"""simple docstring"""







from __future__ import annotations

from math import pi, pow



def       A__    (	lowercase_     :	int | float						)  ->							float:
   if side_length < 0:
      raise ValueError('vol_cube() only accepts non-negative values'						)
   return pow(lowercase_      , 3						)



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , 2						) * (3 * radius - height)



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , lowercase_						)						)

   __lowerCamelCase    		=					(
       (radius_a - radius_a + centers_distance)
       * (radius_a + radius_a - centers_distance)
       / (2 * centers_distance)
   )
   __lowerCamelCase    		=					(
       (radius_a - radius_a + centers_distance)
       * (radius_a + radius_a - centers_distance)
       / (2 * centers_distance)
   )

   return vol_spherical_cap(lowercase_      , lowercase_						) + vol_spherical_cap(lowercase_      , lowercase_						)



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , lowercase_						)						)

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



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   if height < 0 or radius < 0:
      raise ValueError('vol_right_circ_cone() only accepts non-negative values'						)
   return pi * pow(lowercase_      , 2						) * height / 3.0



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float						)  ->							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(lowercase_      , 3						)



def       A__    (	lowercase_     :	float						)  ->							float:
   if radius < 0:
      raise ValueError('vol_hemisphere() only accepts non-negative values'						)
   # Volume is radius cubed * pi * 2/3
   return pow(lowercase_      , 3						) * pi * 2 / 3



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , 2						) * height * pi



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   # Volume - (outer_radius squared - inner_radius squared) * pi * height
   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(lowercase_      , 2						) - pow(lowercase_      , 2						)) * height



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   # Volume is 1/3 * pi * height *
   #           (radius_1 squared + radius_2 squared + radius_1 * radius_2)
   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(lowercase_      , 2						) + pow(lowercase_      , 2						) + radius_a * radius_a)
   )



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   if torus_radius < 0 or tube_radius < 0:
      raise ValueError('vol_torus() only accepts non-negative values'						)
   return 2 * pow(lowercase_      , 2						) * torus_radius * pow(lowercase_      , 2						)



def       A__    (	)  ->							Optional[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()







'''simple docstring'''

import os
import pickle
import unittest
from collections import UserDict, namedtuple

import torch

from accelerate.test_utils.testing import require_cuda, require_torch_min_version
from accelerate.test_utils.training import RegressionModel
from accelerate.utils import (
    convert_outputs_to_fpaa,
    extract_model_from_parallel,
    find_device,
    listify,
    patch_environment,
    recursively_apply,
    send_to_device,
)


lowercase_  		=			namedtuple('''ExampleNamedTuple''', '''a b c''')
class 	SCREAMING_SNAKE_CASE      (    unittest.TestCase):







		"""simple docstring"""






		def 		UpperCamelCase__							( self					)			->  int:
								_lowerCAmelCase					    =torch.randn(5		,    2					)
								_lowerCAmelCase					    =torch.device('cuda'					) if torch.cuda.is_available() else torch.device('cpu'					)

								_lowerCAmelCase					    =send_to_device(__A		,    __A					)
								self.assertTrue(torch.equal(resulta.cpu()		,    __A					)					)

								_lowerCAmelCase					    =send_to_device((tensor, [tensor, tensor], 1)		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta[0].cpu()		,    __A					)					)
								self.assertIsInstance(resulta[1]		,    __A					)
								self.assertTrue(torch.equal(resulta[1][0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta[1][1].cpu()		,    __A					)					)
								self.assertEqual(resulta[2]		,    1					)

								_lowerCAmelCase					    =send_to_device({'a': tensor, 'b': [tensor, tensor], 'c': 1}		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta['a'].cpu()		,    __A					)					)
								self.assertIsInstance(resulta['b']		,    __A					)
								self.assertTrue(torch.equal(resulta['b'][0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta['b'][1].cpu()		,    __A					)					)
								self.assertEqual(resulta['c']		,    1					)

								_lowerCAmelCase					    =send_to_device(ExampleNamedTuple(a=__A		,    b=[tensor, tensor]		,    c=1					)		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta.a.cpu()		,    __A					)					)
								self.assertIsInstance(resulta.b		,    __A					)
								self.assertTrue(torch.equal(resulta.b[0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta.b[1].cpu()		,    __A					)					)
								self.assertEqual(resulta.c		,    1					)

