


import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

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



def      _lowerCAmelCase  (							lowerCAmelCase_							:Dict						,  lowerCAmelCase_							:Dict=0.9_9_9						,  lowerCAmelCase_							:Optional[int]="cosine"						,  )->int:
			'''simple docstring'''






			if alpha_transform_type == "cosine":

						def alpha_bar_fn(lowerCAmelCase_							:Tuple							):
									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(lowerCAmelCase_							:int							):
									return math.exp(t * -1_2.0							)

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

			snake_case_         =   []
			for i in range(__UpperCamelCase							):
						snake_case_         =   i / num_diffusion_timesteps
						snake_case_         =   (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       __lowerCAmelCase       (	__lowerCamelCase	,					__lowerCamelCase   ):






		"""simple docstring"""





		_SCREAMING_SNAKE_CASE						      =    [e.name for e in KarrasDiffusionSchedulers]
		_SCREAMING_SNAKE_CASE						      =    2



		@register_to_config
		def __init__(       self    :    Tuple      ,			_lowerCAmelCase    :    int = 1_0_0_0      ,			_lowerCAmelCase    :    float = 0.00_085      ,			_lowerCAmelCase    :    float = 0.012      ,			_lowerCAmelCase    :    str = "linear"      ,			_lowerCAmelCase    :    Optional[Union[np.ndarray, List[float]]] = None      ,			_lowerCAmelCase    :    str = "epsilon"      ,			_lowerCAmelCase    :    str = "linspace"      ,			_lowerCAmelCase    :    int = 0      ,			)				->	Tuple:




					"""simple docstring"""





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

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

					#  set all values
					self.set_timesteps(_UpperCamelCase      ,			_UpperCamelCase      ,			_UpperCamelCase					)



		def    lowerCAmelCase__					(       self    :    int      ,			_lowerCAmelCase    :    List[str]      ,			_lowerCAmelCase    :    Dict=None					)				->	Tuple:




					"""simple docstring"""





					if schedule_timesteps is None:
								snake_case_         =   self.timesteps

					snake_case_         =   (schedule_timesteps == timestep).nonzero()

					# The sigma index that is taken for the **very** first `step`
					# is always the second index (or the last index if there is only 1)
					# This way we can ensure we don't accidentally skip a sigma in
					# case we start in the middle of the denoising schedule (e.g. for image-to-image)
					if len(self._index_counter					) == 0:
								snake_case_         =   1 if len(_UpperCamelCase					) > 1 else 0
					else:
								snake_case_         =   timestep.cpu().item() if torch.is_tensor(_UpperCamelCase					) else timestep
								snake_case_         =   self._index_counter[timestep_int]

					return indices[pos].item()



		@property
		def    lowerCAmelCase__					(       self    :    Any					)				->	Dict:




					"""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    :    Optional[int]      ,			_lowerCAmelCase    :    torch.FloatTensor      ,			_lowerCAmelCase    :    Union[float, torch.FloatTensor]      ,			)				->	torch.FloatTensor:




					"""simple docstring"""
					snake_case_         =   self.index_for_timestep(_UpperCamelCase					)

					if self.state_in_first_order:
								snake_case_         =   self.sigmas[step_index]
					else:
								snake_case_         =   self.sigmas_interpol[step_index - 1]

					snake_case_         =   sample / ((sigma**2 + 1) ** 0.5)
					return sample



		def    lowerCAmelCase__					(       self    :    List[str]      ,			_lowerCAmelCase    :    int      ,			_lowerCAmelCase    :    Union[str, torch.device] = None      ,			_lowerCAmelCase    :    Optional[int] = None      ,			)				->	Any:




