


"""simple docstring"""



from __future__ import annotations

lowercase_							 =       [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]







class       __a	:







				def __init__(   self			,  UpperCAmelCase      ):

					'''simple docstring'''






					lowerCAmelCase_			       = -1
					lowerCAmelCase_			       = -1
					lowerCAmelCase_			       = [-1] * length
					lowerCAmelCase_			       = None
					lowerCAmelCase_			       = None







				def __repr__(   self      ):

					'''simple docstring'''






					return F"""Node(min_value={self.minn} max_value={self.maxx})"""




def     UpperCAmelCase    (					_lowercase   :      list[int]  )	->   Node | None:


	"""simple docstring"""




	lowerCAmelCase_			       = Node(len(_lowercase  )  )
	lowerCAmelCase_       ,  lowerCAmelCase_			       = min(_lowercase  ), max(_lowercase  )
	# Leaf node case where the node contains only one unique value
	if root.minn == root.maxx:
		return root
	lowerCAmelCase_			       = (root.minn + root.maxx) // 2

	lowerCAmelCase_			       = []
	lowerCAmelCase_			       = []

	for index, num in enumerate(_lowercase  ):
		if num <= pivot:
			left_arr.append(_lowercase  )
		else:
			right_arr.append(_lowercase  )
		lowerCAmelCase_			       = len(_lowercase  )
	lowerCAmelCase_			       = build_tree(_lowercase  )
	lowerCAmelCase_			       = build_tree(_lowercase  )
	return root
def     UpperCAmelCase    (					_lowercase   :      Node | None ,      _lowercase   :      int ,      _lowercase   :      int  )	->   int:


	"""simple docstring"""




	if index < 0 or node is None:
		return 0
	# Leaf node cases
	if node.minn == node.maxx:
		return index + 1 if node.minn == num else 0
	lowerCAmelCase_			       = (node.minn + node.maxx) // 2
	if num <= pivot:
		# go the left subtree and map index to the left subtree
		return rank_till_index(node.left ,      _lowercase ,      node.map_left[index] - 1  )
	else:
		# go to the right subtree and map index to the right subtree
		return rank_till_index(node.right ,      _lowercase ,      index - node.map_left[index]  )
def     UpperCAmelCase    (					_lowercase   :      Node | None ,      _lowercase   :      int ,      _lowercase   :      int ,      _lowercase   :      int  )	->   int:


	"""simple docstring"""




	if start > end:
		return 0
	lowerCAmelCase_			       = rank_till_index(_lowercase ,      _lowercase ,      _lowercase  )
	lowerCAmelCase_			       = rank_till_index(_lowercase ,      _lowercase ,      start - 1  )
	return rank_till_end - rank_before_start
def     UpperCAmelCase    (					_lowercase   :      Node | None ,      _lowercase   :      int ,      _lowercase   :      int ,      _lowercase   :      int  )	->   int:


	"""simple docstring"""




	if index > (end - start) or start > end or node is None:
		return -1
	# Leaf node case
	if node.minn == node.maxx:
		return node.minn
	# Number of elements in the left subtree in interval [start, end]
	lowerCAmelCase_			       = node.map_left[end] - (
	    node.map_left[start - 1] if start else 0
	)
	if num_elements_in_left_tree > index:
		return quantile(
		    node.left ,      _lowercase ,      (node.map_left[start - 1] if start else 0) ,      node.map_left[end] - 1 ,      )
	else:
		return quantile(
		    node.right ,      index - num_elements_in_left_tree ,      start - (node.map_left[start - 1] if start else 0) ,      end - node.map_left[end] ,      )
def     UpperCAmelCase    (					_lowercase   :      Node | None ,      _lowercase   :      int ,      _lowercase   :      int ,      _lowercase   :      int ,      _lowercase   :      int  )	->   int:


	"""simple docstring"""




	if (
	    start > end
	    or node is None
	    or start_num > end_num
	    or node.minn > end_num
	    or node.maxx < start_num
	):
		return 0
	if start_num <= node.minn and node.maxx <= end_num:
		return end - start + 1
	lowerCAmelCase_			       = range_counting(
	    node.left ,      (node.map_left[start - 1] if start else 0) ,      node.map_left[end] - 1 ,      _lowercase ,      _lowercase ,      )
	lowerCAmelCase_			       = range_counting(
	    node.right ,      start - (node.map_left[start - 1] if start else 0) ,      end - node.map_left[end] ,      _lowercase ,      _lowercase ,      )
	return left + right


if __name__ == "__main__":
		import doctest

		doctest.testmod()



"""simple docstring"""



import torch

from diffusers import LMSDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest







class       __a	(   __snake_case       ):
				lowerCamelCase    :					Union[str, Any] 					=(LMSDiscreteScheduler,)
				lowerCamelCase    :					int 					=10







				def     lowerCamelCase_    (   self			,  **UpperCAmelCase      ):

					'''simple docstring'''






					lowerCAmelCase_			       = {
					    '''num_train_timesteps''': 1100,
					    '''beta_start''': 0.0_0_0_1,
					    '''beta_end''': 0.0_2,
					    '''beta_schedule''': '''linear''',
					}

					config.update(**UpperCAmelCase      )
					return config







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					for timesteps in [10, 50, 100, 1000]:
						self.check_over_configs(num_train_timesteps=UpperCAmelCase      )







