






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

import numpy as np
import torch
from scipy import integrate

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




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 							__A	(     a					):





				"""simple docstring"""







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






def 				A	(			a_				,a_=0.999				,a_="cosine"				,)	->		str:
					if alpha_transform_type == "cosine":

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

					elif alpha_transform_type == "exp":

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

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

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




class 							__A	(     a ,	a					):





				"""simple docstring"""







				UpperCamelCase__					: int     					=[e.name for e in KarrasDiffusionSchedulers]
				UpperCamelCase__					: Tuple     					=1


				@register_to_config
				def __init__(					self				,    lowerCamelCase__ = 1000				,    lowerCamelCase__ = 0.0_001				,    lowerCamelCase__ = 0.02				,    lowerCamelCase__ = "linear"				,    lowerCamelCase__ = None				,    lowerCamelCase__ = False				,    lowerCamelCase__ = "epsilon"				,    lowerCamelCase__ = "linspace"				,    lowerCamelCase__ = 0				,    ):




									"""simple docstring"""

									if trained_betas is not None:
														__UpperCamelCase :   Dict									=torch.tensor(lowerCamelCase__				,    dtype=torch.floataa       )
									elif beta_schedule == "linear":
														__UpperCamelCase :   Tuple									=torch.linspace(lowerCamelCase__				,    lowerCamelCase__				,    lowerCamelCase__				,    dtype=torch.floataa       )
									elif beta_schedule == "scaled_linear":
														# this schedule is very specific to the latent diffusion model.
														__UpperCamelCase :   int									=(
														    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 :   Any									=betas_for_alpha_bar(lowerCamelCase__       )
									else:
														raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'       )

									__UpperCamelCase :   List[Any]									=1.0 - self.betas
									__UpperCamelCase :   Union[str, Any]									=torch.cumprod(self.alphas				,    dim=0       )

									__UpperCamelCase :   Any									=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
									__UpperCamelCase :   int									=np.concatenate([sigmas[::-1], [0.0]]       ).astype(np.floataa       )
									__UpperCamelCase :   List[Any]									=torch.from_numpy(lowerCamelCase__       )

									# setable values
									__UpperCamelCase :   List[Any]									=None
									__UpperCamelCase :   Optional[int]									=use_karras_sigmas
									self.set_timesteps(lowerCamelCase__				,    lowerCamelCase__       )
									__UpperCamelCase :   Optional[Any]									=[]
									__UpperCamelCase :   int									=False


				@property
				def  __lowercase				(					self       ):




									"""simple docstring"""

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

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


				def  __lowercase				(					self				,    lowerCamelCase__				,    lowerCamelCase__       ):




									"""simple docstring"""

									if isinstance(lowerCamelCase__				,    torch.Tensor       ):
														__UpperCamelCase :   Tuple									=timestep.to(self.timesteps.device       )
									__UpperCamelCase :   Tuple									=(self.timesteps == timestep).nonzero().item()
									__UpperCamelCase :   Dict									=self.sigmas[step_index]
									__UpperCamelCase :   Union[str, Any]									=sample / ((sigma**2 + 1) ** 0.5)
									__UpperCamelCase :   int									=True
									return sample


				def  __lowercase				(					self				,    lowerCamelCase__				,    lowerCamelCase__				,    lowerCamelCase__       ):




									"""simple docstring"""

									def lms_derivative(lowerCamelCase__       ):
														__UpperCamelCase :   Dict									=1.0
														for k in range(lowerCamelCase__       ):
																			if current_order == k:
																								continue
																			prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
														return prod

									__UpperCamelCase :   int									=integrate.quad(lowerCamelCase__				,    self.sigmas[t]				,    self.sigmas[t + 1]				,    epsrel=1E-4       )[0]

									return integrated_coeff


				def  __lowercase				(					self				,    lowerCamelCase__				,    lowerCamelCase__ = None       ):




									"""simple docstring"""

									__UpperCamelCase :   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":
														__UpperCamelCase :   Dict									=np.linspace(0				,    self.config.num_train_timesteps - 1				,    lowerCamelCase__				,    dtype=lowerCamelCase__       )[
														    ::-1
														].copy()
									elif self.config.timestep_spacing == "leading":
														__UpperCamelCase :   List[str]									=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 :   Dict									=(np.arange(0				,    lowerCamelCase__       ) * step_ratio).round()[::-1].copy().astype(lowerCamelCase__       )
														timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
														__UpperCamelCase :   Tuple									=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 :   Optional[Any]									=(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 :   str									=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
									__UpperCamelCase :   List[str]									=np.log(lowerCamelCase__       )
									__UpperCamelCase :   Optional[Any]									=np.interp(lowerCamelCase__				,    np.arange(0				,    len(lowerCamelCase__       )       )				,    lowerCamelCase__       )

									if self.use_karras_sigmas:
														__UpperCamelCase :   str									=self._convert_to_karras(in_sigmas=lowerCamelCase__       )
														__UpperCamelCase :   Dict									=np.array([self._sigma_to_t(lowerCamelCase__				,    lowerCamelCase__       ) for sigma in sigmas]       )

