





'''simple docstring'''

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 						UpperCamelCase    (							_lowerCamelCase : List[str]						,	_lowerCamelCase : Any=0.9_9_9						,	_lowerCamelCase : List[str]="cosine"						,	):
				if alpha_transform_type == "cosine":

								def alpha_bar_fn(_lowerCamelCase : Dict	):
												return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2	) ** 2

				elif alpha_transform_type == "exp":

								def alpha_bar_fn(_lowerCamelCase : Optional[Any]	):
												return math.exp(t * -12.0	)

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

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






class        UpperCAmelCase     (	UpperCamelCase__      ,	UpperCamelCase__    ):
	__lowercase       		=    [e.name for e in KarrasDiffusionSchedulers]
	__lowercase       		=    2
	@register_to_config
	def __init__(    self				:Optional[int]						,	lowercase_				:int = 10_00						,	lowercase_				:float = 0.0_0_0_8_5						,	lowercase_				:float = 0.0_1_2						,	lowercase_				:str = "linear"						,	lowercase_				:Optional[Union[np.ndarray, List[float]]] = None						,	lowercase_				:str = "epsilon"						,	lowercase_				:Optional[bool] = False						,	lowercase_				:Optional[bool] = False						,	lowercase_				:float = 1.0						,	lowercase_				:str = "linspace"						,	lowercase_				:int = 0						,	)->							Tuple:
					if trained_betas is not None:
									A__    =      torch.tensor(lowercase_						,	dtype=torch.floataa							)
					elif beta_schedule == "linear":
									A__    =      torch.linspace(lowercase_						,	lowercase_						,	lowercase_						,	dtype=torch.floataa							)
					elif beta_schedule == "scaled_linear":
									# this schedule is very specific to the latent diffusion model.
									A__    =      (
									    torch.linspace(beta_start**0.5						,	beta_end**0.5						,	lowercase_						,	dtype=torch.floataa							) ** 2
									)
					elif beta_schedule == "squaredcos_cap_v2":
									# Glide cosine schedule
									A__    =      betas_for_alpha_bar(lowercase_						,	alpha_transform_type="cosine"							)
					elif beta_schedule == "exp":
									A__    =      betas_for_alpha_bar(lowercase_						,	alpha_transform_type="exp"							)
					else:
									raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"							)

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

					#  set all values
					self.set_timesteps(lowercase_						,	lowercase_						,	lowercase_							)
					A__    =      use_karras_sigmas
	def 					UpperCAmelCase_							(    self				:str						,	lowercase_				:Union[str, Any]						,	lowercase_				:Optional[Any]=None							)->							Optional[int]:
					if schedule_timesteps is None:
									A__    =      self.timesteps

					A__    =      (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:
									A__    =      1 if len(lowercase_							) > 1 else 0
					else:
									A__    =      timestep.cpu().item() if torch.is_tensor(lowercase_							) else timestep
									A__    =      self._index_counter[timestep_int]

					return indices[pos].item()
	@property
	def 					UpperCAmelCase_							(    self				:List[str]							)->							Dict:
					# standard deviation of the initial noise distribution
					if self.config.timestep_spacing in ["linspace", "trailing"]:
									return self.sigmas.max()

					return (self.sigmas.max() ** 2 + 1) ** 0.5
	def 					UpperCAmelCase_							(    self				:Optional[int]						,	lowercase_				:torch.FloatTensor						,	lowercase_				:Union[float, torch.FloatTensor]						,	)->							torch.FloatTensor:
					A__    =      self.index_for_timestep(lowercase_							)

					A__    =      self.sigmas[step_index]
					A__    =      sample / ((sigma**2 + 1) ** 0.5)
					return sample
	def 					UpperCAmelCase_							(    self				:str						,	lowercase_				:int						,	lowercase_				:Union[str, torch.device] = None						,	lowercase_				:Optional[int] = None						,	)->							Optional[int]:
					A__    =      num_inference_steps

					A__    =      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":
									A__    =      np.linspace(0						,	num_train_timesteps - 1						,	lowercase_						,	dtype=lowercase_							)[::-1].copy()
					elif self.config.timestep_spacing == "leading":
									A__    =      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
									A__    =      (np.arange(0						,	lowercase_							) * step_ratio).round()[::-1].copy().astype(lowercase_							)
									timesteps += self.config.steps_offset
					elif self.config.timestep_spacing == "trailing":
									A__    =      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
									A__    =      (np.arange(lowercase_						,	0						,	-step_ratio							)).round().copy().astype(lowercase_							)
									timesteps -= 1
					else:
									raise ValueError(
									    F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."							)

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

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

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

					A__    =      torch.from_numpy(lowercase_							)
					A__    =      torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2							)]							)

					if str(lowercase_							).startswith("mps"							):
									# mps does not support float64
									A__    =      timesteps.to(lowercase_						,	dtype=torch.floataa							)
					else:
									A__    =      timesteps.to(device=lowercase_							)

