




from typing import Any

import numpy as np






def    snake_case   (				A     )				->				bool:




	'''simple docstring'''


	assert np.shape(A     )[0] == np.shape(A     )[1]

	# If matrix not symmetric, exit right away.
	if np.allclose(A		,  matrix.T     ) is False:
		return False

	# Get eigenvalues and eignevectors for a symmetric matrix.
	lowerCamelCase_  ,     lowerCamelCase_				:						Tuple				  =				np.linalg.eigh(A     )

	# Check sign of all eigenvalues.
	# np.all returns a value of type np.bool_
	return bool(np.all(eigen_values > 0     )     )






def    snake_case   (				A     )				->				Any:




	'''simple docstring'''


	lowerCamelCase_				:						Optional[int]				  =				np.random.randn(A		,  A     )
	lowerCamelCase_				:						List[Any]				  =				np.dot(A		,  random_matrix.T     )
	assert _is_matrix_spd(A     )
	return spd_matrix






def    snake_case   (				A		,  A		,  A = 1000		,  A = 1e-8		,  )				->				Any:




	'''simple docstring'''


	assert np.shape(A     )[0] == np.shape(A     )[1]
	assert np.shape(A     )[0] == np.shape(A     )[0]
	assert _is_matrix_spd(A     )

	# Initialize solution guess, residual, search direction.
	lowerCamelCase_				:						List[str]				  =				np.zeros((np.shape(A     )[0], 1)     )
	lowerCamelCase_				:						int				  =				np.copy(A     )
	lowerCamelCase_				:						Optional[int]				  =				np.copy(A     )

	# Set initial errors in solution guess and residual.
	lowerCamelCase_				:						Dict				  =				1e9
	lowerCamelCase_				:						int				  =				1e9
	lowerCamelCase_				:						Dict				  =				1e9

	# Set iteration counter to threshold number of iterations.
	lowerCamelCase_				:						List[Any]				  =				0

	while error > tol:
		# Save this value so we only calculate the matrix-vector product once.
		lowerCamelCase_				:						List[Any]				  =				np.dot(A		,  A     )

		# The main algorithm.

		# Update search direction magnitude.
		lowerCamelCase_				:						Optional[Any]				  =				np.dot(ra.T		,  A     ) / np.dot(pa.T		,  A     )
		# Update solution guess.
		lowerCamelCase_				:						int				  =				xa + alpha * pa
		# Calculate new residual.
		lowerCamelCase_				:						int				  =				ra - alpha * w
		# Calculate new Krylov subspace scale.
		lowerCamelCase_				:						List[Any]				  =				np.dot(r.T		,  A     ) / np.dot(ra.T		,  A     )
		# Calculate new A conjuage search direction.
		lowerCamelCase_				:						int				  =				r + beta * pa

		# Calculate errors.
		lowerCamelCase_				:						Union[str, Any]				  =				np.linalg.norm(r - ra     )
		lowerCamelCase_				:						List[Any]				  =				np.linalg.norm(x - xa     )
		lowerCamelCase_				:						str				  =				np.maximum(A		,  A     )

		# Update variables.
		lowerCamelCase_				:						Union[str, Any]				  =				np.copy(A     )
		lowerCamelCase_				:						Any				  =				np.copy(A     )
		lowerCamelCase_				:						int				  =				np.copy(A     )

		# Update number of iterations.
		iterations += 1
		if iterations > max_iterations:
			break

	return x






def    snake_case   (				)				->				None:




	'''simple docstring'''


	lowerCamelCase_				:						int				  =				3
	lowerCamelCase_				:						List[str]				  =				_create_spd_matrix(A     )
	lowerCamelCase_				:						List[str]				  =				np.random.randn(A		,  1     )
	lowerCamelCase_				:						str				  =				np.dot(A		,  A     )

	# Numpy solution.
	lowerCamelCase_				:						Dict				  =				np.linalg.solve(A		,  A     )

	# Our implementation.
	lowerCamelCase_				:						Tuple				  =				conjugate_gradient(A		,  A     )

	# Ensure both solutions are close to x_true (and therefore one another).
	assert np.linalg.norm(x_numpy - x_true     ) <= 1e-6
	assert np.linalg.norm(x_conjugate_gradient - x_true     ) <= 1e-6


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							test_conjugate_gradient()








"""simple docstring"""
import unittest

from cer import CER


A_     :					Union[str, Any]							=     CER()



class 						a_ (      unittest.TestCase					):







      '''simple docstring'''

