'''simple docstring'''




import numpy as np

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_ = 1e-12  ,       SCREAMING_SNAKE_CASE_ = 100  ,       ):
     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_							)
     lowercase_					:       Union[str, 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.

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

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

          # Check convergence.
          lowercase_					:       List[str]     				=					np.abs(lambda_ - lambda_previous							) / lambda_
          iterations += 1

          if error <= error_tol or iterations >= max_iterations:
               lowercase_					:       Optional[Any]     				=					True

          lowercase_					:       str     				=					lambda_

     if is_complex:
          lowercase_					:       List[Any]     				=					np.real(lambda_							)

     return lambda_, vector

def _UpperCamelCase   (       ):
     lowercase_					:       Optional[Any]     				=					np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]							)
     lowercase_					:       Dict     				=					np.array([41, 4, 20]							)
     lowercase_					:       Tuple     				=					real_input_matrix.astype(np.complexaaa							)
     lowercase_					:       List[Any]     				=					np.triu(1J * complex_input_matrix  ,       1							)
     complex_input_matrix += imag_matrix
     complex_input_matrix += -1 * imag_matrix.T
     lowercase_					:       Dict     				=					np.array([41, 4, 20]							).astype(np.complexaaa							)

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

          # Our implementation.
          lowercase_				,lowercase_					:       Union[str, Any]     				=					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).
          lowercase_				,lowercase_					:       int     				=					np.linalg.eigh(SCREAMING_SNAKE_CASE_							)
          # Last eigenvalue is the maximum one.
          lowercase_					:       int     				=					eigen_values[-1]
          # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
          lowercase_					:       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(SCREAMING_SNAKE_CASE_							) - np.abs(SCREAMING_SNAKE_CASE_							)							) <= 1e-6


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 test_power_iteration()





'''simple docstring'''




import math
import os
import sys

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_							):
     lowercase_					:       List[str]     				=					''
     try:
          with open(SCREAMING_SNAKE_CASE_  ,       'rb'							) as binary_file:
               lowercase_					:       Dict     				=					binary_file.read()
          for dat in data:
               lowercase_					:       Union[str, Any]     				=					f'''{dat:08b}'''
               result += curr_byte
          return result
     except OSError:
          print('File not accessible'							)
          sys.exit()

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     lexicon.pop(SCREAMING_SNAKE_CASE_							)
     lowercase_					:       Any     				=					last_match_id

     if math.loga(SCREAMING_SNAKE_CASE_							).is_integer():
          for curr_key in lexicon:
               lowercase_					:       Tuple     				=					'0' + lexicon[curr_key]

     lowercase_					:       Any     				=					bin(SCREAMING_SNAKE_CASE_							)[2:]

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_							):
     lowercase_					:       Dict     				=					{'0': '0', '1': '1'}
     lowercase_				,lowercase_					:       Any     				=					'', ''
     lowercase_					:       List[Any]     				=					len(SCREAMING_SNAKE_CASE_							)

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

          lowercase_					:       str     				=					lexicon[curr_string]
          result += last_match_id
          add_key_to_lexicon(SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							)
          index += 1
          lowercase_					:       List[Any]     				=					''

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

     if curr_string != "":
          lowercase_					:       Optional[Any]     				=					lexicon[curr_string]
          result += last_match_id

     return result

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     lowercase_					:       List[str]     				=					os.path.getsize(SCREAMING_SNAKE_CASE_							)
     lowercase_					:       Any     				=					bin(SCREAMING_SNAKE_CASE_							)[2:]
     lowercase_					:       Optional[Any]     				=					len(SCREAMING_SNAKE_CASE_							)

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

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     lowercase_					:       List[str]     				=					8
     try:
          with open(SCREAMING_SNAKE_CASE_  ,       'wb'							) as opened_file:
               lowercase_					:       List[Any]     				=					[
                   to_write[i : i + byte_length]
                   for i in range(0  ,       len(SCREAMING_SNAKE_CASE_							)  ,       SCREAMING_SNAKE_CASE_							)
               ]

               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(SCREAMING_SNAKE_CASE_  ,       2							).to_bytes(1  ,       byteorder='big'							)							)
     except OSError:
          print('File not accessible'							)
          sys.exit()

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     lowercase_					:       List[str]     				=					read_file_binary(SCREAMING_SNAKE_CASE_							)
     lowercase_					:       List[str]     				=					compress_data(SCREAMING_SNAKE_CASE_							)
     lowercase_					:       Union[str, Any]     				=					add_file_length(SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							)
     write_file_binary(SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							)


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




