

'''simple docstring'''



import torch

from diffusers import DPMSolverSDEScheduler
from diffusers.utils import torch_device
from diffusers.utils.testing_utils import require_torchsde

from .test_schedulers import SchedulerCommonTest







@require_torchsde
class 						lowerCAmelCase__   (      a					):



 """simple docstring"""



 lowerCAmelCase__  					=      (DPMSolverSDEScheduler,)
 lowerCAmelCase__  					=      10
 def       UpperCAmelCase__		(		self					:       str					,							**__SCREAMING_SNAKE_CASE					:       Union[str, Any]			)  -> List[Any]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE     =      {
          """num_train_timesteps""": 1_100,
          """beta_start""": 0.0001,
          """beta_end""": 0.02,
          """beta_schedule""": """linear""",
          """noise_sampler_seed""": 0,
      }

      config.update(**__SCREAMING_SNAKE_CASE			)
      return config
 def       UpperCAmelCase__		(		self					:       str			)  -> str:


      """simple docstring"""




      for timesteps in [10, 50, 100, 1_000]:
           self.check_over_configs(num_train_timesteps=__SCREAMING_SNAKE_CASE			)
 def       UpperCAmelCase__		(		self					:       List[Any]			)  -> List[Any]:


      """simple docstring"""




      for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]					,							[0.0002, 0.002, 0.02]			):
           self.check_over_configs(beta_start=__SCREAMING_SNAKE_CASE					,							beta_end=__SCREAMING_SNAKE_CASE			)
 def       UpperCAmelCase__		(		self					:       Optional[Any]			)  -> Optional[int]:


      """simple docstring"""




      for schedule in ["linear", "scaled_linear"]:
           self.check_over_configs(beta_schedule=__SCREAMING_SNAKE_CASE			)
 def       UpperCAmelCase__		(		self					:       Dict			)  -> List[str]:


      """simple docstring"""




      for prediction_type in ["epsilon", "v_prediction"]:
           self.check_over_configs(prediction_type=__SCREAMING_SNAKE_CASE			)
 def       UpperCAmelCase__		(		self					:       Optional[int]			)  -> Dict:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE     =      self.scheduler_classes[0]
      __SCREAMING_SNAKE_CASE     =      self.get_scheduler_config()
      __SCREAMING_SNAKE_CASE     =      scheduler_class(**__SCREAMING_SNAKE_CASE			)

      scheduler.set_timesteps(self.num_inference_steps			)

      __SCREAMING_SNAKE_CASE     =      self.dummy_model()
      __SCREAMING_SNAKE_CASE     =      self.dummy_sample_deter * scheduler.init_noise_sigma
      __SCREAMING_SNAKE_CASE     =      sample.to(__SCREAMING_SNAKE_CASE			)

      for i, t in enumerate(scheduler.timesteps			):
           __SCREAMING_SNAKE_CASE     =      scheduler.scale_model_input(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      model(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      scheduler.step(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)
           __SCREAMING_SNAKE_CASE     =      output.prev_sample

      __SCREAMING_SNAKE_CASE     =      torch.sum(torch.abs(__SCREAMING_SNAKE_CASE			)			)
      __SCREAMING_SNAKE_CASE     =      torch.mean(torch.abs(__SCREAMING_SNAKE_CASE			)			)

      if torch_device in ["mps"]:
           assert abs(result_sum.item() - 167.47821044921875			) < 1E-2
           assert abs(result_mean.item() - 0.2178705964565277			) < 1E-3
      elif torch_device in ["cuda"]:
           assert abs(result_sum.item() - 171.59352111816406			) < 1E-2
           assert abs(result_mean.item() - 0.22342906892299652			) < 1E-3
      else:
           assert abs(result_sum.item() - 162.52383422851562			) < 1E-2
           assert abs(result_mean.item() - 0.211619570851326			) < 1E-3
 def       UpperCAmelCase__		(		self					:       List[str]			)  -> Tuple:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE     =      self.scheduler_classes[0]
      __SCREAMING_SNAKE_CASE     =      self.get_scheduler_config(prediction_type="""v_prediction"""			)
      __SCREAMING_SNAKE_CASE     =      scheduler_class(**__SCREAMING_SNAKE_CASE			)

      scheduler.set_timesteps(self.num_inference_steps			)

      __SCREAMING_SNAKE_CASE     =      self.dummy_model()
      __SCREAMING_SNAKE_CASE     =      self.dummy_sample_deter * scheduler.init_noise_sigma
      __SCREAMING_SNAKE_CASE     =      sample.to(__SCREAMING_SNAKE_CASE			)

      for i, t in enumerate(scheduler.timesteps			):
           __SCREAMING_SNAKE_CASE     =      scheduler.scale_model_input(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      model(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      scheduler.step(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)
           __SCREAMING_SNAKE_CASE     =      output.prev_sample

