'''simple docstring'''





def 	lowerCAmelCase_				(					snake_case_       : float					,    snake_case_       : float					,    snake_case_       : int			)    ->      float:


     '''simple docstring'''




     if principal <= 0:
          raise Exception("Principal borrowed must be > 0"			)
     if rate_per_annum < 0:
          raise Exception("Rate of interest must be >= 0"			)
     if years_to_repay <= 0 or not isinstance(snake_case_					,    snake_case_			):
          raise Exception("Years to repay must be an integer > 0"			)

     # Yearly rate is divided by 12 to get monthly rate
     UpperCAmelCase_           =   rate_per_annum / 12

     # Years to repay is multiplied by 12 to get number of payments as payment is monthly
     UpperCAmelCase_           =   years_to_repay * 12

     return (
         principal
         * rate_per_month
         * (1 + rate_per_month) ** number_of_payments
         / ((1 + rate_per_month) ** number_of_payments - 1)
     )


if __name__ == "__main__":
    import doctest

    doctest.testmod()





'''simple docstring'''





from copy import deepcopy

import torch
import torch.nn.functional as F
from torch.optim import AdamW
from torch.optim.lr_scheduler import LambdaLR
from torch.utils.data import DataLoader

from accelerate.accelerator import Accelerator
from accelerate.state import GradientState
from accelerate.test_utils import RegressionDataset, RegressionModel
from accelerate.utils import DistributedType, is_torch_version, set_seed





def 	lowerCAmelCase_				(					snake_case_       : Dict					,    snake_case_       : Union[str, Any]					,    snake_case_       : Optional[Any]					,    snake_case_       : List[Any]			)    ->      List[Any]:


     '''simple docstring'''




     for param, grad_param in zip(model_a.parameters()					,    model_b.parameters()			):
          if not param.requires_grad:
               continue
          if not did_step:
               # Grads should not be in sync
               assert (
                   torch.allclose(param.grad					,    grad_param.grad			) is False
               ), f"""Gradients in sync when they should not be at iteration {iteration}:\nmodel_a grad ({param.grad}) == model_b grad ({grad_param.grad})"""
          else:
               # Grads should be in sync
               assert (
                   torch.allclose(param.grad					,    grad_param.grad			) is True
               ), f"""Gradients not in sync when they should be at iteration {iteration}:\nmodel_a grad ({param.grad}) != model_b grad ({grad_param.grad})"""





def 	lowerCAmelCase_				(					snake_case_       : Any					,    snake_case_       : Tuple					,    snake_case_       : Any					,    snake_case_       : List[Any]					,    snake_case_       : str=True			)    ->      Optional[Any]:


     '''simple docstring'''




     model.train()
     UpperCAmelCase_           =   model(snake_case_			)
     UpperCAmelCase_           =   F.mse_loss(snake_case_					,    target.to(output.device			)			)
     if not do_backward:
          loss /= accelerator.gradient_accumulation_steps
          loss.backward()
     else:
          accelerator.backward(snake_case_			)





def 	lowerCAmelCase_				(					snake_case_       : Optional[Any]					,    snake_case_       : Any=False			)    ->      Dict:


     '''simple docstring'''




     set_seed(42			)
     UpperCAmelCase_           =   RegressionModel()
     UpperCAmelCase_           =   deepcopy(snake_case_			)
     UpperCAmelCase_           =   RegressionDataset(length=80			)
     UpperCAmelCase_           =   DataLoader(snake_case_					,    batch_size=16			)
     model.to(accelerator.device			)
     if sched:
          UpperCAmelCase_           =   AdamW(params=model.parameters()					,    lr=1E-3			)
          UpperCAmelCase_           =   AdamW(params=ddp_model.parameters()					,    lr=1E-3			)
          UpperCAmelCase_           =   LambdaLR(snake_case_					,    lr_lambda=lambda snake_case_			: epoch**0.65			)
          UpperCAmelCase_           =   LambdaLR(snake_case_					,    lr_lambda=lambda snake_case_			: epoch**0.65			)
     # Make a copy of `model`
     if sched:
          UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_           =   accelerator.prepare(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
     else:
          UpperCAmelCase_    , UpperCAmelCase_           =   accelerator.prepare(snake_case_					,    snake_case_			)
     if sched:
          return (model, opt, sched, dataloader, ddp_model, ddp_opt, ddp_sched)
     return model, ddp_model, dataloader





def 	lowerCAmelCase_				(					snake_case_       : Any			)    ->      int:


     '''simple docstring'''




     UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_           =   get_training_setup(snake_case_			)
     # Use a single batch
     UpperCAmelCase_    , UpperCAmelCase_           =   next(iter(snake_case_			)			).values()
     for iteration in range(3			):
          # Gather the distributed inputs and targs for the base model
          UpperCAmelCase_    , UpperCAmelCase_           =   accelerator.gather((ddp_input, ddp_target)			)
          UpperCAmelCase_    , UpperCAmelCase_           =   input.to(accelerator.device			), target.to(accelerator.device			)
          # Perform our initial ground truth step in non "DDP"
          step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          # Do "gradient accumulation" (noop)
          if iteration % 2 == 0:
               # Accumulate grads locally
               with accelerator.no_sync(snake_case_			):
                    step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          else:
               # Sync grads
               step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)