					"""simple docstring"""
					snake_case_         =   num_inference_steps

					snake_case_         =   num_train_timesteps or self.config.num_train_timesteps

					# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
					if self.config.timestep_spacing == "linspace":
								snake_case_         =   np.linspace(0      ,			num_train_timesteps - 1      ,			_UpperCamelCase      ,			dtype=_UpperCamelCase					)[::-1].copy()
					elif self.config.timestep_spacing == "leading":
								snake_case_         =   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_         =   (np.arange(0      ,			_UpperCamelCase					) * step_ratio).round()[::-1].copy().astype(_UpperCamelCase					)
								timesteps += self.config.steps_offset
					elif self.config.timestep_spacing == "trailing":
								snake_case_         =   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_         =   (np.arange(_UpperCamelCase      ,			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\'.'''					)

					snake_case_         =   np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
					snake_case_         =   torch.from_numpy(np.log(_UpperCamelCase					)					).to(_UpperCamelCase					)

					snake_case_         =   np.interp(_UpperCamelCase      ,			np.arange(0      ,			len(_UpperCamelCase					)					)      ,			_UpperCamelCase					)
					snake_case_         =   np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)
					snake_case_         =   torch.from_numpy(_UpperCamelCase					).to(device=_UpperCamelCase					)

					# compute up and down sigmas
					snake_case_         =   sigmas.roll(-1					)
					snake_case_         =   0.0
					snake_case_         =   (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
					snake_case_         =   (sigmas_next**2 - sigmas_up**2) ** 0.5
					snake_case_         =   0.0

					# compute interpolated sigmas
					snake_case_         =   sigmas.log().lerp(sigmas_down.log()      ,			0.5					).exp()
					snake_case_         =   0.0

					# set sigmas
					snake_case_         =   torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2					), sigmas[-1:]]					)
					snake_case_         =   torch.cat(
					    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2					), sigmas_interpol[-1:]]					)
					snake_case_         =   torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2					), sigmas_up[-1:]]					)
					snake_case_         =   torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2					), sigmas_down[-1:]]					)

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

					snake_case_         =   self.sigma_to_t(_UpperCamelCase					).to(_UpperCamelCase      ,			dtype=timesteps.dtype					)
					snake_case_         =   torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])      ,			dim=-1					).flatten()

					snake_case_         =   torch.cat([timesteps[:1], interleaved_timesteps]					)

					snake_case_         =   None

					# for exp beta schedules, such as the one for `pipeline_shap_e.py`
					# we need an index counter
					snake_case_         =   defaultdict(_UpperCamelCase					)



		def    lowerCAmelCase__					(       self    :    Tuple      ,			_lowerCAmelCase    :    List[Any]					)				->	int:




					"""simple docstring"""
					snake_case_         =   sigma.log()

					# get distribution
					snake_case_         =   log_sigma - self.log_sigmas[:, None]

					# get sigmas range
					snake_case_         =   dists.ge(0					).cumsum(dim=0					).argmax(dim=0					).clamp(max=self.log_sigmas.shape[0] - 2					)
					snake_case_         =   low_idx + 1

					snake_case_         =   self.log_sigmas[low_idx]
					snake_case_         =   self.log_sigmas[high_idx]

					# interpolate sigmas
					snake_case_         =   (low - log_sigma) / (low - high)
					snake_case_         =   w.clamp(0      ,			1					)

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



		@property
		def    lowerCAmelCase__					(       self    :    Optional[int]					)				->	List[Any]:




					"""simple docstring"""
					return self.sample is None



		def    lowerCAmelCase__					(       self    :    Union[str, Any]      ,			_lowerCAmelCase    :    Union[torch.FloatTensor, np.ndarray]      ,			_lowerCAmelCase    :    Union[float, torch.FloatTensor]      ,			_lowerCAmelCase    :    Union[torch.FloatTensor, np.ndarray]      ,			_lowerCAmelCase    :    Optional[torch.Generator] = None      ,			_lowerCAmelCase    :    bool = True      ,			)				->	Union[SchedulerOutput, Tuple]:




					"""simple docstring"""
					snake_case_         =   self.index_for_timestep(_UpperCamelCase					)

