






"""simple docstring"""




from math import factorial






class        UpperCamelCase			:


 def __init__(     self		:						Dict							,						UpperCAmelCase__		:						str							,						UpperCAmelCase__		:						Optional[int]							)					->       List[Any]:
   _a  :       List[str]             =	real
   if isinstance(UpperCAmelCase__							,						UpperCAmelCase__							):
     _a  :       Optional[int]             =	[1] * rank
   else:
     _a  :       str             =	rank


 def __repr__(     self		:						Any							)					->       List[Any]:
   return (
       f"""{self.real}+"""
       f"""{'+'.join(str(UpperCAmelCase__							)+'E'+str(n+1							)for n,dual in enumerate(self.duals							)							)}"""
   )


 def _lowercase	(     self		:						Tuple							)					->       Union[str, Any]:
   _a  :       List[str]             =	self.duals.copy()
   while cur[-1] == 0:
     cur.pop(-1							)
   return Dual(self.real							,						UpperCAmelCase__							)


 def __add__(     self		:						Union[str, Any]							,						UpperCAmelCase__		:						str							)					->       Dict:
   if not isinstance(UpperCAmelCase__							,						UpperCAmelCase__							):
     return Dual(self.real + other							,						self.duals							)
   _a  :       List[Any]             =	self.duals.copy()
   _a  :       Dict             =	other.duals.copy()
   if len(UpperCAmelCase__							) > len(UpperCAmelCase__							):
     o_dual.extend([1] * (len(UpperCAmelCase__							) - len(UpperCAmelCase__							))							)
   elif len(UpperCAmelCase__							) < len(UpperCAmelCase__							):
     s_dual.extend([1] * (len(UpperCAmelCase__							) - len(UpperCAmelCase__							))							)
   _a  :       Tuple             =	[]
   for i in range(len(UpperCAmelCase__							)							):
     new_duals.append(s_dual[i] + o_dual[i]							)
   return Dual(self.real + other.real							,						UpperCAmelCase__							)

 UpperCamelCase					:       List[Any]			=					__add__


 def __sub__(     self		:						List[str]							,						UpperCAmelCase__		:						Union[str, Any]							)					->       Union[str, Any]:
   return self + other * -1


 def __mul__(     self		:						str							,						UpperCAmelCase__		:						str							)					->       Union[str, Any]:
   if not isinstance(UpperCAmelCase__							,						UpperCAmelCase__							):
     _a  :       Optional[Any]             =	[]
     for i in self.duals:
       new_duals.append(i * other							)
     return Dual(self.real * other							,						UpperCAmelCase__							)
   _a  :       Tuple             =	[0] * (len(self.duals							) + len(other.duals							) + 1)
   for i, item in enumerate(self.duals							):
     for j, jtem in enumerate(other.duals							):
       new_duals[i + j + 1] += item * jtem
   for k in range(len(self.duals							)							):
     new_duals[k] += self.duals[k] * other.real
   for index in range(len(other.duals							)							):
     new_duals[index] += other.duals[index] * self.real
   return Dual(self.real * other.real							,						UpperCAmelCase__							)

 UpperCamelCase					:       Optional[int]			=					__mul__


 def __truediv__(     self		:						Optional[int]							,						UpperCAmelCase__		:						Union[str, Any]							)					->       str:
   if not isinstance(UpperCAmelCase__							,						UpperCAmelCase__							):
     _a  :       List[str]             =	[]
     for i in self.duals:
       new_duals.append(i / other							)
     return Dual(self.real / other							,						UpperCAmelCase__							)
   raise ValueError


 def __floordiv__(     self		:						str							,						UpperCAmelCase__		:						List[str]							)					->       Optional[Any]:
   if not isinstance(UpperCAmelCase__							,						UpperCAmelCase__							):
     _a  :       List[str]             =	[]
     for i in self.duals:
       new_duals.append(i // other							)
     return Dual(self.real // other							,						UpperCAmelCase__							)
   raise ValueError







 def __pow__(     self		:						Optional[Any]							,						UpperCAmelCase__		:						Optional[Any]							)					->       List[str]:
   if n < 0 or isinstance(UpperCAmelCase__							,						UpperCAmelCase__							):
     raise ValueError("""power must be a positive integer"""							)
   if n == 0:
     return 1
   if n == 1:
     return self
   _a  :       Optional[Any]             =	self
   for _ in range(n - 1							):
     x *= self
   return x







def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__				):



