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		,       __lowerCAmelCase=0.999		,       __lowerCAmelCase="cosine"		,       )->	Dict:






      '''simple docstring'''





      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

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

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

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







class       __snake_case (  lowercase_       , lowercase_ ):
 __lowerCamelCase     : Optional[int] 	=   [e.name for e in KarrasDiffusionSchedulers]
 __lowerCamelCase     : Optional[Any] 	=   2
 @register_to_config
 def __init__(	self		, snake_case__ = 1000		, snake_case__ = 0.0_0085		, snake_case__ = 0.012		, snake_case__ = "linear"		, snake_case__ = None		, snake_case__ = "epsilon"		, snake_case__ = "linspace"		, snake_case__ = 0		, )						->				List[str]:
       '''simple docstring'''





       if trained_betas is not None:
             UpperCAmelCase     :			Optional[int]     	=torch.tensor(_lowerCAmelCase		, dtype=torch.floataa    )
       elif beta_schedule == "linear":
             UpperCAmelCase     :			int     	=torch.linspace(_lowerCAmelCase		, _lowerCAmelCase		, _lowerCAmelCase		, dtype=torch.floataa    )
       elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
             UpperCAmelCase     :			List[str]     	=(
                 torch.linspace(beta_start**0.5		, beta_end**0.5		, _lowerCAmelCase		, dtype=torch.floataa    ) ** 2
             )
       elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             UpperCAmelCase     :			Optional[Any]     	=betas_for_alpha_bar(_lowerCAmelCase    )
       else:
             raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''    )

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

       #  set all values
       self.set_timesteps(_lowerCAmelCase		, _lowerCAmelCase		, _lowerCAmelCase    )
 def 						UpperCAmelCase__							(	self		, snake_case__		, snake_case__=None    )						->				Optional[int]:
       '''simple docstring'''





       if schedule_timesteps is None:
             UpperCAmelCase     :			Union[str, Any]     	=self.timesteps

       UpperCAmelCase     :			Dict     	=(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:
             UpperCAmelCase     :			Tuple     	=1 if len(_lowerCAmelCase    ) > 1 else 0
       else:
             UpperCAmelCase     :			str     	=timestep.cpu().item() if torch.is_tensor(_lowerCAmelCase    ) else timestep
             UpperCAmelCase     :			Any     	=self._index_counter[timestep_int]

       return indices[pos].item()
 @property
 def 						UpperCAmelCase__							(	self    )						->				Any:
       '''simple docstring'''





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

       return (self.sigmas.max() ** 2 + 1) ** 0.5
 def 						UpperCAmelCase__							(	self		, snake_case__		, snake_case__		, )						->				int:
       '''simple docstring'''





       UpperCAmelCase     :			List[str]     	=self.index_for_timestep(_lowerCAmelCase    )

       if self.state_in_first_order:
             UpperCAmelCase     :			Union[str, Any]     	=self.sigmas[step_index]
       else:
             UpperCAmelCase     :			Optional[Any]     	=self.sigmas_interpol[step_index - 1]

       UpperCAmelCase     :			Union[str, Any]     	=sample / ((sigma**2 + 1) ** 0.5)
       return sample
 def 						UpperCAmelCase__							(	self		, snake_case__		, snake_case__ = None		, snake_case__ = None		, )						->				int:
       '''simple docstring'''





       UpperCAmelCase     :			Tuple     	=num_inference_steps

       UpperCAmelCase     :			Tuple     	=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":
             UpperCAmelCase     :			Optional[int]     	=np.linspace(0		, num_train_timesteps - 1		, _lowerCAmelCase		, dtype=_lowerCAmelCase    )[::-1].copy()
       elif self.config.timestep_spacing == "leading":
             UpperCAmelCase     :			Tuple     	=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
             UpperCAmelCase     :			Optional[int]     	=(np.arange(0		, _lowerCAmelCase    ) * step_ratio).round()[::-1].copy().astype(_lowerCAmelCase    )
             timesteps += self.config.steps_offset
       elif self.config.timestep_spacing == "trailing":
             UpperCAmelCase     :			str     	=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
             UpperCAmelCase     :			List[Any]     	=(np.arange(_lowerCAmelCase		, 0		, -step_ratio    )).round().copy().astype(_lowerCAmelCase    )
             timesteps -= 1
       else:
             raise ValueError(
                 f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''    )

       UpperCAmelCase     :			List[str]     	=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
       UpperCAmelCase     :			Union[str, Any]     	=torch.from_numpy(np.log(_lowerCAmelCase    )    ).to(_lowerCAmelCase    )

