'''simple docstring'''

import importlib
import math
import os
from dataclasses import dataclass
from enum import Enum
from typing import Any, Dict, Optional, Tuple, Union

import flax
import jax.numpy as jnp

from ..utils import BaseOutput


UpperCamelCase__  :						int					=      'scheduler_config.json'


class 					_lowercase						(   lowerCAmelCase ):
      '''simple docstring'''


      UpperCAmelCase_   :   Optional[int]   				= 1
      UpperCAmelCase_   :   int   				= 2
      UpperCAmelCase_   :   Optional[Any]   				= 3
      UpperCAmelCase_   :   int   				= 4
      UpperCAmelCase_   :   int   				= 5




@dataclass
class 					_lowercase						(   lowerCAmelCase ):
      '''simple docstring'''


      UpperCAmelCase_   :   jnp.ndarray




class 					_lowercase						:
      '''simple docstring'''


      UpperCAmelCase_   :   Union[str, Any]   				= SCHEDULER_CONFIG_NAME
      UpperCAmelCase_   :   Union[str, Any]   				= ['''dtype''']
      UpperCAmelCase_   :   Optional[int]   				= []
      UpperCAmelCase_   :   Optional[Any]   				= True




      @classmethod
      def 		lowerCAmelCase__       (					cls       ,lowerCamelCase_ = None       ,lowerCamelCase_ = None       ,lowerCamelCase_=False       ,**lowerCamelCase_       ,)      ->      List[Any]:



         '''simple docstring'''



         UpperCAmelCase__					,   UpperCAmelCase__				:					Union[str, Any] 					=	cls.load_config(
             pretrained_model_name_or_path=lowerCamelCase_       ,subfolder=lowerCamelCase_       ,return_unused_kwargs=lowerCamelCase_       ,**lowerCamelCase_       ,)
         UpperCAmelCase__					,   UpperCAmelCase__				:					Dict 					=	cls.from_config(lowerCamelCase_       ,return_unused_kwargs=lowerCamelCase_       ,**lowerCamelCase_				)

         if hasattr(lowerCamelCase_       ,'''create_state'''				) and getattr(lowerCamelCase_       ,'''has_state'''       ,lowerCamelCase_				):
            UpperCAmelCase__				:					List[str] 					=	scheduler.create_state()

         if return_unused_kwargs:
            return scheduler, state, unused_kwargs

         return scheduler, state




      def 		lowerCAmelCase__       (					self       ,lowerCamelCase_       ,lowerCamelCase_ = False       ,**lowerCamelCase_				)      ->      Any:



         '''simple docstring'''



         self.save_config(save_directory=lowerCamelCase_       ,push_to_hub=lowerCamelCase_       ,**lowerCamelCase_				)




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



         '''simple docstring'''



         return self._get_compatibles()




      @classmethod
      def 		lowerCAmelCase__       (					cls				)      ->      Tuple:



         '''simple docstring'''



         UpperCAmelCase__				:					Optional[int] 					=	list(set([cls.__name__] + cls._compatibles				)				)
         UpperCAmelCase__				:					Optional[int] 					=	importlib.import_module(__name__.split('''.'''				)[0]				)
         UpperCAmelCase__				:					Dict 					=	[
             getattr(lowerCamelCase_       ,lowerCamelCase_				) for c in compatible_classes_str if hasattr(lowerCamelCase_       ,lowerCamelCase_				)
         ]
         return compatible_classes







def __UpperCamelCase( _A       :					jnp.ndarray	,      _A       :					Tuple[int]     ):
   '''simple docstring'''
   assert len(_A     ) >= x.ndim
   return jnp.broadcast_to(x.reshape(x.shape + (1,) * (len(_A     ) - x.ndim)     )	,      _A     )







def __UpperCamelCase( _A       :					int	,      _A       :					List[Any]=0.9_9_9	,      _A       :					Any=jnp.floataa     ):
   '''simple docstring'''

   def alpha_bar(_A       :					Union[str, Any]     ):
      return math.cos((time_step + 0.0_0_8) / 1.0_0_8 * math.pi / 2     ) ** 2

   UpperCAmelCase__				:					Dict 					=	[]
   for i in range(_A     ):
      UpperCAmelCase__				:					Any 					=	i / num_diffusion_timesteps
      UpperCAmelCase__				:					Union[str, Any] 					=	(i + 1) / num_diffusion_timesteps
      betas.append(min(1 - alpha_bar(_A     ) / alpha_bar(_A     )	,      _A     )     )
   return jnp.array(_A	,      dtype=_A     )


@flax.struct.dataclass
class 					_lowercase						:
      '''simple docstring'''


      UpperCAmelCase_   :   jnp.ndarray
      UpperCAmelCase_   :   jnp.ndarray
      UpperCAmelCase_   :   jnp.ndarray




      @classmethod
      def 		lowerCAmelCase__       (					cls       ,lowerCamelCase_				)      ->      List[str]:



         '''simple docstring'''



         UpperCAmelCase__				:					Dict 					=	scheduler.config

         if config.trained_betas is not None:
            UpperCAmelCase__				:					Optional[Any] 					=	jnp.asarray(config.trained_betas       ,dtype=scheduler.dtype				)
         elif config.beta_schedule == "linear":
            UpperCAmelCase__				:					Dict 					=	jnp.linspace(config.beta_start       ,config.beta_end       ,config.num_train_timesteps       ,dtype=scheduler.dtype				)
         elif config.beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            UpperCAmelCase__				:					Union[str, Any] 					=	(
                jnp.linspace(
                    config.beta_start**0.5       ,config.beta_end**0.5       ,config.num_train_timesteps       ,dtype=scheduler.dtype				)
                ** 2
            )
         elif config.beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            UpperCAmelCase__				:					Dict 					=	betas_for_alpha_bar(config.num_train_timesteps       ,dtype=scheduler.dtype				)
         else:
            raise NotImplementedError(
                f'''beta_schedule {config.beta_schedule} is not implemented for scheduler {scheduler.__class__.__name__}'''				)

         UpperCAmelCase__				:					Optional[int] 					=	1.0 - betas

         UpperCAmelCase__				:					Union[str, Any] 					=	jnp.cumprod(lowerCamelCase_       ,axis=0				)

         return cls(
             alphas=lowerCamelCase_       ,betas=lowerCamelCase_       ,alphas_cumprod=lowerCamelCase_       ,)







def __UpperCamelCase( _A       :					CommonSchedulerState	,      _A       :					jnp.ndarray	,      _A       :					jnp.ndarray	,      _A       :					jnp.ndarray     ):
   '''simple docstring'''
   UpperCAmelCase__				:					List[Any] 					=	state.alphas_cumprod

   UpperCAmelCase__				:					int 					=	alphas_cumprod[timesteps] ** 0.5
   UpperCAmelCase__				:					List[str] 					=	sqrt_alpha_prod.flatten()
   UpperCAmelCase__				:					Dict 					=	broadcast_to_shape_from_left(_A	,      original_samples.shape     )

   UpperCAmelCase__				:					str 					=	(1 - alphas_cumprod[timesteps]) ** 0.5
   UpperCAmelCase__				:					List[Any] 					=	sqrt_one_minus_alpha_prod.flatten()
   UpperCAmelCase__				:					str 					=	broadcast_to_shape_from_left(_A	,      original_samples.shape     )

   return sqrt_alpha_prod, sqrt_one_minus_alpha_prod







def __UpperCamelCase( _A       :					CommonSchedulerState	,      _A       :					jnp.ndarray	,      _A       :					jnp.ndarray	,      _A       :					jnp.ndarray     ):
   '''simple docstring'''
   UpperCAmelCase__					,   UpperCAmelCase__				:					Dict 					=	get_sqrt_alpha_prod(_A	,      _A	,      _A	,      _A     )
   UpperCAmelCase__				:					List[Any] 					=	sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
   return noisy_samples







def __UpperCamelCase( _A       :					CommonSchedulerState	,      _A       :					jnp.ndarray	,      _A       :					jnp.ndarray	,      _A       :					jnp.ndarray     ):
   '''simple docstring'''
   UpperCAmelCase__					,   UpperCAmelCase__				:					Dict 					=	get_sqrt_alpha_prod(_A	,      _A	,      _A	,      _A     )
   UpperCAmelCase__				:					Optional[Any] 					=	sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
   return velocity





'''simple docstring'''

import numpy as np







def __UpperCamelCase( _A       :					np.ndarray	,      _A       :					np.ndarray	,      _A       :					float = 1e-12	,      _A       :					int = 1_00	,      ):
   '''simple docstring'''
   assert np.shape(_A     )[0] == np.shape(_A     )[1]
   # Ensure proper dimensionality.
   assert np.shape(_A     )[0] == np.shape(_A     )[0]
   # Ensure inputs are either both complex or both real
   assert np.iscomplexobj(_A     ) == np.iscomplexobj(_A     )
   UpperCAmelCase__				:					int 					=	np.iscomplexobj(_A     )
   if is_complex:
      # Ensure complex input_matrix is Hermitian
      assert np.array_equal(_A	,      input_matrix.conj().T     )

   # Set convergence to False. Will define convergence when we exceed max_iterations
   # or when we have small changes from one iteration to next.

   UpperCAmelCase__				:					Any 					=	False
   UpperCAmelCase__				:					str 					=	0
   UpperCAmelCase__				:					Optional[int] 					=	0
   UpperCAmelCase__				:					Optional[int] 					=	1e12

   while not convergence:
      # Multiple matrix by the vector.
      UpperCAmelCase__				:					str 					=	np.dot(_A	,      _A     )
      # Normalize the resulting output vector.
      UpperCAmelCase__				:					int 					=	w / np.linalg.norm(_A     )
      # Find rayleigh quotient
      # (faster than usual b/c we know vector is normalized already)
      UpperCAmelCase__				:					int 					=	vector.conj().T if is_complex else vector.T
      UpperCAmelCase__				:					Any 					=	np.dot(_A	,      np.dot(_A	,      _A     )     )

      # Check convergence.
      UpperCAmelCase__				:					List[Any] 					=	np.abs(lambda_ - lambda_previous     ) / lambda_
      iterations += 1

      if error <= error_tol or iterations >= max_iterations:
         UpperCAmelCase__				:					Optional[Any] 					=	True

      UpperCAmelCase__				:					Optional[int] 					=	lambda_

   if is_complex:
      UpperCAmelCase__				:					Tuple 					=	np.real(lambda_     )

   return lambda_, vector







def __UpperCamelCase( ):
   '''simple docstring'''
   UpperCAmelCase__				:					Optional[int] 					=	np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]     )
   UpperCAmelCase__				:					int 					=	np.array([41, 4, 20]     )
   UpperCAmelCase__				:					str 					=	real_input_matrix.astype(np.complexaaa     )
   UpperCAmelCase__				:					Union[str, Any] 					=	np.triu(1J * complex_input_matrix	,      1     )
   complex_input_matrix += imag_matrix
   complex_input_matrix += -1 * imag_matrix.T
   UpperCAmelCase__				:					Tuple 					=	np.array([41, 4, 20]     ).astype(np.complexaaa     )

   for problem_type in ["real", "complex"]:
      if problem_type == "real":
         UpperCAmelCase__				:					Optional[int] 					=	real_input_matrix
         UpperCAmelCase__				:					int 					=	real_vector
      elif problem_type == "complex":
         UpperCAmelCase__				:					int 					=	complex_input_matrix
         UpperCAmelCase__				:					Tuple 					=	complex_vector

      # Our implementation.
      UpperCAmelCase__					,   UpperCAmelCase__				:					str 					=	power_iteration(_A	,      _A     )

      # Numpy implementation.

      # Get eigenvalues and eigenvectors using built-in numpy
      # eigh (eigh used for symmetric or hermetian matrices).
      UpperCAmelCase__					,   UpperCAmelCase__				:					Tuple 					=	np.linalg.eigh(_A     )
      # Last eigenvalue is the maximum one.
      UpperCAmelCase__				:					Dict 					=	eigen_values[-1]
      # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
      UpperCAmelCase__				:					Union[str, Any] 					=	eigen_vectors[:, -1]

      # Check our implementation and numpy gives close answers.
      assert np.abs(eigen_value - eigen_value_max     ) <= 1e-6
      # Take absolute values element wise of each eigenvector.
      # as they are only unique to a minus sign.
      assert np.linalg.norm(np.abs(_A     ) - np.abs(_A     )     ) <= 1e-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_power_iteration()




