



import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput





def 							A			(  _UpperCAmelCase       :     Dict							,     _UpperCAmelCase       :     Any=0.999							,     _UpperCAmelCase       :     Optional[Any]="cosine"							,     )       ->				Any:







			'''simple docstring'''
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(_UpperCAmelCase       :     Any					):
									return math.cos((t + 0.008) / 1.008 * math.pi / 2					) ** 2

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(_UpperCAmelCase       :     int					):
									return math.exp(t * -12.0					)

			else:
						raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"					)

			_UpperCAmelCase	 =     []
			for i in range(snake_case_					):
						_UpperCAmelCase	 =     i / num_diffusion_timesteps
						_UpperCAmelCase	 =     (i + 1) / num_diffusion_timesteps
						betas.append(min(1 - alpha_bar_fn(snake_case_					) / alpha_bar_fn(snake_case_					)							,     snake_case_					)					)
			return torch.tensor(snake_case_							,     dtype=torch.floataa					)







class     __lowerCAmelCase					(    UpperCamelCase__       ,		UpperCamelCase__		):
			UpperCamelCase           =  [e.name for e in KarrasDiffusionSchedulers]
			UpperCamelCase           =  2



			@register_to_config
			def __init__(		self     :						str				,	A     :						str = 10_00				,	A     :						Dict = 0.0_0_0_8_5				,	A     :						List[str] = 0.0_1_2				,	A     :						str = "linear"				,	A     :						List[str] = None				,	A     :						List[Any] = "epsilon"				,	A     :						Dict = False				,	A     :						Tuple = False				,	A     :						Optional[int] = 1.0				,	A     :						Union[str, Any] = "linspace"				,	A     :						int = 0				,	)     ->					int:



						"""simple docstring"""






						if trained_betas is not None:
									_UpperCAmelCase	 =     torch.tensor(_a				,	dtype=torch.floataa)
						elif beta_schedule == "linear":
									_UpperCAmelCase	 =     torch.linspace(_a				,	_a				,	_a				,	dtype=torch.floataa)
						elif beta_schedule == "scaled_linear":
									# this schedule is very specific to the latent diffusion model.
									_UpperCAmelCase	 =     (
									    torch.linspace(beta_start**0.5				,	beta_end**0.5				,	_a				,	dtype=torch.floataa) ** 2
									)
						elif beta_schedule == "squaredcos_cap_v2":
									# Glide cosine schedule
									_UpperCAmelCase	 =     betas_for_alpha_bar(_a				,	alpha_transform_type='cosine')
						elif beta_schedule == "exp":
									_UpperCAmelCase	 =     betas_for_alpha_bar(_a				,	alpha_transform_type='exp')
						else:
									raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}")

						_UpperCAmelCase	 =     1.0 - self.betas
						_UpperCAmelCase	 =     torch.cumprod(self.alphas				,	dim=0)

						#  set all values
						self.set_timesteps(_a				,	_a				,	_a)
						_UpperCAmelCase	 =     use_karras_sigmas



			def 					_lowerCamelCase (		self     :						Dict				,	A     :						Any				,	A     :						Optional[Any]=None)     ->					str:



						"""simple docstring"""






						if schedule_timesteps is None:
									_UpperCAmelCase	 =     self.timesteps

						_UpperCAmelCase	 =     (schedule_timesteps == timestep).nonzero()

						# The sigma index that is taken for the **very** first `step`
						# is always the second index (or the last index if there is only 1)
						# This way we can ensure we don't accidentally skip a sigma in
						# case we start in the middle of the denoising schedule (e.g. for image-to-image)
						if len(self._index_counter) == 0:
									_UpperCAmelCase	 =     1 if len(_a) > 1 else 0
						else:
									_UpperCAmelCase	 =     timestep.cpu().item() if torch.is_tensor(_a) else timestep
									_UpperCAmelCase	 =     self._index_counter[timestep_int]

						return indices[pos].item()



			@property
			def 					_lowerCamelCase (		self     :						Dict)     ->					Any:



