# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

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

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)




@flax.struct.dataclass
class    lowercase_  :



	"""simple docstring"""





	UpperCAmelCase_  :					Any   =				42

	# setable values
	UpperCAmelCase_  :					Any   =				42
	UpperCAmelCase_  :					Optional[int]   =				42
	UpperCAmelCase_  :					List[Any]   =				None


	@classmethod
	def 			SCREAMING_SNAKE_CASE_				(							cls		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE				)						->str:
								return cls(common=lowerCamelCase__		,			init_noise_sigma=lowerCamelCase__		,			timesteps=lowerCamelCase__				)




@dataclass
class    lowercase_  (  UpperCamelCase_						):



	"""simple docstring"""





	UpperCAmelCase_  :					str   =				42




class    lowercase_  (  UpperCamelCase_      ,     UpperCamelCase_						):



	"""simple docstring"""





	UpperCAmelCase_  :					Dict   =				[e.name for e in FlaxKarrasDiffusionSchedulers]

	UpperCAmelCase_  :					int   =				42


	@property
	def 			SCREAMING_SNAKE_CASE_				(							self				)						->Tuple:
								return True


	@register_to_config
	def __init__(							self		,			__SCREAMING_SNAKE_CASE = 1000		,			__SCREAMING_SNAKE_CASE = 0.0_0_0_1		,			__SCREAMING_SNAKE_CASE = 0.0_2		,			__SCREAMING_SNAKE_CASE = "linear"		,			__SCREAMING_SNAKE_CASE = None		,			__SCREAMING_SNAKE_CASE = "fixed_small"		,			__SCREAMING_SNAKE_CASE = True		,			__SCREAMING_SNAKE_CASE = "epsilon"		,			__SCREAMING_SNAKE_CASE = jnp.floataa		,			)						->List[Any]:
								lowerCAmelCase			=		dtype


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE = None				)						->DDPMSchedulerState:
								if common is None:
															lowerCAmelCase			=		CommonSchedulerState.create(self				)

								# standard deviation of the initial noise distribution
								lowerCAmelCase			=		jnp.array(1.0		,			dtype=self.dtype				)

								lowerCAmelCase			=		jnp.arange(0		,			self.config.num_train_timesteps				).round()[::-1]

								return DDPMSchedulerState.create(
								    common=lowerCamelCase__		,			init_noise_sigma=lowerCamelCase__		,			timesteps=lowerCamelCase__		,			)


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE = None				)						->jnp.ndarray:
								return sample


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE = ()				)						->DDPMSchedulerState:
								lowerCAmelCase			=		self.config.num_train_timesteps // num_inference_steps
								# creates integer timesteps by multiplying by ratio
								# rounding to avoid issues when num_inference_step is power of 3
								lowerCAmelCase			=		(jnp.arange(0		,			lowerCamelCase__				) * step_ratio).round()[::-1]

								return state.replace(
								    num_inference_steps=lowerCamelCase__		,			timesteps=lowerCamelCase__		,			)


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE=None		,			__SCREAMING_SNAKE_CASE=None				)						->Optional[int]:
								lowerCAmelCase			=		state.common.alphas_cumprod[t]
								lowerCAmelCase			=		jnp.where(t > 0		,			state.common.alphas_cumprod[t - 1]		,			jnp.array(1.0		,			dtype=self.dtype				)				)

								# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
								# and sample from it to get previous sample
								# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
								lowerCAmelCase			=		(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

								if variance_type is None:
															lowerCAmelCase			=		self.config.variance_type

								# hacks - were probably added for training stability
								if variance_type == "fixed_small":
															lowerCAmelCase			=		jnp.clip(lowerCamelCase__		,			a_min=1e-20				)
								# for rl-diffuser https://arxiv.org/abs/2205.09991
								elif variance_type == "fixed_small_log":
															lowerCAmelCase			=		jnp.log(jnp.clip(lowerCamelCase__		,			a_min=1e-20				)				)
								elif variance_type == "fixed_large":
															lowerCAmelCase			=		state.common.betas[t]
								elif variance_type == "fixed_large_log":
															# Glide max_log
															lowerCAmelCase			=		jnp.log(state.common.betas[t]				)
								elif variance_type == "learned":
															return predicted_variance
								elif variance_type == "learned_range":
															lowerCAmelCase			=		variance
															lowerCAmelCase			=		state.common.betas[t]
															lowerCAmelCase			=		(predicted_variance + 1) / 2
															lowerCAmelCase			=		frac * max_log + (1 - frac) * min_log

								return variance


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE = None		,			__SCREAMING_SNAKE_CASE = True		,			)						->Union[FlaxDDPMSchedulerOutput, Tuple]:
								lowerCAmelCase			=		timestep

								if key is None:
															lowerCAmelCase			=		jax.random.PRNGKey(0				)

								if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
															lowerCAmelCase		,      lowerCAmelCase			=		jnp.split(lowerCamelCase__		,			sample.shape[1]		,			axis=1				)
								else:
															lowerCAmelCase			=		None

								# 1. compute alphas, betas
								lowerCAmelCase			=		state.common.alphas_cumprod[t]
								lowerCAmelCase			=		jnp.where(t > 0		,			state.common.alphas_cumprod[t - 1]		,			jnp.array(1.0		,			dtype=self.dtype				)				)
								lowerCAmelCase			=		1 - alpha_prod_t
								lowerCAmelCase			=		1 - alpha_prod_t_prev

