



'''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


UpperCamelCase__:   Tuple								=			logging.get_logger(__name__)


def  snake_case_     (					_lowerCAmelCase  :						Dict   ,      _lowerCAmelCase  :						List[str]   ,      _lowerCAmelCase  :						List[str]   ,      _lowerCAmelCase  :						List[str]=False  )      ->   List[str]:
							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:
														UpperCAmelCase :       Optional[Any] 							=		os.path.abspath(_lowerCAmelCase  )
														logger.info(f"""Loading PyTorch weights from {pt_path}"""  )

														UpperCAmelCase :       List[str] 							=		torch.load(_lowerCAmelCase   ,      map_location='''cpu'''  )
														logger.info(f"""PyTorch checkpoint contains {sum(t.numel() for t in pt_state_dict.values()  ):,} parameters."""  )

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


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

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

							# layer norm
							UpperCAmelCase :       Dict 							=		pt_tuple_key[:-1] + ('''scale''',)
							if pt_tuple_key[-1] in ["weight", "gamma"] and is_key_or_prefix_key_in_dict(_lowerCAmelCase  ):
														return renamed_pt_tuple_key, pt_tensor

							# batch norm layer mean
							UpperCAmelCase :       List[Any] 							=		pt_tuple_key[:-1] + ('''mean''',)
							if pt_tuple_key[-1] == "running_mean" and not is_key_or_prefix_key_in_dict(_lowerCAmelCase  ):
														return renamed_pt_tuple_key, pt_tensor

							# batch norm layer var
							UpperCAmelCase :       str 							=		pt_tuple_key[:-1] + ('''var''',)
							if pt_tuple_key[-1] == "running_var" and not is_key_or_prefix_key_in_dict(_lowerCAmelCase  ):
														return renamed_pt_tuple_key, pt_tensor

							# embedding
							UpperCAmelCase :       Dict 							=		pt_tuple_key[:-1] + ('''embedding''',)
							if pt_tuple_key[-1] == "weight" and is_key_or_prefix_key_in_dict(_lowerCAmelCase  ):
														return renamed_pt_tuple_key, pt_tensor

							# conv layer
							UpperCAmelCase :       List[str] 							=		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(_lowerCAmelCase  ):
														UpperCAmelCase :       Any 							=		pt_tensor.transpose(2   ,      3   ,      1   ,      0  )
														return renamed_pt_tuple_key, pt_tensor

							# linear layer
							UpperCAmelCase :       Dict 							=		pt_tuple_key[:-1] + ('''kernel''',)
							if pt_tuple_key[-1] == "weight" and not is_key_or_prefix_key_in_dict(_lowerCAmelCase  ):
														UpperCAmelCase :       Dict 							=		pt_tensor.T
														return renamed_pt_tuple_key, pt_tensor

							# old PyTorch layer norm weight
							UpperCAmelCase :       List[str] 							=		pt_tuple_key[:-1] + ('''weight''',)
							if pt_tuple_key[-1] == "gamma":
														return renamed_pt_tuple_key, pt_tensor

							# old PyTorch layer norm bias
							UpperCAmelCase :       List[Any] 							=		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
							UpperCAmelCase :       str 							=		None
							if pt_tuple_key[-3::2] == ("parametrizations", "original0"):
														UpperCAmelCase :       Optional[int] 							=		pt_tuple_key[-2] + '''_g'''
							elif pt_tuple_key[-3::2] == ("parametrizations", "original1"):
														UpperCAmelCase :       Union[str, Any] 							=		pt_tuple_key[-2] + '''_v'''
							if name is not None:
														UpperCAmelCase :       List[Any] 							=		pt_tuple_key[:-3] + (name,)
														return renamed_pt_tuple_key, pt_tensor

							return pt_tuple_key, pt_tensor


def  snake_case_     (					_lowerCAmelCase  :						Optional[Any]   ,      _lowerCAmelCase  :						Optional[Any]  )      ->   Optional[Any]:
							# convert pytorch tensor to numpy
							UpperCAmelCase :       Dict 							=		{k: v.numpy() for k, v in pt_state_dict.items()}

							UpperCAmelCase :       Any 							=		flax_model.base_model_prefix

							# use params dict if the model contains batch norm layers
							if "params" in flax_model.params:
														UpperCAmelCase :       Optional[Any] 							=		flax_model.params['''params''']
							else:
														UpperCAmelCase :       Any 							=		flax_model.params
							UpperCAmelCase :       str 							=		flatten_dict(_lowerCAmelCase  )

							# add batch_stats keys,values to dict
							if "batch_stats" in flax_model.params:
														UpperCAmelCase :       List[str] 							=		flatten_dict(flax_model.params['''batch_stats''']  )
														random_flax_state_dict.update(_lowerCAmelCase  )

