
'''simple docstring'''



class 				_a			:





       """simple docstring"""




       def __init__(							self    ,							A__ )      ->     Optional[int]:
          _SCREAMING_SNAKE_CASE       	=			val
          # Number of nodes in left subtree
          _SCREAMING_SNAKE_CASE       	=			0
          _SCREAMING_SNAKE_CASE       	=			None
          _SCREAMING_SNAKE_CASE       	=			None
          _SCREAMING_SNAKE_CASE       	=			None






       def     UpperCamelCase			(							self    ,							A__ )      ->     int:
          assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

          if self.val < other.val:
             _SCREAMING_SNAKE_CASE       	=			self.right
             _SCREAMING_SNAKE_CASE       	=			None
             if self.right:
                _SCREAMING_SNAKE_CASE       	=			other
             _SCREAMING_SNAKE_CASE       	=			other
             _SCREAMING_SNAKE_CASE       	=			self.left_tree_size * 2 + 1
             return self
          else:
             _SCREAMING_SNAKE_CASE       	=			other.right
             _SCREAMING_SNAKE_CASE       	=			None
             if other.right:
                _SCREAMING_SNAKE_CASE       	=			self
             _SCREAMING_SNAKE_CASE       	=			self
             _SCREAMING_SNAKE_CASE       	=			other.left_tree_size * 2 + 1
             return other






class 				_a			:





       """simple docstring"""




       def __init__(							self    ,							A__=None    ,							A__=None    ,							A__=0 )      ->     List[str]:
          _SCREAMING_SNAKE_CASE       	=			heap_size
          _SCREAMING_SNAKE_CASE       	=			bottom_root
          _SCREAMING_SNAKE_CASE       	=			min_node






       def     UpperCamelCase			(							self    ,							A__ )      ->     List[Any]:

          # Empty heaps corner cases
          if other.size == 0:
             return None
          if self.size == 0:
             _SCREAMING_SNAKE_CASE       	=			other.size
             _SCREAMING_SNAKE_CASE       	=			other.bottom_root
             _SCREAMING_SNAKE_CASE       	=			other.min_node
             return None
          # Update size
          _SCREAMING_SNAKE_CASE       	=			self.size + other.size

          # Update min.node
          if self.min_node.val > other.min_node.val:
             _SCREAMING_SNAKE_CASE       	=			other.min_node
          # Merge

          # Order roots by left_subtree_size
          _SCREAMING_SNAKE_CASE       	=			[]
          _SCREAMING_SNAKE_CASE	,							_SCREAMING_SNAKE_CASE       	=			self.bottom_root, other.bottom_root
          while i or j:
             if i and ((not j) or i.left_tree_size < j.left_tree_size):
                combined_roots_list.append((i, True) )
                _SCREAMING_SNAKE_CASE       	=			i.parent
             else:
                combined_roots_list.append((j, False) )
                _SCREAMING_SNAKE_CASE       	=			j.parent
        # Insert links between them
          for i in range(len(A__ ) - 1 ):
             if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                _SCREAMING_SNAKE_CASE       	=			combined_roots_list[i + 1][0]
                _SCREAMING_SNAKE_CASE       	=			combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
          _SCREAMING_SNAKE_CASE       	=			combined_roots_list[0][0]
          while i.parent:
             if (
                 (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
             ) or (
                 i.left_tree_size == i.parent.left_tree_size
                 and i.left_tree_size != i.parent.parent.left_tree_size
             ):
                # Neighbouring Nodes
                _SCREAMING_SNAKE_CASE       	=			i.left
                _SCREAMING_SNAKE_CASE       	=			i.parent.parent

