






# 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 		_a       :





   '''simple docstring'''






   UpperCamelCase__      					=    None
   UpperCamelCase__      					=    None
   UpperCamelCase__      					=    None





   @classmethod
   def __lowercase    (   cls)	-> List[str]:




          '''simple docstring'''




          return cls()







@dataclass
class 		_a       (						_lowerCamelCase   ):





   '''simple docstring'''






   UpperCamelCase__      					=    42
   UpperCamelCase__      					=    42
   UpperCamelCase__      					=    None







class 		_a       (						_lowerCamelCase    ,					_lowerCamelCase   ):





   '''simple docstring'''






   @property
   def __lowercase    (   self)	-> Optional[Any]:




          '''simple docstring'''




          return True





   @register_to_config
   def __init__(   self			,				UpperCAmelCase_ = 2_000			,				UpperCAmelCase_ = 0.15			,				UpperCAmelCase_ = 0.01			,				UpperCAmelCase_ = 1_348.0			,				UpperCAmelCase_ = 1E-5			,				UpperCAmelCase_ = 1			,				)	-> Optional[Any]:




          '''simple docstring'''




          pass





   def __lowercase    (   self)	-> Any:




          '''simple docstring'''




          lowercase__:    Any        =      ScoreSdeVeSchedulerState.create()
          return self.set_sigmas(
              __UpperCamelCase			,				self.config.num_train_timesteps			,				self.config.sigma_min			,				self.config.sigma_max			,				self.config.sampling_eps			,				)





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_ = ()			,				UpperCAmelCase_ = None)	-> ScoreSdeVeSchedulerState:




          '''simple docstring'''




          lowercase__:    Union[str, Any]        =      sampling_eps if sampling_eps is not None else self.config.sampling_eps

          lowercase__:    str        =      jnp.linspace(1			,				__UpperCamelCase			,				__UpperCamelCase)
          return state.replace(timesteps=__UpperCamelCase)





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_ = None			,				UpperCAmelCase_ = None			,				UpperCAmelCase_ = None			,				)	-> ScoreSdeVeSchedulerState:




          '''simple docstring'''




          lowercase__:    Dict        =      sigma_min if sigma_min is not None else self.config.sigma_min
          lowercase__:    int        =      sigma_max if sigma_max is not None else self.config.sigma_max
          lowercase__:    Tuple        =      sampling_eps if sampling_eps is not None else self.config.sampling_eps
          if state.timesteps is None:
                 lowercase__:    Dict        =      self.set_timesteps(__UpperCamelCase			,				__UpperCamelCase			,				__UpperCamelCase)

          lowercase__:    Optional[int]        =      jnp.exp(jnp.linspace(jnp.log(__UpperCamelCase)			,				jnp.log(__UpperCamelCase)			,				__UpperCamelCase))
          lowercase__:    Union[str, Any]        =      jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps])

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





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_)	-> Optional[Any]:




          '''simple docstring'''




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





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_ = 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__:    Tuple        =      timestep * jnp.ones(
              sample.shape[0]			,				)
          lowercase__:    Dict        =      (timestep * (len(state.timesteps) - 1)).long()

          lowercase__:    List[str]        =      state.discrete_sigmas[timesteps]
          lowercase__:    Dict        =      self.get_adjacent_sigma(__UpperCamelCase			,				__UpperCamelCase			,				__UpperCamelCase)
          lowercase__:    List[Any]        =      jnp.zeros_like(__UpperCamelCase)
          lowercase__:    Union[str, Any]        =      (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__:    List[Any]        =      diffusion.flatten()
          lowercase__:    int        =      broadcast_to_shape_from_left(__UpperCamelCase			,				sample.shape)
          lowercase__:    Union[str, Any]        =      drift - diffusion**2 * model_output

          #  equation 6: sample noise for the diffusion term of
          lowercase__:    Tuple        =      random.split(__UpperCamelCase			,				num=1)
          lowercase__:    str        =      random.normal(key=__UpperCamelCase			,				shape=sample.shape)
          lowercase__:    str        =      sample - drift  # subtract because `dt` is a small negative timestep
          # TODO is the variable diffusion the correct scaling term for the noise?
          lowercase__:    List[str]        =      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=__UpperCamelCase			,				prev_sample_mean=__UpperCamelCase			,				state=__UpperCamelCase)





