
# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class    SCREAMING_SNAKE_CASE__     (	UpperCAmelCase					):





	'''simple docstring'''



	_UpperCAmelCase       :		torch.FloatTensor
	_UpperCAmelCase       :		Optional[torch.FloatTensor]       =					None






def        a_		(       __lowercase   :	Union[str, Any]       ,					__lowercase   :	int=0.9_9_9       ,					__lowercase   :	Any="cosine"       ,					) ->  Tuple:
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(__lowercase   :	Union[str, Any] ):
									return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2 ) ** 2

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(__lowercase   :	Optional[Any] ):
									return math.exp(t * -1_2.0 )

			else:
						raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}''' )

			_snake_case		=			[]
			for i in range(__lowercase ):
						_snake_case		=			i / num_diffusion_timesteps
						_snake_case		=			(i + 1) / num_diffusion_timesteps
						betas.append(min(1 - alpha_bar_fn(__lowercase ) / alpha_bar_fn(__lowercase )       ,					__lowercase ) )
			return torch.tensor(__lowercase       ,					dtype=torch.floataa )




class    SCREAMING_SNAKE_CASE__     (	UpperCAmelCase							,UpperCAmelCase					):





	'''simple docstring'''



	_UpperCAmelCase       :		List[Any]       =					1



	@register_to_config
	def __init__(  self	:    str			,  lowercase	:    int = 1_000			,  lowercase	:    float = 0.0001			,  lowercase	:    float = 0.02			,  lowercase	:    str = "linear"			,  lowercase	:    Optional[Union[np.ndarray, List[float]]] = None			,  lowercase	:    bool = True			,  lowercase	:    bool = True			,  lowercase	:    int = 0			,  lowercase	:    str = "epsilon"			,  lowercase	:    float = 1.0			,  **lowercase	:    Union[str, Any]			,  ):


				'''simple docstring'''


				if kwargs.get('set_alpha_to_one'			,  lowercase	) is not None:
							_snake_case		=			(
							    'The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'
							)
							deprecate('set_alpha_to_one'			,  '1.0.0'			,  lowercase			,  standard_warn=lowercase	)
							_snake_case		=			kwargs['set_alpha_to_one']
				if trained_betas is not None:
							_snake_case		=			torch.tensor(lowercase			,  dtype=torch.floataa	)
				elif beta_schedule == "linear":
							_snake_case		=			torch.linspace(lowercase			,  lowercase			,  lowercase			,  dtype=torch.floataa	)
				elif beta_schedule == "scaled_linear":
							# this schedule is very specific to the latent diffusion model.
							_snake_case		=			(
							    torch.linspace(beta_start**0.5			,  beta_end**0.5			,  lowercase			,  dtype=torch.floataa	) ** 2
							)
				elif beta_schedule == "squaredcos_cap_v2":
							# Glide cosine schedule
							_snake_case		=			betas_for_alpha_bar(lowercase	)
				else:
							raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''	)

				_snake_case		=			1.0 - self.betas
				_snake_case		=			torch.cumprod(self.alphas			,  dim=0	)

				# At every step in inverted ddim, we are looking into the next alphas_cumprod
				# For the final step, there is no next alphas_cumprod, and the index is out of bounds
				# `set_alpha_to_zero` decides whether we set this parameter simply to zero
				# in this case, self.step() just output the predicted noise
				# or whether we use the final alpha of the "non-previous" one.
				_snake_case		=			torch.tensor(0.0	) if set_alpha_to_zero else self.alphas_cumprod[-1]

				# standard deviation of the initial noise distribution
				_snake_case		=			1.0

				# setable values
				_snake_case		=			None
				_snake_case		=			torch.from_numpy(np.arange(0			,  lowercase	).copy().astype(np.intaa	)	)



	def  A							(  self	:    List[str]			,  lowercase	:    torch.FloatTensor			,  lowercase	:    Optional[int] = None	):


				'''simple docstring'''


				return sample



	def  A							(  self	:    List[Any]			,  lowercase	:    int			,  lowercase	:    Union[str, torch.device] = None	):


				'''simple docstring'''


				if num_inference_steps > self.config.num_train_timesteps:
							raise ValueError(
							    f'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
							    f''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
							    f''' maximal {self.config.num_train_timesteps} timesteps.'''	)