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					for beta_start, beta_end in zip([0.0_0_0_0_1, 0.0_0_0_1, 0.0_0_1]			,  [0.0_0_0_2, 0.0_0_2, 0.0_2]      ):
						self.check_over_configs(beta_start=UpperCAmelCase			,  beta_end=UpperCAmelCase      )







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					for schedule in ["linear", "scaled_linear"]:
						self.check_over_configs(beta_schedule=UpperCAmelCase      )







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					for prediction_type in ["epsilon", "v_prediction"]:
						self.check_over_configs(prediction_type=UpperCAmelCase      )







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					for t in [0, 500, 800]:
						self.check_over_forward(time_step=UpperCAmelCase      )







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					lowerCAmelCase_			       = self.scheduler_classes[0]
					lowerCAmelCase_			       = self.get_scheduler_config()
					lowerCAmelCase_			       = scheduler_class(**UpperCAmelCase      )

					scheduler.set_timesteps(self.num_inference_steps      )

					lowerCAmelCase_			       = self.dummy_model()
					lowerCAmelCase_			       = self.dummy_sample_deter * scheduler.init_noise_sigma

					for i, t in enumerate(scheduler.timesteps      ):
						lowerCAmelCase_			       = scheduler.scale_model_input(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = model(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = scheduler.step(UpperCAmelCase			,  UpperCAmelCase			,  UpperCAmelCase      )
						lowerCAmelCase_			       = output.prev_sample

					lowerCAmelCase_			       = torch.sum(torch.abs(UpperCAmelCase      )      )
					lowerCAmelCase_			       = torch.mean(torch.abs(UpperCAmelCase      )      )

					assert abs(result_sum.item() - 1_0_0_6.3_8_8      ) < 1E-2
					assert abs(result_mean.item() - 1.3_1      ) < 1E-3







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					lowerCAmelCase_			       = self.scheduler_classes[0]
					lowerCAmelCase_			       = self.get_scheduler_config(prediction_type='''v_prediction'''      )
					lowerCAmelCase_			       = scheduler_class(**UpperCAmelCase      )

					scheduler.set_timesteps(self.num_inference_steps      )

					lowerCAmelCase_			       = self.dummy_model()
					lowerCAmelCase_			       = self.dummy_sample_deter * scheduler.init_noise_sigma

					for i, t in enumerate(scheduler.timesteps      ):
						lowerCAmelCase_			       = scheduler.scale_model_input(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = model(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = scheduler.step(UpperCAmelCase			,  UpperCAmelCase			,  UpperCAmelCase      )
						lowerCAmelCase_			       = output.prev_sample

					lowerCAmelCase_			       = torch.sum(torch.abs(UpperCAmelCase      )      )
					lowerCAmelCase_			       = torch.mean(torch.abs(UpperCAmelCase      )      )

					assert abs(result_sum.item() - 0.0_0_1_7      ) < 1E-2
					assert abs(result_mean.item() - 2.2_6_7_6E-0_6      ) < 1E-3







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					lowerCAmelCase_			       = self.scheduler_classes[0]
					lowerCAmelCase_			       = self.get_scheduler_config()
					lowerCAmelCase_			       = scheduler_class(**UpperCAmelCase      )

					scheduler.set_timesteps(self.num_inference_steps			,  device=UpperCAmelCase      )

					lowerCAmelCase_			       = self.dummy_model()
					lowerCAmelCase_			       = self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
					lowerCAmelCase_			       = sample.to(UpperCAmelCase      )

					for i, t in enumerate(scheduler.timesteps      ):
						lowerCAmelCase_			       = scheduler.scale_model_input(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = model(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = scheduler.step(UpperCAmelCase			,  UpperCAmelCase			,  UpperCAmelCase      )
						lowerCAmelCase_			       = output.prev_sample

					lowerCAmelCase_			       = torch.sum(torch.abs(UpperCAmelCase      )      )
					lowerCAmelCase_			       = torch.mean(torch.abs(UpperCAmelCase      )      )

					assert abs(result_sum.item() - 1_0_0_6.3_8_8      ) < 1E-2
					assert abs(result_mean.item() - 1.3_1      ) < 1E-3







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					lowerCAmelCase_			       = self.scheduler_classes[0]
					lowerCAmelCase_			       = self.get_scheduler_config()
					lowerCAmelCase_			       = scheduler_class(**UpperCAmelCase			,  use_karras_sigmas=UpperCAmelCase      )

					scheduler.set_timesteps(self.num_inference_steps			,  device=UpperCAmelCase      )

					lowerCAmelCase_			       = self.dummy_model()
					lowerCAmelCase_			       = self.dummy_sample_deter.to(UpperCAmelCase      ) * scheduler.init_noise_sigma
					lowerCAmelCase_			       = sample.to(UpperCAmelCase      )

					for t in scheduler.timesteps:
						lowerCAmelCase_			       = scheduler.scale_model_input(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = model(UpperCAmelCase			,  UpperCAmelCase      )

						lowerCAmelCase_			       = scheduler.step(UpperCAmelCase			,  UpperCAmelCase			,  UpperCAmelCase      )
						lowerCAmelCase_			       = output.prev_sample

					lowerCAmelCase_			       = torch.sum(torch.abs(UpperCAmelCase      )      )
					lowerCAmelCase_			       = torch.mean(torch.abs(UpperCAmelCase      )      )

					assert abs(result_sum.item() - 3_8_1_2.9_9_2_7      ) < 2E-2
					assert abs(result_mean.item() - 4.9_6_4_8      ) < 1E-3