






# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)


@flax.struct.dataclass
class        lowercase__       :
	a_             =42
	a_             =42

	# setable values
	a_             =42
	a_             =42
	a_             =None

	@classmethod
	def 						UpperCAmelCase					(							cls						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      )->   List[Any]:







							'''simple docstring'''





							return cls(
							    common=__UpperCAmelCase						,      final_alpha_cumprod=__UpperCAmelCase						,      init_noise_sigma=__UpperCAmelCase						,      timesteps=__UpperCAmelCase						,      )





@dataclass
class        lowercase__       (     _UpperCAmelCase		):
	a_             =42





class        lowercase__       (     _UpperCAmelCase,   _UpperCAmelCase		):
	a_             =[e.name for e in FlaxKarrasDiffusionSchedulers]

	a_             =42

	@property
	def 						UpperCAmelCase					(							self    )->   List[Any]:







							'''simple docstring'''





							return True

	@register_to_config
	def __init__(							self						,      __UpperCAmelCase = 1000						,      __UpperCAmelCase = 0.0_001						,      __UpperCAmelCase = 0.02						,      __UpperCAmelCase = "linear"						,      __UpperCAmelCase = None						,      __UpperCAmelCase = True						,      __UpperCAmelCase = 0						,      __UpperCAmelCase = "epsilon"						,      __UpperCAmelCase = jnp.floataa						,      )->   List[Any]:







							'''simple docstring'''





							lowerCAmelCase__	 =  dtype

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase = None    )->   DDIMSchedulerState:







							'''simple docstring'''





							if common is None:
													lowerCAmelCase__	 =  CommonSchedulerState.create(self    )

							# At every step in ddim, we are looking into the previous alphas_cumprod
							# For the final step, there is no previous alphas_cumprod because we are already at 0
							# `set_alpha_to_one` decides whether we set this parameter simply to one or
							# whether we use the final alpha of the "non-previous" one.
							lowerCAmelCase__	 =  (
							    jnp.array(1.0						,      dtype=self.dtype    ) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
							)

							# standard deviation of the initial noise distribution
							lowerCAmelCase__	 =  jnp.array(1.0						,      dtype=self.dtype    )

							lowerCAmelCase__	 =  jnp.arange(0						,      self.config.num_train_timesteps    ).round()[::-1]

							return DDIMSchedulerState.create(
							    common=__UpperCAmelCase						,      final_alpha_cumprod=__UpperCAmelCase						,      init_noise_sigma=__UpperCAmelCase						,      timesteps=__UpperCAmelCase						,      )

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase = None    )->   jnp.ndarray:







							'''simple docstring'''





							return sample

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase = ()    )->   DDIMSchedulerState:







							'''simple docstring'''





							lowerCAmelCase__	 =  self.config.num_train_timesteps // num_inference_steps
							# creates integer timesteps by multiplying by ratio
							# rounding to avoid issues when num_inference_step is power of 3
							lowerCAmelCase__	 =  (jnp.arange(0						,      __UpperCAmelCase    ) * step_ratio).round()[::-1] + self.config.steps_offset

							return state.replace(
							    num_inference_steps=__UpperCAmelCase						,      timesteps=__UpperCAmelCase						,      )

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase    )->   Any:







							'''simple docstring'''





							lowerCAmelCase__	 =  state.common.alphas_cumprod[timestep]
							lowerCAmelCase__	 =  jnp.where(
							    prev_timestep >= 0						,      state.common.alphas_cumprod[prev_timestep]						,      state.final_alpha_cumprod    )
							lowerCAmelCase__	 =  1 - alpha_prod_t
							lowerCAmelCase__	 =  1 - alpha_prod_t_prev

							lowerCAmelCase__	 =  (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

							return variance

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase = 0.0						,      __UpperCAmelCase = True						,      )->   Union[FlaxDDIMSchedulerOutput, Tuple]:







							'''simple docstring'''





							if state.num_inference_steps is None:
													raise ValueError(
													    "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"    )

							# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
							# Ideally, read DDIM paper in-detail understanding

