

"""simple docstring"""


from __future__ import annotations

from random import random
from typing import Generic, TypeVar

UpperCAmelCase													=TypeVar("KT")
UpperCAmelCase													=TypeVar("VT")





class lowerCamelCase__   (				Generic[KT, VT]    ):



    '''simple docstring'''




    def __init__( self ,lowerCamelCase_ = "root" ,lowerCamelCase_ = None    )    ->      Dict:
          A				  =		key
          A				  =		value
          A				  =		[]




    def __repr__( self    )    ->      str:
          return f'Node({self.key}: {self.value})'




    @property
    def UpperCamelCase__		( self    )    ->      int:
          return len(self.forward    )





class lowerCamelCase__   (				Generic[KT, VT]    ):



    '''simple docstring'''




    def __init__( self ,lowerCamelCase_ = 0.5 ,lowerCamelCase_ = 1_6    )    ->      List[str]:
          A				  =		Node[KT, VT]()
          A				  =		0
          A				  =		p
          A				  =		max_level




    def __str__( self    )    ->      str:
          A				  =		list(self    )

          if len(__snake_case    ) == 0:
                return f'SkipList(level={self.level})'

          A				  =		max((len(str(__snake_case    )    ) for item in items) ,default=4    )
          A				  =		max(__snake_case ,4    ) + 4

          A				  =		self.head
          A				  =		[]

          A				  =		node.forward.copy()
          lines.append(f'[{node.key}]'.ljust(__snake_case ,"""-"""    ) + """* """ * len(__snake_case    )    )
          lines.append(""" """ * label_size + """| """ * len(__snake_case    )    )

          while len(node.forward    ) != 0:
                A				  =		node.forward[0]

                lines.append(
                    f'[{node.key}]'.ljust(__snake_case ,"""-"""    )
                    + """ """.join(str(n.key    ) if n.key == node.key else """|""" for n in forwards    )    )
                lines.append(""" """ * label_size + """| """ * len(__snake_case    )    )
                A				  =		node.forward

          lines.append("""None""".ljust(__snake_case    ) + """* """ * len(__snake_case    )    )
          return f'SkipList(level={self.level})\n' + "\n".join(__snake_case    )




    def __iter__( self    )    ->      Union[str, Any]:
          A				  =		self.head

          while len(node.forward    ) != 0:
                yield node.forward[0].key
                A				  =		node.forward[0]




    def UpperCamelCase__		( self    )    ->      int:
          A				  =		1
          while random() < self.p and level < self.max_level:
                level += 1

          return level




    def UpperCamelCase__		( self ,lowerCamelCase_    )    ->      tuple[Node[KT, VT] | None, list[Node[KT, VT]]]:
          A				  =		[]

          A				  =		self.head

          for i in reversed(range(self.level    )    ):
                # i < node.level - When node level is lesser than `i` decrement `i`.
                # node.forward[i].key < key - Jumping to node with key value higher
                #                             or equal to searched key would result
                #                             in skipping searched key.
                while i < node.level and node.forward[i].key < key:
                      A				  =		node.forward[i]
                # Each leftmost node (relative to searched node) will potentially have to
                # be updated.
                update_vector.append(__snake_case    )

          update_vector.reverse()  # Note that we were inserting values in reverse order.

          # len(node.forward) != 0 - If current node doesn't contain any further
          #                          references then searched key is not present.
          # node.forward[0].key == key - Next node key should be equal to search key
          #                              if key is present.
          if len(node.forward    ) != 0 and node.forward[0].key == key:
                return node.forward[0], update_vector
          else:
                return None, update_vector




    def UpperCamelCase__		( self ,lowerCamelCase_    )    ->      List[Any]:
          A  ,			A				  =		self._locate_node(__snake_case    )

          if node is not None:
                for i, update_node in enumerate(__snake_case    ):
                      # Remove or replace all references to removed node.
                      if update_node.level > i and update_node.forward[i].key == key:
                            if node.level > i:
                                  A				  =		node.forward[i]
                            else:
                                  A				  =		update_node.forward[:i]




    def UpperCamelCase__		( self ,lowerCamelCase_ ,lowerCamelCase_    )    ->      Tuple:
          A  ,			A				  =		self._locate_node(__snake_case    )
          if node is not None:
                A				  =		value
          else:
                A				  =		self.random_level()

                if level > self.level:
                      # After level increase we have to add additional nodes to head.
                      for _ in range(self.level - 1 ,__snake_case    ):
                            update_vector.append(self.head    )
                      A				  =		level