       UpperCAmelCase     :			Union[str, Any]     	=np.interp(_lowerCAmelCase		, np.arange(0		, len(_lowerCAmelCase    )    )		, _lowerCAmelCase    )
       UpperCAmelCase     :			Optional[Any]     	=np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )
       UpperCAmelCase     :			Optional[Any]     	=torch.from_numpy(_lowerCAmelCase    ).to(device=_lowerCAmelCase    )

       # compute up and down sigmas
       UpperCAmelCase     :			List[Any]     	=sigmas.roll(-1    )
       UpperCAmelCase     :			List[str]     	=0.0
       UpperCAmelCase     :			str     	=(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
       UpperCAmelCase     :			str     	=(sigmas_next**2 - sigmas_up**2) ** 0.5
       UpperCAmelCase     :			int     	=0.0

       # compute interpolated sigmas
       UpperCAmelCase     :			Dict     	=sigmas.log().lerp(sigmas_down.log()		, 0.5    ).exp()
       UpperCAmelCase     :			int     	=0.0

       # set sigmas
       UpperCAmelCase     :			int     	=torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2    ), sigmas[-1:]]    )
       UpperCAmelCase     :			Tuple     	=torch.cat(
           [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2    ), sigmas_interpol[-1:]]    )
       UpperCAmelCase     :			Union[str, Any]     	=torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2    ), sigmas_up[-1:]]    )
       UpperCAmelCase     :			int     	=torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2    ), sigmas_down[-1:]]    )

       if str(_lowerCAmelCase    ).startswith('''mps'''    ):
             # mps does not support float64
             UpperCAmelCase     :			Optional[int]     	=torch.from_numpy(_lowerCAmelCase    ).to(_lowerCAmelCase		, dtype=torch.floataa    )
       else:
             UpperCAmelCase     :			int     	=torch.from_numpy(_lowerCAmelCase    ).to(_lowerCAmelCase    )

       UpperCAmelCase     :			Dict     	=self.sigma_to_t(_lowerCAmelCase    ).to(_lowerCAmelCase		, dtype=timesteps.dtype    )
       UpperCAmelCase     :			List[Any]     	=torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])		, dim=-1    ).flatten()

       UpperCAmelCase     :			Optional[int]     	=torch.cat([timesteps[:1], interleaved_timesteps]    )

       UpperCAmelCase     :			Union[str, Any]     	=None

       # for exp beta schedules, such as the one for `pipeline_shap_e.py`
       # we need an index counter
       UpperCAmelCase     :			Union[str, Any]     	=defaultdict(_lowerCAmelCase    )
 def 						UpperCAmelCase__							(	self		, snake_case__    )						->				str:
       '''simple docstring'''





       UpperCAmelCase     :			Tuple     	=sigma.log()

       # get distribution
       UpperCAmelCase     :			Union[str, Any]     	=log_sigma - self.log_sigmas[:, None]

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

       UpperCAmelCase     :			Optional[int]     	=self.log_sigmas[low_idx]
       UpperCAmelCase     :			Optional[Any]     	=self.log_sigmas[high_idx]

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

       # transform interpolation to time range
       UpperCAmelCase     :			Tuple     	=(1 - w) * low_idx + w * high_idx
       UpperCAmelCase     :			Any     	=t.view(sigma.shape    )
       return t
 @property
 def 						UpperCAmelCase__							(	self    )						->				List[Any]:
       '''simple docstring'''





       return self.sample is None
 def 						UpperCAmelCase__							(	self		, snake_case__		, snake_case__		, snake_case__		, snake_case__ = None		, snake_case__ = True		, )						->				str:
       '''simple docstring'''





       UpperCAmelCase     :			Optional[int]     	=self.index_for_timestep(_lowerCAmelCase    )

       # advance index counter by 1
       UpperCAmelCase     :			Any     	=timestep.cpu().item() if torch.is_tensor(_lowerCAmelCase    ) else timestep
       self._index_counter[timestep_int] += 1

       if self.state_in_first_order:
             UpperCAmelCase     :			List[str]     	=self.sigmas[step_index]
             UpperCAmelCase     :			List[Any]     	=self.sigmas_interpol[step_index]
             UpperCAmelCase     :			int     	=self.sigmas_up[step_index]
             UpperCAmelCase     :			Dict     	=self.sigmas_down[step_index - 1]
       else:
             # 2nd order / KPDM2's method
             UpperCAmelCase     :			List[str]     	=self.sigmas[step_index - 1]
             UpperCAmelCase     :			List[str]     	=self.sigmas_interpol[step_index - 1]
             UpperCAmelCase     :			int     	=self.sigmas_up[step_index - 1]
             UpperCAmelCase     :			Optional[int]     	=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
       UpperCAmelCase     :			Optional[int]     	=0
       UpperCAmelCase     :			int     	=sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

