





'''simple docstring'''






from __future__ import annotations


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE = None  ,      __SCREAMING_SNAKE_CASE = None  ,      __SCREAMING_SNAKE_CASE = False  ,      ):


  """simple docstring"""

  _UpperCamelCase       			=cipher_alphabet or [chr(__SCREAMING_SNAKE_CASE   ) for i in range(97  ,      123   )]

  # If the argument is None or the user provided an empty dictionary
  if not frequencies_dict:
    # Frequencies of letters in the english language (how much they show up)
    _UpperCamelCase       			={
        '''a''': 0.0_8_4_9_7,
        '''b''': 0.0_1_4_9_2,
        '''c''': 0.0_2_2_0_2,
        '''d''': 0.0_4_2_5_3,
        '''e''': 0.1_1_1_6_2,
        '''f''': 0.0_2_2_2_8,
        '''g''': 0.0_2_0_1_5,
        '''h''': 0.0_6_0_9_4,
        '''i''': 0.0_7_5_4_6,
        '''j''': 0.0_0_1_5_3,
        '''k''': 0.0_1_2_9_2,
        '''l''': 0.0_4_0_2_5,
        '''m''': 0.0_2_4_0_6,
        '''n''': 0.0_6_7_4_9,
        '''o''': 0.0_7_5_0_7,
        '''p''': 0.0_1_9_2_9,
        '''q''': 0.0_0_0_9_5,
        '''r''': 0.0_7_5_8_7,
        '''s''': 0.0_6_3_2_7,
        '''t''': 0.0_9_3_5_6,
        '''u''': 0.0_2_7_5_8,
        '''v''': 0.0_0_9_7_8,
        '''w''': 0.0_2_5_6_0,
        '''x''': 0.0_0_1_5_0,
        '''y''': 0.0_1_9_9_4,
        '''z''': 0.0_0_0_7_7,
    }
  else:
    # Custom frequencies dictionary
    _UpperCamelCase       			=frequencies_dict

  if not case_sensitive:
    _UpperCamelCase       			=ciphertext.lower()

  # Chi squared statistic values
  _UpperCamelCase       			={}

  # cycle through all of the shifts
  for shift in range(len(__SCREAMING_SNAKE_CASE   )   ):
    _UpperCamelCase       			=''''''

    # decrypt the message with the shift
    for letter in ciphertext:
      try:
        # Try to index the letter in the alphabet
        _UpperCamelCase       			=(alphabet_letters.index(letter.lower()   ) - shift) % len(
            __SCREAMING_SNAKE_CASE   )
        decrypted_with_shift += (
            alphabet_letters[new_key].upper()
            if case_sensitive and letter.isupper()
            else alphabet_letters[new_key]
        )
      except ValueError:
        # Append the character if it isn't in the alphabet
        decrypted_with_shift += letter

    _UpperCamelCase       			=0.0

    # Loop through each letter in the decoded message with the shift
    for letter in decrypted_with_shift:
      if case_sensitive:
        _UpperCamelCase       			=letter.lower()
        if letter in frequencies:
          # Get the amount of times the letter occurs in the message
          _UpperCamelCase       			=decrypted_with_shift.lower().count(__SCREAMING_SNAKE_CASE   )

          # Get the excepcted amount of times the letter should appear based
          # on letter frequencies
          _UpperCamelCase       			=frequencies[letter] * occurrences

          # Complete the chi squared statistic formula
          _UpperCamelCase       			=((occurrences - expected) ** 2) / expected

          # Add the margin of error to the total chi squared statistic
          chi_squared_statistic += chi_letter_value
      else:
        if letter.lower() in frequencies:
          # Get the amount of times the letter occurs in the message
          _UpperCamelCase       			=decrypted_with_shift.count(__SCREAMING_SNAKE_CASE   )

          # Get the excepcted amount of times the letter should appear based
          # on letter frequencies
          _UpperCamelCase       			=frequencies[letter] * occurrences

          # Complete the chi squared statistic formula
          _UpperCamelCase       			=((occurrences - expected) ** 2) / expected

          # Add the margin of error to the total chi squared statistic
          chi_squared_statistic += chi_letter_value

        # Add the data to the chi_squared_statistic_values dictionary
    _UpperCamelCase       			=(
        chi_squared_statistic,
        decrypted_with_shift,
    )

  # Get the most likely cipher by finding the cipher with the smallest chi squared
  # statistic
  def chi_squared_statistic_values_sorting_key(__SCREAMING_SNAKE_CASE   ) -> tuple[float, str]:
    return chi_squared_statistic_values[key]

  _UpperCamelCase       			=min(
      __SCREAMING_SNAKE_CASE  ,      key=__SCREAMING_SNAKE_CASE  ,      )

  # Get all the data from the most likely cipher (key, decoded message)
  (
      (
      _UpperCamelCase     
  )			,     (
      _UpperCamelCase     
  )			,          
  )       			=chi_squared_statistic_values[most_likely_cipher]

  # Return the data on the most likely shift
  return (
      most_likely_cipher,
      most_likely_cipher_chi_squared_value,
      decoded_most_likely_cipher,
  )













'''simple docstring'''






from pathlib import Path

import cva
import numpy as np
from matplotlib import pyplot as plt


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

  _UpperCamelCase       			=cva.getAffineTransform(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   )
  return cva.warpAffine(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      (rows, cols)   )


if __name__ == "__main__":
      # read original image
      __lowerCamelCase						: List[Any]		=   cva.imread(
          str(Path(__file__).resolve().parent.parent / 'image_data' / 'lena.jpg')
      )
      # turn image in gray scale value
      __lowerCamelCase						: List[Any]		=   cva.cvtColor(image, cva.COLOR_BGR2GRAY)
      # get image shape
      __lowerCamelCase		, __lowerCamelCase						: Any		=   gray_img.shape

      # set different points to rotate image
      __lowerCamelCase						: Optional[Any]		=   np.array([[50, 50], [200, 50], [50, 200]], np.floataa)
      __lowerCamelCase						: Any		=   np.array([[10, 100], [200, 50], [100, 250]], np.floataa)
      __lowerCamelCase						: int		=   np.array([[50, 50], [150, 50], [120, 200]], np.floataa)
      __lowerCamelCase						: List[Any]		=   np.array([[10, 100], [80, 50], [180, 250]], np.floataa)

      # add all rotated images in a list
      __lowerCamelCase						: int		=   [
          gray_img,
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
      ]

      # plot different image rotations
      __lowerCamelCase						: Optional[Any]		=   plt.figure(1)
      __lowerCamelCase						: Tuple		=   ['Original', 'Rotation 1', 'Rotation 2', 'Rotation 3']
      for i, image in enumerate(images):
            plt.subplot(2, 2, i + 1), plt.imshow(image, 'gray')
            plt.title(titles[i])
            plt.axis('off')
            plt.subplots_adjust(left=0.0, bottom=0.0_5, right=1.0, top=0.9_5)
      plt.show()