							UpperCAmelCase :       str 							=		{}

							UpperCAmelCase :       Union[str, Any] 							=		(model_prefix not in flax_model_params) and (
							    model_prefix in {k.split('''.'''  )[0] for k in pt_state_dict.keys()}
							)
							UpperCAmelCase :       Optional[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():
														UpperCAmelCase :       Optional[Any] 							=		tuple(pt_key.split('''.'''  )  )

														# remove base model prefix if necessary
														UpperCAmelCase :       Dict 							=		pt_tuple_key[0] == model_prefix
														if load_model_with_head_into_base_model and has_base_model_prefix:
																					UpperCAmelCase :       Dict 							=		pt_tuple_key[1:]

														# Correctly rename weight parameters
														UpperCAmelCase							,		UpperCAmelCase :       List[Any] 							=		rename_key_and_reshape_tensor(
														    _lowerCAmelCase   ,      _lowerCAmelCase   ,      _lowerCAmelCase   ,      _lowerCAmelCase  )

														# add model prefix if necessary
														UpperCAmelCase :       Optional[int] 							=		(model_prefix,) + flax_key in random_flax_state_dict
														if load_base_model_into_model_with_head and require_base_model_prefix:
																					UpperCAmelCase :       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] or "var" in flax_key[-1]:
																												UpperCAmelCase :       Dict 							=		jnp.asarray(_lowerCAmelCase  )
																												continue
																					# remove num_batches_tracked key
																					if "num_batches_tracked" in flax_key[-1]:
																												flax_state_dict.pop(_lowerCAmelCase   ,      _lowerCAmelCase  )
																												continue

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

														else:
																					# also add unexpected weight so that warning is thrown
																					UpperCAmelCase :       str 							=		jnp.asarray(_lowerCAmelCase  )

							return unflatten_dict(_lowerCAmelCase  )


def  snake_case_     (					_lowerCAmelCase  :						Optional[int]   ,      _lowerCAmelCase  :						Any  )      ->   str:
							import torch

							# Load the index
							UpperCAmelCase :       int 							=		{}
							for shard_file in shard_filenames:
														# load using msgpack utils
														UpperCAmelCase :       str 							=		torch.load(_lowerCAmelCase  )
														UpperCAmelCase :       int 							=		{k: v.numpy() for k, v in pt_state_dict.items()}

														UpperCAmelCase :       Optional[int] 							=		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:
																					UpperCAmelCase :       str 							=		flax_model.params['''params''']

																					UpperCAmelCase :       int 							=		flatten_dict(_lowerCAmelCase  )
																					random_flax_state_dict.update(flatten_dict(flax_model.params['''batch_stats''']  )  )
														else:
																					UpperCAmelCase :       Any 							=		flax_model.params
																					UpperCAmelCase :       List[Any] 							=		flatten_dict(_lowerCAmelCase  )

														UpperCAmelCase :       str 							=		(model_prefix not in flax_model_params) and (
														    model_prefix in {k.split('''.'''  )[0] for k in pt_state_dict.keys()}
														)
														UpperCAmelCase :       Optional[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():
																					UpperCAmelCase :       Any 							=		tuple(pt_key.split('''.'''  )  )

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

																					# Correctly rename weight parameters
																					UpperCAmelCase							,		UpperCAmelCase :       str 							=		rename_key_and_reshape_tensor(
																					    _lowerCAmelCase   ,      _lowerCAmelCase   ,      _lowerCAmelCase   ,      _lowerCAmelCase  )
																					# add model prefix if necessary
																					UpperCAmelCase :       int 							=		(model_prefix,) + flax_key in random_flax_state_dict
																					if load_base_model_into_model_with_head and require_base_model_prefix:
																												UpperCAmelCase :       int 							=		(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]:
																																			UpperCAmelCase :       Tuple 							=		jnp.asarray(_lowerCAmelCase  )
																																			continue
																												if "var" in flax_key[-1]:
																																			UpperCAmelCase :       Tuple 							=		jnp.asarray(_lowerCAmelCase  )
																																			continue
																												# remove num_batches_tracked key
																												if "num_batches_tracked" in flax_key[-1]:
																																			flax_state_dict.pop(_lowerCAmelCase   ,      _lowerCAmelCase  )
																																			continue

																												# also add unexpected weight so that warning is thrown
																												UpperCAmelCase :       int 							=		jnp.asarray(_lowerCAmelCase  )

																					else:
																												# also add unexpected weight so that warning is thrown
																												UpperCAmelCase :       Any 							=		jnp.asarray(_lowerCAmelCase  )
							return unflatten_dict(_lowerCAmelCase  )


def  snake_case_     (					_lowerCAmelCase  :						Dict   ,      _lowerCAmelCase  :						List[Any]  )      ->   Tuple:
							UpperCAmelCase :       Any 							=		os.path.abspath(_lowerCAmelCase  )
							logger.info(f"""Loading Flax weights from {flax_checkpoint_path}"""  )

