






'''simple docstring'''



import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput
@dataclass
class UpperCAmelCase_					(    UpperCAmelCase__				):




      """simple docstring"""




      UpperCamelCase_								=			42
      UpperCamelCase_								=			42





class UpperCAmelCase_					(    UpperCAmelCase__				,       UpperCAmelCase__				):




      """simple docstring"""




      UpperCamelCase_								=			1






      @register_to_config
      def __init__( self			:		Tuple     ,      UpperCAmelCase			:		int = 2000     ,      UpperCAmelCase			:		float = 0.1_5     ,      UpperCAmelCase			:		float = 0.0_1     ,      UpperCAmelCase			:		float = 1348.0     ,      UpperCAmelCase			:		float = 1e-5     ,      UpperCAmelCase			:		int = 1     ,      )  ->  Optional[Any]:


       '''simple docstring'''

       lowercase					:   int				  =sigma_max

       # setable values
       lowercase					:   Any				  =None

       self.set_sigmas(UpperCAmelCase     ,      UpperCAmelCase     ,      UpperCAmelCase     ,      UpperCAmelCase		)






      def 				A__      ( self			:		Any     ,      UpperCAmelCase			:		torch.FloatTensor     ,      UpperCAmelCase			:		Optional[int] = None		)  ->  torch.FloatTensor:


       '''simple docstring'''

       return sample






      def 				A__      ( self			:		List[str]     ,      UpperCAmelCase			:		int     ,      UpperCAmelCase			:		float = None     ,      UpperCAmelCase			:		Union[str, torch.device] = None		)  ->  str:


       '''simple docstring'''

       lowercase					:   Dict				  =sampling_eps if sampling_eps is not None else self.config.sampling_eps

       lowercase					:   int				  =torch.linspace(1     ,      UpperCAmelCase     ,      UpperCAmelCase     ,      device=UpperCAmelCase		)






      def 				A__      ( self			:		Any     ,      UpperCAmelCase			:		int     ,      UpperCAmelCase			:		float = None     ,      UpperCAmelCase			:		float = None     ,      UpperCAmelCase			:		float = None		)  ->  Optional[int]:


       '''simple docstring'''

       lowercase					:   Optional[int]				  =sigma_min if sigma_min is not None else self.config.sigma_min
       lowercase					:   Any				  =sigma_max if sigma_max is not None else self.config.sigma_max
       lowercase					:   Any				  =sampling_eps if sampling_eps is not None else self.config.sampling_eps
       if self.timesteps is None:
        self.set_timesteps(UpperCAmelCase     ,      UpperCAmelCase		)

       lowercase					:   Optional[int]				  =sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
       lowercase					:   Any				  =torch.exp(torch.linspace(math.log(UpperCAmelCase		)     ,      math.log(UpperCAmelCase		)     ,      UpperCAmelCase		)		)
       lowercase					:   List[str]				  =torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]		)






      def 				A__      ( self			:		Dict     ,      UpperCAmelCase			:		List[str]     ,      UpperCAmelCase			:		str		)  ->  Tuple:


       '''simple docstring'''

       return torch.where(
           timesteps == 0     ,      torch.zeros_like(t.to(timesteps.device		)		)     ,      self.discrete_sigmas[timesteps - 1].to(timesteps.device		)     ,      )






      def 				A__      ( self			:		List[Any]     ,      UpperCAmelCase			:		torch.FloatTensor     ,      UpperCAmelCase			:		int     ,      UpperCAmelCase			:		torch.FloatTensor     ,      UpperCAmelCase			:		Optional[torch.Generator] = None     ,      UpperCAmelCase			:		bool = True     ,      )  ->  Union[SdeVeOutput, Tuple]:


       '''simple docstring'''

       if self.timesteps is None:
        raise ValueError(
            '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''		)

       lowercase					:   List[Any]				  =timestep * torch.ones(
           sample.shape[0]     ,      device=sample.device		)  # torch.repeat_interleave(timestep, sample.shape[0])
       lowercase					:   Union[str, Any]				  =(timestep * (len(self.timesteps		) - 1)).long()