					# advance index counter by 1
					snake_case_         =   timestep.cpu().item() if torch.is_tensor(_UpperCamelCase					) else timestep
					self._index_counter[timestep_int] += 1

					if self.state_in_first_order:
								snake_case_         =   self.sigmas[step_index]
								snake_case_         =   self.sigmas_interpol[step_index]
								snake_case_         =   self.sigmas_up[step_index]
								snake_case_         =   self.sigmas_down[step_index - 1]
					else:
								# 2nd order / KPDM2's method
								snake_case_         =   self.sigmas[step_index - 1]
								snake_case_         =   self.sigmas_interpol[step_index - 1]
								snake_case_         =   self.sigmas_up[step_index - 1]
								snake_case_         =   self.sigmas_down[step_index - 1]

					# currently only gamma=0 is supported. This usually works best anyways.
					# We can support gamma in the future but then need to scale the timestep before
					# passing it to the model which requires a change in API
					snake_case_         =   0
					snake_case_         =   sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

					snake_case_         =   model_output.device
					snake_case_         =   randn_tensor(model_output.shape      ,			dtype=model_output.dtype      ,			device=_UpperCamelCase      ,			generator=_UpperCamelCase					)

					# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
					if self.config.prediction_type == "epsilon":
								snake_case_         =   sigma_hat if self.state_in_first_order else sigma_interpol
								snake_case_         =   sample - sigma_input * model_output
					elif self.config.prediction_type == "v_prediction":
								snake_case_         =   sigma_hat if self.state_in_first_order else sigma_interpol
								snake_case_         =   model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
								    sample / (sigma_input**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`'''					)

					if self.state_in_first_order:
								# 2. Convert to an ODE derivative for 1st order
								snake_case_         =   (sample - pred_original_sample) / sigma_hat
								# 3. delta timestep
								snake_case_         =   sigma_interpol - sigma_hat

								# store for 2nd order step
								snake_case_         =   sample
								snake_case_         =   dt
								snake_case_         =   sample + derivative * dt
					else:
								# DPM-Solver-2
								# 2. Convert to an ODE derivative for 2nd order
								snake_case_         =   (sample - pred_original_sample) / sigma_interpol
								# 3. delta timestep
								snake_case_         =   sigma_down - sigma_hat

								snake_case_         =   self.sample
								snake_case_         =   None

								snake_case_         =   sample + derivative * dt
								snake_case_         =   prev_sample + noise * sigma_up

					if not return_dict:
								return (prev_sample,)

					return SchedulerOutput(prev_sample=_UpperCamelCase					)



		def    lowerCAmelCase__					(       self    :    Optional[int]      ,			_lowerCAmelCase    :    torch.FloatTensor      ,			_lowerCAmelCase    :    torch.FloatTensor      ,			_lowerCAmelCase    :    torch.FloatTensor      ,			)				->	torch.FloatTensor:




					"""simple docstring"""
					snake_case_         =   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
								snake_case_         =   self.timesteps.to(original_samples.device      ,			dtype=torch.floataa					)
								snake_case_         =   timesteps.to(original_samples.device      ,			dtype=torch.floataa					)
					else:
								snake_case_         =   self.timesteps.to(original_samples.device					)
								snake_case_         =   timesteps.to(original_samples.device					)

					snake_case_         =   [self.index_for_timestep(_UpperCamelCase      ,			_UpperCamelCase					) for t in timesteps]

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

					snake_case_         =   original_samples + noise * sigma
					return noisy_samples



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




					"""simple docstring"""
					return self.config.num_train_timesteps








from typing import Any

import numpy as np



def      _lowerCAmelCase  (							lowerCAmelCase_							:np.ndarray							)->bool:
   '''simple docstring'''






   assert np.shape(lowerCAmelCase_							)[0] == np.shape(lowerCAmelCase_							)[1]

   # If matrix not symmetric, exit right away.
   if np.allclose(lowerCAmelCase_						,  matrix.T							) is False:
      return False

