
import numpy as np
from numpy import floataa
from numpy.typing import NDArray




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      NDArray[floataa]:

							"""simple docstring"""






							_UpperCAmelCase       ,_UpperCAmelCase  :			int	       =		np.shape(_SCREAMING_SNAKE_CASE  )

							_UpperCAmelCase  :			Dict	       =		np.zeros((rows, 1)      ,	dtype=_SCREAMING_SNAKE_CASE  )
							for row in reversed(range(_SCREAMING_SNAKE_CASE  )  ):
														_UpperCAmelCase  :			Tuple	       =		0
														for col in range(row + 1      ,	_SCREAMING_SNAKE_CASE  ):
																					total += coefficients[row, col] * x[col]

														_UpperCAmelCase  :			int	       =		(vector[row] - total) / coefficients[row, row]

							return x




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      NDArray[floataa]:

							"""simple docstring"""






							_UpperCAmelCase       ,_UpperCAmelCase  :			List[Any]	       =		np.shape(_SCREAMING_SNAKE_CASE  )
							if rows != columns:
														return np.array(()      ,	dtype=_SCREAMING_SNAKE_CASE  )

							# augmented matrix
							_UpperCAmelCase  :			List[str]	       =		np.concatenate((coefficients, vector)      ,	axis=1  )
							_UpperCAmelCase  :			Dict	       =		augmented_mat.astype("float64"  )

							# scale the matrix leaving it triangular
							for row in range(rows - 1  ):
														_UpperCAmelCase  :			Optional[Any]	       =		augmented_mat[row, row]
														for col in range(row + 1      ,	_SCREAMING_SNAKE_CASE  ):
																					_UpperCAmelCase  :			List[Any]	       =		augmented_mat[col, row] / pivot
																					augmented_mat[col, :] -= factor * augmented_mat[row, :]

							_UpperCAmelCase  :			Any	       =		retroactive_resolution(
							    augmented_mat[:, 0:columns]      ,	augmented_mat[:, columns : columns + 1]  )

							return x


if __name__ == "__main__":
				import doctest

				doctest.testmod()






# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

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

import flax
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       A__  :
							lowerCAmelCase__						:		CommonSchedulerState
							lowerCAmelCase__						:		jnp.ndarray

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





							@classmethod
							def      a__					(					cls    :  Optional[Any]	,					_UpperCAmelCase    :  CommonSchedulerState	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  jnp.ndarray	,					)		->						Any:



											"""simple docstring"""


											return cls(
											    common=_UpperCAmelCase	,					final_alpha_cumprod=_UpperCAmelCase	,					init_noise_sigma=_UpperCAmelCase	,					timesteps=_UpperCAmelCase	,					)






@dataclass
class       A__  (		lowerCAmelCase__							):
							lowerCAmelCase__						:		DDIMSchedulerState






class       A__  (		lowerCAmelCase__       ,		lowerCAmelCase__							):
							lowerCAmelCase__						:		Union[str, Any]            =				[e.name for e in FlaxKarrasDiffusionSchedulers]

							lowerCAmelCase__						:		jnp.dtype





							@property
							def      a__					(					self    :  List[str]							)		->						Union[str, Any]:



											"""simple docstring"""


											return True





							@register_to_config
							def __init__(					self    :  str	,					_UpperCAmelCase    :  int = 10_00	,					_UpperCAmelCase    :  float = 0.0_001	,					_UpperCAmelCase    :  float = 0.02	,					_UpperCAmelCase    :  str = "linear"	,					_UpperCAmelCase    :  Optional[jnp.ndarray] = None	,					_UpperCAmelCase    :  bool = True	,					_UpperCAmelCase    :  int = 0	,					_UpperCAmelCase    :  str = "epsilon"	,					_UpperCAmelCase    :  jnp.dtype = jnp.floataa	,					)		->						Any:



											"""simple docstring"""


											__lowercase								=   dtype





							def      a__					(					self    :  Tuple	,					_UpperCAmelCase    :  Optional[CommonSchedulerState] = None							)		->						DDIMSchedulerState:



											"""simple docstring"""


											if common is None:
															__lowercase								=   CommonSchedulerState.create(self							)

											# At every step in ddim, we are looking into the previous alphas_cumprod
											# For the final step, there is no previous alphas_cumprod because we are already at 0
											# `set_alpha_to_one` decides whether we set this parameter simply to one or
											# whether we use the final alpha of the "non-previous" one.
											__lowercase								=   (
											    jnp.array(1.0	,					dtype=self.dtype							) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
											)

