



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       ):
       UpperCamelCase__    :       torch.FloatTensor
       UpperCamelCase__    :       Optional[torch.FloatTensor]		   =		None





def 	__snake_case      (     _UpperCAmelCase  ,					_UpperCAmelCase=0.9_99  ,					_UpperCAmelCase="cosine"  ,					):
    if alpha_transform_type == "cosine":

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

    elif alpha_transform_type == "exp":

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

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

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

class        _A			(      __UpperCAmelCase ,__UpperCAmelCase       ):
       UpperCamelCase__    :       List[Any]		   =		[e.name for e in KarrasDiffusionSchedulers]
       UpperCamelCase__    :       Optional[Any]		   =		1



       @register_to_config
       def __init__(						self				:	Tuple	,						__SCREAMING_SNAKE_CASE				:	int = 1_000	,						__SCREAMING_SNAKE_CASE				:	float = 0.00_01	,						__SCREAMING_SNAKE_CASE				:	float = 0.02	,						__SCREAMING_SNAKE_CASE				:	str = "linear"	,						__SCREAMING_SNAKE_CASE				:	Optional[Union[np.ndarray, List[float]]] = None	,						__SCREAMING_SNAKE_CASE				:	Optional[bool] = False	,						__SCREAMING_SNAKE_CASE				:	str = "epsilon"	,						__SCREAMING_SNAKE_CASE				:	str = "linspace"	,						__SCREAMING_SNAKE_CASE				:	int = 0	,						):


           '''simple docstring'''

           if trained_betas is not None:
               __a					=							torch.tensor(__SCREAMING_SNAKE_CASE	,						dtype=torch.floataa)
           elif beta_schedule == "linear":
               __a					=							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.
               __a					=							(
                   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
               __a					=							betas_for_alpha_bar(__SCREAMING_SNAKE_CASE)
           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(__SCREAMING_SNAKE_CASE)

           # setable values
           __a					=							None
           __a					=							use_karras_sigmas
           self.set_timesteps(__SCREAMING_SNAKE_CASE	,						__SCREAMING_SNAKE_CASE)
           __a					=							[]
           __a					=							False



       @property
       def 						_lowerCamelCase     (						self				:	Tuple):


           '''simple docstring'''

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

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



       def 						_lowerCamelCase     (						self				:	Any	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	Union[float, torch.FloatTensor]):


           '''simple docstring'''

           if isinstance(__SCREAMING_SNAKE_CASE	,						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 						_lowerCamelCase     (						self				:	Union[str, Any]	,						__SCREAMING_SNAKE_CASE				:	str	,						__SCREAMING_SNAKE_CASE				:	int	,						__SCREAMING_SNAKE_CASE				:	Optional[int]):


           '''simple docstring'''

           def lms_derivative(__SCREAMING_SNAKE_CASE				:	str):
               __a					=							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

           __a					=							integrate.quad(__SCREAMING_SNAKE_CASE	,						self.sigmas[t]	,						self.sigmas[t + 1]	,						epsrel=1E-4)[0]

           return integrated_coeff



       def 						_lowerCamelCase     (						self				:	int	,						__SCREAMING_SNAKE_CASE				:	int	,						__SCREAMING_SNAKE_CASE				:	Union[str, torch.device] = None):


           '''simple docstring'''

           __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	,						__SCREAMING_SNAKE_CASE	,						dtype=__SCREAMING_SNAKE_CASE)[
                   ::-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	,						__SCREAMING_SNAKE_CASE) * step_ratio).round()[::-1].copy().astype(__SCREAMING_SNAKE_CASE)
               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(__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\'.')

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

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

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

           __a					=							torch.from_numpy(__SCREAMING_SNAKE_CASE).to(device=__SCREAMING_SNAKE_CASE)
           if str(__SCREAMING_SNAKE_CASE).startswith('''mps'''):
               # mps does not support float64
               __a					=							torch.from_numpy(__SCREAMING_SNAKE_CASE).to(__SCREAMING_SNAKE_CASE	,						dtype=torch.floataa)
           else:
               __a					=							torch.from_numpy(__SCREAMING_SNAKE_CASE).to(device=__SCREAMING_SNAKE_CASE)

           __a					=							[]



       def 						_lowerCamelCase     (						self				:	Optional[int]	,						__SCREAMING_SNAKE_CASE				:	Dict	,						__SCREAMING_SNAKE_CASE				:	Any):


           '''simple docstring'''

           __a					=							np.log(__SCREAMING_SNAKE_CASE)

           # 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(__SCREAMING_SNAKE_CASE	,						0	,						1)

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



       def 						_lowerCamelCase     (						self				:	Optional[Any]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor):


           '''simple docstring'''

           __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 						_lowerCamelCase     (						self				:	Union[str, Any]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	Union[float, torch.FloatTensor]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	int = 4	,						__SCREAMING_SNAKE_CASE				:	bool = 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):
               __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(__SCREAMING_SNAKE_CASE)
           if len(self.derivatives) > order:
               self.derivatives.pop(0)

           # 3. Compute linear multistep coefficients
           __a					=							min(step_index + 1	,						__SCREAMING_SNAKE_CASE)
           __a					=							[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
           __a					=							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 						_lowerCamelCase     (						self				:	Optional[Any]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						):


           '''simple docstring'''

           __a					=							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
               __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				:	List[str]):


           '''simple docstring'''

           return self.config.num_train_timesteps










def 	__snake_case      (     _UpperCAmelCase							):
    __a					=							1
    __a					=							0
    __a					=							1
    __a					=							1
    __a					=							3
    __a					=							3
    __a					=							limit
    __a					=							0

    __a					=							''''''
    while counter != decimal + 1:
        if 4 * q + r - t < n * t:
            result += str(_UpperCAmelCase							)
            if counter == 0:
                result += "."

            if decimal == counter:
                break

            counter += 1
            __a					=							10 * (r - n * t)
            __a					=							((10 * (3 * q + r)) // t) - 10 * n
            q *= 10
            __a					=							nr
        else:
            __a					=							(2 * q + r) * l
            __a					=							(q * (7 * k) + 2 + (r * l)) // (t * l)
            q *= k
            t *= l
            l += 2
            k += 1
            __a					=							nn
            __a					=							nr
    return result





def 	__snake_case      (     ):
    print(f'{calculate_pi(50							) = }'							)
    import doctest

    doctest.testmod()


if __name__ == "__main__":
 main()