							# import correct flax class
							UpperCAmelCase :       Dict 							=		getattr(_lowerCAmelCase   ,      '''Flax''' + model.__class__.__name__  )

							# load flax weight dict
							with open(_lowerCAmelCase   ,      '''rb'''  ) as state_f:
														try:
																					UpperCAmelCase :       Tuple 							=		from_bytes(_lowerCAmelCase   ,      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(_lowerCAmelCase   ,      _lowerCAmelCase  )




def  snake_case_     (					_lowerCAmelCase  :						Optional[int]   ,      _lowerCAmelCase  :						str  )      ->   Any:

							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
							UpperCAmelCase :       Tuple 							=		flatten_dict(jax.tree_util.tree_map(lambda _lowerCAmelCase  : x.dtype == jnp.bfloataa   ,      _lowerCAmelCase  )  ).values()
							if any(_lowerCAmelCase  ):
														# 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.'''  )
														UpperCAmelCase :       Any 							=		jax.tree_util.tree_map(
														    lambda _lowerCAmelCase  : params.astype(np.floataa  ) if params.dtype == jnp.bfloataa else params   ,      _lowerCAmelCase  )

							UpperCAmelCase :       Optional[int] 							=		flatten_dict(_lowerCAmelCase  )
							UpperCAmelCase :       str 							=		pt_model.state_dict()

							UpperCAmelCase :       List[str] 							=		(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()}
							)
							UpperCAmelCase :       Any 							=		(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
							UpperCAmelCase :       Dict 							=		[]
							UpperCAmelCase :       Union[str, Any] 							=		set(pt_model_dict.keys()  )

							for flax_key_tuple, flax_tensor in flax_state_dict.items():
														UpperCAmelCase :       Any 							=		flax_key_tuple[0] == pt_model.base_model_prefix
														UpperCAmelCase :       Optional[Any] 							=		'''.'''.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:
																					UpperCAmelCase :       Tuple 							=		flax_key_tuple[1:]
														elif load_base_model_into_model_with_head and require_base_model_prefix:
																					UpperCAmelCase :       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(_lowerCAmelCase  ) not in pt_model_dict:
																					# conv layer
																					UpperCAmelCase :       str 							=		flax_key_tuple[:-1] + ('''weight''',)
																					UpperCAmelCase :       List[str] 							=		jnp.transpose(_lowerCAmelCase   ,      (3, 2, 0, 1)  )
														elif flax_key_tuple[-1] == "kernel" and ".".join(_lowerCAmelCase  ) not in pt_model_dict:
																					# linear layer
																					UpperCAmelCase :       Any 							=		flax_key_tuple[:-1] + ('''weight''',)
																					UpperCAmelCase :       List[Any] 							=		flax_tensor.T
														elif flax_key_tuple[-1] in ["scale", "embedding"]:
																					UpperCAmelCase :       Optional[int] 							=		flax_key_tuple[:-1] + ('''weight''',)

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

														if "batch_stats" in flax_state:
																					UpperCAmelCase :       Union[str, Any] 							=		'''.'''.join(flax_key_tuple[1:]  )  # Remove the params/batch_stats header
														else:
																					UpperCAmelCase :       Any 							=		'''.'''.join(_lowerCAmelCase  )

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

														if flax_key in special_pt_names:
																					UpperCAmelCase :       Optional[Any] 							=		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
																												UpperCAmelCase :       Optional[int] 							=		np.asarray(_lowerCAmelCase  ) if not isinstance(_lowerCAmelCase   ,      np.ndarray  ) else flax_tensor
																												UpperCAmelCase :       Optional[int] 							=		torch.from_numpy(_lowerCAmelCase  )
																												# remove from missing keys
																												missing_keys.remove(_lowerCAmelCase  )
														else:
																					# weight is not expected by PyTorch model
																					unexpected_keys.append(_lowerCAmelCase  )

							pt_model.load_state_dict(_lowerCAmelCase  )

							# re-transform missing_keys to list
							UpperCAmelCase :       Any 							=		list(_lowerCAmelCase  )

							if len(_lowerCAmelCase  ) > 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(_lowerCAmelCase  ) > 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 math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Optional[int] 							=		tau * frequency / samplerate
							UpperCAmelCase :       List[Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[Any] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       int 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       Any 							=		(1 - _cos) / 2
							UpperCAmelCase :       List[Any] 							=		1 - _cos

							UpperCAmelCase :       Union[str, Any] 							=		1 + alpha
							UpperCAmelCase :       Any 							=		-2 * _cos
							UpperCAmelCase :       Dict 							=		1 - alpha