							# Notation (<variable name> -> <name in paper>
							# - pred_noise_t -> e_theta(x_t, t)
							# - pred_original_sample -> f_theta(x_t, t) or x_0
							# - std_dev_t -> sigma_t
							# - eta -> η
							# - pred_sample_direction -> "direction pointing to x_t"
							# - pred_prev_sample -> "x_t-1"

							# 1. get previous step value (=t-1)
							lowerCAmelCase__	 =  timestep - self.config.num_train_timesteps // state.num_inference_steps

							lowerCAmelCase__	 =  state.common.alphas_cumprod
							lowerCAmelCase__	 =  state.final_alpha_cumprod

							# 2. compute alphas, betas
							lowerCAmelCase__	 =  alphas_cumprod[timestep]
							lowerCAmelCase__	 =  jnp.where(prev_timestep >= 0						,      alphas_cumprod[prev_timestep]						,      __UpperCAmelCase    )

							lowerCAmelCase__	 =  1 - alpha_prod_t

							# 3. compute predicted original sample from predicted noise also called
							# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
							if self.config.prediction_type == "epsilon":
													lowerCAmelCase__	 =  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
													lowerCAmelCase__	 =  model_output
							elif self.config.prediction_type == "sample":
													lowerCAmelCase__	 =  model_output
													lowerCAmelCase__	 =  (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
							elif self.config.prediction_type == "v_prediction":
													lowerCAmelCase__	 =  (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
													lowerCAmelCase__	 =  (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
							else:
													raise ValueError(
													    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
													    " `v_prediction`"    )

							# 4. compute variance: "sigma_t(η)" -> see formula (16)
							# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
							lowerCAmelCase__	 =  self._get_variance(__UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase    )
							lowerCAmelCase__	 =  eta * variance ** 0.5

							# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
							lowerCAmelCase__	 =  (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon

							# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
							lowerCAmelCase__	 =  alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

							if not return_dict:
													return (prev_sample, state)

							return FlaxDDIMSchedulerOutput(prev_sample=__UpperCAmelCase						,      state=__UpperCAmelCase    )

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      )->   jnp.ndarray:







							'''simple docstring'''





							return add_noise_common(state.common						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase    )

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      )->   jnp.ndarray:







							'''simple docstring'''





							return get_velocity_common(state.common						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase    )


	def __len__(							self    )->   Tuple:







							'''simple docstring'''





							return self.config.num_train_timesteps














from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
a_							=      {
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}


def     _a					(       UpperCamelCase_   :			dict[str, list[str]]				)	->				set[tuple[str, str]]:
						"""simple docstring"""







						lowerCAmelCase__	 =  {node: {node} for node in graph}

						lowerCAmelCase__	 =  {node: graph[node][:] for node in graph}

						while len(UpperCamelCase_				) > 2:
												# Choose a random edge.
												lowerCAmelCase__	 =  random.choice(list(graph_copy.keys()				)				)
												lowerCAmelCase__	 =  random.choice(graph_copy[u]				)

												# Contract edge (u, v) to new node uv
												lowerCAmelCase__	 =  u + v
												lowerCAmelCase__	 =  list(set(graph_copy[u] + graph_copy[v]				)				)
												uv_neighbors.remove(UpperCamelCase_				)
												uv_neighbors.remove(UpperCamelCase_				)
												lowerCAmelCase__	 =  uv_neighbors
												for neighbor in uv_neighbors:
																		graph_copy[neighbor].append(UpperCamelCase_				)

												lowerCAmelCase__	 =  set(contracted_nodes[u].union(contracted_nodes[v]				)				)

												# Remove nodes u and v.
												del graph_copy[u]
												del graph_copy[v]
												for neighbor in uv_neighbors:
																		if u in graph_copy[neighbor]:
																								graph_copy[neighbor].remove(UpperCamelCase_				)
																		if v in graph_copy[neighbor]:
																								graph_copy[neighbor].remove(UpperCamelCase_				)

    # Find cutset.
						lowerCAmelCase__	 =  [contracted_nodes[node] for node in graph_copy]
						return {
						    (node, neighbor)
						    for node in groups[0]
						    for neighbor in graph[node]
						    if neighbor in groups[1]
						}


if __name__ == "__main__":
	print(partition_graph(TEST_GRAPH))