  '''simple docstring'''
  if not callable(UpperCamelCase__				):
    raise ValueError("""differentiate() requires a function as input for func"""				)
  if not isinstance(UpperCamelCase__     ,   (float, int)				):
    raise ValueError("""differentiate() requires a float as input for position"""				)
  if not isinstance(UpperCamelCase__     ,   UpperCamelCase__				):
    raise ValueError("""differentiate() requires an int as input for order"""				)
  _a  :       List[str]             =	Dual(UpperCamelCase__     ,   1				)
  _a  :       int             =	func(UpperCamelCase__				)
  if order == 0:
    return result.real
  return result.duals[order - 1] * factorial(UpperCamelCase__				)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 def 			lowerCAmelCase__     (     UpperCamelCase__				):



   '''simple docstring'''
   return y**2 * y**4



 print(differentiate(f, 9, 2))









"""simple docstring"""




import inspect
import unittest

import torch
import torch.nn as nn

from accelerate.hooks import (
    AlignDevicesHook,
    ModelHook,
    SequentialHook,
    add_hook_to_module,
    attach_align_device_hook,
    remove_hook_from_module,
    remove_hook_from_submodules,
)
from accelerate.test_utils import require_multi_gpu






class        UpperCamelCase			(	nn.Module      ):


 def __init__(     self		:						Union[str, Any]							)					->       int:
   super().__init__()
   _a  :       Optional[Any]             =	nn.Linear(3							,						4							)
   _a  :       Tuple             =	nn.BatchNormad(4							)
   _a  :       Dict             =	nn.Linear(4							,						5							)







 def _lowercase	(     self		:						Optional[int]							,						UpperCAmelCase__		:						List[str]							)					->       int:
   return self.lineara(self.batchnorm(self.lineara(UpperCAmelCase__							)							)							)







class        UpperCamelCase			(	snake_case_      ):


 def _lowercase	(     self		:						Any							,						UpperCAmelCase__		:						Any							,						*UpperCAmelCase__		:						List[str]							,						**UpperCAmelCase__		:						Optional[int]							)					->       Optional[int]:
   return (args[0] + 1,) + args[1:], kwargs







class        UpperCamelCase			(	snake_case_      ):


 def _lowercase	(     self		:						Optional[Any]							,						UpperCAmelCase__		:						Tuple							,						UpperCAmelCase__		:						Optional[Any]							)					->       List[str]:
   return output + 1







class        UpperCamelCase			(	unittest.TestCase      ):


 def _lowercase	(     self		:						Dict							)					->       str:
   _a  :       List[Any]             =	ModelForTest()
   _a  :       str             =	ModelHook()

   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)
   self.assertEqual(test_model._hf_hook							,						UpperCAmelCase__							)
   self.assertTrue(hasattr(UpperCAmelCase__							,						"""_old_forward"""							)							)

   # Check adding the hook did not change the name or the signature
   self.assertEqual(test_model.forward.__name__							,						"""forward"""							)
   self.assertListEqual(list(inspect.signature(test_model.forward							).parameters							)							,						["""x"""]							)

   remove_hook_from_module(UpperCAmelCase__							)
   self.assertFalse(hasattr(UpperCAmelCase__							,						"""_hf_hook"""							)							)
   self.assertFalse(hasattr(UpperCAmelCase__							,						"""_old_forward"""							)							)


 def _lowercase	(     self		:						Optional[int]							)					->       Optional[int]:
   _a  :       Dict             =	ModelForTest()
   _a  :       Dict             =	ModelHook()

   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							,						append=UpperCAmelCase__							)

   self.assertEqual(isinstance(test_model._hf_hook							,						UpperCAmelCase__							)							,						UpperCAmelCase__							)
   self.assertEqual(len(test_model._hf_hook.hooks							)							,						2							)
   self.assertTrue(hasattr(UpperCAmelCase__							,						"""_old_forward"""							)							)

   # Check adding the hook did not change the name or the signature
   self.assertEqual(test_model.forward.__name__							,						"""forward"""							)
   self.assertListEqual(list(inspect.signature(test_model.forward							).parameters							)							,						["""x"""]							)

   remove_hook_from_module(UpperCAmelCase__							)
   self.assertFalse(hasattr(UpperCAmelCase__							,						"""_hf_hook"""							)							)
   self.assertFalse(hasattr(UpperCAmelCase__							,						"""_old_forward"""							)							)


 def _lowercase	(     self		:						Dict							)					->       int:
   _a  :       str             =	ModelForTest()
   _a  :       List[Any]             =	torch.randn(2							,						3							)
   _a  :       Optional[Any]             =	test_model(x + 1							)
   _a  :       str             =	test_model(x + 2							)

   _a  :       Union[str, Any]             =	PreForwardHook()
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)
   _a  :       Tuple             =	test_model(UpperCAmelCase__							)
   self.assertTrue(torch.allclose(UpperCAmelCase__							,						UpperCAmelCase__							,						atol=1E-5							)							)

   # Attaching a hook to a model when it already has one replaces, does not chain
   _a  :       int             =	PreForwardHook()
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)
   _a  :       str             =	test_model(UpperCAmelCase__							)
   self.assertTrue(torch.allclose(UpperCAmelCase__							,						UpperCAmelCase__							,						atol=1E-5							)							)

