


"""simple docstring"""


import os
from pickle import UnpicklingError
from typing import Dict, Tuple

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

import transformers

from .utils import logging


__lowerCamelCase      :Dict	    =		logging.get_logger(__name__)




def   snake_case		(     UpperCamelCase__       :						Dict			,				UpperCamelCase__       :						Tuple			,				UpperCamelCase__       :						int			,				UpperCamelCase__       :						Any=False    )   ->      Optional[Any]:
      try:
            import torch  # noqa: F401
      except ImportError:
            logger.error(
                """Loading a PyTorch model in Flax, 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

      if not is_sharded:
            lowerCamelCase					:					Optional[Any]        =	os.path.abspath(UpperCamelCase__    )
            logger.info(F'Loading PyTorch weights from {pt_path}'    )

            lowerCamelCase					:					Any        =	torch.load(UpperCamelCase__			,				map_location="""cpu"""    )
            logger.info(F'PyTorch checkpoint contains {sum(t.numel() for t in pt_state_dict.values()    ):,} parameters.'    )

            lowerCamelCase					:					List[str]        =	convert_pytorch_state_dict_to_flax(UpperCamelCase__			,				UpperCamelCase__    )
      else:
            # model is sharded and pytorch_checkpoint_path already contains the list of .pt shard files
            lowerCamelCase					:					Optional[Any]        =	convert_pytorch_sharded_state_dict_to_flax(UpperCamelCase__			,				UpperCamelCase__    )
      return flax_state_dict




def   snake_case		(     UpperCamelCase__       :						Tuple[str]			,				UpperCamelCase__       :						np.ndarray			,				UpperCamelCase__       :						Dict[str, jnp.ndarray]			,				UpperCamelCase__       :						str			,				)   ->      (Tuple[str], np.ndarray):

      def is_key_or_prefix_key_in_dict(UpperCamelCase__       :						Tuple[str]    ) -> bool:
            return len(set(UpperCamelCase__    ) & {key, (model_prefix,) + key}    ) > 0

      # layer norm
      lowerCamelCase					:					List[Any]        =	pt_tuple_key[:-1] + ("""scale""",)
      if pt_tuple_key[-1] in ["weight", "gamma"] and is_key_or_prefix_key_in_dict(UpperCamelCase__    ):
            return renamed_pt_tuple_key, pt_tensor

      # batch norm layer mean
      lowerCamelCase					:					Optional[int]        =	pt_tuple_key[:-1] + ("""mean""",)
      if pt_tuple_key[-1] == "running_mean" and not is_key_or_prefix_key_in_dict(UpperCamelCase__    ):
            return renamed_pt_tuple_key, pt_tensor

      # batch norm layer var
      lowerCamelCase					:					Union[str, Any]        =	pt_tuple_key[:-1] + ("""var""",)
      if pt_tuple_key[-1] == "running_var" and not is_key_or_prefix_key_in_dict(UpperCamelCase__    ):
            return renamed_pt_tuple_key, pt_tensor

      # embedding
      lowerCamelCase					:					str        =	pt_tuple_key[:-1] + ("""embedding""",)
      if pt_tuple_key[-1] == "weight" and is_key_or_prefix_key_in_dict(UpperCamelCase__    ):
            return renamed_pt_tuple_key, pt_tensor

      # conv layer
      lowerCamelCase					:					Tuple        =	pt_tuple_key[:-1] + ("""kernel""",)
      if pt_tuple_key[-1] == "weight" and pt_tensor.ndim == 4 and not is_key_or_prefix_key_in_dict(UpperCamelCase__    ):
            lowerCamelCase					:					Optional[Any]        =	pt_tensor.transpose(2			,				3			,				1			,				0    )
            return renamed_pt_tuple_key, pt_tensor

      # linear layer
      lowerCamelCase					:					Optional[Any]        =	pt_tuple_key[:-1] + ("""kernel""",)
      if pt_tuple_key[-1] == "weight" and not is_key_or_prefix_key_in_dict(UpperCamelCase__    ):
            lowerCamelCase					:					Optional[Any]        =	pt_tensor.T
            return renamed_pt_tuple_key, pt_tensor

      # old PyTorch layer norm weight
      lowerCamelCase					:					Tuple        =	pt_tuple_key[:-1] + ("""weight""",)
      if pt_tuple_key[-1] == "gamma":
            return renamed_pt_tuple_key, pt_tensor

