


"""simple docstring"""







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


__a			 =   logging.get_logger(__name__)  # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 							lowerCamelCase       (			__SCREAMING_SNAKE_CASE ):


							"""simple docstring"""
							SCREAMING_SNAKE_CASE										=      42
							SCREAMING_SNAKE_CASE										=      None






def 					a__ (       _UpperCamelCase	,			_UpperCamelCase=0.999	,			_UpperCamelCase="cosine"	,			):





						"""simple docstring"""

						if alpha_transform_type == "cosine":

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

						elif alpha_transform_type == "exp":

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

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

						UpperCAmelCase__		=    []
						for i in range(_UpperCamelCase ):
												UpperCAmelCase__		=    i / num_diffusion_timesteps
												UpperCAmelCase__		=    (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 							lowerCamelCase       (			__SCREAMING_SNAKE_CASE				,					__SCREAMING_SNAKE_CASE ):


							"""simple docstring"""
							SCREAMING_SNAKE_CASE										=      [e.name for e in KarrasDiffusionSchedulers]
							SCREAMING_SNAKE_CASE										=      1






							@register_to_config
							def __init__(						self :     Dict		, 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:
																			UpperCAmelCase__		=    torch.tensor(lowerCamelCase_		, dtype=torch.floataa				)
													elif beta_schedule == "linear":
																			UpperCAmelCase__		=    torch.linspace(lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, 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		, lowerCamelCase_		, dtype=torch.floataa				) ** 2
																			)
													elif beta_schedule == "squaredcos_cap_v2":
																			# Glide cosine schedule
																			UpperCAmelCase__		=    betas_for_alpha_bar(lowerCamelCase_				)
													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				)

													UpperCAmelCase__		=    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
													UpperCAmelCase__		=    np.concatenate([sigmas[::-1], [0.0]]				).astype(np.floataa				)
													UpperCAmelCase__		=    torch.from_numpy(lowerCamelCase_				)

													# setable values
													UpperCAmelCase__		=    None
													UpperCAmelCase__		=    np.linspace(0		, num_train_timesteps - 1		, lowerCamelCase_		, dtype=lowerCamelCase_				)[::-1].copy()
													UpperCAmelCase__		=    torch.from_numpy(lowerCamelCase_				)
													UpperCAmelCase__		=    False






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






							def 					lowerCAmelCase     (						self :     List[Any]		, lowerCamelCase_ :     int		, lowerCamelCase_ :     Union[str, torch.device] = None				):
													UpperCAmelCase__		=    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":
																			UpperCAmelCase__		=    np.linspace(0		, self.config.num_train_timesteps - 1		, lowerCamelCase_		, dtype=lowerCamelCase_				)[
																			    ::-1
																			].copy()
													elif self.config.timestep_spacing == "leading":
																			UpperCAmelCase__		=    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
																			UpperCAmelCase__		=    (np.arange(0		, lowerCamelCase_				) * step_ratio).round()[::-1].copy().astype(lowerCamelCase_				)
																			timesteps += self.config.steps_offset
													elif self.config.timestep_spacing == "trailing":
																			UpperCAmelCase__		=    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
																			UpperCAmelCase__		=    (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'."""				)

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






							def 					lowerCAmelCase     (						self :     List[str]		, 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				):
																			UpperCAmelCase__		=    timestep.to(self.timesteps.device				)

													UpperCAmelCase__		=    (self.timesteps == timestep).nonzero().item()
													UpperCAmelCase__		=    self.sigmas[step_index]

													# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
													if self.config.prediction_type == "epsilon":
																			UpperCAmelCase__		=    sample - sigma * model_output
													elif self.config.prediction_type == "v_prediction":
																			# * c_out + input * c_skip
																			UpperCAmelCase__		=    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`"""				)

													UpperCAmelCase__		=    self.sigmas[step_index]
													UpperCAmelCase__		=    self.sigmas[step_index + 1]
													UpperCAmelCase__		=    (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
													UpperCAmelCase__		=    (sigma_to**2 - sigma_up**2) ** 0.5

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

													UpperCAmelCase__		=    sigma_down - sigma

													UpperCAmelCase__		=    sample + derivative * dt

													UpperCAmelCase__		=    model_output.device
													UpperCAmelCase__		=    randn_tensor(model_output.shape		, dtype=model_output.dtype		, device=lowerCamelCase_		, generator=lowerCamelCase_				)

													UpperCAmelCase__		=    prev_sample + noise * sigma_up

													if not return_dict:
																			return (prev_sample,)

													return EulerAncestralDiscreteSchedulerOutput(
													    prev_sample=lowerCamelCase_		, pred_original_sample=lowerCamelCase_				)






							def 					lowerCAmelCase     (						self :     int		, lowerCamelCase_ :     torch.FloatTensor		, lowerCamelCase_ :     torch.FloatTensor		, lowerCamelCase_ :     torch.FloatTensor		, ):
													# Make sure sigmas and timesteps have the same device and dtype as original_samples
													UpperCAmelCase__		=    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
																			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__		=    [(schedule_timesteps == t).nonzero().item() 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 :     Optional[int]				):
													return self.config.num_train_timesteps



"""simple docstring"""







from __future__ import annotations

from collections.abc import Callable






def 					a__ (       _UpperCamelCase	,			_UpperCamelCase	,			_UpperCamelCase	,			_UpperCamelCase = 100	,			):





						"""simple docstring"""

						UpperCAmelCase__		=    x_start
						UpperCAmelCase__		=    fnc(_UpperCamelCase )
						UpperCAmelCase__		=    0.0

						for _ in range(_UpperCamelCase ):
												# Approximates small segments of curve as linear and solve
												# for trapezoidal area
												UpperCAmelCase__		=    (x_end - x_start) / steps + xa
												UpperCAmelCase__		=    fnc(_UpperCamelCase )
												area += abs(fxa + fxa ) * (xa - xa) / 2

												# Increment step
												UpperCAmelCase__		=    xa
												UpperCAmelCase__		=    fxa
						return area


if __name__ == "__main__":






						def 					a__ (       _UpperCamelCase ):





												"""simple docstring"""

												return x**3

						print("f(x) = x^3")
						print("The area between the curve, x = -10, x = 10 and the x axis is:")
						__a			 =   10
						while i <= 10_00_00:
												__a			 =   trapezoidal_area(f, -5, 5, i)
												print(f'''with {i} steps: {area}''')
												i *= 10