      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     Optional[Any]								=		['White House']
       lowerCamelCase__	:     List[str]								=		['white house']
       # S = 2, D = 0, I = 0, N = 11, CER = 2 / 11
       lowerCamelCase__	:     Dict								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.1_818_181_818   ) < 1e-6   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     Union[str, Any]								=		['were wolf']
       lowerCamelCase__	:     Union[str, Any]								=		['werewolf']
       # S = 0, D = 0, I = 1, N = 9, CER = 1 / 9
       lowerCamelCase__	:     Dict								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.1_111_111   ) < 1e-6   )

       lowerCamelCase__	:     List[Any]								=		['werewolf']
       lowerCamelCase__	:     Optional[Any]								=		['weae     wolf']
       # S = 1, D = 1, I = 0, N = 8, CER = 0.25
       lowerCamelCase__	:     List[str]								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.25   ) < 1e-6   )

       # consecutive whitespaces case 1
       lowerCamelCase__	:     Optional[Any]								=		['were wolf']
       lowerCamelCase__	:     Tuple								=		['were               wolf']
       # S = 0, D = 0, I = 0, N = 9, CER = 0
       lowerCamelCase__	:     Tuple								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.0   ) < 1e-6   )

       # consecutive whitespaces case 2
       lowerCamelCase__	:     Any								=		['were   wolf']
       lowerCamelCase__	:     int								=		['were               wolf']
       # S = 0, D = 0, I = 0, N = 9, CER = 0
       lowerCamelCase__	:     Optional[int]								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.0   ) < 1e-6   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     Optional[Any]								=		['werewolf']
       lowerCamelCase__	:     Optional[int]								=		['weaewolf']
       # S = 1, D = 0, I = 0, N = 8, CER = 0.125
       lowerCamelCase__	:     Union[str, Any]								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.125   ) < 1e-6   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     int								=		['werewolf']
       lowerCamelCase__	:     Union[str, Any]								=		['wereawolf']
       # S = 0, D = 1, I = 0, N = 8, CER = 0.125
       lowerCamelCase__	:     Any								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.125   ) < 1e-6   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     List[Any]								=		['werewolf']
       lowerCamelCase__	:     Dict								=		['wereolf']
       # S = 0, D = 0, I = 1, N = 8, CER = 0.125
       lowerCamelCase__	:     int								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.125   ) < 1e-6   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     Optional[int]								=		['werewolf']
       lowerCamelCase__	:     Tuple								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertEqual(lowerCamelCase_,	0.0   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     List[str]								=		['werewolf', 'I am your father']
       lowerCamelCase__	:     List[Any]								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertEqual(lowerCamelCase_,	0.0   )

       lowerCamelCase__	:     Dict								=		['werewolf', 'I am your father', 'doge']
       lowerCamelCase__	:     int								=		['werxwolf', 'I       am your father', 'doge']
       # S = 1, D = 0, I = 0, N = 28, CER = 1 / 28
       lowerCamelCase__	:     Optional[int]								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.03_571_428   ) < 1e-6   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     Union[str, Any]								=		['My hovercraft', 'is full of eels']
       lowerCamelCase__	:     List[Any]								=		['My hovercraft is full', ' of eels']
       # S = 0, D = 0, I = 2, N = 28, CER = 2 / 28
       # whitespace at the front of " of eels" will be strip during preporcessing
       # so need to insert 2 whitespaces
       lowerCamelCase__	:     Dict								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_,	concatenate_texts=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.071_428   ) < 1e-6   )




      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     Optional[Any]								=		['我能吞下玻璃而不伤身体']
       lowerCamelCase__	:     Any								=		[' 能吞虾玻璃而 不霜身体啦']
       # S = 3, D = 2, I = 0, N = 11, CER = 5 / 11
       lowerCamelCase__	:     List[str]								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.4_545_454_545   ) < 1e-6   )

       lowerCamelCase__	:     Optional[Any]								=		['我能吞下玻璃', '而不伤身体']
       lowerCamelCase__	:     Optional[Any]								=		['我    能 吞 下 玻 璃', '而不伤身体']
       # S = 0, D = 5, I = 0, N = 11, CER = 5 / 11
       lowerCamelCase__	:     Dict								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertTrue(abs(char_error_rate - 0.454_545_454_545   ) < 1e-6   )

       lowerCamelCase__	:     Optional[int]								=		['我能吞下玻璃而不伤身体']
       lowerCamelCase__	:     Union[str, Any]								=		cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )
       self.assertFalse(lowerCamelCase_,	0.0   )





      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     Optional[int]								=		['']
       lowerCamelCase__	:     Optional[int]								=		['Hypothesis']
       with self.assertRaises(lowerCamelCase_   ):
        cer.compute(predictions=lowerCamelCase_,	references=lowerCamelCase_   )


if __name__ == "__main__":
      unittest.main()

