





'''simple docstring'''



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 .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def    _lowerCAmelCase						(				lowerCamelCase_			:  Dict		,       lowerCamelCase_			:  List[str]=0.9_99		,       lowerCamelCase_			:  int="cosine"		,       ):
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(lowerCamelCase_			:  int				):
									return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2				) ** 2

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(lowerCamelCase_			:  Optional[Any]				):
									return math.exp(t * -12.0				)

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

			__lowercase										=							[]
			for i in range(lowerCamelCase_				):
						__lowercase										=							i / num_diffusion_timesteps
						__lowercase										=							(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 							__lowercase       (      lowerCAmelCase__ ,      lowerCAmelCase__						):







	'''simple docstring'''

	a    :				str											=       [e.name for e in KarrasDiffusionSchedulers]
	a    :				Dict											=       2


	@register_to_config
	def __init__(self     ,_lowerCamelCase = 1000     ,_lowerCamelCase = 0.0_0_0_8_5     ,_lowerCamelCase = 0.0_1_2     ,_lowerCamelCase = "linear"     ,_lowerCamelCase = None     ,_lowerCamelCase = "epsilon"     ,_lowerCamelCase = False     ,_lowerCamelCase = False     ,_lowerCamelCase = 1.0     ,_lowerCamelCase = "linspace"     ,_lowerCamelCase = 0     ,)							->							List[Any]:







				'''simple docstring'''





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

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

				#  set all values
				self.set_timesteps(_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )
				__lowercase										=							use_karras_sigmas


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase=None )							->							Optional[int]:







				'''simple docstring'''





				if schedule_timesteps is None:
							__lowercase										=							self.timesteps

				__lowercase										=							(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:
							__lowercase										=							1 if len(_lowerCamelCase ) > 1 else 0
				else:
							__lowercase										=							timestep.cpu().item() if torch.is_tensor(_lowerCamelCase ) else timestep
							__lowercase										=							self._index_counter[timestep_int]

				return indices[pos].item()


	@property
	def 						_UpperCAmelCase     (self )							->							Optional[int]:







				'''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     ,_lowerCamelCase     ,_lowerCamelCase     ,)							->							torch.FloatTensor:







				'''simple docstring'''





				__lowercase										=							self.index_for_timestep(_lowerCamelCase )

				__lowercase										=							self.sigmas[step_index]
				__lowercase										=							sample / ((sigma**2 + 1) ** 0.5)
				return sample


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase = None     ,_lowerCamelCase = None     ,)							->							Optional[int]:







				'''simple docstring'''





				__lowercase										=							num_inference_steps

				__lowercase										=							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":
							__lowercase										=							np.linspace(0     ,num_train_timesteps - 1     ,_lowerCamelCase     ,dtype=_lowerCamelCase )[::-1].copy()
				elif self.config.timestep_spacing == "leading":
							__lowercase										=							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
							__lowercase										=							(np.arange(0     ,_lowerCamelCase ) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase )
							timesteps += self.config.steps_offset
				elif self.config.timestep_spacing == "trailing":
							__lowercase										=							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
							__lowercase										=							(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'." )

				__lowercase										=							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
				__lowercase										=							np.log(_lowerCamelCase )
				__lowercase										=							np.interp(_lowerCamelCase     ,np.arange(0     ,len(_lowerCamelCase ) )     ,_lowerCamelCase )

				if self.config.use_karras_sigmas:
							__lowercase										=							self._convert_to_karras(in_sigmas=_lowerCamelCase     ,num_inference_steps=self.num_inference_steps )
							__lowercase										=							np.array([self._sigma_to_t(_lowerCamelCase     ,_lowerCamelCase ) for sigma in sigmas] )

				__lowercase										=							np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
				__lowercase										=							torch.from_numpy(_lowerCamelCase ).to(device=_lowerCamelCase )
				__lowercase										=							torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2 ), sigmas[-1:]] )

				__lowercase										=							torch.from_numpy(_lowerCamelCase )
				__lowercase										=							torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2 )] )

				if str(_lowerCamelCase ).startswith('''mps''' ):
							# mps does not support float64
							__lowercase										=							timesteps.to(_lowerCamelCase     ,dtype=torch.floataa )
				else:
							__lowercase										=							timesteps.to(device=_lowerCamelCase )

				# empty dt and derivative
				__lowercase										=							None
				__lowercase										=							None

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


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase )							->							str:







				'''simple docstring'''





				__lowercase										=							np.log(_lowerCamelCase )

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

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

				__lowercase										=							log_sigmas[low_idx]
				__lowercase										=							log_sigmas[high_idx]

				# interpolate sigmas
				__lowercase										=							(low - log_sigma) / (low - high)
				__lowercase										=							np.clip(_lowerCamelCase     ,0     ,1 )

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


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase )							->							torch.FloatTensor:







				'''simple docstring'''





				__lowercase										=							in_sigmas[-1].item()
				__lowercase										=							in_sigmas[0].item()

				__lowercase										=							7.0  # 7.0 is the value used in the paper
				__lowercase										=							np.linspace(0     ,1     ,_lowerCamelCase )
				__lowercase										=							sigma_min ** (1 / rho)
				__lowercase										=							sigma_max ** (1 / rho)
				__lowercase										=							(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
				return sigmas


	@property
	def 						_UpperCAmelCase     (self )							->							Any:







