





import math
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 SchedulerMixin, SchedulerOutput



class     _UpperCAmelCase   (   _UpperCamelCase		,   _UpperCamelCase   ):

  """simple docstring"""


  a_      =			1






  @register_to_config
  def __init__(    self			:		str ,  lowerCAmelCase_			:		int = 1_0_0_0 ,  lowerCAmelCase_			:		Optional[Union[np.ndarray, List[float]]] = None					)							->						int:
     # set `betas`, `alphas`, `timesteps`
     self.set_timesteps(lowerCAmelCase_					)

     # standard deviation of the initial noise distribution
     __lowerCAmelCase							     =     1.0

     # For now we only support F-PNDM, i.e. the runge-kutta method
     # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
     # mainly at formula (9), (12), (13) and the Algorithm 2.
     __lowerCAmelCase							     =     4

     # running values
     __lowerCAmelCase							     =     []






  def     lowercase		(    self			:		Tuple ,  lowerCAmelCase_			:		int ,  lowerCAmelCase_			:		Union[str, torch.device] = None					)							->						Optional[int]:
     __lowerCAmelCase							     =     num_inference_steps
     __lowerCAmelCase							     =     torch.linspace(1 ,  0 ,  num_inference_steps + 1					)[:-1]
     __lowerCAmelCase							     =     torch.cat([steps, torch.tensor([0.0]					)]					)

     if self.config.trained_betas is not None:
        __lowerCAmelCase							     =     torch.tensor(self.config.trained_betas ,  dtype=torch.floataa					)
     else:
        __lowerCAmelCase							     =     torch.sin(steps * math.pi / 2					) ** 2

     __lowerCAmelCase							     =     (1.0 - self.betas**2) ** 0.5

     __lowerCAmelCase							     =     (torch.atana(self.betas ,  self.alphas					) / math.pi * 2)[:-1]
     __lowerCAmelCase							     =     timesteps.to(lowerCAmelCase_					)

     __lowerCAmelCase							     =     []






  def     lowercase		(    self			:		Optional[int] ,  lowerCAmelCase_			:		torch.FloatTensor ,  lowerCAmelCase_			:		int ,  lowerCAmelCase_			:		torch.FloatTensor ,  lowerCAmelCase_			:		bool = True ,  )							->						Union[SchedulerOutput, Tuple]:
     if self.num_inference_steps is None:
        raise ValueError(
            'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'					)

     __lowerCAmelCase							     =     (self.timesteps == timestep).nonzero().item()
     __lowerCAmelCase							     =     timestep_index + 1

     __lowerCAmelCase							     =     sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
     self.ets.append(lowerCAmelCase_					)

     if len(self.ets					) == 1:
        __lowerCAmelCase							     =     self.ets[-1]
     elif len(self.ets					) == 2:
        __lowerCAmelCase							     =     (3 * self.ets[-1] - self.ets[-2]) / 2
     elif len(self.ets					) == 3:
        __lowerCAmelCase							     =     (2_3 * self.ets[-1] - 1_6 * self.ets[-2] + 5 * self.ets[-3]) / 1_2
     else:
        __lowerCAmelCase							     =     (1 / 2_4) * (5_5 * self.ets[-1] - 5_9 * self.ets[-2] + 3_7 * self.ets[-3] - 9 * self.ets[-4])

     __lowerCAmelCase							     =     self._get_prev_sample(lowerCAmelCase_ ,  lowerCAmelCase_ ,  lowerCAmelCase_ ,  lowerCAmelCase_					)

     if not return_dict:
        return (prev_sample,)

     return SchedulerOutput(prev_sample=lowerCAmelCase_					)






  def     lowercase		(    self			:		str ,  lowerCAmelCase_			:		torch.FloatTensor ,  *lowerCAmelCase_			:		str ,  **lowerCAmelCase_			:		Union[str, Any]					)							->						torch.FloatTensor:
     return sample






  def     lowercase		(    self			:		Optional[int] ,  lowerCAmelCase_			:		Optional[int] ,  lowerCAmelCase_			:		int ,  lowerCAmelCase_			:		Union[str, Any] ,  lowerCAmelCase_			:		int					)							->						Tuple:
     __lowerCAmelCase							     =     self.alphas[timestep_index]
     __lowerCAmelCase							     =     self.betas[timestep_index]

     __lowerCAmelCase							     =     self.alphas[prev_timestep_index]
     __lowerCAmelCase							     =     self.betas[prev_timestep_index]

     __lowerCAmelCase							     =     (sample - sigma * ets) / max(lowerCAmelCase_ ,  1e-8					)
     __lowerCAmelCase							     =     next_alpha * pred + ets * next_sigma

     return prev_sample






  def __len__(    self			:		int					)							->						List[Any]:
     return self.config.num_train_timesteps








import mpmath  # for roots of unity
import numpy as np



class     _UpperCAmelCase   :

