


import mpmath  # for roots of unity
import numpy as np




class 							lowerCamelCase   :


	def __init__(    self				,     lowercase__=None				,     lowercase__=None):
							# Input as list
							__UpperCAmelCase			:							str	    =	list(poly_a or [0])[:]
							__UpperCAmelCase			:							Tuple	    =	list(poly_b or [0])[:]

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

							while self.polyB[-1] == 0:
													self.polyB.pop()
							__UpperCAmelCase			:							Optional[Any]	    =	len(self.polyB)

							# Add 0 to make lengths equal a power of 2
							__UpperCAmelCase			:							Dict	    =	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
							__UpperCAmelCase			:							List[str]	    =	complex(mpmath.root(x=1				,     n=self.c_max_length				,     k=1))

							# The product
							__UpperCAmelCase			:							Optional[int]	    =	self.__multiply()


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

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


	def  A(    self):
							__UpperCAmelCase			:							Tuple	    =	self.__dft('''A''')
							__UpperCAmelCase			:							List[Any]	    =	self.__dft('''B''')
							__UpperCAmelCase			:							List[str]	    =	[[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
							__UpperCAmelCase			:							str	    =	2
							while next_ncol <= self.c_max_length:
													__UpperCAmelCase			:							List[str]	    =	[[] for i in range(lowercase__)]
													__UpperCAmelCase			:							Optional[int]	    =	self.root ** (next_ncol // 2)
													__UpperCAmelCase			:							Tuple	    =	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
													__UpperCAmelCase			:							List[Any]	    =	new_inverse_c
													next_ncol *= 2
							# Unpack
							__UpperCAmelCase			:							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):
							__UpperCAmelCase			:							Any	    =	'''A = ''' + ''' + '''.join(
							    F"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A]))
							__UpperCAmelCase			:							int	    =	'''B = ''' + ''' + '''.join(
							    F"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B]))
							__UpperCAmelCase			:							Optional[Any]	    =	'''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()





import importlib

import torch
import yaml
from omegaconf import OmegaConf
from taming.models.vqgan import VQModel




def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_=False      )		->     Optional[Any]:




						'''simple docstring'''







						__UpperCAmelCase			:							Optional[Any]	    =	OmegaConf.load(lowercase_      )
						if display:
												print(yaml.dump(OmegaConf.to_container(lowercase_      )      )      )
						return config




def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_=None      ,       lowercase_=None      )		->     Union[str, Any]:




						'''simple docstring'''







						if conf_path is None:
												__UpperCAmelCase			:							Optional[int]	    =	'''./model_checkpoints/vqgan_only.yaml'''
						__UpperCAmelCase			:							Dict	    =	load_config(lowercase_      ,       display=lowercase_      )
						__UpperCAmelCase			:							Tuple	    =	VQModel(**config.model.params      )
						if ckpt_path is None:
												__UpperCAmelCase			:							Dict	    =	'''./model_checkpoints/vqgan_only.pt'''
						__UpperCAmelCase			:							int	    =	torch.load(lowercase_      ,       map_location=lowercase_      )
						if ".ckpt" in ckpt_path:
												__UpperCAmelCase			:							Union[str, Any]	    =	sd['''state_dict''']
						model.load_state_dict(lowercase_      ,       strict=lowercase_      )
						model.to(lowercase_      )
						del sd
						return model




def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_      )		->     List[Any]:




						'''simple docstring'''







						__UpperCAmelCase    ,      __UpperCAmelCase    ,      __UpperCAmelCase			:							Optional[Any]	    =	model.encode(lowercase_      )
						print(f"VQGAN --- {model.__class__.__name__}: latent shape: {z.shape[2:]}"      )
						__UpperCAmelCase			:							List[str]	    =	model.decode(lowercase_      )
						return xrec




def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_=False      )		->     int:




						'''simple docstring'''







						__UpperCAmelCase    ,      __UpperCAmelCase			:							Optional[int]	    =	string.rsplit('''.'''      ,       1      )
						if reload:
												__UpperCAmelCase			:							Optional[int]	    =	importlib.import_module(lowercase_      )
												importlib.reload(lowercase_      )
						return getattr(importlib.import_module(lowercase_      ,       package=lowercase_      )      ,       cls      )




def     __SCREAMING_SNAKE_CASE							(       lowercase_      )		->     Union[str, Any]:




						'''simple docstring'''







						if "target" not in config:
												raise KeyError('''Expected key `target` to instantiate.'''      )
						return get_obj_from_str(config['''target''']      )(**config.get('''params'''      ,       {}      )      )




def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_      ,       lowercase_=True      ,       lowercase_=True      )		->     int:




						'''simple docstring'''







						__UpperCAmelCase			:							Dict	    =	instantiate_from_config(lowercase_      )
						if sd is not None:
												model.load_state_dict(lowercase_      )
						if gpu:
												model.cuda()
						if eval_mode:
												model.eval()
						return {"model": model}





def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_      ,       lowercase_      ,       lowercase_      )		->     Optional[Any]:




						'''simple docstring'''







						if ckpt:
												__UpperCAmelCase			:							Optional[int]	    =	torch.load(lowercase_      ,       map_location='''cpu'''      )
												__UpperCAmelCase			:							Union[str, Any]	    =	pl_sd['''global_step''']
												print(f"loaded model from global step {global_step}."      )
						else:
												__UpperCAmelCase			:							Union[str, Any]	    =	{'''state_dict''': None}
												__UpperCAmelCase			:							Optional[int]	    =	None
						__UpperCAmelCase			:							str	    =	load_model_from_config(config.model      ,       pl_sd['''state_dict''']      ,       gpu=lowercase_      ,       eval_mode=lowercase_      )['''model''']
						return model, global_step

