






"""simple docstring"""





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   _lowercase			(  SCREAMING_SNAKE_CASE_    ):
      _a :  Union[str, Any]										= 42
      _a :  Optional[Any]										= None



def      __lowercase       (     a			:					List[Any]							,		a			:					List[Any]=0.9_9_9							,		a			:					Union[str, Any]="cosine"							,		)       ->       Dict:

      if alpha_transform_type == "cosine":

            def alpha_bar_fn(a			:					Dict			):
                  return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2			) ** 2

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(a			:					int			):
                  return math.exp(t * -1_2.0			)

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

      __snake_case   :     List[str]	      =[]
      for i in range(a			):
            __snake_case   :     Optional[Any]	      =i / num_diffusion_timesteps
            __snake_case   :     List[Any]	      =(i + 1) / num_diffusion_timesteps
            betas.append(min(1 - alpha_bar_fn(a			) / alpha_bar_fn(a			)							,		a			)			)
      return torch.tensor(a							,		dtype=torch.floataa			)


class   _lowercase			(  SCREAMING_SNAKE_CASE_		,	SCREAMING_SNAKE_CASE_    ):
      _a :  Optional[Any]										= [e.name for e in KarrasDiffusionSchedulers]
      _a :  Any										= 1


      @register_to_config
      def __init__(     self					:						Tuple				, a					:						Optional[Any] = 1_0_0_0				, a					:						Tuple = 0.0_0_0_1				, a					:						str = 0.0_2				, a					:						List[Any] = "linear"				, a					:						str = None				, a					:						str = False				, a					:						str = "epsilon"				, a					:						List[Any] = "linspace"				, a					:						List[Any] = 0				, ):





            """simple docstring"""







            if trained_betas is not None:
                  __snake_case   :     List[str]	      =torch.tensor(SCREAMING_SNAKE_CASE_				, dtype=torch.floataa    )
            elif beta_schedule == "linear":
                  __snake_case   :     Any	      =torch.linspace(SCREAMING_SNAKE_CASE_				, SCREAMING_SNAKE_CASE_				, SCREAMING_SNAKE_CASE_				, dtype=torch.floataa    )
            elif beta_schedule == "scaled_linear":
                  # this schedule is very specific to the latent diffusion model.
                  __snake_case   :     Tuple	      =(
                      torch.linspace(beta_start**0.5				, beta_end**0.5				, SCREAMING_SNAKE_CASE_				, dtype=torch.floataa    ) ** 2
                  )
            elif beta_schedule == "squaredcos_cap_v2":
                  # Glide cosine schedule
                  __snake_case   :     List[Any]	      =betas_for_alpha_bar(SCREAMING_SNAKE_CASE_    )
            else:
                  raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''    )

            __snake_case   :     List[str]	      =1.0 - self.betas
            __snake_case   :     str	      =torch.cumprod(self.alphas				, dim=0    )

            __snake_case   :     Optional[int]	      =np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
            __snake_case   :     Optional[Any]	      =np.concatenate([sigmas[::-1], [0.0]]    ).astype(np.floataa    )
            __snake_case   :     List[Any]	      =torch.from_numpy(SCREAMING_SNAKE_CASE_    )

            # setable values
            __snake_case   :     List[Any]	      =None
            __snake_case   :     int	      =use_karras_sigmas
            self.set_timesteps(SCREAMING_SNAKE_CASE_				, SCREAMING_SNAKE_CASE_    )
            __snake_case   :     int	      =[]
            __snake_case   :     Union[str, Any]	      =False


      @property
      def _UpperCamelCase    (     self					:						int    ):





            """simple docstring"""







            if self.config.timestep_spacing in ["linspace", "trailing"]:
                  return self.sigmas.max()

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


      def _UpperCamelCase    (     self					:						Dict				, a					:						Union[str, Any]				, a					:						List[Any]    ):





            """simple docstring"""







            if isinstance(SCREAMING_SNAKE_CASE_				, torch.Tensor    ):
                  __snake_case   :     Any	      =timestep.to(self.timesteps.device    )
            __snake_case   :     Optional[int]	      =(self.timesteps == timestep).nonzero().item()
            __snake_case   :     Union[str, Any]	      =self.sigmas[step_index]
            __snake_case   :     str	      =sample / ((sigma**2 + 1) ** 0.5)
            __snake_case   :     Optional[int]	      =True
            return sample


      def _UpperCamelCase    (     self					:						Any				, a					:						int				, a					:						List[str]				, a					:						List[Any]    ):