  """simple docstring"""


  def __init__(    self			:		List[Any] ,  lowerCAmelCase_			:		Dict=None ,  lowerCAmelCase_			:		str=None					)							->						List[Any]:
     # Input as list
     __lowerCAmelCase							     =     list(poly_a or [0]					)[:]
     __lowerCAmelCase							     =     list(poly_b or [0]					)[:]

     # Remove leading zero coefficients
     while self.polyA[-1] == 0:
        self.polyA.pop()
     __lowerCAmelCase							     =     len(self.polyA					)

     while self.polyB[-1] == 0:
        self.polyB.pop()
     __lowerCAmelCase							     =     len(self.polyB					)

     # Add 0 to make lengths equal a power of 2
     __lowerCAmelCase							     =     int(
         2 ** np.ceil(np.loga(len(self.polyA					) + len(self.polyB					) - 1					)					)					)

     while len(self.polyA					) < self.c_max_length:
        self.polyA.append(0					)
     while len(self.polyB					) < self.c_max_length:
        self.polyB.append(0					)
     # A complex root used for the fourier transform
     __lowerCAmelCase							     =     complex(mpmath.root(x=1 ,  n=self.c_max_length ,  k=1					)					)

     # The product
     __lowerCAmelCase							     =     self.__multiply()






  def     lowercase		(    self			:		Optional[int] ,  lowerCAmelCase_			:		str					)							->						Optional[int]:
     __lowerCAmelCase							     =     [[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
     # Corner case
     if len(lowerCAmelCase_					) <= 1:
        return dft[0]
     #
     __lowerCAmelCase							     =     self.c_max_length // 2
     while next_ncol > 0:
        __lowerCAmelCase							     =     [[] for i in range(lowerCAmelCase_					)]
        __lowerCAmelCase							     =     self.root**next_ncol

        # First half of next step
        __lowerCAmelCase							     =     1
        for j in range(self.c_max_length // (next_ncol * 2)					):
           for i in range(lowerCAmelCase_					):
              new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]					)
           current_root *= root
        # Second half of next step
        __lowerCAmelCase							     =     1
        for j in range(self.c_max_length // (next_ncol * 2)					):
           for i in range(lowerCAmelCase_					):
              new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]					)
           current_root *= root
        # Update
        __lowerCAmelCase							     =     new_dft
        __lowerCAmelCase							     =     next_ncol // 2
     return dft[0]






  def     lowercase		(    self			:		Optional[int]					)							->						Any:
     __lowerCAmelCase							     =     self.__dft('A'					)
     __lowerCAmelCase							     =     self.__dft('B'					)
     __lowerCAmelCase							     =     [[dft_a[i] * dft_b[i] for i in range(self.c_max_length					)]]
     del dft_a
     del dft_b

     # Corner Case
     if len(inverce_c[0]					) <= 1:
        return inverce_c[0]
     # Inverse DFT
     __lowerCAmelCase							     =     2
     while next_ncol <= self.c_max_length:
        __lowerCAmelCase							     =     [[] for i in range(lowerCAmelCase_					)]
        __lowerCAmelCase							     =     self.root ** (next_ncol // 2)
        __lowerCAmelCase							     =     1
        # First half of next step
        for j in range(self.c_max_length // next_ncol					):
           for i in range(next_ncol // 2					):
              # Even positions
              new_inverse_c[i].append(
                  (
                      inverce_c[i][j]
                      + inverce_c[i][j + self.c_max_length // next_ncol]
                  )
                  / 2					)
              # Odd positions
              new_inverse_c[i + next_ncol // 2].append(
                  (
                      inverce_c[i][j]
                      - inverce_c[i][j + self.c_max_length // next_ncol]
                  )
                  / (2 * current_root)					)
           current_root *= root
        # Update
        __lowerCAmelCase							     =     new_inverse_c
        next_ncol *= 2
     # Unpack
     __lowerCAmelCase							     =     [round(x[0].real ,  8					) + round(x[0].imag ,  8					) * 1J for x in inverce_c]

     # Remove leading 0's
     while inverce_c[-1] == 0:
        inverce_c.pop()
     return inverce_c






  def __str__(    self			:		Dict					)							->						int:
     __lowerCAmelCase							     =     'A = ' + ' + '.join(
         f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]					)					)
     __lowerCAmelCase							     =     'B = ' + ' + '.join(
         f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]					)					)
     __lowerCAmelCase							     =     'A*B = ' + ' + '.join(
         f"""{coef}*x^{i}""" for coef, i in enumerate(self.product					)					)

     return f"""{a}\n{b}\n{c}"""


# Unit tests
if __name__ == "__main__":
     import doctest

     doctest.testmod()

