





from pickle import UnpicklingError

import jax
import jax.numpy as jnp
import numpy as np
from flax.serialization import from_bytes
from flax.traverse_util import flatten_dict

from ..utils import logging


UpperCamelCase__											= logging.get_logger(__name__)





def     _UpperCamelCase     (a__   :int   ,			a__   :Dict       ):






							"""simple docstring"""





							try:
														with open(a__   ,			"""rb"""       ) as flax_state_f:
																					UpperCamelCase__				     =			from_bytes(a__   ,			flax_state_f.read()       )
							except UnpicklingError as e:
														try:
																					with open(a__       ) as f:
																												if f.read().startswith("""version"""       ):
																																			raise OSError(
																																			    """You seem to have cloned a repository without having git-lfs installed. Please"""
																																			    """ install git-lfs and run `git lfs install` followed by `git lfs pull` in the"""
																																			    """ folder you cloned."""       )
																												else:
																																			raise ValueError from e
														except (UnicodeDecodeError, ValueError):
																					raise EnvironmentError(f"""Unable to convert {model_file} to Flax deserializable object. """       )

							return load_flax_weights_in_pytorch_model(a__   ,			a__       )





def     _UpperCamelCase     (a__   :Dict   ,			a__   :int       ):






							"""simple docstring"""





							try:
														import torch  # noqa: F401
							except ImportError:
														logger.error(
														    """Loading Flax weights in PyTorch requires both PyTorch and Flax to be installed. Please see"""
														    """ https://pytorch.org/ and https://flax.readthedocs.io/en/latest/installation.html for installation"""
														    """ instructions."""       )
														raise

							# check if we have bf16 weights
							UpperCamelCase__				     =			flatten_dict(jax.tree_util.tree_map(lambda a__       : x.dtype == jnp.bfloataa   ,			a__       )       ).values()
							if any(a__       ):
														# convert all weights to fp32 if they are bf16 since torch.from_numpy can-not handle bf16

														# and bf16 is not fully supported in PT yet.
														logger.warning(
														    """Found ``bfloat16`` weights in Flax model. Casting all ``bfloat16`` weights to ``float32`` """
														    """before loading those in PyTorch model."""       )
														UpperCamelCase__				     =			jax.tree_util.tree_map(
														    lambda a__       : params.astype(np.floataa       ) if params.dtype == jnp.bfloataa else params   ,			a__       )

							UpperCamelCase__				     =			""""""

							UpperCamelCase__				     =			flatten_dict(a__   ,			sep="""."""       )
							UpperCamelCase__				     =			pt_model.state_dict()

							# keep track of unexpected & missing keys
							UpperCamelCase__				     =			[]
							UpperCamelCase__				     =			set(pt_model_dict.keys()       )

							for flax_key_tuple, flax_tensor in flax_state_dict.items():
														UpperCamelCase__				     =			flax_key_tuple.split("""."""       )

														if flax_key_tuple_array[-1] == "kernel" and flax_tensor.ndim == 4:
																					UpperCamelCase__				     =			flax_key_tuple_array[:-1] + ["""weight"""]
																					UpperCamelCase__				     =			jnp.transpose(a__   ,			(3, 2, 0, 1)       )
														elif flax_key_tuple_array[-1] == "kernel":
																					UpperCamelCase__				     =			flax_key_tuple_array[:-1] + ["""weight"""]
																					UpperCamelCase__				     =			flax_tensor.T
														elif flax_key_tuple_array[-1] == "scale":
																					UpperCamelCase__				     =			flax_key_tuple_array[:-1] + ["""weight"""]

														if "time_embedding" not in flax_key_tuple_array:
																					for i, flax_key_tuple_string in enumerate(a__       ):
																												UpperCamelCase__				     =			(
																												    flax_key_tuple_string.replace("""_0"""   ,			""".0"""       )
																												    .replace("""_1"""   ,			""".1"""       )
																												    .replace("""_2"""   ,			""".2"""       )
																												    .replace("""_3"""   ,			""".3"""       )
																												    .replace("""_4"""   ,			""".4"""       )
																												    .replace("""_5"""   ,			""".5"""       )
																												    .replace("""_6"""   ,			""".6"""       )
																												    .replace("""_7"""   ,			""".7"""       )
																												    .replace("""_8"""   ,			""".8"""       )
																												    .replace("""_9"""   ,			""".9"""       )
																												)

														UpperCamelCase__				     =			""".""".join(a__       )

														if flax_key in pt_model_dict:
																					if flax_tensor.shape != pt_model_dict[flax_key].shape:
																												raise ValueError(
																												    f"""Flax checkpoint seems to be incorrect. Weight {flax_key_tuple} was expected """
																												    f"""to be of shape {pt_model_dict[flax_key].shape}, but is {flax_tensor.shape}."""       )
																					else:
																												# add weight to pytorch dict
																												UpperCamelCase__				     =			np.asarray(a__       ) if not isinstance(a__   ,			np.ndarray       ) else flax_tensor
																												UpperCamelCase__				     =			torch.from_numpy(a__       )
																												# remove from missing keys
																												missing_keys.remove(a__       )
														else:
																					# weight is not expected by PyTorch model
																					unexpected_keys.append(a__       )

							pt_model.load_state_dict(a__       )

							# re-transform missing_keys to list
							UpperCamelCase__				     =			list(a__       )

							if len(a__       ) > 0:
														logger.warning(
														    """Some weights of the Flax model were not used when initializing the PyTorch model"""
														    f""" {pt_model.__class__.__name__}: {unexpected_keys}\n- This IS expected if you are initializing"""
														    f""" {pt_model.__class__.__name__} from a Flax model trained on another task or with another architecture"""
														    """ (e.g. initializing a BertForSequenceClassification model from a FlaxBertForPreTraining model).\n- This"""
														    f""" IS NOT expected if you are initializing {pt_model.__class__.__name__} from a Flax model that you expect"""
														    """ to be exactly identical (e.g. initializing a BertForSequenceClassification model from a"""
														    """ FlaxBertForSequenceClassification model)."""       )
							if len(a__       ) > 0:
														logger.warning(
														    f"""Some weights of {pt_model.__class__.__name__} were not initialized from the Flax model and are newly"""
														    f""" initialized: {missing_keys}\nYou should probably TRAIN this model on a down-stream task to be able to"""
														    """ use it for predictions and inference."""       )

							return pt_model











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





def     _UpperCamelCase     (a__   :str   ,			a__   :complex   ,			a__   :str = "x"   ,			a__   :float = 10**-10   ,			a__   :int = 1   ,			):






							"""simple docstring"""





							UpperCamelCase__				     =			symbols(a__       )
							UpperCamelCase__				     =			lambdify(a__   ,			a__       )
							UpperCamelCase__				     =			lambdify(a__   ,			diff(a__   ,			a__       )       )

							UpperCamelCase__				     =			starting_point

							while True:
														if diff_function(a__       ) != 0:
																					UpperCamelCase__				     =			prev_guess - multiplicity * func(a__       ) / diff_function(
																					    a__       )
														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

														UpperCamelCase__				     =			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=0.0_05)}""",
					)

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




