mlflow.pytorch

The mlflow.pytorch module provides an API for logging and loading PyTorch models. This module exports PyTorch models with the following flavors:

PyTorch (native) format

This is the main flavor that can be loaded back into PyTorch.

mlflow.pyfunc

Produced for use by generic pyfunc-based deployment tools and batch inference.

mlflow.pytorch.autolog(log_every_n_epoch=1, log_every_n_step=None, log_models=True, log_datasets=True, disable=False, exclusive=False, disable_for_unsupported_versions=False, silent=False, registered_model_name=None, extra_tags=None, checkpoint=True, checkpoint_monitor='val_loss', checkpoint_mode='min', checkpoint_save_best_only=True, checkpoint_save_weights_only=False, checkpoint_save_freq='epoch')[source]

Note

Autologging is known to be compatible with the following package versions: 1.9.0 <= torch <= 2.4.1. Autologging may not succeed when used with package versions outside of this range.

Enables (or disables) and configures autologging from PyTorch Lightning to MLflow.

Autologging is performed when you call the fit method of pytorch_lightning.Trainer().

Explore the complete PyTorch MNIST for an expansive example with implementation of additional lightening steps.

Note: Full autologging is only supported for PyTorch Lightning models, i.e., models that subclass pytorch_lightning.LightningModule. Autologging support for vanilla PyTorch (ie models that only subclass torch.nn.Module) only autologs calls to torch.utils.tensorboard.SummaryWriter’s add_scalar and add_hparams methods to mlflow. In this case, there’s also no notion of an “epoch”.

Parameters
  • log_every_n_epoch – If specified, logs metrics once every n epochs. By default, metrics are logged after every epoch.

  • log_every_n_step – If specified, logs batch metrics once every n training step. By default, metrics are not logged for steps. Note that setting this to 1 can cause performance issues and is not recommended. Metrics are logged against Lightning’s global step number, and when multiple optimizers are used it is assumed that all optimizers are stepped in each training step.

  • log_models – If True, trained models are logged as MLflow model artifacts. If False, trained models are not logged.

  • log_datasets – If True, dataset information is logged to MLflow Tracking. If False, dataset information is not logged.

  • disable – If True, disables the PyTorch Lightning autologging integration. If False, enables the PyTorch Lightning autologging integration.

  • exclusive – If True, autologged content is not logged to user-created fluent runs. If False, autologged content is logged to the active fluent run, which may be user-created.

  • disable_for_unsupported_versions – If True, disable autologging for versions of pytorch and pytorch-lightning that have not been tested against this version of the MLflow client or are incompatible.

  • silent – If True, suppress all event logs and warnings from MLflow during PyTorch Lightning autologging. If False, show all events and warnings during PyTorch Lightning autologging.

  • registered_model_name – If given, each time a model is trained, it is registered as a new model version of the registered model with this name. The registered model is created if it does not already exist.

  • extra_tags – A dictionary of extra tags to set on each managed run created by autologging.

  • checkpoint – Enable automatic model checkpointing, this feature only supports pytorch-lightning >= 1.6.0.

  • checkpoint_monitor – In automatic model checkpointing, the metric name to monitor if you set model_checkpoint_save_best_only to True.

  • checkpoint_mode – one of {“min”, “max”}. In automatic model checkpointing, if save_best_only=True, the decision to overwrite the current save file is made based on either the maximization or the minimization of the monitored quantity.

  • checkpoint_save_best_only – If True, automatic model checkpointing only saves when the model is considered the “best” model according to the quantity monitored and previous checkpoint model is overwritten.

  • checkpoint_save_weights_only – In automatic model checkpointing, if True, then only the model’s weights will be saved. Otherwise, the optimizer states, lr-scheduler states, etc are added in the checkpoint too.

  • checkpoint_save_freq“epoch” or integer. When using “epoch”, the callback saves the model after each epoch. When using integer, the callback saves the model at end of this many batches. Note that if the saving isn’t aligned to epochs, the monitored metric may potentially be less reliable (it could reflect as little as 1 batch, since the metrics get reset every epoch). Defaults to “epoch”.