   # You need to use the sequential hook to chain two or more hooks
   _a  :       int             =	SequentialHook(PreForwardHook()							,						PreForwardHook()							)
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)

   _a  :       Tuple             =	test_model(UpperCAmelCase__							)
   assert torch.allclose(UpperCAmelCase__							,						UpperCAmelCase__							,						atol=1E-5							)


 def _lowercase	(     self		:						Tuple							)					->       int:
   _a  :       Tuple             =	ModelForTest()
   _a  :       Union[str, Any]             =	torch.randn(2							,						3							)
   _a  :       Optional[int]             =	test_model(UpperCAmelCase__							)

   _a  :       int             =	PostForwardHook()
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)
   _a  :       List[str]             =	test_model(UpperCAmelCase__							)
   self.assertTrue(torch.allclose(UpperCAmelCase__							,						output + 1							,						atol=1E-5							)							)

   # Attaching a hook to a model when it already has one replaces, does not chain
   _a  :       List[Any]             =	PostForwardHook()
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)
   _a  :       Dict             =	test_model(UpperCAmelCase__							)
   self.assertTrue(torch.allclose(UpperCAmelCase__							,						output + 1							,						atol=1E-5							)							)

   # You need to use the sequential hook to chain two or more hooks
   _a  :       Any             =	SequentialHook(PostForwardHook()							,						PostForwardHook()							)
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)

   _a  :       Optional[int]             =	test_model(UpperCAmelCase__							)
   assert torch.allclose(UpperCAmelCase__							,						output + 2							,						atol=1E-5							)


 def _lowercase	(     self		:						Dict							)					->       Optional[Any]:
   _a  :       Any             =	ModelForTest()
   _a  :       List[Any]             =	torch.randn(2							,						3							)
   _a  :       Dict             =	test_model(UpperCAmelCase__							)

   _a  :       Any             =	PostForwardHook()
   add_hook_to_module(UpperCAmelCase__							,						UpperCAmelCase__							)
   _a  :       List[str]             =	test_model(UpperCAmelCase__							)
   self.assertTrue(torch.allclose(UpperCAmelCase__							,						output + 1							)							)
   self.assertTrue(outputa.requires_grad							)

   _a  :       Any             =	True
   _a  :       Union[str, Any]             =	test_model(UpperCAmelCase__							)
   self.assertFalse(outputa.requires_grad							)


 @require_multi_gpu
 def _lowercase	(     self		:						Optional[Any]							)					->       str:
   _a  :       List[Any]             =	ModelForTest()
   # Everything is on CPU
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

   # This will move each submodule on different devices
   add_hook_to_module(model.lineara							,						AlignDevicesHook(execution_device=0							)							)
   add_hook_to_module(model.batchnorm							,						AlignDevicesHook(execution_device=0							)							)
   add_hook_to_module(model.lineara							,						AlignDevicesHook(execution_device=1							)							)

   self.assertEqual(model.lineara.weight.device							,						torch.device(0							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device(0							)							)
   self.assertEqual(model.batchnorm.running_mean.device							,						torch.device(0							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device(1							)							)

   # We can still make a forward pass. The input does not need to be on any particular device
   _a  :       Optional[int]             =	torch.randn(2							,						3							)
   _a  :       Any             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						torch.device(1							)							)

   # We can add a general hook to put back output on same device as input.
   add_hook_to_module(UpperCAmelCase__							,						AlignDevicesHook(io_same_device=UpperCAmelCase__							)							)
   _a  :       str             =	torch.randn(2							,						3							).to(0							)
   _a  :       Union[str, Any]             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						torch.device(0							)							)


 def _lowercase	(     self		:						str							)					->       Union[str, Any]:
   _a  :       int             =	ModelForTest()

   # Everything is on CPU
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

   # This will move each submodule on different devices
   _a  :       List[Any]             =	{"""execution_device""": 0 if torch.cuda.is_available() else """cpu""", """offload""": True}

   add_hook_to_module(model.lineara							,						AlignDevicesHook(**UpperCAmelCase__							)							)
   add_hook_to_module(model.batchnorm							,						AlignDevicesHook(**UpperCAmelCase__							)							)
   add_hook_to_module(model.lineara							,						AlignDevicesHook(**UpperCAmelCase__							)							)

   # Parameters have been offloaded, so on the meta device
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   # Buffers are not included in the offload by default, so are on the execution device
   _a  :       Dict             =	torch.device(hook_kwargs["""execution_device"""]							)
   self.assertEqual(model.batchnorm.running_mean.device							,						UpperCAmelCase__							)

   _a  :       int             =	torch.randn(2							,						3							)
   _a  :       str             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						UpperCAmelCase__							)

