

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 				A_					(						snake_case__   ):
     _lowercase     :	torch.FloatTensor
     _lowercase     :	Optional[torch.FloatTensor]        =      None







def _a					(			SCREAMING_SNAKE_CASE						:     Dict       ,   SCREAMING_SNAKE_CASE						:     List[str]=0.9_9_9       ,   SCREAMING_SNAKE_CASE						:     Tuple="cosine"       ,   )       ->       List[Any]:

 """simple docstring"""






 if alpha_transform_type == "cosine":

  def alpha_bar_fn(SCREAMING_SNAKE_CASE						:     Any						):
   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(SCREAMING_SNAKE_CASE						:     Optional[int]						):
   return math.exp(t * -1_2.0						)

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

 __lowerCAmelCase:  Optional[int]        = []
 for i in range(SCREAMING_SNAKE_CASE						):
  __lowerCAmelCase:  Optional[int]        = i / num_diffusion_timesteps
  __lowerCAmelCase:  Tuple        = (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 				A_					(						snake_case__				,      snake_case__   ):
     _lowercase     :	List[Any]        =      [e.name for e in KarrasDiffusionSchedulers]
     _lowercase     :	Tuple        =      1


     @register_to_config
     def __init__(				self     :						Dict     ,    UpperCAmelCase     :						int = 1_0_0_0     ,    UpperCAmelCase     :						float = 0.0001     ,    UpperCAmelCase     :						float = 0.02     ,    UpperCAmelCase     :						str = "linear"     ,    UpperCAmelCase     :						Optional[Union[np.ndarray, List[float]]] = None     ,    UpperCAmelCase     :						str = "epsilon"     ,    UpperCAmelCase     :						str = "linear"     ,    UpperCAmelCase     :						Optional[bool] = False     ,    UpperCAmelCase     :						str = "linspace"     ,    UpperCAmelCase     :						int = 0     ,    )				->      List[str]:
      if trained_betas is not None:
       __lowerCAmelCase:  str        = torch.tensor(UpperCAmelCase     ,    dtype=torch.floataa   )
      elif beta_schedule == "linear":
       __lowerCAmelCase:  str        = torch.linspace(UpperCAmelCase     ,    UpperCAmelCase     ,    UpperCAmelCase     ,    dtype=torch.floataa   )
      elif beta_schedule == "scaled_linear":
       # this schedule is very specific to the latent diffusion model.
       __lowerCAmelCase:  Tuple        = (
           torch.linspace(beta_start**0.5     ,    beta_end**0.5     ,    UpperCAmelCase     ,    dtype=torch.floataa   ) ** 2
       )
      elif beta_schedule == "squaredcos_cap_v2":
       # Glide cosine schedule
       __lowerCAmelCase:  str        = betas_for_alpha_bar(UpperCAmelCase   )
      else:
       raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''   )

      __lowerCAmelCase:  int        = 1.0 - self.betas
      __lowerCAmelCase:  Optional[int]        = torch.cumprod(self.alphas     ,    dim=0   )

      __lowerCAmelCase:  Union[str, Any]        = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
      __lowerCAmelCase:  str        = np.concatenate([sigmas[::-1], [0.0]]   ).astype(np.floataa   )
      __lowerCAmelCase:  Union[str, Any]        = torch.from_numpy(UpperCAmelCase   )

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


     @property
     def     UpperCAmelCase    (				self     :						Tuple   )				->      Union[str, 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     UpperCAmelCase    (				self     :						Dict     ,    UpperCAmelCase     :						torch.FloatTensor     ,    UpperCAmelCase     :						Union[float, torch.FloatTensor]   )				->      torch.FloatTensor:
      if isinstance(UpperCAmelCase     ,    torch.Tensor   ):
       __lowerCAmelCase:  str        = timestep.to(self.timesteps.device   )
      __lowerCAmelCase:  Union[str, Any]        = (self.timesteps == timestep).nonzero().item()
      __lowerCAmelCase:  Optional[int]        = self.sigmas[step_index]

      __lowerCAmelCase:  Optional[int]        = sample / ((sigma**2 + 1) ** 0.5)

      __lowerCAmelCase:  Optional[Any]        = True
      return sample


     def     UpperCAmelCase    (				self     :						Optional[int]     ,    UpperCAmelCase     :						int     ,    UpperCAmelCase     :						Union[str, torch.device] = None   )				->      str:
      __lowerCAmelCase:  Dict        = 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":
       __lowerCAmelCase:  List[str]        = np.linspace(0     ,    self.config.num_train_timesteps - 1     ,    UpperCAmelCase     ,    dtype=UpperCAmelCase   )[
           ::-1
       ].copy()
      elif self.config.timestep_spacing == "leading":
       __lowerCAmelCase:  List[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
       __lowerCAmelCase:  List[Any]        = (np.arange(0     ,    UpperCAmelCase   ) * step_ratio).round()[::-1].copy().astype(UpperCAmelCase   )
       timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
       __lowerCAmelCase:  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
       __lowerCAmelCase:  Union[str, Any]        = (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\'.'''   )

