

from __future__ import annotations







def     A_   (					_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			):
						if not all((nth_term, start_term_a, common_ratio_r)					):
												return []
						SCREAMING_SNAKE_CASE_:				list[float | int]							= []
						SCREAMING_SNAKE_CASE_:				Dict							= 1
						SCREAMING_SNAKE_CASE_:				Union[str, Any]							= common_ratio_r
						for _ in range(int(_UpperCAmelCase					)					):
												if not series:
																		series.append(_UpperCAmelCase					)
												else:
																		power += 1
																		series.append(float(start_term_a * multiple					)					)
																		SCREAMING_SNAKE_CASE_:				Dict							= pow(float(_UpperCAmelCase					)       ,			_UpperCAmelCase					)
						return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						lowerCAmelCase							:						Optional[Any]     			=		float(input("""Enter the last number (n term) of the Geometric Series"""))
						lowerCAmelCase							:						Tuple     			=		float(input("""Enter the starting term (a) of the Geometric Series"""))
						lowerCAmelCase							:						Dict     			=		float(
						    input("""Enter the common ratio between two terms (r) of the Geometric Series""")
						)
						print("""Formula of Geometric Series => a + ar + ar^2 ... +ar^n""")
						print(geometric_series(nth_term, start_term_a, common_ratio_r))









import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


lowerCAmelCase							:						Union[str, Any]     			=		logging.get_logger(__name__)  # pylint: disable=invalid-name



@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 						__lowercase       (				UpperCAmelCase_			):




			"""simple docstring"""







			_UpperCAmelCase     :							torch.FloatTensor
			_UpperCAmelCase     :							Optional[torch.FloatTensor]    							=  None







def     A_   (					_UpperCAmelCase       ,			_UpperCAmelCase=0.9_9_9       ,			_UpperCAmelCase="cosine"       ,			):
						if alpha_transform_type == "cosine":

												def alpha_bar_fn(_UpperCAmelCase					):
																		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(_UpperCAmelCase					):
																		return math.exp(t * -1_2.0					)

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

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



class 						__lowercase       (				UpperCAmelCase_	, UpperCAmelCase_			):




			"""simple docstring"""







			_UpperCAmelCase     :							Tuple    							=  [e.name for e in KarrasDiffusionSchedulers]
			_UpperCAmelCase     :							Optional[Any]    							=  1



			@register_to_config
			def __init__(				self						:  Optional[Any]     ,		lowerCAmelCase__						:  int = 1000     ,		lowerCAmelCase__						:  float = 0.0001     ,		lowerCAmelCase__						:  float = 0.02     ,		lowerCAmelCase__						:  str = "linear"     ,		lowerCAmelCase__						:  Optional[Union[np.ndarray, List[float]]] = None     ,		lowerCAmelCase__						:  str = "epsilon"     ,		lowerCAmelCase__						:  str = "linspace"     ,		lowerCAmelCase__						:  int = 0     ,		):
									if trained_betas is not None:
															SCREAMING_SNAKE_CASE_:				Tuple							= torch.tensor(lowerCAmelCase__     ,		dtype=torch.floataa)
									elif beta_schedule == "linear":
															SCREAMING_SNAKE_CASE_:				List[str]							= torch.linspace(lowerCAmelCase__     ,		lowerCAmelCase__     ,		lowerCAmelCase__     ,		dtype=torch.floataa)
									elif beta_schedule == "scaled_linear":
															# this schedule is very specific to the latent diffusion model.
															SCREAMING_SNAKE_CASE_:				str							= (
															    torch.linspace(beta_start**0.5     ,		beta_end**0.5     ,		lowerCAmelCase__     ,		dtype=torch.floataa) ** 2
															)
									elif beta_schedule == "squaredcos_cap_v2":
															# Glide cosine schedule
															SCREAMING_SNAKE_CASE_:				int							= betas_for_alpha_bar(lowerCAmelCase__)
									else:
															raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}")

									SCREAMING_SNAKE_CASE_:				List[Any]							= 1.0 - self.betas
									SCREAMING_SNAKE_CASE_:				Tuple							= torch.cumprod(self.alphas     ,		dim=0)

									SCREAMING_SNAKE_CASE_:				Optional[int]							= np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
									SCREAMING_SNAKE_CASE_:				Optional[Any]							= np.concatenate([sigmas[::-1], [0.0]]).astype(np.floataa)
									SCREAMING_SNAKE_CASE_:				str							= torch.from_numpy(lowerCAmelCase__)

