


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 ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput



def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				Optional[Any]    ,		_UpperCamelCase      :				int=0.9_9_9    ,		_UpperCamelCase      :				Union[str, Any]="cosine"    ,		)		->					List[Any]:





   '''simple docstring'''







   if alpha_transform_type == "cosine":

      def alpha_bar_fn(_UpperCamelCase      :				Union[str, Any]   ):
         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      :				Optional[int]   ):
         return math.exp(t * -1_2.0   )

   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  UpperCAmelCase (       SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__):
 _lowerCamelCase :					Optional[Any]    					=					[e.name for e in KarrasDiffusionSchedulers]
 _lowerCamelCase :					Optional[int]    					=					2

 @register_to_config
 def __init__( self :	List[str],					a_ :	Optional[Any] = 1000,					a_ :	Optional[int] = 0.00_085,					a_ :	Optional[int] = 0.012,					a_ :	str = "linear",					a_ :	Tuple = None,					a_ :	Optional[int] = "epsilon",					a_ :	str = "linspace",					a_ :	int = 0,					):





    """simple docstring"""



    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					)

    #  set all values
    self.set_timesteps(__lowerCamelCase,					__lowerCamelCase,					__lowerCamelCase					)

 def 		lowercase_						( self :	List[str],					a_ :	Dict,					a_ :	List[Any]=None					):





    """simple docstring"""



    if schedule_timesteps is None:
       UpperCamelCase__ 						=						self.timesteps

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

    return indices[pos].item()

 @property
 def 		lowercase_						( self :	Optional[Any]					):





    """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 :	Any,					a_ :	Union[str, Any],					a_ :	List[Any],					):





    """simple docstring"""



    UpperCamelCase__ 						=						self.index_for_timestep(__lowerCamelCase					)

    if self.state_in_first_order:
       UpperCamelCase__ 						=						self.sigmas[step_index]
    else:
       UpperCamelCase__ 						=						self.sigmas_interpol[step_index - 1]

    UpperCamelCase__ 						=						sample / ((sigma**2 + 1) ** 0.5)
    return sample

 def 		lowercase_						( self :	Optional[int],					a_ :	Tuple,					a_ :	int = None,					a_ :	Tuple = None,					):





    """simple docstring"""



    UpperCamelCase__ 						=						num_inference_steps

    UpperCamelCase__ 						=						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":
       UpperCamelCase__ 						=						np.linspace(0,					num_train_timesteps - 1,					__lowerCamelCase,					dtype=__lowerCamelCase					)[::-1].copy()
    elif self.config.timestep_spacing == "leading":
       UpperCamelCase__ 						=						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__ 						=						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(__lowerCamelCase,					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__ 						=						torch.from_numpy(np.log(__lowerCamelCase					)					).to(__lowerCamelCase					)

    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					)

    # compute up and down sigmas
    UpperCamelCase__ 						=						sigmas.roll(-1					)
    UpperCamelCase__ 						=						0.0
    UpperCamelCase__ 						=						(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
    UpperCamelCase__ 						=						(sigmas_next**2 - sigmas_up**2) ** 0.5
    UpperCamelCase__ 						=						0.0

    # compute interpolated sigmas
    UpperCamelCase__ 						=						sigmas.log().lerp(sigmas_down.log(),					0.5					).exp()
    UpperCamelCase__ 						=						0.0

    # set sigmas
    UpperCamelCase__ 						=						torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2					), sigmas[-1:]]					)
    UpperCamelCase__ 						=						torch.cat(
        [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2					), sigmas_interpol[-1:]]					)
    UpperCamelCase__ 						=						torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2					), sigmas_up[-1:]]					)
    UpperCamelCase__ 						=						torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2					), sigmas_down[-1:]]					)

    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(__lowerCamelCase					)

    UpperCamelCase__ 						=						self.sigma_to_t(__lowerCamelCase					).to(__lowerCamelCase,					dtype=timesteps.dtype					)
    UpperCamelCase__ 						=						torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None]),					dim=-1					).flatten()

    UpperCamelCase__ 						=						torch.cat([timesteps[:1], interleaved_timesteps]					)

    UpperCamelCase__ 						=						None

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

 def 		lowercase_						( self :	Optional[int],					a_ :	Dict					):





    """simple docstring"""



    UpperCamelCase__ 						=						sigma.log()