      __lowerCAmelCase:  Tuple        = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
      __lowerCAmelCase:  Union[str, Any]        = np.log(UpperCAmelCase   )

      if self.config.interpolation_type == "linear":
       __lowerCAmelCase:  str        = np.interp(UpperCAmelCase     ,    np.arange(0     ,    len(UpperCAmelCase   )   )     ,    UpperCAmelCase   )
      elif self.config.interpolation_type == "log_linear":
       __lowerCAmelCase:  Optional[int]        = 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:
       __lowerCAmelCase:  Tuple        = self._convert_to_karras(in_sigmas=UpperCAmelCase     ,    num_inference_steps=self.num_inference_steps   )
       __lowerCAmelCase:  Tuple        = np.array([self._sigma_to_t(UpperCAmelCase     ,    UpperCAmelCase   ) for sigma in sigmas]   )

      __lowerCAmelCase:  Dict        = np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )
      __lowerCAmelCase:  Tuple        = torch.from_numpy(UpperCAmelCase   ).to(device=UpperCAmelCase   )
      if str(UpperCAmelCase   ).startswith('mps'   ):
       # mps does not support float64
       __lowerCAmelCase:  Any        = torch.from_numpy(UpperCAmelCase   ).to(UpperCAmelCase     ,    dtype=torch.floataa   )
      else:
       __lowerCAmelCase:  str        = torch.from_numpy(UpperCAmelCase   ).to(device=UpperCAmelCase   )


     def     UpperCAmelCase    (				self     :						List[Any]     ,    UpperCAmelCase     :						Tuple     ,    UpperCAmelCase     :						Optional[Any]   )				->      Dict:
      # get log sigma
      __lowerCAmelCase:  Optional[int]        = np.log(UpperCAmelCase   )

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

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

      __lowerCAmelCase:  Union[str, Any]        = log_sigmas[low_idx]
      __lowerCAmelCase:  List[str]        = log_sigmas[high_idx]

      # interpolate sigmas
      __lowerCAmelCase:  Optional[Any]        = (low - log_sigma) / (low - high)
      __lowerCAmelCase:  Union[str, Any]        = np.clip(UpperCAmelCase     ,    0     ,    1   )

      # transform interpolation to time range
      __lowerCAmelCase:  List[Any]        = (1 - w) * low_idx + w * high_idx
      __lowerCAmelCase:  Dict        = t.reshape(sigma.shape   )
      return t


     def     UpperCAmelCase    (				self     :						str     ,    UpperCAmelCase     :						torch.FloatTensor     ,    UpperCAmelCase     :						str   )				->      torch.FloatTensor:
      __lowerCAmelCase:  float        = in_sigmas[-1].item()
      __lowerCAmelCase:  float        = in_sigmas[0].item()

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


     def     UpperCAmelCase    (				self     :						List[Any]     ,    UpperCAmelCase     :						torch.FloatTensor     ,    UpperCAmelCase     :						Union[float, torch.FloatTensor]     ,    UpperCAmelCase     :						torch.FloatTensor     ,    UpperCAmelCase     :						float = 0.0     ,    UpperCAmelCase     :						float = 0.0     ,    UpperCAmelCase     :						float = float('inf'   )     ,    UpperCAmelCase     :						float = 1.0     ,    UpperCAmelCase     :						Optional[torch.Generator] = None     ,    UpperCAmelCase     :						bool = True     ,    )				->      Union[EulerDiscreteSchedulerOutput, 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   ):
       __lowerCAmelCase:  Optional[Any]        = timestep.to(self.timesteps.device   )

      __lowerCAmelCase:  Any        = (self.timesteps == timestep).nonzero().item()
      __lowerCAmelCase:  Optional[int]        = self.sigmas[step_index]

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

      __lowerCAmelCase:  Tuple        = randn_tensor(
          model_output.shape     ,    dtype=model_output.dtype     ,    device=model_output.device     ,    generator=UpperCAmelCase   )

      __lowerCAmelCase:  Union[str, Any]        = noise * s_noise
      __lowerCAmelCase:  int        = sigma * (gamma + 1)

      if gamma > 0:
       __lowerCAmelCase:  List[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":
       __lowerCAmelCase:  List[str]        = model_output
      elif self.config.prediction_type == "epsilon":
       __lowerCAmelCase:  Optional[int]        = sample - sigma_hat * model_output
      elif self.config.prediction_type == "v_prediction":
       # * c_out + input * c_skip
       __lowerCAmelCase:  Optional[int]        = 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
      __lowerCAmelCase:  Any        = (sample - pred_original_sample) / sigma_hat

