def    lowerCAmelCase_ (     __A,  __A							)     ->				tuple[float, float]:







      '''simple docstring'''


      if not len(__A							) == len(__A							) == 3:
            raise ValueError("Please enter a valid equation."							)
      if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
            raise ValueError("Both a & b of two equations can't be zero."							)

      # Extract the coefficients
      UpperCAmelCase__		,      UpperCAmelCase__		,      UpperCAmelCase__								=  equationa
      UpperCAmelCase__		,      UpperCAmelCase__		,      UpperCAmelCase__								=  equationa

      # Calculate the determinants of the matrices
      UpperCAmelCase__								=  aa * ba - aa * ba
      UpperCAmelCase__								=  ca * ba - ca * ba
      UpperCAmelCase__								=  aa * ca - aa * ca

      # Check if the system of linear equations has a solution (using Cramer's rule)
      if determinant == 0:
            if determinant_x == determinant_y == 0:
                  raise ValueError("Infinite solutions. (Consistent system)"							)
            else:
                  raise ValueError("No solution. (Inconsistent system)"							)
      else:
            if determinant_x == determinant_y == 0:
                  # Trivial solution (Inconsistent system)
                  return (0.0, 0.0)
            else:
                  UpperCAmelCase__								=  determinant_x / determinant
                  UpperCAmelCase__								=  determinant_y / determinant
                  # Non-Trivial Solution (Consistent system)
                  return (x, y)







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       A    (   nn.Module ):


							def __init__(self					):
									super().__init__()
									__lowercase=			nn.Linear(3      ,				4					)
									__lowercase=			nn.BatchNormad(4					)
									__lowercase=			nn.Linear(4      ,				5					)







							def 			_A       (self      ,				lowerCAmelCase					):
									return self.lineara(self.batchnorm(self.lineara(lowerCAmelCase					)					)					)





class       A    (   A_ ):


							def 			_A       (self      ,				lowerCAmelCase      ,				*lowerCAmelCase      ,				**lowerCAmelCase					):
									return (args[0] + 1,) + args[1:], kwargs





class       A    (   A_ ):


							def 			_A       (self      ,				lowerCAmelCase      ,				lowerCAmelCase					):
									return output + 1





class       A    (   unittest.TestCase ):


							def 			_A       (self					):
									__lowercase=			ModelForTest()
									__lowercase=			ModelHook()

									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)
									self.assertEqual(test_model._hf_hook      ,				lowerCAmelCase					)
									self.assertTrue(hasattr(lowerCAmelCase      ,				'_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(lowerCAmelCase					)
									self.assertFalse(hasattr(lowerCAmelCase      ,				'_hf_hook'					)					)
									self.assertFalse(hasattr(lowerCAmelCase      ,				'_old_forward'					)					)


							def 			_A       (self					):
									__lowercase=			ModelForTest()
									__lowercase=			ModelHook()

									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)
									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase      ,				append=lowerCAmelCase					)

									self.assertEqual(isinstance(test_model._hf_hook      ,				lowerCAmelCase					)      ,				lowerCAmelCase					)
									self.assertEqual(len(test_model._hf_hook.hooks					)      ,				2					)
									self.assertTrue(hasattr(lowerCAmelCase      ,				'_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(lowerCAmelCase					)
									self.assertFalse(hasattr(lowerCAmelCase      ,				'_hf_hook'					)					)
									self.assertFalse(hasattr(lowerCAmelCase      ,				'_old_forward'					)					)


							def 			_A       (self					):
									__lowercase=			ModelForTest()
									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			test_model(x + 1					)
									__lowercase=			test_model(x + 2					)

									__lowercase=			PreForwardHook()
									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)
									__lowercase=			test_model(lowerCAmelCase					)
									self.assertTrue(torch.allclose(lowerCAmelCase      ,				lowerCAmelCase      ,				atol=1E-5					)					)

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

									# You need to use the sequential hook to chain two or more hooks
									__lowercase=			SequentialHook(PreForwardHook()      ,				PreForwardHook()					)
									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)

									__lowercase=			test_model(lowerCAmelCase					)
									assert torch.allclose(lowerCAmelCase      ,				lowerCAmelCase      ,				atol=1E-5					)


							def 			_A       (self					):
									__lowercase=			ModelForTest()
									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			test_model(lowerCAmelCase					)

									__lowercase=			PostForwardHook()
									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)
									__lowercase=			test_model(lowerCAmelCase					)
									self.assertTrue(torch.allclose(lowerCAmelCase      ,				output + 1      ,				atol=1E-5					)					)

