
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     __lowerCAmelCase			(			a__						,    a__=0.999						,    a__="cosine"						,    )       ->  Optional[int]:
				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}"""  )

				__a										=    []
				for i in range(a__  ):
								__a										=    i / num_diffusion_timesteps
								__a										=    (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			):
				snake_case_						   =    [e.name for e in KarrasDiffusionSchedulers]
				snake_case_						   =    2




				@register_to_config
				def __init__(     self		,     _snake_case = 1_000		,     _snake_case = 0.0_0085		,     _snake_case = 0.012		,     _snake_case = "linear"		,     _snake_case = None		,     _snake_case = "epsilon"		,     _snake_case = False		,     _snake_case = False		,     _snake_case = 1.0		,     _snake_case = "linspace"		,     _snake_case = 0		,     )    ->      Dict:


								'''simple docstring'''




								if trained_betas is not None:
												__a										=    torch.tensor(_snake_case		,     dtype=torch.floataa				)
								elif beta_schedule == "linear":
												__a										=    torch.linspace(_snake_case		,     _snake_case		,     _snake_case		,     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		,     _snake_case		,     dtype=torch.floataa				) ** 2
												)
								elif beta_schedule == "squaredcos_cap_v2":
												# Glide cosine schedule
												__a										=    betas_for_alpha_bar(_snake_case		,     alpha_transform_type='''cosine'''				)
								elif beta_schedule == "exp":
												__a										=    betas_for_alpha_bar(_snake_case		,     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(_snake_case		,     _snake_case		,     _snake_case				)
								__a										=    use_karras_sigmas




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case=None				)    ->      List[Any]:


								'''simple docstring'''




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

								return indices[pos].item()




				@property
				def 				SCREAMING_SNAKE_CASE_		(     self				)    ->      Any:


								'''simple docstring'''




								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		,     _snake_case		,     _snake_case		,     )    ->      torch.FloatTensor:


								'''simple docstring'''




								__a										=    self.index_for_timestep(_snake_case				)

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




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case = None		,     _snake_case = None		,     )    ->      Any:


								'''simple docstring'''




								__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		,     _snake_case		,     dtype=_snake_case				)[::-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		,     _snake_case				) * step_ratio).round()[::-1].copy().astype(_snake_case				)
												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(_snake_case		,     0		,     -step_ratio				)).round().copy().astype(_snake_case				)
												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(_snake_case				)
								__a										=    np.interp(_snake_case		,     np.arange(0		,     len(_snake_case				)				)		,     _snake_case				)

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

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

								__a										=    torch.from_numpy(_snake_case				)
								__a										=    torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2				)]				)

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

								# 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(_snake_case				)




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      Optional[int]:


								'''simple docstring'''




								__a										=    np.log(_snake_case				)

								# 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(_snake_case		,     0		,     1				)

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




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      torch.FloatTensor:


								'''simple docstring'''




								__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		,     _snake_case				)
								__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 				SCREAMING_SNAKE_CASE_		(     self				)    ->      Optional[Any]:


								'''simple docstring'''




								return self.dt is None




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case		,     _snake_case		,     _snake_case = True		,     )    ->      Union[SchedulerOutput, Tuple]:


								'''simple docstring'''




								__a										=    self.index_for_timestep(_snake_case				)

								# advance index counter by 1
								__a										=    timestep.cpu().item() if torch.is_tensor(_snake_case				) 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=_snake_case				)




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case		,     _snake_case		,     )    ->      torch.FloatTensor:


								'''simple docstring'''




								__a										=    self.sigmas.to(device=original_samples.device		,     dtype=original_samples.dtype				)
								if original_samples.device.type == "mps" and torch.is_floating_point(_snake_case				):
												# 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(_snake_case		,     _snake_case				) 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				)    ->      List[Any]:


								'''simple docstring'''




								return self.config.num_train_timesteps

def     __lowerCAmelCase			(			a__						,    a__						,    a__  )       ->  list:
				__a										=    len(a__  )
				__a										=    [[0] * n for i in range(a__  )]
				for i in range(a__  ):
								__a										=    y_points[i]

				for i in range(2						,    a__  ):
								for j in range(a__						,    a__  ):
												__a										=    (
												    (xa - x_points[j - i + 1]) * q[j][i - 1]
												    - (xa - x_points[j]) * q[j - 1][i - 1]
												) / (x_points[j] - x_points[j - i + 1])

				return [q[n - 1][n - 1], q]


if __name__ == "__main__":
					import doctest

					doctest.testmod()