       # mps requires indices to be in the same device, so we use cpu as is the default with cuda
       lowercase					:   Optional[int]				  =timesteps.to(self.discrete_sigmas.device		)

       lowercase					:   Optional[int]				  =self.discrete_sigmas[timesteps].to(sample.device		)
       lowercase					:   Any				  =self.get_adjacent_sigma(UpperCAmelCase     ,      UpperCAmelCase		).to(sample.device		)
       lowercase					:   str				  =torch.zeros_like(UpperCAmelCase		)
       lowercase					:   Dict				  =(sigma**2 - adjacent_sigma**2) ** 0.5

       # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
       # also equation 47 shows the analog from SDE models to ancestral sampling methods
       lowercase					:   List[str]				  =diffusion.flatten()
       while len(diffusion.shape		) < len(sample.shape		):
        lowercase					:   Optional[Any]				  =diffusion.unsqueeze(-1		)
       lowercase					:   Tuple				  =drift - diffusion**2 * model_output

       #  equation 6: sample noise for the diffusion term of
       lowercase					:   List[Any]				  =randn_tensor(
           sample.shape     ,      layout=sample.layout     ,      generator=UpperCAmelCase     ,      device=sample.device     ,      dtype=sample.dtype		)
       lowercase					:   str				  =sample - drift  # subtract because `dt` is a small negative timestep
       # TODO is the variable diffusion the correct scaling term for the noise?
       lowercase					:   Dict				  =prev_sample_mean + diffusion * noise  # add impact of diffusion field g

       if not return_dict:
        return (prev_sample, prev_sample_mean)

       return SdeVeOutput(prev_sample=UpperCAmelCase     ,      prev_sample_mean=UpperCAmelCase		)






      def 				A__      ( self			:		Dict     ,      UpperCAmelCase			:		torch.FloatTensor     ,      UpperCAmelCase			:		torch.FloatTensor     ,      UpperCAmelCase			:		Optional[torch.Generator] = None     ,      UpperCAmelCase			:		bool = True     ,      )  ->  Union[SchedulerOutput, Tuple]:


       '''simple docstring'''

       if self.timesteps is None:
        raise ValueError(
            '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''		)

       # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
       # sample noise for correction
       lowercase					:   int				  =randn_tensor(sample.shape     ,      layout=sample.layout     ,      generator=UpperCAmelCase		).to(sample.device		)

       # compute step size from the model_output, the noise, and the snr
       lowercase					:   str				  =torch.norm(model_output.reshape(model_output.shape[0]     ,      -1		)     ,      dim=-1		).mean()
       lowercase					:   Optional[int]				  =torch.norm(noise.reshape(noise.shape[0]     ,      -1		)     ,      dim=-1		).mean()
       lowercase					:   Optional[int]				  =(self.config.snr * noise_norm / grad_norm) ** 2 * 2
       lowercase					:   Optional[int]				  =step_size * torch.ones(sample.shape[0]		).to(sample.device		)
       # self.repeat_scalar(step_size, sample.shape[0])

       # compute corrected sample: model_output term and noise term
       lowercase					:   List[Any]				  =step_size.flatten()
       while len(step_size.shape		) < len(sample.shape		):
        lowercase					:   Optional[Any]				  =step_size.unsqueeze(-1		)
       lowercase					:   List[str]				  =sample + step_size * model_output
       lowercase					:   Any				  =prev_sample_mean + ((step_size * 2) ** 0.5) * noise

       if not return_dict:
        return (prev_sample,)

       return SchedulerOutput(prev_sample=UpperCAmelCase		)






      def 				A__      ( self			:		List[str]     ,      UpperCAmelCase			:		torch.FloatTensor     ,      UpperCAmelCase			:		torch.FloatTensor     ,      UpperCAmelCase			:		torch.FloatTensor     ,      )  ->  torch.FloatTensor:


