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

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin



@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 						snake_case_ (	__A ):
   __A			:	torch.FloatTensor
   __A			:	Optional[torch.FloatTensor]        =       None



def     lowercase_       (    _lowerCamelCase							: List[str]	,			_lowerCamelCase							: List[Any]=0.999	,			_lowerCamelCase							: List[str]="cosine"	,			):
    if alpha_transform_type == "cosine":

        def alpha_bar_fn(_lowerCamelCase							: List[Any]):
            return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(_lowerCamelCase							: str):
            return math.exp(t * -12.0)

    else:
        raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}''')

    lowercase__				:     int					      =       []
    for i in range(_lowerCamelCase):
        lowercase__				:     List[Any]					      =       i / num_diffusion_timesteps
        lowercase__				:     Dict					      =       (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 						snake_case_ (	__A						,__A ):
   __A			:	Any        =       [e.name for e in KarrasDiffusionSchedulers]
   __A			:	Any        =       1






   @register_to_config
   def __init__(   self       :  str			,		lowercase_       :  int = 10_00			,		lowercase_       :  float = 0.00_01			,		lowercase_       :  float = 0.02			,		lowercase_       :  str = "linear"			,		lowercase_       :  Optional[Union[np.ndarray, List[float]]] = None			,		lowercase_       :  Optional[bool] = False			,		lowercase_       :  str = "epsilon"			,		lowercase_       :  str = "linspace"			,		lowercase_       :  int = 0			,		)      ->		List[Any]:
       if trained_betas is not None:
           lowercase__				:     Any					      =       torch.tensor(lowercase_			,		dtype=torch.floataa						)
       elif beta_schedule == "linear":
           lowercase__				:     Optional[Any]					      =       torch.linspace(lowercase_			,		lowercase_			,		lowercase_			,		dtype=torch.floataa						)
       elif beta_schedule == "scaled_linear":
           # this schedule is very specific to the latent diffusion model.
           lowercase__				:     List[Any]					      =       (
               torch.linspace(beta_start**0.5			,		beta_end**0.5			,		lowercase_			,		dtype=torch.floataa						) ** 2
           )
       elif beta_schedule == "squaredcos_cap_v2":
           # Glide cosine schedule
           lowercase__				:     Optional[int]					      =       betas_for_alpha_bar(lowercase_						)
       else:
           raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''						)

       lowercase__				:     List[Any]					      =       1.0 - self.betas
       lowercase__				:     Dict					      =       torch.cumprod(self.alphas			,		dim=0						)

       lowercase__				:     Any					      =       np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
       lowercase__				:     Tuple					      =       np.concatenate([sigmas[::-1], [0.0]]						).astype(np.floataa						)
       lowercase__				:     List[str]					      =       torch.from_numpy(lowercase_						)

       # setable values
       lowercase__				:     Tuple					      =       None
       lowercase__				:     Dict					      =       use_karras_sigmas
       self.set_timesteps(lowercase_			,		lowercase_						)
       lowercase__				:     Optional[int]					      =       []
       lowercase__				:     Dict					      =       False






   @property
   def    __UpperCamelCase  (   self       :  Union[str, Any]						)      ->		Optional[int]:
       # standard deviation of the initial noise distribution
       if self.config.timestep_spacing in ["linspace", "trailing"]:
           return self.sigmas.max()

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






   def    __UpperCamelCase  (   self       :  List[Any]			,		lowercase_       :  torch.FloatTensor			,		lowercase_       :  Union[float, torch.FloatTensor]						)      ->		torch.FloatTensor:
       if isinstance(lowercase_			,		torch.Tensor						):
           lowercase__				:     Dict					      =       timestep.to(self.timesteps.device						)
       lowercase__				:     Optional[int]					      =       (self.timesteps == timestep).nonzero().item()
       lowercase__				:     int					      =       self.sigmas[step_index]
       lowercase__				:     Union[str, Any]					      =       sample / ((sigma**2 + 1) ** 0.5)
       lowercase__				:     Optional[int]					      =       True
       return sample






   def    __UpperCamelCase  (   self       :  Optional[Any]			,		lowercase_       :  int			,		lowercase_       :  Optional[int]			,		lowercase_       :  Tuple						)      ->		List[Any]:

       def lms_derivative(lowercase_       :  Optional[int]						):
           lowercase__				:     Optional[Any]					      =       1.0
           for k in range(lowercase_						):
               if current_order == k:
                   continue
               prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
           return prod

       lowercase__				:     Optional[Any]					      =       integrate.quad(lowercase_			,		self.sigmas[t]			,		self.sigmas[t + 1]			,		epsrel=1E-4						)[0]

       return integrated_coeff






   def    __UpperCamelCase  (   self       :  Optional[Any]			,		lowercase_       :  int			,		lowercase_       :  Union[str, torch.device] = None						)      ->		int:
       lowercase__				:     Union[str, Any]					      =       num_inference_steps

       # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
       if self.config.timestep_spacing == "linspace":
           lowercase__				:     Union[str, Any]					      =       np.linspace(0			,		self.config.num_train_timesteps - 1			,		lowercase_			,		dtype=lowercase_						)[
               ::-1
           ].copy()
       elif self.config.timestep_spacing == "leading":
           lowercase__				:     Optional[int]					      =       self.config.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
           lowercase__				:     Optional[int]					      =       (np.arange(0			,		lowercase_						) * step_ratio).round()[::-1].copy().astype(lowercase_						)
           timesteps += self.config.steps_offset
       elif self.config.timestep_spacing == "trailing":
           lowercase__				:     Optional[Any]					      =       self.config.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
           lowercase__				:     List[Any]					      =       (np.arange(self.config.num_train_timesteps			,		0			,		-step_ratio						)).round().copy().astype(lowercase_						)
           timesteps -= 1
       else:
           raise ValueError(
               F'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''						)

       lowercase__				:     Optional[int]					      =       np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
       lowercase__				:     List[Any]					      =       np.log(lowercase_						)
       lowercase__				:     str					      =       np.interp(lowercase_			,		np.arange(0			,		len(lowercase_						)						)			,		lowercase_						)

       if self.use_karras_sigmas:
           lowercase__				:     Union[str, Any]					      =       self._convert_to_karras(in_sigmas=lowercase_						)
           lowercase__				:     Optional[Any]					      =       np.array([self._sigma_to_t(lowercase_			,		lowercase_						) for sigma in sigmas]						)

       lowercase__				:     List[str]					      =       np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)

       lowercase__				:     Optional[Any]					      =       torch.from_numpy(lowercase_						).to(device=lowercase_						)
       if str(lowercase_						).startswith("mps"						):
           # mps does not support float64
           lowercase__				:     List[str]					      =       torch.from_numpy(lowercase_						).to(lowercase_			,		dtype=torch.floataa						)
       else:
           lowercase__				:     Dict					      =       torch.from_numpy(lowercase_						).to(device=lowercase_						)

       lowercase__				:     Optional[Any]					      =       []






   def    __UpperCamelCase  (   self       :  List[Any]			,		lowercase_       :  str			,		lowercase_       :  Dict						)      ->		Any:
       # get log sigma
       lowercase__				:     Dict					      =       np.log(lowercase_						)

       # get distribution
       lowercase__				:     Any					      =       log_sigma - log_sigmas[:, np.newaxis]

       # get sigmas range
       lowercase__				:     Tuple					      =       np.cumsum((dists >= 0)			,		axis=0						).argmax(axis=0						).clip(max=log_sigmas.shape[0] - 2						)
       lowercase__				:     Union[str, Any]					      =       low_idx + 1

       lowercase__				:     Optional[Any]					      =       log_sigmas[low_idx]
       lowercase__				:     int					      =       log_sigmas[high_idx]

       # interpolate sigmas
       lowercase__				:     int					      =       (low - log_sigma) / (low - high)
       lowercase__				:     Any					      =       np.clip(lowercase_			,		0			,		1						)

       # transform interpolation to time range
       lowercase__				:     str					      =       (1 - w) * low_idx + w * high_idx
       lowercase__				:     int					      =       t.reshape(sigma.shape						)
       return t






   def    __UpperCamelCase  (   self       :  List[str]			,		lowercase_       :  torch.FloatTensor						)      ->		torch.FloatTensor:
       lowercase__				:     float					      =       in_sigmas[-1].item()
       lowercase__				:     float					      =       in_sigmas[0].item()

       lowercase__				:     Any					      =       7.0  # 7.0 is the value used in the paper
       lowercase__				:     Union[str, Any]					      =       np.linspace(0			,		1			,		self.num_inference_steps						)
       lowercase__				:     Optional[Any]					      =       sigma_min ** (1 / rho)
       lowercase__				:     Any					      =       sigma_max ** (1 / rho)
       lowercase__				:     List[str]					      =       (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
       return sigmas






