

'''simple docstring'''




import numpy as np




def 						UpperCamelCase	(			a		,						a		,						a = 1e-12		,						a = 100		,						)				->     tuple[float, np.ndarray]:






     '''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			)
     __magic_name__						       =    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.

     __magic_name__						       =    False
     __magic_name__						       =    0
     __magic_name__						       =    0
     __magic_name__						       =    1e12

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

          # Check convergence.
          __magic_name__						       =    np.abs(lambda_ - lambda_previous			) / lambda_
          iterations += 1

          if error <= error_tol or iterations >= max_iterations:
               __magic_name__						       =    True

          __magic_name__						       =    lambda_

     if is_complex:
          __magic_name__						       =    np.real(lambda_			)

     return lambda_, vector




def 						UpperCamelCase	(			)				->     None:






     '''simple docstring'''
     __magic_name__						       =    np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]			)
     __magic_name__						       =    np.array([41, 4, 20]			)
     __magic_name__						       =    real_input_matrix.astype(np.complexaaa			)
     __magic_name__						       =    np.triu(1j * complex_input_matrix		,						1			)
     complex_input_matrix += imag_matrix
     complex_input_matrix += -1 * imag_matrix.T
     __magic_name__						       =    np.array([41, 4, 20]			).astype(np.complexaaa			)

     for problem_type in ["real", "complex"]:
          if problem_type == "real":
               __magic_name__						       =    real_input_matrix
               __magic_name__						       =    real_vector
          elif problem_type == "complex":
               __magic_name__						       =    complex_input_matrix
               __magic_name__						       =    complex_vector

          # Our implementation.
          __magic_name__       ,  __magic_name__						       =    power_iteration(a		,						a			)

          # Numpy implementation.

          # Get eigenvalues and eigenvectors using built-in numpy
          # eigh (eigh used for symmetric or hermetian matrices).
          __magic_name__       ,  __magic_name__						       =    np.linalg.eigh(a			)
          # Last eigenvalue is the maximum one.
          __magic_name__						       =    eigen_values[-1]
          # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
          __magic_name__						       =    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()









'''simple docstring'''




import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput






class   _SCREAMING_SNAKE_CASE   (   __a		,__a     ):
 __SCREAMING_SNAKE_CASE					:Optional[Any]      	=					1



 @register_to_config
 def __init__(   self		:   Optional[int]			,				a__		:   int = 1000			,				a__		:   Optional[Union[np.ndarray, List[float]]] = None      ):
      # set `betas`, `alphas`, `timesteps`
      self.set_timesteps(a__      )

      # standard deviation of the initial noise distribution
      __magic_name__						       =    1.0

      # For now we only support F-PNDM, i.e. the runge-kutta method
      # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
      # mainly at formula (9), (12), (13) and the Algorithm 2.
      __magic_name__						       =    4

      # running values
      __magic_name__						       =    []



 def 			snake_case__  (   self		:   Dict			,				a__		:   int			,				a__		:   Union[str, torch.device] = None      ):
      __magic_name__						       =    num_inference_steps
      __magic_name__						       =    torch.linspace(1			,				0			,				num_inference_steps + 1      )[:-1]
      __magic_name__						       =    torch.cat([steps, torch.tensor([0.0]      )]      )

      if self.config.trained_betas is not None:
           __magic_name__						       =    torch.tensor(self.config.trained_betas			,				dtype=torch.floataa      )
      else:
           __magic_name__						       =    torch.sin(steps * math.pi / 2      ) ** 2

      __magic_name__						       =    (1.0 - self.betas**2) ** 0.5

      __magic_name__						       =    (torch.atana(self.betas			,				self.alphas      ) / math.pi * 2)[:-1]
      __magic_name__						       =    timesteps.to(a__      )

      __magic_name__						       =    []



 def 			snake_case__  (   self		:   Union[str, Any]			,				a__		:   torch.FloatTensor			,				a__		:   int			,				a__		:   torch.FloatTensor			,				a__		:   bool = True			,				):
      if self.num_inference_steps is None:
           raise ValueError(
               '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''      )

      __magic_name__						       =    (self.timesteps == timestep).nonzero().item()
      __magic_name__						       =    timestep_index + 1

      __magic_name__						       =    sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
      self.ets.append(a__      )

      if len(self.ets      ) == 1:
           __magic_name__						       =    self.ets[-1]
      elif len(self.ets      ) == 2:
           __magic_name__						       =    (3 * self.ets[-1] - self.ets[-2]) / 2
      elif len(self.ets      ) == 3:
           __magic_name__						       =    (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
      else:
           __magic_name__						       =    (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

      __magic_name__						       =    self._get_prev_sample(a__			,				a__			,				a__			,				a__      )

      if not return_dict:
           return (prev_sample,)

      return SchedulerOutput(prev_sample=a__      )



 def 			snake_case__  (   self		:   Any			,				a__		:   torch.FloatTensor			,				*a__		:   Optional[int]			,				**a__		:   Union[str, Any]      ):
      return sample



 def 			snake_case__  (   self		:   str			,				a__		:   Optional[int]			,				a__		:   int			,				a__		:   List[Any]			,				a__		:   List[str]      ):
      __magic_name__						       =    self.alphas[timestep_index]
      __magic_name__						       =    self.betas[timestep_index]

      __magic_name__						       =    self.alphas[prev_timestep_index]
      __magic_name__						       =    self.betas[prev_timestep_index]

      __magic_name__						       =    (sample - sigma * ets) / max(a__			,				1E-8      )
      __magic_name__						       =    next_alpha * pred + ets * next_sigma

      return prev_sample



 def __len__(   self		:   int      ):
      return self.config.num_train_timesteps






