

"""simple docstring"""






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__		(					_lowerCamelCase ,   _lowerCamelCase=0.999 ,   _lowerCamelCase="cosine" ,   ):

    '''simple docstring'''



    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}"""   )

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







class 	__UpperCamelCase    (    a__							,							a__						):
  _UpperCAmelCase          =		[e.name for e in KarrasDiffusionSchedulers]
  _UpperCAmelCase          =		2

  @register_to_config
  def __init__(		self    ,_A = 1000    ,_A = 0.0_0_0_8_5    ,_A = 0.0_1_2    ,_A = "linear"    ,_A = None    ,_A = "epsilon"    ,_A = "linspace"    ,_A = 0    ,):
      '''simple docstring'''

      if trained_betas is not None:
          _lowerCAmelCase       :   str  =    torch.tensor(_A    ,dtype=torch.floataa      )
      elif beta_schedule == "linear":
          _lowerCAmelCase       :   Union[str, Any]  =    torch.linspace(_A    ,_A    ,_A    ,dtype=torch.floataa      )
      elif beta_schedule == "scaled_linear":
          # this schedule is very specific to the latent diffusion model.
          _lowerCAmelCase       :   str  =    (
              torch.linspace(beta_start**0.5    ,beta_end**0.5    ,_A    ,dtype=torch.floataa      ) ** 2
          )
      elif beta_schedule == "squaredcos_cap_v2":
          # Glide cosine schedule
          _lowerCAmelCase       :   Optional[Any]  =    betas_for_alpha_bar(_A      )
      else:
          raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""      )

      _lowerCAmelCase       :   Optional[int]  =    1.0 - self.betas
      _lowerCAmelCase       :   Tuple  =    torch.cumprod(self.alphas    ,dim=0      )

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

  def __lowerCamelCase		(		self    ,_A    ,_A=None      ):
      '''simple docstring'''

      if schedule_timesteps is None:
          _lowerCAmelCase       :   Optional[Any]  =    self.timesteps

      _lowerCAmelCase       :   str  =    (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:
          _lowerCAmelCase       :   Tuple  =    1 if len(_A      ) > 1 else 0
      else:
          _lowerCAmelCase       :   int  =    timestep.cpu().item() if torch.is_tensor(_A      ) else timestep
          _lowerCAmelCase       :   Any  =    self._index_counter[timestep_int]

      return indices[pos].item()

  @property
  def __lowerCamelCase		(		self      ):
      '''simple docstring'''

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

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

  def __lowerCamelCase		(		self    ,_A    ,_A    ,):
      '''simple docstring'''

      _lowerCAmelCase       :   int  =    self.index_for_timestep(_A      )

      if self.state_in_first_order:
          _lowerCAmelCase       :   Tuple  =    self.sigmas[step_index]
      else:
          _lowerCAmelCase       :   int  =    self.sigmas_interpol[step_index]

      _lowerCAmelCase       :   Optional[int]  =    sample / ((sigma**2 + 1) ** 0.5)
      return sample

  def __lowerCamelCase		(		self    ,_A    ,_A = None    ,_A = None    ,):
      '''simple docstring'''

      _lowerCAmelCase       :   Any  =    num_inference_steps

      _lowerCAmelCase       :   int  =    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":
          _lowerCAmelCase       :   Any  =    np.linspace(0    ,num_train_timesteps - 1    ,_A    ,dtype=_A      )[::-1].copy()
      elif self.config.timestep_spacing == "leading":
          _lowerCAmelCase       :   str  =    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
          _lowerCAmelCase       :   int  =    (np.arange(0    ,_A      ) * step_ratio).round()[::-1].copy().astype(_A      )
          timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
          _lowerCAmelCase       :   Optional[Any]  =    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
          _lowerCAmelCase       :   Tuple  =    (np.arange(_A    ,0    ,-step_ratio      )).round().copy().astype(_A      )
          timesteps -= 1
      else:
          raise ValueError(
              F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""      )

      _lowerCAmelCase       :   Union[str, Any]  =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
      _lowerCAmelCase       :   List[Any]  =    torch.from_numpy(np.log(_A      )      ).to(_A      )

      _lowerCAmelCase       :   Optional[int]  =    np.interp(_A    ,np.arange(0    ,len(_A      )      )    ,_A      )
      _lowerCAmelCase       :   Tuple  =    np.concatenate([sigmas, [0.0]]      ).astype(np.floataa      )
      _lowerCAmelCase       :   Union[str, Any]  =    torch.from_numpy(_A      ).to(device=_A      )

      # interpolate sigmas
      _lowerCAmelCase       :   str  =    sigmas.log().lerp(sigmas.roll(1      ).log()    ,0.5      ).exp()

      _lowerCAmelCase       :   Union[str, Any]  =    torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2      ), sigmas[-1:]]      )
      _lowerCAmelCase       :   int  =    torch.cat(
          [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2      ), sigmas_interpol[-1:]]      )

      if str(_A      ).startswith('mps'      ):
          # mps does not support float64
          _lowerCAmelCase       :   int  =    torch.from_numpy(_A      ).to(_A    ,dtype=torch.floataa      )
      else:
          _lowerCAmelCase       :   Any  =    torch.from_numpy(_A      ).to(_A      )

