


'''simple docstring'''




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  _lowercase   :
			# setable values
			_SCREAMING_SNAKE_CASE     :     Optional[jnp.ndarray]									=  None
			_SCREAMING_SNAKE_CASE     :     Optional[jnp.ndarray]									=  None
			_SCREAMING_SNAKE_CASE     :     Optional[jnp.ndarray]									=  None
			@classmethod
			def a     (	cls					:			List[Any]			)   ->       int:
								return cls()




@dataclass
class  _lowercase   (  __lowercase       ):
			_SCREAMING_SNAKE_CASE     :     ScoreSdeVeSchedulerState
			_SCREAMING_SNAKE_CASE     :     jnp.ndarray
			_SCREAMING_SNAKE_CASE     :     Optional[jnp.ndarray]									=  None




class  _lowercase   (  __lowercase	,				__lowercase       ):
			@property
			def a     (	self					:			Any			)   ->       List[Any]:
								return True
			@register_to_config
			def __init__(	self					:			List[Any]					,      SCREAMING_SNAKE_CASE_					:			int = 2000					,      SCREAMING_SNAKE_CASE_					:			float = 0.1_5					,      SCREAMING_SNAKE_CASE_					:			float = 0.0_1					,      SCREAMING_SNAKE_CASE_					:			float = 1348.0					,      SCREAMING_SNAKE_CASE_					:			float = 1e-5					,      SCREAMING_SNAKE_CASE_					:			int = 1					,      )   ->       Dict:
								pass
			def a     (	self					:			str			)   ->       List[str]:
								__snake_case    			=	ScoreSdeVeSchedulerState.create()
								return self.set_sigmas(
								    SCREAMING_SNAKE_CASE_					,      self.config.num_train_timesteps					,      self.config.sigma_min					,      self.config.sigma_max					,      self.config.sampling_eps					,      )
			def a     (	self					:			Optional[int]					,      SCREAMING_SNAKE_CASE_					:			ScoreSdeVeSchedulerState					,      SCREAMING_SNAKE_CASE_					:			int					,      SCREAMING_SNAKE_CASE_					:			Tuple = ()					,      SCREAMING_SNAKE_CASE_					:			float = None			)   ->       ScoreSdeVeSchedulerState:
								__snake_case    			=	sampling_eps if sampling_eps is not None else self.config.sampling_eps

								__snake_case    			=	jnp.linspace(1					,      SCREAMING_SNAKE_CASE_					,      SCREAMING_SNAKE_CASE_			)
								return state.replace(timesteps=SCREAMING_SNAKE_CASE_			)
			def a     (	self					:			int					,      SCREAMING_SNAKE_CASE_					:			ScoreSdeVeSchedulerState					,      SCREAMING_SNAKE_CASE_					:			int					,      SCREAMING_SNAKE_CASE_					:			float = None					,      SCREAMING_SNAKE_CASE_					:			float = None					,      SCREAMING_SNAKE_CASE_					:			float = None					,      )   ->       ScoreSdeVeSchedulerState:
								__snake_case    			=	sigma_min if sigma_min is not None else self.config.sigma_min
								__snake_case    			=	sigma_max if sigma_max is not None else self.config.sigma_max
								__snake_case    			=	sampling_eps if sampling_eps is not None else self.config.sampling_eps
								if state.timesteps is None:
													__snake_case    			=	self.set_timesteps(SCREAMING_SNAKE_CASE_					,      SCREAMING_SNAKE_CASE_					,      SCREAMING_SNAKE_CASE_			)

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

								return state.replace(discrete_sigmas=SCREAMING_SNAKE_CASE_					,      sigmas=SCREAMING_SNAKE_CASE_			)
			def a     (	self					:			Optional[int]					,      SCREAMING_SNAKE_CASE_					:			Optional[Any]					,      SCREAMING_SNAKE_CASE_					:			int					,      SCREAMING_SNAKE_CASE_					:			List[str]			)   ->       Dict:
								return jnp.where(timesteps == 0					,      jnp.zeros_like(SCREAMING_SNAKE_CASE_			)					,      state.discrete_sigmas[timesteps - 1]			)
			def a     (	self					:			List[Any]					,      SCREAMING_SNAKE_CASE_					:			ScoreSdeVeSchedulerState					,      SCREAMING_SNAKE_CASE_					:			jnp.ndarray					,      SCREAMING_SNAKE_CASE_					:			int					,      SCREAMING_SNAKE_CASE_					:			jnp.ndarray					,      SCREAMING_SNAKE_CASE_					:			random.KeyArray					,      SCREAMING_SNAKE_CASE_					:			bool = True					,      )   ->       Union[FlaxSdeVeOutput, Tuple]:
								if state.timesteps is None:
													raise ValueError(
													    '`state.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'			)

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

								__snake_case    			=	state.discrete_sigmas[timesteps]
								__snake_case    			=	self.get_adjacent_sigma(SCREAMING_SNAKE_CASE_					,      SCREAMING_SNAKE_CASE_					,      SCREAMING_SNAKE_CASE_			)
								__snake_case    			=	jnp.zeros_like(SCREAMING_SNAKE_CASE_			)
								__snake_case    			=	(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
								__snake_case    			=	diffusion.flatten()
								__snake_case    			=	broadcast_to_shape_from_left(SCREAMING_SNAKE_CASE_					,      sample.shape			)
								__snake_case    			=	drift - diffusion**2 * model_output

