
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 						__magic_name__			(   __a      :	Union[str, Any]	,		__a      :	List[Any]=0.999	,		__a      :	Union[str, Any]="cosine"	,		):



     '''simple docstring'''




     if alpha_transform_type == "cosine":

          def alpha_bar_fn(__a      :	Optional[Any]						):
               return math.cos((t + 0.008) / 1.008 * math.pi / 2						) ** 2

     elif alpha_transform_type == "exp":

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

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

     UpperCamelCase__				=    []
     for i in range(__a						):
          UpperCamelCase__				=    i / num_diffusion_timesteps
          UpperCamelCase__				=    (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(    UpperCAmelCase_    ,				UpperCAmelCase_			):

  """simple docstring"""
  SCREAMING_SNAKE_CASE__         =      [e.name for e in KarrasDiffusionSchedulers]
  SCREAMING_SNAKE_CASE__         =      2







  @register_to_config
  def __init__(self	,      SCREAMING_SNAKE_CASE_ = 10_00	,      SCREAMING_SNAKE_CASE_ = 0.0_0085	,      SCREAMING_SNAKE_CASE_ = 0.012	,      SCREAMING_SNAKE_CASE_ = "linear"	,      SCREAMING_SNAKE_CASE_ = None	,      SCREAMING_SNAKE_CASE_ = "epsilon"	,      SCREAMING_SNAKE_CASE_ = "linspace"	,      SCREAMING_SNAKE_CASE_ = 0	,      ):
       if trained_betas is not None:
            UpperCamelCase__				=    torch.tensor(__lowercase	,      dtype=torch.floataa						)
       elif beta_schedule == "linear":
            UpperCamelCase__				=    torch.linspace(__lowercase	,      __lowercase	,      __lowercase	,      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	,      __lowercase	,      dtype=torch.floataa						) ** 2
            )
       elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            UpperCamelCase__				=    betas_for_alpha_bar(__lowercase						)
       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(__lowercase	,      __lowercase	,      __lowercase						)







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_=None						):
       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(__lowercase						) > 1 else 0
       else:
            UpperCamelCase__				=    timestep.cpu().item() if torch.is_tensor(__lowercase						) else timestep
            UpperCamelCase__				=    self._index_counter[timestep_int]

       return indices[pos].item()







  @property
  def 	UpperCAmelCase_ (self						):
       # 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 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_	,      ):
       UpperCamelCase__				=    self.index_for_timestep(__lowercase						)

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

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







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_ = None	,      SCREAMING_SNAKE_CASE_ = None	,      ):
       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	,      __lowercase	,      dtype=__lowercase						)[::-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	,      __lowercase						) * step_ratio).round()[::-1].copy().astype(__lowercase						)
            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(__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'."						)

       UpperCamelCase__				=    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
       UpperCamelCase__				=    torch.from_numpy(np.log(__lowercase						)						).to(__lowercase						)

       UpperCamelCase__				=    np.interp(__lowercase	,      np.arange(0	,      len(__lowercase						)						)	,      __lowercase						)
       UpperCamelCase__				=    np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
       UpperCamelCase__				=    torch.from_numpy(__lowercase						).to(device=__lowercase						)

       # interpolate sigmas
       UpperCamelCase__				=    sigmas.log().lerp(sigmas.roll(1						).log()	,      0.5						).exp()

       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:]]						)

       if str(__lowercase						).startswith("""mps"""						):
            # mps does not support float64
            UpperCamelCase__				=    torch.from_numpy(__lowercase						).to(__lowercase	,      dtype=torch.floataa						)
       else:
            UpperCamelCase__				=    torch.from_numpy(__lowercase						).to(__lowercase						)

       # interpolate timesteps
       UpperCamelCase__				=    self.sigma_to_t(__lowercase						).to(__lowercase	,      dtype=timesteps.dtype						)
       UpperCamelCase__				=    torch.stack((timesteps_interpol[1:-1, 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(__lowercase						)







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_						):
       # get log sigma
       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 	UpperCAmelCase_ (self						):
       return self.sample is None







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_ = True	,      ):
       UpperCamelCase__				=    self.index_for_timestep(__lowercase						)

       # advance index counter by 1
       UpperCamelCase__				=    timestep.cpu().item() if torch.is_tensor(__lowercase						) 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 + 1]
            UpperCamelCase__				=    self.sigmas[step_index + 1]
       else:
            # 2nd order / KDPM2's method
            UpperCamelCase__				=    self.sigmas[step_index - 1]
            UpperCamelCase__				=    self.sigmas_interpol[step_index]
            UpperCamelCase__				=    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
       UpperCamelCase__				=    0
       UpperCamelCase__				=    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":
            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
       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_next - sigma_hat

            UpperCamelCase__				=    self.sample
            UpperCamelCase__				=    None

       UpperCamelCase__				=    sample + derivative * dt

       if not return_dict:
            return (prev_sample,)

       return SchedulerOutput(prev_sample=__lowercase						)







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_	,      ):
       # 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(__lowercase						):
            # 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(__lowercase	,      __lowercase						) 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						):
       return self.config.num_train_timesteps







def 						__magic_name__			(   __a      :	int	,		__a      :	int						):



     '''simple docstring'''




     while a != 0:
          UpperCamelCase__		,	UpperCamelCase__				=    b % a, a
     return b






def 						__magic_name__			(   __a      :	int	,		__a      :	int						):



     '''simple docstring'''




     if gcd(__a	,		__a						) != 1:
          UpperCamelCase__				=    f"mod inverse of {a!r} and {m!r} does not exist"
          raise ValueError(__a						)
     UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__				=    1, 0, a
     UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__				=    0, 1, m
     while va != 0:
          UpperCamelCase__				=    ua // va
          UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__				=    (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
     return ua % m