            """simple docstring"""







            def lms_derivative(a					:						Dict    ):
                  __snake_case   :     int	      =1.0
                  for k in range(SCREAMING_SNAKE_CASE_    ):
                        if current_order == k:
                              continue
                        prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
                  return prod

            __snake_case   :     Union[str, Any]	      =integrate.quad(SCREAMING_SNAKE_CASE_				, self.sigmas[t]				, self.sigmas[t + 1]				, epsrel=1e-4    )[0]

            return integrated_coeff


      def _UpperCamelCase    (     self					:						Optional[int]				, a					:						Tuple				, a					:						Any = None    ):





            """simple docstring"""







            __snake_case   :     Tuple	      =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":
                  __snake_case   :     str	      =np.linspace(0				, self.config.num_train_timesteps - 1				, SCREAMING_SNAKE_CASE_				, dtype=SCREAMING_SNAKE_CASE_    )[
                      ::-1
                  ].copy()
            elif self.config.timestep_spacing == "leading":
                  __snake_case   :     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
                  __snake_case   :     str	      =(np.arange(0				, SCREAMING_SNAKE_CASE_    ) * step_ratio).round()[::-1].copy().astype(SCREAMING_SNAKE_CASE_    )
                  timesteps += self.config.steps_offset
            elif self.config.timestep_spacing == "trailing":
                  __snake_case   :     str	      =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
                  __snake_case   :     str	      =(np.arange(self.config.num_train_timesteps				, 0				, -step_ratio    )).round().copy().astype(SCREAMING_SNAKE_CASE_    )
                  timesteps -= 1
            else:
                  raise ValueError(
                      f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''    )

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

            if self.use_karras_sigmas:
                  __snake_case   :     List[Any]	      =self._convert_to_karras(in_sigmas=SCREAMING_SNAKE_CASE_    )
                  __snake_case   :     Dict	      =np.array([self._sigma_to_t(SCREAMING_SNAKE_CASE_				, SCREAMING_SNAKE_CASE_    ) for sigma in sigmas]    )

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

            __snake_case   :     List[Any]	      =torch.from_numpy(SCREAMING_SNAKE_CASE_    ).to(device=SCREAMING_SNAKE_CASE_    )
            if str(SCREAMING_SNAKE_CASE_    ).startswith('''mps'''    ):
                  # mps does not support float64
                  __snake_case   :     Dict	      =torch.from_numpy(SCREAMING_SNAKE_CASE_    ).to(SCREAMING_SNAKE_CASE_				, dtype=torch.floataa    )
            else:
                  __snake_case   :     Tuple	      =torch.from_numpy(SCREAMING_SNAKE_CASE_    ).to(device=SCREAMING_SNAKE_CASE_    )

            __snake_case   :     Dict	      =[]


      def _UpperCamelCase    (     self					:						List[Any]				, a					:						Union[str, Any]				, a					:						List[Any]    ):





            """simple docstring"""







            __snake_case   :     List[str]	      =np.log(SCREAMING_SNAKE_CASE_    )

            # get distribution
            __snake_case   :     Tuple	      =log_sigma - log_sigmas[:, np.newaxis]

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

            __snake_case   :     Optional[int]	      =log_sigmas[low_idx]
            __snake_case   :     Optional[int]	      =log_sigmas[high_idx]

            # interpolate sigmas
            __snake_case   :     str	      =(low - log_sigma) / (low - high)
            __snake_case   :     int	      =np.clip(SCREAMING_SNAKE_CASE_				, 0				, 1    )

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


      def _UpperCamelCase    (     self					:						int				, a					:						Tuple    ):





            """simple docstring"""







            __snake_case   :     Any	      =in_sigmas[-1].item()
            __snake_case   :     Tuple	      =in_sigmas[0].item()

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


      def _UpperCamelCase    (     self					:						int				, a					:						Union[str, Any]				, a					:						str				, a					:						Tuple				, a					:						Any = 4				, a					:						int = True				, ):





            """simple docstring"""







            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(SCREAMING_SNAKE_CASE_				, torch.Tensor    ):
                  __snake_case   :     Optional[Any]	      =timestep.to(self.timesteps.device    )
            __snake_case   :     int	      =(self.timesteps == timestep).nonzero().item()
            __snake_case   :     Optional[int]	      =self.sigmas[step_index]

            # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
            if self.config.prediction_type == "epsilon":
                  __snake_case   :     List[Any]	      =sample - sigma * model_output
            elif self.config.prediction_type == "v_prediction":
                  # * c_out + input * c_skip
                  __snake_case   :     Union[str, Any]	      =model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
            elif self.config.prediction_type == "sample":
                  __snake_case   :     int	      =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
            __snake_case   :     int	      =(sample - pred_original_sample) / sigma
            self.derivatives.append(SCREAMING_SNAKE_CASE_    )
            if len(self.derivatives    ) > order:
                  self.derivatives.pop(0    )

            # 3. Compute linear multistep coefficients
            __snake_case   :     Union[str, Any]	      =min(step_index + 1				, SCREAMING_SNAKE_CASE_    )
            __snake_case   :     Tuple	      =[self.get_lms_coefficient(SCREAMING_SNAKE_CASE_				, SCREAMING_SNAKE_CASE_				, SCREAMING_SNAKE_CASE_    ) for curr_order in range(SCREAMING_SNAKE_CASE_    )]

            # 4. Compute previous sample based on the derivatives path
            __snake_case   :     Optional[Any]	      =sample + sum(
                coeff * derivative for coeff, derivative in zip(SCREAMING_SNAKE_CASE_				, reversed(self.derivatives    )    )    )

            if not return_dict:
                  return (prev_sample,)

            return LMSDiscreteSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_				, pred_original_sample=SCREAMING_SNAKE_CASE_    )


      def _UpperCamelCase    (     self					:						Optional[int]				, a					:						Optional[Any]				, a					:						Dict				, a					:						Optional[Any]				, ):





            """simple docstring"""







            __snake_case   :     str	      =self.sigmas.to(device=original_samples.device				, dtype=original_samples.dtype    )
            if original_samples.device.type == "mps" and torch.is_floating_point(SCREAMING_SNAKE_CASE_    ):
                  # mps does not support float64
                  __snake_case   :     Any	      =self.timesteps.to(original_samples.device				, dtype=torch.floataa    )
                  __snake_case   :     List[Any]	      =timesteps.to(original_samples.device				, dtype=torch.floataa    )
            else:
                  __snake_case   :     Optional[int]	      =self.timesteps.to(original_samples.device    )
                  __snake_case   :     Tuple	      =timesteps.to(original_samples.device    )

            __snake_case   :     Any	      =[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

            __snake_case   :     Dict	      =original_samples + noise * sigma
            return noisy_samples







      def __len__(     self					:						Any    ):





            """simple docstring"""







            return self.config.num_train_timesteps




def 						A_			(				snake_case				: Union[str, Any]			,   snake_case				: Dict			)   ->     Dict:



						'''simple docstring'''

						__UpperCamelCase  	=      (boundary[1] - boundary[0]) / steps
						__UpperCamelCase  	=      boundary[0]
						__UpperCamelCase  	=      boundary[1]
						__UpperCamelCase  	=      make_points(snake_case			,   snake_case			,   snake_case			)
						__UpperCamelCase  	=      0.0
						y += (h / 3.0) * f(snake_case			)
						__UpperCamelCase  	=      2
						for i in x_i:
												y += (h / 3) * (4 - 2 * (cnt % 2)) * f(snake_case			)
												cnt += 1
						y += (h / 3.0) * f(snake_case			)
						return y




def 						A_			(				snake_case				: str			,   snake_case				: Optional[int]			,   snake_case				: Any			)   ->     Optional[int]:



						'''simple docstring'''

						__UpperCamelCase  	=      a + h
						while x < (b - h):
												yield x
												__UpperCamelCase  	=      x + h




def 						A_			(				snake_case				: Union[str, Any]			)   ->     str:  # enter your function here



						'''simple docstring'''

						__UpperCamelCase  	=      (x - 0) * (x - 0)
						return y




def 						A_			(				)   ->     Dict:



						'''simple docstring'''

						__UpperCamelCase  	=      0.0  # Lower bound of integration
						__UpperCamelCase  	=      1.0  # Upper bound of integration
						__UpperCamelCase  	=      10.0  # define number of steps or resolution
						__UpperCamelCase  	=      [a, b]  # define boundary of integration
						__UpperCamelCase  	=      method_a(snake_case			,   snake_case			)
						print(f"y = {y}"			)


if __name__ == "__main__":
				main()




