




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 (_lowerCAmelCase	,     _lowerCAmelCase=0.999	,     _lowerCAmelCase="cosine"	,     ):






							if alpha_transform_type == "cosine":

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

							elif alpha_transform_type == "exp":

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

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

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






class 			__magic_name__    (	__UpperCAmelCase     ,	__UpperCAmelCase):
				'''simple docstring'''







				SCREAMING_SNAKE_CASE__       :				str						   =       [e.name for e in KarrasDiffusionSchedulers]
				SCREAMING_SNAKE_CASE__       :				str						   =       2


				@register_to_config
				def __init__(				self: List[Any]		,       _lowerCamelCase: Optional[int] = 10_00		,       _lowerCamelCase: Dict = 0.0_00_85		,       _lowerCamelCase: List[str] = 0.0_12		,       _lowerCamelCase: Tuple = "linear"		,       _lowerCamelCase: Any = None		,       _lowerCamelCase: List[Any] = "epsilon"		,       _lowerCamelCase: List[str] = False		,       _lowerCamelCase: Dict = False		,       _lowerCamelCase: Optional[int] = 1.0		,       _lowerCamelCase: List[str] = "linspace"		,       _lowerCamelCase: Any = 0		,       ):
											if trained_betas is not None:
																		SCREAMING_SNAKE_CASE_ 						=     torch.tensor(_lowercase		,       dtype=torch.floataa		)
											elif beta_schedule == "linear":
																		SCREAMING_SNAKE_CASE_ 						=     torch.linspace(_lowercase		,       _lowercase		,       _lowercase		,       dtype=torch.floataa		)
											elif beta_schedule == "scaled_linear":
																		# this schedule is very specific to the latent diffusion model.
																		SCREAMING_SNAKE_CASE_ 						=     (
																		    torch.linspace(beta_start**0.5		,       beta_end**0.5		,       _lowercase		,       dtype=torch.floataa		) ** 2
																		)
											elif beta_schedule == "squaredcos_cap_v2":
																		# Glide cosine schedule
																		SCREAMING_SNAKE_CASE_ 						=     betas_for_alpha_bar(_lowercase		,       alpha_transform_type='''cosine'''		)
											elif beta_schedule == "exp":
																		SCREAMING_SNAKE_CASE_ 						=     betas_for_alpha_bar(_lowercase		,       alpha_transform_type='''exp'''		)
											else:
																		raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"		)

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

											#  set all values
											self.set_timesteps(_lowercase		,       _lowercase		,       _lowercase		)
											SCREAMING_SNAKE_CASE_ 						=     use_karras_sigmas


				def      _A				(				self: Any		,       _lowerCamelCase: Tuple		,       _lowerCamelCase: Optional[Any]=None		):
											if schedule_timesteps is None:
																		SCREAMING_SNAKE_CASE_ 						=     self.timesteps

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

											return indices[pos].item()


				@property
				def      _A				(				self: 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      _A				(				self: List[str]		,       _lowerCamelCase: Optional[Any]		,       _lowerCamelCase: Any		,       ):
											SCREAMING_SNAKE_CASE_ 						=     self.index_for_timestep(_lowercase		)

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


				def      _A				(				self: str		,       _lowerCamelCase: List[Any]		,       _lowerCamelCase: List[Any] = None		,       _lowerCamelCase: Tuple = None		,       ):
											SCREAMING_SNAKE_CASE_ 						=     num_inference_steps

											SCREAMING_SNAKE_CASE_ 						=     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":
																		SCREAMING_SNAKE_CASE_ 						=     np.linspace(0		,       num_train_timesteps - 1		,       _lowercase		,       dtype=_lowercase		)[::-1].copy()
											elif self.config.timestep_spacing == "leading":
																		SCREAMING_SNAKE_CASE_ 						=     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_ 						=     (np.arange(0		,       _lowercase		) * step_ratio).round()[::-1].copy().astype(_lowercase		)
																		timesteps += self.config.steps_offset
											elif self.config.timestep_spacing == "trailing":
																		SCREAMING_SNAKE_CASE_ 						=     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_ 						=     (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'."		)