Example
import os

import lightning as L
import torch
from torch.nn import functional as F
from torch.utils.data import DataLoader, Subset
from torchmetrics import Accuracy
from torchvision import transforms
from torchvision.datasets import MNIST

import mlflow.pytorch
from mlflow import MlflowClient


class MNISTModel(L.LightningModule):
    def __init__(self):
        super().__init__()
        self.l1 = torch.nn.Linear(28 * 28, 10)
        self.accuracy = Accuracy("multiclass", num_classes=10)

    def forward(self, x):
        return torch.relu(self.l1(x.view(x.size(0), -1)))

    def training_step(self, batch, batch_nb):
        x, y = batch
        logits = self(x)
        loss = F.cross_entropy(logits, y)
        pred = logits.argmax(dim=1)
        acc = self.accuracy(pred, y)

        # PyTorch `self.log` will be automatically captured by MLflow.
        self.log("train_loss", loss, on_epoch=True)
        self.log("acc", acc, on_epoch=True)
        return loss

    def configure_optimizers(self):
        return torch.optim.Adam(self.parameters(), lr=0.02)


def print_auto_logged_info(r):
    tags = {k: v for k, v in r.data.tags.items() if not k.startswith("mlflow.")}
    artifacts = [f.path for f in MlflowClient().list_artifacts(r.info.run_id, "model")]
    print(f"run_id: {r.info.run_id}")
    print(f"artifacts: {artifacts}")
    print(f"params: {r.data.params}")
    print(f"metrics: {r.data.metrics}")
    print(f"tags: {tags}")


# Initialize our model.
mnist_model = MNISTModel()

# Load MNIST dataset.
train_ds = MNIST(
    os.getcwd(), train=True, download=True, transform=transforms.ToTensor()
)
# Only take a subset of the data for faster training.
indices = torch.arange(32)
train_ds = Subset(train_ds, indices)
train_loader = DataLoader(train_ds, batch_size=8)

# Initialize a trainer.
trainer = L.Trainer(max_epochs=3)

# Auto log all MLflow entities
mlflow.pytorch.autolog()

# Train the model.
with mlflow.start_run() as run:
    trainer.fit(mnist_model, train_loader)

# Fetch the auto logged parameters and metrics.
print_auto_logged_info(mlflow.get_run(run_id=run.info.run_id))
mlflow.pytorch.get_default_conda_env()[source]
Returns

The default Conda environment as a dictionary for MLflow Models produced by calls to save_model() and log_model().

Example
import mlflow

# Log PyTorch model
with mlflow.start_run() as run:
    mlflow.pytorch.log_model(model, "model", signature=signature)

# Fetch the associated conda environment
env = mlflow.pytorch.get_default_conda_env()
print(f"conda env: {env}")
Output
conda env {'name': 'mlflow-env',
           'channels': ['conda-forge'],
           'dependencies': ['python=3.8.15',
                            {'pip': ['torch==1.5.1',
                                     'mlflow',
                                     'cloudpickle==1.6.0']}]}
mlflow.pytorch.get_default_pip_requirements()[source]
Returns

A list of default pip requirements for MLflow Models produced by this flavor. Calls to save_model() and log_model() produce a pip environment that, at minimum, contains these requirements.

mlflow.pytorch.load_checkpoint(model_class, run_id=None, epoch=None, global_step=None, kwargs=None)[source]

If you enable “checkpoint” in autologging, during pytorch-lightning model training execution, checkpointed models are logged as MLflow artifacts. Using this API, you can load the checkpointed model.

If you want to load the latest checkpoint, set both epoch and global_step to None. If “checkpoint_save_freq” is set to “epoch” in autologging, you can set epoch param to the epoch of the checkpoint to load specific epoch checkpoint. If “checkpoint_save_freq” is set to an integer in autologging, you can set global_step param to the global step of the checkpoint to load specific global step checkpoint. epoch param and global_step can’t be set together.

Parameters
  • model_class – The class of the training model, the class should inherit ‘pytorch_lightning.LightningModule’.

  • run_id – The id of the run which model is logged to. If not provided, current active run is used.

  • epoch – The epoch of the checkpoint to be loaded, if you set “checkpoint_save_freq” to “epoch”.

  • global_step – The global step of the checkpoint to be loaded, if you set “checkpoint_save_freq” to an integer.

  • kwargs – Any extra kwargs needed to init the model.

Returns

The instance of a pytorch-lightning model restored from the specified checkpoint.