                A				  =		Node(__snake_case ,__snake_case    )

                for i, update_node in enumerate(update_vector[:level]    ):
                      # Change references to pass through new node.
                      if update_node.level > i:
                            new_node.forward.append(update_node.forward[i]    )

                      if update_node.level < i + 1:
                            update_node.forward.append(__snake_case    )
                      else:
                            A				  =		new_node




    def UpperCamelCase__		( self ,lowerCamelCase_    )    ->      VT | None:
          A  ,			A				  =		self._locate_node(__snake_case    )

          if node is not None:
                return node.value

          return None




def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()
      skip_list.insert("""Key1"""     ,   3				)
      skip_list.insert("""Key2"""     ,   1_2				)
      skip_list.insert("""Key3"""     ,   4_1				)
      skip_list.insert("""Key4"""     ,   -1_9				)

      A				  =		skip_list.head
      A				  =		{}
      while node.level != 0:
            A				  =		node.forward[0]
            A				  =		node.value

      assert len(__lowerCAmelCase				) == 4
      assert all_values["Key1"] == 3
      assert all_values["Key2"] == 1_2
      assert all_values["Key3"] == 4_1
      assert all_values["Key4"] == -1_9



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()
      skip_list.insert("""Key1"""     ,   1_0				)
      skip_list.insert("""Key1"""     ,   1_2				)

      skip_list.insert("""Key5"""     ,   7				)
      skip_list.insert("""Key7"""     ,   1_0				)
      skip_list.insert("""Key10"""     ,   5				)

      skip_list.insert("""Key7"""     ,   7				)
      skip_list.insert("""Key5"""     ,   5				)
      skip_list.insert("""Key10"""     ,   1_0				)

      A				  =		skip_list.head
      A				  =		{}
      while node.level != 0:
            A				  =		node.forward[0]
            A				  =		node.value

      if len(__lowerCAmelCase				) != 4:
            print()
      assert len(__lowerCAmelCase				) == 4
      assert all_values["Key1"] == 1_2
      assert all_values["Key7"] == 7
      assert all_values["Key5"] == 5
      assert all_values["Key10"] == 1_0



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()
      assert skip_list.find("""Some key"""				) is None



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()

      skip_list.insert("""Key2"""     ,   2_0				)
      assert skip_list.find("""Key2"""				) == 2_0

      skip_list.insert("""Some Key"""     ,   1_0				)
      skip_list.insert("""Key2"""     ,   8				)
      skip_list.insert("""V"""     ,   1_3				)

      assert skip_list.find("""Y"""				) is None
      assert skip_list.find("""Key2"""				) == 8
      assert skip_list.find("""Some Key"""				) == 1_0
      assert skip_list.find("""V"""				) == 1_3



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()
      skip_list.delete("""Some key"""				)

      assert len(skip_list.head.forward				) == 0



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()

      skip_list.insert("""Key1"""     ,   1_2				)
      skip_list.insert("""V"""     ,   1_3				)
      skip_list.insert("""X"""     ,   1_4				)
      skip_list.insert("""Key2"""     ,   1_5				)

      skip_list.delete("""V"""				)
      skip_list.delete("""Key2"""				)

      assert skip_list.find("""V"""				) is None
      assert skip_list.find("""Key2"""				) is None



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()

      skip_list.insert("""Key1"""     ,   1_2				)
      skip_list.insert("""V"""     ,   1_3				)
      skip_list.insert("""X"""     ,   1_4				)
      skip_list.insert("""Key2"""     ,   1_5				)

      skip_list.delete("""V"""				)
      assert skip_list.find("""V"""				) is None
      assert skip_list.find("""X"""				) == 1_4
      assert skip_list.find("""Key1"""				) == 1_2
      assert skip_list.find("""Key2"""				) == 1_5

      skip_list.delete("""X"""				)
      assert skip_list.find("""V"""				) is None
      assert skip_list.find("""X"""				) is None
      assert skip_list.find("""Key1"""				) == 1_2
      assert skip_list.find("""Key2"""				) == 1_5

      skip_list.delete("""Key1"""				)
      assert skip_list.find("""V"""				) is None
      assert skip_list.find("""X"""				) is None
      assert skip_list.find("""Key1"""				) is None
      assert skip_list.find("""Key2"""				) == 1_5

      skip_list.delete("""Key2"""				)
      assert skip_list.find("""V"""				) is None
      assert skip_list.find("""X"""				) is None
      assert skip_list.find("""Key1"""				) is None
      assert skip_list.find("""Key2"""				) is None