          # Since `no_sync` is a noop, `ddp_model` and `model` grads should always be in sync
          check_model_parameters(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          for param, ddp_param in zip(model.parameters()					,    ddp_model.parameters()			):
               if not param.requires_grad:
                    continue
               assert torch.allclose(
                   param.grad					,    ddp_param.grad			), f"""Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"""

          # Shuffle ddp_input on each iteration
          torch.manual_seed(13_37 + iteration			)
          UpperCAmelCase_           =   ddp_input[torch.randperm(len(snake_case_			)			)]





def 	lowerCAmelCase_				(					snake_case_       : Tuple			)    ->      str:


     '''simple docstring'''




     UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_           =   get_training_setup(snake_case_			)
     # Use a single batch
     UpperCAmelCase_    , UpperCAmelCase_           =   next(iter(snake_case_			)			).values()
     for iteration in range(3			):
          # Gather the distributed inputs and targs for the base model
          UpperCAmelCase_    , UpperCAmelCase_           =   accelerator.gather((ddp_input, ddp_target)			)
          UpperCAmelCase_    , UpperCAmelCase_           =   input.to(accelerator.device			), target.to(accelerator.device			)
          # Perform our initial ground truth step in non "DDP"
          step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          # Do "gradient accumulation" (noop)
          if iteration % 2 == 0:
               # Accumulate grads locally
               with accelerator.no_sync(snake_case_			):
                    step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          else:
               # Sync grads
               step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)

          # DDP model and model should only be in sync when not (iteration % 2 == 0)
          for param, ddp_param in zip(model.parameters()					,    ddp_model.parameters()			):
               if not param.requires_grad:
                    continue
               if iteration % 2 == 0:
                    # Grads should not be in sync
                    assert (
                        torch.allclose(param.grad					,    ddp_param.grad			) is False
                    ), f"""Gradients in sync when they should not be:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})"""
               else:
                    # Grads should be in sync
                    assert (
                        torch.allclose(param.grad					,    ddp_param.grad			) is True
                    ), f"""Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"""

        # Shuffle ddp_input on each iteration
          torch.manual_seed(13_37 + iteration			)
          UpperCAmelCase_           =   ddp_input[torch.randperm(len(snake_case_			)			)]





def 	lowerCAmelCase_				(					snake_case_       : Optional[int]=False					,    snake_case_       : str=False			)    ->      List[str]:


     '''simple docstring'''




     UpperCAmelCase_           =   Accelerator(
         split_batches=snake_case_					,    dispatch_batches=snake_case_					,    gradient_accumulation_steps=2			)
     # Test that context manager behaves properly
     UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_           =   get_training_setup(snake_case_			)
     for iteration, batch in enumerate(snake_case_			):
          UpperCAmelCase_    , UpperCAmelCase_           =   batch.values()
          # Gather the distributed inputs and targs for the base model
          UpperCAmelCase_    , UpperCAmelCase_           =   accelerator.gather((ddp_input, ddp_target)			)
          UpperCAmelCase_    , UpperCAmelCase_           =   input.to(accelerator.device			), target.to(accelerator.device			)
          # Perform our initial ground truth step in non "DDP"
          step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          # Do "gradient accumulation" (noop)
          with accelerator.accumulate(snake_case_			):
               step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)

          # DDP model and model should only be in sync when not (iteration % 2 == 0)
          for param, ddp_param in zip(model.parameters()					,    ddp_model.parameters()			):
               if not param.requires_grad:
                    continue
               if ((iteration + 1) % 2 == 0) or (iteration == len(snake_case_			) - 1):
                    # Grads should be in sync
                    assert (
                        torch.allclose(param.grad					,    ddp_param.grad			) is True
                    ), f"""Gradients not in sync when they should be at iteration {iteration}:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"""
               else:
                    # Grads should not be in sync
                    assert (
                        torch.allclose(param.grad					,    ddp_param.grad			) is False
                    ), f"""Gradients in sync when they should not be at iteration {iteration}:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})"""

        # Shuffle ddp_input on each iteration
          torch.manual_seed(13_37 + iteration			)
          UpperCAmelCase_           =   ddp_input[torch.randperm(len(snake_case_			)			)]
     GradientState._reset_state()





def 	lowerCAmelCase_				(					snake_case_       : Optional[Any]=False					,    snake_case_       : Tuple=False			)    ->      Union[str, Any]:


     '''simple docstring'''