Example
import mlflow

mlflow.pytorch.autolog(checkpoint=True)

model = MyLightningModuleNet()  # A custom-pytorch lightning model
train_loader = create_train_dataset_loader()
trainer = Trainer()

with mlflow.start_run() as run:
    trainer.fit(model, train_loader)

run_id = run.info.run_id

# load latest checkpoint model
latest_checkpoint_model = mlflow.pytorch.load_checkpoint(MyLightningModuleNet, run_id)

# load history checkpoint model logged in second epoch
checkpoint_model = mlflow.pytorch.load_checkpoint(MyLightningModuleNet, run_id, epoch=2)
mlflow.pytorch.load_model(model_uri, dst_path=None, **kwargs)[source]

Load a PyTorch model from a local file or a run.

Parameters
  • model_uri

    The location, in URI format, of the MLflow model, for example:

    • /Users/me/path/to/local/model

    • relative/path/to/local/model

    • s3://my_bucket/path/to/model

    • runs:/<mlflow_run_id>/run-relative/path/to/model

    • models:/<model_name>/<model_version>

    • models:/<model_name>/<stage>

    For more information about supported URI schemes, see Referencing Artifacts.

  • dst_path – The local filesystem path to which to download the model artifact. This directory must already exist. If unspecified, a local output path will be created.

  • kwargs – kwargs to pass to torch.load method.

Returns

A PyTorch model.

Example
import torch
import mlflow.pytorch


model = nn.Linear(1, 1)

# Log the model
with mlflow.start_run() as run:
    mlflow.pytorch.log_model(model, "model")

# Inference after loading the logged model
model_uri = f"runs:/{run.info.run_id}/model"
loaded_model = mlflow.pytorch.load_model(model_uri)
for x in [4.0, 6.0, 30.0]:
    X = torch.Tensor([[x]])
    y_pred = loaded_model(X)
    print(f"predict X: {x}, y_pred: {y_pred.data.item():.2f}")
Output
predict X: 4.0, y_pred: 7.57
predict X: 6.0, y_pred: 11.64
predict X: 30.0, y_pred: 60.48
mlflow.pytorch.log_model(pytorch_model, artifact_path, conda_env=None, code_paths=None, pickle_module=None, registered_model_name=None, signature: mlflow.models.signature.ModelSignature = None, input_example: Union[pandas.core.frame.DataFrame, numpy.ndarray, dict, list, csr_matrix, csc_matrix, str, bytes, tuple] = None, await_registration_for=300, requirements_file=None, extra_files=None, pip_requirements=None, extra_pip_requirements=None, metadata=None, **kwargs)[source]

Log a PyTorch model as an MLflow artifact for the current run.

Warning

Log the model with a signature to avoid inference errors. If the model is logged without a signature, the MLflow Model Server relies on the default inferred data type from NumPy. However, PyTorch often expects different defaults, particularly when parsing floats. You must include the signature to ensure that the model is logged with the correct data type so that the MLflow model server can correctly provide valid input.

Parameters
  • pytorch_model

    PyTorch model to be saved. Can be either an eager model (subclass of torch.nn.Module) or scripted model prepared via torch.jit.script or torch.jit.trace.

    The model accept a single torch.FloatTensor as input and produce a single output tensor.

    If saving an eager model, any code dependencies of the model’s class, including the class definition itself, should be included in one of the following locations:

    • The package(s) listed in the model’s Conda environment, specified by the conda_env parameter.

    • One or more of the files specified by the code_paths parameter.

  • artifact_path – Run-relative artifact path.

  • conda_env

    Either a dictionary representation of a Conda environment or the path to a conda environment yaml file. If provided, this describes the environment this model should be run in. At a minimum, it should specify the dependencies contained in get_default_conda_env(). If None, a conda environment with pip requirements inferred by mlflow.models.infer_pip_requirements() is added to the model. If the requirement inference fails, it falls back to using get_default_pip_requirements(). pip requirements from conda_env are written to a pip requirements.txt file and the full conda environment is written to conda.yaml. The following is an example dictionary representation of a conda environment:

    {
        "name": "mlflow-env",
        "channels": ["conda-forge"],
        "dependencies": [
            "python=3.8.15",
            {
                "pip": [
                    "torch==x.y.z"
                ],
            },
        ],
    }
    

  • code_paths

    A list of local filesystem paths to Python file dependencies (or directories containing file dependencies). These files are prepended to the system path when the model is loaded. Files declared as dependencies for a given model should have relative imports declared from a common root path if multiple files are defined with import dependencies between them to avoid import errors when loading the model.