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()

      skip_list.insert("""Key1"""     ,   1_2				)
      skip_list.insert("""V"""     ,   1_3				)
      skip_list.insert("""X"""     ,   1_4_2				)
      skip_list.insert("""Key2"""     ,   1_5				)

      skip_list.delete("""X"""				)

      def traverse_keys(_a	:						str				):
            yield node.key
            for forward_node in node.forward:
                  yield from traverse_keys(__lowerCAmelCase				)

      assert len(set(traverse_keys(skip_list.head				)				)				) == 4



def   _A					(	):



      """simple docstring"""






      def is_sorted(_a	:						Optional[Any]				):
            return all(next_item >= item for item, next_item in zip(__lowerCAmelCase     ,   lst[1:]				)				)

      A				  =		SkipList()
      for i in range(1_0				):
            skip_list.insert(__lowerCAmelCase     ,   __lowerCAmelCase				)
      assert is_sorted(list(__lowerCAmelCase				)				)
      skip_list.delete(5				)
      skip_list.delete(8				)
      skip_list.delete(2				)
      assert is_sorted(list(__lowerCAmelCase				)				)
      skip_list.insert(-1_2     ,   -1_2				)
      skip_list.insert(7_7     ,   7_7				)
      assert is_sorted(list(__lowerCAmelCase				)				)



def   _A					(	):



      """simple docstring"""






      for _ in range(1_0_0				):
            # Repeat test 100 times due to the probabilistic nature of skip list
            # random values == random bugs
            test_insert()
            test_insert_overrides_existing_value()

            test_searching_empty_list_returns_none()
            test_search()

            test_deleting_item_from_empty_list_do_nothing()
            test_deleted_items_are_not_founded_by_find_method()
            test_delete_removes_only_given_key()
            test_delete_doesnt_leave_dead_nodes()

            test_iter_always_yields_sorted_values()



def   _A					(	):



      """simple docstring"""






      A				  =		SkipList()
      skip_list.insert(2     ,   """2"""				)
      skip_list.insert(4     ,   """4"""				)
      skip_list.insert(6     ,   """4"""				)
      skip_list.insert(4     ,   """5"""				)
      skip_list.insert(8     ,   """4"""				)
      skip_list.insert(9     ,   """4"""				)

      skip_list.delete(4				)

      print(__lowerCAmelCase				)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()











'''simple docstring'''




# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput
@dataclass
class 			_lowerCAmelCase		(			A__	):






     """simple docstring"""






     snake_case_						      =   42
     snake_case_						      =   42




class 			_lowerCAmelCase		(			A__							,     A__	):






     """simple docstring"""






     snake_case_						      =   1



     @register_to_config
     def __init__(   self							:			str   ,       __snake_case							:			int = 20_00   ,       __snake_case							:			float = 0.15   ,       __snake_case							:			float = 0.01   ,       __snake_case							:			float = 13_48.0   ,       __snake_case							:			float = 1e-5   ,       __snake_case							:			int = 1   ,       )->	str:
        # standard deviation of the initial noise distribution
        snake_case 						=   sigma_max

        # setable values
        snake_case 						=   None

        self.set_sigmas(__snake_case   ,       __snake_case   ,       __snake_case   ,       __snake_case						)



     def      lowerCAmelCase			(   self							:			List[Any]   ,       __snake_case							:			torch.FloatTensor   ,       __snake_case							:			Optional[int] = None						)->	torch.FloatTensor:
        return sample



     def      lowerCAmelCase			(   self							:			List[str]   ,       __snake_case							:			int   ,       __snake_case							:			float = None   ,       __snake_case							:			Union[str, torch.device] = None						)->	Optional[Any]:
        snake_case 						=   sampling_eps if sampling_eps is not None else self.config.sampling_eps

        snake_case 						=   torch.linspace(1   ,       __snake_case   ,       __snake_case   ,       device=__snake_case						)



     def      lowerCAmelCase			(   self							:			Union[str, Any]   ,       __snake_case							:			int   ,       __snake_case							:			float = None   ,       __snake_case							:			float = None   ,       __snake_case							:			float = None						)->	str:
        snake_case 						=   sigma_min if sigma_min is not None else self.config.sigma_min
        snake_case 						=   sigma_max if sigma_max is not None else self.config.sigma_max
        snake_case 						=   sampling_eps if sampling_eps is not None else self.config.sampling_eps
        if self.timesteps is None:
           self.set_timesteps(__snake_case   ,       __snake_case						)

        snake_case 						=   sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
        snake_case 						=   torch.exp(torch.linspace(math.log(__snake_case						)   ,       math.log(__snake_case						)   ,       __snake_case						)						)
        snake_case 						=   torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]						)



     def      lowerCAmelCase			(   self							:			str   ,       __snake_case							:			List[str]   ,       __snake_case							:			str						)->	Optional[int]:
        return torch.where(
            timesteps == 0   ,       torch.zeros_like(t.to(timesteps.device						)						)   ,       self.discrete_sigmas[timesteps - 1].to(timesteps.device						)   ,       )