      # old PyTorch layer norm bias
      lowerCamelCase					:					Optional[int]        =	pt_tuple_key[:-1] + ("""bias""",)
      if pt_tuple_key[-1] == "beta":
            return renamed_pt_tuple_key, pt_tensor

      # New `weight_norm` from https://github.com/huggingface/transformers/pull/24030
      lowerCamelCase					:					int        =	None
      if pt_tuple_key[-3::2] == ("parametrizations", "original0"):
            lowerCamelCase					:					List[Any]        =	pt_tuple_key[-2] + """_g"""
      elif pt_tuple_key[-3::2] == ("parametrizations", "original1"):
            lowerCamelCase					:					Optional[Any]        =	pt_tuple_key[-2] + """_v"""
      if name is not None:
            lowerCamelCase					:					List[Any]        =	pt_tuple_key[:-3] + (name,)
            return renamed_pt_tuple_key, pt_tensor

      return pt_tuple_key, pt_tensor




def   snake_case		(     UpperCamelCase__       :						Optional[Any]			,				UpperCamelCase__       :						int    )   ->      Optional[int]:
      # convert pytorch tensor to numpy
      lowerCamelCase					:					Tuple        =	{k: v.numpy() for k, v in pt_state_dict.items()}

      lowerCamelCase					:					List[str]        =	flax_model.base_model_prefix

      # use params dict if the model contains batch norm layers
      if "params" in flax_model.params:
            lowerCamelCase					:					int        =	flax_model.params["""params"""]
      else:
            lowerCamelCase					:					Union[str, Any]        =	flax_model.params
      lowerCamelCase					:					List[str]        =	flatten_dict(UpperCamelCase__    )

      # add batch_stats keys,values to dict
      if "batch_stats" in flax_model.params:
            lowerCamelCase					:					Optional[Any]        =	flatten_dict(flax_model.params["""batch_stats"""]    )
            random_flax_state_dict.update(UpperCamelCase__    )

      lowerCamelCase					:					int        =	{}

      lowerCamelCase					:					List[str]        =	(model_prefix not in flax_model_params) and (
          model_prefix in {k.split("""."""    )[0] for k in pt_state_dict.keys()}
      )
      lowerCamelCase					:					List[str]        =	(model_prefix in flax_model_params) and (
          model_prefix not in {k.split("""."""    )[0] for k in pt_state_dict.keys()}
      )

      # Need to change some parameters name to match Flax names
      for pt_key, pt_tensor in pt_state_dict.items():
            lowerCamelCase					:					Dict        =	tuple(pt_key.split("""."""    )    )

            # remove base model prefix if necessary
            lowerCamelCase					:					str        =	pt_tuple_key[0] == model_prefix
            if load_model_with_head_into_base_model and has_base_model_prefix:
                  lowerCamelCase					:					int        =	pt_tuple_key[1:]

            # Correctly rename weight parameters
            lowerCamelCase     ,			lowerCamelCase					:					str        =	rename_key_and_reshape_tensor(
                UpperCamelCase__			,				UpperCamelCase__			,				UpperCamelCase__			,				UpperCamelCase__    )

            # add model prefix if necessary
            lowerCamelCase					:					str        =	(model_prefix,) + flax_key in random_flax_state_dict
            if load_base_model_into_model_with_head and require_base_model_prefix:
                  lowerCamelCase					:					str        =	(model_prefix,) + flax_key

            if flax_key in random_flax_state_dict:
                  if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
                        raise ValueError(
                            F'PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape '
                            F'{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}.'    )

        # add batch stats if the model contains batchnorm layers
            if "batch_stats" in flax_model.params:
                  if "mean" in flax_key[-1] or "var" in flax_key[-1]:
                        lowerCamelCase					:					List[str]        =	jnp.asarray(UpperCamelCase__    )
                        continue
                  # remove num_batches_tracked key
                  if "num_batches_tracked" in flax_key[-1]:
                        flax_state_dict.pop(UpperCamelCase__			,				UpperCamelCase__    )
                        continue

                  # also add unexpected weight so that warning is thrown
                  lowerCamelCase					:					Union[str, Any]        =	jnp.asarray(UpperCamelCase__    )

            else:
                  # also add unexpected weight so that warning is thrown
                  lowerCamelCase					:					List[str]        =	jnp.asarray(UpperCamelCase__    )

      return unflatten_dict(UpperCamelCase__    )




def   snake_case		(     UpperCamelCase__       :						str			,				UpperCamelCase__       :						List[str]    )   ->      Optional[int]:
      import torch