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

      __lowerCAmelCase:  Dict        = sample + derivative * dt

      if not return_dict:
       return (prev_sample,)

      return EulerDiscreteSchedulerOutput(prev_sample=UpperCAmelCase     ,    pred_original_sample=UpperCAmelCase   )


     def     UpperCAmelCase    (				self     :						Optional[Any]     ,    UpperCAmelCase     :						torch.FloatTensor     ,    UpperCAmelCase     :						torch.FloatTensor     ,    UpperCAmelCase     :						torch.FloatTensor     ,    )				->      torch.FloatTensor:
      # Make sure sigmas and timesteps have the same device and dtype as original_samples
      __lowerCAmelCase:  Tuple        = 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
       __lowerCAmelCase:  Optional[int]        = self.timesteps.to(original_samples.device     ,    dtype=torch.floataa   )
       __lowerCAmelCase:  int        = timesteps.to(original_samples.device     ,    dtype=torch.floataa   )
      else:
       __lowerCAmelCase:  Dict        = self.timesteps.to(original_samples.device   )
       __lowerCAmelCase:  Optional[Any]        = timesteps.to(original_samples.device   )

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

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

      __lowerCAmelCase:  List[Any]        = original_samples + noise * sigma
      return noisy_samples


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








from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve







def _a					(			SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     np.ndarray						)       ->       np.ndarray:

 """simple docstring"""






 __lowerCAmelCase:  Any        = np.stack((horizontal_flow, vertical_flow)       ,   2						)

 # Create a grid of all pixel coordinates and subtract the flow to get the
 # target pixels coordinates
 __lowerCAmelCase:  List[str]        = np.stack(
     np.meshgrid(np.arange(0       ,   image.shape[1]						)       ,   np.arange(0       ,   image.shape[0]						)						)       ,   2						)
 __lowerCAmelCase:  int        = np.round(grid - flow						).astype(np.intaa						)

 # Find the locations outside of the original image
 __lowerCAmelCase:  Dict        = (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]						))
 __lowerCAmelCase:  str        = 0

 __lowerCAmelCase:  List[str]        = image[grid[:, :, 1], grid[:, :, 0]]

 # Set pixels at invalid locations to 0
 __lowerCAmelCase:  List[str]        = 0

 return warped







def _a					(			SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     SupportsIndex       ,   SCREAMING_SNAKE_CASE						:     float | None = None       ,   )       ->       tuple[np.ndarray, np.ndarray]:

 """simple docstring"""






 if alpha is None:
  __lowerCAmelCase:  Tuple        = 0.1

 # Initialize flow
 __lowerCAmelCase:  Optional[int]        = np.zeros_like(SCREAMING_SNAKE_CASE						)
 __lowerCAmelCase:  Dict        = np.zeros_like(SCREAMING_SNAKE_CASE						)

 # Prepare kernels for the calculation of the derivatives and the average velocity
 __lowerCAmelCase:  List[Any]        = np.array([[-1, 1], [-1, 1]]						) * 0.2_5
 __lowerCAmelCase:  int        = np.array([[-1, -1], [1, 1]]						) * 0.2_5
 __lowerCAmelCase:  Tuple        = np.array([[1, 1], [1, 1]]						) * 0.2_5
 __lowerCAmelCase:  Dict        = np.array(
     [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]						)

 # Iteratively refine the flow
 for _ in range(SCREAMING_SNAKE_CASE						):
  __lowerCAmelCase:  Optional[int]        = warp(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  List[str]        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						) + convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  int        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						) + convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  List[Any]        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						) + convolve(SCREAMING_SNAKE_CASE       ,   -kernel_t						)

  __lowerCAmelCase:  Any        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  Dict        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)

  # This updates the flow as proposed in the paper (Step 12)
  __lowerCAmelCase:  Tuple        = (
      derivative_x * avg_horizontal_velocity
      + derivative_y * avg_vertical_velocity
      + derivative_t
  )
  __lowerCAmelCase:  int        = update / (alpha**2 + derivative_x**2 + derivative_y**2)

  __lowerCAmelCase:  List[Any]        = avg_horizontal_velocity - derivative_x * update
  __lowerCAmelCase:  Union[str, Any]        = avg_vertical_velocity - derivative_y * update

 return horizontal_flow, vertical_flow


if __name__ == "__main__":
  import doctest

  doctest.testmod()





