






# 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    _lowerCAmelCase			:



				"""simple docstring"""



				_lowercase				:   CommonSchedulerState

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



				@classmethod
				def 					__magic_name__							(      cls    :    Optional[int]			,		UpperCamelCase__    :    CommonSchedulerState			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    jnp.ndarray):






											'''simple docstring'''







											return cls(common=UpperCamelCase__			,		init_noise_sigma=UpperCamelCase__			,		timesteps=UpperCamelCase__)


@dataclass
class    _lowerCAmelCase			(		lowercase_      ):



				"""simple docstring"""



				_lowercase				:   DDPMSchedulerState


class    _lowerCAmelCase			(		lowercase_     ,      lowercase_      ):



				"""simple docstring"""



				_lowercase				:   List[Any]      =  [e.name for e in FlaxKarrasDiffusionSchedulers]

				_lowercase				:   jnp.dtype



				@property
				def 					__magic_name__							(      self    :    Dict):






											'''simple docstring'''







											return True



				@register_to_config
				def __init__(      self    :    int			,		UpperCamelCase__    :    int = 1_0_0_0			,		UpperCamelCase__    :    float = 0.00_01			,		UpperCamelCase__    :    float = 0.02			,		UpperCamelCase__    :    str = "linear"			,		UpperCamelCase__    :    Optional[jnp.ndarray] = None			,		UpperCamelCase__    :    str = "fixed_small"			,		UpperCamelCase__    :    bool = True			,		UpperCamelCase__    :    str = "epsilon"			,		UpperCamelCase__    :    jnp.dtype = jnp.floataa			,		):






											'''simple docstring'''







											snake_case__	  =       dtype



				def 					__magic_name__							(      self    :    Tuple			,		UpperCamelCase__    :    Optional[CommonSchedulerState] = None):






											'''simple docstring'''







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

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

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

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



				def 					__magic_name__							(      self    :    str			,		UpperCamelCase__    :    DDPMSchedulerState			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    Optional[int] = None):






											'''simple docstring'''







											return sample



				def 					__magic_name__							(      self    :    Tuple			,		UpperCamelCase__    :    DDPMSchedulerState			,		UpperCamelCase__    :    int			,		UpperCamelCase__    :    Tuple = ()):






											'''simple docstring'''







											snake_case__	  =       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
											snake_case__	  =       (jnp.arange(0			,		UpperCamelCase__) * step_ratio).round()[::-1]

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



				def 					__magic_name__							(      self    :    Dict			,		UpperCamelCase__    :    DDPMSchedulerState			,		UpperCamelCase__    :    Optional[Any]			,		UpperCamelCase__    :    List[Any]=None			,		UpperCamelCase__    :    List[str]=None):






											'''simple docstring'''







											snake_case__	  =       state.common.alphas_cumprod[t]
											snake_case__	  =       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
											snake_case__	  =       (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

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

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

											return variance



				def 					__magic_name__							(      self    :    str			,		UpperCamelCase__    :    DDPMSchedulerState			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    int			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    Optional[jax.random.KeyArray] = None			,		UpperCamelCase__    :    bool = True			,		):






											'''simple docstring'''







											snake_case__	  =       timestep

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

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

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

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

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

											snake_case__	  =       pred_prev_sample + variance

											if not return_dict:
																		return (pred_prev_sample, state)

											return FlaxDDPMSchedulerOutput(prev_sample=UpperCamelCase__			,		state=UpperCamelCase__)



				def 					__magic_name__							(      self    :    List[Any]			,		UpperCamelCase__    :    DDPMSchedulerState			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    jnp.ndarray			,		):






											'''simple docstring'''







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



				def 					__magic_name__							(      self    :    List[str]			,		UpperCamelCase__    :    DDPMSchedulerState			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    jnp.ndarray			,		UpperCamelCase__    :    jnp.ndarray			,		):






											'''simple docstring'''







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



				def __len__(      self    :    Any):






											'''simple docstring'''







											return self.config.num_train_timesteps








from math import factorial

a__       =     {str(digit): factorial(digit) for digit in range(1_0)}

def _UpperCAmelCase   (	a						:	int ):
							if not isinstance(a  ,					a ):
														raise TypeError("""Parameter number must be int""" )

							if number < 0:
														raise ValueError("""Parameter number must be greater than or equal to 0""" )

							# Converts number in string to iterate on its digits and adds its factorial.
							return sum(DIGIT_FACTORIAL[digit] for digit in str(a ) )

def _UpperCAmelCase   (	a						:	int = 60  ,					a						:	int = 100_0000 ):

							if not isinstance(a  ,					a ) or not isinstance(a  ,					a ):
														raise TypeError("""Parameters chain_length and number_limit must be int""" )

							if chain_length <= 0 or number_limit <= 0:
														raise ValueError(
														    """Parameters chain_length and number_limit must be greater than 0""" )

							# the counter for the chains with the exact desired length
							snake_case__	  =       0
							# the cached sizes of the previous chains
							snake_case__	  =       {}

							for start_chain_element in range(1  ,					a ):
														# The temporary set will contain the elements of the chain
														snake_case__	  =       set()
														snake_case__	  =       0

														# Stop computing the chain when you find a cached size, a repeating item or the
														# length is greater then the desired one.
														snake_case__	  =       start_chain_element
														while (
														    chain_element not in chain_sets_lengths
														    and chain_element not in chain_set
														    and chain_set_length <= chain_length
														):
																					chain_set.add(a )
																					chain_set_length += 1
																					snake_case__	  =       digit_factorial_sum(a )

														if chain_element in chain_sets_lengths:
																					chain_set_length += chain_sets_lengths[chain_element]

														snake_case__	  =       chain_set_length

														# If chain contains the exact amount of elements increase the counter
														if chain_set_length == chain_length:
																					chains_counter += 1

							return chains_counter


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(F'''{solution()}''')
