


'''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     __SCREAMING_SNAKE_CASE       (   lowerCamelCase__			):
     UpperCAmelCase			       =					42
     UpperCAmelCase			       =					None







def __UpperCamelCase (      __lowerCamelCase		:			List[str]   ,	__lowerCamelCase		:			Optional[Any]=0.9_99   ,	__lowerCamelCase		:			Union[str, Any]="cosine"   ,	)   ->  Optional[Any]:







     '''simple docstring'''






     if alpha_transform_type == "cosine":

          def alpha_bar_fn(__lowerCamelCase		:			Tuple					):
               return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2					) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(__lowerCamelCase		:			Optional[Any]					):
               return math.exp(t * -12.0					)

     else:
          raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"					)

     _a            =		[]
     for i in range(__lowerCamelCase					):
          _a            =		i / num_diffusion_timesteps
          _a            =		(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     __SCREAMING_SNAKE_CASE       (   lowerCamelCase__			,      lowerCamelCase__			):
     UpperCAmelCase			       =					[e.name for e in KarrasDiffusionSchedulers]
     UpperCAmelCase			       =					1






     @register_to_config
     def __init__(      self  ,				__UpperCamelCase = 1_000  ,				__UpperCamelCase = 0.00_01  ,				__UpperCamelCase = 0.02  ,				__UpperCamelCase = "linear"  ,				__UpperCamelCase = None  ,				__UpperCamelCase = False  ,				__UpperCamelCase = "epsilon"  ,				__UpperCamelCase = "linspace"  ,				__UpperCamelCase = 0  ,				)							->     Optional[int]:
          if trained_betas is not None:
               _a            =		torch.tensor(__UpperCamelCase  ,				dtype=torch.floataa		)
          elif beta_schedule == "linear":
               _a            =		torch.linspace(__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				dtype=torch.floataa		)
          elif beta_schedule == "scaled_linear":
               # this schedule is very specific to the latent diffusion model.
               _a            =		(
                   torch.linspace(beta_start**0.5  ,				beta_end**0.5  ,				__UpperCamelCase  ,				dtype=torch.floataa		) ** 2
               )
          elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               _a            =		betas_for_alpha_bar(__UpperCamelCase		)
          else:
               raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"		)

          _a            =		1.0 - self.betas
          _a            =		torch.cumprod(self.alphas  ,				dim=0		)

          _a            =		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
          _a            =		np.concatenate([sigmas[::-1], [0.0]]		).astype(np.floataa		)
          _a            =		torch.from_numpy(__UpperCamelCase		)

          # setable values
          _a            =		None
          _a            =		use_karras_sigmas
          self.set_timesteps(__UpperCamelCase  ,				__UpperCamelCase		)
          _a            =		[]
          _a            =		False






     @property
     def 			a_       (      self		)							->     Tuple:
          # 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 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase		)							->     torch.FloatTensor:
          if isinstance(__UpperCamelCase  ,				torch.Tensor		):
               _a            =		timestep.to(self.timesteps.device		)
          _a            =		(self.timesteps == timestep).nonzero().item()
          _a            =		self.sigmas[step_index]
          _a            =		sample / ((sigma**2 + 1) ** 0.5)
          _a            =		True
          return sample






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase		)							->     List[Any]:

          def lms_derivative(__UpperCamelCase		):
               _a            =		1.0
               for k in range(__UpperCamelCase		):
                    if current_order == k:
                         continue
                    prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
               return prod

          _a            =		integrate.quad(__UpperCamelCase  ,				self.sigmas[t]  ,				self.sigmas[t + 1]  ,				epsrel=1e-4		)[0]

          return integrated_coeff






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase = None		)							->     Union[str, Any]:
          _a            =		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":
               _a            =		np.linspace(0  ,				self.config.num_train_timesteps - 1  ,				__UpperCamelCase  ,				dtype=__UpperCamelCase		)[
                   ::-1
               ].copy()
          elif self.config.timestep_spacing == "leading":
               _a            =		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
               _a            =		(np.arange(0  ,				__UpperCamelCase		) * step_ratio).round()[::-1].copy().astype(__UpperCamelCase		)
               timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
               _a            =		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
               _a            =		(np.arange(self.config.num_train_timesteps  ,				0  ,				-step_ratio		)).round().copy().astype(__UpperCamelCase		)
               timesteps -= 1
          else:
               raise ValueError(
                   f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."		)

