
"""simple docstring"""




import re

import jax.numpy as jnp
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.random import PRNGKey

from ..utils import logging


UpperCAmelCase__      :    Tuple    							= logging.get_logger(__name__)

def lowercase_  (   _snake_case						):
							SCREAMING_SNAKE_CASE__						:       Dict           =   R"""\w+[.]\d+"""
							SCREAMING_SNAKE_CASE__						:       Dict           =   re.findall(_snake_case   ,_snake_case						)
							for pat in pats:
														SCREAMING_SNAKE_CASE__						:       Dict           =   key.replace(_snake_case   ,"""_""".join(pat.split("""."""						)						)						)
							return key

def lowercase_  (   _snake_case   ,_snake_case   ,_snake_case						):
							SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   pt_tuple_key[:-1] + ("""scale""",)
							if (
							    any("""norm""" in str_ for str_ in pt_tuple_key						)
							    and (pt_tuple_key[-1] == "bias")
							    and (pt_tuple_key[:-1] + ("bias",) not in random_flax_state_dict)
							    and (pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict)
							):
														SCREAMING_SNAKE_CASE__						:       Tuple           =   pt_tuple_key[:-1] + ("""scale""",)
														return renamed_pt_tuple_key, pt_tensor
							elif pt_tuple_key[-1] in ["weight", "gamma"] and pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict:
														SCREAMING_SNAKE_CASE__						:       List[Any]           =   pt_tuple_key[:-1] + ("""scale""",)
														return renamed_pt_tuple_key, pt_tensor

							# embedding
							if pt_tuple_key[-1] == "weight" and pt_tuple_key[:-1] + ("embedding",) in random_flax_state_dict:
														SCREAMING_SNAKE_CASE__						:       Any           =   pt_tuple_key[:-1] + ("""embedding""",)
														return renamed_pt_tuple_key, pt_tensor

							# conv layer
							SCREAMING_SNAKE_CASE__						:       str           =   pt_tuple_key[:-1] + ("""kernel""",)
							if pt_tuple_key[-1] == "weight" and pt_tensor.ndim == 4:
														SCREAMING_SNAKE_CASE__						:       Tuple           =   pt_tensor.transpose(2   ,3   ,1   ,0						)
														return renamed_pt_tuple_key, pt_tensor

							# linear layer
							SCREAMING_SNAKE_CASE__						:       Dict           =   pt_tuple_key[:-1] + ("""kernel""",)
							if pt_tuple_key[-1] == "weight":
														SCREAMING_SNAKE_CASE__						:       str           =   pt_tensor.T
														return renamed_pt_tuple_key, pt_tensor

							# old PyTorch layer norm weight
							SCREAMING_SNAKE_CASE__						:       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
							SCREAMING_SNAKE_CASE__						:       str           =   pt_tuple_key[:-1] + ("""bias""",)
							if pt_tuple_key[-1] == "beta":
														return renamed_pt_tuple_key, pt_tensor

							return pt_tuple_key, pt_tensor

def lowercase_  (   _snake_case   ,_snake_case   ,_snake_case=42						):
							# Step 1: Convert pytorch tensor to numpy
							SCREAMING_SNAKE_CASE__						:       str           =   {k: v.numpy() for k, v in pt_state_dict.items()}

							# Step 2: Since the model is stateless, get random Flax params
							SCREAMING_SNAKE_CASE__						:       Optional[int]           =   flax_model.init_weights(PRNGKey(_snake_case						)						)

							SCREAMING_SNAKE_CASE__						:       Any           =   flatten_dict(_snake_case						)
							SCREAMING_SNAKE_CASE__						:       Dict           =   {}

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

														# Correctly rename weight parameters
														SCREAMING_SNAKE_CASE__      ,      SCREAMING_SNAKE_CASE__						:       Dict           =   rename_key_and_reshape_tensor(_snake_case   ,_snake_case   ,_snake_case						)

														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}.'''						)

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

							return unflatten_dict(_snake_case						)






"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np



class 	lowerCAmelCase_						:


				"""simple docstring"""



				def __init__(self   ,       SCREAMING_SNAKE_CASE__=None   ,       SCREAMING_SNAKE_CASE__=None    )					->		Dict:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   list(poly_a or [0]    )[:]
											SCREAMING_SNAKE_CASE__						:       Tuple           =   list(poly_b or [0]    )[:]

