
from __future__ import annotations

import math






def 	a_		(	__lowercase       :     float	, __lowercase       :     int			)			->  float:
			_snake_case          =      u
			for i in range(1	, __lowercase			):
						_snake_case          =      temp * (u - i)
			return temp






def 	a_		(	)			->  None:
			_snake_case          =      int(input('enter the numbers of values: '			)			)
			_snake_case          =      []
			for _ in range(__lowercase			):
						y.append([]			)
			for i in range(__lowercase			):
						for j in range(__lowercase			):
									y[i].append(__lowercase			)
									_snake_case          =      0

			print('enter the values of parameters in a list: '			)
			_snake_case          =      list(map(__lowercase	, input().split()			)			)

			print('enter the values of corresponding parameters: '			)
			for i in range(__lowercase			):
						_snake_case          =      float(input()			)

			_snake_case          =      int(input('enter the value to interpolate: '			)			)
			_snake_case          =      (value - x[0]) / (x[1] - x[0])

			# for calculating forward difference table

			for i in range(1	, __lowercase			):
						for j in range(n - i			):
									_snake_case          =      y[j + 1][i - 1] - y[j][i - 1]

			_snake_case          =      y[0][0]
			for i in range(1	, __lowercase			):
						summ += (ucal(__lowercase	, __lowercase			) * y[0][i]) / math.factorial(__lowercase			)

			print(f'''the value at {value} is {summ}'''			)


if __name__ == "__main__":
			main()

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()