      # Load the index
      lowerCamelCase					:					List[Any]        =	{}
      for shard_file in shard_filenames:
            # load using msgpack utils
            lowerCamelCase					:					Any        =	torch.load(UpperCamelCase__    )
            lowerCamelCase					:					str        =	{k: v.numpy() for k, v in pt_state_dict.items()}

            lowerCamelCase					:					List[Any]        =	flax_model.base_model_prefix

            # use params dict if the model contains batch norm layers and then add batch_stats keys,values to dict
            if "batch_stats" in flax_model.params:
                  lowerCamelCase					:					str        =	flax_model.params["""params"""]

                  lowerCamelCase					:					List[str]        =	flatten_dict(UpperCamelCase__    )
                  random_flax_state_dict.update(flatten_dict(flax_model.params["""batch_stats"""]    )    )
            else:
                  lowerCamelCase					:					Dict        =	flax_model.params
                  lowerCamelCase					:					List[Any]        =	flatten_dict(UpperCamelCase__    )

            lowerCamelCase					:					Optional[Any]        =	(model_prefix not in flax_model_params) and (
                model_prefix in {k.split("""."""    )[0] for k in pt_state_dict.keys()}
            )
            lowerCamelCase					:					List[Any]        =	(model_prefix in flax_model_params) and (
                model_prefix not in {k.split("""."""    )[0] for k in pt_state_dict.keys()}
            )
            # Need to change some parameters name to match Flax names
            for pt_key, pt_tensor in pt_state_dict.items():
                  lowerCamelCase					:					Tuple        =	tuple(pt_key.split("""."""    )    )

                  # remove base model prefix if necessary
                  lowerCamelCase					:					Optional[int]        =	pt_tuple_key[0] == model_prefix
                  if load_model_with_head_into_base_model and has_base_model_prefix:
                        lowerCamelCase					:					Optional[Any]        =	pt_tuple_key[1:]

                  # Correctly rename weight parameters
                  lowerCamelCase     ,			lowerCamelCase					:					int        =	rename_key_and_reshape_tensor(
                      UpperCamelCase__			,				UpperCamelCase__			,				UpperCamelCase__			,				UpperCamelCase__    )
                  # add model prefix if necessary
                  lowerCamelCase					:					Union[str, Any]        =	(model_prefix,) + flax_key in random_flax_state_dict
                  if load_base_model_into_model_with_head and require_base_model_prefix:
                        lowerCamelCase					:					List[Any]        =	(model_prefix,) + flax_key

                  if flax_key in random_flax_state_dict:
                        if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
                              raise ValueError(
                                  F'PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape '
                                  F'{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}.'    )

            # add batch stats if the model contains batchnorm layers
                  if "batch_stats" in flax_model.params:
                        if "mean" in flax_key[-1]:
                              lowerCamelCase					:					Optional[int]        =	jnp.asarray(UpperCamelCase__    )
                              continue
                        if "var" in flax_key[-1]:
                              lowerCamelCase					:					Any        =	jnp.asarray(UpperCamelCase__    )
                              continue
                        # remove num_batches_tracked key
                        if "num_batches_tracked" in flax_key[-1]:
                              flax_state_dict.pop(UpperCamelCase__			,				UpperCamelCase__    )
                              continue

                        # also add unexpected weight so that warning is thrown
                        lowerCamelCase					:					Tuple        =	jnp.asarray(UpperCamelCase__    )

                  else:
                        # also add unexpected weight so that warning is thrown
                        lowerCamelCase					:					List[Any]        =	jnp.asarray(UpperCamelCase__    )
      return unflatten_dict(UpperCamelCase__    )




def   snake_case		(     UpperCamelCase__       :						Tuple			,				UpperCamelCase__       :						Optional[int]    )   ->      Tuple:
      lowerCamelCase					:					int        =	os.path.abspath(UpperCamelCase__    )
      logger.info(F'Loading Flax weights from {flax_checkpoint_path}'    )

      # import correct flax class
      lowerCamelCase					:					List[str]        =	getattr(UpperCamelCase__			,				"""Flax""" + model.__class__.__name__    )

