
"""simple docstring"""

import unittest

import numpy as np

from transformers.testing_utils import require_flax, require_tf, require_torch
from transformers.utils import (
    expand_dims,
    flatten_dict,
    is_flax_available,
    is_tf_available,
    is_torch_available,
    reshape,
    squeeze,
    transpose,
)


if is_flax_available():
     import jax.numpy as jnp

if is_tf_available():
     import tensorflow as tf

if is_torch_available():
     import torch






class 	_lowercase       (    unittest.TestCase		):




 def       _UpperCamelCase   (			self )		->							str:
   lowerCamelCase					:      Any          =   {
       '''task_specific_params''': {
           '''summarization''': {'''length_penalty''': 1.0, '''max_length''': 128, '''min_length''': 12, '''num_beams''': 4},
           '''summarization_cnn''': {'''length_penalty''': 2.0, '''max_length''': 142, '''min_length''': 56, '''num_beams''': 4},
           '''summarization_xsum''': {'''length_penalty''': 1.0, '''max_length''': 62, '''min_length''': 11, '''num_beams''': 6},
       }
   }
   lowerCamelCase					:      Tuple          =   {
       '''task_specific_params.summarization.length_penalty''': 1.0,
       '''task_specific_params.summarization.max_length''': 128,
       '''task_specific_params.summarization.min_length''': 12,
       '''task_specific_params.summarization.num_beams''': 4,
       '''task_specific_params.summarization_cnn.length_penalty''': 2.0,
       '''task_specific_params.summarization_cnn.max_length''': 142,
       '''task_specific_params.summarization_cnn.min_length''': 56,
       '''task_specific_params.summarization_cnn.num_beams''': 4,
       '''task_specific_params.summarization_xsum.length_penalty''': 1.0,
       '''task_specific_params.summarization_xsum.max_length''': 62,
       '''task_specific_params.summarization_xsum.min_length''': 11,
       '''task_specific_params.summarization_xsum.num_beams''': 6,
   }

   self.assertEqual(flatten_dict(snake_case_ )		,			snake_case_ )




 def       _UpperCamelCase   (			self )		->							List[str]:
   lowerCamelCase					:      List[Any]          =   np.random.randn(3		,			4 )
   self.assertTrue(np.allclose(transpose(snake_case_ )		,			x.transpose() ) )

   lowerCamelCase					:      Union[str, Any]          =   np.random.randn(3		,			4		,			5 )
   self.assertTrue(np.allclose(transpose(snake_case_		,			axes=(1, 2, 0) )		,			x.transpose((1, 2, 0) ) ) )




 @require_torch
 def       _UpperCamelCase   (			self )		->							Any:
   lowerCamelCase					:      List[Any]          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      str          =   torch.tensor(snake_case_ )
   self.assertTrue(np.allclose(transpose(snake_case_ )		,			transpose(snake_case_ ).numpy() ) )

   lowerCamelCase					:      Optional[Any]          =   np.random.randn(3		,			4		,			5 )
   lowerCamelCase					:      Any          =   torch.tensor(snake_case_ )
   self.assertTrue(np.allclose(transpose(snake_case_		,			axes=(1, 2, 0) )		,			transpose(snake_case_		,			axes=(1, 2, 0) ).numpy() ) )




 @require_tf
 def       _UpperCamelCase   (			self )		->							Any:
   lowerCamelCase					:      Any          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      int          =   tf.constant(snake_case_ )
   self.assertTrue(np.allclose(transpose(snake_case_ )		,			transpose(snake_case_ ).numpy() ) )

   lowerCamelCase					:      Optional[Any]          =   np.random.randn(3		,			4		,			5 )
   lowerCamelCase					:      Dict          =   tf.constant(snake_case_ )
   self.assertTrue(np.allclose(transpose(snake_case_		,			axes=(1, 2, 0) )		,			transpose(snake_case_		,			axes=(1, 2, 0) ).numpy() ) )




 @require_flax
 def       _UpperCamelCase   (			self )		->							Tuple:
   lowerCamelCase					:      Optional[Any]          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      List[str]          =   jnp.array(snake_case_ )
   self.assertTrue(np.allclose(transpose(snake_case_ )		,			np.asarray(transpose(snake_case_ ) ) ) )

   lowerCamelCase					:      int          =   np.random.randn(3		,			4		,			5 )
   lowerCamelCase					:      Optional[int]          =   jnp.array(snake_case_ )
   self.assertTrue(np.allclose(transpose(snake_case_		,			axes=(1, 2, 0) )		,			np.asarray(transpose(snake_case_		,			axes=(1, 2, 0) ) ) ) )




 def       _UpperCamelCase   (			self )		->							Optional[Any]:
   lowerCamelCase					:      Optional[Any]          =   np.random.randn(3		,			4 )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(4, 3) )		,			np.reshape(snake_case_		,			(4, 3) ) ) )

   lowerCamelCase					:      Any          =   np.random.randn(3		,			4		,			5 )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(12, 5) )		,			np.reshape(snake_case_		,			(12, 5) ) ) )




 @require_torch
 def       _UpperCamelCase   (			self )		->							List[Any]:
   lowerCamelCase					:      Union[str, Any]          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      str          =   torch.tensor(snake_case_ )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(4, 3) )		,			reshape(snake_case_		,			(4, 3) ).numpy() ) )

   lowerCamelCase					:      List[Any]          =   np.random.randn(3		,			4		,			5 )
   lowerCamelCase					:      int          =   torch.tensor(snake_case_ )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(12, 5) )		,			reshape(snake_case_		,			(12, 5) ).numpy() ) )




 @require_tf
 def       _UpperCamelCase   (			self )		->							Union[str, Any]:
   lowerCamelCase					:      Union[str, Any]          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      Dict          =   tf.constant(snake_case_ )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(4, 3) )		,			reshape(snake_case_		,			(4, 3) ).numpy() ) )

   lowerCamelCase					:      Tuple          =   np.random.randn(3		,			4		,			5 )
   lowerCamelCase					:      Optional[Any]          =   tf.constant(snake_case_ )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(12, 5) )		,			reshape(snake_case_		,			(12, 5) ).numpy() ) )




 @require_flax
 def       _UpperCamelCase   (			self )		->							Union[str, Any]:
   lowerCamelCase					:      Optional[Any]          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      List[Any]          =   jnp.array(snake_case_ )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(4, 3) )		,			np.asarray(reshape(snake_case_		,			(4, 3) ) ) ) )

   lowerCamelCase					:      Any          =   np.random.randn(3		,			4		,			5 )
   lowerCamelCase					:      Optional[Any]          =   jnp.array(snake_case_ )
   self.assertTrue(np.allclose(reshape(snake_case_		,			(12, 5) )		,			np.asarray(reshape(snake_case_		,			(12, 5) ) ) ) )




 def       _UpperCamelCase   (			self )		->							List[Any]:
   lowerCamelCase					:      str          =   np.random.randn(1		,			3		,			4 )
   self.assertTrue(np.allclose(squeeze(snake_case_ )		,			np.squeeze(snake_case_ ) ) )

   lowerCamelCase					:      Dict          =   np.random.randn(1		,			4		,			1		,			5 )
   self.assertTrue(np.allclose(squeeze(snake_case_		,			axis=2 )		,			np.squeeze(snake_case_		,			axis=2 ) ) )




 @require_torch
 def       _UpperCamelCase   (			self )		->							str:
   lowerCamelCase					:      Optional[int]          =   np.random.randn(1		,			3		,			4 )
   lowerCamelCase					:      List[Any]          =   torch.tensor(snake_case_ )
   self.assertTrue(np.allclose(squeeze(snake_case_ )		,			squeeze(snake_case_ ).numpy() ) )

   lowerCamelCase					:      Tuple          =   np.random.randn(1		,			4		,			1		,			5 )
   lowerCamelCase					:      Optional[int]          =   torch.tensor(snake_case_ )
   self.assertTrue(np.allclose(squeeze(snake_case_		,			axis=2 )		,			squeeze(snake_case_		,			axis=2 ).numpy() ) )




 @require_tf
 def       _UpperCamelCase   (			self )		->							Optional[int]:
   lowerCamelCase					:      str          =   np.random.randn(1		,			3		,			4 )
   lowerCamelCase					:      int          =   tf.constant(snake_case_ )
   self.assertTrue(np.allclose(squeeze(snake_case_ )		,			squeeze(snake_case_ ).numpy() ) )

   lowerCamelCase					:      Optional[Any]          =   np.random.randn(1		,			4		,			1		,			5 )
   lowerCamelCase					:      Any          =   tf.constant(snake_case_ )
   self.assertTrue(np.allclose(squeeze(snake_case_		,			axis=2 )		,			squeeze(snake_case_		,			axis=2 ).numpy() ) )