      __SCREAMING_SNAKE_CASE     =      torch.sum(torch.abs(__SCREAMING_SNAKE_CASE			)			)
      __SCREAMING_SNAKE_CASE     =      torch.mean(torch.abs(__SCREAMING_SNAKE_CASE			)			)

      if torch_device in ["mps"]:
           assert abs(result_sum.item() - 124.77149200439453			) < 1E-2
           assert abs(result_mean.item() - 0.16226289014816284			) < 1E-3
      elif torch_device in ["cuda"]:
           assert abs(result_sum.item() - 128.1663360595703			) < 1E-2
           assert abs(result_mean.item() - 0.16688326001167297			) < 1E-3
      else:
           assert abs(result_sum.item() - 119.8487548828125			) < 1E-2
           assert abs(result_mean.item() - 0.1560530662536621			) < 1E-3
 def       UpperCAmelCase__		(		self					:       Dict			)  -> Union[str, Any]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE     =      self.scheduler_classes[0]
      __SCREAMING_SNAKE_CASE     =      self.get_scheduler_config()
      __SCREAMING_SNAKE_CASE     =      scheduler_class(**__SCREAMING_SNAKE_CASE			)

      scheduler.set_timesteps(self.num_inference_steps					,							device=__SCREAMING_SNAKE_CASE			)

      __SCREAMING_SNAKE_CASE     =      self.dummy_model()
      __SCREAMING_SNAKE_CASE     =      self.dummy_sample_deter.to(__SCREAMING_SNAKE_CASE			) * scheduler.init_noise_sigma

      for t in scheduler.timesteps:
           __SCREAMING_SNAKE_CASE     =      scheduler.scale_model_input(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      model(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      scheduler.step(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)
           __SCREAMING_SNAKE_CASE     =      output.prev_sample

      __SCREAMING_SNAKE_CASE     =      torch.sum(torch.abs(__SCREAMING_SNAKE_CASE			)			)
      __SCREAMING_SNAKE_CASE     =      torch.mean(torch.abs(__SCREAMING_SNAKE_CASE			)			)

      if torch_device in ["mps"]:
           assert abs(result_sum.item() - 167.46957397460938			) < 1E-2
           assert abs(result_mean.item() - 0.21805934607982635			) < 1E-3
      elif torch_device in ["cuda"]:
           assert abs(result_sum.item() - 171.59353637695312			) < 1E-2
           assert abs(result_mean.item() - 0.22342908382415771			) < 1E-3
      else:
           assert abs(result_sum.item() - 162.52383422851562			) < 1E-2
           assert abs(result_mean.item() - 0.211619570851326			) < 1E-3


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


      """simple docstring"""




      __SCREAMING_SNAKE_CASE     =      self.scheduler_classes[0]
      __SCREAMING_SNAKE_CASE     =      self.get_scheduler_config()
      __SCREAMING_SNAKE_CASE     =      scheduler_class(**__SCREAMING_SNAKE_CASE					,							use_karras_sigmas=__SCREAMING_SNAKE_CASE			)

      scheduler.set_timesteps(self.num_inference_steps					,							device=__SCREAMING_SNAKE_CASE			)

      __SCREAMING_SNAKE_CASE     =      self.dummy_model()
      __SCREAMING_SNAKE_CASE     =      self.dummy_sample_deter.to(__SCREAMING_SNAKE_CASE			) * scheduler.init_noise_sigma
      __SCREAMING_SNAKE_CASE     =      sample.to(__SCREAMING_SNAKE_CASE			)

      for t in scheduler.timesteps:
           __SCREAMING_SNAKE_CASE     =      scheduler.scale_model_input(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      model(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)

           __SCREAMING_SNAKE_CASE     =      scheduler.step(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)
           __SCREAMING_SNAKE_CASE     =      output.prev_sample

      __SCREAMING_SNAKE_CASE     =      torch.sum(torch.abs(__SCREAMING_SNAKE_CASE			)			)
      __SCREAMING_SNAKE_CASE     =      torch.mean(torch.abs(__SCREAMING_SNAKE_CASE			)			)

      if torch_device in ["mps"]:
           assert abs(result_sum.item() - 176.66974135742188			) < 1E-2
           assert abs(result_mean.item() - 0.23003872730981811			) < 1E-2
      elif torch_device in ["cuda"]:
           assert abs(result_sum.item() - 177.63653564453125			) < 1E-2
           assert abs(result_mean.item() - 0.23003872730981811			) < 1E-2
      else:
           assert abs(result_sum.item() - 170.3135223388672			) < 1E-2
           assert abs(result_mean.item() - 0.23003872730981811			) < 1E-2









'''simple docstring'''



import numpy as np







def    a__       (  a__      ,    a__      ,    a__ = 1E-1_2      ,    a__ = 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__						)
     __SCREAMING_SNAKE_CASE     =      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.

     __SCREAMING_SNAKE_CASE     =      False
     __SCREAMING_SNAKE_CASE     =      0
     __SCREAMING_SNAKE_CASE     =      0
     __SCREAMING_SNAKE_CASE     =      1E1_2

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

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

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

          __SCREAMING_SNAKE_CASE     =      lambda_

     if is_complex:
          __SCREAMING_SNAKE_CASE     =      np.real(lambda_						)

     return lambda_, vector







def    a__       (  ):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]						)
     __SCREAMING_SNAKE_CASE     =      np.array([41, 4, 20]						)
     __SCREAMING_SNAKE_CASE     =      real_input_matrix.astype(np.complexaaa						)
     __SCREAMING_SNAKE_CASE     =      np.triu(1J * complex_input_matrix      ,    1						)
     complex_input_matrix += imag_matrix
     complex_input_matrix += -1 * imag_matrix.T
     __SCREAMING_SNAKE_CASE     =      np.array([41, 4, 20]						).astype(np.complexaaa						)

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

          # Our implementation.
          __SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE     =      power_iteration(a__      ,    a__						)

          # Numpy implementation.

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