									__UpperCamelCase :   Optional[Any]									=np.concatenate([sigmas, [0.0]]       ).astype(np.floataa       )

									__UpperCamelCase :   Optional[Any]									=torch.from_numpy(lowerCamelCase__       ).to(device=lowerCamelCase__       )
									if str(lowerCamelCase__       ).startswith('mps'       ):
														# mps does not support float64
														__UpperCamelCase :   Any									=torch.from_numpy(lowerCamelCase__       ).to(lowerCamelCase__				,    dtype=torch.floataa       )
									else:
														__UpperCamelCase :   Tuple									=torch.from_numpy(lowerCamelCase__       ).to(device=lowerCamelCase__       )

									__UpperCamelCase :   Dict									=[]


				def  __lowercase				(					self				,    lowerCamelCase__				,    lowerCamelCase__       ):




									"""simple docstring"""

									__UpperCamelCase :   str									=np.log(lowerCamelCase__       )

									# get distribution
									__UpperCamelCase :   List[Any]									=log_sigma - log_sigmas[:, np.newaxis]

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

									__UpperCamelCase :   Tuple									=log_sigmas[low_idx]
									__UpperCamelCase :   List[Any]									=log_sigmas[high_idx]

									# interpolate sigmas
									__UpperCamelCase :   Any									=(low - log_sigma) / (low - high)
									__UpperCamelCase :   Any									=np.clip(lowerCamelCase__				,    0				,    1       )

									# transform interpolation to time range
									__UpperCamelCase :   Optional[Any]									=(1 - w) * low_idx + w * high_idx
									__UpperCamelCase :   Optional[int]									=t.reshape(sigma.shape       )
									return t


				def  __lowercase				(					self				,    lowerCamelCase__       ):




									"""simple docstring"""

									__UpperCamelCase :   float									=in_sigmas[-1].item()
									__UpperCamelCase :   float									=in_sigmas[0].item()

									__UpperCamelCase :   Tuple									=7.0  # 7.0 is the value used in the paper
									__UpperCamelCase :   int									=np.linspace(0				,    1				,    self.num_inference_steps       )
									__UpperCamelCase :   Union[str, Any]									=sigma_min ** (1 / rho)
									__UpperCamelCase :   int									=sigma_max ** (1 / rho)
									__UpperCamelCase :   List[str]									=(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
									return sigmas


				def  __lowercase				(					self				,    lowerCamelCase__				,    lowerCamelCase__				,    lowerCamelCase__				,    lowerCamelCase__ = 4				,    lowerCamelCase__ = True				,    ):




									"""simple docstring"""

									if not self.is_scale_input_called:
														warnings.warn(
														    '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 :   Optional[int]									=timestep.to(self.timesteps.device       )
									__UpperCamelCase :   Optional[Any]									=(self.timesteps == timestep).nonzero().item()
									__UpperCamelCase :   Union[str, Any]									=self.sigmas[step_index]

									# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
									if self.config.prediction_type == "epsilon":
														__UpperCamelCase :   Optional[int]									=sample - sigma * model_output
									elif self.config.prediction_type == "v_prediction":
														# * c_out + input * c_skip
														__UpperCamelCase :   Tuple									=model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
									elif self.config.prediction_type == "sample":
														__UpperCamelCase :   int									=model_output
									else:
														raise ValueError(
														    f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'       )

									# 2. Convert to an ODE derivative
									__UpperCamelCase :   Optional[int]									=(sample - pred_original_sample) / sigma
									self.derivatives.append(lowerCamelCase__       )
									if len(self.derivatives       ) > order:
														self.derivatives.pop(0       )

									# 3. Compute linear multistep coefficients
									__UpperCamelCase :   Optional[Any]									=min(step_index + 1				,    lowerCamelCase__       )
									__UpperCamelCase :   Optional[int]									=[self.get_lms_coefficient(lowerCamelCase__				,    lowerCamelCase__				,    lowerCamelCase__       ) for curr_order in range(lowerCamelCase__       )]

									# 4. Compute previous sample based on the derivatives path
									__UpperCamelCase :   List[str]									=sample + sum(
									    coeff * derivative for coeff, derivative in zip(lowerCamelCase__				,    reversed(self.derivatives       )       )       )

									if not return_dict:
														return (prev_sample,)

									return LMSDiscreteSchedulerOutput(prev_sample=lowerCamelCase__				,    pred_original_sample=lowerCamelCase__       )


				def  __lowercase				(					self				,    lowerCamelCase__				,    lowerCamelCase__				,    lowerCamelCase__				,    ):




									"""simple docstring"""

									__UpperCamelCase :   Dict									=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 :   Dict									=self.timesteps.to(original_samples.device				,    dtype=torch.floataa       )
														__UpperCamelCase :   int									=timesteps.to(original_samples.device				,    dtype=torch.floataa       )
									else:
														__UpperCamelCase :   List[str]									=self.timesteps.to(original_samples.device       )
														__UpperCamelCase :   List[Any]									=timesteps.to(original_samples.device       )

									__UpperCamelCase :   List[Any]									=[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

									__UpperCamelCase :   Union[str, Any]									=original_samples + noise * sigma
									return noisy_samples







				def __len__(					self       ):




									"""simple docstring"""

									return self.config.num_train_timesteps









from __future__ import annotations






def 				A	(			a_				,a_   )	->		list[int]:
					__UpperCamelCase :   dict[int, int]									={}
					for index, val in enumerate(a_   ):
										__UpperCamelCase :   Union[str, Any]									=target - val
										if compl in chk_map:
															return [chk_map[compl], index]
										__UpperCamelCase :   List[Any]									=index
					return []


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(f"{two_sum([2, 7, 11, 15], 9) = }")

