


from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						)     ->			list[float]:







 """simple docstring"""


 _lowercase      ,    _lowercase							      =coefficient_matrix.shape
 _lowercase      ,    _lowercase							      =constant_matrix.shape

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

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

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

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

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

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

 _lowercase      ,    _lowercase							      =table.shape

 strictly_diagonally_dominant(__snake_case						)

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

 return [float(__snake_case						) for i in new_val]
def 				UpperCAmelCase_					(							__snake_case						)     ->			bool:







 """simple docstring"""


 _lowercase      ,    _lowercase							      =table.shape

 _lowercase							      =True

 for i in range(0     ,						__snake_case						):
  _lowercase							      =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()





import copy
from dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import Audio, Features, Value
from .base import TaskTemplate







@dataclass(frozen=lowercase__)
class 			_lowercase (							lowercase__):


       """simple docstring"""




       A__											=			field(default="automatic-speech-recognition"							,  metadata={"include_in_asdict_even_if_is_default": True})
       A__											=			Features({"audio": Audio()})
       A__											=			Features({"transcription": Value("string")})
       A__											=			"audio"
       A__											=			"transcription"





       def 						lowerCAmelCase     (   self							:			Any					,      __lowerCamelCase							:			int       ):


             '''simple docstring'''



             if self.audio_column not in features:
                   raise ValueError(f"Column {self.audio_column} is not present in features."       )
             if not isinstance(features[self.audio_column]					,      __lowerCamelCase       ):
                   raise ValueError(f"Column {self.audio_column} is not an Audio type."       )
             lowerCamelCase__		:				Tuple    =  copy.deepcopy(self       )
             lowerCamelCase__		:				Tuple    =  self.input_schema.copy()
             lowerCamelCase__		:				Optional[int]    =  features[self.audio_column]
             lowerCamelCase__		:				int    =  input_schema
             return task_template





       @property
       def 						lowerCAmelCase     (   self							:			int       ):


             '''simple docstring'''



             return {self.audio_column: "audio", self.transcription_column: "transcription"}


