
"""simple docstring"""







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 				A__ (			UpperCamelCase_):
		A_		: Optional[int]            =			4_2
		A_		: Union[str, Any]            =			4_2




class 				A__ (			UpperCamelCase_ ,  UpperCamelCase_):
		A_		: int            =			1

		@register_to_config
		def __init__(   self ,	_SCREAMING_SNAKE_CASE = 20_00 ,	_SCREAMING_SNAKE_CASE = 0.15 ,	_SCREAMING_SNAKE_CASE = 0.01 ,	_SCREAMING_SNAKE_CASE = 13_48.0 ,	_SCREAMING_SNAKE_CASE = 1E-5 ,	_SCREAMING_SNAKE_CASE = 1 ,	):
			__lowerCAmelCase    :		List[Any]		    =   sigma_max

			# setable values
			__lowerCAmelCase    :		Optional[int]		    =   None

			self.set_sigmas(__a ,	__a ,	__a ,	__a				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE = None				):
			return sample

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE = None ,	_SCREAMING_SNAKE_CASE = None				):
			__lowerCAmelCase    :		Optional[Any]		    =   sampling_eps if sampling_eps is not None else self.config.sampling_eps

			__lowerCAmelCase    :		Optional[int]		    =   torch.linspace(1 ,	__a ,	__a ,	device=__a				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE = None ,	_SCREAMING_SNAKE_CASE = None ,	_SCREAMING_SNAKE_CASE = None				):
			__lowerCAmelCase    :		List[Any]		    =   sigma_min if sigma_min is not None else self.config.sigma_min
			__lowerCAmelCase    :		List[Any]		    =   sigma_max if sigma_max is not None else self.config.sigma_max
			__lowerCAmelCase    :		Optional[Any]		    =   sampling_eps if sampling_eps is not None else self.config.sampling_eps
			if self.timesteps is None:
				self.set_timesteps(__a ,	__a				)

			__lowerCAmelCase    :		List[str]		    =   sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
			__lowerCAmelCase    :		str		    =   torch.exp(torch.linspace(math.log(__a				) ,	math.log(__a				) ,	__a				)				)
			__lowerCAmelCase    :		Dict		    =   torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			return torch.where(
			    timesteps == 0 ,	torch.zeros_like(t.to(timesteps.device				)				) ,	self.discrete_sigmas[timesteps - 1].to(timesteps.device				) ,	)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE = None ,	_SCREAMING_SNAKE_CASE = True ,	):






			if self.timesteps is None:
				raise ValueError(
				    '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'				)

			__lowerCAmelCase    :		List[str]		    =   timestep * torch.ones(
			    sample.shape[0] ,	device=sample.device				)  # torch.repeat_interleave(timestep, sample.shape[0])
			__lowerCAmelCase    :		Optional[int]		    =   (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
			__lowerCAmelCase    :		str		    =   timesteps.to(self.discrete_sigmas.device				)

			__lowerCAmelCase    :		Tuple		    =   self.discrete_sigmas[timesteps].to(sample.device				)
			__lowerCAmelCase    :		List[Any]		    =   self.get_adjacent_sigma(__a ,	__a				).to(sample.device				)
			__lowerCAmelCase    :		int		    =   torch.zeros_like(__a				)
			__lowerCAmelCase    :		int		    =   (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
			__lowerCAmelCase    :		Optional[Any]		    =   diffusion.flatten()
			while len(diffusion.shape				) < len(sample.shape				):
				__lowerCAmelCase    :		List[Any]		    =   diffusion.unsqueeze(-1				)
			__lowerCAmelCase    :		List[Any]		    =   drift - diffusion**2 * model_output

			#  equation 6: sample noise for the diffusion term of
			__lowerCAmelCase    :		Tuple		    =   randn_tensor(
			    sample.shape ,	layout=sample.layout ,	generator=__a ,	device=sample.device ,	dtype=sample.dtype				)
			__lowerCAmelCase    :		Any		    =   sample - drift  # subtract because `dt` is a small negative timestep
			# TODO is the variable diffusion the correct scaling term for the noise?
			__lowerCAmelCase    :		Optional[int]		    =   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=__a ,	prev_sample_mean=__a				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE = None ,	_SCREAMING_SNAKE_CASE = True ,	):






			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
			__lowerCAmelCase    :		Optional[int]		    =   randn_tensor(sample.shape ,	layout=sample.layout ,	generator=__a				).to(sample.device				)

