


'''simple docstring'''

from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff






def __UpperCamelCase   (			__lowerCamelCase		: str      ,  __lowerCamelCase		: Dict      ,  __lowerCamelCase		: Tuple = 10**-10				)      ->     float:







     '''simple docstring'''






     _a						=		a
     while True:
          _a						=		Decimal(__snake_case				) - (
              Decimal(eval(__snake_case				)				) / Decimal(eval(str(diff(__snake_case				)				)				)				)  # noqa: S307
          )
          # This number dictates the accuracy of the answer
          if abs(eval(__snake_case				)				) < precision:  # noqa: S307
               return float(__snake_case				)


# 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
   print(f'''The root of x**2 - 5*x + 2 = 0 is {newton_raphson("x**2 - 5*x + 2", 0.4)}''')
   # Find Square Root of 5
   print(f'''The root of log(x) - 1 = 0 is {newton_raphson("log(x) - 1", 2)}''')
   # Exponential Roots
   print(f'''The root of exp(x) - 1 = 0 is {newton_raphson("exp(x) - 1", 0)}''')





'''simple docstring'''

import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
lowercase__				     =		object()

# For specifying empty leaf dict `{}`
lowercase__				     =		object()






def __UpperCamelCase   (			__lowerCamelCase		: Tuple      ,  __lowerCamelCase		: Tuple				)      ->     Union[str, Any]:







     '''simple docstring'''






     _a						=		tuple((re.compile(x + "$"				) for x in qs)				)
     for i in range(len(__lowerCamelCase				) - len(__lowerCamelCase				) + 1				):
          _a						=		[x.match(__lowerCamelCase				) for x, y in zip(__lowerCamelCase      ,  ks[i:]				)]
          if matches and all(__lowerCamelCase				):
               return True
     return False






def __UpperCamelCase   (			__lowerCamelCase		: int				)      ->     Union[str, Any]:







     '''simple docstring'''






     def replace(__lowerCamelCase		: Tuple      ,  __lowerCamelCase		: Any				):
          for rule, replacement in rules:
               if _match(__lowerCamelCase      ,  __lowerCamelCase				):
                    return replacement
          return val

     return replace






def __UpperCamelCase   (			)      ->     Tuple:







     '''simple docstring'''






     return [
         # embeddings
         (("transformer", "wpe", "embedding"), P("mp"      ,  __lowerCamelCase				)),
         (("transformer", "wte", "embedding"), P("mp"      ,  __lowerCamelCase				)),
         # atention
         (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(__lowerCamelCase      ,  "mp"				)),
         (("attention", "out_proj", "kernel"), P("mp"      ,  __lowerCamelCase				)),
         (("attention", "out_proj", "bias"), None),
         # mlp
         (("mlp", "c_fc", "kernel"), P(__lowerCamelCase      ,  "mp"				)),
         (("mlp", "c_fc", "bias"), P("mp"				)),
         (("mlp", "c_proj", "kernel"), P("mp"      ,  __lowerCamelCase				)),
         (("mlp", "c_proj", "bias"), None),
         # layer norms
         ((r"ln_\d+", "bias"), None),
         ((r"\d+", r"ln_\d+", "scale"), None),
         (("ln_f", "bias"), None),
         (("ln_f", "scale"), None),
     ]






def __UpperCamelCase   (			__lowerCamelCase		: Dict				)      ->     Tuple:







     '''simple docstring'''






     _a						=		_get_partition_rules()
     _a						=		_replacement_rules(__lowerCamelCase				)
     _a						=		{k: _unmatched for k in flatten_dict(__lowerCamelCase				)}
     _a						=		{k: replace(__lowerCamelCase      ,  __lowerCamelCase				) for k, v in initd.items()}
     assert _unmatched not in result.values(), "Incomplete partition spec."
     return freeze(unflatten_dict(__lowerCamelCase				)				)

