


'''simple docstring'''






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        __snake_case	:







				"""simple docstring"""



				lowercase       			= 42

				# setable values
				lowercase       			= 42
				lowercase       			= 42
				lowercase       			= None

				@classmethod
				def __lowercase       (       cls   :  str   ,						lowerCamelCase   :  CommonSchedulerState   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  jnp.ndarray		)       ->  Union[str, Any]:
						return cls(common=lowerCamelCase   ,						init_noise_sigma=lowerCamelCase   ,						timesteps=lowerCamelCase		)







@dataclass
class        __snake_case	(       _SCREAMING_SNAKE_CASE):







				"""simple docstring"""



				lowercase       			= 42







class        __snake_case	(       _SCREAMING_SNAKE_CASE     ,_SCREAMING_SNAKE_CASE):







				"""simple docstring"""



				lowercase       			= [e.name for e in FlaxKarrasDiffusionSchedulers]

				lowercase       			= 42

				@property
				def __lowercase       (       self   :  Optional[int]		)       ->  int:
						return True

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

				def __lowercase       (       self   :  Optional[Any]   ,						lowerCamelCase   :  Optional[CommonSchedulerState] = None		)       ->  DDPMSchedulerState:
						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_      :				int      =       jnp.arange(0   ,						self.config.num_train_timesteps		).round()[::-1]

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

				def __lowercase       (       self   :  Tuple   ,						lowerCamelCase   :  DDPMSchedulerState   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  Optional[int] = None		)       ->  jnp.ndarray:
						return sample

				def __lowercase       (       self   :  Union[str, Any]   ,						lowerCamelCase   :  DDPMSchedulerState   ,						lowerCamelCase   :  int   ,						lowerCamelCase   :  Tuple = ()		)       ->  DDPMSchedulerState:
						lowerCAmelCase_      :				int      =       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_      :				Optional[int]      =       (jnp.arange(0   ,						lowerCamelCase		) * step_ratio).round()[::-1]

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

				def __lowercase       (       self   :  Tuple   ,						lowerCamelCase   :  DDPMSchedulerState   ,						lowerCamelCase   :  Any   ,						lowerCamelCase   :  str=None   ,						lowerCamelCase   :  Optional[Any]=None		)       ->  Union[str, Any]:
						lowerCAmelCase_      :				Optional[int]      =       state.common.alphas_cumprod[t]
						lowerCAmelCase_      :				Tuple      =       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_      :				Optional[Any]      =       (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

						if variance_type is None:
								lowerCAmelCase_      :				Optional[int]      =       self.config.variance_type

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

						return variance

				def __lowercase       (       self   :  Dict   ,						lowerCamelCase   :  DDPMSchedulerState   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  int   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  Optional[jax.random.KeyArray] = None   ,						lowerCamelCase   :  bool = True   ,						)       ->  Union[FlaxDDPMSchedulerOutput, Tuple]:
						lowerCAmelCase_      :				Optional[Any]      =       timestep

						if key is None:
								lowerCAmelCase_      :				List[Any]      =       jax.random.PRNGKey(0		)

						if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
								lowerCAmelCase_      :				Union[str, Any]      =       jnp.split(lowerCamelCase   ,						sample.shape[1]   ,						axis=1		)
						else:
								lowerCAmelCase_      :				int      =       None

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

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

						lowerCAmelCase_      :				Union[str, Any]      =       jnp.where(t > 0   ,						random_variance()   ,						jnp.zeros(model_output.shape   ,						dtype=self.dtype		)		)

						lowerCAmelCase_      :				Tuple      =       pred_prev_sample + variance

						if not return_dict:
								return (pred_prev_sample, state)

						return FlaxDDPMSchedulerOutput(prev_sample=lowerCamelCase   ,						state=lowerCamelCase		)

				def __lowercase       (       self   :  Optional[int]   ,						lowerCamelCase   :  DDPMSchedulerState   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  jnp.ndarray   ,						)       ->  jnp.ndarray:
						return add_noise_common(state.common   ,						lowerCamelCase   ,						lowerCamelCase   ,						lowerCamelCase		)

				def __lowercase       (       self   :  Tuple   ,						lowerCamelCase   :  DDPMSchedulerState   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  jnp.ndarray   ,						lowerCamelCase   :  jnp.ndarray   ,						)       ->  jnp.ndarray:
						return get_velocity_common(state.common   ,						lowerCamelCase   ,						lowerCamelCase   ,						lowerCamelCase		)





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







'''simple docstring'''






from __future__ import annotations







def     UpperCamelCase_      (   A__ :       int | float | str							,   A__ :       int | float | str ):
  '''simple docstring'''





  if nth_term == "":
    return [""]
  lowerCAmelCase_      :				str      =       int(A__ )
  lowerCAmelCase_      :				Tuple      =       int(A__ )
  lowerCAmelCase_      :				list[str]      =       []
  for temp in range(int(A__ ) ):
    series.append(f'1 / {pow(temp + 1							,   int(A__ ) )}' if series else """1""" )
  return series


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  __A :  str    							=				int(input("Enter the last number (nth term) of the P-Series"))
  __A :  Tuple    							=				int(input("Enter the power for  P-Series"))
  print("Formula of P-Series => 1+1/2^p+1/3^p ..... 1/n^p")
  print(p_series(nth_term, power))



