






'''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 					a__    (			lowerCamelCase						):
					'''simple docstring'''







					_snake_case             =  42
					_snake_case             =  None







def 						_UpperCamelCase							(     snake_case__							,			snake_case__=0.999							,			snake_case__="cosine"							,			):
						if alpha_transform_type == "cosine":

												def alpha_bar_fn(snake_case__							):
																		return math.cos((t + 0.008) / 1.008 * math.pi / 2							) ** 2

						elif alpha_transform_type == "exp":

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

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

						__A		   =      []
						for i in range(snake_case__							):
												__A		   =      i / num_diffusion_timesteps
												__A		   =      (i + 1) / num_diffusion_timesteps
												betas.append(min(1 - alpha_bar_fn(snake_case__							) / alpha_bar_fn(snake_case__							)							,			snake_case__							)							)
						return torch.tensor(snake_case__							,			dtype=torch.floataa							)






class 					a__    (			lowerCamelCase ,						lowerCamelCase						):
					'''simple docstring'''







					_snake_case             =  [e.name for e in KarrasDiffusionSchedulers]
					_snake_case             =  1






					@register_to_config
					def __init__(self    :	str				,				lowercase__    :	int = 1000				,				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				,				)  ->       Union[str, Any]:
											if trained_betas is not None:
																	__A		   =      torch.tensor(lowercase__				,				dtype=torch.floataa					)
											elif beta_schedule == "linear":
																	__A		   =      torch.linspace(lowercase__				,				lowercase__				,				lowercase__				,				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				,				lowercase__				,				dtype=torch.floataa					) ** 2
																	)
											elif beta_schedule == "squaredcos_cap_v2":
																	# Glide cosine schedule
																	__A		   =      betas_for_alpha_bar(lowercase__					)
											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(lowercase__					)

											# setable values
											__A		   =      None
											__A		   =      use_karras_sigmas
											self.set_timesteps(lowercase__				,				lowercase__					)
											__A		   =      []
											__A		   =      False






					@property
					def     _UpperCamelCase   (self    :	Optional[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    :	int				,				lowercase__    :	torch.FloatTensor				,				lowercase__    :	Union[float, torch.FloatTensor]					)  ->       torch.FloatTensor:
											if isinstance(lowercase__				,				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     _UpperCamelCase   (self    :	Dict				,				lowercase__    :	Any				,				lowercase__    :	str				,				lowercase__    :	Union[str, Any]					)  ->       Any:

											def lms_derivative(lowercase__    :	Optional[Any]					):
																	__A		   =      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

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

											return integrated_coeff






					def     _UpperCamelCase   (self    :	Any				,				lowercase__    :	int				,				lowercase__    :	Union[str, torch.device] = 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				,				lowercase__				,				dtype=lowercase__					)[
																	    ::-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				,				lowercase__					) * step_ratio).round()[::-1].copy().astype(lowercase__					)
																	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(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'."					)

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

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

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

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

											__A		   =      []






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

											# 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(lowercase__				,				0				,				1					)

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






					def     _UpperCamelCase   (self    :	Union[str, Any]				,				lowercase__    :	torch.FloatTensor					)  ->       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     _UpperCamelCase   (self    :	Union[str, Any]				,				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					):
																	__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(lowercase__					)
											if len(self.derivatives					) > order:
																	self.derivatives.pop(0					)

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

											# 4. Compute previous sample based on the derivatives path
											__A		   =      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    :	int				,				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
											__A		   =      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
																	__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    :	Tuple					)  ->       Optional[int]:
											return self.config.num_train_timesteps










'''simple docstring'''







def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if n < 0:
            return 0
      # table[i] represents the number of ways to get to amount i
      __A		   =      [0] * (n + 1)

      # There is exactly 1 way to get to zero(You pick no coins).
      __A		   =      1

      # Pick all coins one by one and update table[] values
      # after the index greater than or equal to the value of the
      # picked coin
      for coin_val in s:
            for j in range(snake_case__							,			n + 1							):
                  table[j] += table[j - coin_val]

      return table[n]


if __name__ == "__main__":
       import doctest

       doctest.testmod()


