





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


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







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 						_lowerCAmelCase(						_a):

  """simple docstring"""







  lowerCamelCase__      					=   42
  lowerCamelCase__      					=   None
def 				__UpperCamelCase  (		snake_case    ,	snake_case=0.999    ,	snake_case="cosine"    ,	)  ->						List[Any]:


   '''simple docstring'''







   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 						_lowerCAmelCase(						_a		,   _a):

  """simple docstring"""







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

  @register_to_config
  def __init__( self  ,    UpperCAmelCase = 10_00  ,    UpperCAmelCase = 0.0001  ,    UpperCAmelCase = 0.02  ,    UpperCAmelCase = "linear"  ,    UpperCAmelCase = None  ,    UpperCAmelCase = "epsilon"  ,    UpperCAmelCase = "linspace"  ,    UpperCAmelCase = 0  ,    )-> str:
     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				 =       np.linspace(0  ,    num_train_timesteps - 1  ,    UpperCAmelCase  ,    dtype=UpperCAmelCase     )[::-1].copy()
     __A				 =       torch.from_numpy(UpperCAmelCase     )
     __A				 =       False

  @property
  def 		SCREAMING_SNAKE_CASE__	( self     )-> List[Any]:
     # 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 		SCREAMING_SNAKE_CASE__	( 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 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase  ,    UpperCAmelCase = None     )-> List[str]:
     __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.interp(UpperCAmelCase  ,    np.arange(0  ,    len(UpperCAmelCase     )     )  ,    UpperCAmelCase     )
     __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     )

  def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase  ,    UpperCAmelCase  ,    UpperCAmelCase  ,    UpperCAmelCase = None  ,    UpperCAmelCase = True  ,    )-> Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:

     if (
         isinstance(UpperCAmelCase  ,    UpperCAmelCase     )
         or isinstance(UpperCAmelCase  ,    torch.IntTensor     )
         or isinstance(UpperCAmelCase  ,    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(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":
        raise NotImplementedError('''prediction_type not implemented yet: sample'''     )
     else:
        raise ValueError(
            f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"     )

     __A				 =       self.sigmas[step_index]
     __A				 =       self.sigmas[step_index + 1]
     __A				 =       (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
     __A				 =       (sigma_to**2 - sigma_up**2) ** 0.5

     # 2. Convert to an ODE derivative
     __A				 =       (sample - pred_original_sample) / sigma

     __A				 =       sigma_down - sigma

     __A				 =       sample + derivative * dt

     __A				 =       model_output.device
     __A				 =       randn_tensor(model_output.shape  ,    dtype=model_output.dtype  ,    device=UpperCAmelCase  ,    generator=UpperCAmelCase     )

     __A				 =       prev_sample + noise * sigma_up

     if not return_dict:
        return (prev_sample,)

     return EulerAncestralDiscreteSchedulerOutput(
         prev_sample=UpperCAmelCase  ,    pred_original_sample=UpperCAmelCase     )

  def 		SCREAMING_SNAKE_CASE__	( 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     )-> Tuple:
     return self.config.num_train_timesteps








import numpy as np
def 				__UpperCamelCase  (		snake_case     )  ->						Any:


   '''simple docstring'''







   __A ,						__A				 =       a.shape
   __A				 =       min(snake_case    ,	snake_case     )
   __A				 =       np.eye(snake_case     )
   __A				 =       a.copy()

   for k in range(t - 1     ):
      # select a column of modified matrix A':
      __A				 =       r[k:, [k]]
      # construct first basis vector
      __A				 =       np.zeros_like(snake_case     )
      __A				 =       1.0
      # determine scaling factor
      __A				 =       np.linalg.norm(snake_case     )
      # construct vector v for Householder reflection
      __A				 =       x + np.sign(x[0]     ) * alpha * ea
      v /= np.linalg.norm(snake_case     )

      # construct the Householder matrix
      __A				 =       np.eye(m - k     ) - 2.0 * v @ v.T
      # pad with ones and zeros as necessary
      __A				 =       np.block([[np.eye(snake_case     ), np.zeros((k, m - k)     )], [np.zeros((m - k, k)     ), q_k]]     )

      __A				 =       q @ q_k.T
      __A				 =       q_k @ r

   return q, r


if __name__ == "__main__":
    import doctest

    doctest.testmod()