   # Removing hooks loads back the weights in the model.
   remove_hook_from_module(model.lineara							)
   remove_hook_from_module(model.batchnorm							)
   remove_hook_from_module(model.lineara							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

   # Now test with buffers included in the offload
   _a  :       List[str]             =	{
       """execution_device""": 0 if torch.cuda.is_available() else """cpu""",
       """offload""": True,
       """offload_buffers""": True,
   }

   add_hook_to_module(model.lineara							,						AlignDevicesHook(**UpperCAmelCase__							)							)
   add_hook_to_module(model.batchnorm							,						AlignDevicesHook(**UpperCAmelCase__							)							)
   add_hook_to_module(model.lineara							,						AlignDevicesHook(**UpperCAmelCase__							)							)

   # Parameters have been offloaded, so on the meta device, buffers included
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.running_mean.device							,						torch.device("""meta"""							)							)

   _a  :       Tuple             =	torch.randn(2							,						3							)
   _a  :       Union[str, Any]             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						UpperCAmelCase__							)

   # Removing hooks loads back the weights in the model.
   remove_hook_from_module(model.lineara							)
   remove_hook_from_module(model.batchnorm							)
   remove_hook_from_module(model.lineara							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)


 def _lowercase	(     self		:						Tuple							)					->       List[str]:
   _a  :       str             =	ModelForTest()

   # Everything is on CPU
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

   # This will move each submodule on different devices
   _a  :       Union[str, Any]             =	0 if torch.cuda.is_available() else """cpu"""
   attach_align_device_hook(UpperCAmelCase__							,						execution_device=UpperCAmelCase__							,						offload=UpperCAmelCase__							)

   # Parameters have been offloaded, so on the meta device
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   # Buffers are not included in the offload by default, so are on the execution device
   _a  :       Dict             =	torch.device(UpperCAmelCase__							)
   self.assertEqual(model.batchnorm.running_mean.device							,						UpperCAmelCase__							)

   _a  :       Union[str, Any]             =	torch.randn(2							,						3							)
   _a  :       List[Any]             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						UpperCAmelCase__							)

   # Removing hooks loads back the weights in the model.
   remove_hook_from_submodules(UpperCAmelCase__							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

   # Now test with buffers included in the offload
   attach_align_device_hook(UpperCAmelCase__							,						execution_device=UpperCAmelCase__							,						offload=UpperCAmelCase__							,						offload_buffers=UpperCAmelCase__							)

   # Parameters have been offloaded, so on the meta device, buffers included
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.running_mean.device							,						torch.device("""meta"""							)							)

   _a  :       List[str]             =	torch.randn(2							,						3							)
   _a  :       Union[str, Any]             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						UpperCAmelCase__							)

   # Removing hooks loads back the weights in the model.
   remove_hook_from_submodules(UpperCAmelCase__							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)







 def _lowercase	(     self		:						Dict							)					->       str:
   _a  :       Optional[Any]             =	ModelForTest()

   # Everything is on CPU
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

   # This will move each submodule on different devices
   _a  :       str             =	0 if torch.cuda.is_available() else """cpu"""
   attach_align_device_hook(
       UpperCAmelCase__							,						execution_device=UpperCAmelCase__							,						offload=UpperCAmelCase__							,						weights_map=model.state_dict()							)

   # Parameters have been offloaded, so on the meta device
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   # Buffers are not included in the offload by default, so are on the execution device
   _a  :       Union[str, Any]             =	torch.device(UpperCAmelCase__							)
   self.assertEqual(model.batchnorm.running_mean.device							,						UpperCAmelCase__							)

   _a  :       Union[str, Any]             =	torch.randn(2							,						3							)
   _a  :       int             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						UpperCAmelCase__							)

   # Removing hooks loads back the weights in the model.
   remove_hook_from_submodules(UpperCAmelCase__							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

   # Now test with buffers included in the offload
   attach_align_device_hook(
       UpperCAmelCase__							,						execution_device=UpperCAmelCase__							,						offload=UpperCAmelCase__							,						weights_map=model.state_dict()							,						offload_buffers=UpperCAmelCase__							,						)

   # Parameters have been offloaded, so on the meta device, buffers included
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""meta"""							)							)
   self.assertEqual(model.batchnorm.running_mean.device							,						torch.device("""meta"""							)							)

   _a  :       Any             =	torch.randn(2							,						3							)
   _a  :       int             =	model(UpperCAmelCase__							)
   self.assertEqual(output.device							,						UpperCAmelCase__							)

   # Removing hooks loads back the weights in the model.
   remove_hook_from_submodules(UpperCAmelCase__							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.batchnorm.weight.device							,						torch.device("""cpu"""							)							)
   self.assertEqual(model.lineara.weight.device							,						torch.device("""cpu"""							)							)