                # Merging trees
                _SCREAMING_SNAKE_CASE       	=			i.merge_trees(i.parent )

                # Updating links
                _SCREAMING_SNAKE_CASE       	=			previous_node
                _SCREAMING_SNAKE_CASE       	=			next_node
                if previous_node:
                   _SCREAMING_SNAKE_CASE       	=			i
                if next_node:
                   _SCREAMING_SNAKE_CASE       	=			i
             else:
                _SCREAMING_SNAKE_CASE       	=			i.parent
        # Updating self.bottom_root
          while i.left:
             _SCREAMING_SNAKE_CASE       	=			i.left
          _SCREAMING_SNAKE_CASE       	=			i

          # Update other
          _SCREAMING_SNAKE_CASE       	=			self.size
          _SCREAMING_SNAKE_CASE       	=			self.bottom_root
          _SCREAMING_SNAKE_CASE       	=			self.min_node

          # Return the merged heap
          return self






       def     UpperCamelCase			(							self    ,							A__ )      ->     List[Any]:
          if self.size == 0:
             _SCREAMING_SNAKE_CASE       	=			Node(A__ )
             _SCREAMING_SNAKE_CASE       	=			1
             _SCREAMING_SNAKE_CASE       	=			self.bottom_root
          else:
             # Create new node
             _SCREAMING_SNAKE_CASE       	=			Node(A__ )

             # Update size
             self.size += 1

             # update min_node
             if val < self.min_node.val:
                _SCREAMING_SNAKE_CASE       	=			new_node
             # Put new_node as a bottom_root in heap
             _SCREAMING_SNAKE_CASE       	=			new_node
             _SCREAMING_SNAKE_CASE       	=			self.bottom_root
             _SCREAMING_SNAKE_CASE       	=			new_node

             # Consecutively merge roots with same left_tree_size
             while (
                 self.bottom_root.parent
                 and self.bottom_root.left_tree_size
                 == self.bottom_root.parent.left_tree_size
             ):
                # Next node
                _SCREAMING_SNAKE_CASE       	=			self.bottom_root.parent.parent

                # Merge
                _SCREAMING_SNAKE_CASE       	=			self.bottom_root.merge_trees(self.bottom_root.parent )

                # Update Links
                _SCREAMING_SNAKE_CASE       	=			next_node
                _SCREAMING_SNAKE_CASE       	=			None
                if next_node:
                   _SCREAMING_SNAKE_CASE       	=			self.bottom_root






       def     UpperCamelCase			(							self )      ->     int:
          return self.min_node.val






       def     UpperCamelCase			(							self )      ->     Dict:
          return self.size == 0






       def     UpperCamelCase			(							self )      ->     List[Any]:
          _SCREAMING_SNAKE_CASE       	=			self.min_node.val

          # Last element in heap corner case
          if self.size == 1:
             # Update size
             _SCREAMING_SNAKE_CASE       	=			0

             # Update bottom root
             _SCREAMING_SNAKE_CASE       	=			None

             # Update min_node
             _SCREAMING_SNAKE_CASE       	=			None

             return min_value
          # No right subtree corner case
          # The structure of the tree implies that this should be the bottom root
          # and there is at least one other root
          if self.min_node.right is None:
             # Update size
             self.size -= 1

             # Update bottom root
             _SCREAMING_SNAKE_CASE       	=			self.bottom_root.parent
             _SCREAMING_SNAKE_CASE       	=			None

             # Update min_node
             _SCREAMING_SNAKE_CASE       	=			self.bottom_root
             _SCREAMING_SNAKE_CASE       	=			self.bottom_root.parent
             while i:
                if i.val < self.min_node.val:
                   _SCREAMING_SNAKE_CASE       	=			i
                _SCREAMING_SNAKE_CASE       	=			i.parent
             return min_value
          # General case
          # Find the BinomialHeap of the right subtree of min_node
          _SCREAMING_SNAKE_CASE       	=			self.min_node.right
          _SCREAMING_SNAKE_CASE       	=			None
          _SCREAMING_SNAKE_CASE       	=			bottom_of_new
          _SCREAMING_SNAKE_CASE       	=			1