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_ = 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__:    Tuple        =      random.split(__UpperCamelCase			,				num=1)
          lowercase__:    Tuple        =      random.normal(key=__UpperCamelCase			,				shape=sample.shape)

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

          # compute corrected sample: model_output term and noise term
          lowercase__:    Union[str, Any]        =      step_size.flatten()
          lowercase__:    Dict        =      broadcast_to_shape_from_left(__UpperCamelCase			,				sample.shape)
          lowercase__:    List[Any]        =      sample + step_size * model_output
          lowercase__:    List[Any]        =      prev_sample_mean + ((step_size * 2) ** 0.5) * noise

          if not return_dict:
                 return (prev_sample, state)

          return FlaxSdeVeOutput(prev_sample=__UpperCamelCase			,				state=__UpperCamelCase)





   def __len__(   self)	-> Dict:




          '''simple docstring'''




          return self.config.num_train_timesteps














"""simple docstring"""





import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

UpperCamelCase			=      0.25 + 0.0j
UpperCamelCase			=      -0.4 + 0.6j
UpperCamelCase			=      -0.1 + 0.651j
UpperCamelCase			=      -2.0
UpperCamelCase			=      56
UpperCamelCase			=      2.0
UpperCamelCase			=      6_66






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       return numpy.exp(snake_case_		) + c_parameter






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       return z_values * z_values + c_parameter






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    str        =      numpy.linspace(-window_size						,       snake_case_						,       snake_case_		)
       lowercase__:    Union[str, Any]        =      x.reshape((nb_pixels, 1)		)
       lowercase__:    Any        =      numpy.linspace(-window_size						,       snake_case_						,       snake_case_		)
       lowercase__:    List[Any]        =      y.reshape((1, nb_pixels)		)
       return x + 1.0J * y






def     A(  snake_case_						,       snake_case_						,       snake_case_						,       snake_case_						,       snake_case_ = None						,       ):
       """simple docstring"""





       lowercase__:    List[Any]        =      z_a.astype("complex64"		)
       for _ in range(snake_case_		):
              lowercase__:    Any        =      eval_function(snake_case_						,       snake_case_		)
              if infinity is not None:
                     numpy.nan_to_num(snake_case_						,       copy=snake_case_						,       nan=snake_case_		)
                     lowercase__:    Union[str, Any]        =      infinity
       return z_n






def     A(  snake_case_						,       snake_case_						,       snake_case_						,       snake_case_						,       ):
       """simple docstring"""





       lowercase__:    Union[str, Any]        =      (abs(snake_case_		)).transpose()
       lowercase__:    List[Any]        =      abs_z_final[::-1, :]
       pyplot.matshow(abs_z_final < escape_radius		)
       pyplot.title(F"""Julia set of ${function_label}$, $c={function_params}$"""		)
       pyplot.show()






def     A(  ):
       """simple docstring"""





       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in multiply"		)
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="invalid value encountered in multiply"						,       )
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in absolute"		)
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in exp"		)


if __name__ == "__main__":
  UpperCamelCase			=      prepare_grid(window_size, nb_pixels)

  ignore_overflow_warnings()  # See file header for explanations

  UpperCamelCase			=      24
  UpperCamelCase			=      2 * abs(c_cauliflower) + 1
  UpperCamelCase			=      iterate_function(
      eval_quadratic_polynomial,
      c_cauliflower,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("""z^2+c""", c_cauliflower, escape_radius, z_final)

  UpperCamelCase			=      64
  UpperCamelCase			=      2 * abs(c_polynomial_a) + 1
  UpperCamelCase			=      iterate_function(
      eval_quadratic_polynomial,
      c_polynomial_a,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)

  UpperCamelCase			=      1_61
  UpperCamelCase			=      2 * abs(c_polynomial_a) + 1
  UpperCamelCase			=      iterate_function(
      eval_quadratic_polynomial,
      c_polynomial_a,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)

  UpperCamelCase			=      12
  UpperCamelCase			=      10_000.0
  UpperCamelCase			=      iterate_function(
      eval_exponential,
      c_exponential,
      nb_iterations,
      z_a + 2,
      infinity=1.0e10,
  )
  show_results("""e^z+c""", c_exponential, escape_radius, z_final)