      # interpolate timesteps
      _lowerCAmelCase       :   List[Any]  =    self.sigma_to_t(_A      ).to(_A    ,dtype=timesteps.dtype      )
      _lowerCAmelCase       :   Union[str, Any]  =    torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])    ,dim=-1      ).flatten()

      _lowerCAmelCase       :   List[str]  =    torch.cat([timesteps[:1], interleaved_timesteps]      )

      _lowerCAmelCase       :   int  =    None

      # for exp beta schedules, such as the one for `pipeline_shap_e.py`
      # we need an index counter
      _lowerCAmelCase       :   str  =    defaultdict(_A      )

  def __lowerCamelCase		(		self    ,_A      ):
      '''simple docstring'''

      _lowerCAmelCase       :   int  =    sigma.log()

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

      # get sigmas range
      _lowerCAmelCase       :   Optional[int]  =    dists.ge(0      ).cumsum(dim=0      ).argmax(dim=0      ).clamp(max=self.log_sigmas.shape[0] - 2      )
      _lowerCAmelCase       :   List[str]  =    low_idx + 1

      _lowerCAmelCase       :   Optional[Any]  =    self.log_sigmas[low_idx]
      _lowerCAmelCase       :   Any  =    self.log_sigmas[high_idx]

      # interpolate sigmas
      _lowerCAmelCase       :   List[Any]  =    (low - log_sigma) / (low - high)
      _lowerCAmelCase       :   str  =    w.clamp(0    ,1      )

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

  @property
  def __lowerCamelCase		(		self      ):
      '''simple docstring'''

      return self.sample is None

  def __lowerCamelCase		(		self    ,_A    ,_A    ,_A    ,_A = True    ,):
      '''simple docstring'''

      _lowerCAmelCase       :   List[Any]  =    self.index_for_timestep(_A      )

      # advance index counter by 1
      _lowerCAmelCase       :   str  =    timestep.cpu().item() if torch.is_tensor(_A      ) else timestep
      self._index_counter[timestep_int] += 1

      if self.state_in_first_order:
          _lowerCAmelCase       :   Optional[Any]  =    self.sigmas[step_index]
          _lowerCAmelCase       :   Optional[int]  =    self.sigmas_interpol[step_index + 1]
          _lowerCAmelCase       :   List[Any]  =    self.sigmas[step_index + 1]
      else:
          # 2nd order / KDPM2's method
          _lowerCAmelCase       :   Any  =    self.sigmas[step_index - 1]
          _lowerCAmelCase       :   List[Any]  =    self.sigmas_interpol[step_index]
          _lowerCAmelCase       :   int  =    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
      _lowerCAmelCase       :   Optional[int]  =    0
      _lowerCAmelCase       :   int  =    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":
          _lowerCAmelCase       :   Dict  =    sigma_hat if self.state_in_first_order else sigma_interpol
          _lowerCAmelCase       :   str  =    sample - sigma_input * model_output
      elif self.config.prediction_type == "v_prediction":
          _lowerCAmelCase       :   Tuple  =    sigma_hat if self.state_in_first_order else sigma_interpol
          _lowerCAmelCase       :   Union[str, Any]  =    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
          _lowerCAmelCase       :   List[str]  =    (sample - pred_original_sample) / sigma_hat
          # 3. delta timestep
          _lowerCAmelCase       :   Optional[Any]  =    sigma_interpol - sigma_hat

          # store for 2nd order step
          _lowerCAmelCase       :   List[str]  =    sample
      else:
          # DPM-Solver-2
          # 2. Convert to an ODE derivative for 2nd order
          _lowerCAmelCase       :   List[str]  =    (sample - pred_original_sample) / sigma_interpol

          # 3. delta timestep
          _lowerCAmelCase       :   Tuple  =    sigma_next - sigma_hat

          _lowerCAmelCase       :   int  =    self.sample
          _lowerCAmelCase       :   str  =    None

      _lowerCAmelCase       :   Tuple  =    sample + derivative * dt

      if not return_dict:
          return (prev_sample,)

      return SchedulerOutput(prev_sample=_A      )

  def __lowerCamelCase		(		self    ,_A    ,_A    ,_A    ,):
      '''simple docstring'''

      _lowerCAmelCase       :   Optional[Any]  =    self.sigmas.to(device=original_samples.device    ,dtype=original_samples.dtype      )
      if original_samples.device.type == "mps" and torch.is_floating_point(_A      ):
          # mps does not support float64
          _lowerCAmelCase       :   str  =    self.timesteps.to(original_samples.device    ,dtype=torch.floataa      )
          _lowerCAmelCase       :   List[str]  =    timesteps.to(original_samples.device    ,dtype=torch.floataa      )
      else:
          _lowerCAmelCase       :   Optional[Any]  =    self.timesteps.to(original_samples.device      )
          _lowerCAmelCase       :   Optional[int]  =    timesteps.to(original_samples.device      )

