





import argparse
from collections import defaultdict

import yaml


_lowerCAmelCase 				=     """docs/source/en/_toctree.yml"""



def     _lowerCAmelCase		(  _lowerCAmelCase     ):
   '''simple docstring'''


   A_     :				Optional[int]			      =	defaultdict(_lowerCAmelCase     )
   for doc in model_doc:
      counts[doc["local"]] += 1
   A_     :				int			      =	[key for key, value in counts.items() if value > 1]

   A_     :				Any			      =	[]
   for duplicate_key in duplicates:
      A_     :				List[str]			      =	list({doc["""title"""] for doc in model_doc if doc["""local"""] == duplicate_key}     )
      if len(_lowerCAmelCase     ) > 1:
         raise ValueError(
             f"""{duplicate_key} is present several times in the documentation table of content at """
             """`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the """
             """others."""     )
      # Only add this once
      new_doc.append({"""local""": duplicate_key, """title""": titles[0]}     )

   # Add none duplicate-keys
   new_doc.extend([doc for doc in model_doc if counts[doc["""local"""]] == 1]     )

   # Sort
   return sorted(_lowerCAmelCase  ,key=lambda _lowerCAmelCase     : s["title"].lower()     )



def     _lowerCAmelCase		(  _lowerCAmelCase=False     ):
   '''simple docstring'''


   with open(_lowerCAmelCase  ,encoding="""utf-8"""     ) as f:
      A_     :				Optional[int]			      =	yaml.safe_load(f.read()     )

   # Get to the API doc
   A_     :				Any			      =	0
   while content[api_idx]["title"] != "API":
      api_idx += 1
   A_     :				int			      =	content[api_idx]["""sections"""]

   # Then to the model doc
   A_     :				Dict			      =	0
   while api_doc[model_idx]["title"] != "Models":
      model_idx += 1

   A_     :				Union[str, Any]			      =	api_doc[model_idx]["""sections"""]

   A_     :				List[str]			      =	[(idx, section) for idx, section in enumerate(_lowerCAmelCase     ) if """sections""" in section]
   A_     :				str			      =	False
   for idx, modality_doc in modalities_docs:
      A_     :				str			      =	modality_doc["""sections"""]
      A_     :				Any			      =	clean_model_doc_toc(_lowerCAmelCase     )

      if old_modality_doc != new_modality_doc:
         A_     :				Dict			      =	True
         if overwrite:
            A_     :				Optional[Any]			      =	new_modality_doc

   if diff:
      if overwrite:
         A_     :				Optional[int]			      =	model_doc
         A_     :				Optional[Any]			      =	api_doc
         with open(_lowerCAmelCase  ,"""w"""  ,encoding="""utf-8"""     ) as f:
            f.write(yaml.dump(_lowerCAmelCase  ,allow_unicode=_lowerCAmelCase     )     )
      else:
         raise ValueError(
             """The model doc part of the table of content is not properly sorted, run `make style` to fix this."""     )


if __name__ == "__main__":
      _lowerCAmelCase 				=     argparse.ArgumentParser()
      parser.add_argument("""--fix_and_overwrite""", action="""store_true""", help="""Whether to fix inconsistencies.""")
      _lowerCAmelCase 				=     parser.parse_args()

      check_model_doc(args.fix_and_overwrite)










from __future__ import annotations

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



def     _lowerCAmelCase		(  _lowerCAmelCase  ,_lowerCAmelCase  ,_lowerCAmelCase  ,_lowerCAmelCase  ,):
   '''simple docstring'''


   A_      ,				A_     :				int			      =	coefficient_matrix.shape
   A_      ,				A_     :				Tuple			      =	constant_matrix.shape

   if rowsa != colsa:
      A_     :				int			      =	f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
      raise ValueError(_lowerCAmelCase     )

   if colsa != 1:
      A_     :				List[Any]			      =	f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
      raise ValueError(_lowerCAmelCase     )

   if rowsa != rowsa:
      A_     :				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:
      A_     :				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"""     )

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

   A_      ,				A_     :				str			      =	table.shape

   strictly_diagonally_dominant(_lowerCAmelCase     )

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

   return [float(_lowerCAmelCase     ) for i in new_val]



def     _lowerCAmelCase		(  _lowerCAmelCase     ):
   '''simple docstring'''


   A_      ,				A_     :				str			      =	table.shape

   A_     :				Any			      =	True

   for i in range(0  ,_lowerCAmelCase     ):
      A_     :				Optional[Any]			      =	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()






