
'''simple docstring'''
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


a_           =    logging.get_logger(__name__)  # pylint: disable=invalid-name






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class  UpperCAmelCase_					(						snake_case__       ):
 UpperCAmelCase_		     =    42
 UpperCAmelCase_		     =    None


def     UpperCamelCase_  (						__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE=0.999,		__SCREAMING_SNAKE_CASE="cosine",		):
    """simple docstring"""






    if alpha_transform_type == "cosine":

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

    elif alpha_transform_type == "exp":

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

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

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






class  UpperCAmelCase_					(						snake_case__     ,    snake_case__       ):
 UpperCAmelCase_		     =    [e.name for e in KarrasDiffusionSchedulers]
 UpperCAmelCase_		     =    1





 @register_to_config
 def __init__(     self			,							lowercase_ = 10_00			,							lowercase_ = 0.0_001			,							lowercase_ = 0.02			,							lowercase_ = "linear"			,							lowercase_ = None			,							lowercase_ = "epsilon"			,							lowercase_ = "linear"			,							lowercase_ = False			,							lowercase_ = "linspace"			,							lowercase_ = 0			,							):
     if trained_betas is not None:
         snake_case_			:     str        =    torch.tensor(lowercase_			,							dtype=torch.floataa)
     elif beta_schedule == "linear":
         snake_case_			:     int        =    torch.linspace(lowercase_			,							lowercase_			,							lowercase_			,							dtype=torch.floataa)
     elif beta_schedule == "scaled_linear":
         # this schedule is very specific to the latent diffusion model.
         snake_case_			:     List[str]        =    (
             torch.linspace(beta_start**0.5			,							beta_end**0.5			,							lowercase_			,							dtype=torch.floataa) ** 2
         )
     elif beta_schedule == "squaredcos_cap_v2":
         # Glide cosine schedule
         snake_case_			:     Optional[Any]        =    betas_for_alpha_bar(lowercase_)
     else:
         raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}')

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

     snake_case_			:     str        =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
     snake_case_			:     List[Any]        =    np.concatenate([sigmas[::-1], [0.0]]).astype(np.floataa)
     snake_case_			:     Dict        =    torch.from_numpy(lowercase_)

     # setable values
     snake_case_			:     int        =    None
     snake_case_			:     Optional[int]        =    np.linspace(0			,							num_train_timesteps - 1			,							lowercase_			,							dtype=lowercase_)[::-1].copy()
     snake_case_			:     Dict        =    torch.from_numpy(lowercase_)
     snake_case_			:     Optional[Any]        =    False
     snake_case_			:     int        =    use_karras_sigmas





 @property
 def 							snake_case__		(     self):
     # 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 							snake_case__		(     self			,							lowercase_			,							lowercase_):
     if isinstance(lowercase_			,							torch.Tensor):
         snake_case_			:     List[Any]        =    timestep.to(self.timesteps.device)
     snake_case_			:     Optional[Any]        =    (self.timesteps == timestep).nonzero().item()
     snake_case_			:     str        =    self.sigmas[step_index]

     snake_case_			:     List[Any]        =    sample / ((sigma**2 + 1) ** 0.5)

     snake_case_			:     Optional[int]        =    True
     return sample





 def 							snake_case__		(     self			,							lowercase_			,							lowercase_ = None):
     snake_case_			:     List[str]        =    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_			:     List[Any]        =    np.linspace(0			,							self.config.num_train_timesteps - 1			,							lowercase_			,							dtype=lowercase_)[
             ::-1
         ].copy()
     elif self.config.timestep_spacing == "leading":
         snake_case_			:     int        =    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_			:     Union[str, Any]        =    (np.arange(0			,							lowercase_) * step_ratio).round()[::-1].copy().astype(lowercase_)
         timesteps += self.config.steps_offset
     elif self.config.timestep_spacing == "trailing":
         snake_case_			:     Union[str, 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_			:     Union[str, Any]        =    (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\'.')

     snake_case_			:     Dict        =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
     snake_case_			:     List[Any]        =    np.log(lowercase_)

     if self.config.interpolation_type == "linear":
         snake_case_			:     str        =    np.interp(lowercase_			,							np.arange(0			,							len(lowercase_))			,							lowercase_)
     elif self.config.interpolation_type == "log_linear":
         snake_case_			:     Tuple        =    torch.linspace(np.log(sigmas[-1])			,							np.log(sigmas[0])			,							num_inference_steps + 1).exp()
     else:
         raise ValueError(
             F'{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'
             " 'linear' or 'log_linear'")

     if self.use_karras_sigmas:
         snake_case_			:     Tuple        =    self._convert_to_karras(in_sigmas=lowercase_			,							num_inference_steps=self.num_inference_steps)
         snake_case_			:     Dict        =    np.array([self._sigma_to_t(lowercase_			,							lowercase_) for sigma in sigmas])

     snake_case_			:     Dict        =    np.concatenate([sigmas, [0.0]]).astype(np.floataa)
     snake_case_			:     Union[str, Any]        =    torch.from_numpy(lowercase_).to(device=lowercase_)
     if str(lowercase_).startswith("mps"):
         # mps does not support float64
         snake_case_			:     Union[str, Any]        =    torch.from_numpy(lowercase_).to(lowercase_			,							dtype=torch.floataa)
     else:
         snake_case_			:     Optional[Any]        =    torch.from_numpy(lowercase_).to(device=lowercase_)





 def 							snake_case__		(     self			,							lowercase_			,							lowercase_):
     # get log sigma
     snake_case_			:     Optional[int]        =    np.log(lowercase_)

