

"""simple docstring"""


import numpy as np




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase = 1E-12  ,					__lowerCAmelCase = 100  ,					)       ->				tuple[float, np.ndarray]:
      assert np.shape(__lowerCAmelCase							)[0] == np.shape(__lowerCAmelCase							)[1]
      # Ensure proper dimensionality.
      assert np.shape(__lowerCAmelCase							)[0] == np.shape(__lowerCAmelCase							)[0]
      # Ensure inputs are either both complex or both real
      assert np.iscomplexobj(__lowerCAmelCase							) == np.iscomplexobj(__lowerCAmelCase							)
      SCREAMING_SNAKE_CASE__   :      int      		=	np.iscomplexobj(__lowerCAmelCase							)
      if is_complex:
            # Ensure complex input_matrix is Hermitian
            assert np.array_equal(__lowerCAmelCase  ,					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__   :      Any      		=	False
      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	0
      SCREAMING_SNAKE_CASE__   :      List[str]      		=	0
      SCREAMING_SNAKE_CASE__   :      int      		=	1E12

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

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

            if error <= error_tol or iterations >= max_iterations:
                  SCREAMING_SNAKE_CASE__   :      Tuple      		=	True

            SCREAMING_SNAKE_CASE__   :      List[str]      		=	lambda_

      if is_complex:
            SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	np.real(lambda_							)

      return lambda_, vector




def  _lowercase					(    )       ->				None:
      SCREAMING_SNAKE_CASE__   :      Tuple      		=	np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]							)
      SCREAMING_SNAKE_CASE__   :      Any      		=	np.array([41, 4, 20]							)
      SCREAMING_SNAKE_CASE__   :      Dict      		=	real_input_matrix.astype(np.complexaaa							)
      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	np.triu(1j * complex_input_matrix  ,					1							)
      complex_input_matrix += imag_matrix
      complex_input_matrix += -1 * imag_matrix.T
      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	np.array([41, 4, 20]							).astype(np.complexaaa							)

      for problem_type in ["real", "complex"]:
            if problem_type == "real":
                  SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	real_input_matrix
                  SCREAMING_SNAKE_CASE__   :      List[str]      		=	real_vector
            elif problem_type == "complex":
                  SCREAMING_SNAKE_CASE__   :      int      		=	complex_input_matrix
                  SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	complex_vector

            # Our implementation.
            SCREAMING_SNAKE_CASE__   :      Dict      		=	power_iteration(__lowerCAmelCase  ,					__lowerCAmelCase							)

            # Numpy implementation.

            # Get eigenvalues and eigenvectors using built-in numpy
            # eigh (eigh used for symmetric or hermetian matrices).
            SCREAMING_SNAKE_CASE__   :      List[Any]      		=	np.linalg.eigh(__lowerCAmelCase							)
            # Last eigenvalue is the maximum one.
            SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	eigen_values[-1]
            # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
            SCREAMING_SNAKE_CASE__   :      Dict      		=	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(__lowerCAmelCase							) - np.abs(__lowerCAmelCase							)							) <= 1E-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_power_iteration()







"""simple docstring"""


import torch

from diffusers import DDPMScheduler

from .test_schedulers import SchedulerCommonTest

class      __a							(UpperCamelCase_):






     '''simple docstring'''
     _SCREAMING_SNAKE_CASE						:Tuple       = (DDPMScheduler,)

     def 					_a			(						self	,    **_a  )  ->      List[str]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      int      		=	{
               """num_train_timesteps""": 1_000,
               """beta_start""": 0.0_001,
               """beta_end""": 0.02,
               """beta_schedule""": """linear""",
               """variance_type""": """fixed_small""",
               """clip_sample""": True,
           }

           config.update(**_a  )
           return config

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for timesteps in [1, 5, 100, 1_000]:
                 self.check_over_configs(num_train_timesteps=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for beta_start, beta_end in zip([0.0_001, 0.001, 0.01, 0.1]	,    [0.002, 0.02, 0.2, 2]  ):
                 self.check_over_configs(beta_start=_a	,    beta_end=_a  )

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


           """simple docstring"""


           for schedule in ["linear", "squaredcos_cap_v2"]:
                 self.check_over_configs(beta_schedule=_a  )

     def 					_a			(						self  )  ->      Any:


           """simple docstring"""


           for variance in ["fixed_small", "fixed_large", "other"]:
                 self.check_over_configs(variance_type=_a  )

     def 					_a			(						self  )  ->      Optional[int]:


           """simple docstring"""


           for clip_sample in [True, False]:
                 self.check_over_configs(clip_sample=_a  )

     def 					_a			(						self  )  ->      int:


           """simple docstring"""


           self.check_over_configs(thresholding=_a  )
           for threshold in [0.5, 1.0, 2.0]:
                 for prediction_type in ["epsilon", "sample", "v_prediction"]:
                       self.check_over_configs(
                           thresholding=_a	,    prediction_type=_a	,    sample_max_value=_a	,    )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for prediction_type in ["epsilon", "sample", "v_prediction"]:
                 self.check_over_configs(prediction_type=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for t in [0, 500, 999]:
                 self.check_over_forward(time_step=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      int      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Dict      		=	scheduler_class(**_a  )

           assert torch.sum(torch.abs(scheduler._get_variance(0  ) - 0.0  )  ) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(487  ) - 0.00_979  )  ) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(999  ) - 0.02  )  ) < 1E-5

     def 					_a			(						self  )  ->      List[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      int      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Any      		=	len(_a  )

           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.dummy_model()
           SCREAMING_SNAKE_CASE__   :      str      		=	self.dummy_sample_deter
           SCREAMING_SNAKE_CASE__   :      str      		=	torch.manual_seed(0  )

           for t in reversed(range(_a  )  ):
                 # 1. predict noise residual
                 SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	model(_a	,    _a  )

                 # 2. predict previous mean of sample x_t-1
                 SCREAMING_SNAKE_CASE__   :      int      		=	scheduler.step(_a	,    _a	,    _a	,    generator=_a  ).prev_sample

                 # if t > 0:
                 #     noise = self.dummy_sample_deter
                 #     variance = scheduler.get_variance(t) ** (0.5) * noise
                 #
                 # sample = pred_prev_sample + variance
                 SCREAMING_SNAKE_CASE__   :      str      		=	pred_prev_sample

           SCREAMING_SNAKE_CASE__   :      str      		=	torch.sum(torch.abs(_a  )  )
           SCREAMING_SNAKE_CASE__   :      Any      		=	torch.mean(torch.abs(_a  )  )

           assert abs(result_sum.item() - 258.9_606  ) < 1E-2
           assert abs(result_mean.item() - 0.3_372  ) < 1E-3

     def 					_a			(						self  )  ->      Optional[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.get_scheduler_config(prediction_type="""v_prediction"""  )
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Dict      		=	len(_a  )

           SCREAMING_SNAKE_CASE__   :      List[str]      		=	self.dummy_model()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	self.dummy_sample_deter
           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	torch.manual_seed(0  )

           for t in reversed(range(_a  )  ):
                 # 1. predict noise residual
                 SCREAMING_SNAKE_CASE__   :      int      		=	model(_a	,    _a  )

                 # 2. predict previous mean of sample x_t-1
                 SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler.step(_a	,    _a	,    _a	,    generator=_a  ).prev_sample

                 # if t > 0:
                 #     noise = self.dummy_sample_deter
                 #     variance = scheduler.get_variance(t) ** (0.5) * noise
                 #
                 # sample = pred_prev_sample + variance
                 SCREAMING_SNAKE_CASE__   :      Tuple      		=	pred_prev_sample

           SCREAMING_SNAKE_CASE__   :      Any      		=	torch.sum(torch.abs(_a  )  )
           SCREAMING_SNAKE_CASE__   :      int      		=	torch.mean(torch.abs(_a  )  )

           assert abs(result_sum.item() - 202.0_296  ) < 1E-2
           assert abs(result_mean.item() - 0.2_631  ) < 1E-3

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


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Dict      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	[100, 87, 50, 1, 0]

           scheduler.set_timesteps(timesteps=_a  )

           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	scheduler.timesteps

           for i, timestep in enumerate(_a  ):
                 if i == len(_a  ) - 1:
                       SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	-1
                 else:
                       SCREAMING_SNAKE_CASE__   :      Tuple      		=	timesteps[i + 1]

                 SCREAMING_SNAKE_CASE__   :      int      		=	scheduler.previous_timestep(_a  )
                 SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	prev_t.item()

                 self.assertEqual(_a	,    _a  )

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


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      int      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[100, 87, 50, 51, 0]

           with self.assertRaises(_a	,    msg="""`custom_timesteps` must be in descending order."""  ):
                 scheduler.set_timesteps(timesteps=_a  )

     def 					_a			(						self  )  ->      List[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      int      		=	[100, 87, 50, 1, 0]
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	len(_a  )

           with self.assertRaises(_a	,    msg="""Can only pass one of `num_inference_steps` or `custom_timesteps`."""  ):
                 scheduler.set_timesteps(num_inference_steps=_a	,    timesteps=_a  )





     def 					_a			(						self  )  ->      Tuple:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[scheduler.config.num_train_timesteps]

           with self.assertRaises(
               _a	,    msg="""`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}"""	,    ):
                 scheduler.set_timesteps(timesteps=_a  )




