






"""simple docstring"""



def 			_snake_case    (					lowerCamelCase__     :   list    ,						lowerCamelCase__     :   list    ,						lowerCamelCase__     :   int  )    ->     list:
							lowerCamelCase_	:							Union[str, Any]									=len(lowerCamelCase__  )
							lowerCamelCase_	:							Dict									=[[0] * n for i in range(lowerCamelCase__  )]
							for i in range(lowerCamelCase__  ):
														lowerCamelCase_	:							int									=y_points[i]

							for i in range(2    ,						lowerCamelCase__  ):
														for j in range(lowerCamelCase__    ,						lowerCamelCase__  ):
																					lowerCamelCase_	:							Tuple									=(
																					    (xa - x_points[j - i + 1]) * q[j][i - 1]
																					    - (xa - x_points[j]) * q[j - 1][i - 1]
																					) / (x_points[j] - x_points[j - i + 1])

							return [q[n - 1][n - 1], q]


if __name__ == "__main__":
						import doctest

						doctest.testmod()











"""simple docstring"""



# 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__      :
			_UpperCAmelCase		:CommonSchedulerState

			# setable values
			_UpperCAmelCase		:jnp.ndarray
			_UpperCAmelCase		:jnp.ndarray
			_UpperCAmelCase		:Optional[int]             =			None


			@classmethod
			def      UpperCAmelCase__						(				cls					:  int       ,	snake_case__					:  CommonSchedulerState       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  jnp.ndarray ):
										return cls(common=snake_case__       ,	init_noise_sigma=snake_case__       ,	timesteps=snake_case__ )







@dataclass
class        lowercase__      (							snake_case__       ):
			_UpperCAmelCase		:DDPMSchedulerState







class        lowercase__      (							snake_case__,       snake_case__       ):
			_UpperCAmelCase		:Any             =			[e.name for e in FlaxKarrasDiffusionSchedulers]

			_UpperCAmelCase		:jnp.dtype


			@property
			def      UpperCAmelCase__						(				self					:  Optional[Any] ):
										return True


			@register_to_config
			def __init__(				self					:  Optional[int]       ,	snake_case__					:  int = 1000       ,	snake_case__					:  float = 0.0_001       ,	snake_case__					:  float = 0.02       ,	snake_case__					:  str = "linear"       ,	snake_case__					:  Optional[jnp.ndarray] = None       ,	snake_case__					:  str = "fixed_small"       ,	snake_case__					:  bool = True       ,	snake_case__					:  str = "epsilon"       ,	snake_case__					:  jnp.dtype = jnp.floataa       ,	):
										lowerCamelCase_	:							str									=dtype


			def      UpperCAmelCase__						(				self					:  List[str]       ,	snake_case__					:  Optional[CommonSchedulerState] = None ):
										if common is None:
																	lowerCamelCase_	:							int									=CommonSchedulerState.create(self )

										# standard deviation of the initial noise distribution
										lowerCamelCase_	:							Optional[Any]									=jnp.array(1.0       ,	dtype=self.dtype )

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

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


			def      UpperCAmelCase__						(				self					:  Optional[int]       ,	snake_case__					:  DDPMSchedulerState       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  Optional[int] = None ):
										return sample


			def      UpperCAmelCase__						(				self					:  Optional[Any]       ,	snake_case__					:  DDPMSchedulerState       ,	snake_case__					:  int       ,	snake_case__					:  Tuple = () ):
										lowerCamelCase_	:							Any									=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_	:							List[str]									=(jnp.arange(0       ,	snake_case__ ) * step_ratio).round()[::-1]

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


			def      UpperCAmelCase__						(				self					:  Union[str, Any]       ,	snake_case__					:  DDPMSchedulerState       ,	snake_case__					:  Union[str, Any]       ,	snake_case__					:  List[Any]=None       ,	snake_case__					:  Any=None ):
										lowerCamelCase_	:							List[str]									=state.common.alphas_cumprod[t]
										lowerCamelCase_	:							Union[str, Any]									=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_	:							Tuple									=(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

										if variance_type is None:
																	lowerCamelCase_	:							List[Any]									=self.config.variance_type

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

										return variance


			def      UpperCAmelCase__						(				self					:  int       ,	snake_case__					:  DDPMSchedulerState       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  int       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  Optional[jax.random.KeyArray] = None       ,	snake_case__					:  bool = True       ,	):
										lowerCamelCase_	:							Union[str, Any]									=timestep

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

										if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
																	lowerCamelCase_							,						lowerCamelCase_	:							Optional[Any]									=jnp.split(snake_case__       ,	sample.shape[1]       ,	axis=1 )
										else:
																	lowerCamelCase_	:							List[str]									=None

										# 1. compute alphas, betas
										lowerCamelCase_	:							Union[str, Any]									=state.common.alphas_cumprod[t]
										lowerCamelCase_	:							Dict									=jnp.where(t > 0       ,	state.common.alphas_cumprod[t - 1]       ,	jnp.array(1.0       ,	dtype=self.dtype ) )
										lowerCamelCase_	:							Any									=1 - alpha_prod_t
										lowerCamelCase_	:							List[str]									=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_	:							int									=(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
										elif self.config.prediction_type == "sample":
																	lowerCamelCase_	:							List[Any]									=model_output
										elif self.config.prediction_type == "v_prediction":
																	lowerCamelCase_	:							Tuple									=(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_	:							List[Any]									=jnp.clip(snake_case__       ,	-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_	:							int									=(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
										lowerCamelCase_	:							Optional[Any]									=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_	:							Any									=pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

										# 6. Add noise
										def random_variance():
																	lowerCamelCase_	:							Union[str, Any]									=jax.random.split(snake_case__       ,	num=1 )
																	lowerCamelCase_	:							List[Any]									=jax.random.normal(snake_case__       ,	shape=model_output.shape       ,	dtype=self.dtype )
																	return (self._get_variance(snake_case__       ,	snake_case__       ,	predicted_variance=snake_case__ ) ** 0.5) * noise

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

										lowerCamelCase_	:							str									=pred_prev_sample + variance

										if not return_dict:
																	return (pred_prev_sample, state)

										return FlaxDDPMSchedulerOutput(prev_sample=snake_case__       ,	state=snake_case__ )


			def      UpperCAmelCase__						(				self					:  Dict       ,	snake_case__					:  DDPMSchedulerState       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  jnp.ndarray       ,	):
										return add_noise_common(state.common       ,	snake_case__       ,	snake_case__       ,	snake_case__ )


			def      UpperCAmelCase__						(				self					:  int       ,	snake_case__					:  DDPMSchedulerState       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  jnp.ndarray       ,	snake_case__					:  jnp.ndarray       ,	):
										return get_velocity_common(state.common       ,	snake_case__       ,	snake_case__       ,	snake_case__ )


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