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

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

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

											SCREAMING_SNAKE_CASE_ 						=     torch.from_numpy(_lowercase		)
											SCREAMING_SNAKE_CASE_ 						=     torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2		)]		)

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

											# empty dt and derivative
											SCREAMING_SNAKE_CASE_ 						=     None
											SCREAMING_SNAKE_CASE_ 						=     None

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


				def      _A				(				self: Union[str, Any]		,       _lowerCamelCase: str		,       _lowerCamelCase: List[str]		):
											# get log sigma
											SCREAMING_SNAKE_CASE_ 						=     np.log(_lowercase		)

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

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

											SCREAMING_SNAKE_CASE_ 						=     log_sigmas[low_idx]
											SCREAMING_SNAKE_CASE_ 						=     log_sigmas[high_idx]

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

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


				def      _A				(				self: Optional[int]		,       _lowerCamelCase: Any		,       _lowerCamelCase: Tuple		):
											SCREAMING_SNAKE_CASE_ 						=     in_sigmas[-1].item()
											SCREAMING_SNAKE_CASE_ 						=     in_sigmas[0].item()

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


				@property
				def      _A				(				self: Dict		):
											return self.dt is None


				def      _A				(				self: Union[str, Any]		,       _lowerCamelCase: Union[str, Any]		,       _lowerCamelCase: str		,       _lowerCamelCase: Union[str, Any]		,       _lowerCamelCase: Union[str, Any] = True		,       ):
											SCREAMING_SNAKE_CASE_ 						=     self.index_for_timestep(_lowercase		)

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

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

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

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

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

											SCREAMING_SNAKE_CASE_ 						=     sample + derivative * dt

											if not return_dict:
																		return (prev_sample,)

											return SchedulerOutput(prev_sample=_lowercase		)


				def      _A				(				self: Optional[Any]		,       _lowerCamelCase: int		,       _lowerCamelCase: List[Any]		,       _lowerCamelCase: Optional[Any]		,       ):
											# Make sure sigmas and timesteps have the same device and dtype as original_samples
											SCREAMING_SNAKE_CASE_ 						=     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
																		SCREAMING_SNAKE_CASE_ 						=     self.timesteps.to(original_samples.device		,       dtype=torch.floataa		)
																		SCREAMING_SNAKE_CASE_ 						=     timesteps.to(original_samples.device		,       dtype=torch.floataa		)
											else:
																		SCREAMING_SNAKE_CASE_ 						=     self.timesteps.to(original_samples.device		)
																		SCREAMING_SNAKE_CASE_ 						=     timesteps.to(original_samples.device		)

											SCREAMING_SNAKE_CASE_ 						=     [self.index_for_timestep(_lowercase		,       _lowercase		) for t in timesteps]

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

											SCREAMING_SNAKE_CASE_ 						=     original_samples + noise * sigma
											return noisy_samples





				def __len__(				self: Optional[Any]		):
											return self.config.num_train_timesteps





import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest






class 						__magic_name__					(							snake_case				):
     UpperCamelCase_	:Dict										=      (KDPMaDiscreteScheduler,)
     UpperCamelCase_	:str										=      1_0






     def 	UpperCAmelCase_				(				self		,						**_lowercase	)->     str:
         UpperCamelCase_			  =						{
             "num_train_timesteps": 1_100,
             "beta_start": 0.0_001,
             "beta_end": 0.02,
             "beta_schedule": "linear",
         }

         config.update(**_lowercase	)
         return config






     def 	UpperCAmelCase_				(				self	)->     Union[str, Any]:
         for timesteps in [10, 50, 100, 1_000]:
             self.check_over_configs(num_train_timesteps=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     int:
         for beta_start, beta_end in zip([0.00_001, 0.0_001, 0.001]		,						[0.0_002, 0.002, 0.02]	):
             self.check_over_configs(beta_start=_lowercase		,						beta_end=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     str:
         for schedule in ["linear", "scaled_linear"]:
             self.check_over_configs(beta_schedule=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     Any:
         for prediction_type in ["epsilon", "v_prediction"]:
             self.check_over_configs(prediction_type=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     Optional[int]:
         UpperCamelCase_			  =						self.scheduler_classes[0]
         UpperCamelCase_			  =						self.get_scheduler_config(prediction_type="v_prediction"	)
         UpperCamelCase_			  =						scheduler_class(**_lowercase	)

         scheduler.set_timesteps(self.num_inference_steps	)