					# empty dt and derivative
					A__    =      None
					A__    =      None

					# for exp beta schedules, such as the one for `pipeline_shap_e.py`
					# we need an index counter
					A__    =      defaultdict(lowercase_							)
	def 					UpperCAmelCase_							(    self				:List[Any]						,	lowercase_				:Any						,	lowercase_				:Tuple							)->							Any:
					# get log sigma
					A__    =      np.log(lowercase_							)

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

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

					A__    =      log_sigmas[low_idx]
					A__    =      log_sigmas[high_idx]

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

					# transform interpolation to time range
					A__    =      (1 - w) * low_idx + w * high_idx
					A__    =      t.reshape(sigma.shape							)
					return t
	def 					UpperCAmelCase_							(    self				:str						,	lowercase_				:torch.FloatTensor						,	lowercase_				:Optional[Any]							)->							torch.FloatTensor:
					A__    =      in_sigmas[-1].item()
					A__    =      in_sigmas[0].item()

					A__    =      7.0  # 7.0 is the value used in the paper
					A__    =      np.linspace(0						,	1						,	lowercase_							)
					A__    =      sigma_min ** (1 / rho)
					A__    =      sigma_max ** (1 / rho)
					A__    =      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
					return sigmas
	@property
	def 					UpperCAmelCase_							(    self				:Dict							)->							Tuple:
					return self.dt is None
	def 					UpperCAmelCase_							(    self				:List[Any]						,	lowercase_				:Union[torch.FloatTensor, np.ndarray]						,	lowercase_				:Union[float, torch.FloatTensor]						,	lowercase_				:Union[torch.FloatTensor, np.ndarray]						,	lowercase_				:bool = True						,	)->							Union[SchedulerOutput, Tuple]:
					A__    =      self.index_for_timestep(lowercase_							)

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

					if self.state_in_first_order:
									A__    =      self.sigmas[step_index]
									A__    =      self.sigmas[step_index + 1]
					else:
									# 2nd order / Heun's method
									A__    =      self.sigmas[step_index - 1]
									A__    =      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
					A__    =      0
					A__    =      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":
									A__    =      sigma_hat if self.state_in_first_order else sigma_next
									A__    =      sample - sigma_input * model_output
					elif self.config.prediction_type == "v_prediction":
									A__    =      sigma_hat if self.state_in_first_order else sigma_next
									A__    =      model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
									    sample / (sigma_input**2 + 1)
									)
					elif self.config.prediction_type == "sample":
									A__    =      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:
									A__    =      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
									A__    =      (sample - pred_original_sample) / sigma_hat
									# 3. delta timestep
									A__    =      sigma_next - sigma_hat

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

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

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

					A__    =      sample + derivative * dt

					if not return_dict:
									return (prev_sample,)

					return SchedulerOutput(prev_sample=lowercase_							)
	def 					UpperCAmelCase_							(    self				:Union[str, Any]						,	lowercase_				:torch.FloatTensor						,	lowercase_				:torch.FloatTensor						,	lowercase_				:torch.FloatTensor						,	)->							torch.FloatTensor:
					# Make sure sigmas and timesteps have the same device and dtype as original_samples
					A__    =      self.sigmas.to(device=original_samples.device						,	dtype=original_samples.dtype							)
					if original_samples.device.type == "mps" and torch.is_floating_point(lowercase_							):
									# mps does not support float64
									A__    =      self.timesteps.to(original_samples.device						,	dtype=torch.floataa							)
									A__    =      timesteps.to(original_samples.device						,	dtype=torch.floataa							)
					else:
									A__    =      self.timesteps.to(original_samples.device							)
									A__    =      timesteps.to(original_samples.device							)

					A__    =      [self.index_for_timestep(lowercase_						,	lowercase_							) for t in timesteps]

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

					A__    =      original_samples + noise * sigma
					return noisy_samples



	def __len__(    self				:Dict							)->							Any:
					return self.config.num_train_timesteps










'''simple docstring'''

def 						UpperCamelCase    (							_lowerCamelCase : int = 1_00_00_00	):
    A__    =      set(range(3						,	_lowerCamelCase						,	2	)	)
    primes.add(2	)
    for p in range(3						,	_lowerCamelCase						,	2	):
        if p not in primes:
            continue
        primes.difference_update(set(range(p * p						,	_lowerCamelCase						,	_lowerCamelCase	)	)	)

    A__    =      [float(_lowerCamelCase	) for n in range(limit + 1	)]

    for p in primes:
        for n in range(_lowerCamelCase						,	limit + 1						,	_lowerCamelCase	):
            phi[n] *= 1 - 1 / p

    return int(sum(phi[2:]	)	)


if __name__ == "__main__":
  print(f"""{solution() = }""")



