



import argparse
from collections import defaultdict

import yaml


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




def 	UpperCAmelCase   (						_lowerCamelCase    ):
   A							:					Union[str, Any]              =						defaultdict(_lowerCamelCase    )
   A							:					Dict              =						[]
   A							:					List[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(_lowerCamelCase    )

   A							:					str              =						new_doc_list
   A							:					Optional[int]              =						[key for key, value in counts.items() if value > 1]

   A							:					Optional[int]              =						[]
   for duplicate_key in duplicates:
      A							:					Optional[Any]              =						list({doc["title"] for doc in doc_list 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 doc_list if "local" not in counts or counts[doc["local"]] == 1]    )
   A							:					Optional[int]              =						sorted(_lowerCamelCase ,    key=lambda _lowerCamelCase    : s["title"].lower()    )

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

   overview_doc.extend(_lowerCamelCase    )

   # Sort
   return overview_doc




def 	UpperCAmelCase   (						_lowerCamelCase=False    ):
   with open(_lowerCamelCase ,    encoding="utf-8"    ) as f:
      A							:					List[Any]              =						yaml.safe_load(f.read()    )

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

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

   A							:					Tuple              =						api_doc[scheduler_idx]["sections"]
   A							:					int              =						clean_doc_toc(_lowerCamelCase    )

   A							:					List[Any]              =						False
   if new_scheduler_doc != scheduler_doc:
      A							:					List[Any]              =						True
      if overwrite:
         A							:					Tuple              =						new_scheduler_doc

   if diff:
      if overwrite:
         A							:					Optional[int]              =						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."    )




def 	UpperCAmelCase   (						_lowerCamelCase=False    ):
   with open(_lowerCamelCase ,    encoding="utf-8"    ) as f:
      A							:					Optional[Any]              =						yaml.safe_load(f.read()    )

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

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

   A							:					Any              =						False
   A							:					int              =						api_doc[pipeline_idx]["sections"]
   A							:					Tuple              =						[]

   # sort sub pipeline docs
   for pipeline_doc in pipeline_docs:
      if "section" in pipeline_doc:
         A							:					str              =						pipeline_doc["section"]
         A							:					Optional[int]              =						clean_doc_toc(_lowerCamelCase    )
         if overwrite:
            A							:					Any              =						new_sub_pipeline_doc
      new_pipeline_docs.append(_lowerCamelCase    )

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

   if new_pipeline_docs != pipeline_docs:
      A							:					Tuple              =						True
      if overwrite:
         A							:					Union[str, Any]              =						new_pipeline_docs

   if diff:
      if overwrite:
         A							:					int              =						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__":
       __SCREAMING_SNAKE_CASE           =  argparse.ArgumentParser()
       parser.add_argument("""--fix_and_overwrite""", action="""store_true""", help="""Whether to fix inconsistencies.""")
       __SCREAMING_SNAKE_CASE           =  parser.parse_args()

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




from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase = "x" ,    _lowerCamelCase = 10**-10 ,    _lowerCamelCase = 1 ,    ):
			A							:					str              =						symbols(_lowerCamelCase    )
			A							:					int              =						lambdify(_lowerCamelCase ,    _lowerCamelCase    )
			A							:					List[str]              =						lambdify(_lowerCamelCase ,    diff(_lowerCamelCase ,    _lowerCamelCase    )    )

			A							:					Optional[int]              =						starting_point

			while True:
						if diff_function(_lowerCamelCase    ) != 0:
									A							:					Optional[Any]              =						prev_guess - multiplicity * func(_lowerCamelCase    ) / diff_function(
									    _lowerCamelCase    )
						else:
									raise ZeroDivisionError("Could not find root"    ) from None

						# Precision is checked by comparing the difference of consecutive guesses
						if abs(next_guess - prev_guess    ) < precision:
									return next_guess

						A							:					int              =						next_guess


# Let's Execute
if __name__ == "__main__":
							# Find root of trigonometric function
							# Find value of pi
							print(F"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

							# Find root of polynomial
							# Find fourth Root of 5
							print(F"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}""")

							# Find value of e
							print(
							    """The root of log(y) - 1 = 0 is """,
							    F"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
							)

							# Exponential Roots
							print(
							    """The root of exp(x) - 1 = 0 is""",
							    F"""{newton_raphson('exp(x) - 1', 10, precision=0.005)}""",
							)

							# Find root of cos(x)
							print(F"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")