          # Size, min_node and bottom_root
          while bottom_of_new.left:
             _SCREAMING_SNAKE_CASE       	=			size_of_new * 2 + 1
             _SCREAMING_SNAKE_CASE       	=			bottom_of_new.left
             if bottom_of_new.val < min_of_new.val:
                _SCREAMING_SNAKE_CASE       	=			bottom_of_new
        # Corner case of single root on top left path
          if (not self.min_node.left) and (not self.min_node.parent):
             _SCREAMING_SNAKE_CASE       	=			size_of_new
             _SCREAMING_SNAKE_CASE       	=			bottom_of_new
             _SCREAMING_SNAKE_CASE       	=			min_of_new
             # print("Single root, multiple nodes case")
             return min_value
          # Remaining cases
          # Construct heap of right subtree
          _SCREAMING_SNAKE_CASE       	=			BinomialHeap(
              bottom_root=A__    ,							min_node=A__    ,							heap_size=A__ )

          # Update size
          _SCREAMING_SNAKE_CASE       	=			self.size - 1 - size_of_new

          # Neighbour nodes
          _SCREAMING_SNAKE_CASE       	=			self.min_node.left
          _SCREAMING_SNAKE_CASE       	=			self.min_node.parent

          # Initialize new bottom_root and min_node
          _SCREAMING_SNAKE_CASE       	=			previous_node or next_node
          _SCREAMING_SNAKE_CASE       	=			next_node

          # Update links of previous_node and search below for new min_node and
          # bottom_root
          if previous_node:
             _SCREAMING_SNAKE_CASE       	=			next_node

             # Update bottom_root and search for min_node below
             _SCREAMING_SNAKE_CASE       	=			previous_node
             _SCREAMING_SNAKE_CASE       	=			previous_node
             while self.bottom_root.left:
                _SCREAMING_SNAKE_CASE       	=			self.bottom_root.left
                if self.bottom_root.val < self.min_node.val:
                   _SCREAMING_SNAKE_CASE       	=			self.bottom_root
          if next_node:
             _SCREAMING_SNAKE_CASE       	=			previous_node

             # Search for new min_node above min_node
             _SCREAMING_SNAKE_CASE       	=			next_node
             while i:
                if i.val < self.min_node.val:
                   _SCREAMING_SNAKE_CASE       	=			i
                _SCREAMING_SNAKE_CASE       	=			i.parent
        # Merge heaps
          self.merge_heaps(A__ )

          return min_value






       def     UpperCamelCase			(							self )      ->     Optional[Any]:
          _SCREAMING_SNAKE_CASE       	=			self.bottom_root
          while top_root.parent:
             _SCREAMING_SNAKE_CASE       	=			top_root.parent
          # preorder
          _SCREAMING_SNAKE_CASE       	=			[]
          self.__traversal(A__    ,							A__ )
          return heap_pre_order






       def     UpperCamelCase			(							self    ,							A__    ,							A__    ,							A__=0 )      ->     List[str]:
          if curr_node:
             preorder.append((curr_node.val, level) )
             self.__traversal(curr_node.left    ,							A__    ,							level + 1 )
             self.__traversal(curr_node.right    ,							A__    ,							level + 1 )
          else:
             preorder.append(("""#""", level) )






       def __str__(							self )      ->     Optional[Any]:
          if self.is_empty():
             return ""
          _SCREAMING_SNAKE_CASE       	=			self.pre_order()

          return "\n".join(("""-""" * level + str(A__ )) for value, level in preorder_heap )


# Unit Tests
if __name__ == "__main__":
     import doctest

     doctest.testmod()








'''simple docstring'''



import torch

from diffusers import DDIMScheduler

from .test_schedulers import SchedulerCommonTest

class 				_a			(_lowerCamelCase):





       """simple docstring"""




