





from math import pi, sqrt, tan



def _a				(	lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if side_length < 0:
            raise ValueError('''surface_area_cube() only accepts non-negative values''' )
      return 6 * side_length**2



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if length < 0 or breadth < 0 or height < 0:
            raise ValueError('''surface_area_cuboid() only accepts non-negative values''' )
      return 2 * ((length * breadth) + (breadth * height) + (length * height))



def _a				(	lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if radius < 0:
            raise ValueError('''surface_area_sphere() only accepts non-negative values''' )
      return 4 * pi * radius**2



def _a				(	lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if radius < 0:
            raise ValueError('''surface_area_hemisphere() only accepts non-negative values''' )
      return 3 * pi * radius**2



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if radius < 0 or height < 0:
            raise ValueError('''surface_area_cone() only accepts non-negative values''' )
      return pi * radius * (radius + (height**2 + radius**2) ** 0.5)



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if radius_a < 0 or radius_a < 0 or height < 0:
            raise ValueError(
                '''surface_area_conical_frustum() only accepts non-negative values''' )
      __A          =				(height**2 + (radius_a - radius_a) ** 2) ** 0.5
      return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if radius < 0 or height < 0:
            raise ValueError('''surface_area_cylinder() only accepts non-negative values''' )
      return 2 * pi * radius * (height + radius)



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if torus_radius < 0 or tube_radius < 0:
            raise ValueError('''surface_area_torus() only accepts non-negative values''' )
      if torus_radius < tube_radius:
            raise ValueError(
                '''surface_area_torus() does not support spindle or self intersecting tori''' )
      return 4 * pow(lowerCamelCase					,				2 ) * torus_radius * tube_radius



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if length < 0 or width < 0:
            raise ValueError('''area_rectangle() only accepts non-negative values''' )
      return length * width



def _a				(	lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if side_length < 0:
            raise ValueError('''area_square() only accepts non-negative values''' )
      return side_length**2



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if base < 0 or height < 0:
            raise ValueError('''area_triangle() only accepts non-negative values''' )
      return (base * height) / 2



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if sidea < 0 or sidea < 0 or sidea < 0:
            raise ValueError('''area_triangle_three_sides() only accepts non-negative values''' )
      elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
            raise ValueError('''Given three sides do not form a triangle''' )
      __A          =				(sidea + sidea + sidea) / 2
      __A          =				sqrt(
          semi_perimeter
          * (semi_perimeter - sidea)
          * (semi_perimeter - sidea)
          * (semi_perimeter - sidea) )
      return area



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if base < 0 or height < 0:
            raise ValueError('''area_parallelogram() only accepts non-negative values''' )
      return base * height



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if basea < 0 or basea < 0 or height < 0:
            raise ValueError('''area_trapezium() only accepts non-negative values''' )
      return 1 / 2 * (basea + basea) * height



def _a				(	lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if radius < 0:
            raise ValueError('''area_circle() only accepts non-negative values''' )
      return pi * radius**2



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if radius_x < 0 or radius_y < 0:
            raise ValueError('''area_ellipse() only accepts non-negative values''' )
      return pi * radius_x * radius_y



def _a				(	lowerCamelCase:   float					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if diagonal_a < 0 or diagonal_a < 0:
            raise ValueError('''area_rhombus() only accepts non-negative values''' )
      return 1 / 2 * diagonal_a * diagonal_a



def _a				(	lowerCamelCase:   int					,				lowerCamelCase:   float )	->						float:







      '''simple docstring'''






      if not isinstance(lowerCamelCase					,				lowerCamelCase ) or sides < 3:
            raise ValueError(
                '''area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides''' )
      elif length < 0:
            raise ValueError(
                '''area_reg_polygon() only accepts non-negative values as \
length of a side''' )
      return (sides * length**2) / (4 * tan(pi / sides ))
      return (sides * length**2) / (4 * tan(pi / sides ))


if __name__ == "__main__":
       import doctest

       doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

       print('[DEMO] Areas of various geometric shapes: \n')
       print(f'Rectangle: {area_rectangle(10, 20) = }')
       print(f'Square: {area_square(10) = }')
       print(f'Triangle: {area_triangle(10, 10) = }')
       print(f'Triangle: {area_triangle_three_sides(5, 12, 13) = }')
       print(f'Parallelogram: {area_parallelogram(10, 20) = }')
       print(f'Rhombus: {area_rhombus(10, 20) = }')
       print(f'Trapezium: {area_trapezium(10, 20, 30) = }')
       print(f'Circle: {area_circle(20) = }')
       print(f'Ellipse: {area_ellipse(10, 20) = }')
       print('\nSurface Areas of various geometric shapes: \n')
       print(f'Cube: {surface_area_cube(20) = }')
       print(f'Cuboid: {surface_area_cuboid(10, 20, 30) = }')
       print(f'Sphere: {surface_area_sphere(20) = }')
       print(f'Hemisphere: {surface_area_hemisphere(20) = }')
       print(f'Cone: {surface_area_cone(10, 20) = }')
       print(f'Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }')
       print(f'Cylinder: {surface_area_cylinder(10, 20) = }')
       print(f'Torus: {surface_area_torus(20, 10) = }')
       print(f'Equilateral Triangle: {area_reg_polygon(3, 10) = }')
       print(f'Square: {area_reg_polygon(4, 10) = }')
       print(f'Reqular Pentagon: {area_reg_polygon(5, 10) = }')












import numpy as np
from PIL import Image



def _a				(	lowerCamelCase:   np.ndarray					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						np.ndarray:







      '''simple docstring'''






      __A          =				np.array(lowerCamelCase )
      if arr.shape[0] != arr.shape[1]:
            raise ValueError('''The input array is not a square matrix''' )
      __A          =				0
      __A          =				0
      __A          =				0
      __A          =				0

      # compute the shape of the output matrix
      __A          =				(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape maxpool_shape
      __A          =				np.zeros((maxpool_shape, maxpool_shape) )

      while i < arr.shape[0]:
            if i + size > arr.shape[0]:
                  # if the end of the matrix is reached, break
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the maximum of the pooling matrix
                  __A          =				np.max(arr[i : i + size, j : j + size] )
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1

            # reset the column index to 0
            __A          =				0
            __A          =				0

      return updated_arr



def _a				(	lowerCamelCase:   np.ndarray					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						np.ndarray:







      '''simple docstring'''






      __A          =				np.array(lowerCamelCase )
      if arr.shape[0] != arr.shape[1]:
            raise ValueError('''The input array is not a square matrix''' )
      __A          =				0
      __A          =				0
      __A          =				0
      __A          =				0

      # compute the shape of the output matrix
      __A          =				(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape avgpool_shape
      __A          =				np.zeros((avgpool_shape, avgpool_shape) )

      while i < arr.shape[0]:
            # if the end of the matrix is reached, break
            if i + size > arr.shape[0]:
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the average of the pooling matrix
                  __A          =				int(np.average(arr[i : i + size, j : j + size] ) )
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1
            # reset the column index to 0
            __A          =				0
            __A          =				0

      return updated_arr


# Main Function
if __name__ == "__main__":
       from doctest import testmod

       testmod(name='avgpooling', verbose=True)

       # Loading the image
       snake_case__					:							Optional[Any]													=     Image.open('path_to_image')

       # Converting the image to numpy array and maxpooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

       # Converting the image to numpy array and averagepooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()