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

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

											return DDIMSchedulerState.create(
											    common=_UpperCAmelCase	,					final_alpha_cumprod=_UpperCAmelCase	,					init_noise_sigma=_UpperCAmelCase	,					timesteps=_UpperCAmelCase	,					)





							def      a__					(					self    :  Optional[Any]	,					_UpperCAmelCase    :  DDIMSchedulerState	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  Optional[int] = None							)		->						jnp.ndarray:



											"""simple docstring"""


											return sample





							def      a__					(					self    :  int	,					_UpperCAmelCase    :  DDIMSchedulerState	,					_UpperCAmelCase    :  int	,					_UpperCAmelCase    :  Tuple = ()							)		->						DDIMSchedulerState:



											"""simple docstring"""


											__lowercase								=   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
											__lowercase								=   (jnp.arange(0	,					_UpperCAmelCase							) * step_ratio).round()[::-1] + self.config.steps_offset

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





							def      a__					(					self    :  Tuple	,					_UpperCAmelCase    :  DDIMSchedulerState	,					_UpperCAmelCase    :  Union[str, Any]	,					_UpperCAmelCase    :  int							)		->						int:



											"""simple docstring"""


											__lowercase								=   state.common.alphas_cumprod[timestep]
											__lowercase								=   jnp.where(
											    prev_timestep >= 0	,					state.common.alphas_cumprod[prev_timestep]	,					state.final_alpha_cumprod							)
											__lowercase								=   1 - alpha_prod_t
											__lowercase								=   1 - alpha_prod_t_prev

											__lowercase								=   (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

											return variance





							def      a__					(					self    :  List[Any]	,					_UpperCAmelCase    :  DDIMSchedulerState	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  int	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  float = 0.0	,					_UpperCAmelCase    :  bool = True	,					)		->						Union[FlaxDDIMSchedulerOutput, Tuple]:



											"""simple docstring"""


											if state.num_inference_steps is None:
															raise ValueError(
															    'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'							)

											# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
											# Ideally, read DDIM paper in-detail understanding

											# Notation (<variable name> -> <name in paper>
											# - pred_noise_t -> e_theta(x_t, t)
											# - pred_original_sample -> f_theta(x_t, t) or x_0
											# - std_dev_t -> sigma_t
											# - eta -> η
											# - pred_sample_direction -> "direction pointing to x_t"
											# - pred_prev_sample -> "x_t-1"

											# 1. get previous step value (=t-1)
											__lowercase								=   timestep - self.config.num_train_timesteps // state.num_inference_steps

											__lowercase								=   state.common.alphas_cumprod
											__lowercase								=   state.final_alpha_cumprod

											# 2. compute alphas, betas
											__lowercase								=   alphas_cumprod[timestep]
											__lowercase								=   jnp.where(prev_timestep >= 0	,					alphas_cumprod[prev_timestep]	,					_UpperCAmelCase							)

											__lowercase								=   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":
															__lowercase								=   (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
															__lowercase								=   model_output
											elif self.config.prediction_type == "sample":
															__lowercase								=   model_output
															__lowercase								=   (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
											elif self.config.prediction_type == "v_prediction":
															__lowercase								=   (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
															__lowercase								=   (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. compute variance: "sigma_t(η)" -> see formula (16)
											# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
											__lowercase								=   self._get_variance(_UpperCAmelCase	,					_UpperCAmelCase	,					_UpperCAmelCase							)
											__lowercase								=   eta * variance ** 0.5

											# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
											__lowercase								=   (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon

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

											if not return_dict:
															return (prev_sample, state)

											return FlaxDDIMSchedulerOutput(prev_sample=_UpperCAmelCase	,					state=_UpperCAmelCase							)





							def      a__					(					self    :  Union[str, Any]	,					_UpperCAmelCase    :  DDIMSchedulerState	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  jnp.ndarray	,					)		->						jnp.ndarray:



											"""simple docstring"""


											return add_noise_common(state.common	,					_UpperCAmelCase	,					_UpperCAmelCase	,					_UpperCAmelCase							)





							def      a__					(					self    :  Optional[int]	,					_UpperCAmelCase    :  DDIMSchedulerState	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  jnp.ndarray	,					_UpperCAmelCase    :  jnp.ndarray	,					)		->						jnp.ndarray:



											"""simple docstring"""


											return get_velocity_common(state.common	,					_UpperCAmelCase	,					_UpperCAmelCase	,					_UpperCAmelCase							)





							def __len__(					self    :  List[Any]							)		->						List[str]:



											"""simple docstring"""


											return self.config.num_train_timesteps