							UpperCAmelCase :       Union[str, Any] 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Any 							=		tau * frequency / samplerate
							UpperCAmelCase :       Tuple 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Tuple 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Dict 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       int 							=		(1 + _cos) / 2
							UpperCAmelCase :       List[Any] 							=		-1 - _cos

							UpperCAmelCase :       Tuple 							=		1 + alpha
							UpperCAmelCase :       List[str] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha

							UpperCAmelCase :       Tuple 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Optional[int] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Optional[int] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Tuple 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[int] 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       Union[str, Any] 							=		_sin / 2
							UpperCAmelCase :       Any 							=		0
							UpperCAmelCase :       int 							=		-ba

							UpperCAmelCase :       Optional[Any] 							=		1 + alpha
							UpperCAmelCase :       List[Any] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha

							UpperCAmelCase :       int 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       List[str] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Union[str, Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       str 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[Any] 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       List[str] 							=		1 - alpha
							UpperCAmelCase :       Any 							=		-2 * _cos
							UpperCAmelCase :       Optional[int] 							=		1 + alpha

							UpperCAmelCase :       Union[str, Any] 							=		IIRFilter(2  )
							filt.set_coefficients([ba, ba, ba]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )   ,      )      ->   IIRFilter:
							UpperCAmelCase :       Optional[Any] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Union[str, Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[int] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Dict 							=		_sin / (2 * q_factor)
							UpperCAmelCase :       str 							=		10 ** (gain_db / 40)

							UpperCAmelCase :       int 							=		1 + alpha * big_a
							UpperCAmelCase :       Union[str, Any] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha * big_a
							UpperCAmelCase :       Union[str, Any] 							=		1 + alpha / big_a
							UpperCAmelCase :       Tuple 							=		-2 * _cos
							UpperCAmelCase :       Any 							=		1 - alpha / big_a

							UpperCAmelCase :       Optional[Any] 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )   ,      )      ->   IIRFilter:
							UpperCAmelCase :       Any 							=		tau * frequency / samplerate
							UpperCAmelCase :       Optional[int] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Union[str, Any] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       str 							=		_sin / (2 * q_factor)
							UpperCAmelCase :       List[str] 							=		10 ** (gain_db / 40)
							UpperCAmelCase :       Optional[int] 							=		(big_a + 1) - (big_a - 1) * _cos
							UpperCAmelCase :       int 							=		(big_a + 1) + (big_a - 1) * _cos
							UpperCAmelCase :       int 							=		(big_a - 1) - (big_a + 1) * _cos
							UpperCAmelCase :       Optional[int] 							=		(big_a - 1) + (big_a + 1) * _cos
							UpperCAmelCase :       str 							=		2 * sqrt(_lowerCAmelCase  ) * alpha

							UpperCAmelCase :       Dict 							=		big_a * (pmc + aaa)
							UpperCAmelCase :       Any 							=		2 * big_a * mpc
							UpperCAmelCase :       Union[str, Any] 							=		big_a * (pmc - aaa)
							UpperCAmelCase :       Optional[int] 							=		ppmc + aaa
							UpperCAmelCase :       Optional[Any] 							=		-2 * pmpc
							UpperCAmelCase :       Optional[Any] 							=		ppmc - aaa

							UpperCAmelCase :       int 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt




def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )   ,      )      ->   IIRFilter:
							UpperCAmelCase :       int 							=		tau * frequency / samplerate
							UpperCAmelCase :       Union[str, Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Union[str, Any] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Any 							=		_sin / (2 * q_factor)
							UpperCAmelCase :       int 							=		10 ** (gain_db / 40)
							UpperCAmelCase :       List[str] 							=		(big_a + 1) - (big_a - 1) * _cos
							UpperCAmelCase :       Union[str, Any] 							=		(big_a + 1) + (big_a - 1) * _cos
							UpperCAmelCase :       Optional[Any] 							=		(big_a - 1) - (big_a + 1) * _cos
							UpperCAmelCase :       Union[str, Any] 							=		(big_a - 1) + (big_a + 1) * _cos
							UpperCAmelCase :       List[str] 							=		2 * sqrt(_lowerCAmelCase  ) * alpha

							UpperCAmelCase :       Any 							=		big_a * (ppmc + aaa)
							UpperCAmelCase :       str 							=		-2 * big_a * pmpc
							UpperCAmelCase :       List[Any] 							=		big_a * (ppmc - aaa)
							UpperCAmelCase :       Optional[Any] 							=		pmc + aaa
							UpperCAmelCase :       Any 							=		2 * mpc
							UpperCAmelCase :       str 							=		pmc - aaa

							UpperCAmelCase :       Union[str, Any] 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt





