




from math import pi, sqrt, tan







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      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 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      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 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      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'      )
				__lowerCamelCase		       =    (height**2 + (radius_a - radius_a) ** 2) ** 0.5
				return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      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 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      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(UpperCamelCase__ ,     2      ) * torus_radius * tube_radius







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      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'      )
				__lowerCamelCase		       =    (sidea + sidea + sidea) / 2
				__lowerCamelCase		       =    sqrt(
				    semi_perimeter
				    * (semi_perimeter - sidea)
				    * (semi_perimeter - sidea)
				    * (semi_perimeter - sidea)      )
				return area







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      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 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      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 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      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 			lowerCamelCase_		(       UpperCamelCase__				:      int ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if not isinstance(UpperCamelCase__ ,     UpperCamelCase__      ) 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) = }''')









"""simple docstring"""
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin






@dataclass
class 					_SCREAMING_SNAKE_CASE(   A  ):
       SCREAMING_SNAKE_CASE_   :      torch.FloatTensor
       SCREAMING_SNAKE_CASE_   :      torch.FloatTensor
       SCREAMING_SNAKE_CASE_   :      Optional[torch.FloatTensor]							=  None






class 					_SCREAMING_SNAKE_CASE(   A    ,	A  ):
       SCREAMING_SNAKE_CASE_   :      Any							=  2




       @register_to_config
       def __init__(						self		,SCREAMING_SNAKE_CASE__ = 0.0_2		,SCREAMING_SNAKE_CASE__ = 1_00		,SCREAMING_SNAKE_CASE__ = 1.0_0_7		,SCREAMING_SNAKE_CASE__ = 80		,SCREAMING_SNAKE_CASE__ = 0.0_5		,SCREAMING_SNAKE_CASE__ = 50		,)			->      Union[str, Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Any						=  sigma_max

             # setable values
             __SCREAMING_SNAKE_CASE   :int						=  None
             __SCREAMING_SNAKE_CASE   :np.IntTensor						=  None
             __SCREAMING_SNAKE_CASE   :torch.FloatTensor						=  None  # sigma(t_i)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = None							)			->      torch.FloatTensor:





             """simple docstring"""






             return sample




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = None							)			->      List[Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  num_inference_steps
             __SCREAMING_SNAKE_CASE   :int						=  np.arange(0		,self.num_inference_steps							)[::-1].copy()
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  torch.from_numpy(SCREAMING_SNAKE_CASE__							).to(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Any						=  [
                 (
                     self.config.sigma_max**2
                     * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
                 )
                 for i in self.timesteps
             ]
             __SCREAMING_SNAKE_CASE   :List[str]						=  torch.tensor(SCREAMING_SNAKE_CASE__		,dtype=torch.floataa		,device=SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = None							)			->      Tuple[torch.FloatTensor, float]:





             """simple docstring"""






             if self.config.s_min <= sigma <= self.config.s_max:
                   __SCREAMING_SNAKE_CASE   :List[str]						=  min(self.config.s_churn / self.num_inference_steps		,2**0.5 - 1							)
             else:
                   __SCREAMING_SNAKE_CASE   :Optional[Any]						=  0

             # sample eps ~ N(0, S_noise^2 * I)
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  self.config.s_noise * randn_tensor(sample.shape		,generator=SCREAMING_SNAKE_CASE__							).to(sample.device							)
             __SCREAMING_SNAKE_CASE   :List[str]						=  sigma + gamma * sigma
             __SCREAMING_SNAKE_CASE   :str						=  sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

             return sample_hat, sigma_hat




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = True		,)			->      Union[KarrasVeOutput, Tuple]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :str						=  sample_hat + sigma_hat * model_output
             __SCREAMING_SNAKE_CASE   :Tuple						=  (sample_hat - pred_original_sample) / sigma_hat
             __SCREAMING_SNAKE_CASE   :List[Any]						=  sample_hat + (sigma_prev - sigma_hat) * derivative

             if not return_dict:
                   return (sample_prev, derivative)

             return KarrasVeOutput(
                 prev_sample=SCREAMING_SNAKE_CASE__		,derivative=SCREAMING_SNAKE_CASE__		,pred_original_sample=SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = True		,)			->      Union[KarrasVeOutput, Tuple]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Any						=  sample_prev + sigma_prev * model_output
             __SCREAMING_SNAKE_CASE   :List[Any]						=  (sample_prev - pred_original_sample) / sigma_prev
             __SCREAMING_SNAKE_CASE   :Dict						=  sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

             if not return_dict:
                   return (sample_prev, derivative)

             return KarrasVeOutput(
                 prev_sample=SCREAMING_SNAKE_CASE__		,derivative=SCREAMING_SNAKE_CASE__		,pred_original_sample=SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)			->      Union[str, Any]:





             """simple docstring"""






             raise NotImplementedError()