         UpperCamelCase_			  =						self.dummy_model()
         UpperCamelCase_			  =						self.dummy_sample_deter * scheduler.init_noise_sigma
         UpperCamelCase_			  =						sample.to(_lowercase	)

         for i, t in enumerate(scheduler.timesteps	):
             UpperCamelCase_			  =						scheduler.scale_model_input(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						model(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						scheduler.step(_lowercase		,						_lowercase		,						_lowercase	)
             UpperCamelCase_			  =						output.prev_sample

         UpperCamelCase_			  =						torch.sum(torch.abs(_lowercase	)	)
         UpperCamelCase_			  =						torch.mean(torch.abs(_lowercase	)	)

         if torch_device in ["cpu", "mps"]:
             assert abs(result_sum.item() - 4.6_9_3_4e-0_7	) < 1e-2
             assert abs(result_mean.item() - 6.1_1_1_2e-1_0	) < 1e-3
         else:
             # CUDA
             assert abs(result_sum.item() - 4.6_9_3_4_2_8_6_5_0_1_7_0_9_7_2e-0_7	) < 1e-2
             assert abs(result_mean.item() - 0.0_002	) < 1e-3






     def 	UpperCAmelCase_				(				self	)->     Dict:
         if torch_device == "mps":
             return
         UpperCamelCase_			  =						self.scheduler_classes[0]
         UpperCamelCase_			  =						self.get_scheduler_config()
         UpperCamelCase_			  =						scheduler_class(**_lowercase	)

         scheduler.set_timesteps(self.num_inference_steps	)

         UpperCamelCase_			  =						self.dummy_model()
         UpperCamelCase_			  =						self.dummy_sample_deter * scheduler.init_noise_sigma
         UpperCamelCase_			  =						sample.to(_lowercase	)

         for i, t in enumerate(scheduler.timesteps	):
             UpperCamelCase_			  =						scheduler.scale_model_input(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						model(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						scheduler.step(_lowercase		,						_lowercase		,						_lowercase	)
             UpperCamelCase_			  =						output.prev_sample

         UpperCamelCase_			  =						torch.sum(torch.abs(_lowercase	)	)
         UpperCamelCase_			  =						torch.mean(torch.abs(_lowercase	)	)

         if torch_device in ["cpu", "mps"]:
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3
         else:
             # CUDA
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3






     def 	UpperCAmelCase_				(				self	)->     Optional[int]:
         if torch_device == "mps":
             return
         UpperCamelCase_			  =						self.scheduler_classes[0]
         UpperCamelCase_			  =						self.get_scheduler_config()
         UpperCamelCase_			  =						scheduler_class(**_lowercase	)

         scheduler.set_timesteps(self.num_inference_steps		,						device=_lowercase	)

         UpperCamelCase_			  =						self.dummy_model()
         UpperCamelCase_			  =						self.dummy_sample_deter.to(_lowercase	) * scheduler.init_noise_sigma

         for t in scheduler.timesteps:
             UpperCamelCase_			  =						scheduler.scale_model_input(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						model(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						scheduler.step(_lowercase		,						_lowercase		,						_lowercase	)
             UpperCamelCase_			  =						output.prev_sample

         UpperCamelCase_			  =						torch.sum(torch.abs(_lowercase	)	)
         UpperCamelCase_			  =						torch.mean(torch.abs(_lowercase	)	)

         if str(_lowercase	).startswith("cpu"	):
             # The following sum varies between 148 and 156 on mps. Why?
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3
         else:
             # CUDA
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3