    # get distribution
    UpperCamelCase__ 						=						log_sigma - self.log_sigmas[:, None]

    # get sigmas range
    UpperCamelCase__ 						=						dists.ge(0					).cumsum(dim=0					).argmax(dim=0					).clamp(max=self.log_sigmas.shape[0] - 2					)
    UpperCamelCase__ 						=						low_idx + 1

    UpperCamelCase__ 						=						self.log_sigmas[low_idx]
    UpperCamelCase__ 						=						self.log_sigmas[high_idx]

    # interpolate sigmas
    UpperCamelCase__ 						=						(low - log_sigma) / (low - high)
    UpperCamelCase__ 						=						w.clamp(0,					1					)

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

 @property
 def 		lowercase_						( self :	Union[str, Any]					):





    """simple docstring"""



    return self.sample is None

 def 		lowercase_						( self :	Dict,					a_ :	int,					a_ :	str,					a_ :	int,					a_ :	Tuple = None,					a_ :	Any = True,					):





    """simple docstring"""



    UpperCamelCase__ 						=						self.index_for_timestep(__lowerCamelCase					)

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

    if self.state_in_first_order:
       UpperCamelCase__ 						=						self.sigmas[step_index]
       UpperCamelCase__ 						=						self.sigmas_interpol[step_index]
       UpperCamelCase__ 						=						self.sigmas_up[step_index]
       UpperCamelCase__ 						=						self.sigmas_down[step_index - 1]
    else:
       # 2nd order / KPDM2's method
       UpperCamelCase__ 						=						self.sigmas[step_index - 1]
       UpperCamelCase__ 						=						self.sigmas_interpol[step_index - 1]
       UpperCamelCase__ 						=						self.sigmas_up[step_index - 1]
       UpperCamelCase__ 						=						self.sigmas_down[step_index - 1]

    # 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
    UpperCamelCase__ 						=						0
    UpperCamelCase__ 						=						sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

    UpperCamelCase__ 						=						model_output.device
    UpperCamelCase__ 						=						randn_tensor(model_output.shape,					dtype=model_output.dtype,					device=__lowerCamelCase,					generator=__lowerCamelCase					)

    # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
    if self.config.prediction_type == "epsilon":
       UpperCamelCase__ 						=						sigma_hat if self.state_in_first_order else sigma_interpol
       UpperCamelCase__ 						=						sample - sigma_input * model_output
    elif self.config.prediction_type == "v_prediction":
       UpperCamelCase__ 						=						sigma_hat if self.state_in_first_order else sigma_interpol
       UpperCamelCase__ 						=						model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
           sample / (sigma_input**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`'					)

    if self.state_in_first_order:
       # 2. Convert to an ODE derivative for 1st order
       UpperCamelCase__ 						=						(sample - pred_original_sample) / sigma_hat
       # 3. delta timestep
       UpperCamelCase__ 						=						sigma_interpol - sigma_hat

       # store for 2nd order step
       UpperCamelCase__ 						=						sample
       UpperCamelCase__ 						=						dt
       UpperCamelCase__ 						=						sample + derivative * dt
    else:
       # DPM-Solver-2
       # 2. Convert to an ODE derivative for 2nd order
       UpperCamelCase__ 						=						(sample - pred_original_sample) / sigma_interpol
       # 3. delta timestep
       UpperCamelCase__ 						=						sigma_down - sigma_hat

       UpperCamelCase__ 						=						self.sample
       UpperCamelCase__ 						=						None

       UpperCamelCase__ 						=						sample + derivative * dt
       UpperCamelCase__ 						=						prev_sample + noise * sigma_up

    if not return_dict:
       return (prev_sample,)

    return SchedulerOutput(prev_sample=__lowerCamelCase					)

 def 		lowercase_						( self :	Any,					a_ :	int,					a_ :	Optional[Any],					a_ :	Optional[Any],					):





    """simple docstring"""



    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__ 						=						[self.index_for_timestep(__lowerCamelCase,					__lowerCamelCase					) 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 :	int					):





    """simple docstring"""



    return self.config.num_train_timesteps



'''simple docstring'''

def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				int = 10_00   )		->					int:





   '''simple docstring'''







   return sum(i for i in range(_UpperCamelCase   ) if i % 3 == 0 or i % 5 == 0   )


if __name__ == "__main__":
       print(F"""{solution() = }""")