								# 2. compute predicted original sample from predicted noise also called
								# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
								if self.config.prediction_type == "epsilon":
															lowerCAmelCase			=		(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
								elif self.config.prediction_type == "sample":
															lowerCAmelCase			=		model_output
								elif self.config.prediction_type == "v_prediction":
															lowerCAmelCase			=		(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
								else:
															raise ValueError(
															    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` "
															    ''' for the FlaxDDPMScheduler.'''				)

								# 3. Clip "predicted x_0"
								if self.config.clip_sample:
															lowerCAmelCase			=		jnp.clip(lowerCamelCase__		,			-1		,			1				)

								# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								lowerCAmelCase			=		(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
								lowerCAmelCase			=		state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

								# 5. Compute predicted previous sample µ_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								lowerCAmelCase			=		pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

								# 6. Add noise
								def random_variance():
															lowerCAmelCase			=		jax.random.split(lowerCamelCase__		,			num=1				)
															lowerCAmelCase			=		jax.random.normal(lowerCamelCase__		,			shape=model_output.shape		,			dtype=self.dtype				)
															return (self._get_variance(lowerCamelCase__		,			lowerCamelCase__		,			predicted_variance=lowerCamelCase__				) ** 0.5) * noise

								lowerCAmelCase			=		jnp.where(t > 0		,			random_variance()		,			jnp.zeros(model_output.shape		,			dtype=self.dtype				)				)

								lowerCAmelCase			=		pred_prev_sample + variance

								if not return_dict:
															return (pred_prev_sample, state)

								return FlaxDDPMSchedulerOutput(prev_sample=lowerCamelCase__		,			state=lowerCamelCase__				)


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			)						->jnp.ndarray:
								return add_noise_common(state.common		,			lowerCamelCase__		,			lowerCamelCase__		,			lowerCamelCase__				)


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			)						->jnp.ndarray:
								return get_velocity_common(state.common		,			lowerCamelCase__		,			lowerCamelCase__		,			lowerCamelCase__				)




	def __len__(							self				)						->List[str]:
								return self.config.num_train_timesteps









from __future__ import annotations

# This is the precision for this function which can be altered.
# It is recommended for users to keep this number greater than or equal to 10.
__A        =    10







def 			lowerCamelCase_		(       UpperCamelCase__				:      int ,     UpperCamelCase__				:      int ,     UpperCamelCase__				:      list[int] ,     UpperCamelCase__				:      int      )     ->       int:





				"""simple docstring"""


				for i in range(UpperCamelCase__ ,     UpperCamelCase__      ):
								if array[i] == target:
												return i
				return -1







def 			lowerCamelCase_		(       UpperCamelCase__				:      list[int] ,     UpperCamelCase__				:      int      )     ->       int:





				"""simple docstring"""


				__lowerCamelCase		       =    0
				__lowerCamelCase		       =    len(UpperCamelCase__      )
				while left <= right:
								if right - left < precision:
												return lin_search(UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__      )

								__lowerCamelCase		       =    (left + right) // 3 + 1
								__lowerCamelCase		       =    2 * (left + right) // 3 + 1

								if array[one_third] == target:
												return one_third
								elif array[two_third] == target:
												return two_third

								elif target < array[one_third]:
												__lowerCamelCase		       =    one_third - 1
								elif array[two_third] < target:
												__lowerCamelCase		       =    two_third + 1

								else:
												__lowerCamelCase		       =    one_third + 1
												__lowerCamelCase		       =    two_third - 1
				else:
								return -1







def 			lowerCamelCase_		(       UpperCamelCase__				:      int ,     UpperCamelCase__				:      int ,     UpperCamelCase__				:      list[int] ,     UpperCamelCase__				:      int      )     ->       int:





				"""simple docstring"""


				if left < right:
								if right - left < precision:
												return lin_search(UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__      )
								__lowerCamelCase		       =    (left + right) // 3 + 1
								__lowerCamelCase		       =    2 * (left + right) // 3 + 1

								if array[one_third] == target:
												return one_third
								elif array[two_third] == target:
												return two_third

								elif target < array[one_third]:
												return rec_ternary_search(UpperCamelCase__ ,     one_third - 1 ,     UpperCamelCase__ ,     UpperCamelCase__      )
								elif array[two_third] < target:
												return rec_ternary_search(two_third + 1 ,     UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__      )
								else:
												return rec_ternary_search(one_third + 1 ,     two_third - 1 ,     UpperCamelCase__ ,     UpperCamelCase__      )
				else:
								return -1


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					__A        =    input("Enter numbers separated by comma:\n").strip()
					__A        =    [int(item.strip()) for item in user_input.split(",")]
					assert collection == sorted(collection), f"List must be ordered.\n{collection}."
					__A        =    int(input("Enter the number to be found in the list:\n").strip())
					__A        =    ite_ternary_search(collection, target)
					__A        =    rec_ternary_search(0, len(collection) - 1, collection, target)
					if resulta != -1:
										print(f'''Iterative search: {target} found at positions: {resulta}''')
										print(f'''Recursive search: {target} found at positions: {resulta}''')
					else:
										print("Not found")