    For a detailed explanation of code_paths functionality, recommended usage patterns and limitations, see the code_paths usage guide.

  • pickle_module – The module that PyTorch should use to serialize (“pickle”) the specified pytorch_model. This is passed as the pickle_module parameter to torch.save(). By default, this module is also used to deserialize (“unpickle”) the PyTorch model at load time.

  • registered_model_name – If given, create a model version under registered_model_name, also create a registered model if one with the given name does not exist.

  • signature

    an instance of the ModelSignature class that describes the model’s inputs and outputs. If not specified but an input_example is supplied, a signature will be automatically inferred based on the supplied input example and model. To disable automatic signature inference when providing an input example, set signature to False. To manually infer a model signature, call infer_signature() on datasets with valid model inputs, such as a training dataset with the target column omitted, and valid model outputs, like model predictions made on the training dataset, for example:

    from mlflow.models import infer_signature
    
    train = df.drop_column("target_label")
    predictions = ...  # compute model predictions
    signature = infer_signature(train, predictions)
    

  • input_example – one or several instances of valid model input. The input example is used as a hint of what data to feed the model. It will be converted to a Pandas DataFrame and then serialized to json using the Pandas split-oriented format, or a numpy array where the example will be serialized to json by converting it to a list. Bytes are base64-encoded. When the signature parameter is None, the input example is used to infer a model signature.

  • await_registration_for – Number of seconds to wait for the model version to finish being created and is in READY status. By default, the function waits for five minutes. Specify 0 or None to skip waiting.

  • requirements_file

    Warning

    requirements_file has been deprecated. Please use pip_requirements instead.

    A string containing the path to requirements file. Remote URIs are resolved to absolute filesystem paths. For example, consider the following requirements_file string:

    requirements_file = "s3://my-bucket/path/to/my_file"
    

    In this case, the "my_file" requirements file is downloaded from S3. If None, no requirements file is added to the model.

  • extra_files

    A list containing the paths to corresponding extra files, if None, no extra files are added to the model. Remote URIs are resolved to absolute filesystem paths. For example, consider the following extra_files list:

    extra_files = ["s3://my-bucket/path/to/my_file1", "s3://my-bucket/path/to/my_file2"]
    

    In this case, the "my_file1 & my_file2" extra file is downloaded from S3.

  • pip_requirements – Either an iterable of pip requirement strings (e.g. ["torch", "-r requirements.txt", "-c constraints.txt"]) or the string path to a pip requirements file on the local filesystem (e.g. "requirements.txt"). If provided, this describes the environment this model should be run in. If None, a default list of requirements is inferred by mlflow.models.infer_pip_requirements() from the current software environment. If the requirement inference fails, it falls back to using get_default_pip_requirements(). Both requirements and constraints are automatically parsed and written to requirements.txt and constraints.txt files, respectively, and stored as part of the model. Requirements are also written to the pip section of the model’s conda environment (conda.yaml) file.

  • extra_pip_requirements

    Either an iterable of pip requirement strings (e.g. ["pandas", "-r requirements.txt", "-c constraints.txt"]) or the string path to a pip requirements file on the local filesystem (e.g. "requirements.txt"). If provided, this describes additional pip requirements that are appended to a default set of pip requirements generated automatically based on the user’s current software environment. Both requirements and constraints are automatically parsed and written to requirements.txt and constraints.txt files, respectively, and stored as part of the model. Requirements are also written to the pip section of the model’s conda environment (conda.yaml) file.

    Warning

    The following arguments can’t be specified at the same time:

    • conda_env

    • pip_requirements

    • extra_pip_requirements

    This example demonstrates how to specify pip requirements using pip_requirements and extra_pip_requirements.

  • metadata – Custom metadata dictionary passed to the model and stored in the MLmodel file.

  • kwargs – kwargs to pass to torch.save method.

Returns

A ModelInfo instance that contains the metadata of the logged model.