			# compute step size from the model_output, the noise, and the snr
			__lowerCAmelCase    :		Tuple		    =   torch.norm(model_output.reshape(model_output.shape[0] ,	-1				) ,	dim=-1				).mean()
			__lowerCAmelCase    :		Union[str, Any]		    =   torch.norm(noise.reshape(noise.shape[0] ,	-1				) ,	dim=-1				).mean()
			__lowerCAmelCase    :		Tuple		    =   (self.config.snr * noise_norm / grad_norm) ** 2 * 2
			__lowerCAmelCase    :		List[str]		    =   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
			__lowerCAmelCase    :		Dict		    =   step_size.flatten()
			while len(step_size.shape				) < len(sample.shape				):
				__lowerCAmelCase    :		Any		    =   step_size.unsqueeze(-1				)
			__lowerCAmelCase    :		Optional[int]		    =   sample + step_size * model_output
			__lowerCAmelCase    :		Any		    =   prev_sample_mean + ((step_size * 2) ** 0.5) * noise

			if not return_dict:
				return (prev_sample,)

			return SchedulerOutput(prev_sample=__a				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	):
			__lowerCAmelCase    :		Any		    =   timesteps.to(original_samples.device				)
			__lowerCAmelCase    :		int		    =   self.discrete_sigmas.to(original_samples.device				)[timesteps]
			__lowerCAmelCase    :		str		    =   (
			    noise * sigmas[:, None, None, None]
			    if noise is not None
			    else torch.randn_like(__a				) * sigmas[:, None, None, None]
			)
			__lowerCAmelCase    :		Union[str, Any]		    =   noise + original_samples
			return noisy_samples







		def __len__(   self				):
			return self.config.num_train_timesteps

"""simple docstring"""







from collections.abc import Sequence
from queue import Queue




class 				A__ :

		def __init__(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE=None ,	_SCREAMING_SNAKE_CASE=None				):
			__lowerCAmelCase    :		List[str]		    =   start
			__lowerCAmelCase    :		Union[str, Any]		    =   end
			__lowerCAmelCase    :		Union[str, Any]		    =   val
			__lowerCAmelCase    :		Dict		    =   (start + end) // 2
			__lowerCAmelCase    :		Dict		    =   left
			__lowerCAmelCase    :		List[Any]		    =   right







		def __repr__(   self				):
			return f"SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})"




class 				A__ :

		def __init__(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		Optional[Any]		    =   collection
			__lowerCAmelCase    :		Optional[int]		    =   function
			if self.collection:
				__lowerCAmelCase    :		str		    =   self._build_tree(0 ,	len(_SCREAMING_SNAKE_CASE				) - 1				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			self._update_tree(self.root ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			return self._query_range(self.root ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			if start == end:
				return SegmentTreeNode(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	self.collection[start]				)
			__lowerCAmelCase    :		Tuple		    =   (start + end) // 2
			__lowerCAmelCase    :		List[str]		    =   self._build_tree(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)
			__lowerCAmelCase    :		Dict		    =   self._build_tree(mid + 1 ,	_SCREAMING_SNAKE_CASE				)
			return SegmentTreeNode(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	self.fn(left.val ,	right.val				) ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			if node.start == i and node.end == i:
				__lowerCAmelCase    :		int		    =   val
				return
			if i <= node.mid:
				self._update_tree(node.left ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)
			else:
				self._update_tree(node.right ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)
			__lowerCAmelCase    :		Optional[Any]		    =   self.fn(node.left.val ,	node.right.val				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			if node.start == i and node.end == j:
				return node.val

			if i <= node.mid:
				if j <= node.mid:
					# range in left child tree
					return self._query_range(node.left ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)
				else:
					# range in left child tree and right child tree
					return self.fn(
					    self._query_range(node.left ,	_SCREAMING_SNAKE_CASE ,	node.mid				) ,	self._query_range(node.right ,	node.mid + 1 ,	_SCREAMING_SNAKE_CASE				) ,	)
			else:
				# range in right child tree
				return self._query_range(node.right ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)







		def 							__lowerCamelCase							(   self				):
			if self.root is not None:
				__lowerCAmelCase    :		Optional[Any]		    =   Queue()
				queue.put(self.root				)
				while not queue.empty():
					__lowerCAmelCase    :		str		    =   queue.get()
					yield node

					if node.left is not None:
						queue.put(node.left				)

					if node.right is not None:
						queue.put(node.right				)


if __name__ == "__main__":
							import operator

							for fn in [operator.add, max, min]:
														print("""*""" * 50)
														lowerCamelCase__           =	SegmentTree([2, 1, 5, 3, 4], fn)
														for node in arr.traverse():
																					print(node)
														print()

														arr.update(1, 5)
														for node in arr.traverse():
																					print(node)
														print()

														print(arr.query_range(3, 4))  # 7
														print(arr.query_range(2, 2))  # 5
														print(arr.query_range(1, 3))  # 13
														print()