
'''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							(    __UpperCAmelCase			):
			lowerCamelCase							:							torch.FloatTensor
			lowerCamelCase							:							Optional[torch.FloatTensor]    						=					None





def 	_A						(							lowercase__						,						lowercase__=0.9_9_9						,						lowercase__="cosine"						,						):
						if alpha_transform_type == "cosine":

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

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

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







class      A							(    __UpperCAmelCase						,  __UpperCAmelCase			):
			lowerCamelCase							:							str    						=					[e.name for e in KarrasDiffusionSchedulers]
			lowerCamelCase							:							int    						=					1



			@register_to_config
			def __init__(   self    ,       lowerCamelCase__ = 1_000    ,       lowerCamelCase__ = 0.00_01    ,       lowerCamelCase__ = 0.02    ,       lowerCamelCase__ = "linear"    ,       lowerCamelCase__ = None    ,       lowerCamelCase__ = False    ,       lowerCamelCase__ = "epsilon"    ,       lowerCamelCase__ = "linspace"    ,       lowerCamelCase__ = 0    ,       )     ->						Any:




									'''simple docstring'''



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

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

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

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



			@property
			def A__	(   self    )     ->						Any:




									'''simple docstring'''



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

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



			def A__	(   self    ,       lowerCamelCase__    ,       lowerCamelCase__    )     ->						torch.FloatTensor:




									'''simple docstring'''



									if isinstance(lowerCamelCase__    ,       torch.Tensor    ):
															lowercase__								=    timestep.to(self.timesteps.device    )
									lowercase__								=    (self.timesteps == timestep).nonzero().item()
									lowercase__								=    self.sigmas[step_index]
									lowercase__								=    sample / ((sigma**2 + 1) ** 0.5)
									lowercase__								=    True
									return sample



			def A__	(   self    ,       lowerCamelCase__    ,       lowerCamelCase__    ,       lowerCamelCase__    )     ->						int:




									'''simple docstring'''



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

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

									return integrated_coeff



			def A__	(   self    ,       lowerCamelCase__    ,       lowerCamelCase__ = None    )     ->						Optional[Any]:




									'''simple docstring'''



									lowercase__								=    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__								=    np.linspace(0    ,       self.config.num_train_timesteps - 1    ,       lowerCamelCase__    ,       dtype=lowerCamelCase__    )[
															    ::-1
															].copy()
									elif self.config.timestep_spacing == "leading":
															lowercase__								=    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__								=    (np.arange(0    ,       lowerCamelCase__    ) * step_ratio).round()[::-1].copy().astype(lowerCamelCase__    )
															timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
															lowercase__								=    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__								=    (np.arange(self.config.num_train_timesteps    ,       0    ,       -step_ratio    )).round().copy().astype(lowerCamelCase__    )
															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__								=    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
									lowercase__								=    np.log(lowerCamelCase__    )
									lowercase__								=    np.interp(lowerCamelCase__    ,       np.arange(0    ,       len(lowerCamelCase__    )    )    ,       lowerCamelCase__    )

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

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

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

									lowercase__								=    []



			def A__	(   self    ,       lowerCamelCase__    ,       lowerCamelCase__    )     ->						Any:




									'''simple docstring'''



									lowercase__								=    np.log(lowerCamelCase__    )

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

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

									lowercase__								=    log_sigmas[low_idx]
									lowercase__								=    log_sigmas[high_idx]

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

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



			def A__	(   self    ,       lowerCamelCase__    )     ->						torch.FloatTensor:




									'''simple docstring'''



									lowercase__								=    in_sigmas[-1].item()
									lowercase__								=    in_sigmas[0].item()

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



			def A__	(   self    ,       lowerCamelCase__    ,       lowerCamelCase__    ,       lowerCamelCase__    ,       lowerCamelCase__ = 4    ,       lowerCamelCase__ = True    ,       )     ->						Union[LMSDiscreteSchedulerOutput, Tuple]:




									'''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(lowerCamelCase__    ,       torch.Tensor    ):
															lowercase__								=    timestep.to(self.timesteps.device    )
									lowercase__								=    (self.timesteps == timestep).nonzero().item()
									lowercase__								=    self.sigmas[step_index]

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

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

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

									if not return_dict:
															return (prev_sample,)

									return LMSDiscreteSchedulerOutput(prev_sample=lowerCamelCase__    ,       pred_original_sample=lowerCamelCase__    )



			def A__	(   self    ,       lowerCamelCase__    ,       lowerCamelCase__    ,       lowerCamelCase__    ,       )     ->						torch.FloatTensor:




									'''simple docstring'''



									lowercase__								=    self.sigmas.to(device=original_samples.device    ,       dtype=original_samples.dtype    )
									if original_samples.device.type == "mps" and torch.is_floating_point(lowerCamelCase__    ):
															# mps does not support float64
															lowercase__								=    self.timesteps.to(original_samples.device    ,       dtype=torch.floataa    )
															lowercase__								=    timesteps.to(original_samples.device    ,       dtype=torch.floataa    )
									else:
															lowercase__								=    self.timesteps.to(original_samples.device    )
															lowercase__								=    timesteps.to(original_samples.device    )

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

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

									lowercase__								=    original_samples + noise * sigma
									return noisy_samples



			def __len__(   self    )     ->						Optional[Any]:




									'''simple docstring'''



									return self.config.num_train_timesteps








'''simple docstring'''



def 	_A						(							lowercase__		):
						if not isinstance(lowercase__						,						lowercase__		):
												raise ValueError("""Input series is not valid, valid series - [1, 2/3, 2]"""		)
						if len(lowercase__		) == 0:
												raise ValueError("""Input list must be a non empty list"""		)
						if len(lowercase__		) == 1 and series[0] != 0:
												return True
						lowercase__								=    []
						lowercase__								=    len(lowercase__		)
						for i in range(0						,						lowercase__		):
												if series[i] == 0:
																		raise ValueError("""Input series cannot have 0 as an element"""		)
												rec_series.append(1 / series[i]		)
						lowercase__								=    rec_series[1] - rec_series[0]
						for index in range(2						,						lowercase__		):
												if rec_series[index] - rec_series[index - 1] != common_diff:
																		return False
						return True





def 	_A						(							lowercase__		):
						if not isinstance(lowercase__						,						lowercase__		):
												raise ValueError("""Input series is not valid, valid series - [2, 4, 6]"""		)
						if len(lowercase__		) == 0:
												raise ValueError("""Input list must be a non empty list"""		)
						lowercase__								=    0
						for val in series:
												answer += 1 / val
						return len(lowercase__		) / answer


if __name__ == "__main__":
				import doctest

				doctest.testmod()