          _a            =		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
          _a            =		np.log(__UpperCamelCase		)
          _a            =		np.interp(__UpperCamelCase  ,				np.arange(0  ,				len(__UpperCamelCase		)		)  ,				__UpperCamelCase		)

          if self.use_karras_sigmas:
               _a            =		self._convert_to_karras(in_sigmas=__UpperCamelCase		)
               _a            =		np.array([self._sigma_to_t(__UpperCamelCase  ,				__UpperCamelCase		) for sigma in sigmas]		)

          _a            =		np.concatenate([sigmas, [0.0]]		).astype(np.floataa		)

          _a            =		torch.from_numpy(__UpperCamelCase		).to(device=__UpperCamelCase		)
          if str(__UpperCamelCase		).startswith("mps"		):
               # mps does not support float64
               _a            =		torch.from_numpy(__UpperCamelCase		).to(__UpperCamelCase  ,				dtype=torch.floataa		)
          else:
               _a            =		torch.from_numpy(__UpperCamelCase		).to(device=__UpperCamelCase		)

          _a            =		[]






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase		)							->     Union[str, Any]:
          # get log sigma
          _a            =		np.log(__UpperCamelCase		)

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

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

          _a            =		log_sigmas[low_idx]
          _a            =		log_sigmas[high_idx]

          # interpolate sigmas
          _a            =		(low - log_sigma) / (low - high)
          _a            =		np.clip(__UpperCamelCase  ,				0  ,				1		)

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






     def 			a_       (      self  ,				__UpperCamelCase		)							->     torch.FloatTensor:
          _a            =		in_sigmas[-1].item()
          _a            =		in_sigmas[0].item()

          _a            =		7.0  # 7.0 is the value used in the paper
          _a            =		np.linspace(0  ,				1  ,				self.num_inference_steps		)
          _a            =		sigma_min ** (1 / rho)
          _a            =		sigma_max ** (1 / rho)
          _a            =		(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
          return sigmas






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase = 4  ,				__UpperCamelCase = 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(__UpperCamelCase  ,				torch.Tensor		):
               _a            =		timestep.to(self.timesteps.device		)
          _a            =		(self.timesteps == timestep).nonzero().item()
          _a            =		self.sigmas[step_index]

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
               _a            =		sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
               # * c_out + input * c_skip
               _a            =		model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          elif self.config.prediction_type == "sample":
               _a            =		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
          _a            =		(sample - pred_original_sample) / sigma
          self.derivatives.append(__UpperCamelCase		)
          if len(self.derivatives		) > order:
               self.derivatives.pop(0		)

          # 3. Compute linear multistep coefficients
          _a            =		min(step_index + 1  ,				__UpperCamelCase		)
          _a            =		[self.get_lms_coefficient(__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase		) for curr_order in range(__UpperCamelCase		)]

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

          if not return_dict:
               return (prev_sample,)

          return LMSDiscreteSchedulerOutput(prev_sample=__UpperCamelCase  ,				pred_original_sample=__UpperCamelCase		)






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				)							->     torch.FloatTensor:
          # Make sure sigmas and timesteps have the same device and dtype as original_samples
          _a            =		self.sigmas.to(device=original_samples.device  ,				dtype=original_samples.dtype		)
          if original_samples.device.type == "mps" and torch.is_floating_point(__UpperCamelCase		):
               # mps does not support float64
               _a            =		self.timesteps.to(original_samples.device  ,				dtype=torch.floataa		)
               _a            =		timesteps.to(original_samples.device  ,				dtype=torch.floataa		)
          else:
               _a            =		self.timesteps.to(original_samples.device		)
               _a            =		timesteps.to(original_samples.device		)

          _a            =		[(schedule_timesteps == t).nonzero().item() for t in timesteps]

          _a            =		sigmas[step_indices].flatten()
          while len(sigma.shape		) < len(original_samples.shape		):
               _a            =		sigma.unsqueeze(-1		)

          _a            =		original_samples + noise * sigma
          return noisy_samples






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





'''simple docstring'''

def __UpperCamelCase (      __lowerCamelCase		:			float   ,	__lowerCamelCase		:			float   ,	__lowerCamelCase		:			float					)   ->  float:







     '''simple docstring'''






     if mass < 0:
          raise ValueError("The mass of the body cannot be negative"					)
     if radius <= 0:
          raise ValueError("The radius is always a positive non zero integer"					)
     return (mass * (velocity) ** 2) / radius


if __name__ == "__main__":
   import doctest

   doctest.testmod(verbose=True)