      # load flax weight dict
      with open(UpperCamelCase__			,				"""rb"""    ) as state_f:
            try:
                  lowerCamelCase					:					Optional[int]        =	from_bytes(UpperCamelCase__			,				state_f.read()    )
            except UnpicklingError:
                  raise EnvironmentError(F'Unable to convert {flax_checkpoint_path} to Flax deserializable object. '    )

      return load_flax_weights_in_pytorch_model(UpperCamelCase__			,				UpperCamelCase__    )






def   snake_case		(     UpperCamelCase__       :						Union[str, Any]			,				UpperCamelCase__       :						str    )   ->      Optional[int]:

      try:
            import torch  # noqa: F401
      except ImportError:
            logger.error(
                """Loading a 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
      lowerCamelCase					:					List[Any]        =	flatten_dict(jax.tree_util.tree_map(lambda UpperCamelCase__    : x.dtype == jnp.bfloataa			,				UpperCamelCase__    )    ).values()
      if any(UpperCamelCase__    ):
            # convert all weights to fp32 if the 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."""    )
            lowerCamelCase					:					Optional[Any]        =	jax.tree_util.tree_map(
                lambda UpperCamelCase__    : params.astype(np.floataa    ) if params.dtype == jnp.bfloataa else params			,				UpperCamelCase__    )

      lowerCamelCase					:					List[Any]        =	flatten_dict(UpperCamelCase__    )
      lowerCamelCase					:					Optional[Any]        =	pt_model.state_dict()

      lowerCamelCase					:					int        =	(pt_model.base_model_prefix in flax_state) and (
          pt_model.base_model_prefix not in {k.split("""."""    )[0] for k in pt_model_dict.keys()}
      )
      lowerCamelCase					:					List[str]        =	(pt_model.base_model_prefix not in flax_state) and (
          pt_model.base_model_prefix in {k.split("""."""    )[0] for k in pt_model_dict.keys()}
      )

      # keep track of unexpected & missing keys
      lowerCamelCase					:					Union[str, Any]        =	[]
      lowerCamelCase					:					List[str]        =	set(pt_model_dict.keys()    )

      for flax_key_tuple, flax_tensor in flax_state_dict.items():
            lowerCamelCase					:					Dict        =	flax_key_tuple[0] == pt_model.base_model_prefix
            lowerCamelCase					:					int        =	""".""".join((pt_model.base_model_prefix,) + flax_key_tuple    ) in pt_model_dict

            # adapt flax_key to prepare for loading from/to base model only
            if load_model_with_head_into_base_model and has_base_model_prefix:
                  lowerCamelCase					:					Optional[int]        =	flax_key_tuple[1:]
            elif load_base_model_into_model_with_head and require_base_model_prefix:
                  lowerCamelCase					:					List[str]        =	(pt_model.base_model_prefix,) + flax_key_tuple

            # rename flax weights to PyTorch format
            if flax_key_tuple[-1] == "kernel" and flax_tensor.ndim == 4 and ".".join(UpperCamelCase__    ) not in pt_model_dict:
                  # conv layer
                  lowerCamelCase					:					Tuple        =	flax_key_tuple[:-1] + ("""weight""",)
                  lowerCamelCase					:					Dict        =	jnp.transpose(UpperCamelCase__			,				(3, 2, 0, 1)    )
            elif flax_key_tuple[-1] == "kernel" and ".".join(UpperCamelCase__    ) not in pt_model_dict:
                  # linear layer
                  lowerCamelCase					:					str        =	flax_key_tuple[:-1] + ("""weight""",)
                  lowerCamelCase					:					str        =	flax_tensor.T
            elif flax_key_tuple[-1] in ["scale", "embedding"]:
                  lowerCamelCase					:					Any        =	flax_key_tuple[:-1] + ("""weight""",)

            # adding batch stats from flax batch norm to pt
            elif "mean" in flax_key_tuple[-1]:
                  lowerCamelCase					:					Tuple        =	flax_key_tuple[:-1] + ("""running_mean""",)
            elif "var" in flax_key_tuple[-1]:
                  lowerCamelCase					:					Tuple        =	flax_key_tuple[:-1] + ("""running_var""",)

            if "batch_stats" in flax_state:
                  lowerCamelCase					:					int        =	""".""".join(flax_key_tuple[1:]    )  # Remove the params/batch_stats header
            else:
                  lowerCamelCase					:					Optional[int]        =	""".""".join(UpperCamelCase__    )