									# setable values
									SCREAMING_SNAKE_CASE_:				Union[str, Any]							= None
									SCREAMING_SNAKE_CASE_:				Optional[Any]							= np.linspace(0     ,		num_train_timesteps - 1     ,		lowerCAmelCase__     ,		dtype=lowerCAmelCase__)[::-1].copy()
									SCREAMING_SNAKE_CASE_:				Optional[int]							= torch.from_numpy(lowerCAmelCase__)
									SCREAMING_SNAKE_CASE_:				str							= False



			@property
			def  _SCREAMING_SNAKE_CASE    (				self						:  List[Any]):
									# 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  _SCREAMING_SNAKE_CASE    (				self						:  Any     ,		lowerCAmelCase__						:  torch.FloatTensor     ,		lowerCAmelCase__						:  Union[float, torch.FloatTensor]):
									if isinstance(lowerCAmelCase__     ,		torch.Tensor):
															SCREAMING_SNAKE_CASE_:				Dict							= timestep.to(self.timesteps.device)
									SCREAMING_SNAKE_CASE_:				List[Any]							= (self.timesteps == timestep).nonzero().item()
									SCREAMING_SNAKE_CASE_:				Optional[Any]							= self.sigmas[step_index]
									SCREAMING_SNAKE_CASE_:				List[str]							= sample / ((sigma**2 + 1) ** 0.5)
									SCREAMING_SNAKE_CASE_:				int							= True
									return sample



			def  _SCREAMING_SNAKE_CASE    (				self						:  List[Any]     ,		lowerCAmelCase__						:  int     ,		lowerCAmelCase__						:  Union[str, torch.device] = None):
									SCREAMING_SNAKE_CASE_:				Dict							= num_inference_steps

									# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
									if self.config.timestep_spacing == "linspace":
															SCREAMING_SNAKE_CASE_:				str							= np.linspace(0     ,		self.config.num_train_timesteps - 1     ,		lowerCAmelCase__     ,		dtype=lowerCAmelCase__)[
															    ::-1
															].copy()
									elif self.config.timestep_spacing == "leading":
															SCREAMING_SNAKE_CASE_:				List[Any]							= self.config.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
															SCREAMING_SNAKE_CASE_:				Optional[Any]							= (np.arange(0     ,		lowerCAmelCase__) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__)
															timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
															SCREAMING_SNAKE_CASE_:				Optional[Any]							= self.config.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
															SCREAMING_SNAKE_CASE_:				int							= (np.arange(self.config.num_train_timesteps     ,		0     ,		-step_ratio)).round().copy().astype(lowerCAmelCase__)
															timesteps -= 1
									else:
															raise ValueError(
															    F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'.")

									SCREAMING_SNAKE_CASE_:				Union[str, Any]							= np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
									SCREAMING_SNAKE_CASE_:				Any							= np.interp(lowerCAmelCase__     ,		np.arange(0     ,		len(lowerCAmelCase__))     ,		lowerCAmelCase__)
									SCREAMING_SNAKE_CASE_:				Optional[Any]							= np.concatenate([sigmas, [0.0]]).astype(np.floataa)
									SCREAMING_SNAKE_CASE_:				Optional[Any]							= torch.from_numpy(lowerCAmelCase__).to(device=lowerCAmelCase__)
									if str(lowerCAmelCase__).startswith("mps"):
															# mps does not support float64
															SCREAMING_SNAKE_CASE_:				Optional[int]							= torch.from_numpy(lowerCAmelCase__).to(lowerCAmelCase__     ,		dtype=torch.floataa)
									else:
															SCREAMING_SNAKE_CASE_:				Optional[Any]							= torch.from_numpy(lowerCAmelCase__).to(device=lowerCAmelCase__)



			def  _SCREAMING_SNAKE_CASE    (				self						:  Union[str, Any]     ,		lowerCAmelCase__						:  torch.FloatTensor     ,		lowerCAmelCase__						:  Union[float, torch.FloatTensor]     ,		lowerCAmelCase__						:  torch.FloatTensor     ,		lowerCAmelCase__						:  Optional[torch.Generator] = None     ,		lowerCAmelCase__						:  bool = True     ,		):

									if (
									    isinstance(lowerCAmelCase__     ,		lowerCAmelCase__)
									    or isinstance(lowerCAmelCase__     ,		torch.IntTensor)
									    or isinstance(lowerCAmelCase__     ,		torch.LongTensor)
									):
															raise ValueError(
															    (
															        "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
															        " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
															        " one of the `scheduler.timesteps` as a timestep."
															    )     ,		)

									if not self.is_scale_input_called:
															logger.warning(
															    "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
															    "See `StableDiffusionPipeline` for a usage example.")

