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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def find_learning_rate_model(params: Params, serialization_dir: str, start_lr: float = 1e-5, end_lr: float = 10, num_batches: int = 100, linear_steps: bool = False, stopping_factor: float = None, force: bool = False) -> None: """ Runs learning rate search for given `num_batches` and saves the results in ``serialization_dir`` Parameters params : ``Params`` A parameter object specifying an AllenNLP Experiment. serialization_dir : ``str`` The directory in which to save results. start_lr: ``float`` Learning rate to start the search. end_lr: ``float`` Learning rate upto which search is done. num_batches: ``int`` Number of mini-batches to run Learning rate finder. linear_steps: ``bool`` Increase learning rate linearly if False exponentially. stopping_factor: ``float`` Stop the search when the current loss exceeds the best loss recorded by multiple of stopping factor. If ``None`` search proceeds till the ``end_lr`` force: ``bool`` If True and the serialization directory already exists, everything in it will be removed prior to finding the learning rate. """

    if os.path.exists(serialization_dir) and force:
        shutil.rmtree(serialization_dir)

    if os.path.exists(serialization_dir) and os.listdir(serialization_dir):
        raise ConfigurationError(f'Serialization directory {serialization_dir} already exists and is '
                                 f'not empty.')
    else:
        os.makedirs(serialization_dir, exist_ok=True)

    prepare_environment(params)

    cuda_device = params.params.get('trainer').get('cuda_device', -1)
    check_for_gpu(cuda_device)

    all_datasets = datasets_from_params(params)
    datasets_for_vocab_creation = set(params.pop("datasets_for_vocab_creation", all_datasets))

    for dataset in datasets_for_vocab_creation:
        if dataset not in all_datasets:
            raise ConfigurationError(f"invalid 'dataset_for_vocab_creation' {dataset}")

    logger.info("From dataset instances, %s will be considered for vocabulary creation.",
                ", ".join(datasets_for_vocab_creation))
    vocab = Vocabulary.from_params(
            params.pop("vocabulary", {}),
            (instance for key, dataset in all_datasets.items()
             for instance in dataset
             if key in datasets_for_vocab_creation)
    )

    model = Model.from_params(vocab=vocab, params=params.pop('model'))
    iterator = DataIterator.from_params(params.pop("iterator"))
    iterator.index_with(vocab)

    train_data = all_datasets['train']

    trainer_params = params.pop("trainer")
    no_grad_regexes = trainer_params.pop("no_grad", ())
    for name, parameter in model.named_parameters():
        if any(re.search(regex, name) for regex in no_grad_regexes):
            parameter.requires_grad_(False)


    trainer_choice = trainer_params.pop("type", "default")
    if trainer_choice != "default":
        raise ConfigurationError("currently find-learning-rate only works with the default Trainer")
    trainer = Trainer.from_params(model=model,
                                  serialization_dir=serialization_dir,
                                  iterator=iterator,
                                  train_data=train_data,
                                  validation_data=None,
                                  params=trainer_params,
                                  validation_iterator=None)

    logger.info(f'Starting learning rate search from {start_lr} to {end_lr} in {num_batches} iterations.')
    learning_rates, losses = search_learning_rate(trainer,
                                                  start_lr=start_lr,
                                                  end_lr=end_lr,
                                                  num_batches=num_batches,
                                                  linear_steps=linear_steps,
                                                  stopping_factor=stopping_factor)
    logger.info(f'Finished learning rate search.')
    losses = _smooth(losses, 0.98)

    _save_plot(learning_rates, losses, os.path.join(serialization_dir, 'lr-losses.png'))