Example
import numpy as np
import torch
import mlflow
from mlflow import MlflowClient
from mlflow.models import infer_signature

# Define model, loss, and optimizer
model = nn.Linear(1, 1)
criterion = torch.nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.001)

# Create training data with relationship y = 2X
X = torch.arange(1.0, 26.0).reshape(-1, 1)
y = X * 2

# Training loop
epochs = 250
for epoch in range(epochs):
    # Forward pass: Compute predicted y by passing X to the model
    y_pred = model(X)

    # Compute the loss
    loss = criterion(y_pred, y)

    # Zero gradients, perform a backward pass, and update the weights.
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

# Create model signature
signature = infer_signature(X.numpy(), model(X).detach().numpy())

# Log the model
with mlflow.start_run() as run:
    mlflow.pytorch.log_model(model, "model")

    # convert to scripted model and log the model
    scripted_pytorch_model = torch.jit.script(model)
    mlflow.pytorch.log_model(scripted_pytorch_model, "scripted_model")

# Fetch the logged model artifacts
print(f"run_id: {run.info.run_id}")
for artifact_path in ["model/data", "scripted_model/data"]:
    artifacts = [
        f.path for f in MlflowClient().list_artifacts(run.info.run_id, artifact_path)
    ]
    print(f"artifacts: {artifacts}")
Output
run_id: 1a1ec9e413ce48e9abf9aec20efd6f71
artifacts: ['model/data/model.pth',
            'model/data/pickle_module_info.txt']
artifacts: ['scripted_model/data/model.pth',
            'scripted_model/data/pickle_module_info.txt']
../_images/pytorch_logged_models.png

PyTorch logged models

mlflow.pytorch.save_model(pytorch_model, path, conda_env=None, mlflow_model=None, code_paths=None, pickle_module=None, signature: mlflow.models.signature.ModelSignature = None, input_example: Union[pandas.core.frame.DataFrame, numpy.ndarray, dict, list, csr_matrix, csc_matrix, str, bytes, tuple] = None, requirements_file=None, extra_files=None, pip_requirements=None, extra_pip_requirements=None, metadata=None, **kwargs)[source]

Save a PyTorch model to a path on the local file system.

Parameters
  • pytorch_model

    PyTorch model to be saved. Can be either an eager model (subclass of torch.nn.Module) or a scripted model prepared via torch.jit.script or torch.jit.trace.

    To save an eager model, any code dependencies of the model’s class, including the class definition itself, should be included in one of the following locations:

    • The package(s) listed in the model’s Conda environment, specified by the conda_env parameter.

    • One or more of the files specified by the code_paths parameter.

  • path – Local path where the model is to be saved.

  • conda_env

    Either a dictionary representation of a Conda environment or the path to a conda environment yaml file. If provided, this describes the environment this model should be run in. At a minimum, it should specify the dependencies contained in get_default_conda_env(). If None, a conda environment with pip requirements inferred by mlflow.models.infer_pip_requirements() is added to the model. If the requirement inference fails, it falls back to using get_default_pip_requirements(). pip requirements from conda_env are written to a pip requirements.txt file and the full conda environment is written to conda.yaml. The following is an example dictionary representation of a conda environment:

    {
        "name": "mlflow-env",
        "channels": ["conda-forge"],
        "dependencies": [
            "python=3.8.15",
            {
                "pip": [
                    "torch==x.y.z"
                ],
            },
        ],
    }
    

  • mlflow_modelmlflow.models.Model this flavor is being added to.

  • code_paths

    A list of local filesystem paths to Python file dependencies (or directories containing file dependencies). These files are prepended to the system path when the model is loaded. Files declared as dependencies for a given model should have relative imports declared from a common root path if multiple files are defined with import dependencies between them to avoid import errors when loading the model.

    For a detailed explanation of code_paths functionality, recommended usage patterns and limitations, see the code_paths usage guide.

  • pickle_module – The module that PyTorch should use to serialize (“pickle”) the specified pytorch_model. This is passed as the pickle_module parameter to torch.save(). By default, this module is also used to deserialize (“unpickle”) the model at loading time.