						"""simple docstring"""






						if self.config.timestep_spacing in ["linspace", "trailing"]:
									return self.sigmas.max()

						return (self.sigmas.max() ** 2 + 1) ** 0.5



			def 					_lowerCamelCase (		self     :						Optional[Any]				,	A     :						Dict				,	A     :						Any				,	)     ->					torch.FloatTensor:



						"""simple docstring"""






						_UpperCAmelCase	 =     self.index_for_timestep(_a)

						_UpperCAmelCase	 =     self.sigmas[step_index]
						_UpperCAmelCase	 =     sample / ((sigma**2 + 1) ** 0.5)
						return sample



			def 					_lowerCamelCase (		self     :						str				,	A     :						List[str]				,	A     :						Tuple = None				,	A     :						Any = None				,	)     ->					Union[str, Any]:



						"""simple docstring"""






						_UpperCAmelCase	 =     num_inference_steps

						_UpperCAmelCase	 =     num_train_timesteps or self.config.num_train_timesteps

						# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
						if self.config.timestep_spacing == "linspace":
									_UpperCAmelCase	 =     np.linspace(0				,	num_train_timesteps - 1				,	_a				,	dtype=_a)[::-1].copy()
						elif self.config.timestep_spacing == "leading":
									_UpperCAmelCase	 =     num_train_timesteps // self.num_inference_steps
									# creates integer timesteps by multiplying by ratio
									# casting to int to avoid issues when num_inference_step is power of 3
									_UpperCAmelCase	 =     (np.arange(0				,	_a) * step_ratio).round()[::-1].copy().astype(_a)
									timesteps += self.config.steps_offset
						elif self.config.timestep_spacing == "trailing":
									_UpperCAmelCase	 =     num_train_timesteps / self.num_inference_steps
									# creates integer timesteps by multiplying by ratio
									# casting to int to avoid issues when num_inference_step is power of 3
									_UpperCAmelCase	 =     (np.arange(_a				,	0				,	-step_ratio)).round().copy().astype(_a)
									timesteps -= 1
						else:
									raise ValueError(
									    F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.")

						_UpperCAmelCase	 =     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
						_UpperCAmelCase	 =     np.log(_a)
						_UpperCAmelCase	 =     np.interp(_a				,	np.arange(0				,	len(_a))				,	_a)

						if self.config.use_karras_sigmas:
									_UpperCAmelCase	 =     self._convert_to_karras(in_sigmas=_a				,	num_inference_steps=self.num_inference_steps)
									_UpperCAmelCase	 =     np.array([self._sigma_to_t(_a				,	_a) for sigma in sigmas])

						_UpperCAmelCase	 =     np.concatenate([sigmas, [0.0]]).astype(np.floataa)
						_UpperCAmelCase	 =     torch.from_numpy(_a).to(device=_a)
						_UpperCAmelCase	 =     torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2), sigmas[-1:]])

						_UpperCAmelCase	 =     torch.from_numpy(_a)
						_UpperCAmelCase	 =     torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2)])

						if str(_a).startswith('mps'):
									# mps does not support float64
									_UpperCAmelCase	 =     timesteps.to(_a				,	dtype=torch.floataa)
						else:
									_UpperCAmelCase	 =     timesteps.to(device=_a)

						# empty dt and derivative
						_UpperCAmelCase	 =     None
						_UpperCAmelCase	 =     None

						# for exp beta schedules, such as the one for `pipeline_shap_e.py`
						# we need an index counter
						_UpperCAmelCase	 =     defaultdict(_a)



			def 					_lowerCamelCase (		self     :						str				,	A     :						int				,	A     :						Tuple)     ->					List[Any]:



						"""simple docstring"""






						_UpperCAmelCase	 =     np.log(_a)

						# get distribution
						_UpperCAmelCase	 =     log_sigma - log_sigmas[:, np.newaxis]

						# get sigmas range
						_UpperCAmelCase	 =     np.cumsum((dists >= 0)				,	axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
						_UpperCAmelCase	 =     low_idx + 1