									if isinstance(lowerCAmelCase__     ,		torch.Tensor):
															SCREAMING_SNAKE_CASE_:				Optional[Any]							= timestep.to(self.timesteps.device)

									SCREAMING_SNAKE_CASE_:				int							= (self.timesteps == timestep).nonzero().item()
									SCREAMING_SNAKE_CASE_:				str							= self.sigmas[step_index]

									# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
									if self.config.prediction_type == "epsilon":
															SCREAMING_SNAKE_CASE_:				List[Any]							= sample - sigma * model_output
									elif self.config.prediction_type == "v_prediction":
															# * c_out + input * c_skip
															SCREAMING_SNAKE_CASE_:				Optional[Any]							= model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
									elif self.config.prediction_type == "sample":
															raise NotImplementedError("prediction_type not implemented yet: sample")
									else:
															raise ValueError(
															    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`")

									SCREAMING_SNAKE_CASE_:				Union[str, Any]							= self.sigmas[step_index]
									SCREAMING_SNAKE_CASE_:				Tuple							= self.sigmas[step_index + 1]
									SCREAMING_SNAKE_CASE_:				Union[str, Any]							= (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
									SCREAMING_SNAKE_CASE_:				List[str]							= (sigma_to**2 - sigma_up**2) ** 0.5

									# 2. Convert to an ODE derivative
									SCREAMING_SNAKE_CASE_:				int							= (sample - pred_original_sample) / sigma

									SCREAMING_SNAKE_CASE_:				List[str]							= sigma_down - sigma

									SCREAMING_SNAKE_CASE_:				Optional[Any]							= sample + derivative * dt

									SCREAMING_SNAKE_CASE_:				Any							= model_output.device
									SCREAMING_SNAKE_CASE_:				Union[str, Any]							= randn_tensor(model_output.shape     ,		dtype=model_output.dtype     ,		device=lowerCAmelCase__     ,		generator=lowerCAmelCase__)

									SCREAMING_SNAKE_CASE_:				Dict							= prev_sample + noise * sigma_up

									if not return_dict:
															return (prev_sample,)

									return EulerAncestralDiscreteSchedulerOutput(
									    prev_sample=lowerCAmelCase__     ,		pred_original_sample=lowerCAmelCase__)



			def  _SCREAMING_SNAKE_CASE    (				self						:  Any     ,		lowerCAmelCase__						:  torch.FloatTensor     ,		lowerCAmelCase__						:  torch.FloatTensor     ,		lowerCAmelCase__						:  torch.FloatTensor     ,		):
									# Make sure sigmas and timesteps have the same device and dtype as original_samples
									SCREAMING_SNAKE_CASE_:				Optional[int]							= self.sigmas.to(device=original_samples.device     ,		dtype=original_samples.dtype)
									if original_samples.device.type == "mps" and torch.is_floating_point(lowerCAmelCase__):
															# mps does not support float64
															SCREAMING_SNAKE_CASE_:				Union[str, Any]							= self.timesteps.to(original_samples.device     ,		dtype=torch.floataa)
															SCREAMING_SNAKE_CASE_:				List[str]							= timesteps.to(original_samples.device     ,		dtype=torch.floataa)
									else:
															SCREAMING_SNAKE_CASE_:				int							= self.timesteps.to(original_samples.device)
															SCREAMING_SNAKE_CASE_:				Dict							= timesteps.to(original_samples.device)

									SCREAMING_SNAKE_CASE_:				Optional[Any]							= [(schedule_timesteps == t).nonzero().item() for t in timesteps]

									SCREAMING_SNAKE_CASE_:				List[Any]							= sigmas[step_indices].flatten()
									while len(sigma.shape) < len(original_samples.shape):
															SCREAMING_SNAKE_CASE_:				int							= sigma.unsqueeze(-1)

									SCREAMING_SNAKE_CASE_:				str							= original_samples + noise * sigma
									return noisy_samples




			def __len__(				self						:  int):
									return self.config.num_train_timesteps






