
"""simple docstring"""
# 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      lowerCAmelCase_						:



							'''simple docstring'''





							_snake_case		     =						42
							_snake_case		     =						42

							# setable values
							_snake_case		     =						42
							_snake_case		     =						42
							_snake_case		     =						None




							@classmethod
							def  A__		(				cls  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							)   ->       List[str]:
													return cls(
													    common=snake_case_  ,							final_alpha_cumprod=snake_case_  ,							init_noise_sigma=snake_case_  ,							timesteps=snake_case_  ,							)
@dataclass
class      lowerCAmelCase_						(							A__				):



							'''simple docstring'''





							_snake_case		     =						42
class      lowerCAmelCase_						(							A__							,							A__				):



							'''simple docstring'''





							_snake_case		     =						[e.name for e in FlaxKarrasDiffusionSchedulers]

							_snake_case		     =						42




							@property
							def  A__		(				self							)   ->       List[str]:
													return True




							@register_to_config
							def __init__(				self  ,							snake_case_ = 1_000  ,							snake_case_ = 0.0_001  ,							snake_case_ = 0.02  ,							snake_case_ = "linear"  ,							snake_case_ = None  ,							snake_case_ = True  ,							snake_case_ = 0  ,							snake_case_ = "epsilon"  ,							snake_case_ = jnp.floataa  ,							)   ->       Optional[int]:
													__lowerCAmelCase        =       dtype




							def  A__		(				self  ,							snake_case_ = None							)   ->       DDIMSchedulerState:
													if common is None:
																			__lowerCAmelCase        =       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.
													__lowerCAmelCase        =       (
													    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
													__lowerCAmelCase        =       jnp.array(1.0  ,							dtype=self.dtype							)

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

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




							def  A__		(				self  ,							snake_case_  ,							snake_case_  ,							snake_case_ = None							)   ->       jnp.ndarray:
													return sample




							def  A__		(				self  ,							snake_case_  ,							snake_case_  ,							snake_case_ = ()							)   ->       DDIMSchedulerState:
													__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  ,							snake_case_							) * step_ratio).round()[::-1] + self.config.steps_offset

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




							def  A__		(				self  ,							snake_case_  ,							snake_case_  ,							snake_case_							)   ->       Tuple:
													__lowerCAmelCase        =       state.common.alphas_cumprod[timestep]
													__lowerCAmelCase        =       jnp.where(
													    prev_timestep >= 0  ,							state.common.alphas_cumprod[prev_timestep]  ,							state.final_alpha_cumprod							)
													__lowerCAmelCase        =       1 - alpha_prod_t
													__lowerCAmelCase        =       1 - alpha_prod_t_prev

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

													return variance




							def  A__		(				self  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							snake_case_ = 0.0  ,							snake_case_ = True  ,							)   ->       Union[FlaxDDIMSchedulerOutput, Tuple]:
													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)
													__lowerCAmelCase        =       timestep - self.config.num_train_timesteps // state.num_inference_steps

													__lowerCAmelCase        =       state.common.alphas_cumprod
													__lowerCAmelCase        =       state.final_alpha_cumprod

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

													__lowerCAmelCase        =       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":
																			__lowerCAmelCase        =       (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
																			__lowerCAmelCase        =       model_output
													elif self.config.prediction_type == "sample":
																			__lowerCAmelCase        =       model_output
																			__lowerCAmelCase        =       (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
													elif self.config.prediction_type == "v_prediction":
																			__lowerCAmelCase        =       (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
																			__lowerCAmelCase        =       (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)
													__lowerCAmelCase        =       self._get_variance(snake_case_  ,							snake_case_  ,							snake_case_							)
													__lowerCAmelCase        =       eta * variance ** 0.5

													# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
													__lowerCAmelCase        =       (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
													__lowerCAmelCase        =       alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

													if not return_dict:
																			return (prev_sample, state)

													return FlaxDDIMSchedulerOutput(prev_sample=snake_case_  ,							state=snake_case_							)




							def  A__		(				self  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							)   ->       jnp.ndarray:
													return add_noise_common(state.common  ,							snake_case_  ,							snake_case_  ,							snake_case_							)




							def  A__		(				self  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							snake_case_  ,							)   ->       jnp.ndarray:
													return get_velocity_common(state.common  ,							snake_case_  ,							snake_case_  ,							snake_case_							)




							def __len__(				self							)   ->       Optional[Any]:
													return self.config.num_train_timesteps


"""simple docstring"""
def 				lowercase      (_lowerCAmelCase		):
						# must be
						__lowerCAmelCase        =       [list(_lowerCAmelCase		) for row in matrix]
						if matrix and isinstance(_lowerCAmelCase				,  _lowerCAmelCase		):
												if isinstance(matrix[0]				,  _lowerCAmelCase		):
																		__lowerCAmelCase        =       0
																		for row in matrix:
																								if prev_len == 0:
																														__lowerCAmelCase        =       len(_lowerCAmelCase		)
																														__lowerCAmelCase        =       True
																								else:
																														__lowerCAmelCase        =       prev_len == len(_lowerCAmelCase		)
												else:
																		__lowerCAmelCase        =       True
						else:
												__lowerCAmelCase        =       False

						return result

def 				lowercase      (_lowerCAmelCase		):
						if check_matrix(_lowerCAmelCase		) and len(_lowerCAmelCase		) > 0:
												__lowerCAmelCase        =       [list(_lowerCAmelCase		) for row in a]
												__lowerCAmelCase        =       len(_lowerCAmelCase		)
												if isinstance(a[0]				,  _lowerCAmelCase		):
																		__lowerCAmelCase        =       len(a[0]		)
												else:
																		for dat in a:
																								print(_lowerCAmelCase		)
																		return

												# horizotal printing increasing
												for i in range(0				,  _lowerCAmelCase		):
																		print(a[0][i]		)
												# vertical printing down
												for i in range(1				,  _lowerCAmelCase		):
																		print(a[i][mat_col - 1]		)
												# horizotal printing decreasing
												if mat_row > 1:
																		for i in range(mat_col - 2				,  -1				,  -1		):
																								print(a[mat_row - 1][i]		)
        # vertical printing up
												for i in range(mat_row - 2				,  0				,  -1		):
																		print(a[i][0]		)
												__lowerCAmelCase        =       [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]]
												if len(_lowerCAmelCase		) > 0:
																		spiral_print_clockwise(_lowerCAmelCase		)
												else:
																		return
						else:
												print("""Not a valid matrix"""		)
												return

def 				lowercase      (_lowerCAmelCase		):
						if matrix:
												return list(matrix.pop(0		)		) + spiral_traversal(list(zip(*_lowerCAmelCase		)		)[::-1]		)
						else:
												return []


# driver code
if __name__ == "__main__":
			import doctest

			doctest.testmod()

			SCREAMING_SNAKE_CASE_			      =					[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
			spiral_print_clockwise(a)