						_UpperCAmelCase	 =     log_sigmas[low_idx]
						_UpperCAmelCase	 =     log_sigmas[high_idx]

						# interpolate sigmas
						_UpperCAmelCase	 =     (low - log_sigma) / (low - high)
						_UpperCAmelCase	 =     np.clip(_a				,	0				,	1)

						# transform interpolation to time range
						_UpperCAmelCase	 =     (1 - w) * low_idx + w * high_idx
						_UpperCAmelCase	 =     t.reshape(sigma.shape)
						return t



			def 					_lowerCamelCase (		self     :						List[str]				,	A     :						Optional[Any]				,	A     :						List[Any])     ->					torch.FloatTensor:



						"""simple docstring"""






						_UpperCAmelCase	 =     in_sigmas[-1].item()
						_UpperCAmelCase	 =     in_sigmas[0].item()

						_UpperCAmelCase	 =     7.0  # 7.0 is the value used in the paper
						_UpperCAmelCase	 =     np.linspace(0				,	1				,	_a)
						_UpperCAmelCase	 =     sigma_min ** (1 / rho)
						_UpperCAmelCase	 =     sigma_max ** (1 / rho)
						_UpperCAmelCase	 =     (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
						return sigmas



			@property
			def 					_lowerCamelCase (		self     :						str)     ->					Dict:



						"""simple docstring"""






						return self.dt is None



			def 					_lowerCamelCase (		self     :						Optional[Any]				,	A     :						Tuple				,	A     :						str				,	A     :						Dict				,	A     :						Optional[Any] = True				,	)     ->					Union[SchedulerOutput, Tuple]:



						"""simple docstring"""






						_UpperCAmelCase	 =     self.index_for_timestep(_a)

						# advance index counter by 1
						_UpperCAmelCase	 =     timestep.cpu().item() if torch.is_tensor(_a) else timestep
						self._index_counter[timestep_int] += 1

						if self.state_in_first_order:
									_UpperCAmelCase	 =     self.sigmas[step_index]
									_UpperCAmelCase	 =     self.sigmas[step_index + 1]
						else:
									# 2nd order / Heun's method
									_UpperCAmelCase	 =     self.sigmas[step_index - 1]
									_UpperCAmelCase	 =     self.sigmas[step_index]

						# currently only gamma=0 is supported. This usually works best anyways.
						# We can support gamma in the future but then need to scale the timestep before
						# passing it to the model which requires a change in API
						_UpperCAmelCase	 =     0
						_UpperCAmelCase	 =     sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
						if self.config.prediction_type == "epsilon":
									_UpperCAmelCase	 =     sigma_hat if self.state_in_first_order else sigma_next
									_UpperCAmelCase	 =     sample - sigma_input * model_output
						elif self.config.prediction_type == "v_prediction":
									_UpperCAmelCase	 =     sigma_hat if self.state_in_first_order else sigma_next
									_UpperCAmelCase	 =     model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
									    sample / (sigma_input**2 + 1)
									)
						elif self.config.prediction_type == "sample":
									_UpperCAmelCase	 =     model_output
						else:
									raise ValueError(
									    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`")

						if self.config.clip_sample:
									_UpperCAmelCase	 =     pred_original_sample.clamp(
									    -self.config.clip_sample_range				,	self.config.clip_sample_range)

						if self.state_in_first_order:
									# 2. Convert to an ODE derivative for 1st order
									_UpperCAmelCase	 =     (sample - pred_original_sample) / sigma_hat
									# 3. delta timestep
									_UpperCAmelCase	 =     sigma_next - sigma_hat

									# store for 2nd order step
									_UpperCAmelCase	 =     derivative
									_UpperCAmelCase	 =     dt
									_UpperCAmelCase	 =     sample
						else:
									# 2. 2nd order / Heun's method
									_UpperCAmelCase	 =     (sample - pred_original_sample) / sigma_next
									_UpperCAmelCase	 =     (self.prev_derivative + derivative) / 2