									# Attaching a hook to a model when it already has one replaces, does not chain
									__lowercase=			PostForwardHook()
									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)
									__lowercase=			test_model(lowerCAmelCase					)
									self.assertTrue(torch.allclose(lowerCAmelCase      ,				output + 1      ,				atol=1E-5					)					)

									# You need to use the sequential hook to chain two or more hooks
									__lowercase=			SequentialHook(PostForwardHook()      ,				PostForwardHook()					)
									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)

									__lowercase=			test_model(lowerCAmelCase					)
									assert torch.allclose(lowerCAmelCase      ,				output + 2      ,				atol=1E-5					)


							def 			_A       (self					):
									__lowercase=			ModelForTest()
									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			test_model(lowerCAmelCase					)

									__lowercase=			PostForwardHook()
									add_hook_to_module(lowerCAmelCase      ,				lowerCAmelCase					)
									__lowercase=			test_model(lowerCAmelCase					)
									self.assertTrue(torch.allclose(lowerCAmelCase      ,				output + 1					)					)
									self.assertTrue(outputa.requires_grad					)

									__lowercase=			True
									__lowercase=			test_model(lowerCAmelCase					)
									self.assertFalse(outputa.requires_grad					)


							@require_multi_gpu
							def 			_A       (self					):
									__lowercase=			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
									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			model(lowerCAmelCase					)
									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(lowerCAmelCase      ,				AlignDevicesHook(io_same_device=lowerCAmelCase					)					)
									__lowercase=			torch.randn(2      ,				3					).to(0					)
									__lowercase=			model(lowerCAmelCase					)
									self.assertEqual(output.device      ,				torch.device(0					)					)


							def 			_A       (self					):
									__lowercase=			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
									__lowercase=			{'execution_device': 0 if torch.cuda.is_available() else 'cpu', 'offload': True}

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

									# 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
									__lowercase=			torch.device(hook_kwargs['execution_device']					)
									self.assertEqual(model.batchnorm.running_mean.device      ,				lowerCAmelCase					)

									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			model(lowerCAmelCase					)
									self.assertEqual(output.device      ,				lowerCAmelCase					)

									# 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
									__lowercase=			{
									    'execution_device': 0 if torch.cuda.is_available() else 'cpu',
									    'offload': True,
									    'offload_buffers': True,
									}

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

									# 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'					)					)

									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			model(lowerCAmelCase					)
									self.assertEqual(output.device      ,				lowerCAmelCase					)

									# 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 			_A       (self					):
									__lowercase=			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
									__lowercase=			0 if torch.cuda.is_available() else 'cpu'
									attach_align_device_hook(lowerCAmelCase      ,				execution_device=lowerCAmelCase      ,				offload=lowerCAmelCase					)

									# 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
									__lowercase=			torch.device(lowerCAmelCase					)
									self.assertEqual(model.batchnorm.running_mean.device      ,				lowerCAmelCase					)

									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			model(lowerCAmelCase					)
									self.assertEqual(output.device      ,				lowerCAmelCase					)

									# Removing hooks loads back the weights in the model.
									remove_hook_from_submodules(lowerCAmelCase					)
									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(lowerCAmelCase      ,				execution_device=lowerCAmelCase      ,				offload=lowerCAmelCase      ,				offload_buffers=lowerCAmelCase					)

									# 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'					)					)

									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			model(lowerCAmelCase					)
									self.assertEqual(output.device      ,				lowerCAmelCase					)

									# Removing hooks loads back the weights in the model.
									remove_hook_from_submodules(lowerCAmelCase					)
									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 			_A       (self					):
									__lowercase=			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
									__lowercase=			0 if torch.cuda.is_available() else 'cpu'
									attach_align_device_hook(
									    lowerCAmelCase      ,				execution_device=lowerCAmelCase      ,				offload=lowerCAmelCase      ,				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
									__lowercase=			torch.device(lowerCAmelCase					)
									self.assertEqual(model.batchnorm.running_mean.device      ,				lowerCAmelCase					)

									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			model(lowerCAmelCase					)
									self.assertEqual(output.device      ,				lowerCAmelCase					)

									# Removing hooks loads back the weights in the model.
									remove_hook_from_submodules(lowerCAmelCase					)
									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(
									    lowerCAmelCase      ,				execution_device=lowerCAmelCase      ,				offload=lowerCAmelCase      ,				weights_map=model.state_dict()      ,				offload_buffers=lowerCAmelCase      ,				)

									# 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'					)					)

									__lowercase=			torch.randn(2      ,				3					)
									__lowercase=			model(lowerCAmelCase					)
									self.assertEqual(output.device      ,				lowerCAmelCase					)

									# Removing hooks loads back the weights in the model.
									remove_hook_from_submodules(lowerCAmelCase					)
									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'					)					)