      _lowerCAmelCase       :   Tuple  =    [self.index_for_timestep(_A    ,_A      ) for t in timesteps]

      _lowerCAmelCase       :   List[Any]  =    sigmas[step_indices].flatten()
      while len(sigma.shape      ) < len(original_samples.shape      ):
          _lowerCAmelCase       :   int  =    sigma.unsqueeze(-1      )

      _lowerCAmelCase       :   int  =    original_samples + noise * sigma
      return noisy_samples







  def __len__(		self      ):
      '''simple docstring'''

      return self.config.num_train_timesteps








"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

_lowerCAmelCase						=		list[list[float | int]]

def 		lowerCamelCase__		(					_lowerCamelCase ,   _lowerCamelCase   ):

    '''simple docstring'''



    _lowerCAmelCase       :   int  =    len(_lowerCamelCase   )
    _lowerCAmelCase       :   Matrix  =    [[0 for _ in range(size + 1   )] for _ in range(_lowerCamelCase   )]
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   float

    for row in range(_lowerCamelCase   ):
        for col in range(_lowerCamelCase   ):
            _lowerCAmelCase       :   Union[str, Any]  =    matrix[row][col]

        _lowerCAmelCase       :   Tuple  =    vector[row][0]

    _lowerCAmelCase       :   Dict  =    0
    _lowerCAmelCase       :   Any  =    0
    while row < size and col < size:
        # pivoting
        _lowerCAmelCase       :   Optional[int]  =    max((abs(augmented[rowa][col]   ), rowa) for rowa in range(_lowerCamelCase ,   _lowerCamelCase   )   )[
            1
        ]
        if augmented[pivot_row][col] == 0:
            col += 1
            continue
        else:
            _lowerCAmelCase,					_lowerCAmelCase       :   Tuple  =    augmented[pivot_row], augmented[row]

        for rowa in range(row + 1 ,   _lowerCamelCase   ):
            _lowerCAmelCase       :   Dict  =    augmented[rowa][col] / augmented[row][col]
            _lowerCAmelCase       :   Optional[Any]  =    0
            for cola in range(col + 1 ,   size + 1   ):
                augmented[rowa][cola] -= augmented[row][cola] * ratio

        row += 1
        col += 1

    # back substitution
    for col in range(1 ,   _lowerCamelCase   ):
        for row in range(_lowerCamelCase   ):
            _lowerCAmelCase       :   int  =    augmented[row][col] / augmented[col][col]
            for cola in range(_lowerCamelCase ,   size + 1   ):
                augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
    return [
        [round(augmented[row][size] / augmented[row][row] ,   10   )] for row in range(_lowerCamelCase   )
    ]

def 		lowerCamelCase__		(					_lowerCamelCase   ):

    '''simple docstring'''



    _lowerCAmelCase       :   int  =    len(_lowerCamelCase   )
    _lowerCAmelCase       :   Matrix  =    [[0 for _ in range(_lowerCamelCase   )] for _ in range(_lowerCamelCase   )]
    _lowerCAmelCase       :   Matrix  =    [[0] for _ in range(_lowerCamelCase   )]
    _lowerCAmelCase       :   Matrix
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int

    for x_val, y_val in enumerate(_lowerCamelCase   ):
        for col in range(_lowerCamelCase   ):
            _lowerCAmelCase       :   Union[str, Any]  =    (x_val + 1) ** (size - col - 1)
        _lowerCAmelCase       :   Optional[int]  =    y_val

    _lowerCAmelCase       :   List[Any]  =    solve(_lowerCamelCase ,   _lowerCamelCase   )

    def interpolated_func(_lowerCamelCase   ) -> int:
        return sum(
            round(coeffs[x_val][0]   ) * (var ** (size - x_val - 1))
            for x_val in range(_lowerCamelCase   )   )

    return interpolated_func

def 		lowerCamelCase__		(					_lowerCamelCase   ):

    '''simple docstring'''



    return (
        1
        - variable
        + variable**2
        - variable**3
        + variable**4
        - variable**5
        + variable**6
        - variable**7
        + variable**8
        - variable**9
        + variable**10
    )

def 		lowerCamelCase__		(					_lowerCamelCase = question_function ,   _lowerCamelCase = 10   ):

    '''simple docstring'''



    _lowerCAmelCase       :   list[int]  =    [func(_lowerCamelCase   ) for x_val in range(1 ,   order + 1   )]

    _lowerCAmelCase       :   list[Callable[[int], int]]  =    [
        interpolate(data_points[:max_coeff]   ) for max_coeff in range(1 ,   order + 1   )
    ]

    _lowerCAmelCase       :   int  =    0
    _lowerCAmelCase       :   Callable[[int], int]
    _lowerCAmelCase       :   int

    for poly in polynomials:
        _lowerCAmelCase       :   Any  =    1
        while func(_lowerCamelCase   ) == poly(_lowerCamelCase   ):
            x_val += 1

        ret += poly(_lowerCamelCase   )

    return ret


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





