


# 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					(			_UpperCAmelCase   ):
     UpperCAmelCase__ :  torch.FloatTensor
     UpperCAmelCase__ :  torch.FloatTensor



class        a					(			_UpperCAmelCase     ,_UpperCAmelCase   ):
     UpperCAmelCase__ :  int						      =	1





     @register_to_config
     def __init__(    self					:				List[str]    ,	SCREAMING_SNAKE_CASE_					:				int = 2000    ,	SCREAMING_SNAKE_CASE_					:				float = 0.15    ,	SCREAMING_SNAKE_CASE_					:				float = 0.01    ,	SCREAMING_SNAKE_CASE_					:				float = 1348.0    ,	SCREAMING_SNAKE_CASE_					:				float = 1E-5    ,	SCREAMING_SNAKE_CASE_					:				int = 1    ,	):
        # standard deviation of the initial noise distribution
        __lowerCamelCase:				List[str]     =	sigma_max

        # setable values
        __lowerCamelCase:				Optional[int]     =	None

        self.set_sigmas(SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	SCREAMING_SNAKE_CASE_					:				Optional[int] = None							):
        return sample





     def  SCREAMING_SNAKE_CASE__       (    self					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				float = None    ,	SCREAMING_SNAKE_CASE_					:				Union[str, torch.device] = None							):
        __lowerCamelCase:				int     =	sampling_eps if sampling_eps is not None else self.config.sampling_eps

        __lowerCamelCase:				List[Any]     =	torch.linspace(1    ,	SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_    ,	device=SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Any    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				float = None    ,	SCREAMING_SNAKE_CASE_					:				float = None    ,	SCREAMING_SNAKE_CASE_					:				float = None							):
        __lowerCamelCase:				Union[str, Any]     =	sigma_min if sigma_min is not None else self.config.sigma_min
        __lowerCamelCase:				Tuple     =	sigma_max if sigma_max is not None else self.config.sigma_max
        __lowerCamelCase:				int     =	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_							)

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





     def  SCREAMING_SNAKE_CASE__       (    self					:				List[Any]    ,	SCREAMING_SNAKE_CASE_					:				List[str]    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]							):
        return torch.where(
            timesteps == 0    ,	torch.zeros_like(t.to(timesteps.device							)							)    ,	self.discrete_sigmas[timesteps - 1].to(timesteps.device							)    ,	)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	SCREAMING_SNAKE_CASE_					:				Optional[torch.Generator] = None    ,	SCREAMING_SNAKE_CASE_					:				bool = True    ,	):
        if self.timesteps is None:
           raise ValueError(
               """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""							)

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

        __lowerCamelCase:				Union[str, Any]     =	self.discrete_sigmas[timesteps].to(sample.device							)
        __lowerCamelCase:				Dict     =	self.get_adjacent_sigma(SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_							).to(sample.device							)
        __lowerCamelCase:				Tuple     =	torch.zeros_like(SCREAMING_SNAKE_CASE_							)
        __lowerCamelCase:				List[str]     =	(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
        __lowerCamelCase:				Union[str, Any]     =	diffusion.flatten()
        while len(diffusion.shape							) < len(sample.shape							):
           __lowerCamelCase:				Union[str, Any]     =	diffusion.unsqueeze(-1							)
        __lowerCamelCase:				List[str]     =	drift - diffusion**2 * model_output

        #  equation 6: sample noise for the diffusion term of
        __lowerCamelCase:				Dict     =	randn_tensor(
            sample.shape    ,	layout=sample.layout    ,	generator=SCREAMING_SNAKE_CASE_    ,	device=sample.device    ,	dtype=sample.dtype							)
        __lowerCamelCase:				int     =	sample - drift  # subtract because `dt` is a small negative timestep
        # TODO is the variable diffusion the correct scaling term for the noise?
        __lowerCamelCase:				Union[str, Any]     =	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  SCREAMING_SNAKE_CASE__       (    self					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	SCREAMING_SNAKE_CASE_					:				Optional[torch.Generator] = None    ,	SCREAMING_SNAKE_CASE_					:				bool = True    ,	):
        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
        __lowerCamelCase:				Optional[Any]     =	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
        __lowerCamelCase:				Optional[int]     =	torch.norm(model_output.reshape(model_output.shape[0]    ,	-1							)    ,	dim=-1							).mean()
        __lowerCamelCase:				List[Any]     =	torch.norm(noise.reshape(noise.shape[0]    ,	-1							)    ,	dim=-1							).mean()
        __lowerCamelCase:				Optional[int]     =	(self.config.snr * noise_norm / grad_norm) ** 2 * 2
        __lowerCamelCase:				Tuple     =	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
        __lowerCamelCase:				List[str]     =	step_size.flatten()
        while len(step_size.shape							) < len(sample.shape							):
           __lowerCamelCase:				Any     =	step_size.unsqueeze(-1							)
        __lowerCamelCase:				int     =	sample + step_size * model_output
        __lowerCamelCase:				Any     =	prev_sample_mean + ((step_size * 2) ** 0.5) * noise

        if not return_dict:
           return (prev_sample,)

        return SchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	SCREAMING_SNAKE_CASE_					:				torch.FloatTensor    ,	):
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        __lowerCamelCase:				List[str]     =	timesteps.to(original_samples.device							)
        __lowerCamelCase:				Optional[int]     =	self.discrete_sigmas.to(original_samples.device							)[timesteps]
        __lowerCamelCase:				List[Any]     =	(
            noise * sigmas[:, None, None, None]
            if noise is not None
            else torch.randn_like(SCREAMING_SNAKE_CASE_							) * sigmas[:, None, None, None]
        )
        __lowerCamelCase:				int     =	noise + original_samples
        return noisy_samples







     def __len__(    self					:				List[str]							):
        return self.config.num_train_timesteps






def     __lowerCAmelCase						(							snake_case	:    int = 100 )       ->							int:
   __lowerCamelCase:				List[Any]     =	0
   __lowerCamelCase:				int     =	0
   for i in range(1						,      n + 1 ):
      sum_of_squares += i**2
      sum_of_ints += i
   return sum_of_ints**2 - sum_of_squares


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