 @require_flax
 def       _UpperCamelCase   (			self )		->							Optional[int]:
   lowerCamelCase					:      Tuple          =   np.random.randn(1		,			3		,			4 )
   lowerCamelCase					:      str          =   jnp.array(snake_case_ )
   self.assertTrue(np.allclose(squeeze(snake_case_ )		,			np.asarray(squeeze(snake_case_ ) ) ) )

   lowerCamelCase					:      Union[str, Any]          =   np.random.randn(1		,			4		,			1		,			5 )
   lowerCamelCase					:      Dict          =   jnp.array(snake_case_ )
   self.assertTrue(np.allclose(squeeze(snake_case_		,			axis=2 )		,			np.asarray(squeeze(snake_case_		,			axis=2 ) ) ) )




 def       _UpperCamelCase   (			self )		->							Union[str, Any]:
   lowerCamelCase					:      Any          =   np.random.randn(3		,			4 )
   self.assertTrue(np.allclose(expand_dims(snake_case_		,			axis=1 )		,			np.expand_dims(snake_case_		,			axis=1 ) ) )




 @require_torch
 def       _UpperCamelCase   (			self )		->							Optional[int]:
   lowerCamelCase					:      Dict          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      Any          =   torch.tensor(snake_case_ )
   self.assertTrue(np.allclose(expand_dims(snake_case_		,			axis=1 )		,			expand_dims(snake_case_		,			axis=1 ).numpy() ) )




 @require_tf
 def       _UpperCamelCase   (			self )		->							int:
   lowerCamelCase					:      Union[str, Any]          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      Optional[Any]          =   tf.constant(snake_case_ )
   self.assertTrue(np.allclose(expand_dims(snake_case_		,			axis=1 )		,			expand_dims(snake_case_		,			axis=1 ).numpy() ) )




 @require_flax
 def       _UpperCamelCase   (			self )		->							Union[str, Any]:
   lowerCamelCase					:      Dict          =   np.random.randn(3		,			4 )
   lowerCamelCase					:      str          =   jnp.array(snake_case_ )
   self.assertTrue(np.allclose(expand_dims(snake_case_		,			axis=1 )		,			np.asarray(expand_dims(snake_case_		,			axis=1 ) ) ) )








"""simple docstring"""

import numpy as np
def 		UpperCAmelCase (		a_,						a_,						a_ = 1E-12,						a_ = 100,						):





		'''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_      )
		lowerCamelCase					:      Optional[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.

		lowerCamelCase					:      Union[str, Any]          =   False
		lowerCamelCase					:      List[str]          =   0
		lowerCamelCase					:      Any          =   0
		lowerCamelCase					:      Dict          =   1E12

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

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

				if error <= error_tol or iterations >= max_iterations:
						lowerCamelCase					:      int          =   True

				lowerCamelCase					:      Optional[Any]          =   lambda_

		if is_complex:
				lowerCamelCase					:      Any          =   np.real(lambda_      )

		return lambda_, vector
def 		UpperCAmelCase (		):





		'''simple docstring'''


		lowerCamelCase					:      str          =   np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]      )
		lowerCamelCase					:      str          =   np.array([41, 4, 20]      )
		lowerCamelCase					:      Optional[Any]          =   real_input_matrix.astype(np.complexaaa      )
		lowerCamelCase					:      Dict          =   np.triu(1j * complex_input_matrix,						1      )
		complex_input_matrix += imag_matrix
		complex_input_matrix += -1 * imag_matrix.T
		lowerCamelCase					:      List[Any]          =   np.array([41, 4, 20]      ).astype(np.complexaaa      )

		for problem_type in ["real", "complex"]:
				if problem_type == "real":
						lowerCamelCase					:      str          =   real_input_matrix
						lowerCamelCase					:      Any          =   real_vector
				elif problem_type == "complex":
						lowerCamelCase					:      str          =   complex_input_matrix
						lowerCamelCase					:      Dict          =   complex_vector

				# Our implementation.
				lowerCamelCase     ,   lowerCamelCase					:      List[str]          =   power_iteration(a_,						a_      )

				# Numpy implementation.

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






