :			str						   =						field(
       default=F'train_memory_{round(time()      )}.csv', metadata={'help': 'CSV filename used if saving memory results to csv for training.'}, )
   __UpperCamelCase :			str						   =						field(
       default=F'env_info_{round(time()      )}.csv', metadata={'help': 'CSV filename used if saving environment information.'}, )
   __UpperCamelCase :			str						   =						field(
       default=F'log_{round(time()      )}.csv', metadata={'help': 'Log filename used if print statements are saved in log.'}, )
   __UpperCamelCase :			int						   =						field(default=3, metadata={'help': 'Times an experiment will be run.'}      )
   __UpperCamelCase :			bool						   =						field(
       default=_snake_case, metadata={
           'help': (
               'Instead of loading the model as defined in `config.architectures` if exists, just load the pretrain'
               ' model weights.'
           )
       }, )





   def   UpperCAmelCase__  (       self					:      List[Any]     ):

      '''simple docstring'''

      warnings.warn(
          f"""The class {self.__class__} is deprecated. Hugging Face Benchmarking utils"""
          """ are deprecated in general and it is advised to use external Benchmarking libraries """
          """ to benchmark Transformer models."""					,lowerCamelCase					,)





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      return json.dumps(dataclasses.asdict(self     )					,indent=2     )





   @property
   def   UpperCAmelCase__  (       self					:      str     ):

      '''simple docstring'''

      if len(self.models     ) <= 0:
         raise ValueError(
             """Please make sure you provide at least one model name / model identifier, *e.g.* `--models"""
             """ bert-base-cased` or `args.models = ['bert-base-cased']."""     )
      return self.models





   @property
   def   UpperCAmelCase__  (       self					:      Tuple     ):

      '''simple docstring'''

      if not self.multi_process:
         return False
      elif self.is_tpu:
         logger.info("""Multiprocessing is currently not possible on TPU."""     )
         return False
      else:
         return True





