




import argparse
from collections import defaultdict

import yaml


_lowerCamelCase      :  Tuple      						=						"docs/source/en/_toctree.yml"




def 							_UpperCAmelCase  (UpperCamelCase_ : Any       ):
				'''simple docstring'''
				_lowerCAmelCase    :    Union[str, Any]										=      defaultdict(UpperCamelCase_       )
				_lowerCAmelCase    :    Any										=      []
				_lowerCAmelCase    :    Any										=      []
				for doc in doc_list:
								if "local" in doc:
												counts[doc["local"]] += 1

								if doc["title"].lower() == "overview":
												overview_doc.append({"""local""": doc["""local"""], """title""": doc["""title"""]}       )
								else:
												new_doc_list.append(UpperCamelCase_       )

				_lowerCAmelCase    :    List[str]										=      new_doc_list
				_lowerCAmelCase    :    Dict										=      [key for key, value in counts.items() if value > 1]

				_lowerCAmelCase    :    List[str]										=      []
				for duplicate_key in duplicates:
								_lowerCAmelCase    :    Union[str, Any]										=      list({doc["""title"""] for doc in doc_list if doc["""local"""] == duplicate_key}       )
								if len(UpperCamelCase_       ) > 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 doc_list if """local""" not in counts or counts[doc["""local"""]] == 1]       )
				_lowerCAmelCase    :    Any										=      sorted(UpperCamelCase_      ,    key=lambda UpperCamelCase_       : s["title"].lower()       )

				# "overview" gets special treatment and is always first
				if len(UpperCamelCase_       ) > 1:
								raise ValueError("""{doc_list} has two 'overview' docs which is not allowed."""       )

				overview_doc.extend(UpperCamelCase_       )

				# Sort
				return overview_doc




def 							_UpperCAmelCase  (UpperCamelCase_ : Any=False       ):
				'''simple docstring'''
				with open(UpperCamelCase_      ,    encoding="""utf-8"""       ) as f:
								_lowerCAmelCase    :    List[Any]										=      yaml.safe_load(f.read()       )

				# Get to the API doc
				_lowerCAmelCase    :    List[str]										=      0
				while content[api_idx]["title"] != "API":
								api_idx += 1
				_lowerCAmelCase    :    str										=      content[api_idx]["""sections"""]

				# Then to the model doc
				_lowerCAmelCase    :    List[str]										=      0
				while api_doc[scheduler_idx]["title"] != "Schedulers":
								scheduler_idx += 1

				_lowerCAmelCase    :    Any										=      api_doc[scheduler_idx]["""sections"""]
				_lowerCAmelCase    :    Dict										=      clean_doc_toc(UpperCamelCase_       )

				_lowerCAmelCase    :    int										=      False
				if new_scheduler_doc != scheduler_doc:
								_lowerCAmelCase    :    Optional[int]										=      True
								if overwrite:
												_lowerCAmelCase    :    Dict										=      new_scheduler_doc

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




def 							_UpperCAmelCase  (UpperCamelCase_ : List[Any]=False       ):
				'''simple docstring'''
				with open(UpperCamelCase_      ,    encoding="""utf-8"""       ) as f:
								_lowerCAmelCase    :    str										=      yaml.safe_load(f.read()       )

				# Get to the API doc
				_lowerCAmelCase    :    str										=      0
				while content[api_idx]["title"] != "API":
								api_idx += 1
				_lowerCAmelCase    :    Union[str, Any]										=      content[api_idx]["""sections"""]

				# Then to the model doc
				_lowerCAmelCase    :    Dict										=      0
				while api_doc[pipeline_idx]["title"] != "Pipelines":
								pipeline_idx += 1

				_lowerCAmelCase    :    Optional[Any]										=      False
				_lowerCAmelCase    :    str										=      api_doc[pipeline_idx]["""sections"""]
				_lowerCAmelCase    :    Optional[int]										=      []

				# sort sub pipeline docs
				for pipeline_doc in pipeline_docs:
								if "section" in pipeline_doc:
												_lowerCAmelCase    :    List[Any]										=      pipeline_doc["""section"""]
												_lowerCAmelCase    :    Union[str, Any]										=      clean_doc_toc(UpperCamelCase_       )
												if overwrite:
																_lowerCAmelCase    :    Union[str, Any]										=      new_sub_pipeline_doc
								new_pipeline_docs.append(UpperCamelCase_       )

				# sort overall pipeline doc
				_lowerCAmelCase    :    Union[str, Any]										=      clean_doc_toc(UpperCamelCase_       )

				if new_pipeline_docs != pipeline_docs:
								_lowerCAmelCase    :    Optional[Any]										=      True
								if overwrite:
												_lowerCAmelCase    :    Union[str, Any]										=      new_pipeline_docs

				if diff:
								if overwrite:
												_lowerCAmelCase    :    Optional[Any]										=      api_doc
												with open(UpperCamelCase_      ,    """w"""      ,    encoding="""utf-8"""       ) as f:
																f.write(yaml.dump(UpperCamelCase_      ,    allow_unicode=UpperCamelCase_       )       )
								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      :  Dict      						=						argparse.ArgumentParser()
	parser.add_argument("--fix_and_overwrite", action="store_true", help="Whether to fix inconsistencies.")
	_lowerCamelCase      :  str      						=						parser.parse_args()

	check_scheduler_doc(args.fix_and_overwrite)
	check_pipeline_doc(args.fix_and_overwrite)







from __future__ import annotations

from decimal import Decimal

from numpy import array




def 							_UpperCAmelCase  (UpperCamelCase_ : list[list[float]]       ):
				'''simple docstring'''
				_lowerCAmelCase    :    int										=      Decimal