       SCREAMING_SNAKE_CASE =					(DDIMScheduler,)
       SCREAMING_SNAKE_CASE =					(('eta', 0.0), ('num_inference_steps', 50))






       def     UpperCamelCase			(							self    ,							**A__ )      ->     Optional[int]:
          _SCREAMING_SNAKE_CASE       	=			{
              """num_train_timesteps""": 10_00,
              """beta_start""": 0.0001,
              """beta_end""": 0.02,
              """beta_schedule""": """linear""",
              """clip_sample""": True,
          }

          config.update(**A__ )
          return config






       def     UpperCamelCase			(							self    ,							**A__ )      ->     List[str]:
          _SCREAMING_SNAKE_CASE       	=			self.scheduler_classes[0]
          _SCREAMING_SNAKE_CASE       	=			self.get_scheduler_config(**A__ )
          _SCREAMING_SNAKE_CASE       	=			scheduler_class(**A__ )

          _SCREAMING_SNAKE_CASE	,							_SCREAMING_SNAKE_CASE       	=			10, 0.0

          _SCREAMING_SNAKE_CASE       	=			self.dummy_model()
          _SCREAMING_SNAKE_CASE       	=			self.dummy_sample_deter

          scheduler.set_timesteps(A__ )

          for t in scheduler.timesteps:
             _SCREAMING_SNAKE_CASE       	=			model(A__    ,							A__ )
             _SCREAMING_SNAKE_CASE       	=			scheduler.step(A__    ,							A__    ,							A__    ,							A__ ).prev_sample

          return sample






       def     UpperCamelCase			(							self )      ->     str:
          for timesteps in [1_00, 5_00, 10_00]:
             self.check_over_configs(num_train_timesteps=A__ )






       def     UpperCamelCase			(							self )      ->     int:
          for steps_offset in [0, 1]:
             self.check_over_configs(steps_offset=A__ )

          _SCREAMING_SNAKE_CASE       	=			self.scheduler_classes[0]
          _SCREAMING_SNAKE_CASE       	=			self.get_scheduler_config(steps_offset=1 )
          _SCREAMING_SNAKE_CASE       	=			scheduler_class(**A__ )
          scheduler.set_timesteps(5 )
          assert torch.equal(scheduler.timesteps    ,							torch.LongTensor([8_01, 6_01, 4_01, 2_01, 1] ) )






       def     UpperCamelCase			(							self )      ->     Tuple:
          for beta_start, beta_end in zip([0.0001, 0.001, 0.01, 0.1]    ,							[0.002, 0.02, 0.2, 2] ):
             self.check_over_configs(beta_start=A__    ,							beta_end=A__ )






       def     UpperCamelCase			(							self )      ->     Optional[Any]:
          for schedule in ["linear", "squaredcos_cap_v2"]:
             self.check_over_configs(beta_schedule=A__ )






       def     UpperCamelCase			(							self )      ->     List[str]:
          for prediction_type in ["epsilon", "v_prediction"]:
             self.check_over_configs(prediction_type=A__ )






       def     UpperCamelCase			(							self )      ->     Tuple:
          for clip_sample in [True, False]:
             self.check_over_configs(clip_sample=A__ )






       def     UpperCamelCase			(							self )      ->     Any:
          for timestep_spacing in ["trailing", "leading"]:
             self.check_over_configs(timestep_spacing=A__ )






       def     UpperCamelCase			(							self )      ->     int:
          for rescale_betas_zero_snr in [True, False]:
             self.check_over_configs(rescale_betas_zero_snr=A__ )






       def     UpperCamelCase			(							self )      ->     List[Any]:
          self.check_over_configs(thresholding=A__ )
          for threshold in [0.5, 1.0, 2.0]:
             for prediction_type in ["epsilon", "v_prediction"]:
                self.check_over_configs(
                    thresholding=A__    ,							prediction_type=A__    ,							sample_max_value=A__    ,							)






       def     UpperCamelCase			(							self )      ->     Optional[int]:
          for t in [1, 10, 49]:
             self.check_over_forward(time_step=A__ )