								_lowerCAmelCase					    =send_to_device(UserDict({'a': tensor, 'b': [tensor, tensor], 'c': 1}					)		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta['a'].cpu()		,    __A					)					)
								self.assertIsInstance(resulta['b']		,    __A					)
								self.assertTrue(torch.equal(resulta['b'][0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta['b'][1].cpu()		,    __A					)					)
								self.assertEqual(resulta['c']		,    1					)






		def 		UpperCamelCase__							( self					)			->  Optional[int]:
								with self.assertRaises(__A					) as cm:
														_lowerCAmelCase					    =recursively_apply(torch.tensor		,    (torch.tensor(1					), 1)		,    error_on_other_type=__A					)
								self.assertEqual(
								    str(cm.exception					)		,    'Unsupported types (<class \'int\'>) passed to `tensor`. Only nested list/tuple/dicts of objects that are valid for `is_torch_tensor` should be passed.'		,    )






		def 		UpperCamelCase__							( self					)			->  int:
								_lowerCAmelCase					    =torch.tensor([1, 2, 3, 4, 5]					)
								self.assertEqual(listify(__A					)		,    [1, 2, 3, 4, 5]					)

								_lowerCAmelCase					    =torch.tensor([[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]					)
								self.assertEqual(listify(__A					)		,    [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]					)

								_lowerCAmelCase					    =torch.tensor([[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]], [[11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]]					)
								self.assertEqual(
								    listify(__A					)		,    [[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]], [[11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]]					)






		def 		UpperCamelCase__							( self					)			->  List[Any]:
								with patch_environment(aa=1		,    BB=2					):
														self.assertEqual(os.environ.get('AA'					)		,    '1'					)
														self.assertEqual(os.environ.get('BB'					)		,    '2'					)

								self.assertNotIn('AA'		,    os.environ					)
								self.assertNotIn('BB'		,    os.environ					)






		def 		UpperCamelCase__							( self					)			->  Union[str, Any]:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =model.forward
								_lowerCAmelCase					    =convert_outputs_to_fpaa(model.forward					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A		,    keep_fpaa_wrapper=__A					)
								_lowerCAmelCase					    =pickle.dumps(__A					)






		@require_cuda
		def 		UpperCamelCase__							( self					)			->  Dict:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =model.forward
								_lowerCAmelCase					    =torch.cuda.amp.autocast(dtype=torch.floataa					)(model.forward					)
								_lowerCAmelCase					    =convert_outputs_to_fpaa(model.forward					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A		,    keep_fpaa_wrapper=__A					)
								_lowerCAmelCase					    =pickle.dumps(__A					)






		@require_cuda
		@require_torch_min_version(version='2.0'					)
		def 		UpperCamelCase__							( self					)			->  int:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =model.forward
								_lowerCAmelCase					    =torch.cuda.amp.autocast(dtype=torch.floataa					)(model.forward					)
								_lowerCAmelCase					    =convert_outputs_to_fpaa(model.forward					)
								_lowerCAmelCase					    =torch.compile(model.forward		,    backend='inductor'					)
								_lowerCAmelCase					    =torch.randn(4		,    10					).cuda()
								_lowerCAmelCase					    =model(__A					)






		def 		UpperCamelCase__							( self					)			->  Optional[int]:
								_lowerCAmelCase					    =RegressionModel()
								# could also do a test with DistributedDataParallel, but difficult to run on CPU or single GPU
								_lowerCAmelCase					    =torch.nn.parallel.DataParallel(__A					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A					)

								self.assertEqual(__A		,    __A					)






		@require_torch_min_version(version='2.0'					)
		def 		UpperCamelCase__							( self					)			->  str:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =torch.compile(__A					)

								# could also do a test with DistributedDataParallel, but difficult to run on CPU or single GPU
								_lowerCAmelCase					    =torch.nn.parallel.DataParallel(__A					)
								_lowerCAmelCase					    =torch.compile(__A					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A					)

								self.assertEqual(compiled_model._orig_mod		,    compiled_model_unwrapped._orig_mod					)






		def 		UpperCamelCase__							( self					)			->  Tuple:
								self.assertEqual(find_device([1, 'a', torch.tensor([1, 2, 3]					)]					)		,    torch.device('cpu'					)					)
								self.assertEqual(find_device({'a': 1, 'b': torch.tensor([1, 2, 3]					)}					)		,    torch.device('cpu'					)					)
								self.assertIsNone(find_device([1, 'a']					)					)