				# Check if the provided matrix has 2 rows and 2 columns
				# since this implementation only works for 2x2 matrices
				if len(UpperCamelCase_       ) == 2 and len(matrix[0]       ) == 2 and len(matrix[1]       ) == 2:
								# Calculate the determinant of the matrix
								_lowerCAmelCase    :    Optional[Any]										=      float(
								    d(matrix[0][0]       ) * d(matrix[1][1]       ) - d(matrix[1][0]       ) * d(matrix[0][1]       )       )
								if determinant == 0:
												raise ValueError("""This matrix has no inverse."""       )

								# Creates a copy of the matrix with swapped positions of the elements
								_lowerCAmelCase    :    Union[str, Any]										=      [[0.0, 0.0], [0.0, 0.0]]
								_lowerCAmelCase					,    _lowerCAmelCase    :    Any										=      matrix[1][1], matrix[0][0]
								_lowerCAmelCase					,    _lowerCAmelCase    :    Optional[Any]										=      -matrix[1][0], -matrix[0][1]

								# Calculate the inverse of the matrix
								return [
								    [(float(d(UpperCamelCase_       )       ) / determinant) or 0.0 for n in row] for row in swapped_matrix
								]
				elif (
				    len(UpperCamelCase_       ) == 3
				    and len(matrix[0]       ) == 3
				    and len(matrix[1]       ) == 3
				    and len(matrix[2]       ) == 3
				):
								# Calculate the determinant of the matrix using Sarrus rule
								_lowerCAmelCase    :    List[str]										=      float(
								    (
								        (d(matrix[0][0]       ) * d(matrix[1][1]       ) * d(matrix[2][2]       ))
								        + (d(matrix[0][1]       ) * d(matrix[1][2]       ) * d(matrix[2][0]       ))
								        + (d(matrix[0][2]       ) * d(matrix[1][0]       ) * d(matrix[2][1]       ))
								    )
								    - (
								        (d(matrix[0][2]       ) * d(matrix[1][1]       ) * d(matrix[2][0]       ))
								        + (d(matrix[0][1]       ) * d(matrix[1][0]       ) * d(matrix[2][2]       ))
								        + (d(matrix[0][0]       ) * d(matrix[1][2]       ) * d(matrix[2][1]       ))
								    )       )
								if determinant == 0:
												raise ValueError("""This matrix has no inverse."""       )

								# Creating cofactor matrix
								_lowerCAmelCase    :    Optional[Any]										=      [
								    [d(0.0       ), d(0.0       ), d(0.0       )],
								    [d(0.0       ), d(0.0       ), d(0.0       )],
								    [d(0.0       ), d(0.0       ), d(0.0       )],
								]
								_lowerCAmelCase    :    Optional[Any]										=      (d(matrix[1][1]       ) * d(matrix[2][2]       )) - (
								    d(matrix[1][2]       ) * d(matrix[2][1]       )
								)
								_lowerCAmelCase    :    str										=      -(
								    (d(matrix[1][0]       ) * d(matrix[2][2]       )) - (d(matrix[1][2]       ) * d(matrix[2][0]       ))
								)
								_lowerCAmelCase    :    Any										=      (d(matrix[1][0]       ) * d(matrix[2][1]       )) - (
								    d(matrix[1][1]       ) * d(matrix[2][0]       )
								)
								_lowerCAmelCase    :    List[str]										=      -(
								    (d(matrix[0][1]       ) * d(matrix[2][2]       )) - (d(matrix[0][2]       ) * d(matrix[2][1]       ))
								)
								_lowerCAmelCase    :    Tuple										=      (d(matrix[0][0]       ) * d(matrix[2][2]       )) - (
								    d(matrix[0][2]       ) * d(matrix[2][0]       )
								)
								_lowerCAmelCase    :    Any										=      -(
								    (d(matrix[0][0]       ) * d(matrix[2][1]       )) - (d(matrix[0][1]       ) * d(matrix[2][0]       ))
								)
								_lowerCAmelCase    :    int										=      (d(matrix[0][1]       ) * d(matrix[1][2]       )) - (
								    d(matrix[0][2]       ) * d(matrix[1][1]       )
								)
								_lowerCAmelCase    :    Optional[Any]										=      -(
								    (d(matrix[0][0]       ) * d(matrix[1][2]       )) - (d(matrix[0][2]       ) * d(matrix[1][0]       ))
								)
								_lowerCAmelCase    :    Tuple										=      (d(matrix[0][0]       ) * d(matrix[1][1]       )) - (
								    d(matrix[0][1]       ) * d(matrix[1][0]       )
								)

								# Transpose the cofactor matrix (Adjoint matrix)
								_lowerCAmelCase    :    List[str]										=      array(UpperCamelCase_       )
								for i in range(3       ):
												for j in range(3       ):
																_lowerCAmelCase    :    List[Any]										=      cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
								_lowerCAmelCase    :    Tuple										=      array(UpperCamelCase_       )
								for i in range(3       ):
												for j in range(3       ):
																inverse_matrix[i][j] /= d(UpperCamelCase_       )

        # Calculate the inverse of the matrix
								return [[float(d(UpperCamelCase_       )       ) or 0.0 for n in row] for row in inverse_matrix]
				raise ValueError("""Please provide a matrix of size 2x2 or 3x3."""       )

