



import math






def      _A				(UpperCamelCase		:      int )  ->bool:



			'''simple docstring'''







			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(UpperCamelCase ) + 1 )      ,			6 ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True






def      _A				(UpperCamelCase		:      float = 0.1 )  ->int:



			'''simple docstring'''







			lowerCamelCase__ :      Optional[Any]								=		3
			lowerCamelCase__ :      Tuple								=		3

			while primes / (2 * j - 1) >= ratio:
						for i in range(j * j + j + 1      ,			(j + 2) * (j + 2)      ,			j + 1 ):
									primes += is_prime(UpperCamelCase )
						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				(UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      int )  ->np.ndarray:



			'''simple docstring'''







			lowerCamelCase__ :      Union[str, Any]								=		cva.getAffineTransform(UpperCamelCase      ,			UpperCamelCase )
			return cva.warpAffine(UpperCamelCase      ,			UpperCamelCase      ,			(rows, cols) )


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

				# set different points to rotate image
				_lowercase     							=						np.array([[50, 50], [2_00, 50], [50, 2_00]], np.floataa)
				_lowercase     							=						np.array([[10, 1_00], [2_00, 50], [1_00, 2_50]], np.floataa)
				_lowercase     							=						np.array([[50, 50], [1_50, 50], [1_20, 2_00]], np.floataa)
				_lowercase     							=						np.array([[10, 1_00], [80, 50], [1_80, 2_50]], np.floataa)

				# add all rotated images in a list
				_lowercase     							=						[
				    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
				_lowercase     							=						plt.figure(1)
				_lowercase     							=						['''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=0.05, right=1.0, top=0.95)
				plt.show()