  • signature

    an instance of the ModelSignature class that describes the model’s inputs and outputs. If not specified but an input_example is supplied, a signature will be automatically inferred based on the supplied input example and model. To disable automatic signature inference when providing an input example, set signature to False. To manually infer a model signature, call infer_signature() on datasets with valid model inputs, such as a training dataset with the target column omitted, and valid model outputs, like model predictions made on the training dataset, for example:

    from mlflow.models import infer_signature
    
    train = df.drop_column("target_label")
    predictions = ...  # compute model predictions
    signature = infer_signature(train, predictions)
    

  • input_example – one or several instances of valid model input. The input example is used as a hint of what data to feed the model. It will be converted to a Pandas DataFrame and then serialized to json using the Pandas split-oriented format, or a numpy array where the example will be serialized to json by converting it to a list. Bytes are base64-encoded. When the signature parameter is None, the input example is used to infer a model signature.

  • requirements_file

    Warning

    requirements_file has been deprecated. Please use pip_requirements instead.

    A string containing the path to requirements file. Remote URIs are resolved to absolute filesystem paths. For example, consider the following requirements_file string:

    requirements_file = "s3://my-bucket/path/to/my_file"
    

    In this case, the "my_file" requirements file is downloaded from S3. If None, no requirements file is added to the model.

  • extra_files

    A list containing the paths to corresponding extra files. Remote URIs are resolved to absolute filesystem paths. For example, consider the following extra_files list -

    extra_files = [“s3://my-bucket/path/to/my_file1”, “s3://my-bucket/path/to/my_file2”]

    In this case, the "my_file1 & my_file2" extra file is downloaded from S3.

    If None, no extra files are added to the model.

  • pip_requirements – Either an iterable of pip requirement strings (e.g. ["torch", "-r requirements.txt", "-c constraints.txt"]) or the string path to a pip requirements file on the local filesystem (e.g. "requirements.txt"). If provided, this describes the environment this model should be run in. If None, a default list of requirements is inferred by mlflow.models.infer_pip_requirements() from the current software environment. If the requirement inference fails, it falls back to using get_default_pip_requirements(). Both requirements and constraints are automatically parsed and written to requirements.txt and constraints.txt files, respectively, and stored as part of the model. Requirements are also written to the pip section of the model’s conda environment (conda.yaml) file.

  • extra_pip_requirements

    Either an iterable of pip requirement strings (e.g. ["pandas", "-r requirements.txt", "-c constraints.txt"]) or the string path to a pip requirements file on the local filesystem (e.g. "requirements.txt"). If provided, this describes additional pip requirements that are appended to a default set of pip requirements generated automatically based on the user’s current software environment. Both requirements and constraints are automatically parsed and written to requirements.txt and constraints.txt files, respectively, and stored as part of the model. Requirements are also written to the pip section of the model’s conda environment (conda.yaml) file.

    Warning

    The following arguments can’t be specified at the same time:

    • conda_env

    • pip_requirements

    • extra_pip_requirements

    This example demonstrates how to specify pip requirements using pip_requirements and extra_pip_requirements.

  • metadata – Custom metadata dictionary passed to the model and stored in the MLmodel file.

  • kwargs – kwargs to pass to torch.save method.

Example
import os
import mlflow
import torch


model = nn.Linear(1, 1)

# Save PyTorch models to current working directory
with mlflow.start_run() as run:
    mlflow.pytorch.save_model(model, "model")

    # Convert to a scripted model and save it
    scripted_pytorch_model = torch.jit.script(model)
    mlflow.pytorch.save_model(scripted_pytorch_model, "scripted_model")

# Load each saved model for inference
for model_path in ["model", "scripted_model"]:
    model_uri = f"{os.getcwd()}/{model_path}"
    loaded_model = mlflow.pytorch.load_model(model_uri)
    print(f"Loaded {model_path}:")
    for x in [6.0, 8.0, 12.0, 30.0]:
        X = torch.Tensor([[x]])
        y_pred = loaded_model(X)
        print(f"predict X: {x}, y_pred: {y_pred.data.item():.2f}")
    print("--")
Output
Loaded model:
predict X: 6.0, y_pred: 11.90
predict X: 8.0, y_pred: 15.92
predict X: 12.0, y_pred: 23.96
predict X: 30.0, y_pred: 60.13
--
Loaded scripted_model:
predict X: 6.0, y_pred: 11.90
predict X: 8.0, y_pred: 15.92
predict X: 12.0, y_pred: 23.96
predict X: 30.0, y_pred: 60.13