


import numpy as np



def        UpperCamelCase_(   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				)
    _lowercase :							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.

    _lowercase :							Any   	=	False
    _lowercase :							Optional[int]   	=	0
    _lowercase :							List[str]   	=	0
    _lowercase :							int   	=	1e12

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

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

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

        _lowercase :							List[str]   	=	lambda_

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

    return lambda_, vector



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

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

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

        # Numpy implementation.

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




import unittest

from transformers.testing_utils import require_bsa
from transformers.utils import is_bsa_available

from ...test_feature_extraction_common import FeatureExtractionSavingTestMixin


if is_bsa_available():
 from transformers import MarkupLMFeatureExtractor






class _lowerCamelCase(		unittest.TestCase     ):
       def __init__(      self,   lowerCamelCase) ->     List[str]:




           """simple docstring"""

           _lowercase :							Optional[int]   	=	parent




       def     UpperCamelCase  (      self) ->     str:




           """simple docstring"""

           return {}



def        UpperCamelCase_(   )					->		List[str]:
    _lowercase :							int   	=	'<HTML>\n\n    <HEAD>\n    <TITLE>sample document</TITLE>\n    </HEAD>\n\n    <BODY BGCOLOR="FFFFFF">\n    <HR>\n    <a href="http://google.com">Goog</a>\n    <H1>This is one header</H1>\n    <H2>This is a another Header</H2>\n    <P>Travel from\n        <P>\n        <B>SFO to JFK</B>\n        <BR>\n        <B><I>on May 2, 2015 at 2:00 pm. For details go to confirm.com </I></B>\n        <HR>\n        <div style="color:#0000FF">\n            <h3>Traveler <b> name </b> is\n            <p> John Doe </p>\n        </div>'

    _lowercase :							List[Any]   	=	'\n    <!DOCTYPE html>\n    <html>\n    <body>\n\n    <h1>My First Heading</h1>\n    <p>My first paragraph.</p>\n\n    </body>\n    </html>\n    '

    return [html_string_a, html_string_a]






@require_bsa
class _lowerCamelCase(		_a,				unittest.TestCase     ):
       lowercase_				:			Tuple									=    MarkupLMFeatureExtractor if is_bsa_available() else None
       def     UpperCamelCase  (      self) ->     Optional[int]:




           """simple docstring"""

           _lowercase :							Tuple   	=	MarkupLMFeatureExtractionTester(self)
       @property
       def     UpperCamelCase  (      self) ->     List[Any]:




           """simple docstring"""

           return self.feature_extract_tester.prepare_feat_extract_dict()




       def     UpperCamelCase  (      self) ->     List[str]:




           """simple docstring"""

           _lowercase :							int   	=	self.feature_extraction_class()

           # Test not batched input
           _lowercase :							List[Any]   	=	get_html_strings()[0]
           _lowercase :							Optional[Any]   	=	feature_extractor(lowerCamelCase)

           # fmt: off
           _lowercase :							str   	=	[['sample document', 'Goog', 'This is one header', 'This is a another Header', 'Travel from', 'SFO to JFK', 'on May 2, 2015 at 2:00 pm. For details go to confirm.com', 'Traveler', 'name', 'is', 'John Doe']]
           _lowercase :							Dict   	=	[['/html/head/title', '/html/body/a', '/html/body/h1', '/html/body/h2', '/html/body/p', '/html/body/p/p/b[1]', '/html/body/p/p/b[2]/i', '/html/body/p/p/div/h3', '/html/body/p/p/div/h3/b', '/html/body/p/p/div/h3', '/html/body/p/p/div/h3/p']]
           # fmt: on

           self.assertEqual(encoding.nodes,   lowerCamelCase)
           self.assertEqual(encoding.xpaths,   lowerCamelCase)

           # Test batched
           _lowercase :							Optional[int]   	=	get_html_strings()
           _lowercase :							Tuple   	=	feature_extractor(lowerCamelCase)

           # fmt: off
           _lowercase :							List[Any]   	=	expected_nodes + [['My First Heading', 'My first paragraph.']]
           _lowercase :							List[str]   	=	expected_xpaths + [['/html/body/h1', '/html/body/p']]

           self.assertEqual(len(encoding.nodes),   2)
           self.assertEqual(len(encoding.xpaths),   2)

           self.assertEqual(encoding.nodes,   lowerCamelCase)
           self.assertEqual(encoding.xpaths,   lowerCamelCase)


