from __future__ import annotations

from math import pi, pow




def   _UpperCamelCase   (			snake_case__							)						->   float:





							if side_length < 0:
														raise ValueError("vol_cube() only accepts non-negative values"							)
							return pow(__a,    3							)




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   float:





							if height < 0 or radius < 0:
														raise ValueError("vol_spherical_cap() only accepts non-negative values"							)
							# Volume is 1/3 pi * height squared * (3 * radius - height)
							return 1 / 3 * pi * pow(__a,    2							) * (3 * radius - height)




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__							)						->   float:





							if radius_a < 0 or radius_a < 0 or centers_distance < 0:
														raise ValueError("vol_spheres_intersect() only accepts non-negative values"							)
							if centers_distance == 0:
														return vol_sphere(min(__a,    __a							)							)

							__UpperCAmelCase						:			Dict         =   (
							    (radius_a - radius_a + centers_distance)
							    * (radius_a + radius_a - centers_distance)
							    / (2 * centers_distance)
							)
							__UpperCAmelCase						:			Tuple         =   (
							    (radius_a - radius_a + centers_distance)
							    * (radius_a + radius_a - centers_distance)
							    / (2 * centers_distance)
							)

							return vol_spherical_cap(__a,    __a							) + vol_spherical_cap(__a,    __a							)




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__							)						->   float:





							if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
														raise ValueError(
														    "vol_spheres_union() only accepts non-negative values, non-zero radius"							)

							if centers_distance == 0:
														return vol_sphere(max(__a,    __a							)							)

							return (
							    vol_sphere(__a							)
							    + vol_sphere(__a							)
							    - vol_spheres_intersect(__a,    __a,    __a							)
							)




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__							)						->   float:





							if width < 0 or height < 0 or length < 0:
														raise ValueError("vol_cuboid() only accepts non-negative values"							)
							return float(width * height * length							)




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   float:





							if height < 0 or area_of_base < 0:
														raise ValueError("vol_cone() only accepts non-negative values"							)
							return area_of_base * height / 3.0




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   float:





							if height < 0 or radius < 0:
														raise ValueError("vol_right_circ_cone() only accepts non-negative values"							)
							return pi * pow(__a,    2							) * height / 3.0




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   float:





							if height < 0 or area_of_base < 0:
														raise ValueError("vol_prism() only accepts non-negative values"							)
							return float(area_of_base * height							)




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   float:





							if height < 0 or area_of_base < 0:
														raise ValueError("vol_pyramid() only accepts non-negative values"							)
							return area_of_base * height / 3.0




def   _UpperCamelCase   (			snake_case__							)						->   float:





							if radius < 0:
														raise ValueError("vol_sphere() only accepts non-negative values"							)
							# Volume is 4/3 * pi * radius cubed
							return 4 / 3 * pi * pow(__a,    3							)




def   _UpperCamelCase   (			snake_case__							)						->   float:





							if radius < 0:
														raise ValueError("vol_hemisphere() only accepts non-negative values"							)
							# Volume is radius cubed * pi * 2/3
							return pow(__a,    3							) * pi * 2 / 3




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   float:





							if height < 0 or radius < 0:
														raise ValueError("vol_circular_cylinder() only accepts non-negative values"							)
							# Volume is radius squared * height * pi
							return pow(__a,    2							) * height * pi




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__							)						->   float:





							if inner_radius < 0 or outer_radius < 0 or height < 0:
														raise ValueError(
														    "vol_hollow_circular_cylinder() only accepts non-negative values"							)
							if outer_radius <= inner_radius:
														raise ValueError("outer_radius must be greater than inner_radius"							)
							return pi * (pow(__a,    2							) - pow(__a,    2							)) * height




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__							)						->   float:





							if radius_a < 0 or radius_a < 0 or height < 0:
														raise ValueError("vol_conical_frustum() only accepts non-negative values"							)
							return (
							    1
							    / 3
							    * pi
							    * height
							    * (pow(__a,    2							) + pow(__a,    2							) + radius_a * radius_a)
							)