				_snake_case		=			num_inference_steps
				_snake_case		=			self.config.num_train_timesteps // self.num_inference_steps
				# creates integer timesteps by multiplying by ratio
				# casting to int to avoid issues when num_inference_step is power of 3
				_snake_case		=			(np.arange(0			,  lowercase	) * step_ratio).round().copy().astype(np.intaa	)
				_snake_case		=			torch.from_numpy(lowercase	).to(lowercase	)
				self.timesteps += self.config.steps_offset



	def  A							(  self	:    str			,  lowercase	:    torch.FloatTensor			,  lowercase	:    int			,  lowercase	:    torch.FloatTensor			,  lowercase	:    float = 0.0			,  lowercase	:    bool = False			,  lowercase	:    Optional[torch.FloatTensor] = None			,  lowercase	:    bool = True			,  ):


				'''simple docstring'''


				_snake_case		=			timestep + self.config.num_train_timesteps // self.num_inference_steps

				# 2. compute alphas, betas
				# change original implementation to exactly match noise levels for analogous forward process
				_snake_case		=			self.alphas_cumprod[timestep]
				_snake_case		=			(
				    self.alphas_cumprod[prev_timestep]
				    if prev_timestep < self.config.num_train_timesteps
				    else self.final_alpha_cumprod
				)

				_snake_case		=			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":
							_snake_case		=			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
							_snake_case		=			model_output
				elif self.config.prediction_type == "sample":
							_snake_case		=			model_output
							_snake_case		=			(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
				elif self.config.prediction_type == "v_prediction":
							_snake_case		=			(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
							_snake_case		=			(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. Clip or threshold "predicted x_0"
				if self.config.clip_sample:
							_snake_case		=			pred_original_sample.clamp(
							    -self.config.clip_sample_range			,  self.config.clip_sample_range	)

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

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

				if not return_dict:
							return (prev_sample, pred_original_sample)
				return DDIMSchedulerOutput(prev_sample=lowercase			,  pred_original_sample=lowercase	)





	def __len__(  self	:    Union[str, Any]	):


				'''simple docstring'''


				return self.config.num_train_timesteps

from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt






def        a_		(       __lowercase   :	Sequence[float]       ,					__lowercase   :	int       ,					__lowercase   :	int ) ->  tuple[int | None, int | None, float]:
			if not arr:
						return None, None, 0
			if low == high:
						return low, high, arr[low]

			_snake_case		=			(low + high) // 2
			_snake_case	,					_snake_case	,					_snake_case		=			max_subarray(__lowercase       ,					__lowercase       ,					__lowercase )
			_snake_case	,					_snake_case	,					_snake_case		=			max_subarray(__lowercase       ,					mid + 1       ,					__lowercase )
			_snake_case	,					_snake_case	,					_snake_case		=			max_cross_sum(__lowercase       ,					__lowercase       ,					__lowercase       ,					__lowercase )
			if left_sum >= right_sum and left_sum >= cross_sum:
						return left_low, left_high, left_sum
			elif right_sum >= left_sum and right_sum >= cross_sum:
						return right_low, right_high, right_sum
			return cross_left, cross_right, cross_sum






def        a_		(       __lowercase   :	Sequence[float]       ,					__lowercase   :	int       ,					__lowercase   :	int       ,					__lowercase   :	int ) ->  tuple[int, int, float]:
			_snake_case	,					_snake_case		=			float('-inf' ), -1
			_snake_case	,					_snake_case		=			float('-inf' ), -1

			_snake_case		=			0
			for i in range(__lowercase       ,					low - 1       ,					-1 ):
						summ += arr[i]
						if summ > left_sum:
									_snake_case		=			summ
									_snake_case		=			i

			_snake_case		=			0
			for i in range(mid + 1       ,					high + 1 ):
						summ += arr[i]
						if summ > right_sum:
									_snake_case		=			summ
									_snake_case		=			i

			return max_left, max_right, (left_sum + right_sum)






def        a_		(       __lowercase   :	int ) ->  float:
			_snake_case		=			[randint(1       ,					__lowercase ) for _ in range(__lowercase )]
			_snake_case		=			time.time()
			max_subarray(__lowercase       ,					0       ,					input_size - 1 )
			_snake_case		=			time.time()
			return end - start






def        a_		(       ) ->  None:
			_snake_case		=			[10, 100, 1_000, 10_000, 50_000, 100_000, 200_000, 300_000, 400_000, 500_000]
			_snake_case		=			[time_max_subarray(__lowercase ) for input_size in input_sizes]
			print('No of Inputs\t\tTime Taken' )
			for input_size, runtime in zip(__lowercase       ,					__lowercase ):
						print(__lowercase       ,					'\t\t'       ,					__lowercase )
			plt.plot(__lowercase       ,					__lowercase )
			plt.xlabel('Number of Inputs' )
			plt.ylabel('Time taken in seconds' )
			plt.show()


if __name__ == "__main__":
			from doctest import testmod

			testmod()