								#  equation 6: sample noise for the diffusion term of
								__snake_case    			=	random.split(SCREAMING_SNAKE_CASE_					,      num=1			)
								__snake_case    			=	random.normal(key=SCREAMING_SNAKE_CASE_					,      shape=sample.shape			)
								__snake_case    			=	sample - drift  # subtract because `dt` is a small negative timestep
								# TODO is the variable diffusion the correct scaling term for the noise?
								__snake_case    			=	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=SCREAMING_SNAKE_CASE_					,      prev_sample_mean=SCREAMING_SNAKE_CASE_					,      state=SCREAMING_SNAKE_CASE_			)
			def a     (	self					:			Any					,      SCREAMING_SNAKE_CASE_					:			ScoreSdeVeSchedulerState					,      SCREAMING_SNAKE_CASE_					:			jnp.ndarray					,      SCREAMING_SNAKE_CASE_					:			jnp.ndarray					,      SCREAMING_SNAKE_CASE_					:			random.KeyArray					,      SCREAMING_SNAKE_CASE_					:			bool = True					,      )   ->       Union[FlaxSdeVeOutput, Tuple]:
								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
								__snake_case    			=	random.split(SCREAMING_SNAKE_CASE_					,      num=1			)
								__snake_case    			=	random.normal(key=SCREAMING_SNAKE_CASE_					,      shape=sample.shape			)

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

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

								if not return_dict:
													return (prev_sample, state)

								return FlaxSdeVeOutput(prev_sample=SCREAMING_SNAKE_CASE_					,      state=SCREAMING_SNAKE_CASE_			)





			def __len__(	self					:			Optional[int]			)   ->       Any:
								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

_a      :      Optional[int]       				=      0.25 + 0.0J
_a      :      Dict       				=      -0.4 + 0.6J
_a      :      List[str]       				=      -0.1 + 0.651J
_a      :      Optional[int]       				=      -2.0
_a      :      List[str]       				=      56
_a      :      Tuple       				=      2.0
_a      :      List[str]       				=      666





def      _a		(lowercase__ :      complex       ,      lowercase__ :      numpy.ndarray	) -> numpy.ndarray:






     """simple docstring"""
     return numpy.exp(lowercase__	) + c_parameter





def      _a		(lowercase__ :      complex       ,      lowercase__ :      numpy.ndarray	) -> numpy.ndarray:






     """simple docstring"""
     return z_values * z_values + c_parameter





def      _a		(lowercase__ :      float       ,      lowercase__ :      int	) -> numpy.ndarray:






     """simple docstring"""
     __snake_case    			=	numpy.linspace(-window_size       ,      lowercase__       ,      lowercase__	)
     __snake_case    			=	x.reshape((nb_pixels, 1)	)
     __snake_case    			=	numpy.linspace(-window_size       ,      lowercase__       ,      lowercase__	)
     __snake_case    			=	y.reshape((1, nb_pixels)	)
     return x + 1.0J * y





def      _a		(lowercase__ :      Callable[[Any, numpy.ndarray], numpy.ndarray]       ,      lowercase__ :      Any       ,      lowercase__ :      int       ,      lowercase__ :      numpy.ndarray       ,      lowercase__ :      float | None = None       ,      ) -> numpy.ndarray:






     """simple docstring"""
     __snake_case    			=	z_a.astype('complex64'	)
     for _ in range(lowercase__	):
          __snake_case    			=	eval_function(lowercase__       ,      lowercase__	)
          if infinity is not None:
               numpy.nan_to_num(lowercase__       ,      copy=lowercase__       ,      nan=lowercase__	)
               __snake_case    			=	infinity
     return z_n





def      _a		(lowercase__ :      str       ,      lowercase__ :      Any       ,      lowercase__ :      float       ,      lowercase__ :      numpy.ndarray       ,      ) -> None:






     """simple docstring"""
     __snake_case    			=	(abs(lowercase__	)).transpose()
     __snake_case    			=	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		() -> None:






     """simple docstring"""
     warnings.filterwarnings(
         'ignore'       ,      category=lowercase__       ,      message='overflow encountered in multiply'	)
     warnings.filterwarnings(
         'ignore'       ,      category=lowercase__       ,      message='invalid value encountered in multiply'       ,      )
     warnings.filterwarnings(
         'ignore'       ,      category=lowercase__       ,      message='overflow encountered in absolute'	)
     warnings.filterwarnings(
         'ignore'       ,      category=lowercase__       ,      message='overflow encountered in exp'	)


if __name__ == "__main__":
       _a      :      List[Any]       				=      prepare_grid(window_size, nb_pixels)

       ignore_overflow_warnings()  # See file header for explanations

       _a      :      Optional[Any]       				=      24
       _a      :      Optional[int]       				=      2 * abs(c_cauliflower) + 1
       _a      :      List[str]       				=      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)

       _a      :      str       				=      64
       _a      :      Tuple       				=      2 * abs(c_polynomial_a) + 1
       _a      :      List[Any]       				=      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)

       _a      :      List[Any]       				=      161
       _a      :      Tuple       				=      2 * abs(c_polynomial_a) + 1
       _a      :      int       				=      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)

       _a      :      str       				=      12
       _a      :      Optional[Any]       				=      10_000.0
       _a      :      Dict       				=      iterate_function(
           eval_exponential,
           c_exponential,
           nb_iterations,
           z_a + 2,
           infinity=1.0e1_0,
       )
       show_results("e^z+c", c_exponential, escape_radius, z_final)