       def     UpperCamelCase			(							self )      ->     Optional[Any]:
          for t, num_inference_steps in zip([1, 10, 50]    ,							[10, 50, 5_00] ):
             self.check_over_forward(time_step=A__    ,							num_inference_steps=A__ )






       def     UpperCamelCase			(							self )      ->     str:
          for t, eta in zip([1, 10, 49]    ,							[0.0, 0.5, 1.0] ):
             self.check_over_forward(time_step=A__    ,							eta=A__ )






       def     UpperCamelCase			(							self )      ->     Optional[int]:
          _SCREAMING_SNAKE_CASE       	=			self.scheduler_classes[0]
          _SCREAMING_SNAKE_CASE       	=			self.get_scheduler_config()
          _SCREAMING_SNAKE_CASE       	=			scheduler_class(**A__ )

          assert torch.sum(torch.abs(scheduler._get_variance(0    ,							0 ) - 0.0 ) ) < 1E-5
          assert torch.sum(torch.abs(scheduler._get_variance(4_20    ,							4_00 ) - 0.1_4771 ) ) < 1E-5
          assert torch.sum(torch.abs(scheduler._get_variance(9_80    ,							9_60 ) - 0.3_2460 ) ) < 1E-5
          assert torch.sum(torch.abs(scheduler._get_variance(0    ,							0 ) - 0.0 ) ) < 1E-5
          assert torch.sum(torch.abs(scheduler._get_variance(4_87    ,							4_86 ) - 0.0_0979 ) ) < 1E-5
          assert torch.sum(torch.abs(scheduler._get_variance(9_99    ,							9_98 ) - 0.02 ) ) < 1E-5






       def     UpperCamelCase			(							self )      ->     List[Any]:
          _SCREAMING_SNAKE_CASE       	=			self.full_loop()

          _SCREAMING_SNAKE_CASE       	=			torch.sum(torch.abs(A__ ) )
          _SCREAMING_SNAKE_CASE       	=			torch.mean(torch.abs(A__ ) )

          assert abs(result_sum.item() - 172.0067 ) < 1E-2
          assert abs(result_mean.item() - 0.22_3967 ) < 1E-3






       def     UpperCamelCase			(							self )      ->     str:
          _SCREAMING_SNAKE_CASE       	=			self.full_loop(prediction_type="""v_prediction""" )

          _SCREAMING_SNAKE_CASE       	=			torch.sum(torch.abs(A__ ) )
          _SCREAMING_SNAKE_CASE       	=			torch.mean(torch.abs(A__ ) )

          assert abs(result_sum.item() - 52.5302 ) < 1E-2
          assert abs(result_mean.item() - 0.0684 ) < 1E-3






       def     UpperCamelCase			(							self )      ->     List[Any]:
          # We specify different beta, so that the first alpha is 0.99
          _SCREAMING_SNAKE_CASE       	=			self.full_loop(set_alpha_to_one=A__    ,							beta_start=0.01 )
          _SCREAMING_SNAKE_CASE       	=			torch.sum(torch.abs(A__ ) )
          _SCREAMING_SNAKE_CASE       	=			torch.mean(torch.abs(A__ ) )

          assert abs(result_sum.item() - 149.8295 ) < 1E-2
          assert abs(result_mean.item() - 0.1951 ) < 1E-3






       def     UpperCamelCase			(							self )      ->     Any:
          # We specify different beta, so that the first alpha is 0.99
          _SCREAMING_SNAKE_CASE       	=			self.full_loop(set_alpha_to_one=A__    ,							beta_start=0.01 )
          _SCREAMING_SNAKE_CASE       	=			torch.sum(torch.abs(A__ ) )
          _SCREAMING_SNAKE_CASE       	=			torch.mean(torch.abs(A__ ) )

          assert abs(result_sum.item() - 149.0784 ) < 1E-2
          assert abs(result_mean.item() - 0.1941 ) < 1E-3