											# Remove leading zero coefficients
											while self.polyA[-1] == 0:
																		self.polyA.pop()
											SCREAMING_SNAKE_CASE__						:       int           =   len(self.polyA    )

											while self.polyB[-1] == 0:
																		self.polyB.pop()
											SCREAMING_SNAKE_CASE__						:       List[str]           =   len(self.polyB    )

											# Add 0 to make lengths equal a power of 2
											SCREAMING_SNAKE_CASE__						:       Optional[int]           =   int(
											    2 ** np.ceil(np.loga(len(self.polyA    ) + len(self.polyB    ) - 1    )    )    )

											while len(self.polyA    ) < self.c_max_length:
																		self.polyA.append(0    )
											while len(self.polyB    ) < self.c_max_length:
																		self.polyB.append(0    )
											# A complex root used for the fourier transform
											SCREAMING_SNAKE_CASE__						:       List[str]           =   complex(mpmath.root(x=1   ,       n=self.c_max_length   ,       k=1    )    )

											# The product
											SCREAMING_SNAKE_CASE__						:       Tuple           =   self.__multiply()



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Union[str, Any]:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       str           =   [[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
											# Corner case
											if len(SCREAMING_SNAKE_CASE__    ) <= 1:
																		return dft[0]
											#
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   self.c_max_length // 2
											while next_ncol > 0:
																		SCREAMING_SNAKE_CASE__						:       Any           =   [[] for i in range(SCREAMING_SNAKE_CASE__    )]
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   self.root**next_ncol

																		# First half of next step
																		SCREAMING_SNAKE_CASE__						:       str           =   1
																		for j in range(self.c_max_length // (next_ncol * 2)    ):
																									for i in range(SCREAMING_SNAKE_CASE__    ):
																																new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]    )
																									current_root *= root
																		# Second half of next step
																		SCREAMING_SNAKE_CASE__						:       int           =   1
																		for j in range(self.c_max_length // (next_ncol * 2)    ):
																									for i in range(SCREAMING_SNAKE_CASE__    ):
																																new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]    )
																									current_root *= root
																		# Update
																		SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   new_dft
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   next_ncol // 2
											return dft[0]



				def 	__magic_name__    (self    )					->		int:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   self.__dft("""A"""    )
											SCREAMING_SNAKE_CASE__						:       Dict           =   self.__dft("""B"""    )
											SCREAMING_SNAKE_CASE__						:       List[Any]           =   [[dft_a[i] * dft_b[i] for i in range(self.c_max_length    )]]
											del dft_a
											del dft_b

											# Corner Case
											if len(inverce_c[0]    ) <= 1:
																		return inverce_c[0]
											# Inverse DFT
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   2
											while next_ncol <= self.c_max_length:
																		SCREAMING_SNAKE_CASE__						:       List[str]           =   [[] for i in range(SCREAMING_SNAKE_CASE__    )]
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   self.root ** (next_ncol // 2)
																		SCREAMING_SNAKE_CASE__						:       Any           =   1
																		# First half of next step
																		for j in range(self.c_max_length // next_ncol    ):
																									for i in range(next_ncol // 2    ):
																																# Even positions
																																new_inverse_c[i].append(
																																    (
																																        inverce_c[i][j]
																																        + inverce_c[i][j + self.c_max_length // next_ncol]
																																    )
																																    / 2    )
																																# Odd positions
																																new_inverse_c[i + next_ncol // 2].append(
																																    (
																																        inverce_c[i][j]
																																        - inverce_c[i][j + self.c_max_length // next_ncol]
																																    )
																																    / (2 * current_root)    )
																									current_root *= root
																		# Update
																		SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   new_inverse_c
																		next_ncol *= 2
											# Unpack
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   [round(x[0].real   ,       8    ) + round(x[0].imag   ,       8    ) * 1j for x in inverce_c]

											# Remove leading 0's
											while inverce_c[-1] == 0:
																		inverce_c.pop()
											return inverce_c



				def __str__(self    )					->		List[str]:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       List[str]           =   """A = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]    )    )
											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   """B = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]    )    )
											SCREAMING_SNAKE_CASE__						:       int           =   """A*B = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.product    )    )

											return F'''{a}\n{b}\n{c}'''


# Unit tests
if __name__ == "__main__":
					import doctest

					doctest.testmod()




