
import math






def 	a_		(	__lowercase       :     int			)			->  bool:

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5	, int(math.sqrt(__lowercase			) + 1			)	, 6			):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True






def 	a_		(	__lowercase       :     float = 0.1			)			->  int:
			_snake_case          =      3
			_snake_case          =      3

			while primes / (2 * j - 1) >= ratio:
						for i in range(j * j + j + 1	, (j + 2) * (j + 2)	, j + 1			):
									primes += is_prime(__lowercase			)
						j += 2
			return j


if __name__ == "__main__":
			import doctest

			doctest.testmod()

from pathlib import Path

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






def 	a_		(	__lowercase       :     np.ndarray	, __lowercase       :     np.ndarray	, __lowercase       :     np.ndarray	, __lowercase       :     int	, __lowercase       :     int			)			->  np.ndarray:
			_snake_case          =      cva.getAffineTransform(__lowercase	, __lowercase			)
			return cva.warpAffine(__lowercase	, __lowercase	, (rows, cols)			)


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

			# set different points to rotate image
			_lowerCamelCase	:    str          =      np.array([[50, 50], [200, 50], [50, 200]], np.floataa)
			_lowerCamelCase	:    Optional[Any]          =      np.array([[10, 100], [200, 50], [100, 250]], np.floataa)
			_lowerCamelCase	:    List[str]          =      np.array([[50, 50], [150, 50], [120, 200]], np.floataa)
			_lowerCamelCase	:    Dict          =      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	:    Any          =      plt.figure(1)
			_lowerCamelCase	:    List[Any]          =      ['''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()