				'''simple docstring'''





				return self.dt is None


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase = True     ,)							->							Union[SchedulerOutput, Tuple]:







				'''simple docstring'''





				__lowercase										=							self.index_for_timestep(_lowerCamelCase )

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

				if self.state_in_first_order:
							__lowercase										=							self.sigmas[step_index]
							__lowercase										=							self.sigmas[step_index + 1]
				else:
							# 2nd order / Heun's method
							__lowercase										=							self.sigmas[step_index - 1]
							__lowercase										=							self.sigmas[step_index]

				# 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
				__lowercase										=							0
				__lowercase										=							sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

				# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
				if self.config.prediction_type == "epsilon":
							__lowercase										=							sigma_hat if self.state_in_first_order else sigma_next
							__lowercase										=							sample - sigma_input * model_output
				elif self.config.prediction_type == "v_prediction":
							__lowercase										=							sigma_hat if self.state_in_first_order else sigma_next
							__lowercase										=							model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
							    sample / (sigma_input**2 + 1)
							)
				elif self.config.prediction_type == "sample":
							__lowercase										=							model_output
				else:
							raise ValueError(
							    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`" )

				if self.config.clip_sample:
							__lowercase										=							pred_original_sample.clamp(
							    -self.config.clip_sample_range     ,self.config.clip_sample_range )

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

							# store for 2nd order step
							__lowercase										=							derivative
							__lowercase										=							dt
							__lowercase										=							sample
				else:
							# 2. 2nd order / Heun's method
							__lowercase										=							(sample - pred_original_sample) / sigma_next
							__lowercase										=							(self.prev_derivative + derivative) / 2

							# 3. take prev timestep & sample
							__lowercase										=							self.dt
							__lowercase										=							self.sample

							# free dt and derivative
							# Note, this puts the scheduler in "first order mode"
							__lowercase										=							None
							__lowercase										=							None
							__lowercase										=							None

				__lowercase										=							sample + derivative * dt

				if not return_dict:
							return (prev_sample,)

				return SchedulerOutput(prev_sample=_lowerCamelCase )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase     ,)							->							torch.FloatTensor:







				'''simple docstring'''





				__lowercase										=							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
							__lowercase										=							self.timesteps.to(original_samples.device     ,dtype=torch.floataa )
							__lowercase										=							timesteps.to(original_samples.device     ,dtype=torch.floataa )
				else:
							__lowercase										=							self.timesteps.to(original_samples.device )
							__lowercase										=							timesteps.to(original_samples.device )

				__lowercase										=							[self.index_for_timestep(_lowerCamelCase     ,_lowerCamelCase ) for t in timesteps]

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

				__lowercase										=							original_samples + noise * sigma
				return noisy_samples


	def __len__(self )							->							Dict:







				'''simple docstring'''





				return self.config.num_train_timesteps












'''simple docstring'''



from __future__ import annotations

from typing import Any






class 							__lowercase       :







	'''simple docstring'''

	def __init__(self     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				__lowercase										=							num_of_nodes
				__lowercase										=							[]
				__lowercase										=							{}


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				self.m_edges.append([u_node, v_node, weight] )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase )							->							int:







				'''simple docstring'''





				if self.m_component[u_node] == u_node:
							return u_node
				return self.find_component(self.m_component[u_node] )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				if self.m_component[u_node] != u_node:
							for k in self.m_component:
										__lowercase										=							self.find_component(_lowerCamelCase )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				if component_size[u_node] <= component_size[v_node]:
							__lowercase										=							v_node
							component_size[v_node] += component_size[u_node]
							self.set_component(_lowerCamelCase )

				elif component_size[u_node] >= component_size[v_node]:
							__lowercase										=							self.find_component(_lowerCamelCase )
							component_size[u_node] += component_size[v_node]
							self.set_component(_lowerCamelCase )


	def 						_UpperCAmelCase     (self )							->							None:







				'''simple docstring'''





				__lowercase										=							[]
				__lowercase										=							0

				__lowercase										=							[-1] * self.m_num_of_nodes

				# A list of components (initialized to all of the nodes)
				for node in range(self.m_num_of_nodes ):
							self.m_component.update({node: node} )
							component_size.append(1 )

				__lowercase										=							self.m_num_of_nodes

				while num_of_components > 1:
							for edge in self.m_edges:
										__lowercase						,		__lowercase						,		__lowercase										=							edge

										__lowercase										=							self.m_component[u]
										__lowercase										=							self.m_component[v]

										if u_component != v_component:

													for component in (u_component, v_component):
																if (
																    minimum_weight_edge[component] == -1
																    or minimum_weight_edge[component][2] > w
																):
																			__lowercase										=							[u, v, w]

							for edge in minimum_weight_edge:
										if isinstance(_lowerCamelCase     ,_lowerCamelCase ):
													__lowercase						,		__lowercase						,		__lowercase										=							edge

													__lowercase										=							self.m_component[u]
													__lowercase										=							self.m_component[v]

													if u_component != v_component:
																mst_weight += w
																self.union(_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )
																print(f"Added edge [{u} - {v}]\nAdded weight: {w}\n" )
																num_of_components -= 1

							__lowercase										=							[-1] * self.m_num_of_nodes
				print(f"The total weight of the minimal spanning tree is: {mst_weight}" )





def    _lowerCAmelCase						(				):
			pass


if __name__ == "__main__":
	import doctest

	doctest.testmod()