									# 3. take prev timestep & sample
									_UpperCAmelCase	 =     self.dt
									_UpperCAmelCase	 =     self.sample

									# free dt and derivative
									# Note, this puts the scheduler in "first order mode"
									_UpperCAmelCase	 =     None
									_UpperCAmelCase	 =     None
									_UpperCAmelCase	 =     None

						_UpperCAmelCase	 =     sample + derivative * dt

						if not return_dict:
									return (prev_sample,)

						return SchedulerOutput(prev_sample=_a)



			def 					_lowerCamelCase (		self     :						Dict				,	A     :						Any				,	A     :						str				,	A     :						Union[str, Any]				,	)     ->					torch.FloatTensor:



						"""simple docstring"""






						_UpperCAmelCase	 =     self.sigmas.to(device=original_samples.device				,	dtype=original_samples.dtype)
						if original_samples.device.type == "mps" and torch.is_floating_point(_a):
									# mps does not support float64
									_UpperCAmelCase	 =     self.timesteps.to(original_samples.device				,	dtype=torch.floataa)
									_UpperCAmelCase	 =     timesteps.to(original_samples.device				,	dtype=torch.floataa)
						else:
									_UpperCAmelCase	 =     self.timesteps.to(original_samples.device)
									_UpperCAmelCase	 =     timesteps.to(original_samples.device)

						_UpperCAmelCase	 =     [self.index_for_timestep(_a				,	_a) for t in timesteps]

						_UpperCAmelCase	 =     sigmas[step_indices].flatten()
						while len(sigma.shape) < len(original_samples.shape):
									_UpperCAmelCase	 =     sigma.unsqueeze(-1)

						_UpperCAmelCase	 =     original_samples + noise * sigma
						return noisy_samples



			def __len__(		self     :						int)     ->					List[str]:



						"""simple docstring"""






						return self.config.num_train_timesteps





from collections import Counter
from timeit import timeit





def 							A			(  _UpperCAmelCase       :     str = ""							,     )       ->				bool:







			'''simple docstring'''
			return sum(c % 2 for c in Counter(input_str.replace(' '							,     ''					).lower()					).values()					) < 2





def 							A			(  _UpperCAmelCase       :     str = ""					)       ->				bool:







			'''simple docstring'''
			if len(_UpperCAmelCase					) == 0:
						return True
			_UpperCAmelCase	 =     input_str.replace(' '							,     ''					).lower()
			# character_freq_dict: Stores the frequency of every character in the input string
			_UpperCAmelCase	 =     {}

			for character in lower_case_input_str:
						_UpperCAmelCase	 =     character_freq_dict.get(_UpperCAmelCase							,     0					) + 1
			_UpperCAmelCase	 =     0

			for character_count in character_freq_dict.values():
						if character_count % 2:
									odd_char += 1
			if odd_char > 1:
						return False
			return True





def 							A			(  _UpperCAmelCase       :     str = ""					)       ->				None:







			'''simple docstring'''
			print('\nFor string = '							,     _UpperCAmelCase							,     ':'					)
			print(
			    '> can_string_be_rearranged_as_palindrome_counter()'							,     '\tans ='							,     can_string_be_rearranged_as_palindrome_counter(_UpperCAmelCase					)							,     '\ttime ='							,     timeit(
			        'z.can_string_be_rearranged_as_palindrome_counter(z.check_str)'							,     setup='import __main__ as z'							,     )							,     'seconds'							,     )
			print(
			    '> can_string_be_rearranged_as_palindrome()'							,     '\tans ='							,     can_string_be_rearranged_as_palindrome(_UpperCAmelCase					)							,     '\ttime ='							,     timeit(
			        'z.can_string_be_rearranged_as_palindrome(z.check_str)'							,     setup='import __main__ as z'							,     )							,     'seconds'							,     )


if __name__ == "__main__":
							UpperCAmelCase__     = input(
							    "Enter string to determine if it can be rearranged as a palindrome or not: "
							).strip()
							benchmark(check_str)
							UpperCAmelCase__     = can_string_be_rearranged_as_palindrome_counter(check_str)
							print(f"""{check_str} can {"" if status else "not "}be rearranged as a palindrome""")
