import numpy as np



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE = 1e-12  ,			SCREAMING_SNAKE_CASE = 100  ,			):
    '''simple docstring'''







    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[1]
    # Ensure proper dimensionality.
    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[0]
    # Ensure inputs are either both complex or both real
    assert np.iscomplexobj(SCREAMING_SNAKE_CASE	) == np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    __UpperCamelCase     :List[Any]			  =		np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    if is_complex:
        # Ensure complex input_matrix is Hermitian
        assert np.array_equal(SCREAMING_SNAKE_CASE  ,			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.

    __UpperCamelCase     :str			  =		False
    __UpperCamelCase     :int			  =		0
    __UpperCamelCase     :Optional[Any]			  =		0
    __UpperCamelCase     :Union[str, Any]			  =		1e12

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

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

        if error <= error_tol or iterations >= max_iterations:
            __UpperCamelCase     :Dict			  =		True

        __UpperCamelCase     :List[Any]			  =		lambda_

    if is_complex:
        __UpperCamelCase     :Tuple			  =		np.real(lambda_	)

    return lambda_, vector



def lowerCamelCase  (   ):
    '''simple docstring'''







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

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

        # Our implementation.
        __UpperCamelCase  ,       __UpperCamelCase     :Dict			  =		power_iteration(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)

        # Numpy implementation.

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    test_power_iteration()









import math
import os
import sys

def       lowercase_		(		_A			:    str						):

      """simple docstring"""




      lowerCamelCase__		:				str    =  ""
      try:
            with open(_A    ,					"rb"						) as binary_file:
                  lowerCamelCase__		:				Union[str, Any]    =  binary_file.read()
            for dat in data:
                  lowerCamelCase__		:				Optional[Any]    =  F"{dat:08b}"
                  result += curr_byte
            return result
      except OSError:
            print("File not accessible"						)
            sys.exit()

def       lowercase_		(		_A			:    dict[str, str]    ,					_A			:    str    ,					_A			:    int    ,					_A			:    str						):

      """simple docstring"""




      lexicon.pop(_A						)
      lowerCamelCase__		:				List[Any]    =  last_match_id

      if math.loga(_A						).is_integer():
            for curr_key in lexicon:
                  lowerCamelCase__		:				Any    =  "0" + lexicon[curr_key]

      lowerCamelCase__		:				Tuple    =  bin(_A						)[2:]

def       lowercase_		(		_A			:    str						):

      """simple docstring"""




      lowerCamelCase__		:				Tuple    =  {"0": "0", "1": "1"}
      lowerCamelCase__    ,   lowerCamelCase__		:				int    =  "", ""
      lowerCamelCase__		:				int    =  len(_A						)

      for i in range(len(_A						)						):
            curr_string += data_bits[i]
            if curr_string not in lexicon:
                  continue

            lowerCamelCase__		:				Optional[Any]    =  lexicon[curr_string]
            result += last_match_id
            add_key_to_lexicon(_A    ,					_A    ,					_A    ,					_A						)
            index += 1
            lowerCamelCase__		:				Dict    =  ""

      while curr_string != "" and curr_string not in lexicon:
            curr_string += "0"

      if curr_string != "":
            lowerCamelCase__		:				int    =  lexicon[curr_string]
            result += last_match_id

      return result

def       lowercase_		(		_A			:    str    ,					_A			:    str						):

      """simple docstring"""




      lowerCamelCase__		:				List[str]    =  os.path.getsize(_A						)
      lowerCamelCase__		:				Dict    =  bin(_A						)[2:]
      lowerCamelCase__		:				List[Any]    =  len(_A						)

      return "0" * (length_length - 1) + file_length_binary + compressed

def       lowercase_		(		_A			:    str    ,					_A			:    str						):

      """simple docstring"""




      lowerCamelCase__		:				Dict    =  8
      try:
            with open(_A    ,					"wb"						) as opened_file:
                  lowerCamelCase__		:				Any    =  [
                      to_write[i : i + byte_length]
                      for i in range(0    ,					len(_A						)    ,					_A						)
                  ]

                  if len(result_byte_array[-1]						) % byte_length == 0:
                        result_byte_array.append("10000000"						)
                  else:
                        result_byte_array[-1] += "1" + "0" * (
                            byte_length - len(result_byte_array[-1]						) - 1
                        )

                  for elem in result_byte_array:
                        opened_file.write(int(_A    ,					2						).to_bytes(1    ,					byteorder="big"						)						)
      except OSError:
            print("File not accessible"						)
            sys.exit()

def       lowercase_		(		_A			:    str    ,					_A			:    str						):

      """simple docstring"""




      lowerCamelCase__		:				Dict    =  read_file_binary(_A						)
      lowerCamelCase__		:				List[Any]    =  compress_data(_A						)
      lowerCamelCase__		:				str    =  add_file_length(_A    ,					_A						)
      write_file_binary(_A    ,					_A						)


if __name__ == "__main__":
    compress(sys.argv[1], sys.argv[2])