     def      lowerCAmelCase			(   self							:			int   ,       __snake_case							:			torch.FloatTensor   ,       __snake_case							:			int   ,       __snake_case							:			torch.FloatTensor   ,       __snake_case							:			Optional[torch.Generator] = None   ,       __snake_case							:			bool = True   ,       )->	Union[SdeVeOutput, Tuple]:
        if self.timesteps is None:
           raise ValueError(
               """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""						)

        snake_case 						=   timestep * torch.ones(
            sample.shape[0]   ,       device=sample.device						)  # torch.repeat_interleave(timestep, sample.shape[0])
        snake_case 						=   (timestep * (len(self.timesteps						) - 1)).long()

        # mps requires indices to be in the same device, so we use cpu as is the default with cuda
        snake_case 						=   timesteps.to(self.discrete_sigmas.device						)

        snake_case 						=   self.discrete_sigmas[timesteps].to(sample.device						)
        snake_case 						=   self.get_adjacent_sigma(__snake_case   ,       __snake_case						).to(sample.device						)
        snake_case 						=   torch.zeros_like(__snake_case						)
        snake_case 						=   (sigma**2 - adjacent_sigma**2) ** 0.5

        # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
        # also equation 47 shows the analog from SDE models to ancestral sampling methods
        snake_case 						=   diffusion.flatten()
        while len(diffusion.shape						) < len(sample.shape						):
           snake_case 						=   diffusion.unsqueeze(-1						)
        snake_case 						=   drift - diffusion**2 * model_output

        #  equation 6: sample noise for the diffusion term of
        snake_case 						=   randn_tensor(
            sample.shape   ,       layout=sample.layout   ,       generator=__snake_case   ,       device=sample.device   ,       dtype=sample.dtype						)
        snake_case 						=   sample - drift  # subtract because `dt` is a small negative timestep
        # TODO is the variable diffusion the correct scaling term for the noise?
        snake_case 						=   prev_sample_mean + diffusion * noise  # add impact of diffusion field g

        if not return_dict:
           return (prev_sample, prev_sample_mean)

        return SdeVeOutput(prev_sample=__snake_case   ,       prev_sample_mean=__snake_case						)



     def      lowerCAmelCase			(   self							:			Optional[Any]   ,       __snake_case							:			torch.FloatTensor   ,       __snake_case							:			torch.FloatTensor   ,       __snake_case							:			Optional[torch.Generator] = None   ,       __snake_case							:			bool = True   ,       )->	Union[SchedulerOutput, Tuple]:
        if self.timesteps is None:
           raise ValueError(
               """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""						)

        # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
        # sample noise for correction
        snake_case 						=   randn_tensor(sample.shape   ,       layout=sample.layout   ,       generator=__snake_case						).to(sample.device						)

        # compute step size from the model_output, the noise, and the snr
        snake_case 						=   torch.norm(model_output.reshape(model_output.shape[0]   ,       -1						)   ,       dim=-1						).mean()
        snake_case 						=   torch.norm(noise.reshape(noise.shape[0]   ,       -1						)   ,       dim=-1						).mean()
        snake_case 						=   (self.config.snr * noise_norm / grad_norm) ** 2 * 2
        snake_case 						=   step_size * torch.ones(sample.shape[0]						).to(sample.device						)
        # self.repeat_scalar(step_size, sample.shape[0])

        # compute corrected sample: model_output term and noise term
        snake_case 						=   step_size.flatten()
        while len(step_size.shape						) < len(sample.shape						):
           snake_case 						=   step_size.unsqueeze(-1						)
        snake_case 						=   sample + step_size * model_output
        snake_case 						=   prev_sample_mean + ((step_size * 2) ** 0.5) * noise

        if not return_dict:
           return (prev_sample,)

        return SchedulerOutput(prev_sample=__snake_case						)



     def      lowerCAmelCase			(   self							:			str   ,       __snake_case							:			torch.FloatTensor   ,       __snake_case							:			torch.FloatTensor   ,       __snake_case							:			torch.FloatTensor   ,       )->	torch.FloatTensor:
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        snake_case 						=   timesteps.to(original_samples.device						)
        snake_case 						=   self.discrete_sigmas.to(original_samples.device						)[timesteps]
        snake_case 						=   (
            noise * sigmas[:, None, None, None]
            if noise is not None
            else torch.randn_like(__snake_case						) * sigmas[:, None, None, None]
        )
        snake_case 						=   noise + original_samples
        return noisy_samples



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