       '''simple docstring'''

       lowercase					:   Union[str, Any]				  =timesteps.to(original_samples.device		)
       lowercase					:   Tuple				  =self.discrete_sigmas.to(original_samples.device		)[timesteps]
       lowercase					:   str				  =(
           noise * sigmas[:, None, None, None]
           if noise is not None
           else torch.randn_like(UpperCAmelCase		) * sigmas[:, None, None, None]
       )
       lowercase					:   Any				  =noise + original_samples
       return noisy_samples






      def __len__( self			:		List[Any]		)  ->  Dict:


       '''simple docstring'''

       return self.config.num_train_timesteps











'''simple docstring'''



import mpmath  # for roots of unity
import numpy as np
class UpperCAmelCase_					:




      """simple docstring"""




      def __init__( self			:		List[Any]     ,      UpperCAmelCase			:		Dict=None     ,      UpperCAmelCase			:		Optional[int]=None		)  ->  Optional[Any]:


       '''simple docstring'''

       lowercase					:   Any				  =list(poly_a or [0]		)[:]
       lowercase					:   Dict				  =list(poly_b or [0]		)[:]

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

       while self.polyB[-1] == 0:
        self.polyB.pop()
       lowercase					:   List[str]				  =len(self.polyB		)

       # Add 0 to make lengths equal a power of 2
       lowercase					:   Tuple				  =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
       lowercase					:   Optional[int]				  =complex(mpmath.root(x=1     ,      n=self.c_max_length     ,      k=1		)		)

       # The product
       lowercase					:   str				  =self.__multiply()






      def 				A__      ( self			:		Optional[Any]     ,      UpperCAmelCase			:		Union[str, Any]		)  ->  Tuple:


       '''simple docstring'''

       lowercase					:   Tuple				  =[[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
       # Corner case
       if len(UpperCAmelCase		) <= 1:
        return dft[0]
       #
       lowercase					:   List[Any]				  =self.c_max_length // 2
       while next_ncol > 0:
        lowercase					:   str				  =[[] for i in range(UpperCAmelCase		)]
        lowercase					:   List[str]				  =self.root**next_ncol

        # First half of next step
        lowercase					:   Union[str, Any]				  =1
        for j in range(self.c_max_length // (next_ncol * 2)		):
         for i in range(UpperCAmelCase		):
          new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]		)
         current_root *= root
        # Second half of next step
        lowercase					:   Any				  =1
        for j in range(self.c_max_length // (next_ncol * 2)		):
         for i in range(UpperCAmelCase		):
          new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]		)
         current_root *= root
        # Update
        lowercase					:   Tuple				  =new_dft
        lowercase					:   List[Any]				  =next_ncol // 2
       return dft[0]






      def 				A__      ( self			:		int		)  ->  str:


       '''simple docstring'''

       lowercase					:   List[Any]				  =self.__dft('''A'''		)
       lowercase					:   Union[str, Any]				  =self.__dft('''B'''		)
       lowercase					:   Any				  =[[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
       lowercase					:   Tuple				  =2
       while next_ncol <= self.c_max_length:
        lowercase					:   Tuple				  =[[] for i in range(UpperCAmelCase		)]
        lowercase					:   Tuple				  =self.root ** (next_ncol // 2)
        lowercase					:   Optional[int]				  =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
        lowercase					:   List[Any]				  =new_inverse_c
        next_ncol *= 2
       # Unpack
       lowercase					:   List[str]				  =[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		)  ->  Optional[Any]:


       '''simple docstring'''

       lowercase					:   Optional[Any]				  ='''A = ''' + ''' + '''.join(
           f'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]		)		)
       lowercase					:   List[str]				  ='''B = ''' + ''' + '''.join(
           f'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]		)		)
       lowercase					:   Optional[Any]				  ='''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()



