




'''simple docstring'''





# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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        _a    (						__lowerCAmelCase							):
     SCREAMING_SNAKE_CASE_							:   torch.FloatTensor
     SCREAMING_SNAKE_CASE_							:   torch.FloatTensor







class        _a    (						__lowerCAmelCase , __lowerCAmelCase							):
     SCREAMING_SNAKE_CASE_							:   Optional[Any]       =						1






     @register_to_config
     def __init__(			self ,_SCREAMING_SNAKE_CASE = 2_000 ,_SCREAMING_SNAKE_CASE = 0.1_5 ,_SCREAMING_SNAKE_CASE = 0.0_1 ,_SCREAMING_SNAKE_CASE = 1_3_4_8.0 ,_SCREAMING_SNAKE_CASE = 1e-5 ,_SCREAMING_SNAKE_CASE = 1 ,)							->      Dict:
          # standard deviation of the initial noise distribution
          _snake_case							=				sigma_max

          # setable values
          _snake_case							=				None

          self.set_sigmas(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE   )






     def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE = None   )							->      torch.FloatTensor:
          return sample






     def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE = None ,_SCREAMING_SNAKE_CASE = None   )							->      List[Any]:
          _snake_case							=				sampling_eps if sampling_eps is not None else self.config.sampling_eps

          _snake_case							=				torch.linspace(1 ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,device=_SCREAMING_SNAKE_CASE   )






     def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE = None ,_SCREAMING_SNAKE_CASE = None ,_SCREAMING_SNAKE_CASE = None   )							->      List[Any]:
          _snake_case							=				sigma_min if sigma_min is not None else self.config.sigma_min
          _snake_case							=				sigma_max if sigma_max is not None else self.config.sigma_max
          _snake_case							=				sampling_eps if sampling_eps is not None else self.config.sampling_eps
          if self.timesteps is None:
               self.set_timesteps(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE   )

          _snake_case							=				sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
          _snake_case							=				torch.exp(torch.linspace(math.log(_SCREAMING_SNAKE_CASE   ) ,math.log(_SCREAMING_SNAKE_CASE   ) ,_SCREAMING_SNAKE_CASE   )   )
          _snake_case							=				torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]   )






     def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE   )							->      Tuple:
          return torch.where(
              timesteps == 0 ,torch.zeros_like(t.to(timesteps.device   )   ) ,self.discrete_sigmas[timesteps - 1].to(timesteps.device   ) ,)






     def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE = None ,_SCREAMING_SNAKE_CASE = True ,)							->      Union[SdeVeOutput, Tuple]:
          if self.timesteps is None:
               raise ValueError(
                   "`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"   )

          _snake_case							=				timestep * torch.ones(
              sample.shape[0] ,device=sample.device   )  # torch.repeat_interleave(timestep, sample.shape[0])
          _snake_case							=				(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
          _snake_case							=				timesteps.to(self.discrete_sigmas.device   )

          _snake_case							=				self.discrete_sigmas[timesteps].to(sample.device   )
          _snake_case							=				self.get_adjacent_sigma(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE   ).to(sample.device   )
          _snake_case							=				torch.zeros_like(_SCREAMING_SNAKE_CASE   )
          _snake_case							=				(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
          _snake_case							=				diffusion.flatten()
          while len(diffusion.shape   ) < len(sample.shape   ):
               _snake_case							=				diffusion.unsqueeze(-1   )
          _snake_case							=				drift - diffusion**2 * model_output

          #  equation 6: sample noise for the diffusion term of
          _snake_case							=				randn_tensor(
              sample.shape ,layout=sample.layout ,generator=_SCREAMING_SNAKE_CASE ,device=sample.device ,dtype=sample.dtype   )
          _snake_case							=				sample - drift  # subtract because `dt` is a small negative timestep
          # TODO is the variable diffusion the correct scaling term for the noise?
          _snake_case							=				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=_SCREAMING_SNAKE_CASE ,prev_sample_mean=_SCREAMING_SNAKE_CASE   )






     def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE = None ,_SCREAMING_SNAKE_CASE = True ,)							->      Union[SchedulerOutput, Tuple]:
          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
          _snake_case							=				randn_tensor(sample.shape ,layout=sample.layout ,generator=_SCREAMING_SNAKE_CASE   ).to(sample.device   )

          # compute step size from the model_output, the noise, and the snr
          _snake_case							=				torch.norm(model_output.reshape(model_output.shape[0] ,-1   ) ,dim=-1   ).mean()
          _snake_case							=				torch.norm(noise.reshape(noise.shape[0] ,-1   ) ,dim=-1   ).mean()
          _snake_case							=				(self.config.snr * noise_norm / grad_norm) ** 2 * 2
          _snake_case							=				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
          _snake_case							=				step_size.flatten()
          while len(step_size.shape   ) < len(sample.shape   ):
               _snake_case							=				step_size.unsqueeze(-1   )
          _snake_case							=				sample + step_size * model_output
          _snake_case							=				prev_sample_mean + ((step_size * 2) ** 0.5) * noise

          if not return_dict:
               return (prev_sample,)

          return SchedulerOutput(prev_sample=_SCREAMING_SNAKE_CASE   )






     def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,)							->      torch.FloatTensor:
          # Make sure sigmas and timesteps have the same device and dtype as original_samples
          _snake_case							=				timesteps.to(original_samples.device   )
          _snake_case							=				self.discrete_sigmas.to(original_samples.device   )[timesteps]
          _snake_case							=				(
              noise * sigmas[:, None, None, None]
              if noise is not None
              else torch.randn_like(_SCREAMING_SNAKE_CASE   ) * sigmas[:, None, None, None]
          )
          _snake_case							=				noise + original_samples
          return noisy_samples






     def __len__(			self   )							->      Tuple:
          return self.config.num_train_timesteps








'''simple docstring'''





from __future__ import annotations

from collections.abc import Callable





def      __a     (       _UpperCamelCase:   Callable[[int | float], int | float] ,						_UpperCamelCase:   int | float ,						_UpperCamelCase:   int | float ,						_UpperCamelCase:   int = 100 ,						)						->			float:

     """simple docstring"""




     _snake_case							=				x_start
     _snake_case							=				fnc(_UpperCamelCase   )
     _snake_case							=				0.0
     for _ in range(_UpperCamelCase   ):
          # Approximates small segments of curve as linear and solve
          # for trapezoidal area
          _snake_case							=				(x_end - x_start) / steps + xa
          _snake_case							=				fnc(_UpperCamelCase   )
          area += abs(fxa + fxa   ) * (xa - xa) / 2
          # Increment step
          _snake_case							=				xa
          _snake_case							=				fxa
     return area


if __name__ == "__main__":





   def      __a     (       _UpperCamelCase:   Any   )						->			Optional[int]:

        """simple docstring"""




        return x**3 + x**2

   print('''f(x) = x^3 + x^2''')
   print('''The area between the curve, x = -5, x = 5 and the x axis is:''')
   UpperCamelCase_						:      Optional[int]       =						10
   while i <= 100000:
      print(F'with {i} steps: {trapezoidal_area(f, -5, 5, i)}')
      i *= 10