   def    __UpperCamelCase  (   self       :  str			,		lowercase_       :  torch.FloatTensor			,		lowercase_       :  Union[float, torch.FloatTensor]			,		lowercase_       :  torch.FloatTensor			,		lowercase_       :  int = 4			,		lowercase_       :  bool = True			,		)      ->		Union[LMSDiscreteSchedulerOutput, Tuple]:
       if not self.is_scale_input_called:
           warnings.warn(
               "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
               "See `StableDiffusionPipeline` for a usage example."						)

       if isinstance(lowercase_			,		torch.Tensor						):
           lowercase__				:     Optional[int]					      =       timestep.to(self.timesteps.device						)
       lowercase__				:     str					      =       (self.timesteps == timestep).nonzero().item()
       lowercase__				:     Tuple					      =       self.sigmas[step_index]

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       if self.config.prediction_type == "epsilon":
           lowercase__				:     Dict					      =       sample - sigma * model_output
       elif self.config.prediction_type == "v_prediction":
           # * c_out + input * c_skip
           lowercase__				:     List[Any]					      =       model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
       elif self.config.prediction_type == "sample":
           lowercase__				:     List[str]					      =       model_output
       else:
           raise ValueError(
               F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''						)

       # 2. Convert to an ODE derivative
       lowercase__				:     List[Any]					      =       (sample - pred_original_sample) / sigma
       self.derivatives.append(lowercase_						)
       if len(self.derivatives						) > order:
           self.derivatives.pop(0						)

       # 3. Compute linear multistep coefficients
       lowercase__				:     str					      =       min(step_index + 1			,		lowercase_						)
       lowercase__				:     Optional[Any]					      =       [self.get_lms_coefficient(lowercase_			,		lowercase_			,		lowercase_						) for curr_order in range(lowercase_						)]

       # 4. Compute previous sample based on the derivatives path
       lowercase__				:     Dict					      =       sample + sum(
           coeff * derivative for coeff, derivative in zip(lowercase_			,		reversed(self.derivatives						)						)						)

       if not return_dict:
           return (prev_sample,)

       return LMSDiscreteSchedulerOutput(prev_sample=lowercase_			,		pred_original_sample=lowercase_						)






   def    __UpperCamelCase  (   self       :  Optional[Any]			,		lowercase_       :  torch.FloatTensor			,		lowercase_       :  torch.FloatTensor			,		lowercase_       :  torch.FloatTensor			,		)      ->		torch.FloatTensor:
       # Make sure sigmas and timesteps have the same device and dtype as original_samples
       lowercase__				:     Any					      =       self.sigmas.to(device=original_samples.device			,		dtype=original_samples.dtype						)
       if original_samples.device.type == "mps" and torch.is_floating_point(lowercase_						):
           # mps does not support float64
           lowercase__				:     Union[str, Any]					      =       self.timesteps.to(original_samples.device			,		dtype=torch.floataa						)
           lowercase__				:     Any					      =       timesteps.to(original_samples.device			,		dtype=torch.floataa						)
       else:
           lowercase__				:     List[Any]					      =       self.timesteps.to(original_samples.device						)
           lowercase__				:     Optional[Any]					      =       timesteps.to(original_samples.device						)

       lowercase__				:     int					      =       [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

       lowercase__				:     int					      =       original_samples + noise * sigma
       return noisy_samples







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




def     lowercase_       (    _lowerCamelCase							: str	,			_lowerCamelCase							: Optional[int]):
    if len(str(_lowerCamelCase)) == 1 or len(str(_lowerCamelCase)) == 1:
        return a * b

    lowercase__				:     Tuple					      =       max(len(str(_lowerCamelCase))	,			len(str(_lowerCamelCase)))
    lowercase__				:     Union[str, Any]					      =       ma // 2

    lowercase__      ,     lowercase__				:     Union[str, Any]					      =       divmod(_lowerCamelCase	,			10**ma)
    lowercase__      ,     lowercase__				:     Tuple					      =       divmod(_lowerCamelCase	,			10**ma)

    lowercase__				:     int					      =       karatsuba(_lowerCamelCase	,			_lowerCamelCase)
    lowercase__				:     Dict					      =       karatsuba((aa + aa)	,			(ba + ba))
    lowercase__				:     Optional[int]					      =       karatsuba(_lowerCamelCase	,			_lowerCamelCase)

    return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)

def     lowercase_       (    ):
    print(karatsuba(1_5463	,			2_3489))


if __name__ == "__main__":
      main()