     UpperCAmelCase_           =   Accelerator(
         split_batches=snake_case_					,    dispatch_batches=snake_case_					,    gradient_accumulation_steps=2			)
     # Test that context manager behaves properly
     UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_    , UpperCAmelCase_           =   get_training_setup(snake_case_					,    snake_case_			)
     for iteration, batch in enumerate(snake_case_			):
          UpperCAmelCase_    , UpperCAmelCase_           =   batch.values()
          # Gather the distributed inputs and targs for the base model
          UpperCAmelCase_    , UpperCAmelCase_           =   accelerator.gather((ddp_input, ddp_target)			)
          UpperCAmelCase_    , UpperCAmelCase_           =   input.to(accelerator.device			), target.to(accelerator.device			)
          # Perform our initial ground truth step in non "DDP"
          model.train()
          ddp_model.train()
          step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          opt.step()

          if ((iteration + 1) % 2 == 0) or ((iteration + 1) == len(snake_case_			)):
               if split_batches:
                    sched.step()
               else:
                    for _ in range(accelerator.num_processes			):
                         sched.step()
          opt.zero_grad()
          # Perform gradient accumulation under wrapper
          with accelerator.accumulate(snake_case_			):
               step_model(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
               ddp_opt.step()
               ddp_sched.step()
               ddp_opt.zero_grad()

          # Learning rates should be the same
          assert (
              opt.param_groups[0]["lr"] == ddp_opt.param_groups[0]["lr"]
          ), f"""Learning rates found in each optimizer did not align\nopt: {opt.param_groups[0]["lr"]}\nDDP opt: {ddp_opt.param_groups[0]["lr"]}\n"""
          UpperCAmelCase_           =   (((iteration + 1) % 2) == 0) or ((iteration + 1) == len(snake_case_			))
          if accelerator.num_processes > 1:
               check_model_parameters(snake_case_					,    snake_case_					,    snake_case_					,    snake_case_			)
          # Shuffle ddp_input on each iteration
          torch.manual_seed(13_37 + iteration			)
     GradientState._reset_state()





def 	lowerCAmelCase_				(					)    ->      List[Any]:


     '''simple docstring'''




     UpperCAmelCase_           =   Accelerator()

     UpperCAmelCase_           =   RegressionDataset(length=80			)
     UpperCAmelCase_           =   DataLoader(snake_case_					,    batch_size=16			)
     UpperCAmelCase_           =   RegressionDataset(length=96			)
     UpperCAmelCase_           =   DataLoader(snake_case_					,    batch_size=16			)
     UpperCAmelCase_    , UpperCAmelCase_           =   accelerator.prepare(snake_case_					,    snake_case_			)
     assert accelerator.gradient_state.active_dataloader is None
     for iteration, _ in enumerate(snake_case_			):
          assert id(accelerator.gradient_state.active_dataloader			) == id(snake_case_			)
          if iteration < len(snake_case_			) - 1:
               assert not accelerator.gradient_state.end_of_dataloader
               if iteration == 1:
                    for batch_num, _ in enumerate(snake_case_			):
                         assert id(accelerator.gradient_state.active_dataloader			) == id(snake_case_			)
                         if batch_num < len(snake_case_			) - 1:
                              assert not accelerator.gradient_state.end_of_dataloader
                         else:
                              assert accelerator.gradient_state.end_of_dataloader
          else:
               assert accelerator.gradient_state.end_of_dataloader
     assert accelerator.gradient_state.active_dataloader is None





def 	lowerCAmelCase_				(					)    ->      str:


     '''simple docstring'''




     UpperCAmelCase_           =   Accelerator()
     UpperCAmelCase_           =   accelerator.state
     if state.local_process_index == 0:
          print("**Test `accumulate` gradient accumulation with dataloader break**"			)
     test_dataloader_break()
     if state.distributed_type == DistributedType.NO:
          if state.local_process_index == 0:
               print("**Test NOOP `no_sync` context manager**"			)
          test_noop_sync(snake_case_			)
     if state.distributed_type in (DistributedType.MULTI_GPU, DistributedType.MULTI_CPU):
          if state.local_process_index == 0:
               print("**Test Distributed `no_sync` context manager**"			)
          test_distributed_sync(snake_case_			)
     if state.distributed_type == DistributedType.MULTI_GPU:
          for split_batch in [True, False]:
               for dispatch_batches in [True, False]:
                    if state.local_process_index == 0:
                         print(
                             "**Test `accumulate` gradient accumulation, "					,    f"""`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**"""					,    )
                    test_gradient_accumulation(snake_case_					,    snake_case_			)

    # Currently will break on torch 2.0 +, need to investigate why
     if is_torch_version("<"					,    "2.0"			) or state.distributed_type == DistributedType.NO:
          if state.local_process_index == 0:
               print(
                   "**Test `accumulate` gradient accumulation with optimizer and scheduler, "					,    "`split_batches=False`, `dispatch_batches=False`**"					,    )
          test_gradient_accumulation_with_opt_and_scheduler()
          if state.distributed_type == DistributedType.MULTI_GPU:
               for split_batch in [True, False]:
                    for dispatch_batches in [True, False]:
                         if not split_batch and not dispatch_batches:
                              continue
                         if state.local_process_index == 0:
                              print(
                                  "**Test `accumulate` gradient accumulation with optimizer and scheduler, "					,    f"""`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**"""					,    )
                         test_gradient_accumulation_with_opt_and_scheduler(snake_case_					,    snake_case_			)





def 	lowerCAmelCase_				(					snake_case_       : Dict			)    ->      int:


     '''simple docstring'''




     main()


if __name__ == "__main__":
    main()