     # get distribution
     snake_case_			:     Union[str, Any]        =    log_sigma - log_sigmas[:, np.newaxis]

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

     snake_case_			:     Tuple        =    log_sigmas[low_idx]
     snake_case_			:     str        =    log_sigmas[high_idx]

     # interpolate sigmas
     snake_case_			:     int        =    (low - log_sigma) / (low - high)
     snake_case_			:     Optional[Any]        =    np.clip(lowercase_			,							0			,							1)

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





 def 							snake_case__		(     self			,							lowercase_			,							lowercase_):
     snake_case_			:     float        =    in_sigmas[-1].item()
     snake_case_			:     float        =    in_sigmas[0].item()

     snake_case_			:     List[str]        =    7.0  # 7.0 is the value used in the paper
     snake_case_			:     Optional[int]        =    np.linspace(0			,							1			,							lowercase_)
     snake_case_			:     str        =    sigma_min ** (1 / rho)
     snake_case_			:     Dict        =    sigma_max ** (1 / rho)
     snake_case_			:     List[str]        =    (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
     return sigmas





 def 							snake_case__		(     self			,							lowercase_			,							lowercase_			,							lowercase_			,							lowercase_ = 0.0			,							lowercase_ = 0.0			,							lowercase_ = float("inf")			,							lowercase_ = 1.0			,							lowercase_ = None			,							lowercase_ = True			,							):

     if (
         isinstance(lowercase_			,							lowercase_)
         or isinstance(lowercase_			,							torch.IntTensor)
         or isinstance(lowercase_			,							torch.LongTensor)
     ):
         raise ValueError(
             (
                 "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                 " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
                 " one of the `scheduler.timesteps` as a timestep."
             )			,							)

     if not self.is_scale_input_called:
         logger.warning(
             "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):
         snake_case_			:     int        =    timestep.to(self.timesteps.device)

     snake_case_			:     Dict        =    (self.timesteps == timestep).nonzero().item()
     snake_case_			:     str        =    self.sigmas[step_index]

     snake_case_			:     str        =    min(s_churn / (len(self.sigmas) - 1)			,							2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0

     snake_case_			:     Dict        =    randn_tensor(
         model_output.shape			,							dtype=model_output.dtype			,							device=model_output.device			,							generator=lowercase_)

     snake_case_			:     Dict        =    noise * s_noise
     snake_case_			:     Optional[int]        =    sigma * (gamma + 1)

     if gamma > 0:
         snake_case_			:     Any        =    sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

     # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
     # NOTE: "original_sample" should not be an expected prediction_type but is left in for
     # backwards compatibility
     if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
         snake_case_			:     Optional[int]        =    model_output
     elif self.config.prediction_type == "epsilon":
         snake_case_			:     Dict        =    sample - sigma_hat * model_output
     elif self.config.prediction_type == "v_prediction":
         # * c_out + input * c_skip
         snake_case_			:     List[Any]        =    model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
     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_			:     Optional[int]        =    (sample - pred_original_sample) / sigma_hat

     snake_case_			:     Optional[Any]        =    self.sigmas[step_index + 1] - sigma_hat

     snake_case_			:     List[Any]        =    sample + derivative * dt

     if not return_dict:
         return (prev_sample,)

     return EulerDiscreteSchedulerOutput(prev_sample=lowercase_			,							pred_original_sample=lowercase_)





 def 							snake_case__		(     self			,							lowercase_			,							lowercase_			,							lowercase_			,							):
     # Make sure sigmas and timesteps have the same device and dtype as original_samples
     snake_case_			:     Tuple        =    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
         snake_case_			:     Any        =    self.timesteps.to(original_samples.device			,							dtype=torch.floataa)
         snake_case_			:     Tuple        =    timesteps.to(original_samples.device			,							dtype=torch.floataa)
     else:
         snake_case_			:     Optional[Any]        =    self.timesteps.to(original_samples.device)
         snake_case_			:     int        =    timesteps.to(original_samples.device)

     snake_case_			:     int        =    [(schedule_timesteps == t).nonzero().item() for t in timesteps]

     snake_case_			:     Tuple        =    sigmas[step_indices].flatten()
     while len(sigma.shape) < len(original_samples.shape):
         snake_case_			:     Optional[int]        =    sigma.unsqueeze(-1)

     snake_case_			:     List[str]        =    original_samples + noise * sigma
     return noisy_samples





 def __len__(     self):
     return self.config.num_train_timesteps






'''simple docstring'''
def     UpperCamelCase_  (						__SCREAMING_SNAKE_CASE							):
    """simple docstring"""






    if number != int(__SCREAMING_SNAKE_CASE							):
        raise ValueError("factorial() only accepts integral values"							)
    if number < 0:
        raise ValueError("factorial() not defined for negative values"							)
    snake_case_			:     int        =    1
    for i in range(1,		number + 1							):
        value *= i
    return value

def     UpperCamelCase_  (						__SCREAMING_SNAKE_CASE							):
    """simple docstring"""






    if not isinstance(__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							):
        raise ValueError("factorial() only accepts integral values"							)
    if n < 0:
        raise ValueError("factorial() not defined for negative values"							)
    return 1 if n == 0 or n == 1 else n * factorial(n - 1							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  a_           =    int(input("Enter a positive integer: ").strip() or 0)
  print(f"""factorial{n} is {factorial(n)}""")