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   float:





							if torus_radius < 0 or tube_radius < 0:
														raise ValueError("vol_torus() only accepts non-negative values"							)
							return 2 * pow(__a,    2							) * torus_radius * pow(__a,    2							)




def   _UpperCamelCase   (			)						->   List[Any]:
							print("Volumes:"							)
							print(f'''Cube: {vol_cube(2							) = }'''							)  # = 8
							print(f'''Cuboid: {vol_cuboid(2,    2,    2							) = }'''							)  # = 8
							print(f'''Cone: {vol_cone(2,    2							) = }'''							)  # ~= 1.33
							print(f'''Right Circular Cone: {vol_right_circ_cone(2,    2							) = }'''							)  # ~= 8.38
							print(f'''Prism: {vol_prism(2,    2							) = }'''							)  # = 4
							print(f'''Pyramid: {vol_pyramid(2,    2							) = }'''							)  # ~= 1.33
							print(f'''Sphere: {vol_sphere(2							) = }'''							)  # ~= 33.5
							print(f'''Hemisphere: {vol_hemisphere(2							) = }'''							)  # ~= 16.75
							print(f'''Circular Cylinder: {vol_circular_cylinder(2,    2							) = }'''							)  # ~= 25.1
							print(f'''Torus: {vol_torus(2,    2							) = }'''							)  # ~= 157.9
							print(f'''Conical Frustum: {vol_conical_frustum(2,    2,    4							) = }'''							)  # ~= 58.6
							print(f'''Spherical cap: {vol_spherical_cap(1,    2							) = }'''							)  # ~= 5.24
							print(f'''Spheres intersetion: {vol_spheres_intersect(2,    2,    1							) = }'''							)  # ~= 21.21
							print(f'''Spheres union: {vol_spheres_union(2,    2,    1							) = }'''							)  # ~= 45.81
							print(
							    f'''Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1,    2,    3							) = }'''							)  # ~= 28.3


if __name__ == "__main__":
	main()





import numpy as np
import requests




def   _UpperCamelCase   (			)						->   Tuple:
							__UpperCAmelCase						:			Tuple         =   requests.get(
							    "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"
							    "master/Week1/ADRvsRating.csv"							)
							__UpperCAmelCase						:			List[Any]         =   response.text.splitlines()
							__UpperCAmelCase						:			Any         =   []
							for item in lines:
														__UpperCAmelCase						:			Any         =   item.split(","							)
														data.append(snake_case__							)
							data.pop(0							)  # This is for removing the labels from the list
							__UpperCAmelCase						:			List[str]         =   np.matrix(snake_case__							)
							return dataset




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__,    snake_case__,    snake_case__							)						->   Optional[Any]:
							__UpperCAmelCase						:			Tuple         =   len_data

							__UpperCAmelCase						:			int         =   np.dot(snake_case__,    data_x.transpose()							)
							prod -= data_y.transpose()
							__UpperCAmelCase						:			Optional[int]         =   np.dot(snake_case__,    snake_case__							)
							__UpperCAmelCase						:			List[Any]         =   theta - (alpha / n) * sum_grad
							return theta




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__,    snake_case__							)						->   Optional[int]:
							__UpperCAmelCase						:			Any         =   np.dot(snake_case__,    data_x.transpose()							)
							prod -= data_y.transpose()
							__UpperCAmelCase						:			Optional[int]         =   np.sum(np.square(snake_case__							)							)
							__UpperCAmelCase						:			List[Any]         =   sum_elem / (2 * len_data)
							return error




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   Tuple:
							__UpperCAmelCase						:			Any         =   10_0000
							__UpperCAmelCase						:			Dict         =   0.000_1550

							__UpperCAmelCase						:			str         =   data_x.shape[1]
							__UpperCAmelCase						:			Any         =   data_x.shape[0] - 1

							__UpperCAmelCase						:			List[str]         =   np.zeros((1, no_features)							)

							for i in range(0,    snake_case__							):
														__UpperCAmelCase						:			Union[str, Any]         =   run_steep_gradient_descent(snake_case__,    snake_case__,    snake_case__,    snake_case__,    snake_case__							)
														__UpperCAmelCase						:			Any         =   sum_of_square_error(snake_case__,    snake_case__,    snake_case__,    snake_case__							)
														print(f'''At Iteration {i + 1} - Error is {error:.5f}'''							)

							return theta




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   Optional[int]:
							__UpperCAmelCase						:			str         =   sum(abs(y - predicted_y[i]							) for i, y in enumerate(snake_case__							)							)
							return total / len(snake_case__							)




def   _UpperCamelCase   (			)						->   List[str]:
							__UpperCAmelCase						:			str         =   collect_dataset()

							__UpperCAmelCase						:			List[Any]         =   data.shape[0]
							__UpperCAmelCase						:			Union[str, Any]         =   np.c_[np.ones(snake_case__							), data[:, :-1]].astype(snake_case__							)
							__UpperCAmelCase						:			int         =   data[:, -1].astype(snake_case__							)

							__UpperCAmelCase						:			List[Any]         =   run_linear_regression(snake_case__,    snake_case__							)
							__UpperCAmelCase						:			List[str]         =   theta.shape[1]
							print("Resultant Feature vector : "							)
							for i in range(0,    snake_case__							):
														print(f'''{theta[0, i]:.5f}'''							)


if __name__ == "__main__":
	main()




