
"""simple docstring"""




from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff



def 							a__ (				lowerCAmelCase	:       str       ,    lowerCAmelCase	:       float | Decimal       ,    lowerCAmelCase	:       float = 10**-10		):






     '''simple docstring'''
     UpperCAmelCase__							: str 							=						a
     while True:
          UpperCAmelCase__							: Tuple 							=						Decimal(lowerCAmelCase		) - (
              Decimal(eval(lowerCAmelCase		)		) / Decimal(eval(str(diff(lowerCAmelCase		)		)		)		)  # noqa: S307
          )
          # This number dictates the accuracy of the answer
          if abs(eval(lowerCAmelCase		)		) < precision:  # noqa: S307
               return float(lowerCAmelCase		)


# Let's Execute
if __name__ == "__main__":
    # Find root of trigonometric function
    # Find value of pi
    print(f"""The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}""")
    # Find root of polynomial
    print(f"""The root of x**2 - 5*x + 2 = 0 is {newton_raphson("x**2 - 5*x + 2", 0.4)}""")
    # Find Square Root of 5
    print(f"""The root of log(x) - 1 = 0 is {newton_raphson("log(x) - 1", 2)}""")
    # Exponential Roots
    print(f"""The root of exp(x) - 1 = 0 is {newton_raphson("exp(x) - 1", 0)}""")





"""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						:


     '''simple docstring'''





     _A								=							42

     # setable values
     _A								=							42
     _A								=							42
     _A								=							None



     @classmethod
     def  lowerCAmelCase__       (      cls ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase  )->					Union[str, Any]:
          return cls(common=__UpperCamelCase ,			init_noise_sigma=__UpperCamelCase ,			timesteps=__UpperCamelCase  )







@dataclass
class   _lowercase						(       lowerCAmelCase_				):


     '''simple docstring'''





     _A								=							42







class   _lowercase						(       lowerCAmelCase_	,   lowerCAmelCase_				):


     '''simple docstring'''





     _A								=							[e.name for e in FlaxKarrasDiffusionSchedulers]

     _A								=							42



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



     @register_to_config
     def __init__(      self ,			__UpperCamelCase = 10_00 ,			__UpperCamelCase = 0.0001 ,			__UpperCamelCase = 0.02 ,			__UpperCamelCase = "linear" ,			__UpperCamelCase = None ,			__UpperCamelCase = "fixed_small" ,			__UpperCamelCase = True ,			__UpperCamelCase = "epsilon" ,			__UpperCamelCase = jnp.floataa ,			)->					List[str]:
          UpperCAmelCase__							: int 							=						dtype



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase = None  )->					DDPMSchedulerState:
          if common is None:
               UpperCAmelCase__							: int 							=						CommonSchedulerState.create(self  )

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

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

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



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase = None  )->					jnp.ndarray:
          return sample



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase = ()  )->					DDPMSchedulerState:
          UpperCAmelCase__							: Dict 							=						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
          UpperCAmelCase__							: Optional[int] 							=						(jnp.arange(0 ,			__UpperCamelCase  ) * step_ratio).round()[::-1]

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



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase=None ,			__UpperCamelCase=None  )->					Union[str, Any]:
          UpperCAmelCase__							: Optional[Any] 							=						state.common.alphas_cumprod[t]
          UpperCAmelCase__							: int 							=						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
          UpperCAmelCase__							: Any 							=						(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

          if variance_type is None:
               UpperCAmelCase__							: Union[str, Any] 							=						self.config.variance_type

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

          return variance



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase = None ,			__UpperCamelCase = True ,			)->					Union[FlaxDDPMSchedulerOutput, Tuple]:
          UpperCAmelCase__							: List[str] 							=						timestep

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

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

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

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

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

          UpperCAmelCase__							: Any 							=						pred_prev_sample + variance

          if not return_dict:
               return (pred_prev_sample, state)

          return FlaxDDPMSchedulerOutput(prev_sample=__UpperCamelCase ,			state=__UpperCamelCase  )



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase ,			)->					jnp.ndarray:
          return add_noise_common(state.common ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase  )



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase ,			)->					jnp.ndarray:
          return get_velocity_common(state.common ,			__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase  )



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