            # We also need to look at `pt_model_dict` and see if there are keys requiring further transformation.
            lowerCamelCase					:					Tuple        =	{}
            # New `weight_norm` from https://github.com/huggingface/transformers/pull/24030
            for key in pt_model_dict:
                  lowerCamelCase					:					Any        =	key.split("""."""    )
                  lowerCamelCase					:					Any        =	None
                  if key_components[-3::2] == ["parametrizations", "original0"]:
                        lowerCamelCase					:					Optional[Any]        =	key_components[-2] + """_g"""
                  elif key_components[-3::2] == ["parametrizations", "original1"]:
                        lowerCamelCase					:					int        =	key_components[-2] + """_v"""
                  if name is not None:
                        lowerCamelCase					:					str        =	key_components[:-3] + [name]
                        lowerCamelCase					:					int        =	""".""".join(UpperCamelCase__    )
                        lowerCamelCase					:					Any        =	key

            if flax_key in special_pt_names:
                  lowerCamelCase					:					Optional[int]        =	special_pt_names[flax_key]

            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
                        lowerCamelCase					:					List[Any]        =	np.asarray(UpperCamelCase__    ) if not isinstance(UpperCamelCase__			,				np.ndarray    ) else flax_tensor
                        lowerCamelCase					:					Tuple        =	torch.from_numpy(UpperCamelCase__    )
                        # remove from missing keys
                        missing_keys.remove(UpperCamelCase__    )
            else:
                  # weight is not expected by PyTorch model
                  unexpected_keys.append(UpperCamelCase__    )

      pt_model.load_state_dict(UpperCamelCase__    )

      # re-transform missing_keys to list
      lowerCamelCase					:					Union[str, Any]        =	list(UpperCamelCase__    )

      if len(UpperCamelCase__    ) > 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)."""    )
      else:
            logger.warning(F'All Flax model weights were used when initializing {pt_model.__class__.__name__}.\n'    )
      if len(UpperCamelCase__    ) > 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."""    )
      else:
            logger.warning(
                F'All the weights of {pt_model.__class__.__name__} were initialized from the Flax model.\n'
                """If your task is similar to the task the model of the checkpoint was trained on, """
                F'you can already use {pt_model.__class__.__name__} for predictions without further training.'    )

      return pt_model








"""simple docstring"""


from __future__ import annotations

import math




def   snake_case		(     UpperCamelCase__       :						float			,				UpperCamelCase__       :						int    )   ->      float:
      lowerCamelCase					:					Dict        =	u
      for i in range(1			,				UpperCamelCase__    ):
            lowerCamelCase					:					List[str]        =	temp * (u - i)
      return temp




def   snake_case		(     )   ->      None:
      lowerCamelCase					:					List[Any]        =	int(input("""enter the numbers of values: """    )    )
      lowerCamelCase					:					list[list[float]]        =	[]
      for _ in range(UpperCamelCase__    ):
            y.append([]    )
      for i in range(UpperCamelCase__    ):
            for j in range(UpperCamelCase__    ):
                  y[i].append(UpperCamelCase__    )
                  lowerCamelCase					:					Union[str, Any]        =	0

      print("""enter the values of parameters in a list: """    )
      lowerCamelCase					:					Any        =	list(map(UpperCamelCase__			,				input().split()    )    )

      print("""enter the values of corresponding parameters: """    )
      for i in range(UpperCamelCase__    ):
            lowerCamelCase					:					int        =	float(input()    )

      lowerCamelCase					:					Dict        =	int(input("""enter the value to interpolate: """    )    )
      lowerCamelCase					:					List[Any]        =	(value - x[0]) / (x[1] - x[0])

      # for calculating forward difference table

      for i in range(1			,				UpperCamelCase__    ):
            for j in range(n - i    ):
                  lowerCamelCase					:					str        =	y[j + 1][i - 1] - y[j][i - 1]

      lowerCamelCase					:					Any        =	y[0][0]
      for i in range(1			,				UpperCamelCase__    ):
            summ += (ucal(UpperCamelCase__			,				UpperCamelCase__    ) * y[0][i]) / math.factorial(UpperCamelCase__    )

      print(F'the value at {value} is {summ}'    )


if __name__ == "__main__":
    main()