       UpperCAmelCase     :			Any     	=model_output.device
       UpperCAmelCase     :			str     	=randn_tensor(model_output.shape		, dtype=model_output.dtype		, device=_lowerCAmelCase		, generator=_lowerCAmelCase    )

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       if self.config.prediction_type == "epsilon":
             UpperCAmelCase     :			List[Any]     	=sigma_hat if self.state_in_first_order else sigma_interpol
             UpperCAmelCase     :			str     	=sample - sigma_input * model_output
       elif self.config.prediction_type == "v_prediction":
             UpperCAmelCase     :			List[str]     	=sigma_hat if self.state_in_first_order else sigma_interpol
             UpperCAmelCase     :			Optional[int]     	=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
             UpperCAmelCase     :			Union[str, Any]     	=(sample - pred_original_sample) / sigma_hat
             # 3. delta timestep
             UpperCAmelCase     :			int     	=sigma_interpol - sigma_hat

             # store for 2nd order step
             UpperCAmelCase     :			str     	=sample
             UpperCAmelCase     :			str     	=dt
             UpperCAmelCase     :			Optional[Any]     	=sample + derivative * dt
       else:
             # DPM-Solver-2
             # 2. Convert to an ODE derivative for 2nd order
             UpperCAmelCase     :			Tuple     	=(sample - pred_original_sample) / sigma_interpol
             # 3. delta timestep
             UpperCAmelCase     :			Dict     	=sigma_down - sigma_hat

             UpperCAmelCase     :			Union[str, Any]     	=self.sample
             UpperCAmelCase     :			Any     	=None

             UpperCAmelCase     :			str     	=sample + derivative * dt
             UpperCAmelCase     :			Any     	=prev_sample + noise * sigma_up

       if not return_dict:
             return (prev_sample,)

       return SchedulerOutput(prev_sample=_lowerCAmelCase    )
 def 						UpperCAmelCase__							(	self		, snake_case__		, snake_case__		, snake_case__		, )						->				Union[str, Any]:
       '''simple docstring'''





       UpperCAmelCase     :			List[Any]     	=self.sigmas.to(device=original_samples.device		, dtype=original_samples.dtype    )
       if original_samples.device.type == "mps" and torch.is_floating_point(_lowerCAmelCase    ):
             # mps does not support float64
             UpperCAmelCase     :			List[str]     	=self.timesteps.to(original_samples.device		, dtype=torch.floataa    )
             UpperCAmelCase     :			Optional[Any]     	=timesteps.to(original_samples.device		, dtype=torch.floataa    )
       else:
             UpperCAmelCase     :			Union[str, Any]     	=self.timesteps.to(original_samples.device    )
             UpperCAmelCase     :			Tuple     	=timesteps.to(original_samples.device    )

       UpperCAmelCase     :			Optional[int]     	=[self.index_for_timestep(_lowerCAmelCase		, _lowerCAmelCase    ) for t in timesteps]

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

       UpperCAmelCase     :			Union[str, Any]     	=original_samples + noise * sigma
       return noisy_samples






 def __len__(	self    )						->				Any:
       '''simple docstring'''





       return self.config.num_train_timesteps







from typing import Any

import numpy as np





def  __UpperCamelCase   (     a)			->bool:
					assert np.shape(a)[0] == np.shape(a)[1]

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

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

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





def  __UpperCamelCase   (     a)			->Any:
					lowerCamelCase__      =							np.random.randn(a,  a)
					lowerCamelCase__      =							np.dot(a,  random_matrix.T)
					assert _is_matrix_spd(a)
					return spd_matrix





def  __UpperCamelCase   (     a,  a,  a = 1000,  a = 1E-8,  )			->Any:
					assert np.shape(a)[0] == np.shape(a)[1]
					assert np.shape(a)[0] == np.shape(a)[0]
					assert _is_matrix_spd(a)

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

					# Set initial errors in solution guess and residual.
					lowerCamelCase__      =							1E9
					lowerCamelCase__      =							1E9
					lowerCamelCase__      =							1E9

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

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

										# The main algorithm.

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

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

										# Update variables.
										lowerCamelCase__      =							np.copy(a)
										lowerCamelCase__      =							np.copy(a)
										lowerCamelCase__      =							np.copy(a)

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

					return x





def  __UpperCamelCase   (     )			->None:
					lowerCamelCase__      =							3
					lowerCamelCase__      =							_create_spd_matrix(a)
					lowerCamelCase__      =							np.random.randn(a,  1)
					lowerCamelCase__      =							np.dot(a,  a)

					# Numpy solution.
					lowerCamelCase__      =							np.linalg.solve(a,  a)

					# Our implementation.
					lowerCamelCase__      =							conjugate_gradient(a,  a)

					# 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()

