




'''simple docstring'''
# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left






@flax.struct.dataclass
class 			SCREAMING_SNAKE_CASE:
       # setable values
       snake_case_					:	Optional[jnp.ndarray]       =   None
       snake_case_					:	Optional[jnp.ndarray]       =   None
       snake_case_					:	Optional[jnp.ndarray]       =   None

       @classmethod
       def        snake_case__     (       cls	)       ->   Any:

           """simple docstring"""



           return cls()






@dataclass
class 			SCREAMING_SNAKE_CASE(							__A	):
       snake_case_					:	ScoreSdeVeSchedulerState
       snake_case_					:	jnp.ndarray
       snake_case_					:	Optional[jnp.ndarray]       =   None






class 			SCREAMING_SNAKE_CASE(							__A  , __A	):

       @property
       def        snake_case__     (       self	)       ->   int:

           """simple docstring"""



           return True

       @register_to_config
       def __init__(       self   ,						lowerCamelCase__ = 2000   ,						lowerCamelCase__ = 0.15   ,						lowerCamelCase__ = 0.01   ,						lowerCamelCase__ = 13_48.0   ,						lowerCamelCase__ = 1E-5   ,						lowerCamelCase__ = 1   ,						)       ->   str:

           """simple docstring"""



           pass

       def        snake_case__     (       self	)       ->   Dict:

           """simple docstring"""



           __lowercase     							=		ScoreSdeVeSchedulerState.create()
           return self.set_sigmas(
               lowerCamelCase__   ,						self.config.num_train_timesteps   ,						self.config.sigma_min   ,						self.config.sigma_max   ,						self.config.sampling_eps   ,						)

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__ = ()   ,						lowerCamelCase__ = None	)       ->   ScoreSdeVeSchedulerState:

           """simple docstring"""



           __lowercase     							=		sampling_eps if sampling_eps is not None else self.config.sampling_eps

           __lowercase     							=		jnp.linspace(1   ,						lowerCamelCase__   ,						lowerCamelCase__	)
           return state.replace(timesteps=lowerCamelCase__	)

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__ = None   ,						lowerCamelCase__ = None   ,						lowerCamelCase__ = None   ,						)       ->   ScoreSdeVeSchedulerState:

           """simple docstring"""



           __lowercase     							=		sigma_min if sigma_min is not None else self.config.sigma_min
           __lowercase     							=		sigma_max if sigma_max is not None else self.config.sigma_max
           __lowercase     							=		sampling_eps if sampling_eps is not None else self.config.sampling_eps
           if state.timesteps is None:
               __lowercase     							=		self.set_timesteps(lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__	)

           __lowercase     							=		jnp.exp(jnp.linspace(jnp.log(lowerCamelCase__	)   ,						jnp.log(lowerCamelCase__	)   ,						lowerCamelCase__	)	)
           __lowercase     							=		jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]	)

           return state.replace(discrete_sigmas=lowerCamelCase__   ,						sigmas=lowerCamelCase__	)

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__	)       ->   Tuple:

           """simple docstring"""



           return jnp.where(timesteps == 0   ,						jnp.zeros_like(lowerCamelCase__	)   ,						state.discrete_sigmas[timesteps - 1]	)

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__ = True   ,						)       ->   Union[FlaxSdeVeOutput, Tuple]:

           """simple docstring"""



           if state.timesteps is None:
               raise ValueError(
                   """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""	)

           __lowercase     							=		timestep * jnp.ones(
               sample.shape[0]   ,						)
           __lowercase     							=		(timestep * (len(state.timesteps	) - 1)).long()

           __lowercase     							=		state.discrete_sigmas[timesteps]
           __lowercase     							=		self.get_adjacent_sigma(lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__	)
           __lowercase     							=		jnp.zeros_like(lowerCamelCase__	)
           __lowercase     							=		(sigma**2 - adjacent_sigma**2) ** 0.5

           # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
           # also equation 47 shows the analog from SDE models to ancestral sampling methods
           __lowercase     							=		diffusion.flatten()
           __lowercase     							=		broadcast_to_shape_from_left(lowerCamelCase__   ,						sample.shape	)
           __lowercase     							=		drift - diffusion**2 * model_output

           #  equation 6: sample noise for the diffusion term of
           __lowercase     							=		random.split(lowerCamelCase__   ,						num=1	)
           __lowercase     							=		random.normal(key=lowerCamelCase__   ,						shape=sample.shape	)
           __lowercase     							=		sample - drift  # subtract because `dt` is a small negative timestep
           # TODO is the variable diffusion the correct scaling term for the noise?
           __lowercase     							=		prev_sample_mean + diffusion * noise  # add impact of diffusion field g

           if not return_dict:
               return (prev_sample, prev_sample_mean, state)

           return FlaxSdeVeOutput(prev_sample=lowerCamelCase__   ,						prev_sample_mean=lowerCamelCase__   ,						state=lowerCamelCase__	)

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__ = True   ,						)       ->   Union[FlaxSdeVeOutput, Tuple]:

           """simple docstring"""



           if state.timesteps is None:
               raise ValueError(
                   """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""	)

           # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
           # sample noise for correction
           __lowercase     							=		random.split(lowerCamelCase__   ,						num=1	)
           __lowercase     							=		random.normal(key=lowerCamelCase__   ,						shape=sample.shape	)

           # compute step size from the model_output, the noise, and the snr
           __lowercase     							=		jnp.linalg.norm(lowerCamelCase__	)
           __lowercase     							=		jnp.linalg.norm(lowerCamelCase__	)
           __lowercase     							=		(self.config.snr * noise_norm / grad_norm) ** 2 * 2
           __lowercase     							=		step_size * jnp.ones(sample.shape[0]	)

           # compute corrected sample: model_output term and noise term
           __lowercase     							=		step_size.flatten()
           __lowercase     							=		broadcast_to_shape_from_left(lowerCamelCase__   ,						sample.shape	)
           __lowercase     							=		sample + step_size * model_output
           __lowercase     							=		prev_sample_mean + ((step_size * 2) ** 0.5) * noise

           if not return_dict:
               return (prev_sample, state)

           return FlaxSdeVeOutput(prev_sample=lowerCamelCase__   ,						state=lowerCamelCase__	)




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

           """simple docstring"""



           return self.config.num_train_timesteps










'''simple docstring'''
from math import gcd
def 							snake_case_    (  a__						:      int = 1_20_00     ):



    """simple docstring"""




    __lowercase     							=		0
    for d in range(max_d + 1     ):
        for n in range(d // 3 + 1       ,(d + 1) // 2     ):
            if gcd(a__       ,a__     ) == 1:
                fractions_number += 1
    return fractions_number


if __name__ == "__main__":
  print(F"""{solution() = }""")