   # Get eigenvalues and eignevectors for a symmetric matrix.
   snake_case_      ,      snake_case_         =   np.linalg.eigh(lowerCAmelCase_							)

   # Check sign of all eigenvalues.
   # np.all returns a value of type np.bool_
   return bool(np.all(eigen_values > 0							)							)



def      _lowerCAmelCase  (							lowerCAmelCase_							:int							)->Any:
   '''simple docstring'''






   snake_case_         =   np.random.randn(lowerCAmelCase_						,  lowerCAmelCase_							)
   snake_case_         =   np.dot(lowerCAmelCase_						,  random_matrix.T							)
   assert _is_matrix_spd(lowerCAmelCase_							)
   return spd_matrix



def      _lowerCAmelCase  (							lowerCAmelCase_							:np.ndarray						,  lowerCAmelCase_							:np.ndarray						,  lowerCAmelCase_							:int = 1_000						,  lowerCAmelCase_							:float = 1e-8						,  )->Any:
   '''simple docstring'''






   assert np.shape(lowerCAmelCase_							)[0] == np.shape(lowerCAmelCase_							)[1]
   assert np.shape(lowerCAmelCase_							)[0] == np.shape(lowerCAmelCase_							)[0]
   assert _is_matrix_spd(lowerCAmelCase_							)

   # Initialize solution guess, residual, search direction.
   snake_case_         =   np.zeros((np.shape(lowerCAmelCase_							)[0], 1)							)
   snake_case_         =   np.copy(lowerCAmelCase_							)
   snake_case_         =   np.copy(lowerCAmelCase_							)

   # Set initial errors in solution guess and residual.
   snake_case_         =   1e9
   snake_case_         =   1e9
   snake_case_         =   1e9

   # Set iteration counter to threshold number of iterations.
   snake_case_         =   0

   while error > tol:
      # Save this value so we only calculate the matrix-vector product once.
      snake_case_         =   np.dot(lowerCAmelCase_						,  lowerCAmelCase_							)

      # The main algorithm.

      # Update search direction magnitude.
      snake_case_         =   np.dot(ra.T						,  lowerCAmelCase_							) / np.dot(pa.T						,  lowerCAmelCase_							)
      # Update solution guess.
      snake_case_         =   xa + alpha * pa
      # Calculate new residual.
      snake_case_         =   ra - alpha * w
      # Calculate new Krylov subspace scale.
      snake_case_         =   np.dot(r.T						,  lowerCAmelCase_							) / np.dot(ra.T						,  lowerCAmelCase_							)
      # Calculate new A conjuage search direction.
      snake_case_         =   r + beta * pa

      # Calculate errors.
      snake_case_         =   np.linalg.norm(r - ra							)
      snake_case_         =   np.linalg.norm(x - xa							)
      snake_case_         =   np.maximum(lowerCAmelCase_						,  lowerCAmelCase_							)

      # Update variables.
      snake_case_         =   np.copy(lowerCAmelCase_							)
      snake_case_         =   np.copy(lowerCAmelCase_							)
      snake_case_         =   np.copy(lowerCAmelCase_							)

      # Update number of iterations.
      iterations += 1
      if iterations > max_iterations:
         break

   return x



def      _lowerCAmelCase  (							)->None:
   '''simple docstring'''






   snake_case_         =   3
   snake_case_         =   _create_spd_matrix(lowerCAmelCase_							)
   snake_case_         =   np.random.randn(lowerCAmelCase_						,  1							)
   snake_case_         =   np.dot(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Numpy solution.
   snake_case_         =   np.linalg.solve(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Our implementation.
   snake_case_         =   conjugate_gradient(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Ensure both solutions are close to x_true (and therefore one another).
   assert np.linalg.norm(x_numpy - x_true							) <= 1e-6
   assert np.linalg.norm(x_conjugate_gradient - x_true							) <= 1e-6


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   test_conjugate_gradient()




